Germanium Silicon: Physics & Materials (Semiconductors and Semimetals, Volume 56)

Germanium Silicon: Physics and Materials SEMICONDUCTORS AND SEMIMETALS Volume 56

Semiconductors and Semimetals A Treatise

Eicke R. Weber Edited by R. K. Willardson CONSULTING PHYSICIST DEPARTMENT OF MATERIALS AND MINERAL SPOKANE, WASHINGTON SCIENCE ENGINEERING UNIVERSITY OF CALIFORNIA AT BERKELEY

Germanium Silicon: Physics and Materials

SEMICONDUCTORS AND SEMIMETALS Volume 56 Volume Editors

ROBERT HULL DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING UNIVERSITY OF VlRGINIA CHARLO'ITESVILLE, VIRGINIA

JOHN C. BEAN SCHOOL OF ENGINEERING AND APPLIED SCIENCE UNIVERSITY OF VIRGINIA CHARLO'ITESVILLE, VIRGINIA

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1

Contents LISTOF CONTRIBUTORS ......................................

xi

Chapter 1 Growth Techniques and Procedures

John C. Bean I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Generichsues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Common Growth Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Rapid Thermal Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . 3 . Ultra-high Vacuum Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . 4. Atmospheric Pressure Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . 5 . GasSourceMBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Comparison of Growth Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . LayerThickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Majority Carrier Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Minority Carrier Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Nonplanar Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Atomicordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Islands and Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Selective Area Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Strain-Relaxed GeSi and GeSi Pseudo-Substrates . . . . . . . . . . . . . . . . . . . . . VI . Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 3 6 6 13 16 22 24 24 25 28 28 29 29 30 31 32 38 40 45 45

Chapter 2 Fundamental Mechanisms of Film Growth Donald E. Savage. Feng Liu. Volkmar Zielasek. and Max G. Lagally I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Equilibrium Growth Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Kinetic Processes During Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . 3. Kinetic Growth Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI. Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Growth of Si on Si(OO1) (Atomistic Mechanisms) . . . . . . . . . . . . . . . . . . . . . 3. Thermodynamic Properties and Equilibrium Surface Morphology . . . . . . . . . . . . V

49 50 52 53 56

’ 37 62 75

vi

CONTENTS 111. Heteroepitaxial Growth: Ge on Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Growth of the Ge Wetting Layer on Si(OO1) . . . . . . . . . . . . . . . . . . . . . . . .

2 . Nucleation of Coherent ‘Hut’-Islands . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. SiGe Alloy Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Roughening and Coherent 3-D Island Formation in Alloys . . . . . . . . . . . . . . . . 2. Multilayer Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3

79 79 86

90 92 93 94 96

Misfit Strain and Accommodation in SiGe Heterostructures

R . Hull I . Origin of Strain in Heteroepitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Accommodation of Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Elastic Distortion of Atomic Bonds in the Epitaxial Layer . . . . . . . . . . . . . . . . 2 . Roughening of the Epitaxial Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Interdiffusion across the EpiIayedSubstrate Interface . . . . . . . . . . . . . . . . . . . 4 . Plastic Relaxation of Strain by Misfit Dislocations . . . . . . . . . . . . . . . . . . . . 5 . Competition Between Different Strain Relief Mechanisms . . . . . . . . . . . . . . . . 111. Review of Basic Dislocation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Definition and Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Energy of Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Forces on Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Glide and Climb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Geometry of Interfacial Misfit Dislocation Arrays . . . . . . . . . . . . . . . . . . . . . 6 . Motion of Dislocations: Kinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 . Dislocation Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Partial versus Total Misfit Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Excess Stress. Equilibrium Strain and Critical Thickness . . . . . . . . . . . . . . . . . . . 1. introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Matthews-Blakeslee Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Accuracy of the MB Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Other Critical Thickness Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Extension to Partial Misfit Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . Models for Critical Thickness iu Multilayer Structures . . . . . . . . . . . . . . . . . . V. Metastability and Misfit Dislocation Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Misfit Dislocation Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Misfit Dislocation Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Misfit Dislocation Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Kinetic Modeling of Strain Relaxation by Misfit Dislocations . . . . . . . . . . . . . . . VI . Misfit and Threading Dislocation Reduction Techniques . . . . . . . . . . . . . . . . . . . 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . BufferLayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Threading Dislocation Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102 103 103 105 105 107 108 109 109 111 112 112 113 116 117 119 120 120 120 124

124 126

128 131 131 133 144 149

152 155 155 156 157 161 164

CONTENTS

vii

Chapter 4 Fundamental Physics of Strained Layer GeSi: Quo Vadis?

M . J . Shaw and A4. Jaros I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Perfect Superlattice Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Basic Concepts of Superlattice Bandstructures . . . . . . . . . . . . . . . . . . . . . . 2 . GeSi Bandstructures fromEmpirica1 Pseudopotential Calculations . . . . . . . . . . . . 111. Electronic Structure of Imperfect and Finite Systems . . . . . . . . . . . . . . . . . . . . . 1. Bandstructure of Ordered and Disordered Systems . . . . . . . . . . . . . . . . . . . . 2. Optical Transitions in a Finite Superlattice . . . . . . . . . . . . . . . . . . . . . . . . IV. Luminescence and Interface Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Experimental Optical Spectra of SiGe Systems . . . . . . . . . . . . . . . . . . . . . . 2 . Impurities at Interface Islands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Microscopic Signature of GeSi Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. First-Principles Calculations of SYGe Superlattices . . . . . . . . . . . . . . . . . . . . 2 . Interface-Induced Localization at Donor Impurities . . . . . . . . . . . . . . . . . . . . 3. Defect Perturbations to Conduction States . . . . . . . . . . . . . . . . . . . . . . . . 4 . Localization at Ge Impurities in Si Layers . . . . . . . . . . . . . . . . . . . . . . . . VI . Microscopic Electronic Structure Effects in Optical Spectra . . . . . . . . . . . . . . . . . VII . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

169 174 174 182 189 189 193 195 195 197 199 200 203 207 211 212 219 221

Chapter 5 Optical Properties Fernando Cerdeira I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Forms of Differential Spectroscopy Based on Reflection or Absorption of Light . . . . . . . 1. General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. On Pseudo-direct Optical Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Other Optical Transitions in Si/Ge,Sil-, and Ge/Ge,Sil-, Microstructures . . . . . . 4 . Other Optical Transitions in Ge,Si, Quantum Wells and Superlattices . . . . . . . . . I11. Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Raman Scattering in Bulk Ge,Sil-, Random Alloys . . . . . . . . . . . . . . . . . . . 3. Raman Scattering by Optic Modes in Ge..Si, QWs and SLs . . . . . . . . . . . . . . . 4. Raman Scattering by Acoustical Phonons in Si/Ge Microstructures . . . . . . . . . . . 5 . Resonant Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . PL from Bulk Ge,Sil-, Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . PL from Si/Ge,Si1-, Microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . 4. PL from Ultrathin Ge,Si, QWs and SLs . . . . . . . . . . . . . . . . . . . . . . . . . V. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

226 226 226 231 236 243 253 253 256 258 260 265 276 277 277 278 280 286 288 289

viii

CONTENTS

Chapter 6 Electronic Properties and Deep Levels in Germanium-Silicon Steven A . Ringel and Patrick N . Grillot I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Deep Levels in Ge,Si .................................. 1 . DLTS Identification and Analysis of Extended Defect States in Ge,Sil-, . . . . . . . . 2 . Electron Traps in GexSil-, Alloys for x = 0 - 1 . . . . . . . . . . . . . . . . . . . . 3 . Hole Traps in Ge,Sil-, from x = 0 - 1 . . . . . . . . . . . . . . . . . . . . . . . . . 111. Influence of Defects on Electrical Properties of Ge,Sil_, Alloys . . . . . . . . . . . . . . 1. Doping Compensation in Relaxed Ge,Sil-, Layers . . . . . . . . . . . . . . . . . . . 2 . Carrier Generation-Recombination in Relaxed Ge, Sil Layers . . . . . . . . . . . . . IV. Camer Transport Properties of Ge,Sil-, .......................... 1. Carrier Mobilities in Strained and Unstrained Bulk GexSil-, . . . . . . . . . . . . . . 2 . Two-Dimensional Carrier Transport in GeSi/Si Heterostructures . . . . . . . . . . . . . 3 . Minority Carrier Lifetimes and Diffusion Coefficients . . . . . . . . . . . . . . . . . . V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-,

293 295 296 303 309 319 319 322 326 327 334 339 341 343

Chapter 7 Optoelectronics in Silicon and Germanium Silicon Joe C. Campbell I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Avalanche and p-i-n Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Resonant-Cavity Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Metal-Semiconductor-Metal Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Integrated Optical Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Light Emitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I . PorousSilicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Erbium-doped Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Si]-*Ge, Quantum Wells and (Si),(Ge), Strained Layer Superlattices . . . . . . . . . IV. Guided-Wave Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Integrated and Active Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 8 Sil-,C, and Sil-.-.Ge.C.

347 348 348 352 356 362 363 363 367 369 371 371 375

380 380

Alloy Layers

Karl Eberl. Karl Brunner and Oliver G. Schmidt I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. General Remarks on the Material Combination of Si. Ge and C . . . . . . . . . . . . . . . I11. Preparation of Sil_,C, and Sil_,_,,Ge,C, Layers by Molecular Beam Epitaxy . . . . . . IV. Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Thermal Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Local Strain of Substitutional C in Si . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . Si1_,C, Alloy Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . SiGeC Alloy Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

387 390 392 394 394 397 401 401 404

CONTENTS

ix

3. Si/Ge/Sil-yCy Quantum Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Carbon-Induced Ge Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . V1. Electrical Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII . SummaryiDevices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

408 410 413 418 419

INDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONTENTS OF VOLUMES IN THISSERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

423 429

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List of Contributors Numbers in parenthesis indicate the pages on which the authors’ contributions begin.

JOHNC. BEAN(I), Department of Electrical Engineering, University of Virginia, Charlottesville, Virginia KARLBRUNNER (387), Ma-Planck-Institutfir Festkorperforschung, Stuttgart, Germany JOE C . CAMPBELL(347), University of Texas, Microelectronics Research Center; Austin, Texas FERNANDO CERDEIRA (226), Instituto de Fisica, Universidade Estadual de Campinas, UNICAMP, S6o Paulo, Brazil KARLEBERL(387), Max-Planck-Institutfur FestkBrpet$orschung, Stuttgart, Germany PATRICKN. GRILLOT(293), Hewlett Packard Optoelectronics, Sun Jose, California R. HULL(102), Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia M. JAROS(l69), Department of Physics, The University of Newcastle upon Tyne, Newcastle upon Tyne, United Kingdom MAX G. LAGALLY (49), University of Wisconsin, Madison, Wisconsin FENGLIU (49), University of Wisconsin, Mudison, Wisconsin STEVENA. RINGEL(293), The Ohio State University, Department of Electrical Engineering, Columbus, Ohio DONALDE. SAVAGE (49), University of Wisconsin, Madison, Wisconsin OLIVERG. SCHMIDT(387), Max-Planck-Institut fur Festkorperforschung, Stuttgart, Germany M. J. SHAW (169), Department of Physics, The University of Newcastle upon Tyne, Newcastle upon Tyne, United Kingdom VOLKMAR ZIELASEK(49), University of Wisconsin, Madison, Wisconsin

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SEMICONDUCTORSAND SEMIMETALS. VOL. 56

CHAPTER1

Growth Techniques and Procedures John C. Bean DEPARTMENT OF ELECTRICAL ENGINEERING UNIVERSITY OF VIRGINIA CHARLOTTESVILLE. VIRGINIA

I . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1 . GENERICISSUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. COMMONGROWTH TECHNIQUES ............................... 1 . Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Rapid Thermal Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Ultra-high Vacuum Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . 4 . Atmospheric Pressure Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . 5. Gas Source MBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iv. COMPARISON OF GROWTHRESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . LayerThickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Majority Carrier Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Minority Carrier Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. NONPLANAR GROWTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Atomic Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Islands and Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Selective Area E p i t q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Strain-Relaxed GeSi and GeSi Pseudo-Substrates . . . . . . . . . . . . . . . . . . . . . . V L S U M M A R Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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This chapter will focus on the actual growth of GeSi strained layers. Information will be directed at users of GeSi and will provide candid information on what is possible or most readily accomplished by crystal growth colleagues . Molecular beam epitaxy Copynght @ 1999 by Academic Press All nghts of reproductionin any form reserved. ISBN 0-12-752164-X 0080-8784199 $30.00

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(MBE) will be described along with three types of chemical vapor deposition: ultrahigh vacuum (UHVCVD), atmospheric pressure (APCVD) and rapid thermal chemical vapor deposition (RTCVD). All of these techniques produce high-quality crystal growth at temperatures far below those used in traditional CVD. All were first used for Si growth years or even decades before they were applied to GeSi growth. Their use was driven by device requirements for very thin doped layers or layers with very steep doping gradients. Ultimately, many of these requirements were met by alternate, ion-implantation techniques. However, temperature did remain the key issue for GeSi growth and, as such, all of these techniques have come to be identified with this material. Another historical point should be noted. In most discussions of GeSi, growth techniques are presented ufier the theoretical framework has been established. This makes for a clean and logical presentation. This book covers growth first. The reason is simple: breakthroughs in growth came first and opened this field. In fact, earlier theoretical work “proved’ that useful strained layer GeSi growth would not be possible. It was only after we had succeeded in growing material that was far in excess of predicted limits that theories were revised and extended to account for experimental results. This point is inserted to encourage other experimentalists who would attempt that which has been “shown” to be impossible. The development of GeSi growth techniques has been highly competitive. This has produced rapid progress but has also led to an environment in which differences were sometimes exaggerated and common features obscured. Many claims have been based on measurements requiring esoteric apparatus or skills that are not widely available and, indeed, it is extremely rare to find a paper that actually compares material from different growth techniques, head-to-head. Other controversies, such as that concerning Ge segregation, have been almost entirely divorced from any discussion of actual technology requirements. Questionable data have been generated by groups with no prior or subsequent history of quality growth in this admittedly challenging materials system. Finally, while there has been intense discussion of the “device worthiness” of material grown by various techniques, in the GeSi materials system, only very few research groups have actually applied their work to fabrication of challenging devices. This contrasts sharply with, for instance, AlGaAs growth where most efforts were established with the exclusive aim of supplying material for device work. It has been this author’s often humbling experience that there is no test anywhere so demanding as fabrication of a successful minority carrier device. Until this challenge is successfully confronted, it is likely that material will not have been perfected and may not be representative of a technique’s ultimate capabilities. This chapter will address these issues and attempt to provide a more balanced, or at least a more device-relevant view. At the outset, generic issues and concerns will be discussed. In the second section, the apparatus and basic procedures for each technique will be separately detailed. A third section will compare material grown by these techniques, including data on GeSi layer control, carrier mobility, lifetime, and lumi-

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nesence. The fourth section will describe unconventional or unexpected growth modes including spontaneous atomic ordering, islanding and self-assembly, selective epitaxy, and growth of thick, relaxed pseudo-bulk GeSi layers. Because many readers may be motivated by the possible commercial application of GeSi, throughout the discussion comments will be included on relevant strengths, weaknesses, or unresolved issues relevant to various techniques.

11. Generic Issues In its simplest form, crystal growth consists of the arrival and proper arrangement of an atom at a solid surface. One GeSi growth technique, MBE, approaches this ideal as closely as any other. Both Si and Ge evaporate from thermal sources as simple atoms, a situation that does not occur in even 111-V MBE. At typical growth temperatures of 400-1O0O0C, these atoms have an overwhelming tendency to condense on the substrate surface without re-evaporation. For materials such as GeSi, a fully coordinated cubic crystalline site provides the lowest possible bonding state for the arriving atom. Thus, for any temperature above absolute zero, it is simply a matter of patience: wait long enough for thermally activated surface migration to move the atom to a proper site and epitaxial growth will occur. This simplified view makes two assumptions. The first is that the original atom will not be buried or interfered with by a 2nd aniving atom in such a way that it cannot reach a coordinated site. This condition can be crudely expressed by the requirement that the surface migration time be shorter than the interval between arriving atoms (with some constants taking areas into account). If one assumes that surface migration , crystal growth will velocity varies as a simple Boltzmann factor of e - E a / k T single then be possible at all temperatures, provided that the maximum deposition rate is limited by the reciprocal of that same factor. There is no absolute minimum growth temperature. The second, and implicit, assumption is that there are no other species present-in particular, that there are no other species that will obstruct surface migration or disrupt the formation of an ideal crystal. The use of ultrahigh vacuum in MBE is driven by this desire to reduce grossly the concentration of such interfering species, and CVD techniques now emulate this feature. It is incorrect, however, to assume that the use of an ultrahigh vacuum, alone, is sufficient. From kinetic gas theory one can derive the rule of thumb that gas impingement rates vary as the gas partial torr, that impingement rate is still approximately pressure. For a gas pressure of 1 atomic monolayer per s (- IOl5 toms/cm2-s). This is about the same rate at which most epitaxy is grown. Clearly vacuum alone, even heroic, interstellar class torr vacuums, would not produce hyperpure, interference-free epitaxy. Most epitaxy, no matter how pure, thus relies on growth in temperature windows to avoid the aforementioned impurity effects. These windows can be at-

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tributed to two thermal mechanisms: disassociation and desorbtion. A contaminant arrives bound within a molecule. It requires some minimum substrate temperature to disassociate that molecule and to adhere to the crystal surface. At a higher temperature, if secondary reactions do not occur, re-evaporation increases to the point that the impurity surface concentration again falls effectively to zero. One must avoid the middle range for which surface impurity concentrations are significant. Different gas impurities adhere over different temperature ranges. With luck, however, there will be temperature gaps over which the most damaging impurities are absent. For Si epitaxy, 0 2 begins to react and adhere at a very low temperature. However, the Si-0 bond is relatively weak and re-evaporation occurs readily for temperatures above 600°C. On the other hand, at very high temperatures, gas species such as N2 begin to decompose and bond with Si surfaces. These reactions suggest a growth temperature range of 550-1000°C. This range is then somewhat narrowed by the realization that in Si, common dopants begin to diffuse rapidly at temperatures above 800-900°C. Together, these considerations yield the 550-850°C growth-temperature window used for almost all of the techniques described in this chapter. For CVD growth, one must deal with another high-concentration source of “impurities,” the reactant gas itself. The very low vapor pressures of atomic Si and Ge enable MBE but at the same time make supply of Si or Ge “gas” to CVD impossible. Si and Ge are, instead, generally supplied as molecules with hydrogen such as silane (SiH4), disilane (Si2H6) or the Ge analogs. The simplicity of these molecules means that they can be readily purified to rigorous semiconductor standards. Their shortcoming is that when these molecules bond to the Si surface, they do so by releasing a single H atom. Unlike molecular H2, this atomic H is highly reactive and will generally bond to an adjacent Si atom. That Si atom will then only be freed for subsequent epitaxy when its H combines with another to release H2 from the surface. This occurs only very slowly at temperatures below 650°C and provides an additional low temperature constraint for CVD processes that will be detailed here. There is another particularly pernicious impurity: carbon. Carbon has an extremely strong bond with silicon. This is evident in a comparison of pure Si’s melting point of 1415°C and Sic’s melting point of 2700°C. It is also demonstrated by the hardness of Sic. The Si-C affinity means that once C becomes bonded to a Si surface, it is extremely difficult to remove. Indeed, early high-temperature heat treatments, once thought to evaporate C from Si, are now known to function only by diffusing C from the surface into the bulk of the crystal. To make things worse, S i c has multiple crystal structures that are very different in spacing or arrangement from that of Si. In Si homoepitaxy, a surface inclusion of S i c on Si will, therefore, nucleate a crystallographic defect. For GeSi, where a combination of strain and chemical differences exists, even smaller S i c clusters can provide sites that promote anomalous nucleation, nonplanar growth, or premature strain relaxation. For these reasons, carbon is a preoccupation for most Si crystal growers (as AlGaAs growers are obsessed with the damaging affinity of aluminum for oxygen).

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This legitimate fear also accounts for the absence of organometallic Si growth techniques parallelling those widely used for compound semiconductors. Even when deliberate introduction of carbon is avoided, one must still deal with spontaneous contamination due to ever-present oils and polymers. Fortunately, many of these species are reactive or have fairly low vapor pressures. In the growth chamber and its plumbing, they can generally be isolated by sorption or cryogenic traps, at least if they are not produced in huge quantities through the misguided use of hydrocarbon-based pumps. Thus, GeSi MBE is dominated by the use of oil-free cryogenic pumps. However, these accumulation pumps are not suitable for the toxic and even explosive gases used in CVD. There, turbo-molecular pumps, with their very minor use of bearing oil, are employed. Another generic growth concern relates to wafer cleaning. To promote epitaxy, one must expose a perfect crystal surface. This, it would be expected, should be the goal of the pregrowth cleaning technique. Initial ex situ Si cleaning steps are directed towards impurity removal. This is greatly facilitated by the fact that Si is extremely resistant to almost all acids and bases. Very harsh solutions can be employed to remove virtually all metallic and organic surface impurities. One of the oldest of these, the so-called “RCA” (Kern and hotinen, 1970) clean employs a sequence of heated, peroxide-charged hydrochloric acid and ammonia hydroxide baths. Variants of this are employed in the “Henderson” (1972) or more recent “Shiraki“ (Ishizaka and Shiraki, 1986) recipes. As effective as the early steps of these recipes are at removing impurities, the final step is directed at adding one: oxygen. This strategy evolved because bare Si will almost immediately react with and bind to impurities that are always present in the air and in aqueous solutions. In contrast, an oxygenated silicon surface is quite inert (witness the universal use of glass containers). A glassy surface thus protects the Si and is readily produced by use of a chemical oxidant, such as peroxide. A hot peroxide solution grows a 10-20 A-thick oxide that can then be evaporated within the crystal growth reactor by briefly heating the wafer to 800-900°C. More recently, chemical cleaning procedures have moved towards solutions producing a final hydrogen passivating layer. Surface hydrogen can be removed at somewhat lower in situ annealing temperatures. Additionally, hydrogen simply desorbs. This contrasts with glass evaporation, which occurs by the reaction Si02 + Si = 2 SiO (vapor), which must consume some of the substrate Si. This miniscule Si consumption is not in itself a problem. It has been shown, however, that with normal, slightly nonuniform Si02, the Si will be supplied at thin spots or pinholes and thus leads to pitting of the underlying surface. Surface pits again provide attractive sites for nucleation of defects or anomalous growth morphologies. Hydrogen surface passivation is generally accomplished by a final etch in very weak HF solution, followed by a flowing rinse in extremely pure DI water. Indeed, there is a growing consensus among many Si device workers that the purity of the final chemicals (and cleaning environment) is far more important in preparing a clean passivated Si surface than the exact chemical recipe employed.

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The preceding issues must be addressed if one is to grow pure, high-quality GeSi. For the vast majority of applications one must then go another step and add electrically active dopant impurities. Doping is an often complicated and frustrating process for low-temperature growth techniques such as those used for GeSi. Both Si and GeSi have strongly bound lattices into which much smaller or larger atoms, such as B and As do not readily fit. In the bulk of a crystal, dopant atoms have the “choice” of either being incorporated as lone substitutional atoms or of forming second-phase precipitates. Both alternatives carry energy penalties. At the surface of a growing crystal, there is a third, often more energetically attractive alternative: segregation. Segregation is the process wherein a previously deposited dopant atom that “should’ be buried by subsequent Si or Ge atoms instead switches places to remain at the surface. This process is driven by that fact that the variety of less constrained surface sites may more easily accommodate the mis-sized dopant atom. This process may sharply limit maximum low-temperature dopant concentrations or even lead to the build-up of surface dopant “reservoirs” that are only gradually depleted, producing a blurring of intended doping profiles. For chemical vapor deposition techniques, surface processes are even more complicated and doping can produce dramatic unexpected effects, such as radical changes in growth rate. Doping anomalies will be described here for every growth technique. However, one must bear in mind that many device applications call for only very simple doping profiles. Further, in production, growth recipes are fixed and while those complications already mentioned may make it initially difficult to define a recipe, in the long run, that inconvenience may be inconsequential.

111. Common Growth Techniques 1. MOLECULAR BEAMEPITAXY Here MBE will be described first because of both its conceptual simplicity and its historical priority in the growth of GeSi; GeSi MBE consists of the line-of-sight evaporation of atomic species onto a mildly heated Si substrate. In a vacuum, the mean free path of a gas atom, between scattering events, varies as the reciprocal of the pressure ton: The MBE chambers, with and has a value of 1 m for a pressure of about dimensions on the order of a meter and base pressures of 5 lop9 torr, easily meet this standard. The second requirement is that the evaporant itself not “reflect” off chamber surfaces. If this is prevented, flux to the substrate can be controlled, simply and instantaneously, by inserting a “shutter” in the path between the evaporation source and the growth substrate. This is the basis for the superb atomic level control of the MBE technique. For both Si and Ge, significant re-evaporation is extremely low for temperatures below 1000°C and reflection is effectively absent, as intended. Dopants do not behave in such an ideal manner. Many of the more readily evaporated species can re-evaporate at the growth surface, somewhat compromising control.

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Others are prone to surface segregation and for simple evaporated dopants, maximum doping level is generally limited to relatively modest peak concentrations on the order of lO”/cm (Becker and Bean, 1977; Bean, 1978; Ishizaki and Shiraki, 1986.). This constraint has been the basis for considerable research and has led to the use of dramatic alternatives such as the dual low-energy dopant ion-implantation scheme developed by the author (Bean et al., 1988). Ion implantation can insert dopants far enough from a growth surface (e.g., 20-30A) that re-evaporation and surface segregation are effectively eliminated. Upper doping limits can thus be extended towards 1020/cm3but at an obvious penalty in the complexity of the apparatus. Generic work on Si MBE centers on achieving the preceding, simple, atomistic process. Base vacuums in the requisite to high lo-” torr range are achieved by a now well-established combination of high-capacity closed cycle He cryopumps, baked stainless steel chambers, and sample introduction load-locks. A modem system is shown in Fig. 1. In such a system, there is no absolute vacuum requirement. Instead, as indicated in the preceding, it is a question of ambient impurities competing with deposition species. For the 1-10 Ah deposition rates typically used, very high crystalline quality is achieved for Si on Si growth at temperatures above 450°C with a low torr base pressure. These rates are slow enough that the motion of mechanical shutters generally gives the desired atomic monolayer control of flux. For GeSi, however, there is an additional tendency, detailed below, for nonplanar growth. This is almost, but not entirely, suppressed at temperatures of 450°C. Experiments on

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FIG. 1. Depiction of the author’s double-ended, dual-growth chamber MBE system based on a VG Semicon “VG-90” design. This system handles wafers up to 150mm diameter, processing them individually but loading up to 20 at one time. Si and Ge are evaporated from “e-gun” evaporation sources. Dopants are depicted as being evaporated from conventional, resistively heated, Knudsen cells. In the actual system, these have been replaced with a dual 3-keV dopant ion-implantation system that mates with the descending flange at the right extreme of the system. (Used by permission of VG Semicon.)

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growth of single atomic monolayer structures are thus sometimes conducted at lower temperatures and/or at lower growth rates, requiring even better base vacuums. Much of the work on GeSi material has been directed at growth of layers for heterojunction bipolar transistors (HBTs). Minority carrier lifetime plays a key role in the performance of such devices. For indirect bandgap GeSi materials, minority carrier recombination occurs almost exclusively at metal impurity sites. State-of-the-art HBT performance depends on carrier lifetimes in excess of 1 pS, which in turn dictates residual metal impurity concentrations of less than 1 ppb. These low concentrations are not easily achieved, particularly in ail-metal MBE chambers. This fact has been overlooked by a majority of those growing GeSi MBE and this accounts for much of the confusion and contention about ultimate MBE film quality. As such, its discussion justifies a short digression. Within a GeSi MBE chamber, most metal is introduced into the film by one of two mechanisms. In the dominant commercial MBE system, substrates are heated by resistively heated tantalum ribbons. Because these ribbons expand and droop upon heating, they were given additional support from insulating rods. Unfortunately, red-hot tantalum reacts with the insulator to produce volatile metal oxides and nitrides that are then incorporated in trace amounts into the epi. More recent designs either eliminate the insulator supports or exchange the tantalum ribbons for rigid graphite serpentines. However, these more advanced designs account for only a small fraction of those systems in use and MBE results are rarely correlated with the heater design. A second metal contamination route occurs via the deposition sources and, to the author’s knowledge, has not been addressed by any commercial MBE vendor. Because Si and Ge have very low vapor pressures, they are generally sourced from high-energy electron beam evaporators (Fig. 2). In these devices, the Si or Ge solid charge is seated in a grounded, water-cooled metal crucible and bombarded by an electron beam at 10 keV energy and 1 A current. The filament structure that emits the electrons is generally hidden below the crucible and the emerging electron beam bent in an arc, to the charge, by means of a magnetic field. Because the filament then can not be seen by the substrate, metals evaporated from it generally will not find their way into the deposit and these “guns” are a workhorse of the semiconductor industry. In that industry, however, they are not expected to yield ppb deposition purity as they are. in MBE. At those concentrations, one must fully appreciate the subtleties of such sources. Even when they are used in ultrahigh vacuum, the effective vapor pressure of the evaporant, immediately above the source, can be quite high. Indeed, it can be so high that the mean free scattering path falls below 1 cm, creating a “virtual source” in a spherical volume above the crucible. Evaporant atoms then follow paths from this virtual source rather than from the melt surface. Further, this virtual source volume is traversed by the incoming electron beam, which will ionize some fraction of the Si and Ge atoms. The ionized Si+ or Gef will be at ground potential but they will be strongly attracted to the filament assembly with its -10 kV bias. From the virtual source, the filament itself is usually not visible. However, most vendors route

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ELECTRON’ EMITTER ASSEMBLY (-H.V.) FIG. 2. Cross section through conventional “e-gun” evaporation source, such as the 40 cc and 150 cc capacity models offered by Temescal and others. Emitter assembly is biased at - 10 kV such that emitted electrons impact the charge of Si (or Ge) with 10 keV energy. The path of the electrons is bent by a permanent magnet and pole pieces so that the “dirty” filament can be hidden below the body of the source with no lineof-site to the substrate placed above this source. E-guns are commonly used with lower vapor pressure solids for which very high temperatures ( i t . > 1000°C) must be reached to achieve significant evaporation rates.

the heavy copper leads to the filament in such a way that they are seen by the source cloud. This can produce massive sputtering of those leads by the evaporant ions and much of the sputtered surface is positioned such that material can flow into the epi layer. A simple solution can be employed: the filament leads must also be carefully tucked below the body of the e-gun where sputtering is grossly reduced and there is no line-of-sight to the substrate. Attention to these details, and to rigorous substrate cleaning, has produced MBE Si and GeSi with ,LLS lifetimes, suitable for fabrication into high-performance devices. This has, however, involved a long and often frustrating learning process, which only a small minority of the workers in the MBE field have mastered. In the context of potential commercial application, a final equipment point should be noted. Advocates of competing CVD techniques criticized MBE’s dependence on load-locks and extended chamber bake-outs to achieve required vacuum quality. As will be shown, it is ironic that CVD has now been compelled to adopt virtually identical practices. However, MBE does have one inherent weakness when it comes to high-throughput growth. The issue is not throughput itself, for MBE systems do deposit on multiple wafers and even more ambitious schemes have been explored (Bean and Butcher, 1985). The issue is with control of particulates. As already noted, MBE is built on the use of evaporants that will deposit on all surfaces. These surfaces include

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the chamber walls where millimeter thicknesses of Si and Ge can eventually buildup. These deposits can be removed when the chamber is vented for servicing but, for high-throughput growth, venting will only occur after a large number of layers have been deposited. In the interval between cleaning, wall deposits may reach sufficient thickness that they will begin to peel off as fine particulates. This release can be accelerated if the MBE system uses internal liquid nitrogen shrouds that were developed for AlGaAs MBE but continue to be used in older Si MBE systems. In Si MBE SYStems, wafers generally face downward but it has been shown that the pressure of the evaporant itself can drive the particulates back up into the depositing layer where their inclusion can nucleate defects (Matteson and Bowling, 1988). In the mid 1970s, before many of the preceding issues were fully understood, Kasper and co-workers first investigated growth of GeSi strained layers on Si (Kasper et al., 1975; Kasper and Pabst, 1976; Kasper and Herzog, 1977). They found that highquality growth was possible only for temperatures above 750°C. Above 750°C GeSi alloys grew as rough discontinuous films if the Ge fraction was increased above 0.15. Further, within the 0-0.15 limit, crystallographic analysis indicated that strain-relaxing defects formed whenever film thickness exceeded the equilibrium values calculated by theories such as those described by Hull in Chapter I11 of this volume. The intersection of these constraints was that only very dilute thin films were possible. This situation was worsened by the assumption that the bandgap of GeSi films would still be described by data collected on bulk GeSi crystals in the 1960s (Braunstein et al., 1958). These data indicated that the GeSi alloy bandgap did not change in a linear manner between the 1.1 eV value of Si towards the 0.65 eV value of Ge. Instead, as Ge was added, there was initially only a very slow reduction in bandgap until concentration exceeded 50%. These thin, dilute films would thus be expected to have bandgaps only marginally smaller than Si, thereby precluding their use in heterostructure devices. After ten years of refinement, and with particular attention to the foregoing details, in 1984 we demonstrated growth of GeSi alloys on Si, at temperatures at or below 550°C (Bean et al., 1984a; Bean et al., 1984b). This produced the first critical breakthrough, the ability to grow smooth continuous films of all Ge fractions. Early morphology data are presented in Fig. 3. It is seen that as Ge content is increased, lower and lower growth temperatures must be used until, at 550"C, all alloys grow smoothly. These data are consistent with the idea that as Ge content is increased, strain energy increases, driving the deposit towards formation of isolated islands instead of continuous films. In threedimensional islands, strain relaxation occurs more readily and it has been shown that islands can become the energetically favored morphology (Luryi and Suhir, 1986). The temperature dependence of Fig. 3 then represents a competition between this islanding driving force and the reduction in surface diffusion lengths as temperature is decreased. That is, at higher Ge fractions, the larger islanding tendency can be frozen out by use of lower growth temperatures where migration cannot occur over the distances required to assemble islands.

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FIG. 3 . Compilation of data from the earliest MBE GeSi experiments depicting the combinations of GeSi composition and growth temperature that produce islanded (visually hazy) or smooth planar growth. Boundaries are unexpectedly sharp with transition to rough growth occumng with very slight increases in Ge content. Below 550"C, all compositions grow smoothly. Limited data on other techniques, such as RTCVD, show an unexpectedly similar trend.

The aforementioned processes are thermally activated and can occur on different length scales. One would therefore expect the boundary between smooth and islanded growth to be a function of film thickness and for the transition to be gradual with a pronounced dependence on growth rate. Figure 3 is based on MBE data for films grown 1000 A. Subsequent MBE work directed towards at about 1 A l s to thicknesses of growth of single monolayer thickness films has indeed shown that to avoid islanding on this much finer scale, growth temperatures must be decreased to temperatures at or below 450°C. Other details of the 2D to 3D transition are less expected. In the above experiments, separate Si and Ge evaporation sources produced a gradation in composition across the then 3-cm wide sample, such that one end had about 1.05 times the target composition and the other end .95. In spite of this small variation, the transition from a smooth, fully specular 2D morphology to a rough hazy 3D growth occurred within a band only a millimeter or so wide along the sample length (that is, over a composition range on the order of 1%). The other variable is growth rate. Within the relatively narrow 0.5-5 A l s range of MBE growth rate, significant morphological changes have not

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been reported. However, because morphology involves a competition between growth rate and surface migration velocity, one would expect radically altered 2D to 3D curves for CVD techniques with their often very different surface chemistries and reconstructions. Surprisingly, this does not appear to be the case and the limited available morphology data for CVD appear to be remarkably consistent with the original MBE results of Fig. 3. In early work, the goal was to avoid islanding. As boundaries were determined, and they proved consistent with qualitative models, work turned towards application. More recently, islanding has become a possible virtue as it is explored as the possible basis for device “self-assembly” processes. Although these prospects are exciting, discrepancies, such as the apparent insensitivity of morphology to growth technique, clearly illustrate the limitations of current data and the need for a deeper understanding of these processes. In addition to overcoming morphology problems, lower MBE growth temperatures produced two other related results, cementing the current interest in GeSi. First, TEM images indicated that defect-free strained films were growing to thicknesses far greater than then predicted by equilibrium theories. The early data and theory are shown by the lower curve in Fig. 4. It is now known that as low-temperature growth tends to freeze

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FIG. 4. Data for “critical layer thickness” below which GeSi layers grow on Si purely by strain accommodation, with no misfit dislocations. Theoretical curve, based on assumption of equilibrium energy configuration, shown at lower left. Earliest growth experiments supported those theoretical calculations in the &15% Ge range. Subsequent, lower temperature MBE growth produced markedly thicker strained films based on kinetic avoidance of dislocation formation.

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INDIRECT EANDGAP OF BULK Ge I x ) SI ( 4 - x ) ON - S I 110 113

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FIG.5. Bandgap data for both “bulk” unstrained GeSi material (from Braunstein et al., 1958) and GeSi strained layers on Si substrates (from Lang e l al., 1985). Bandgap for strained layers is markedly reduced and falls sharply at even dilute Ge fractions.

out islanding, it also grossly suppresses the formation of strain-relieving defects. This is particularly pronounced for dilute films where layers can be grown 10-100 times beyond the point where relaxation becomes energetically favorable. This enhancement is shown by the upper curve of Fig. 4, which defines the “metastable critical thickness” for strained-layer growth of GeSi on Si. The strain in such films is surprisingly large, on the order of that produced by pressures of 100,000atm. These pressures produced a second key breakthrough: the pronounced alteration in the GeSi bandstructure as shown in Fig. 5. Not only was the bandgap reduced below bulk unstrained values, but the bandgap began to fall immediately as Ge was introduced. Thus, in contrast to bulk GeSi data, useful heterostructures are produced when even dilute GeSi is grown on Si. Metastable GeSi growth and strain effects on bandstructure are detailed by Hull in Chapter 3 and Shaw and Jaros in Chapter 4 of this volume.

2.

RAPIDTHERMAL CHEMICAL VAPORDEPOSITION

In industry, Si epitaxy has long been grown by CVD using reactants based on hydrogen, chlorine, or both. Typical Si precursors include S i c 4 and SiH4. Chlorides have the advantage that the reaction S i c 4 = Si 2C12 can be more easily reversed to facilitate in situ sample cleaning. The etching effect of the halogen can also be used to facilitate selective area epitaxy. That is, single crystal Si will grow in a window through

+

14

JOHN

c. BEAN

an oxide mask but the chlorine will etch away polycrystal Si that would otherwise deposit on that mask. This process is detailed in a subsequent section. On the other hand, in classic CVD it was shown that hydride chemistries, particularly dihydrides such as Si2H6, had the advantage of producing crystalline growth at significantly lower temperatures (e.g., 950°C for SiH4 vs. 1100°C for SiC14). As already discussed here, lower temperatures are a key to GeSi growth and much CVD work has thus focused on hydride or mixed hydride-halogen chemistries. In some of the earliest CVD GeSi work, the temperature question was addressed indirectly. Low-temperature chemistry presents significant challenges as will be discussed in Section 111.3 on UHVCVD. Workers at Stanford realized that temperature itself is not always the issue. More commonly, it is the time-temperature product. It is this product that indirectly governs important parameters such as diffusion length, which in turn control factors such as growth morphology and even defect growth. For conventional high-temperature CVD, much of the time-temperature integral comes in slow temperature ramps to and from the growth temperature. These ramps serve no other purpose than getting the bulky and thermally massive reactors to and from the desired reaction conditions. These investigators reasoned that if they could edit out or “limit” these ramps, the remaining reaction time might be so short that high temperature problems would be largely alleviated. This was accomplished by replacing conventional CVD epi furnaces with single wafer reactors where the wafer was heated by external infrared lamps. They named their technique “limited reaction processing” (Gibbons et al., 1985), but the name did not stick and follow-up work is now generally described as rapid thermal CVD (RTCVD). An RTCVD reactor is depicted in Fig. 6. These reactors operate at deposition pressures of 1-20 ton: While lower than some CVD systems, this reduced pressure operation is, in itself, not that unusual and it facilitates flow control and flow switching. The very unusual feature of these reactors is their heating and cooling rates of 1-5ms/C (or, 200-1000°C/s!). More or less conventional SiH4 growth temperatures of 920-980°C were initially used. However, by effectively eliminating heating and cooling times, high-temperature thermal exposure could be limited to periods of a minute or less and yet still produce useful epi thicknesses. These intervals are so short that gas switching cannot occur on this time scale. Thus, in RTCVD, reactant flows are established before heat is applied, while the wafer is still at or near room temperature. There will then be some reaction as the wafer rapidly warms to the desired temperature. If these ramps were slow, that low temperature growth could result in polycrystalline or even amorphous deposition. In RTCVD, however, ramps are so quick that growth during the ramp is less than one atomic monolayer. These layers are both largely insignificant and they are strongly driven towards a fully crystalline form by the proximity of the substrate. Several years after its initial development, RTCVD was applied to the growth of GeSi layers for use in HBT device structures (King et al., 1989; Noble et al., 1989). Because growth was narrowly targeted to this application, which requires only moderately dilute

1

GROWTHTECHNIQUES AND PROCEDURES

15

FIG. 6 . Schematic of RTCVD system developed at the Franhofer Institute for Solar Energy Systems. This system resembles those used in early GeSi work in its use of a tubular furnace and a single bank of IR lamps above the substrate. More modem production systems tend to be rectangular with the entire top of the system lifting off for loading (reprinted with the permission of F. R. Faller, Franhofer Institute, Freiburg, Germany)

1520% Ge layers, the data set is not as broad as the MBE work already mentioned. However, the available data are strikingly similar to MBE results in one particular: the trade-off between growth temperature and morphology. For 22% Ge films, smooth growth compelled the use of a growth temperature of 625"C, a value consistent with the MBE data of Fig. 3. Private communications with the authors confirmed this trend. Because morphology should be controlled by surface migration, the results suggest that, at least under these conditions, RTCVD surfaces must be largely free of hydrogen reaction products. This will not be the case for the lower-temperature UHVCVD data discussed in what follows. Doping data for RTCVD are also somewhat limited. For Si on Si, where layer growth occurs at more or less standard CVD growth temperatures, conventional hydride gases work well for both N- and P-type dopants. There is one detailed report on B2H6 doped Si films grown at 850°C, which demonstrates abrupt doping steps. Indeed, doping was varied from the SIMS background detection limit up to extremely high levels in excess of lO2'/crn3 (Gronet et al., 1986). GeSi doping data also confirm the successful use of diborane but provides very little information of N-type doping. The paucity of data can be attributed to the relatively limited use of the RTCVD technique and the very tight focus, in the literature, on its application to HBTs with their single P-type GeSi layers. Although RTCVD epi has found somewhat limited commercial application, rapid thermal techniques, in general, are in heavy use. From this, at least one manufacturing

16

JOHN C.

BEAN

issue can be identified. Not too surprisingly, it is how one achieves control of temperature. Conventional CVD furnaces had been made thermally massive to address just this issue. In the extremely nimble, lamp-heated RT systems, the challenge is how to heat a wafer uniformly and ensure that it arrives at and holds the desired reaction temperature. In the extreme, the wafer may be heated so nonunifomly that crystalline slip defects form due to thermal stresses. This can be minimized by increasing the lamp output at the generally cooler wafer edges. However, the balance of heating will change as the temperature increases and wafer thermal emission varies. For this, and for determination of the brief final reaction temperature, the challenge is not how to tune the temperature but how to measure it. Thermocouples are not readily attached to the wafers. While they could be embedded in underlying “susceptors,” the thermal mass of these plates might seriously compromise rapid temperature cycling. For these reasons, indirect, often noncontacting, temperature-measurement schemes are being heavily investigated. A second possible potential problem, wall deposition, is probably inhibited by RTCVD’s use of chloride chemistries. Even if such deposition occurred, RTCVD growth chambers could be opened for regular cleaning. Regular venting can be tolerated because at the higher (e.g., 9OOOC) growth temperatures, impurity incorporation is less of an issue. Indeed, for growth at these temperatures, load-locks may not be absolutely necessary.

3. ULTRA-HIGHVACUUM CHEMICAL VAPORDEPOSITION The RTCVD largely sidestepped CVD temperature constraints by a combination of editing and cycling between different growth temperatures for different layers. However, the above MBE data clearly demonstrated the desirability of a simple lowtemperature version of CVD. Conventional CVD epitaxy of Si had been limited to temperatures above 900°C. Below this temperature heavily defective or polycrystalline growth was produced. This occurred despite MBE data indicating that Si surface diffusion lengths were still on the order of a micron at 500°C, considerably larger than the distance an arriving atom would need to travel to find a crystalline site. This discrepancy prompted a concerted effort to discover the mechanism that was disrupting low-temperature CVD. The key was identified in papers by Ghidini and Smith (1984) and Smith and Ghidini (1982). Their work provided detailed data on the reaction of water vapor with clean Si surfaces. Those data are represented in Fig. 7. The figure quantifies the balance between Si surface oxidation and oxide re-evaporation. It indicates that, as the Si temperature decreases, water partial pressures must be driven ever lower if one is to maintain an oxide-free surface. These general trends were understood, and were discussed in the MBE section. However, the absolute numbers had not been fully appreciated, especially within the CVD community. An extrapolation of these data indicates that as Si

1

,

-5 L

,

,

GROWTHTECHNIQUES AND PROCEDURES TEMPERATURE (C) 10;

p 1 ,I;,,,

90;

17

OXIDE COVERED

10-1

t W

K

3 10-2

3 w

E

s I-

10-3

K

U a

10-4

5

s t

I-

OXIDE-FREE

I

10-5

10-6 6.4

6.8

7.2

7.6

8.0

8.4

8.8

10000 I TEMPERATURE (K)

FIG.7. Equilibrium surface condition of silicon exposed to water vapor. Crystal growth requires essentially no contamination of the substrate template. For Si, this will be achieved only for those water vapor partial pressures falling at the bottom left of the figure. This requirement is the basis for the base vacuum requirements in both MBE and UHVCVD, and for restrictions on CVD reactant gas purities. Data from Ghidini and Smith.

temperatures are lowered from 900°C to 600”C, Si surfaces will be kept free of oxide torr to below only if water partial pressure is decreased from ton. These are equilibrium numbers. In fact, the initial oxide can be desorbed at higher temperatures and then lowered quickly for growth. Nevertheless, these numbers demonstrate that MBE paranoia about residual gases was not misplaced and, indeed, would have to be shared by CVD growers if crystalline low-temperature films were to be produced. In addition, CVD reactors would have to become every bit as leak tight as MBE systems and similar measures would have to be taken to prevent their contamination during sample loading. Meyerson et al. (1986) first appreciated this point and designed a CVD reactor to these stringent standards. He named his variant ultrahigh-vacuum CVD, which, while literally a misnomer, nevertheless emphasized the basis for its success. That is, although growth, in fact, occurred using reactant pressures in the “roughing vacuum” range of 1-10 mtorr, the background impurity gas pressures were maintained torr. The UHVCVD apparatus is shown in at “ultrahigh-vacuum’’ values below simplified form in Fig. 8. The deposition chamber is made of glass and heated by an

18

JOHNC. BEAN

GROWTH FURNACE

m 1

LOAD-LOCK n

FORE/G ROW1- L J ROUGHING PUMPS

lLzz2r

‘ ”“””‘

u FORE PUMP

FIG. 8. Schematic of UHVCVD apparatus (after Meyerson, 1986). Turbo-pumped sample load-lock with insertion arm at right. Multiple samples are loaded, stacked back-to-back in carrier. Growth chamber at center consists of a vacuum tight tube enclosed by a furnace. In at least early experiments, an RF excitation coil was included (not shown) to facilitate cleaning of this section. The left turbopump is used on initial evacuation of the chamber to remove impurities and attain the requisite UHV background pressure. However, during growth with reactant pressures above 1 mtorr, the turbopump is presumably either closed off or throttled back with the bulk of the pumping provided by the roughing pumps of the left of the figure.

external furnace. It is pumped out using a turbopump and precleaned by inducing a hydrogen plasma that, in effect, replaces the extended 150°C bake-outs used for MBE systems. As with MBE systems, once it is pumped down and cleaned, it is kept at vacuum for extended periods of time while samples are introduced using a separately pumped load-lock. Growth occurs by introduction of Si& and GeH4. If these gases are used at 10 mtorr, Fig. 7 indicates that, to prevent 600°C surface oxide build-up, they must be free of water vapor to a level of about 10 ppb. Not only are these gas purities extraordinarily hard to produce, they can be very hard to maintain as gases pass from high-purity tanks through mazes of piping into the growth chamber. Details have not been fully disclosed but it is apparent, if only from the difficulty others had in reproducing results, that particular care must be taken in preparing the reactor and its supply piping, and it is probable that modern specialized point-of-use gas purifiers are used. This care parallels that which be must employed in MBE to prevent metal contamination. MBE can be modeled as a simple condensation process in which impurities are treated only as second-order spoilers. However, with even the above precautions, UHVCVD must confront immediate “impurity” effects in the form of decomposition products. In a Si- molecule, hydrogen atoms are distributed at tetrahedral angles that maximize their separation around the core Si atom. At typical 500--10OO0Ctemperatures, such a molecule will react with a bare Si surface in such a way as to begin the

19

1 GROWTH TECHNIQUES AND PROCEDURES

deposition process. However, their geometry makes it very unlikely the S i b molecules will, at least initially, release a pair of hydrogen atoms in such a way that a volatile H2 molecule can form. It is much more likely that at the Si surface, one Si-H bond will be broken to give a tethered SiH3 molecule and the liberated H atom will then bond to an adjacent Si surface atom. As already noted, surface hydrogen is in many respects benign and, in cleaning procedures, is used to protect the Si surface from reaction with other species. Unfortunately, the same blocking effect occurs in CVD as surface Si atoms, which have become tethered to H, refuse to react with subsequent arriving SiH4 molecules. Thus, growth rate very quickly comes to depend not on reactant arrival rate but only on the rate of H desorption. This available “site-limited” growth is depicted at the right of Fig. 9. The experimental growth rate data of Fig. 10 confirm the transition from reactant limited to site limited growth as silane based growth temperature is decreased. Site-limited growth is a “good-newshad-news” proposition. As Meyerson et al. 1986 has pointed out, it means that deposition rate can be determined by a single thermally activated parameter, completely independent of reactor and gas flow geometries. This is, in effect, the antithesis of MBE where lines-of-sight are used to control the deposition precisely on a limited number of substrates. Instead, for surface hydrogen limited growth, if they are at the same temperature, all surfaces of all wafers will grow at the same rate, as long as an undepleted gas flow can reach them. This will occur even if 50-100 wafers are stacked back to back. For this hydrogen desorbtion limited growth, reaction probabilities are indeed extremely small, and reactant gas depletion is low enough that the aforementioned conditions are met. This gives UHVCVD a huge

REACTANT LIMITED

SiH4

SiH4

1

1

Sin4

Si-Si-Si-Si-Si-Si-Si I

I

I

I

I

Si-Si-Si-Si-Si-Si-Si

I

SITE LIMITED

I

SiH4

H H H H H H I I 1 1 . 1 1 . 1 Si-Si-Si-Si-Si-Si-Si I

I

I

I

I

I

I

Si-Si-Si-Si-Si-Si-Si FIG. 9. Schematic of Si surface upon exposure to silane reactant gas. At high growth temperatures, silane readily decomposes at surface, depositing silicon and releasing two H2 gas molecules. Growth rate is then limited by the arrival rate of silane reactant at the Si surface. At lower temperatures, silane molecule instead breaks a single Si-H bond. It is then tethered to the Si surface but the liberated, reactive, H atom attaches to a neighboring Si. Subsequent silane molecules cannot react at those H “passivated” sites and growth is then completely limited by the thermal desorption rate of H.

JOHN C. BEAN

20 700 1000

600

, ,,

500

400

I

I

\

100

10

1 10

12

11

1000

/

13

14

15

TEMPERATURE (K)

FIG. 10. Silicon growth rate as a function of temperature and S i b reactant gas pressure. Data are from the RTCVD experiments of Liehr et al. (1990) but similar trends are expected for all CVD techniques using this reactant. At higher temperatures, the growth rate is a function of reactant gas pressure, indicating that growth is limited by the anival rate of the reactant at the substrate surface. At lower temperatures, growth rate is a function of only substrate temperature, indicating the "site-limited' growth mode of Fig. 9. Slope of the site limited curve provides the hydrogen surface binding energy to silicon of 46 Kcalimol or 2.0 eV per atom.

advantage for multiwafer growth. This advantage is, however, somewhat moderated by the fact that simultaneous deposition is facilitated by the low reaction probabilities at temperatures below 600°C. These low probabilities also mean that growth rates are extremely low and, as shown in Fig. 10, fall to values of 0.1 to 0.01 A/s at typical growth temperatures. Surface hydrogen limited growth presents an additional challenge. Desorption is controlled by a 2 eV thermal reaction barrier (46 KcaYmol). For this activation energy, at 6OO0C,the hydrogen desorption rate will change by 5% with only a 1.25"C change in Si temperature. Because the desorption process gates the SiH4 adsorption, growth rate will vary in a similar manner. Devices frequently require epi layer control at or beyond this level. The wafer temperatures within a UHVCVD reactor must, therefore, be controlled to extraordinary accuracy both across the reactor and from growth run to growth run. Thermal chemistry is further complicated as one moves to growth of GeSi. At the low 550-650°C temperatures necessary for growth of smooth strained GeSi layers,

1

GROWTH TECHNIQUES AND PROCEDURES

21

there is the above very slow release of H from Si surfaces. It has been shown, however, that H is much more weakly bound to surface Ge atoms and it will still rapidly desorb from these sites. It is further evident that, while a Si atom will not release H to the vacuum, it will readily transfer it to a neighboring Si atom, allowing H to migrate freely along the surface. The net result is that Ge atoms catalyze the release of H from the growing epi surface, ultimately freeing Si sites and dramatically increasing overall growth rate. Figure 11 documents this complex effect for both UHVCVD and APCVD (Racanelli and Greve, 1990, 1991a; Jang and Reif 1991). Dopant atoms can also influence growth rate. Detailed boron data have not been presented for UHVCVD but it has been shown that introduction of PH3 produces a mild inhibition of growth (Greve and Racanelli, 1991). These effects mean that deposition becomes a complex, coupled, thermally activated, problem. This contrasts with MBE where growth rates are essentially linear, thermally independent, with no coupling between deposition species. The complexity of low-temperature CVD processes does not, in itself, rule out growth

UHVCVD

IW

Q

610 C

I

600 C

0 c.3

0 0

0.05

0.10

0.15

0.20

0.25

Ge FRACTION

FIG. 1 1 . Effect of Ge content on growth rate for fixed SiH4 reactant pressure in both UHVCVD and APCVD growth. APCVD data from Meyer and Kamins (1992). UHVCVD data at 500'C from Meyerson (1988). Balance of UHVCVD data from Racanelli and Greve (1991). Initial growth enhancement (in all but 750°C curve) can be attributed to low-temperature "site-limited" growth and tendency of bound surface hydrogen to be released at Ge surface atoms sites. However, variations and ultimate downturn of most curves clearly indicate more complex mechanisms.

22

JOHN C . BEAN

of a given doped GeSi structure. It may, however, affect reproducibility and certainly increases the challenge of developing the recipe for a new structure. For UHVCVD, diborane has proved to be an outstanding source for P-type films and extremely high doping levels have been achieved (Meyerson et al., 1987). On the other hand, the early sustained absence data on N-type dopant incorporation indicated that this presented significant difficulties. However, data were ultimately published indicating that N-type doping could be achieved with PH3 but that incorporation would not exceed 5 5 x 10i8/cm3 (Greve and Racanelli, 1991). This might limit certain applications of UHVCVD but it has not been a critical issue in the dominant HBT application where UHVCVD has been used only for the growth of the single P-type GeSi base layer (Patton et al., 1990). Finally, it should be noted that while UHVCVD offers clear multiwafer throughput advantages, a key manufacturing issue has not been publicly addressed: SiH4 reactants will also produce deposition on the hot quartz walls of the UHVCVD reactor, where those deposits should eventually produce the same particulates seen in MBE. This could provide an ultimate limit on the crystallographic quality of UHVCVD films or put constraints on the length of time such a system can be operated between disassembly and cleaning. This might be sidestepped by periodic use of alternate Si etching chemistries but if these, or other solutions, have been employed they have not been disclosed.

4.

ATMOSPHERIC PRESSURECHEMICALVAPORDEPOSITION

Two final forms of CVD will be described. They are, however, variants on the foregoing and discussion will be brief. The first is atmospheric pressure CVD (APCVD). As the name indicates, unlike both UHVCVD and RTCVD, reduced reactant gas pressure is not used. This, it is claimed, leads to simplifications in the apparatus that reduce its cost. From the published system diagram, that simplification apparently comes largely in the elimination of the turbopump. Otherwise, the system diagram looks remarkably like that of the UHVCVD system presented here, right down to its use of a valve isolated sample load-lock. Publications do not make it clear whether that loadlock is purged, or if another simpler pump is used. The similarity to the UHVCVD apparatus is not coincidental. To grow at reduced temperatures, APCVD must still take extraordinary precautions to eliminate impurities. Sedgewick and Agnello did work on APCVD that cites water partial pressures down to lop6 torr in the reactor (Sedgewick and Agnello, 1992). As a fraction of the reactant pressure, this is in fact better than that achieved in UHVCVD work. However, according to the Ghidini data of Fig. 7, it is not low enough to prevent oxidation of Si surfaces at the low, 625-700°C growth temperatures employed. The absence of such oxidation, as indicated by film quality, is attributed, in part, to the addition of a hydrogen carrier gas in the reactor. It is known that H2 can scavenge surface oxides and it is a standard component in conventional CVD (but not in UHVCVD).

1 GROWTH TECHNIQUES AND PROCEDURES

23

Another change is made in the processing environment: dichlorosilane (DCS) is substituted for simple silane. As in RTCVD, the use of chlorides, with their tendency to etch amorphous deposits, makes it possible for APCVD to deposit selectively on Si exposed in oxide windows. Selective growth is not possible with MBE or the straight hydride chemistries of UHVCVD, and is the topic of a separate section that follows. The same selectivity should apply to the hot glass walls of the reactor. That is, although it is not spelled out in the literature, it is probable that chloride-based APCVD is at least partially free from the wall deposition and particulate formation problems that can occur in both MBE and UHVCVD. For APCVD, unusually complete data have been published on the effects of dopants on growth rate (Sedgewick and Agnello, 1992; Sedgewick and Grutzmacher, 1995). Some of these data are shown in Fig. 12. Both N- and P-type doping radically increase the low-temperaturegrowth rate of Si. These changes are so large that it seems unlikely that the isolated dopant atoms affect the capture of DCS molecules. It seems more probable that the dopant atoms act in a manner similar to that of Ge in UHVCVD. That is, they catalyze the release of a surface atom, in this case either H or C1, that would otherwise block the reaction with the incoming Si molecule. While this analogy is plausible, it should be noted that the strong PH3-induced enhancement of growth rate is very dif-

1000

+ B2H6

100 +PH3 10

UNDOPED

1

8.5

9.5

10.5

\ 11.5

12.5

I0000 I TEMPERATURE (K)

FIG. 12. Acceleration of APCVD growth upon addition of dopants. Data from Sedgewick and Agnello (1992) and Sedgewick and Grutzmacher (1995).

24

J O H N C . BEAN

ferent from the slight inhibition observed in UHVCVD. Workers in APCVD speculate that this is due to the unique role of C1, but the complete mechanism is not currently understood. In Fig. 12, the growth rate for undoped films falls sharply at low temperatures, suggesting that in a manner similar to UHVCVD it is limited by H coverage of the Si surface. For UHVCVD this coverage makes the growth rate independent of reactant concentration, and enables simultaneous deposition on large numbers of wafers. The similarity of the data suggests that uniform multiple wafer deposition would also be possible in APCVD, but this claim is not made in the literature.

5. GAS SOURCE MBE MBE has been combined with GeSi CVD precursors to produce so-called “gassource” MBE (GSMBE). For GeSi, it was developed primarily by Hirayama et al. (1990a, 1990b, 1991) at NEC. Its use has spread to Shiraki’s group at the University of Tokyo but it has otherwise been picked up by very few groups. For disilane precursors, growth rates and dopant incorporation have been investigated and generally parallel the results found in UHVCVD. Selective epitaxy has also been achieved, in contrast to conventional MBE, and these results will be detailed later in this chapter. Further, excellent device results have been obtained. The limited use of GeSi GSMBE may be attributed to the fact that, while gas sources can enhance MBE, as a production tool their use may also combine the least desirable features of MBE and CVD. Specifically, one brings together the complexity of metal-sealed vacuum chambers with the tremendous safety precautions demanded by the toxic and even explosive behavior of both Si and Ge hydride precursors. The overall installation cost may thus be doubled. In conventional MBE, metal chambers provide the space for sources, substrate heaters, and flow-controlling shutters, and yield unique performance advantages. For GSMBE, it might be argued that because these functions can be moved outside the main growth chamber (as they are in UHVCVD), the use of a simple glass reaction tube makes more sense. In fact, it is the author’s experience that the use of conventional MBE heaters within the growth chamber can lead to side reaction of gas precursors that can complicate or damage growth quality. As a research tool, GSMBE uses CVD chemistries in a high vacuum environment where powerful gas and surface analysis tools can be easily employed. Thus, while its commercial application may be uncertain, GSMBE could be a critical tool in reaching a detailed understanding of complex CVD reaction mechanisms described in the foregoing.

IV. Comparison of Growth Results This section will compare the quality and features of material grown by the different techniques. Data are combined with the specific intent of adding a perspective that has often been missing in GeSi literature that most often focuses on the development of a

1

GROWTH TECHNIQUES A N D PROCEDURES

25

single technique. To that end, this chapter will highlight figures of merit that have been demonstrated for all or most of the foregoing techniques. Further, as already indicated, I will weigh most heavily results relevant to the application of GeSi in devices such as the HBT. At the outset, it should be noted that all of the preceding techniques have been successfully applied to the growth of fast, high-gain, minority carrier HBT devices. That is not to say that all material, grown by all workers, by any technique, is up to this high standard. In fact, there is strong evidence of a considerable range of quality in material grown by most techniques. It does suggest, however, that most of the literature variability is in fact not indicative of the ultimate capabilities of each technique and that selective citations can be very misleading. For each technique, only the best results known to the author will be described.

1.

LAYERTHICKNESS

The most basic figure of merit for all GeSi growth techniques is the ability to grow with control the thin GeSi layers called for in present and future devices. The mildest demand would be for the base layer of an HBT, which is generally 300-500 8, thick. Tunneling devices then require barriers on the order of 100 A.Photodetectors, based on tuned quantum wells, involve thicknesses of -20-100 A. The ultimate demand might be in devices based on the changes in bandstructure that may occur in superlattices with 1-10 atomic monolayer periods (1.5-15 A). For conventional high-temperature CVD, growth rates can fall in a pndmin range that would make all but perhaps the HBT application impossible. Growth rates for the newer GeSi techniques are compared in Fig. 13. For all but MBE, these rates can be strongly enhanced as Ge is added and, for simplicity, the rates for only pure Si growth are given. In the temperature ranges used for GeSi growth, rates are from 1-100 A/min (or -.Ol-IONS). Rates for CVD and gas-source techniques are thermally activated, The rate for MBE can be varied arbitrarily within the capabilities of the e-gun sources. All rates are low enough that flow or flux switching can occur fast enough to permit growth of very thin layers. Minimum layer thicknesses have been documented by a number of indirect techniques. These have been employed because imaging techniques, such as TEM, average over a significant sample thickness and may thus under-represent local roughness. For MBE, continuous layers can be grown down to thicknesses approaching a single monolayer. This was demonstrated by electroreflectance spectroscopy on a series of samples with diminishing layer thickness. These optical signals varied in a systematic and predictable manner as layers were thinned down to 2 atomic monolayers (ML) (Pearsall et nl., 1987; Pearsall et al., 1989). At an intended layer thickness of 1 ML, there were anomalous spectral features suggesting either lack of continuity or atomic

26

JOHNC. BEAN TEMPERATURE (C) 850

IOOOJ-

650

550

q

I

8.5

750

I 9.5

I

I 10.5

I

I I 11.5

I 12.5

I

1000 I TEMPERATURE (K)

FIG. 13. Comparison of growth rates by various growth techniques. The APCVD and UHVCVD data were extracted from preceding figures. The GSMBE data are from Hirayama el al. (1991). For these CVDbased techniques, data all fall sharply at lower growth temperatures. The MBE growth rate is independent of substrate temperature (over the indicated range) and a function only of e-gun evaporation sources. Data are given for an MBE system such as that of Fig. 1 using 150 cc capacity, 7.5 cm diameter Si charges spaced approximately 500 cm from substrate.

steps. Raman data also support the conclusion that MBE GeSi layers can be grown smoothly and continuously down to almost one ML, at which point roughness or steps limit the lateral continuous dimension of the layer (Araujo Silva et al., 1996a, b). For RTCVD, minimum layer thickness has been inferred from photoluminescence (PL) measurements on quantum wells of diminishing thickness (Xiao et al., 1992b). As well thickness decreases, quantum size effects should push up bound energy states leading to a blue shift in the PL signal. This was, indeed, observed and it indicated that wells of well-defined thickness could be grown down to at least 33A. For UHVCVD, TEM data and electrical results from resonant tunneling devices (Ismail et al., 1991) indicate good layer control down to at least 50 A. The real number is probably considerably lower than this as suggested by APCVD data that examined

1

GROWTHTECHNIQUES AND PROCEDURES

27

this issue more completely. In that APCVD work, a combination of X-ray diffraction data and PL quantum size effects suggested that layers could be grown at thicknesses of 10 A with interfacial roughness < 2 A. There is a second, more subtle, aspect of GeSi layer thickness control: the observed tendency of Ge, in GeSi layers, to move into overlaying Si layers. The movement is not symmetric, ruling out diffusion as the mechanism. Instead, Ge moves upward towards the growth surface and it is almost certain that this is a surface segregation phenomenon similar to that observed for many dopant atoms. Early Ge segregation data came primarily from surface analytical tools found on MBE systems (Zalm et al., 1989; Grevesteijn et al., 1989; Godbey and Ancona, 1993). Later, more quantitative profile data have been measured by SIMS on materials grown by various techniques. SIMS has the advantage of following concentration tails down to trace levels, but it is not accurate at the top of the profile where ionization probabilities will be affected by the impurity concentration. In general, SIMS segregation profiles are approximately exponential and, where possible, these curves have been converted into a characteristic decay length. For single Ge monolayers grown in Si by MBE at 500"C, a decay length of -20 A was measured (Ohta et al., 1994). Addition of either atomic or molecular 5 x torr, cut this length to -5A. In the one pubhydrogen, at pressures of lication comparing techniques (Grutzmacher et al., 1993b); both MBE and APCVD segregation lengths were approximately independent of growth temperature. An MBE value of 20 8, was again measured, compared to 8 A for APCVD. UHVCVD values did vary with growth temperature, falling from -45 A at 700°C to less than 10 8, at 515°C. These results again support the suppression of segregation by hydrogen, in that APCVD is grown in an H2 ambient and UHVCVD films are known to retain surface H at the lower growth temperature. As a trace element in Si, Ge is soluble and produces no direct electrical activity. The more important question is thus whether segregation hinders growth of thin GeSi layers by blurring one interface. Extrapolation of the SIMS trace data suggest that at least in MBE films of 10-20 A, thickness control could, indeed, be degraded. However, that extrapolation contradicts a large body of MBE data showing well-defined superlattice growth at 2-10 atomic monolayers (3-15 8,). If one applies the SIMS decay length of 20A, one would conclude that it would be essentially impossible to grow a Si/GeSi MBE superlattice with 2 ML (3 A) layer thicknesses (i.e., e-3/20 = 0.86). With even 10 ML silicon spacer layers, in those spacers, alloy composition would fall by only 50%. This conclusion clearly contradicts electroreflectance, Raman and TEM data and suggests that the initial Ge fall is significantly more abrupt than measured in the tail of the SIMS distribution. Strong, high level, segregation is also inconsistent with a variety of MBE superlattice device and bandstructure measurements. It thus seems most likely that Ge segregation produces only very dilute tails for which there will be little modulation of bandstructure and hence little or no effect on device structures.

-

JOHN

2.

c. BEAN

DOPING

Doping presents challenges for all of the foregoing low-temperature growth techniques. Details were given in the foregoing but are summarized here for comparison. For conventional MBE, using evaporated elemental dopants, extremely sharp profiles can be grown but maximum doping levels are limited by segregation effects to values in the mid-10'8/cm3 range. Doping by simultaneous low-energy implantation overcomes segregation and maximum concentrations are then limited by the available implanter 1 x 10'9/cm3 is current. For the author's system, at low growth rate, doping of possible. Implantation energy blurs dopant profiles at a resolution of about 25 A as inferred from both theory and measurements of setback effects in modulated doped structures. For all of the CVD-based techniques, similar dopant chemistries lead to similar incorporation behavior. Boron works extremely well as a P-type dopant producing abrupt profiles and maximum concentrations are well above lO2'/crn3. The N-type is significantly more difficult. With phosphine, reports indicate an incorporation limit similar to the thermal MBE limit of 5 x 10'8/cm3. APCVD data, at least, also describe an apparent reactor memory effect for P that could limit profile abruptness and minimum doping levels.

-

3.

MAJORITY CARRIERTRANSPORT

In the GeSi literature, there has been intense competition to achieve high electron mobilities with modulation-doped structures. However, these data are measured in films that are grown well above strained layer limits such that relaxation occurs by formation of misfit dislocation networks. This relaxation is necessary to produce tension in Si layers that induces the conduction band discontinuity necessary for carrier segregation. In principle, the necessary relaxation could occur without extending defects into the electrically active layers. However, for reasons to be detailed in what follows, this does not occur, and all of these N-type modulation-doped layers have high defect densities of 106-10'2/cm2. These densities are not so much a feature of which growth technique is used as they are a product of layer thicknesses, compositions, and growth rates. As such, they should not be used as a basis for comparing techniques but will be discussed in the section on pseudo-bulk GeSi. P-type modulation doping does not depend on misfit dislocation formation and should provide valid comparison of nominally defect-free material. The earliest reports of P-modulation doping cited 10 K values of 3000-4000 cm2N-s for MBE layers (People et al., 1984; People and Bean, 1987). A subsequent UHVCVD publication, while claiming "the highest hole mobilities ever reported" had a near identical value of 3800cm2N-s (Wang et al., 1989). The APCVD and RTCVD papers report values of 2000 (Grutzmacher et al., 1993c) and 2500 (Venkataraman et al., 1991) cm2N-s,

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respectively. In these 2D hole gases, mobility depends critically on the exact choice of both carrier concentration and the very small (-100 A) separation between the gas and the dopant ions. These values are so close that differences could easily be due to variation in these parameters.

4.

PHOTOLUMINESCENCE

In Si and GeSi, the indirect bandgap precludes efficient electron hole recombination to produce light. Weak photoluminescence (PL) can be observed, but there is strong competition from recombination at nonluminescent sites such as metallic impurities. Those same impurity sites accelerate the recombination of electrically injected minority carriers in key devices such as HBTs. In the HBT, the reduction in minority carrier lifetime will reduce current gain and adversely affect leakage characteristics. Because photoluminescence strengthens as interfering impurities are eliminated, it can be used to assess material purity. Further, in certain instances, the luminescence features can be used to identify specific impurities or defects. Unfortunately, for Si materials it is a difficult technique with few skilled practitioners. Data on PL are briefly reviewed by Cerdeira in Chapter V. To summarize, some of the most complete results have been measured by many researchers (Xiao et al., 1992; Mi et al., 1992; Souifi et al., 1992) for RTCVD materials. In these and related reports, particular importance is attached to the presence of spectral features such as “no phonon lines”. Qualitatively similar, nearbandedge, spectra have been reported for MBE (Fukastsu et al., 1992; Usami et al., 1992) UHVCVD (Terashima et aZ., 1993) and APCVD (Grutzmacher et al., 1993a). In principle, intensities could yield comparative information but PL data are always reported in “arbitrary units” (presumably because of experimental challenges). As such, the following electrical measurements of minority canier lifetime yield a more quantitative comparison of minority carrier behavior. In addition to near-bandedge data, there have been recurring reports of broad, subbandgap emission for MBE layers grown at particularly low temperatures, such as 400°C. These features disappeared in more conventional 600°C layers and are attributed to defects induced by extreme low temperature growth where, in a sense, incomplete ordering at the growth surface induces formation of point defects, such as Si interstitials or vacancies (Noel et al., 1990; Terashima et al., 1993). This attribution is supported by in situ comparisons of material grown with and without the presence of surface hydrogen, which would be expected to sharply alter surface point defect generation.

5. MINORITY CARRIER LIFETIME More direct, electrical measurement of minority carrier lifetime is still far from straightforward. The effect of interest, recombination at impurities and defects, can

JOHNC. BEAN

30

be easily masked by intrinsic recombination at layer surfaces. For Si on Si epitaxy, surface recombination can be eliminated by oxidation at T > lOOO"C, which then also facilitates determination of bulk lifetime from the inversion behavior of MOS capacitors. This is not possible for GeSi layers where 1000°C post-growth processing can cause catastrophic degradation. Further, the limited thicknesses of GeSi layers means that there is always a nearby Si/GeSi interface at which recombination may occur in even hyperpure and perfect material. Thus, a growth technique is best judged by the Si on Si lifetime, which provides an upper limit on the intrinsic GeSi value. Lifetimes inferred from GeSi/Si diodes then give a lower, but almost certainly pessimistic, bound that may be dominated by heterojunction recombination. For MBE of Si on Si, an upper bound of 75 pS was reported for a system in which heaters and e-gun sources are carefully configured, as described in the foregoing (Higashi et d., 1990). For the same system, a lower bound of 5 1 p S was determined for thin GeSi layers. For RTCVD, an upper bound of 94 pS was reported for Si on Si (Sturm et al., 1986) and a lower bound of l p S for GeSi (Schwarz and Sturm, 1990). For UHVCVD, a Si on Si upper bound of 160 pS has been cited (Nguyen et al., 1986) but newer data on GeSi are bit muddier. In particular, a report on an electron cyclotron resonance variant of UHVCVD cites GeSi lifetimes values of up to 100 pS (Hwang et al., 1996). However, not only is it unclear how heterojunction recombination was avoided for such long-lived carriers, but in fact, layer thicknesses were not even given in this report. Overall, an upward trend is suggested for Si on Si values, as one moves from totally metal MBE systems to metal and glass RTCVD systems, to fully glass UHVCVD tubes. However, differences between the best data are relatively small and are dwarfed by variations reported within a given technique by different authors. The obvious conclusion is that current results more strongly reflect the care and sophistication employed in particular experiments rather than the ultimate limitations of the techniques. These variations can be readily explained by the sensitivities of the various techniques to impurities, but the persistent variability represents a challenge to the entire growth community.

-

V.

Nonplanar Growth

GeSi is cited (Swalin 1972) as a prototypical alloy for which phase segregation will not occur and many properties can be linearly interpolated from Si and Ge end points. This ideality was thought to persist to atomic dimensions where Si and Ge atoms would randomly substitute for one another within the tetrahedral crystal structure. On a larger scale, films did exhibit nonideal tendencies towards roughening and defect formation but, as detailed here, conditions were found under which these could be largely avoided. As such, early work mostly ignored or avoided these irregularities and focused on growth of very thin, uniform, planar films. More recently, however, attention has turned to films that are either spontaneously or deliberately nonuniform. This section will

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discuss that work, focusing first on spontaneous mechanisms of atomic ordering and islanding, and then turning to deliberate growth of limited, selective layers and pseudobulk GeSi.

1. ATOMICORDERING Atomic ordering has been one of the more intriguing yet frustrating phenomena encountered in GeSi. In 1985, Ourmazd and Bean (1985) observed weak superlattice electron diffraction spots in GeSi layers. These spots indicated a clear, spontaneous, rearrangement of Si and Ge atoms to form an alternating sequence of atomic planes, as depicted in Fig. 14. This layering occurred on { 111) planes even though the epi layer, itself, was deposited on a (100) surface. In the as-grown layers, the diffraction spots were very weak but could be enhanced by a sequence of annealing and quenching. Overall, diffraction intensities indicated that a relatively small volume of the epi layer had assumed the ordered configuration. Nevertheless, the result was exciting because it suggested a spontaneous means by which the normal cubic symmetry of column IV semiconductors could be broken. This, in turn, could enable phenomena, such as piezoelectricity or optical second harmonic generation, that would otherwise be prohibited by the symmetry of normal Si crystals or in random GeSi alloys.

FIG. 14. Depiction of the spontaneous atomic ordering inferred from electron diffraction data on GeSi films. Along a [l 113 direction, the atomic stacking sequence is Ge-Ge-Si-Si. This ordering is not a function of growth which, in fact, occurred on a (100) plane (equivalent to the top horizontal face of the cube).

32

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c. B E A N

Models suggested that ordering occurred as a means of slightly reducing the strain energy in lattice mismatched films (Littlewood, 1986; Martins and Zunger, 1986). These could be interpreted in terms of bond stiffness: the stronger, higher melting point Si had the strongest, stiffest, bond (Si-Si). Ge had the weakest (Ge-Ge). Si-Ge could be expected to be intermediate in stiffness. A random ordering of the weaker Si-Ge and Ge-Ge bonds would not facilitate larger scale strain relaxation along atomic planes. The Si-Si-Ge-Ge ordering would allow this by creating long range, more flexible Ge-Ge shear planes. These models did not entirely resolve the precise atomic order for, in addition to the structure shown in Fig. 14, the Si-Si-Ge-Ge stacking sequence could be offset by one plane, putting the Si-Ge bonds perpendicular to the stacking direction. Either sequence would account for the observed diffraction data, although strain relief models favored the original structure. It became more problematic when researchers at IBM (LeGoues et al., 1989; Kuan and Iyer, 1991), reported similar but much stronger, ordered diffraction data in thick, relaxed GeSi on Si films. These films were nominally strain free, removing the apparent driving force for ordering. Further, their analysis suggested the alternate layering structure already discussed here. These data prompted new models of the ordering process based on segregation phenomena occurring at the growing crystal surface. This work, due largely to Jesson et al. (199 1; 1992; 1993) examined the details of atomic bonding at single atomic surface steps as they grow across a crystal surface. As the step moves laterally, it covers atomic sites that alternate in their detailed atomic configuration. These configurations have different energies and, it is suggested, should be energetically more attractive to either Si or Ge atoms. It is thus argued that, although deposition may lead to random Si and Ge site selection, at the step edge these energetics will drive the displacement of energetically misplaced atoms (e.g., Ge in GeSi) to form a surface structure that ultimately lays down a bulk-ordered atomic configuration. There is still significant controversy as to whether surface segregation or bulk strainrelief processes drive the aforementioned ordering and about the precise details of the resultant arrangements (LeGoues et al., 1993a, b). These effects, while weak and elusive, have nevertheless now been observed by many research groups. Further, there have been experimental observations of both piezoelectric (Xie et al., 1987) and optical second harmonic generation (Baribeau, private communication) that could not occur in random alloys. These and other effects could be of significant device utility if ordering processes could be better controlled and strengthened. A clear resolution of the mechanisms might yield the understanding necessary to drive such improvements.

2.

ISLANDS AND

WIRES

In the 1980s, work on GeSi was almost entirely directed at defining those conditions that would produce smooth continuous layer growth. When “adverse,” nonplanar growth conditions were encountered, they were recorded (as in Fig. 3) and avoided.

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Starting about 1990, n o ~ p h l a Igrowth ’ was revisited as a possible virtue to be studied and exploited. This reversal was prompted by the recognition that, as structures approach the scale of quantum mechanical wavelengths, their physical properties may be radically altered. These alterations, broadly described as “quantum size effects,” include changes in the density of states and folding of bandstructure that can be used to tune the absorption strength and wavelength of semiconductor structures (Sakaki, 1994). Additionally, in these quantum microstructures there is at least the theoretical possibility that one might finally achieve light emission, the “holy grail” of silicon materials research (Bean, 1992). In the spirit of this chapter, this section will survey techniques that have been employed to fabricate such microstructures but will leave detailed discussion of their properties to other more appropriate chapters of this book. TO fabricate quantum structures, the natural response is use the lithographic techniques that have made microelectronics so successful. There is, unfortunately, a problem of scale. Conventional photolithography depends on photons at UV wavelengths of no smaller than 0.2 p m . Quantum effects are most strongly manifested at much smaller dimensions, in the 10-100 nm range. Thus one must: 1) Turn to more exotic but finer scale electron beam lithography; 2) find a means of shrinking conventional optical lithographic features; or 3) take an entirely different approach. Electron beam lithography might be used to pattern existing uniform layers, removing material such that the remaining structure exhibits quantum effects. However, at very fine scales, etching generally requires “dry” processes employing energetic atoms that can leave damaged material at the edges of an etched semiconductor layer. As the edge to volume ratio of a fine quantum dot is particularly high, edge damage might completely mask or eliminate quantum effects. An alternative is to use lithography only for definition of a shadow masking layer through which epi will then be deposited. At comparatively crude millimeter scales, this approach was first applied by Tsang and Illegems (1977) and Tsang and Cho (1978) for free-standing masks with III-V MBE. For more conventional surface oxide masks and Si MBE, this was extended to 0.5 p m dimensions by Bean and Rozgonyi (1982). Finally, as the significance of quantum dots was fully appreciated, Bruner et al. (1994) used this approach to fabricate micronsized GeSi quantum dots for which the photoluminescence signals gave clear evidence of size effects. Their fabrication scheme is depicted schematically in Fig. 15. They fabricated dots down to 2 p m diameter but much smaller masks could be defined with electron beam lithography. For MBE and hydride-based CVD techniques one would ultimately be limited by deposition on the mask producing a narrowing and eventual occlusion of fine openings. This should not occur in halogen-based CVD. However, this author is not aware of work that has combined and fully exploited these elements to produce shadow masked epi structures at sub 0.1 p m dimensions. The second alternative is to use a combination of more conventional lithography and to implement some means of shrinking features. The most common approach, again first demonstrated with III-V semiconductors, is to first use optical lithography to define relatively coarse grooved masks. Anisotropic chemical etches are then

34

JOHN C.

BEAN

FIG. 15. Geometry used by Bruner er al. (1994) in early experiments to fabricate arrays of GeSi dots. Holes were defined by photolithography on a two-layer dielectric mask. Etching solutions were chosen such that the lower layer over-etched producing an overhang. Materials deposited on this shadow mask then formed the desired isolated dots on the substrate. Mask (and material deposited on the mask) could then be chemically “lifted off” for evaluation of the dots.

selected such that the “V” shaped trenches are etched in the substrate. The mask is then removed and the patterned substrate exposed to reactant fluxes that would normally produce uniform deposition. However, at the “V” trenches, under conditions of high adatom of mobility, there is a natural tendency for excessive material to accumulate at the bottom of the trench and for the deposit to thin or grow discontinuously at the sharp upper comers. This produces triangular cross-section “wires” of epi. For GeSi, this approach was demonstrated by the work of Usami et al.( 1994) using the geometry at the left of Fig. 16. Wire pairs have also been grown in the parallel corners of flatbottomed grooves (Hartman et al., 1995) or on ridged structures. Aside from the use of more conventional, coarser, optical lithography, these approaches have the advantage that wire dimensions can be tuned by limiting the thickness of the deposit or by biasing growth conditions between uniform or more localized growth. Wires are illustrated but square dots would be similarly produced at the bottoms of square pyramidal depressions. These structures have been successfully employed to explore quantum size effects at scales smaller than those of the shadow masked dots that have already been discussed here. Looking forward to possible quantum devices, this technique would appear to have two principal limitations. The first is that while fine structures can be produced, they would be separated by the coarser “V” trench dimensions, limiting packing densities. Further, for the finest structures grown only at the apex of the “V,” the extreme nonplanxity of the surface might challenge subsequent metallization or lithographic steps needed to complete a circuit structure. In the absence of simple ultrafine lithographic techniques, recent work has turned towards exploitation of spontaneous film islanding. In even strain free films, chemical dissimilarities between substrate and epi yield high interfacial energies that can drive

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FIG. 16. Depictions of schemes to produce quantum wires. Substrate with (100) surface is masked by oxide and stripes opened by photolithography. Exposed substrate is then etched by anisotropic etches (such as KOH or ethylene-diamine-pyrocatechol)for which etching is ultimately limited by (1 11) planes (Petersen, 1992). Result is a substrate with fine V-shaped grooves or ridges. The etched substrate is overgrown with GeSi epi under conditions of high adatom mobility (generally, higher temperatures). Epi then tends to round off comers, producing isolated deposits in bottoms of grooves or on top of ridges. For V-groove at left, “quantum wire” can be narrowed below the photolithographic dimension of groove by early termination of GeSi epi.

the formation of discontinuous layers. The simple and familiar analog is the beading of water on a clean glass surface. Detailed atomistic models predict more complicated phenomena, such as the Stranski-Krastinov mode in which islanding occurs only after the initial growth of several smooth layers. Strain, such as that found in commensurate growth of GeSi on Si provides an additional islanding force. As described in early models by Luryi and Suhir (1986), islands add lateral free surfaces at which a strained deposit partially relaxes. This reduces the net system energy and provides a tendency towards islanding even in the absence of interfacial energy terms. These effects were understood in the earliest experimental work but, outside of a few detailed studies (Pidduck et al., 1992), experimentalists largely sought growth conditions that would avoid nonplanar growth and thereby facilitate growth of very thin layers and superlattices. The potential of quantum structures kindled the recent hope that islanding alone might now be exploited as a fundamental nonlithographic means of making large numbers of fine quantum structures. Early data, such as Fig. 3, define the growth conditions under which islanding will occur but provide no information on island sizes or distributions. Over the last few years a flurry of investigations have attempted to fill in these details and provide evidence of quantum effects through phenomena such as photoluminescence (Apetz et al., 1995; Sunamura et al., 1995; Schittenhelm et al., 1995; Krishnamurthy et al., 1997; Kim et al., 1997; Chen et al., 1997; Persans, 1997). At the physics level, these studies have been both interesting and promising. However, regardless of the occasional use of terms such as “self-organized” or “self-assembled” in titles, this work has largely documented the random statistical nature of nucleation

36

JOHN

C. BEAN

2.5 nm Si,,,Ge,,s/Si(OO1)

FIG. 17. The A F M image of surface of single Ge75Si25 layer with average thickness of 2.5 nm, grown under conditions in which islands are produced. Note wide range of island sizes and essentially random distribution.

processes. That is, while there are average island sizes and average separations determined by surface kinetics and energetics, variations are quite large. An example is given by the AFM data of Fig. 17 (from Physics Today, May 1996). These surfaces do indeed provide a ready means of producing a large number of very fine semiconductor dots. However, it is difficult to envision a circuit structure that could make use of such randomized distribution of sites and sizes. The preceding data are for single layers of islands. Work by Carlino et al., (1996a, b) explored multiple roughened GeSi layers embedded in superlattices. In this work there were indications that in multilayer structures, thickness variations were no longer entirely random in position. The indication, in a sense negative, was “conical shaped defects” wherein a thick or Ge-enriched region on an early layer apparently produced a strain field that led to enhanced concentration of Ge above that point, in overlaying layers. The overall effect was to produce an expanding, upward facing, cone of Ge enriched regions that could grow to the point that the localization of strain would nucleate crystallographic defects. These observations were consistent with concurrent calculations by Tersoff et al. (1996) on the strain interaction between multiple islanded layers within GeSi/Si superlattices. The results of these calculations are depicted schematically in Fig. 18. In the 1st Ge (or GeSi) layer on Si, island size and position are approximately random. However, larger islands do require collection of more material and thus larger islands will tend to be farther apart. This 1st islanded Ge layer is then overgrown with a Si spacer layer of some fixed thickness (vertical island sizes are greatly exaggerated in Fig. 18), and a 2nd Ge island layer grown. Above the 1st layer Ge islands, their larger atoms

1 GROWTHTECHNIQUES AND PROCEDURES

37

Ge layer 5 4

3

2

Ge layer 1

FIG. 18. Schematic representation of Tersoff et al. model (1996) taking into account influence of strain produced by initial layer of GeSi islands on arrangement of islands in subsequent GeSi layers. The GeSi layers are separated by fixed thickness Si spacer layers. Islands are depicted as pyramids only to show their relative volume and position (actual islands would be much smaller and have more complex geometries). Strain of initial GeSi islands tends to dilate Si spacer layer above, enhancing growth of Znd layer islands at those positions. However, as growth progresses, islands tend towards spacing tbat is entirely independent of initial island pattern. Ultimate spacing is, instead, a multiple of the Si spacer layer thickness.

induce a local lattice dilation that extends through the overlying Si spacer layer. This local dilation then provides a particularly attractive (low mismatch) site for the 2nd Ge island layer and, as found in this simulation, 2nd layer islands tend to nucleate immediately above 1st layer islands. This effect, also evident in von Kanel’s conical defects, is readily understood. The surprise occurs when the calculation continues, evaluating strain interactions and energy minimization through the growth of a full island superlattice. Islands ultimately shift to a spacing that is, instead, a simple multiple of the Si spacer layer thickness! In the simulation of Fig. 18, this final spacing is smaller than that of the 1st island layer. However, a companion simulation, assuming a very fine 1st layer distribution, converged on the same (then coarser) spacing in the final layer. As island spacing becomes more regular, so should the size distribution. As strange as these simulations are, they have been confirmed experimentally (Teichert et al., 1996) as indicated by our AFh4 data showing the surface of such an island superlattice in Fig. 19. Ordering is not perfect but the contrast with the single island layer of Fig. 17 is dramatic and the progress towards true self-organization significant. Results do, however, still fall short of the organizational perfection one expects of a circuit. Work will continue on harnessing these spontaneous mechanisms as device physicists begin to give serious thought as to how these organized 3D quantum structures might be incorporated in functional device architectures.

38

JOHN

20 x (2.5 nm Si,,,Ge,,,

c. BEAN / 10 nm S i ) on Si(001)

m

FIG,19. Experimental confirmation of model in Fig. 18. The AFM image of the surface of 2Cperiod superlattice of nominal 2.5 nm Si.025Ge0.75 layers separated by 10-nm Si spacers. Note strong increase in island regularity compared to single island layer of Fig. 17.

3 . SELECTIVE AREAEPITAXY Selective area epitaxy (SAG) is produced in situations where precursors can be chosen such that deposition will continue on an exposed semiconductor but not on common masking materials, such as Si02 and Si3N4. Selective area growth has already been alluded to and certain advantages described. However, its true significance is appreciated only when one contemplates the full sequence of steps necessary to fabricate a modem integrated circuit. Normal, planar, nonselective epitaxy must be applied only very early in that sequence when either the full substrate is still exposed or at least large areas are revealed. One might think that a “lift off’ process might be applied later in this sequence, but for crystalline device material it is difficult to define windows and lift off overgrown material without leaving damaged boundaries (if, indeed, damaged boundaries do not occur during growth!). If epi is deposited across the wafer, early in the fabrication sequence, one is limited to rather simple morphologies (planes now and perhaps organized islands in the future). Further, this layer will be exposed to all of the subsequent processing steps, many of which involve significant heating. This heating can yield undesirable diffusion of dopants, interdiffusion of layers or, for metastable GeSi layers, nucleation of defects. Many attractive alternatives are opened up if one can come in late in the circuit fabrication sequence and instead deposit small, isolated, high-quality epi layers in lithographically defined windows. Indeed, through factors

1

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such as the reduction of coupling capacitances, this option can make the difference between satisfactory and unsatisfactory circuit performance. MBE provides the antithesis of SAG growth: its precursors, atomic Si and Ge, will condense on any cool surface regardless of its chemistry. The situation is very different when halogen precursors such as Sic14 are employed. Silicon tetrachloride decomposes via the reaction Sic14 = Si 2C12. This reaction is reversible in that free Cl2 will etch Si. Under normal growth conditions, this etch rate is obviously rather slow for crystalline Si (or growth might slow and stop as C12 reaction products accumulated). However, the rate is much higher for amorphous and polycrystalline Si. This discrepancy means that should a S i c 4 molecule react and deposit Si on a surrounding mask, noncrystalline Si will be rapidly etched away even as Si continues to grow in an adjacent open window to the substrate. Halogen selective area growth is a “classic” effect in CVD epitaxy and it is relevant to this chapter only where it has been extended to selective area growth of GeSi. The Stanford RTCVD group reported one of the earliest such experiments (Noble et al., 1990). They employed G e a and dichlorosilane precursors with GeSi growth occurring at 625°C over a Si substrate partially covered by thin Si02 fingers. Auger spectroscopy gave no evidence of Ge deposition on the oxide mask, despite the fact that its precursor was not halogenated. It was noted, however, that the GeSi window deposits did contain arrays of misfit dislocations with typical spacings of 0.5 bm. The 2000 A thick Si8oGe20 layer would have strain exceeding equilibrium limits, but in uniform layers significant defect nucleation would not be expected. This discrepancy was thus attributed to enhanced nucleation of defects at the edges of the deposits. A similar paper by Zhong et al. (1990) confirmed selective growth with the same use of only a single halogenated precursor but provided no defect data. Sedgewick’s APCVD group published a series of papers on selective GeSi growth, culminating in the fabrication of a selectively grown resonant tunneling diode. The initial work (Agnello et al., 1991) used a simple dichlorosilane and germane precursor mix, identical to the RTCVD work already discussed, and reported on growth of layers with 1 5 4 4 % Ge. Smooth, unfaceted selective layers were grown but, while it was noted that in TEM analysis “occasional defects originate at the oxide sidewall,” no densities or spacings were given. High-resolution x-ray diffraction was also employed for a 260 ASi56Ge~layer grown at 550°C. Roclung curve widths were interpreted to give an upper bound of no more than lo5 misfit dislocations/cm2. In follow-up papers (Segewick et al., 1993; Zaslavsky et al., 1992), HC1 was added to the reaction environment in what is described as a “more traditional” approach to selective epitaxy. The implication was that selective growth quality improved and data from a successful selectively grown resonant tunnel diode were given. However, in the absence of comparable TEM or x-ray data, the degree of improvement and thus the importance of the added HC1 are not clear. For GSMBE, the NEC group has provided a number of reports on selective GeSi growth. In contrast to the work already discussed, and most of the CVD work, they

+

40

JOHN

c. B E A N

did not use halogens. Simple disilane and germane precursors were instead employed at temperatures of 630°C to produce films of 16, 22 and 31% Ge (Hirayama et ul., 1990a). It was reported that RHEED patterns degraded for x = .3 1, usually an indicator of either surface roughening and/or high defect densities. In conventional CVD, hydride precursors produce selective epitaxy only for a brief initial growth period, after which deposits are nucleated and grow rapidly on masking oxides. For low temperature growth of pure Si, a maximum selective thickness of 500 A was reported before onset of oxide overgrowth (Murota et al., 1989). In this GSMBE paper, the claim of hydridebased selectivity is supported only by the apparent absence of the normally rough polycrystalline surfaces on the oxide mask and on a comparison of layer thicknesses. These data support a significant degree of selectivity (i.e. growth rate in window >> growth rate over oxide). However, the near absolute selectivity seen for halogen precursors is neither confirmed nor expected. In most applications, it is not absolutely necessary that no material grow on the mask. However, it can be very damaging if imperfect material grows at the edge of the window where it can serve as a current leakage path or as the source for subsequent defect nucleation. A subsequent paper uses the aforementioned GSMBE recipe to fabricate a selectively grown GeSi heterojunction bipolar transistor (Hirayama et ul., 1990b). Transistor characteristics confirm the expected heterojunction suppression of reverse injection from the base. However, detailed and wide range I-V data are not given and it is thus not possible to exclude the possible existence of perimeter defects. The question of possible nonhalogenated selective growth is also addressed in a lone report of selectivity by hydride UHVCVD. This paper by Racanelli and Greve (1991b) does not claim absolute selectivity but instead describes an extension of the “incubation period” over which nucleation and growth on the oxide mask are delayed. The extension is attributed to the etching of early nuclei by either hydrogen or germane. A maximum delay of 67 min was reported, during which up to 1070 A of 600°C material could be deposited within the masking windows, prior to loss of selectivity. This incubation period was used to grow selective P- SissGels layers on N-Si substrates. Forward I-V characteristics were comparable to those achieved with nonselective diodes. However, reverse leakage scaled as the perimeter length of the selective diodes, again suggesting the possibility of defective edge growth.

4.

STRAIN-RELAXED GESI AND GESI PSEUDO-SUBSTRATES

The preceding discussion focused exclusively on growth of pseudomorphic or strained layer GeSi: that is, layers for which the lattice mismatch between Si and GeSi was accommodated purely by compression of the alloy layers. The alternative, misfit dislocation accommodated growth is depicted at the top right of Fig. 20. In their idealized forms, both modes produce epitaxy in which there are no dislocations within the epitaxial layers. However, in the misfit mode, at the boundary between layers, the

1

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MISFIT EPITAXIAL LAYER

SUBSTRATE CRYSTAL STRAIN

FIG.20. Schematic of alternate growth modes when epitaxial layer is grown on substrate with smaller lattice constant (e.g., GeSi on Si). Top right: misfit dislocation accommodated growth where both layers retain bulk, cubic, unstrained lattice configuration. In this mode, the difference in lattice constant is manifested by occasional planes ending at the interface, with edges of incompletely bonded atoms. These “perfect edge dislocations” would occur approximately once every 100/(lattice mismatch in %) planes. Bottom right: alternate strained-layer growth mode in which thinner epi layers compress laterally to adopt substrate planar spacing. This mode requires no energetic dislocations and is generally favored as epi growth begins.

net difference in atomic spacing means that periodically a plane must terminate. The atoms at that termination will not have normal 4-fold tetrahedral bonding. That row of atoms thus constitutes a “dislocation line” at which anomalies such as carrier trapping and generation may occur. This would obviously present a problem in thin layers for which interfaces are nearby. However, for thick layers (e.g., “thick” 2 carrier diffusion lengths) there might be little electrical disadvantage to using such layers. Further, there is one strong disadvantage in limiting oneself to strained layer epitaxy: for GeSi/Si structures in which only GeSi is strained, the difference in bandgap is manifested almost exclusively in the valence bandedge discontinuity. This is ideal for NPN HBT’s but effectively eliminates most other heterojunction device-based ideas that involve confinement of electrons. In particular it precludes modulation-doped transistors (or HEMTs) and heterojunction N-MOS alternatives. Electrons can be confined if Si layers are grown under tension (details of these effects are discussed by Jaros and Shaw in Chapter 4). This can be achieved if a Si substrate is overgrown with a very thick GeSi layer. That GeSi layer will then form misfit dislocations, relaxing its strain to provide what might be considered a “pseudo

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GeSi substrate.” Thin Si layers grown on such a “substrate” would then be subject to tension, producing a conduction bandedge discontinuity that can trap electrons. These possibilities have been actively explored, particularly by Kasper and Abstreiter, with the goal of developing fast electron-based GeSi/Si devices. Unfortunately, at a larger scale, the misfit configuration of Fig. 20 is almost never achieved. The problem is that for very thin layers, the alternative strained layer growth mode is almost always energetically favored. It is not until that strained layer grows to a certain thickness that the energetic expense of dislocations is justified and that dislocations will begin to form. However, at that point, planes must be added (or deleted) from the crystal surface. That process is depicted schematically in Fig. 21. As each plane grows downward and then sideward, both its bottom and side edges will be bounded by lines of incompletely bonded, dislocated atoms. The extensions of that dislocation line through the layer are referred to as “threading” dislocation segments. Unlike the ideal, interfacial, misfit segment, these threading arms penetrate the entire epi thickness, compromising any device within that volume. Figure 21 depicts misfit “half-loops’’ of varying length. To fully relax the strain in a layer, a total interfacial misfit dislocation length is required (as this is equivalent to a net length of added or deleted atomic plane). There is no requirement on the net threading dislocation length. Indeed, for a wafer, loops might grow all the way to the wafer edge, producing strain relief without threading arms. In real life, as the strained layer critical thickness is passed, strain drives both the lateral extension of an existing loop

FIG. 21. Three-dimensional depiction of “dislocation lines” bounding the deleted planes of Fig. 20, top right. If plane extends all the way to the limits of the crystal (far left of figure), there is a row of misbonded atoms only in the interfacial plane. Because planes are deleted only after epi thickness has built up. more likely configuration is shown at center where there are a number of smaller growing deletions. These are bounded by dislocation “loops” having an edge of mis-bonded atoms in both the interface and two “threading arms” through the epi. At right, possible consolidation of two loops to form a larger loop, eliminating two such threading arms.

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and the nucleation of new loops. A given loop will only grow to the edge of a wafer if it can do so before strain is completely relieved by nucleation of additional, shorter, halfloops. Because loop extension and nucleation are both thermally activated, the balance between a few long loops and many short loops will be a function of temperature. Activation energies are given by Hull in Chapter 111. Unfortunately, at the low temperatures commonly required to avoid GeSi roughening and islanding, those energies strongly favor the nucleation of new loops before existing loops can extend all of the way to wafer boundaries. The common resulting configuration is the one found in the center of Fig. 21, in which epi is compromised by threading dislocations. The alternate configuration has been achieved only for very dilute GeSi layers (2% Ge), where islanding could be avoided in high temperature (lO8O0C),high-growth rate CVD epitaxy (Rozgonyi et al., 1987). These layers were almost completely threading dislocation free, but to avoid roughening, they were limited to Ge fractions so low that they effectively offered no useful heterojunction characteristics. Several ideas have been investigated to overcome the aforementioned situation. First, the energetics mean that while early loops cannot grow to the wafer edge quickly enough, they might grow to the edge of a more sharply limited mesa of deposit. This alternative, explored by Fitzgerald (1989) using MBE on trenched Si substrates, showed some promise. However, a more circuit-compatible, planar alternative is presented by selective area growth in mask windows. This was the motivation for much of the SAG work discussed here. While that work contains some evidence of dislocation extension to SAG edges, no group has yet provided a dramatic demonstration of a SAG, strainrelaxed device. A third approach, explored by Hull et al. (1992), instead used MBE growth over oxide islands to force threading dislocation arms into known, avoidable locations. Those islands were staggered such that any growing dislocation loop would quickly extend laterally to intersect an oxide pad where its extension would cease. The idea was then that device patterns might be laid out in the known regions between those pads, effectively avoiding threading dislocation arms. Again, at the level of TEM defect assessment, this idea looked promising but it has not yet been extended to successful device fabrication. Another approach involves possible merging of two dislocation loops into one. Loops are driven to extension by the strain they relieve as they add (or delete) a plane of atoms. On the other hand, their extension is inhibited by the energy of the misbonded atoms on the dislocation loop. As the loop extends, the number of misbonded atoms increases, effectively producing a line tension. This tension inhibits the growth of an isolated loop but can drive the consolidation of two loops. As depicted in Fig. 22a, when two loops meet (or approach), their consolidation relieves the same net strain energy but, by eliminating the adjacent threading arms, reduces the net dislocation length and energy. This process results in a net 50% decrease in areal density of threading arms and might continue until virtually all loops combine into an ideal pure interfacial misfit dislocation array. There was early experimental evidence that this process could be enhanced within multistrained layer semiconductor superlattices. In such a

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FIG. 22. Cross-sectional depiction of possible consolidation of dislocation loops in misfit accommodated GeSi on Si growth. At left, consolidation of two loops, such as that shown in Fig. 21, right. At right, more complex sample having many strained GeSi layers, spaced by Si (with or without strain). Loops will then tend to jog at any strained interface. Multiplicity of jogs may enhance probability of loops merging and consolidating.

superlattice, there is a tendency for loops to extend not only at the substrate interface but at each strained layer interface, maximizing the chance of intersection (Fig 22b). These superlattice “dislocation filters” were proposed as an almost magical solution to misfit accommodated epitaxy. There was, indeed, evidence that they could be used to decrease threading dislocation densities from very high levels (10’0-10’2/cm2) to much lower levels (e.g., 105-106/cm2), but from these lower levels, further progress could not be made (Hull et al., 1988). Dramatic realtime TEM films (Hull and Bean, 1993) of ongoing relaxation of GeSi strained layers proved that the problem lay in the 3D nature of the dislocation intersection problem. If by pure chance, two dislocation loops nucleate and grow along the same atomic plane, the process occurs as described here. However, if loops grow together on parallel but somewhat displaced planes, a different situation may develop. Consider, for instance, relaxation of 1% mismatched layer (e.g., Ge25Si75 on Si). In this situation, strain is fully relaxed by the deletion of planes 100 atomic planes apart. If two loops nucleate and grow together at a separation of less than 100 planes, their extension and overlap would actually overrelieve the strain placing the GeSi locally in tension. This increase in energy stops further loop extension, resulting in a configuration where adjacent threading arms are too far apart to combine and are frozen in place. The final and ultimately most heavily utilized means of growing relaxed GeSi relies on a combination of the aforementioned mechanisms. Very thick, compositionally

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graded GeSi buffer layers are grown at high temperature to maximize the velocity of loop extension and the probability of ultimate loop-to-loop recombination. As defined in experiments by Fitzgerald et al. (1991a; 1992), the sharpest defect reduction may require total thicknesses approaching 10 ,um with growth often conducted at 900°C by RTCVD. Threading dislocation counts at the surface of such layers were measured at densities down to 105/cm2. While far from bulk Si densities of near zero, or strained-layer GeSi densities more typically in the 10-1 000/cm2 range, these values are nevertheless low enough that they have facilitated a variety of exploratory device investigations on electron confinement. However, the final defect density in these “substrates” is judged, even by their developers, to be much too high for application in circuits (Fitzgerald et al., 1991b). There have been rare attempts at growth of true GeSi substrates by bulk crystal growth techniques (Losada et al., 1995) but commercially available substrates are not yet available. Thus commercially oriented work on GeSi devices is limited to the much more perfect, strained layer GeSi on Si configurations detailed in this chapter.

-

VI. Summary GeSi strained layer materials have now been grown by a variety of techniques, with control at or approaching atomic dimensions. Contrary to certain claims, the best material grown by each technique is generally similar and of a very high quality, as demonstrated by device results. Distinctions occur primarily in subtleties such as doping or selectivity, or in issues relating to suitability for manufacturing. On the other hand, there persist significant gaps in our understanding of these growth processes. Some of these gaps, such as a detailed understanding of CVD doping, may be esoteric. Others, such as understanding of roughening and ordering of both atoms and islands, may be critical in enabling future, radically altered, and improved device technologies.

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Bean, J.C., Feldman, L.C., Fiory, A.T., Nakahara, S., and Robinson, I. (1984b). J. Vac. Sci. Technol., A 2, 436. Bean, J.C., and Rozgonyi, G.A. (1982). Appl. Phys. Lett., 41,752. Bean, J.C., Sheng, T.T., Feldman, L.C., Fiory, A.T., and Lynch, R. (1984a). Appl. Phys. Let?., 44, 102. Becker, G.E., and Bean, J.C., (1977). J. Appl. Phys., 48, 3395. Braunstein, R., Moore, A.R., and Herman, F. (1958). Phys. Rev., 109,695. Bruner, J., Rupp, T.S., Gossner, H., Ritter, R., Eisele, I., and Abstreiter, G. (1994). Appl. Phys. Lett., 64,994. Carlino, E., Giannini, C., Geraredi, C., Tapfer, L., Mader, K.A., and von Kanel, H. (1996a) J. Appl. Phys., 79, 1441. Carlino, E., Tapfer, L., and von Kanel, H. (1996b). Appl. Phys. Lett., 69. 2546. Chen, H., Cheng, W.Q., Xie, X.G., Huang, Q., and Zhou, Z.M. (1997). Appl. Phys. Lett., 70,446. Fitzgerald, E.A. (1989). J.Vuc. Sci. Technol., B 7,782. Fitzgerald, E.A., Xie, Y-H, Green, M.L., Brasen, D., Kortan, A.R., Michel, J., Mii, Y-J, and Weir, B.E. (1991a). Appl. Phys. Lett., 59,811. Fitzgerald, E.A., Xie, Y-H, Green, M.L., Brasen, D., Kortan, A.R., Mii, Y-J, and Weir, B.E. (1991b). Appl. Phys. Lett., 5 9 , s 1 1. Fitzgerald, E.A., Xie, Y-H, Monroe, D., Silverman, P.J., Kuo, J.M., Kortan, A.R., Theil, F.A., and Weir, B.E. (1992). J. Vuc. Sci. Technol., B 10, 1807. Fukatsu, S., Yoshida, H., Fujiwara, A., Takahashi, Y., Shiraki, Y., and Ito, R. (1992). Appl. Phys. Lett., 61, 804. Ghidini, G. and Smith, F.W. (1984). J. Electrochem., 131,2924-8. Gibbons, J.F.. Gronet, C.M., and Williams, K.E. (1985). Appl. Phys. Lett., 47, 721-3. Godbey, D.J. and Ancona, M.G. (1993). J. Vac. Sci. Technol., B 11, 1 120-3. Greve, D.W. and Racanelli, M. (1991). J. Electrochem., 138, 1744-9. Grevesteijn, D., Zalm, P., van de Walle, G., Vriezema, C., van Gorkum, A., and van Ijzendoorn, L. (1989). Thin Solid Films, 183, 191. Gronet, C.M., Sturm, J.C., Williams, K.E., and Gibbons, J.F. (1986).Appl. Phys. Left., 48, 10124. Grutzmacher, D.A., Sedgewick, T.O., Northrop, G.A., Zaslavsky, A., Powell, A.R., and Kesan, V.P. (1993a). J. Vac. Sci. Technol., B 11, 1083. Grutzmacher, D.A., Sedgewick, T.O., Powell, A.R., Tejwani. M., Iyer, S.S., Cotte, J.. and Cardone, F. (1993b). Appl. Phys. Lett., 63,2531-3. Grutzmacher, D.A., Sedgewick, T.O., Zaslavsky, A,, Powell, A.R., Kiehl, R.A., Ziegler, W., and Cotte, J. (1993~).J. Electronic Materials, 22, 303-8. Hartman, A., Dieker, C., Loo, R., Vescan, L., Luth, H., and Bangert, U . (1995). Appl. Phys. Lerr., 67, 1888. Henderson, R.C. (1972). J. Electrochem. Soc., 119,772. Higashi, G.S., Bean, J.C., Buescher, C., Yadvish, R. and Temkin, H. (1990). Appl. Phys. Left., 56. 2560. Hirayama, H., Hiroi, M., Koyama, K.K., and Tatsumi, T. (1990a). Appl. Phys. Lett., 56, 1107. Hirayama, H., Hiroi, M., Koyama, K.K., and Tatsumi, T. (1990b)Appl. Phys. Lett., 56, 2645. Hirayama, H., Hiroi, M., Koyama, K.K., Tatsumi, T., and Sato, M. (1991). In Silicon Molecirlur Beurn Epitaxy, J.C. Bean, S.S. Iyer, and K.L. Wang eds., Mat. Res. Soc. Proc., 220. Hull, R., Bean, J.C., Higashi, G., Green, M.L., Peticolas, L.J., and Bahnck, D. (1992). Appl. Phys. Lett., 60, 1468-70. Hull, R., Bean, J.C., Leibenguth, R E , and Werder, D.J. (1988). J. Appl. fhys., 65 (12), 47234729. Hull, R. and Bean, J.C. (1993). Phys. Stat. Sol. 138,533. Hwang, S-H, Eo, Y-P, Seo, J-H, Whang, K-W, Yoon, E., and Tae, H-S. (1966). J. Vuc. Sci. Techno/., A 14, 1033. Ishizaka, A. and Shriaki, A. (1986). J. Electrochem. Soc., 133,666. Ismail, K., Meyerson, B.S., and Wang, P.J. (1991). Electron resonant tunneling in SdGeSi double barrier diodes, Appl. Phys. Lett., 59, 973-5. Jang, S-M and Reif, R. (1991). Appl. Phys. Lett., 59,31624.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 56

CHAPTER2

Fundamental Mechanisms of Film Growth Donald E. Savage, Feng Liu,Volkmar Zielasek, and Max G. Lagally UNIVERSITY

OF

WISCONSIN

MADISON.WISCONSIN

I. INTRODUCTION. . . . . . . . . . . . . , . . , . , . . , , , . . . . . , . . . . . . . . . . I . Equilibrium Growth Modes . . . . . . . . . . . . , . . . . . . . . , . . . . . . . . . . . 2. Kinetic Processes During Vapor Deposition . . . . . . . . . , . . , . , . . . . , . . . . . 3. Kinetic Growth Modes . . . . . . . . . . . . . , , 11. SILICON . . . . . . . , . . . . . . . . . . . . . , . . 1. Crystal Structure . . . . . . . . . . . . . . . . . . 2. Growth of Si on Si(OO1)(Atomistic Mechanisms) . ,

, . . . . . . . , .., ., .., . .... ... .. ...... ... 3. Thermodynamic Properties and Equilibrium Surface Morphology . . 111. HETEROEPITAXIAL GROWTH: GE ON SI , . . . . . . . . . , . . . . . I . Growth of the Ge Wetting Layer on Si(OO1) . . . . , . . . . . . . . . 2. Nucleation of Coherent ‘Hut’-Islands . . . . , . . . . , , . . . . , . IV. SIGE ALLOYFILMS. . . . . , , . . . . . . . . . . . . . . . . . , . , I . Roughening and Coherent 3-0 Island Formation in Alloys . . . . . . 2. Multilayer Growth . . . . . . . . . . . . . . . . . . . . . . . . . I

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V. SUMMARY ........................................... REFERENCES

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I. Introduction In this chapter, we review the fundamental mechanisms involved in the process of growing epitaxial films. We will begin with a general discussion of thermodynamic predictions of film morphology and continue with a discussion of equilibrium growth modes. We will then identify key kinetic processes occurring during growth that may limit the film’s ability to equilibrate. Our initial discussion will be applicable to any growth system. We will then focus on the specific system of silicon on silicon, concentrating on recent work to extract atomicscale mechanisms of growth. We will finally describe Ge and SiGe alloy growth on Si, in which an understanding of both thermodynamics and kinetics is needed to explain and ultimately to control film structure and morphology. Copynght @ 1999 b) Academic Press All nghts of reprduction in any form reperved ISBN 0-12-7521 61-X 0080-8784199 $30 00

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DONALD E. SAVAGE, FENGLIU,VOLKMAR ZIELASEK,

AND

MAX G. LAGALLY

1. EQUILIBRIUM GROWTHMODES

A natural starting point for learning about film growth is a discussion of the SOcalled equilibrium growth modes (Bauer, 1958), which represent limiting cases of how a film can grow on a substrate. While no growth can occur at equilibrium and most film growth is performed far from equilibrium, it is useful to consider thermodynamic limits. Thin crystalline films grown near equilibrium exhibit one of three growth modes, depicted schematically in Fig. 1, the Frank-van der Menve (layer-by-layer), StranskiKrastanov (layer-cluster), and Volmer-Weber (cluster) modes (Bauer, 1958). The mode in which a particular materials combination will grow depends on the relative bond strengths of atoms in the deposited layer and between these atoms and the substrate atoms, as well as the degree of lattice match between the two materials. A film will initially wet the substrate if the adlayer-substrate bond is sufficiently stronger than the

FIG. 1. A schematic illustration of the three equilibrium growth modes: (a) Frank-van der Merwe (layer-by-layer): adatoms fill in a layer before nucleating the next; (b) Stranski-Krastanov (layer-cluster): the growth initially starts layer-by-layer but changes over to cluster growth due to the buildup of strain energy: and (c) Volmer-Weber (cluster): the 3-D clusters form immediately because the deposited atoms do not wet the substrate.

2 FUNDAMENTAL MECHANISMS OF FILMGROWTH

51

adlayer-adlayer bond to overcome any strain energy generated to grow the adlayer in registry with the substrate. In this simple description of growth, reaction or interdiffusion is not allowed. A more formal way to predict growth mode involves the relationship between surface and interfacial free energies. Surface free energy is defined as the free energy to create a unit area of surface on an infinite bulk solid. Given specific (per area) surface energies for the substrate and film as ys, y f , respectively (where these are the values for the semi-infinite crystals), and an interfacial energy yin, where the subscript i stands for interface and n stands for the number of monolayers of film deposited, monolayer-bymonolayer growth occurs only when

for all values of n (Bauer and van der Merwe, 1986). The term y f . differs from y f to allow for an n-dependent surface strain. The term yin includes the excess free energy needed to create the initial interface between two different materials yio. plus the additional free energy arising from strain due to lattice mismatch between the overlayer film and the substrate. In the opposite extreme, one obtains cluster growth when, for all values of n, AYn = Y f n

+ Yin - Y,> 0

(2)

In this case the overlayer does not wet the substrate. In the intermediate case, the adlayer initially wets the substrate, but because of lattice mismatch, as n increases, strain energy contributes to yin to the point at which the film no longer wets. Typically, at this point, misfit dislocations are incorporated to relieve strain and, given sufficient mobility of adatoms, preferential growth will occur in the relaxed region, leading to the nucleation of 3-D clusters. Alternatively, roughening of the growth front can relieve strain at the expense of additional surface energy. For example, for pure Ge deposited on Si(OO1) nondislocated 3-D structures form to relieve strain energy (this will be discussed in detail in Section 111). The film thickness at which Eq. (1) no longer holds is one of the definitions of the critical thickness, below which the overlayer film grows in registry with the substrate. The concept of critical thickness will be discussed in more detail in Section 111, with specific application to strain relaxation in the absence of dislocation formation, for which strain is relieved by growth-front roughening or islanding. The concept of critical thickness, applicable in the limit in which dislocation formation relieves strain, is covered in detail by Hull in Chapter 3. In principle, layer-by-layer growth occurs only for a material deposited on itself. In that special case yf,, = ys and f i n = 0. For species deposited on an unlike substrate there is generally some lattice mismatch and layer-by-layer growth will occur only up to some finite thickness. Thus for a system of B deposited on A one expects either the layer-cluster or the cluster-growth mode. There are exceptions in more complicated growth systems, such as ternary and quaternary 111-V alloys, in which it is possible

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DONALD E. SAVAGE, FENGLIU, VOLKMAR

ZIELASEK, A N D

M A X G. LAGALLY

to have essentially lattice-matched growth by choosing the appropriate alloy composition. Equations (1) and (2) show that it would be quite difficult to grow a coherent strainedlayer superlattice of two unlike materials A and 8.If A wets B, then B will not wet A. The fact that binary strained-layer superlattices can be grown shows that more is involved than thermodynamics, that is, kinetics also plays a role. To grow a binary zz 0. Interdiffusion, chemstrained-layer superlattice, one would like ) / A x Y B and ical reaction, or surface segregation also can change surface wetting and the growth mode. We will return to superlattices towards the end of the chapter. So far, we have discussed thermodynamic predictions only and these in a very simplistic way. While thermodynamics cannot be violated, it is clear that additional terms can be folded into interfacial energy. For example, where surface segregation of the more weakly bonded material occurs to reduce surface free energy, the resulting natural wetting layer, sometimes called a surfactant, can alter growth dramatically. Materials that form strongly bonded compounds at the interface or strongly interdiffuse will also change the interfacial energy. All the terms needed to describe fully the thermodynamics of growth are therefore not a priori obvious.

2.

KINETICPROCESSESDURINGVAPORDEPOSITION

Film growth cannot occur, by definition, under equilibrium conditions. In most cases growth occurs under conditions of supersaturation far from equilibrium. Therefore, kinetics will play an important role in determining film morphology. One can obtain a great range of growth morphologies when one considers the kinetics (Zhang and Lagally, 1997). Kinetic processes can be partly controlled by varying substrate temperature and deposition rate. In an evaporative growth process, such molecular-beam epitaxy (MBE), in which one can independently control sample temperature and deposition rate, one can influence which of the kinetic processes is rate limiting, allowing some control over film morphology. During vapor deposition, a clean substrate in an ultrahigh-vacuum environment is exposed to the vapor of the growth materials. As adatoms are continuously deposited onto the substrate, the system is driven into supersaturation, that is, the 2-D vapor pressure is higher than at equilibrium. A condensed phase, either a 2-D island or 3-D cluster, will then form to relax the system back toward equilibrium. Two major processes form a condensed phase from a 2-D vapor: nucleation and growth (see, for example, Matthews, 1975; and Lewis and Anderson, 1978). Arriving atoms make a random walk on the surface and, when meeting each other, form islands. The rate limiting step is the formation of a critical nucleus, which is defined as an island that is more likely to grow than decay (Venables, 1973). The nucleated islands grow by further addition of adatoms, and the lateral accommodation kinetics determine the growth shape of the islands. Growth continues until deposition is interrupted. Thereafter, coarsening, in

2 FUNDAMENTAL MECHANISMS OF FILMGROWTH

deposition

0

I step incorporation i I

53

deposition

0

re-evaporation

r-CX)-

j.,nucleation v interdiffusion

tI

I

0 island coarsening incorporation

1 surface migration

FIG.2. Schematic illustration of major processes occumng during growth from the vapor.

which islands evaporate laterally and the adatoms diffuse to larger islands, controls the dynamics of further ordering. The driving force is the difference between the local equilibrium vapor pressures around the large and small islands. An adatom, in addition to meeting another to form a nucleus, meeting an existing island (growth), or traveling between existing islands along a concentration gradient (coarsening), may also meet one of these fates: walking into a special sink site like a substrate step, diffusing into the bulk of the substrate, or re-evaporating from the surface. Figure 2 schematically illustrates these processes during growth from the vapor. Not shown in the figure is another possible influence of steps, the presence of repulsive or attractive potentials that reduce or enhance surface migration in the vicinity of steps. We will discuss each of the individual kinetic processes in more detail for the specific case of Si deposited on Si(OO1) in Section 11.2. Before doing so we begin with a qualitative discussion of the influence of kinetics on growth in terms of commonly observed kinetic growth modes.

3 . KINETICGROWTH MODES Because film growth can be performed under conditions far from equilibrium, a variety of growth-front morphologies can be obtained depending on which kinetic process is rate limiting (Zhang and Lagally, 1997). Several growth regimes have been observed so frequently they have been given specific names. These should not be confused with the idealized equilibrium growth modes discussed in Section I. 1. In Fig. 3, examples of three kinetic growth modes observed in homoepitaxy (the deposition of a material onto a like substrate) are shown schematically. They are kinetically rough growth, layer-bylayer growth, and step-flow growth. Kinetically rough growth occurs in the extreme limit of a high deposition rate and slow lateral diffusion of adatoms, in which atoms migrate only on the order of a few lattice sites before they incorporate into the growing film or are buried. Growth under such conditions leads to a rough surface for which the roughness amplitude increases with increasing film thickness (Yang et al., 1993).

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DONALD E. SAVAGE, FENGLIU,VOLKMAR ZIELASEK, AND MAX G . LAGALLY

FIG. 3. A schematic illustration of three commonly observed kinetic growth modes at 1/2 (left column) and 1 monolayer (right column) coverage. (a) Step-flow growth: deposited atoms incorporate only at steps. (b) Layer-by-layer growth: there is insufficient mobility for adatoms to reach steps and 2-D islands nucleate, grow, and coalesce. There will be some second-layer nucleation before the first is completed, causing a gradual roughening of the surface. (c) Kinetically rough growth: there is no lateral diffusion, that is, an atom sticks where it lands.

In the extreme case, if the surface diffusion coefficient is zero and all adatoms stay where they land, the roughness of the growth front will diverge following the Poisson distribution as the thickness increases. As the growth rate is reduced or the substrate temperature is raised (increasing adatom mobility), the regime of layer-by-layer growth can be achieved. In this growth mode, adatoms have sufficient mobility to find one another, nucleate 2-D islands that grow, coalesce, and ultimately fill in the initial starting surface at -1 monolayer of deposition. This mode is characterized by the periodic increase and decrease of surface steps (boundaries of the 2-D islands). The period corresponds to the deposition of a monolayer. This mode was initially observed by indirect methods, that is, by reflection high-energy electron diffraction (RHEED) and low-energy electron diffraction (LEED) (Larsen and Dobson, 1988) and more recently by direct atomic-scale imaging methods

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55

such as scanning tunneling microscopy (STM) and low-energy electron microscopy (LEEM) in which 2-D islands are imaged directly. The layer-by-layer growth mode usually shows an increase of surface roughness with coverage because the previously deposited layer is never completely filled in before the next layer nucleates. A better way to ensure a smooth surface during deposition is to grow in the stepflow growth-mode. All crystal surfaces will contain some density of monatomic-height steps, at the least those steps tilting the surface away from a high-index crystallographic face caused by polishing error. For example, prime Si(OO1) wafers have a typical miscut of 0.1 to 0.2”, giving a monatomic-height step every 70 nm to 35 nm, respectively. The surface looks like a staircase with atomic-height risers. Step-flow growth is achieved when deposited atoms have sufficient time to migrate and incorporate into a step before other atoms deposited on the surface increase the supersaturation sufficiently to force nucleation on the terraces. The staircase structure is preserved as steps simply migrate across the surface. Growth in step flow is desirable for keeping the surface smooth. To maintain it, one either deposits relatively slowly or heats the substrate to a high enough temperature for adatoms to diffuse far enough to incorporate into steps before nucleating islands. 970 K for a growth rate of For example, one needs typically a temperature of -1 ML/min to achieve step-flow growth during MBE growth of Si on Si(OO1) (Theis and Tromp, 1996). Potential-energy barriers for crossing steps can play an important role in stabilizing or destabilizing a smooth growth morphology. If, for example, there is a kinetic barrier for diffusion downward over steps, rough growth occurs because 2-D islands will nucleate preferentially on top of existing 2-D islands. In the limit of fast lateral diffusion, but no diffusion downward over steps, a “layer-cake structure” develops. An example (Esch, 1996) is shown in Fig. 4. A barrier comparable to or smaller than the adatom lateral diffusion barrier will allow atoms to diffuse off the top terrace of 2-D islands. If, in addition, the island edges are good sinks (attachment sites) for growth, there is a net depletion of adatoms in the vicinity of island edges and a concentration gradient helping downward diffusion develops. The supersaturation on top of islands is therefore lowered, reducing the probability of nucleation, especially near an island edge. This behavior helps to smooth the growing film by delaying nucleation on existing 2-D islands. A barrier to “downward” diffusion over steps helps to stabilize the step-flow growth mode by making the step spacing more regular. Flux captured by a terrace will be incorporated into its uphill step if it cannot diffuse over the downhill step. Thus, initially wider terraces will capture more adatoms, causing the adjacent “up” terraces to grow more quickly, thereby reducing the width of the initially wide terrace. Conversely, a reduction in the bamer to downward diffusion can destabilize the step-flow mode, as wide terraces advance more quickly than narrow ones, leading to step bunching and ultimately to 2-D island nucleation on the wide terraces, as the diffusion distance no longer suffices for adatoms to reach steps.

-

-

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DONALD E. SAVAGE,FENGLiu, VOLKMAR ZIELASEK, AND M A XG. LAGALLY

FIG.4. An STM image (lateral scale 4400 A) of 5 monolayers of Pt deposited on Pt(ll1) at 470 K exhibiting a “layer-cake” morphology indicating high barriers for diffusion downward over steps. The height distribution of the deposited material can be modeled with a Poisson distribution (reprinted with permission from Esch, 1996).

11. Silicon

We will introduce concepts of growth kinetics using the model system of the evaporative growth of Si on Si(OO1). Thermodynamics predicts smooth growth because a material will always wet itself. Departures from smooth growth will be caused by kinetic barriers. By studying these departures quantitatively on the atomic scale, one can infer the energies of activated processes. One of the main features of Si(OOl), its

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highly anisotropic surface structure, has an important influence on the growth morphology and kinetics. Before we discuss the specifics of growth, we briefly review the crystal structure of the (001) face of silicon, which is most commonly used as the growth substrate.

1.

CRYSTAL STRUCTURE

Today, crystal growth techniques render available device-quality Si wafers as large as 300 mm (12 in) in diameter (Wacker, MEMC), cut from dislocation-free singlecrystal rods. The Si bulk structure is determined by (sp3)-hybridization of the silicon atoms, leading to four equivalent covalent bonds to nearest neighbors in a tetrahedral coordination. The bulk lattice is diamond-like, that is, face-centered cubic with a basis formed of two Si atoms at (0, 0,O) and (1/4, 1/4, 1/4), respectively (see Fig. 5). The cubic lattice constant is 0.543 nm at room temperature, corresponding to a Si-Si bond length of 0.235 nm. All low-index surfaces exhibit reconstructions, that is, a reordering of the surface atoms with respect to their bulk positions. In general, the reordering of the surface atoms is induced by a partial rebonding of their highly directional dangling orbitals, lowering the surface free energy significantly. With few exceptions the subsequent discussion of growth on Si will be restricted to the (001) surface orientation (Fig. 6). It is technologically the most important and has been investigated thoroughly. The formation of dimers (Fig. 6b) lowers the sur-

FIG.5 . Perspective view of the silicon bulk lattice. The cubic unit cell and the face-centered positions are denoted by straight and dashed lines, respectively. The four atoms that are located fully within the unit cell are shown with their nearest neighbor bonds (dark lines).

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VOLKMAR

ZIELASEK, A N D MAX G . LAGALLY

FIG.6. Dangling-bond configurations on (100) surfaces of elemental group IV semiconductors. (a) Two dangling bonds (hybrids with a single electron) on each surface atom in an ideal bulk-terminated surface. (b) One dangling bond on each atom in a dimer. (c) Charge transfer from downward atom to upward atom in a buckled dimer.

face energy by about 2 eV per dimer, reducing the number of dangling bonds by one per surface atom at the expense of introducing an additional anisotropic surface stress. Proposed by Schlier and Farnsworth (1959) on the basis of low-energy electron diffraction experiments, the dimerization was first directly “seen” using STM by Tromp et ul. (1985). The dimers form rows along the { 110) directions perpendicular to the dimer bonds, leading to pronounced anisotropies in surface properties that are relevant to growth, such as adatom diffusion and interaction between adatoms and substrate steps. The surface energy can be lowered by rehybridization of surface bonds, which leads to the tilting (“buckling”) of the surface dimers. One atom of the dimer adopts a planar sp’-like configuration and moves down while the other moves up and adopts a p-like configuration (Fig. 6c). The buckling, like the dimerization, decreases electronic energy at the expense of increasing strain energy. Its minimization leads to alternate

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buckling directions along the dimer rows, giving rise to c(4 x 2) and p(2 x 2) reconstructions (Fig. 7), which have been observed at low temperatures by low-energy electron diffraction (LEED) (Kevan and Stoffel, 1984; Tabata et al., 1987) and by STM (Wolkow, 1992). Ab initio calculations (Pandey, 1985; Payne et al., 1989; Roberts and Needs, 1990; and Ramstad et al., 1995) show that the surface energy of buckled dimers is indeed lower than that of symmetric dimers, but the energy difference is very small (about 1.0 eV). Thus, at high temperatures, where most growth processes are carried out, surface dimers rapidly switch their orientation, leading to an averaged symmetric appearance in STM and (2 x 1) patterns in LEED. At 120 K the c(4 x 2) reconstruction is most prevalent. Dimer buckling at high temperatures is often induced by surface defects and steps (Wolkow, 1992). We refer only to the (2 x 1) reconstruction in the following discussion.

FIG. 7. Schematic top view of three possible reconstructions on Si(OO1). Top region: (2 x 1); middle: p(2 x 2); bottom; c(4 x 2). Open and solid circles mark atom positions: their size indicates different layers of atoms, with the largest circles in the outer layer. In the lower two reconstructions, the two atoms in a dimer having slightly different heights because of buckling are indicated by solid and open circles. The unit mesh of each reconstruction is depicted by a dark rectangle. For the c(4 x 2) structure, the primitive unit mesh is depicted by the rhombus.

ZIELASEK,A N D MAXG. LAGALLY 60 DONALDE. SAVAGE,FENGLIU,VOLKMAR

Because of the symmetry of the diamond structure, the dimer row direction is orthogonal on terraces separated by an odd number of monatomic steps, giving rise to both (2 x 1) and (1 x 2) domains. These domains occur even on nominally perfectly oriented surfaces, which have few accidental (polishing induced) steps. The surface stress anisotropy induced by the dimer rows gives rise to long-range step-step interactions and causes the steps on these surfaces to meander significantly. Two types of monatomic steps exist. Step segments for which the upper-terrace dimer rows are parallel (perpendicular) to the step are called SA(Sg) (Chadi, 1987). On vicinal surfaces miscut towards a { 110)direction by a few degrees or less, the two types of steps alternate. Usually, SA steps are smooth while SB steps are rough, containing many kinks and segments of SA termination. For simplicity, however, we still call a step nominally SA ( S g ) if it is oriented in the (110) direction and step segments along the average edge are SA ( S B ) .We call terraces on the upper side of the rough Sg steps (2 x I ) and the other orientation (1x 2). Surfaces with miscut toward the [ 1001direction are composed of steps that run nominally at 45" to the dimers; for such surfaces all the steps and terraces are indistinguishable and the (2 x l), (1 x 2) nomenclature becomes arbitrary. If the surface is miscut by more than -1.5" towards (110), double-atomic-height steps begin to form and their fraction increases with increasing miscut angle (Schluter, 1988; Griffith and Kochanski, 1990; Wierenga et al., 1987; Griffith et al., 1989). Although there can be two types of double steps ( D A and Dg)(Chadi, 1987), only D B steps form (Wierenga et al., 1987; Griffith et al., 1989). Combined with stress-induced step-step interactions (Alerhand et al., 1990) this energetic preference leads to a predominance of (2 x 1) domains over (1 x 2) domains. The B-type of steps (Sg and D B ) can have two kinds of edge structures: rebonded and nonrebonded. Experiments (Wierenga et al., 1987; Griffith et al., 1989; Kitamura et al., 1993) show that the rebonded S B and D g step edges appear much more frequently than their nonrebonded counterparts on natural surfaces, in agreement with total-energy calculations (Chadi, 1987). Figure 8 shows a schematic side view of the atomic structure of single- and double-atomic-height steps on Si(O01).

FIG. 8. Schematic side view of (a) single- and (b) double-atomic-height steps on Si(OO1). Prefixes nand r- denote nonrebonded and rebonded steps. Horizontal bonds are dimers of (1 x 2) terrace; solid circles denote projections of dimers of (2 x 1) terrace, whose bond directions are normal to the plane of the figure.

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FUNDAMENTAL MECHANISMS OF FILMGROWTH

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FIG. 9. Top and side views of the dimer-adatom-stacking fault (DAS) model of the Si(l11)-(7 x 7) reconstruction. The adatom layer (large shaded circles) and two double layers (open and solid circles) are indicated. The stacking fault is in the left half of the unit cell. (Reprinted with permission from Takayanagi et al., 1985.) The side view is taken along the long diagonal of the unit cell.

The { 111) surface of Si is of some interest because it has served extensively as a substrate for experiments on surface structure and film growth. Si( 111) exhibits a prominent (7 x 7) reconstruction (Schlier and Farnsworth, 1959) after annealing or when grown epitaxially. The number of dangling bonds is reduced by adatoms that saturate three dangling surface bonds by introducing only one new one. The stress induced by the adatoms is relieved by a complex surface structure, the dimer-adatom-stackingfault (DAS) model (Takayanagi et al., 1985), shown in Fig. 9. The (7 x 7) unit cell consists of two triangular subunits. One of them (left half, Fig. 9) contains a stacking fault, producing wurtzite-type stacking of the outermost two double layers. There are six adatoms in each subunit, in a ( 2 x 2) arrangement. They are located directly over the second-layer atoms and each binds to three first-layer atoms. The faulted and unfaulted subunits are separated by a triangular network of partial dislocations, and dangling bonds along these dislocations are partially saturated by the formation of dimers (three dimers at each triangle edge), which are linked by 8-member rings. At the corners of the unit cell, that is, the crossing points of the dislocations, there are holes (comer holes) exposing large portions of the second double layer. Around the corner holes, atoms are connected by 12-member rings.

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DONALDE. SAVAGE, FENGLIU, VOLKMAR Z I E L A S E K , A N D M A X G. LAGALLY

2.

GROWTH OF

SI ON SI(001) (ATOMISTICMECHANISMS)

a. Adatom Adsorption: The Initiation of Growth In order to begin growing a film, adatoms exposed to the substrate must initially stick to the surface. Typically an adatom adsorbs in a metastable site on the surface, from which it can migrate and ultimately incorporate into the growing film. There is also the possibility of re-evaporation. If the holding potential, the binding energy to the initial adsorption site, is high compared to the thermal energy of the substrate (kT), the adatom will have a high probability of remaining on the surface until it is incorporated. For Si growth on Si below the temperature at which evaporation becomes significant (T < 800 "C),the sticking coefficient (the ratio of atoms that remain on the surface to those impinging on the surface) is, for all practical purposes, 1, a regime called complete condensation. For a semiconductor surface, the presence of dangling bonds, the directionality of bonding, and surface reconstruction produce multiple adatom adsorption sites (Fig. 10) as well as complex diffusion pathways. The observation of the formation of Si islands with atomic resolution at the initial stage of MBE growth has become possible with STM (Hamers etal., 1989 and 1990; Lagally et al., 1989 and 1990; Mo et al., 1989 and 1990a; Hoeven et al., 1989 and 1990), but it has not been possible in general, because of its rapid motion, to image directly the individual adatom, especially to record its exact location and its motion. At low enough temperature, a single adatom (bound only

0

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0 0

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0 0

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FIG. 10. Potential-energy minima (solid squares) for a Si adatom adsorbed at various sites in the Si(OO1) (2 x 1) unit cell calculated by ab inifio (a) and Stillinger-Weber (b) potentials. The global minima are at M and F in (a) and (b), respectively. Arrows mark the proposed diffusion pathways. ( c ) Four possible high-symmetry ad-dimer configurations.

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FUNDAMENTAL MECHANISMS OF FILMGROWTH

63

to the atoms in a lower plane) can be observed by STM. Two recent low-temperature STM experiments (Wolkow, 1995; Wu, 1996) have identified multiple adsorption sites for an adatom, but the most probable position for an adatom to sit is at the midpoint of the ends of two adjacent dimers along a dimer row (M site in Fig. 10(a)), in agreement with the absolute minimum predicted by ah initio theories (Brocks et al., 1991; Q.-M. Zhang et al., 1995; Smith et al., 1995). These studies indicate that the location of an adatom can be influenced by substrate-mediated long-range adatom-adatom interactions, making the scenario of Si adatom adsorption more complicated. In addition to the multiplicity of potential adsorption sites, the dynamics of the adsorption process of Si on Si(OO1) is expected to be strongly temperature-dependent. There have been extensive theoretical investigations of Si adatom adsorption and diffusion on Si(OO1). The potential-energy surface of a Si adatom on Si(OO1) has been mapped out by both ah initio (Brocks et al., 1991; Q.-M. Zhang et al., 1995; Smith et al., 1995) and empirical calculations (Smith et al., 1995; Wang and Rockett, 1991; Z. Y. Zhang, 1991; Lu et al., 1991; Srivastava and Garrison, 1991; Toh, 1992; Roland, 1992a), but the empirical calculations, using either Tersoff (I 989) or Stillinger-Weber (SW) (1985) potentials, are all in disagreement with ah initio calculations in predicting the most stable adsorption site. In Fig. 10, local minima in the potential-energy surface for an adatom sitting at various sites in the (2 x 1) unit cell are marked for two representative calculations: one (Brocks et nl., 1991) based on density functional theory Fig. 10(a), the other (Z. Y. Zhang et al., 1991; Lu et al., 1991) using the SW potential, Fig. lO(b). Besides the difference in total number of local minima, in Fig. 10(a) the absolute minimum is at the M site, while in Fig. 10(b) it is at F. Figure lO(c) shows several possible ad-dimer attachment sites, where B-B is the site consistent with growth of the bulk crystal lattice. In principle, ah initio calculations are capable of giving reliable predictions. At the present time, however, limited computational resources prevent ab initio calculations from achieving their full potential. Approximations are often made in model system size, basis function expansion, and Brillouin zone sampling (integration) (Ramstad et al., 1995). Empirical calculations are quantitatively less reliable, especially when they are applied to surfaces, because the empirical potentials are usually developed by fitting to bulk properties. Also, a short-range cutoff employed in the empirical potentials introduces additional errors in treating a dynamic process like surface adsorption or diffusion, in which bond-breaking and bond-formation processes are involved. Regardless of these shortcomings, the computational efficiency gives empirical potentials the advantage that they can be easily implemented into molecular dynamics and Monte Carlo algorithms to simulate adsorption and diffusion in real time so that more insightful information of growth dynamics can be obtained. Two such studies, by Z. Y. Zhang et al. (1991) and Srivastava and Garrison (1991), reveal that as atoms are deposited onto the surface, the most preferable adsorption sites at the initial stage are not necessarily the energetically most stable sites. Because the system is far from equilibrium, the population at a given local minimum site is not

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DONALD E. SAVAGE, FENGLIU,V O L K M A R Z I E L A S E K , AND MAX G . LAGALLY

determined by its energy relative to other sites but rather determined by the escape rate of an adatom at this site. The kinetic barriers calculated from empirical potentials suggest that the Si adatoms are preferentially adsorbed on top of the dimer rows rather than in more stable places between dimer rows, leading to a so-called “population inversion” (Z. Y. Zhang et al., 1991; Lu et al., 1991). Kinetic barriers obtained in a recent ab initio calculation (Q.-M. Zhang et al., 1995) may also produce this inversion. According to this calculation, if an adatom lands on top of a dimer row, the kinetic barrier to migrate along the dimer row is 0.55 eV and the barrier to escape from the dimer row by jumping into the trough between dimer rows is 0.60 eV, so the adatom spends a long time on top of the dimer row before jumping into the trough (see Fig. 10). If an adatom lands in the trough between dimer rows, the kinetic barrier to migrate along the trough is at least 0.75 eV and the barrier to leave the trough is 0.70 eV, so the adatom stays a short time in the trough before jumping onto the top of a dimer row. Consequently, more adatoms will end up diffusing on top of the dimer rows at the initial stage of growth. Such a population inversion may have an impact on nucleation (see Section 11.3). b. Direct Measurement of Si Self-Diffusion with STM Surface diffusion is the most important kinetic process during growth. Technologically, understanding surface diffusion will lead to better control of the growth parameters necessary to achieve atomically smooth interfaces. For layer-by-layer growth surface migration helps to smooth the growth front, hence a low diffusion coefficient will result in a rough surface. In the extreme case, if the surface diffusion coefficient is zero and all adatoms stay where they land, the roughness of the growth front will diverge following the Poisson distribution as the film thickness increases. The diffusion of adatoms on a solid material is a fundamental problem in surface science, one that has attracted attention for many years. In spite of its importance, however, reliable measurements of surface diffusion coefficients are rare, especially for semiconductor surfaces. In particular, the diffusion coefficient at zero coverage, that is, the pure migration of adatoms on the surface, is difficult to determine. Macroscopic methods based on the observation of the spreading of an initially well-defined distribution of adatoms (Bonzel, 1972; Mak et al., 1987) or the decay of intensity oscillations in reflection high-energy electron diffraction with increasing temperature (Neave et al., 1983) may be ambiguous because of the influence of surface defects such as steps and because of interactions between adatoms themselves. Field ion microscopy (Ehrlich and Hudda, 1966) can measure the pure migration of a single adatom in an elegant manner. However, it is limited in the materials that can be studied because of the high field necessary for imaging, and has seen little application to semiconductors. Because STM gives atomic resolution, it would seem to be an ideal method to follow the diffusing atom to give a direct measurement of the diffusion coefficient. The rapid motion of Si adatoms at temperatures typical for STM operation has so far prevented

2 FUNDAMENTAL MECHANISMS OF FILMGROWTH

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such measurements. Alternatively one can examine 2-D island densities for a fixed coverage at different growth temperatures following a quench to room temperature. If the dose is low enough that a significant number of islands is not lost to coalescence (growing together), the island density equals the density of critical nuclei, We will use the growth of Si on Si(OO1) as an example of this method. Mo et al. performed the seminal work to determine the surface diffusion coefficient of Si on Si(OO1) in a series of papers in 1991 and 1992. Based on STM analysis of the number density of islands far from steps and the width of denuded zones at the steps, the activation energy for diffusion is determined to be Ea = 0.67 f 0.08 eV with a prefactor of DO lop3cm2/s. The diffusion is highly anisotropic: the surface migration is at least 1000 times faster along the dimer rows than perpendicular to them. The method has since been widely applied to other systems (Voigtlander et al., 1993; Stroscio et al., 1993; Brune et al., 1994; Dun et al., 1995; Vasek et al., 1995; Bott et al., 1996). In this section, we review the major details of the work by Mo et al. (e.g., 1991 and 1992).

-

Dependence of island number density on the diffusion coefficient (theory) As adatoms are deposited on a surface at sufficiently low temperatures, they either form islands or walk into steps. The competition between island formation and step incorporation results in a spatial distribution of stable islands with denuded zones around those steps that are good sinks for the adatom and a uniform distribution far from the steps. By establishing the dependence of island number density on the diffusion coefficient, it is possible to determine the diffusion coefficient by measuring the island density without observing the individual adatom. At the center region of a wide terrace (hence a negligible influence of steps), an arriving adatom will either form a new island with another free adatom (nucleation) or walk into an existing island (growth). The surface diffusion coefficient determines how large an area an adatom interrogates in unit time. Therefore, the diffusion coefficient controls the outcome of the competition between nucleation and growth, and hence determines the number density of stable islands after deposition to a certain dose at a given deposition rate. A large diffusion coefficient, for instance, means a high probability for an arriving adatom to find an existing island before another adatom is deposited in its vicinity to provide a chance for nucleation. As a result, a large diffusion coefficient yields a lower number density of stable islands. Quantitatively, the relationship between island number density and diffusion coefficient has been established through a simple dimensional argument (Mo et al., 1991 and 1992; Pimpinelli et al., 1992). The deposited adatoms make a random walk on the surface. The diffusion coefficient, D , for a random walk process is D = J a2

(3)

where J is the number of hops made in unit time and a is the step size, here taken to be the lattice spacing. The lifetime T A of an adatom is controlled by two different

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DONALD E. SAVAGE, FENGLIU,VOLKMARZIELASEK, AND MAXG.

collision rates, W A A (adatom-adatom collision) and such a way that the “death rate” of adatoms is n/TA

= 2WAA

+

WAI

LAGALLY

(adatom-island collision), in

WAl

(4)

where n is the number density of free adatoms deposited at a rate of R , n = R ~ A . According to the theory of random walks (Montroll, 1964; Barber and Ninham, 1970), the number of sites visited by the adatoms after J = DrA/a2 hops (for large J’s) during their lifetime is approximately C ( D t A / a 2 ) d / 2where , d is the dimension of the random walk and C is a constant that depends on the dimensionality and the capture number of the single adatoms or islands. On the average, an area of 1 / n is~associated with each adatom ( n =~ n ) or island ( n =~ N ) enclosing l/(nBU2)lattice sites. Hence the probability of an arriving adatom to collide with an existing adatom or island is Cn B a2( D t A/ a2)d/2. Multiplying this by nsA yields the collision rates W A A and W A J , WAB

= C?lnBa2-d(DrA)d’2/tA

(5)

The nucleation rate or the rate of increase of the island number density is d N / d t = W A A = Cn2a2-d(DtA)di2/tA

(6)

At the very beginning of the deposition, the island density is negligible, so the decay of adatom density is mainly caused by nucleation, that is, n/rA = 2WAA. For a large enough diffusion coefficient, the island density catches up rapidly and collision with islands becomes the dominant factor in limiting the adatom lifetime t ~which , should be much shorter than the deposition time t (in order for this analysis to hold). Now n / r A E W A I , so that C N u ~ - ~ ( D ~=A1 ) ~ / ~ (7) Substituting Eq. (7) into Eq. (6) yields N2/d+i

d N = ~ - 2 / d ( ~ 2 ~ 2 - I4 D /d ) dt

(8)

By integration, we have N(2+2id)= C-2/d(2 + 2/d)(RQ/D)a(2-4/d)

(9)

where Q = Rt is the total dose deposited up to time t . Thus we have a general form of the dependence of the island number density on diffusion coefficient as N

-

x

=

1/(2

+2/d)

(10)

For isotropic diffusion, d = 2, x = 113; for highly anisotropic diffusion, d = 1, x = 114 (Pimpinelli et al., 1992; Mo et al., 1992a). An example applying this analysis will be shown in Section II.2.b. Several assumptions and approximations have been made in the aforementioned dimensional argument. Therefore the analysis can be applied only under appropriate

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FUNDAMENTAL

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conditions. For Eq. (6) to be valid, the dimer must be the stable nucleus (critical nucleus i = 1 atom). Generally speaking, this assumption appears to be correct for strongly bonded materials (metals, semiconductors) (Lewis and Campbell, 1967) at not too high temperatures. For Si/Si(OOl), single dimers are observed to be stable up to 600 K by STM (Mo et al., 1991). However, a LEEM experiment shows that the stable-nucleus size increases rapidly with increasing growth temperature, reaching a size of 650 dimers at 970 K (Theis and Tromp, 1996). The authors extrapolated their measurements to the temperature range in which STM experiments were performed and showed that their results were consistent with a single-dimer stable nucleus at the STM growth conditions. Recent STM experiments suggest that the picture that the dimer sitting in a minimumfree-energy site is the stable nucleus from which 2-D islands grow may be overly simplistic, at least at low temperature. This issue will be explored in more detail in Section 11.2.c.

Diffusional anisotropy measurement Because Si(OO1) has two-fold symmetry, it is natural to expect the surface migration to be anisotropic. Mo and Lagally (1991a,b) showed direct experimental evidence of anisotropy in the surface diffusion of Si and Ge on Si(OOl), based on STM analysis of the width of denuded zones (areas without islands because adatoms can reach and incorporate into steps before nucleating islands). All theoretical studies based on total-energy calculations (discussed in Section 11.1) confirm the experimental determination that surface diffusion is faster along the dimer rows. As shown in Fig. 11, on the down terrace of an SB step, dimer rows are parallel to the step [(l x 2) domain], while on the up terrace of an Sg step, dimer rows are perpendicular to the step [(2 x 1) domain]. Thus, the mechanisms of diffusion toward the step on these two neighboring terraces are different: either along or perpendicular to the dimer rows. Because S g steps are symmetric sinks that absorb adatoms equally well from up and down terraces (Mo and Lagally, 1991a; Mo, 1991), an anisotropy in the diffusion rate will result in an asymmetry in the two denuded zones around an Sg step. Diffusion coefficient and activation energy In Section II.2.b we showed that the surface diffusion coefficient of adatoms can be determined by measuring the island number density after deposition at a given rate and to a certain dose. One such measurement for Si diffusion on Si(OO1) has been made (Mo et d.,1991). The outline of their experiments is as follows: a sub-ML dose (e.g., 0.07 ML) of Si adatoms is deposited onto Si(OO1) held at different temperatures; when the deposition is shut off, the sample temperature is simultaneously quenched to near room temperature by turning off the heating power; the sample is then transferred to the STM for scanning; scans are made near the centers of the large terraces to avoid the interference of steps; many scans are obtained to achieve good statistics; and the number of islands in each scan is

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DONALDE. SAVAGE, FENGLIU, VOLKMAR ZIELASEK, A N D MAXG. LAGALLY

FIG. 11. Scanning tunneling micrographs, 5000 A x 5000 A, showing the asymmetry of denuded zones around Se steps. The Si is deposited at a rate of 1/400 ML/s to 0.1 ML coverage at two growth temperatures: (a) 563 K; (b) 593 K. The surface steps down from the upper left to the lower right. The white bars correspond to the directions of the dimer rows on the terrace. (Reprinted from Surface Science, 268, Y.W. Mo, J. Kleiner, M.B. Webb, and M.G. Lagally, Surface self-diffusion of Si on Si(OOl), pp. 275-295, (1992) with permission from Elsevier Science.)

counted to obtain an average number density. Equations (9) and (10) are then used to obtain the diffusion coefficient. Figure 12 shows STM images of 2-D islands formed after deposition at different temperatures. From such images, a plot of island density vs inverse temperature can be constructed. It shows Arrhenius behavior over a range of temperatures. At too low a temperature the quench rate after deposition is too slow to ensure that all islands are formed during deposition, a necessary condition of the modeling relating island number density to the diffusion coefficient. At too high a temperature the island number density drops dramatically because of coarsening, an additional ordering mechanism that becomes important at low deposition rates when the supersaturation is small. Using such data a quantitative determination of the diffusion coefficient is made with the aid of computer simulations. Simulated island densities have been compared to the experiments for the same total deposited dose, using a solid-on-solid model (Mo et al., 1991). Figure 13(a) is a plot of the calculated number density of islands vs the jump rate, for three models that incorporate different diffusional and sticking anisotropies. For a sufficiently high jump rate, the island number density is proportional to J-'13 for isotropic diffusion and J-'14 for anisotropic diffusion, in agreement with the dimensional argument. For a very small jump rate, the mean time for adatoms to find an existing island is longer than the total deposition time and most islands are formed after deposition, resulting in a constant island number density (Mo, 1991). Figure 13(b) shows Arrhenius plots of the diffusion coefficients obtained by fitting the three models in Fig. 13(a) to the measured island density at several temper-

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FUNDAMENTAL MECHANISMS OF FILM GROWTH

69

FIG. 12. Scanning tunneling micrographs of islands formed after deposition at different substrate temperatures at a rate of 11600 ML/s to 0.07 ML coverage. (a) T = 348 K, 250 A x 250 A; (b) T = 400 K, 300 A x 300 A: (c) T = 443 K, 300 8, x 300 A; (d) T = 500 K, 400 8, x 400 A. The islands formed at higher deposition temperatures are larger than those at lower temperatures, with lower number densities, because of the larger diffusion coefficients at higher temperatures. The islands in each image are counted to obtain an average number density for each temperature. (Reprinted from Surface Science, 268, Y.W. Mo, J. Kleiner, M.B. Webb, and M.G. Lagally, Surface self-diffusion of Si on Si(OOl), pp. 275-295, (1992) with permission from Elsevier Science.)

atures. Using the curve that incorporates a 1OOO:l diffusional anisotropy, an activation energy for surface diffusion of adatoms of 0.67 eV and a pre-exponential factor of cm2/s are obtained (Mo et al., 1991j (a higher anisotropy gives a virtually identical activation energy). Assuming the diffusional anisotropy is all ascribed to a difference in activation energy, the activation energy for diffusion across dimer rows becomes 1 eV. Although essentially all calculations predict the anisotropic diffusion, the kinetic barriers from ab initio calculations agree quantitatively better with these experimental values. The experimentally derived barriers for diffusion should be considered as average values because only a single adsorption site and two orthogonal diffusional directions are used in the computer simulations; on a real surface, multiple adsorption sites and complex diffusion pathways can be involved. From the measured diffusion coefficient, one would expect that the motion of a monomer will be slow enough to be observable at -200 K. However, in reality monomers can be observed only at much lower temperatures (Wolkow, 1992; Wu, 1996) suggesting that there exists on top of the dimer rows a fast diffusion pathway with lower barrier than the average, leading to a faster motion of monomers than what one would have expected. Several different models have been proposed theoretically: Brocks et al. (1991) proposed a zigzag path connecting two most stable adsorption sites (Fig. lO(aj); Z. Y. Zhang et aE. (1991) and Srivastava and

-

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DONALDE. SAVAGE, FENGLIU,VOLKMAR ZIELASEK, AND MAX G. LAGALLY

FIG. 13. Determination of diffusion coefficient from island densities. (a) Calculated relationship between the island number density and the jump rates of adatoms. Three of the curves are from computer simulations with different diffusional anisotropy assumptions while the fourth curve is from rate equation calculations. Circles: isotropic sticking and diffusion. Diamonds: rate equation, isotropic sticking and diffusion. Squares: anisotropic sticking and isotropic diffusion. Triangles: anisotropic sticking and diffusion. The anisotropic diffusion assumes a jump rate along the dimer rows of 1000 times that perpendicular to the dimer rows. The anisotropic sticking assumes a probability of one for sticking at the ends and zero at the sides of islands. Simulations are for the same deposition condition as in experiments (Fig. 12). (b) Diffusion coefficients obtained from comparison of the measured island number density with those from computer simulations using three different models. Notations are the same as in (a) (Mo et al., 1992b). (Reprinted from Sutfuce Science, 268, Y.W. Mo, J. Kleiner, M.B. Webb, and M.G. Lagally, Surface self-diffusion of Si on Wool), pp. 275-295, (1992) with permission from Elsevier Science.)

Garrison (1991) proposed that the diffusion occurs predominantly on top of dimer rows (Fig. 1 O(b)); Roland and Gilmer (1992a) suggested exchange events between adatoms and substrate atoms during diffusion. c.

Growth: Adatom-step Interaction

Epitaxial island growth and step flow growth are understood better than the initial nucleation step. At typical STM experimental deposition rates of -0.001 MWs to -0.01 MLh, between room temperature and -500 K, the growth proceeds via 2-D islands (Harners et al., 1989 and 1990; Lagally et al., 1989 and 1990; Mo et al., 1989 and 1990a); above 500 K, the growth proceeds via step flow (Hoeven et al., 1989 and 1990). Annealing experiments (Mo et al., 1989 and 1990a) clearly show that the shape of the as-grown islands is controlled by kinetics, because it differs from the equilibrium shape. The as-grown islands consist of a few dimer rows with an aspect ratio as high as 20: 1 (Hamers et al., 1989 and 1990; Lagally et al., 1989 and 1990; Mo et al., 1989 and 1990a). Analyses show that the highly anisotropic shape is caused by the large difference of lateral accommodation coefficient in two orthogonal directions rather than by anisotropic diffusion (Mo et al., 1989 and 1990a). Arriving adatonis stick to the

2 FUNDAMENTAL MECHANISMS OF FILMGROWTH

71

ends of dimer rows ( S B steps) at least one order of magnitude better than to the sides of the rows (SA steps). For the same reason, in the higher-temperature step-flow growth mode, SB steps advance to catch up with SAsteps, resulting in a single-domain surface (Hoeven et al., 1989 and 1990). The anisotropic accommodation has also been shown to play a key role in the 2-D kinetic roughening of the growth front of the step under step-flow or near-step-flow conditions (Wu et al., 1993). In the following we discuss experiments (Mo and Lagally, 1991a; Mo, 1991) that allow one to investigate in detail the nature of the adatom-step interaction. The interaction between adatoms and surface steps is one of the most important microscopic aspects of growth kinetics. The nature of this interaction determines the growth rate and shape of islands, the mode of step-flow growth, and the width and asymmetry of the denuded zone around steps. The width of a denuded zone is controlled by the adatom sticking coefficient at the step and the energy barrier for adatoms to cross the step, in addition to surface diffusion and its anisotropy. It is possible to address each effect individually. The relative magnitudes of the lateral sticking coefficients of adatoms at the SA and SB steps can be studied by analyzing denuded zones on any single terrace that is bounded by the two types of steps. Figure 14 shows an STM image of a large

FIG. 14. The spatial distribution of 2-D islands on a large terrace (-700 & . wide), showing a large anisotropy in the denuded zones that reflects the anisotropy of the lateral sticking coefficients of adatoms at Sa and Ss steps. Field of view: 1.0 x 0.9 bm. Approximately 0.1 ML was deposited at 563 K and at a rate of 1/4000 ML/s. The surface steps down from the lower left to the upper right. (Reprinted from Surface Science, 248, Y.W. Mo and M.G. Lagally, Anisotropy in surface migration of Si and Ge on Si(001), pp. 313-320, (1991) with permission from Elsevier Science.)

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DONALDE. SAVAGE,FENGLIU, VOLKMARZIELASEK, AND MAX G. LAGALLY

single terrace about 7000 A wide, created by applying a small external stress to the wafer (Men et al., 1988) (the effect of the external strain on growth kinetics is negligible) (Webb et aL, 1990 and 1991). The terrace is bounded by an SB step at the downstairs side (the upper left) and an SA step at the upstairs side (the lower right). On each side are much smaller minor-domain terraces. The bright strings on the terrace are 2-D islands. An obvious asymmetry exists in the spatial distribution of the islands: the denuded zone near the SB step is much larger than that near the S A step. Because diffusion towards the two steps must be the same everywhere, this asymmetry is clear evidence for the anisotropy in the lateral sticking coefficients of adatoms at the two types of monatomic steps: Sg steps are good sinks for adatoms while SA steps are not. Quantitative analysis of the highly anisotropic shape of growth islands shows that the ratio of sticking coefficients of a monomer at Sg and S A steps is at least 1O:l (Mo et al., 1989 and 1990a; Mo, 1991; Wu, 1996). Mo (1991) also pointed out that for a dimer-wide island to grow preferentially at its ends, a monomer must have some residence time at the end of the row, waiting for another monomer to come to form the next dimer. Indeed, monomers trapped at the end of dimer rows have since been frequently observed (Bedrossian, 1995; Wu, 1996; Swartzentruber, 1997). S B steps are not only good sinks but also symmetric sinks: that is, they adsorb adatoms coming from either up or down terraces equally well (Mo and Lagally, 1991a). This conclusion is reached by analyzing the denuded zones around steps in (100) directions, which are at 45" to the dimer rows of both domains. In this configuration, all the terraces are equivalent and the diffusion toward any step on both the up and the down terraces is identical. Figure 15 shows STM images of the island distributions around (100) steps. In Fig. 15(a), the four denuded zones shown have the same widths. The middle terrace is so narrow that the two denuded zones from the bounding steps nearly overlap. For the conditions in Fig. 15(b), the denuded zones are wider than the terrace. Although 45" steps are not pure Sg steps, microscopically the Sg step segments are adsorbing the adatoms with at least one order of magnitude greater sticking coefficient (Mo et al., 1989 and 1990a; Wu, 1996). Thus one can conclude that SB steps are symmetric sinks for adatoms either from up or down terraces. The existence of a large denuded zone on the up-terrace side of S B steps (Fig. 14) suggests that, in addition to Sg steps being good sinks, there can be no significant barrier for adatoms to cross downward over S B steps, because a barrier would act to keep atoms on the terrace and thus reduce the denuded zone even if the sticking coefficient at the S B step is large. The absence of a denuded zone on the down-terrace side of SA steps indicates that SA steps are poor sinks and, at least to a certain degree, mirrors for arriving adatoms. In Fig. 14, the SA step at the lower right corner is very close to the next Sg step. If adatoms could easily cross an SA step from the down (2 x 1) terrace, they would climb over to the up (1 x 2) terrace and get absorbed by the next SB step or by the kinks in the SA step. This step crossing would result in a large denuded zone on the down ( 2 x 1) terrace of the SA steps even though SA steps

2

FUNDAMENTAL

MECHANISMS OF FILMGROWTH

73

FIG. 15. Scanning tunneling micrographs, 5000 A x 5000 8,showing symmetric denuded zones around (100) steps. Approximately 0.1 ML of Si was deposited at a rate of 11400 ML/s, at (a) 563 K, and (b) 593 K, respectively. The surface steps down from top to bottom. The underlying dimer rows run 45' to the steps and form a chevron pattern orthogonal to the directions of the long axes of the deposited islands. (Reprinted from Surfiuce Science, 248, Y.W. Mo and M.G. Lagally, Anisotropy in surface migration of Si and Ge on Si(O01), pp. 313-320, (1991) with permission from Elsevier Science.)

themselves are poor sinks. No such denuded zone is observed; hence the S A steps must have a significant stepcrossing barrier. The adatom-step interaction has also been studied extensively by theory (Q.-M. Zhang, 1995; Roland and Gilmer, 1991 and 1992b; Z. Y. Zhang et al., 1992; Srivastava and Garrison, 1993). The results of an ab initio calculation (Q.-M. Zhang et al., 1995) are in very good agreement with the experimental conclusions described above, showing that SA steps are poor sinks for adatoms both because the binding energy of an adatom at the SA step edge is comparable to that on the terrace and because the barrier for adatoms that have adsorbed to the SA step from the lower terrace to escape the S A step is low. These are necessary conditions for SA to act as a mirror, but a significant stepcrossing barrier is also needed. Rebonded Sg steps (see Fig. 8) are good sinks for adatoms because the binding energy to the SB step is large and because adatoms approaching the SB step from the upper terrace encounter only small barriers to cross the step edge. All empirical calculations (Roland and Gilmer, 1991 and 1992b; Z. Y. Zhang et al., 1992; Srivastava and Garrison, 1993) have reached the conclusion that Sg steps are much better sinks for adatoms than SA steps, but they wrongly predict that only nonrebonded SB steps bind adatoms strongly. Experiments (Kitamura et al., 1993; Wu, 1996) show that most SB steps appearing on the surface are rebonded and hence for growth to occur they must bind adatoms also. The measurements of Swartzentruber (1997) corroborate this conclusion, showing that monomers attach preferentially to rebonded S B steps.

74

DONALDE. SAVAGE,FENGLIU,VOLKMAR ZIELASEK, A N D MAXG. LAGALLY

One of the remaining challenging questions concerning growth of Si on Si(OO1) is how ad-dimers (stable nuclei) transform into epitaxial dimer-row islands or even whether they do. Although a single ad-dimer is most frequently observed at the epitaxial position on top of a dimer row, it does not bind an adatom (Brocks and Kelly, 1996); theory predicts that only in-trough dimers can attract adatoms, but they form “dilute” ad-dimer rows rather than epitaxial dimer rows (Bedrossian, 1995; Brocks and Kelly, 1996). A high-resolution STM image of a dilute dimer row is shown in Fig. 16: the location of the ad-dimers is found to be at D-D* sites, schematically shown in Fig. IO(c). It has been speculated that the dilute ad-dimer rows are transient structures mediating the formation of anisotropic epitaxial dimer-wide islands from single addimer nuclei (Mo et al., 1989 and 1990a; Bedrossian, 1995; Brocks and Kelly, 1996). Several molecular dynamics (Z. Y. Zhang and Metiu, 1991; Rockett, 1994) and Monte Carlo simulations (Dijkkamp et al., 1992) have been carried out to explore the microscopic mechanisms of the formation and growth of epitaxial islands, but none has observed the dilute ad-dimer row structure. Other mechanisms, for example, substrate dimer opening due to adatom insertion, have been proposed (Z. Y. Zhang and Metiu, 1991; Rockett, 1994). But these also have not been confirmed experimentally. Thus there remains a large gap in understanding the very initial stage of island formation from the stable nucleus.

FIG. 16. A high-resolution STM image of an adsorbed diluted-dimer row island containing 11 atoms, with a monomer attached at the left end. The ad-dimer bonds are parallel to the dimer bonds in the underlying rows and centered between the rows (sites D-D* in Fig. 1O(c)). The image is taken at a sample bias of +0.8 eV. In this example the ad-dirners are Ge deposited on Si(OO1) at room temperature (from Qin et a / . , 1998). The diluted-dimer row is indistinguishable from a Si diluted-dimer row. The dimer structure is affected by the presence of the dimer row island.

2 FUNDAMENTAL MECHANISMS OF FILMGROWTH

d.

75

Growth: Coarsening

If growth is performed under conditions close to equilibrium or if deposition is interrupted, coarsening must be included in an analysis of the growth process. The average supersaturation of free adatoms on the surface continues to reduce through nucleation and growth until it is nearly eliminated. At this stage, islands of different sizes exist in equilibrium with their local vapor pressures. The local equilibrium vapor pressure, that is, the concentration of free adatoms around an island, is inversely proportional to the radius of the island (Porter and Easterling, 1981; Mo, 1991). Hence there will be locally different concentrations of free adatoms on the surface. As a consequence of Fick’s law of diffusion, net fluxes of adatoms flow from small islands to large ones. Following nucleation and growth, therefore, the system is further organized by the coarsening process: large islands grow at the expense of small ones. The driving force decreases as the islands become more uniform in size, leading to the phenomenon of Ostwald ripening (Ostwald, 1901) in which a distribution of islands with uniform size results. Theis and Tromp (1996) have shown, using LEEM, that Si growth on Si(OO1) at elevated temperatures occurs very near equilibrium. Under the deposition conditions of TSubstrate = 970 K and growth rates ranging from 0.1-2 monolayers per min, the impinging flux increased the adatom concentration by only 1.75% above the equilibrium adatom concentration. As most Si films for technological use are deposited at such “high” temperatures, rather than at the lower temperatures of an STM experiment, coarsening can be an important process in the growth of Si films used for device applications. In separate work, Theis, Bartelt, and Tromp (1995) concluded, from a LEEM study, that the coarsening of 2-D islands on Si(OO1) can be understood in a common framework with step fluctuations. In addition, they demonstrate that coarsening is strongly influenced by the nearest-neighbor correlations between islands. Thus, coarsening is more complicated than the simple model of 2-D islands communicating with an average 2-D gas of adatoms arising from the average 2-D “vapor pressure” of the islands.

3. THERMODYNAMIC PROPERTIES AND EQUILIBRIUM SURFACE MORPHOLOGY While it is essential to understand growth kinetics to achieve controlled film growth, manipulating kinetic processes also requires a good understanding of the thermodynamic properties of the surface. The relative rate of a kinetic process is dependent on thermodynamic balances among different configurational states. By choosing properly the initial configuration of states, it is possible to alter the kinetic route for subsequent growth. For example, the growth of 111-Vsemiconductors on vicinal Si(OO1) templates is largely controlled by the initial step configurations (Kroemer, 1986; Fukui and Saito,

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DONALD E. SAVAGE, FENGLIU,VOLKMAR ZIELASEK, AND MAX G . LAGALLY

1987). In this section, we discuss the thermodynamic properties of equilibrium surface structures and morphologies on Si(OO1). a.

Equilibrium Shape of Si Islands and Energetics of Steps

It has been shown that the highly anisotropic shape of as-grown Si islands, with an aspect ratio as large as 15 to 20, is determined by growth kinetics rather than being an equilibrium property (Mo et al., 1989 and 1990b). Upon annealing at -600 K, the islands become more rounded, with a much smaller aspect ratio of about 2 to 3 (Mo et al., 1989 and 1990b). This has also been confirmed by two LEEM experiments in the same temperature range (Swiech and Bauer, 1991; Theis ef al., 1995). At equilibrium, the shape of an island is controlled by its boundary free energy. For Si(OOl), S A and Sg steps comprise the island boundary, and so the difference in the free energies of these two steps determines the island anisotropy. At low temperature, when the entropy contribution to the free energy is small, the aspect ratio of the equilibrium island shape reflects the ratio of S A and SB step energies. The observed aspect ratio of islands of 2 to 3 at 600 K is in accord with the measured step energies (Swartzentruber et al., 1990; Swartzentruber, 1992), once entropy has been included. Swartzentruber et al.( 1990) have performed an STM analysis of the equilibrium distribution of steps and kinks on Si(OO1). For steps bounding wide terraces, the kink excitations at the individual step sites are shown to be statistically independent and each excitation obeys a simple Boltzmann distribution. From the analysis, Swartzentruber et al. derived S A and SB step energies of 0.028 eV1atom and 0.09 eVlatom, respectively. A similar analysis by Zandvliet et al. in 1992, involving a somewhat more complicated model, gives S A and S B step energies of 0.026 eV1atom and 0.06 eV/atom, respectively. The S A and SB step energies have also been determined from LEEM measurements of island shape and step fluctuations (Bartelt et al., 1994; Theis et al., 1995). The results from STM and LEEM are in very good agreement (Bartelt et al., 1994). As temperature increases, the entropy component of the free energy becomes dominant and the difference between S A and Sg step free energies becomes smaller, leading to a more isotropic shape of islands. The LEEM images (Swiech and Bauer, 1991; Theis et al., 1995) show that the equilibrium aspect ratio of island decreases from 2.6 at 970 K to 1.5 at 1370 K. The higher-temperature ratio is consistent with values of 1.25 to 1.43 observed for single-atom deep sublimation holes (trenches) by reflection electron microscopy at 1200-1400 K (Latyshev et al., 1988; Mktois and Wolf, 1993). This agreement is no surprise, as these trenches are also bounded by SA and SB steps. b. Equilibrium Step Conjigurations

Nominal surface Step configurations on vicinal Si(OO1) surfaces have been a subject of intensive study because, in practice, vicinal surfaces are used in device fabrication

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as the growth template, utilizing the steps to facilitate smooth growth by step flow. On vicinal Si(OO1) with a small miscut (< 1.5") toward [110], SA and SB steps alternate, separating 2 x 1 and 1 x 2 domains. If the surface is nominally singular (miscut by less than a few tenths of a degree), the equilibrium populations of these two domains are about equal (Men et al., 1988). Men et al. showed that the relative populations of the two domains can be changed if uniaxial stress is applied to the wafer at a temperature sufficiently high so that the step mobility is high. The domain that is compressed along the dimer bond by the applied stress is favored. The experiment is well understood by a theoretical model developed in 1988 by Alerhand et al. The theory shows that, in the presence of an anisotropic intrinsic surface stress, a flat surface, for example, Si(OOl), is unstable to the formation of elastic-stress domains separated by steps. The discontinuity of stress at the step introduces a force monopole, giving rise to an elastic step-step interaction that lowers the surface energy with a logarithmic dependence on step separation ( L ) (Marchenko, 1981; Alerhand et al., 1988), E s = C1 - C2 ln(L/a), where C1 denotes the step formation energy per unit length, C2 reflects the strength of the interaction, which is related to the stress anisotropy and elastic constants, and a is a microscopic cutoff length on the order of a lattice constant. The surface assumes the lowest-energy configuration with an optimal step separation of LO= n u exp(Cl/C2 1). Therefore, a surface with sufficiently low step density could reduce its energy by introducing extra steps. When a uniaxial external stress is applied to such a surface, the favored domain type will grow at the expense of the other, as shown by experiment (Men et al., 1988). Further LEED and STM experiments have been done to determine quantitatively the intrinsic surface stress anisotropy of Si(OO1) (Webb et al., 1990 and 1991). A measurement of the population asymmetry of (2 x 1) and (1 x 2) domains as a function of the external strain gives a value of 0.07 f 0.01 eV/A for this anisotropy. The stress anisotropy of Si(OO1) has also been calculated by various theoretical methods (Payne et al., 1989; Meade and Vanderbilt, 1990; Garcia and Northrup, 1993; Dabrowski et al., 1994) and good agreement with experiment has finally been reached after several years of controversy (Garcia and Northrup, 1993; Dabrowslu et al., 1994). Although the theory of Alerhand et al. (1988) provides a good understanding of the experimentally observed behavior of steps on Si(OO1) under an external stress, the spontaneous formation of extra steps to reduce the size of the stress domain predicted by theory is not observed on nominally singular Si(OO1). Instead, the existing steps become wavy in the low-step-density regions, as observed in 1992 by Tromp and Reuter in a LEEM experiment. Calculations by Tersoff and Pehlke in 1992 also predict that at large enough step separations, straight steps are unstable against the formation of long-wavelength undulations. These undulations lower the surface strain energy by effectively reducing the size of the stress domains so that the step-step separations become closer to the optimal value of LO. Furthermore, step undulations are kinetically preferred and are compatible with step flow. Therefore, step undulations preempt the formation of extra steps.

+

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Vicinal surface Step configurations on vicinal surfaces are more complicated and their behavior is less well understood. As the miscut angle increases, double-atomicheight steps ( D B ) start to form (Olshanetzky and Shklyaev, 1979; Kaplan, 1980; Wierenga et al., 1987; Aumann et al., 1988; Griffith et al., 1989; Griffith and Kochanski, 1990). Theoretical calculations (Chadi, 1987) show that the formation energy of D B steps is lower than the sum of SA and SB step energies. But, as first pointed out by Vanderbilt et al. in 1989, the elastic step-step interactions must be included to determine the equilibrium step configurations on a vicinal surface. Using a onedimensional elastic model, Alerhand et al. in 1990 showed that the surface with singleatomic-height steps at a small miscut angle is actually a true equilibrium structure rather than a kinetically limited structure, as had been thought earlier. The model also predicts that, at T = 0, there exists a first-order phase transition from the single0.05" atomic-height-step surface to the double-atomic-height-step surface at 0, as the miscut angle (0) increases. At finite temperature, thermal roughening of SB steps shifts the transition to higher angles, for example, giving a value of S, 2" at T = 500 K. This model was extended (Poon et al., 1990 and 1992) by adding extra elastic interaction terms that result from the force dipoles associated with steps (Marchenko, 1981). The predicted phase transition was then shifted to -1" at T = 0 and -3" at T = 500 K. Pehlke and Tersoff (1991) searched for the global minimum step configuration of a vicinal Si(OO1) surface in a T = 0 analysis by extending Poon's calculation, allowing a random mixture of single and double steps and the variation of all the step positions. They show that, at the small angle at which only single-atomic-height steps appear, the population of (2 x 1) and (1 x 2) domains can be asymmetric, and the population of (2 x 1) domains increases gradually with increasing miscut angle, in good agreement with RHEED (Tong and Bennett, 1991) and STM experiments (Swartzentruber et al., 1992). As the angle increases, doubleatomic-height steps start to form and their concentration increases with increasing angle. However, they appear in a mixed phase, consisting of a complex sequence of single and double steps, rather than a pure phase or a coexistence of two spatially separated phases. Extending the T = 0 analysis to higher temperature, Pehlke and Tersoff (1991) constructed the phase diagram of the vicinal Si(001) surface. They showed that there is a critical temperature above which no phase transition exists at all. Below the critical temperature, the transition takes place through a quasi-continuous sequence of weak first-order transitions. Experimentally, however, no indication of a first-order phase transition has been observed. Instead, the step concentration changes continuously with both miscut angle (Swartzentruber et al., 1992) and temperature (de Miguel et al., 1991). Experiments also indicate that at high temperature and large angles, a simple one-dimensional elastic model becomes unsatisfactory (de Miguel, 1992).

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111. Heteroepitaxial Growth: Ge on Si Because of the technological potential of Si-Ge and Si-GeSi heterojunctions, for example in high-speed heterobipolar transistors and in optoelectronic devices, the growth of germanium on silicon has been studied intensively for several years. Qualitatively, Si and Ge are quite similar in their structural and electronic properties. They both form with the diamond crystal structure. The Ge lattice, however, is expanded by 4.2% with respect to the Si lattice and the Ge-Ge bond is weaker than the Si-Si bond, leading to a smaller surface energy. Consequenlly the system Ge/Si is usually discussed as a classical model for the Stranski-Krastanov growth-mode (see Section 1.1). The simple picture of a smooth pseudomorphic wetting layer growing up to a certain critical thickness and being followed by the introduction of dislocations and the growth of dislocated 3-D clusters, however, provides only one limiting thermodynamic guideline. The compressed Ge overlayer shows a variety of morphological instabilities with respect to the underlying substrate in order to relieve strain (Liu et al., 1997). The instabilities are not necessarily accompanied by misfit dislocation formation, but instead offer alternative pathways for strain relief.

OF THE GE WETTING LAYERON sI(oo1) 1. GROWTH

a. Submonolayer Growth The strain induced by the lattice mismatch between the substrate and the growing species affects both thermodynamics and kinetics (Liu et al., 1997). In the submonolayer regime the 4.2% lattice mismatch between Ge and Si has only little effect on the kinetics of growth of Ge on Si(OO1) and it has been shown both experimentally (Mo and Lagally, 1991a; Lagally, 1993) and theoretically (Srivastava and Garrison, 1992; Roland and Gilmer, 1993; Milman et al., 1994) that Ge submonolayer growth on Si(OO1) is essentially the same as Si(OO1) homoepitaxy. In general, Ge atoms deposited onto a Si(OO1) substrate at room temperature form 2-D epitaxial islands and follow the sequence (Mo and Lagally, 1991a and 1991b; Mo ef al., 1991; Mo et al., 1992b; Lagally, 1993; Liu and Lagally, 1997a) of adatom adsorption, adatom diffusion, nucleation of islands, and growth of dimer row islands just as in silicon homoepitaxy (Section 11.2.b). A first-principles calculation of the potential-energy surface for a Ge adatom on Si(OO1) (Milman et al., 1994) shows that the most stable adsorption site for a Ge adatom is at an “M-site,” that is, in the trough next to a dimer row and midway between two dimers along the row, just as for a Si adatom (Brocks et al., 1991). Analogous to the STM measurements of Si diffusion on Si(OO1) (Section 11.2) the activation energy, the prefactor, and the anisotropy were determined for Ge diffusion on Si(O01) from the temperature dependence of the island density and the areas of denuded

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FIG. 17. Ge islands grown on Si(001) at low coverages. The spatial distribution (here for 0.1 ML Ge deposited within 100 s at 570 K) shows essentially the same anisotropies that are observed for Si(001) homoepitaxy. The STM scan range is 500 nm x 500 nm. The surface reconstruction alternates between (2 x 1) (terraces 1 and 3) and (1 x 2) (terrace 2) domains separated by atomic-height steps. The surface steps down from lower right to upper left. A denuded zone forms near to the SB step on terrace 3. (Reprinted from Sutface Science, 248, Y.W. Mo and M.G. Lagally, Anisotropy in surface migration of Si and Ge on Si(001), pp. 31 3-320, (1991) with permission from Elsevier Science.)

zones that appear at steps. Figure 17 shows Ge islands on Si(OO1) grown at 620 K and a denuded zone near the Sg step. The diffusion coefficients for Ge on clean Si(OO1) and on Si(OO1) covered by 1 monolayer of Ge are compared to the results for Si diffusion on Si(OO1) in Fig. 18. On clean Si(OO1) the diffusion of Ge adatoms is highly anisotropic and single atoms move along the dimer row direction about 1000 times faster than across the dimer rows, the same result as for Si adatom diffusion on Si(OO1). The activation barrier for diffusion of Ge on clean Si(OO1) also resembles that of Si, but the prefactor is an order of magnitude smaller, implying that Ge atoms diffuse more slowly on Si(OO1) than do Si atoms (Lagally, 1993). The calculated diffusion barriers (Milman et al., 1994; Brocks et al., 1991) agree well with the experiments. Diffusion of Ge on Si(OO1) covered by 1 ML of Ge is different: it is nearly isotropic, the activation energy is lower, 0.48 eV vs 0.67 eV, but the prefactor is also lower, sufficiently so that the diffusion coefficient is overall lower. The explanation is believed (Lagally, 1993) to be related to scattering of the diffusing Ge atoms off the dimer vacancy lines discussed in Section lb. At room temperature, for growth of Ge, the as-grown 2-D epitaxial islands again have a highly anisotropic shape, because of the large difference in sticking coefficients of adatoms to different step edges (Mo and Lagally, 199 1a and 199 1b; Mo et al., 199 1; Mo et al., 1992b; Lagally, 1993) annealing at higher temperatures (-600 K) changes

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-si~\

81

Q M X X ) G e on Si(OO1) ULAAA Si Ge on on Si(OO1) 1ML Ge o n Si(OO1)

A A

0 a, 10

a 10

FIG. 18. Comparison of the monomer diffusion coefficients for Si on Si(OOI), Ge on clean Si(OOl), and Ge on 1 ML Ge/Si(001) after formation of dimer vacancy lines. The diffusion coefficient is highly anisotropic for Si and Ge on clean Si(OO1) and nearly isotropic for Ge on 1 ML Ge/Si(OOl). The activation energy for diffusion changes from 0.67 eV for Si and Ge diffusing on clean Si(OO1) to 0.48 eV for Ge diffusing on 1 ML GelSi(001).

the islands into a much more rounded shape whose aspect ratio is determined by the energetics of two types of monatomic-height steps (Mo et al., 1989). The smallest and the most obvious stable structure on the surface at room temperature is a single Ge ad-dimer, from which it is deduced that the size of critical nuclei is one atom (Mo and Lagally, 1991a and 1991b; Mo et al., 1991; Mo et al., 1992b; Lagally, 1993). It should be noted that an understanding of the atomistic pathway from a single adatom to islands of ad-dimers is still missing for both Si and Ge on Si(OO1). Recent STM measurements demonstrate that two Ge adatoms on adjoining "M-sites" of the Si(OO1) substrate (adsorption sites D-D* in Fig. IO(c)) can form a stable pair of adatoms that differs from an ad-dimer (Qin and Lagally, 1997). Because chains of these adatom pairs have been observed, it is suggested that adatom pairs and metastable structures of various sizes involving adatom pairs represent the missing link between single monomers and the formation of dimer row islands (Qin et al., 1997). If this is the case, island formation might not be dominated by the nucleation of single addimers on top of the substrate dimer rows, and hence the concept of the critical nucleus and the diffusion parameters derived from this concept would have to be reevaluated.

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b. Formation of Dimer Vacancy Lines Initial strain relaxation of the Ge overlayer is primarily achieved by forming additional dirner vacancies. Total-energy calculations (Tersoff, 1992; Yu and Oshiyama, 1995; Liu and Lagally, 1996) show that dimer vacancies actually have a negative formation energy on the Ge/Si(OOl) surface with respect to the uniformly strained Ge overlayer, and hence they are energetically even more favored to form in a Ge layer on Si(OO1) than on clean Si(OO1). Although the kinetics of vacancy formation are not known, we should expect that dimer vacancies are also kinetically more favored to form on Ge/Si(OOl) than on clean Si(OOl), because it is easier to break Si-Ge or Ge-Ge bonds than to break Si-Si bonds. A rebonding of second-layer atoms in the dimer vacancies plays an important role in the mechanisms of vacancy formation and strain relaxation in Ge-covered Si(OO1). Vacancies can serve as a strain-relief mechanism by simply providing room for the expansion of the Ge overlayer. Without rebonding, however, vacancy formation would cost too much chemical energy through the creation of dangling bonds. The rebonding of second-layer atoms in the vacancies not only eliminates the dangling bonds but also introduces a large tensile stress, which cancels and actually overcompensates the large compression along the dimer rows in the Ge overlayer (Tersoff, 1992; Liu and Lagally, 1996). Thus, vacancy formation is driven both by the reduction in the number of dangling bonds and by strain relaxation. As the Ge coverage (ffG,) approaches 1, surface vacancies order into lines forming a (2 x n ) reconstruction consisting of dimer rows that are interrupted by missing dimers every n lattice spacings where n is typically 10-12. The reconstruction that has been observed by both STM (Mo and Lagally, 1991b; Kohler et af., 1992; Iwawaki et al., 1 9 9 2 ~ and ) LEED (Kohler et al., 1992; Iwawaki et al., 1992a,b). Although dimer vacancies readily form on clean Si(OOl), a well defined (2 x n ) pattern begins to appear only beyond 0.8 ML Ge coverage (&,) (Wu et al., 1995; Wu, 1996), suggesting that the reconstruction (i.e., the ordering of vacancies) is related to relief of misfit-induced compressive strain in the surface (Tersoff, 1992; Kohler et al., 1992). This conclusion is supported by an STM observation (Mo and Lagally, 1991b) that at the tops of large 3-D Ge clusters, where the strain is relaxed, flat (001) facets show only a perfect (2 x 1) reconstruction. Figure 19 shows an STM image of a (2 x n ) structure on a Ge-covered Si(OO1) surface with QG, 1.6 ML. The vacancy lines (VLs) are dark because of the lower altitudes of the dimer-vacancy sites. The (2 x n ) reconstruction is not perfect; each dimer vacancy (DV) fluctuates around its mean position. The meandering of the VLs is dictated by the competition between the ordering process, driven by the DV-DV interaction to minimize elastic energy, and the disordering process, driven by a desire of the system to maximize its configurational entropy. There exists a preferred spacing, nag, between two neighboring DVs on the same dimer row. When they are too far apart, the compressive stress in the overlayer is not relieved enough; if they are too close, the stress is “over-relieved.” Effectively, this

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FIG.19. Scanning tunneling micrographs (45 nmx45 nm) of Si(OO1)coveredby -1.6 MLGe, showing atomically resolved structures on three terraces separated by monatomic steps. The dimer vacancy lines, visible as dark lines, and the dimer rows that are perpendicular to the vacancy lines form a (2 x n ) superstmcture on the terraces.

balancing of tensile and compressive stresses amounts to a short-range repulsive, longrange attractive interaction between DVs on the same dimer row, as shown directly by total-energy calculations (Tersoff, 1992; Liu and Lagally, 1996). The thermal fluctuation of DVs causes n to have a distribution function P,(n), peaked at an optimal value of n (P,(n) is the probability of finding dimer vacancies on the same dimer row separated by n dimers). Figure 20 shows two such distribution functions for Bee = 0.8 ML and 1.6 ML, respectively (Wu et al., 1995). They are determined by counting n in individual dimer rows of many STM images like those shown in Fig. 19. As the Ge coverage increases, more vacancies are created to relieve the increasing misfit strain. Consequently, the optimal value of n in Fig. 20 decreases with increasing Ge coverage, from -1 1 at 0.8 ML to -9 at 1.6 ML, consistent with an earlier LEED measurement (Kohler et aE., 1992) and a recent theory (Liu and Lagally, 1996). The formation of dimer vacancy lines drastically changes the kinetics of growth of Ge after the completion of the first Ge monolayer. It has been shown that the diffusion of Ge adatoms on a one-monolayer Ge-covered Si(OO1) surface is much less anisotropic than on clean Si(OO1) and that overall the effective diffusion coefficient is lower (see Fig. 18) (Lagally, 1993). The lower activation energy evaluated from Fig. 18 would indicate that it is easier for Ge atoms to diffuse over a Ge lattice than a Si lattice. Because the microscopic diffusion mechanism along unperturbed sections of the dimer rows is expected to be the same as on the clean Si(OO1) surface, that is, anisotropic and fast along the dimer rows, it is suggested that the dimer vacancy lines impose an additional barrier for diffusion along the dimer rows, making the diffusion overall slower and more isotropic. This view is supported by simulations (Roland and Gilmer, 1993; Yu and Oshiyama, 1995).

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3

Separation n(a,) FIG.20. Separation probability distributions P, of adjacent dimer vacancies on the same dimer row at (A) OG, 0.8 ML and (B) 0Ge 1.6 ML, respectively. Distributions are determined from images such as the one shown in Fig. 19. The graph shows that dimer vacancies organize into regular lines at higher Ge coverage.

-

-

c. Intermixing Using deposition from a Ge source at typical evaporation rates onto a Si(O01) substrate with small miscut at temperatures of 500-700 "C one would expect the layer to form via step-flow growth, that is, the atoms have enough mobility to reach steps. Under these growth conditions, however, interdiffusion between Si and Ge becomes significant. Theory (Liu and Lagally, 1996) shows that, at true equilibrium, there should be considerable intermixing of Ge into the top few Si layers. The Ge adatoms are not just incorporated at the steps but over the entire surface by exchanging places with Si atoms in the surface dimers to form Si-Ge mixed dimers or Ge dimers. The displaced Si atoms diffuse to and are incorporated at the steps to give the typical signature for step flow. This picture is inferred from experimental observations (Tromp, 1993; Patthey et al., 1995). If the Ge adatoms were adsorbed at step edges, forming continuous areas of Ge-covered Si that expand with increasing coverage, one would expect immediate formation of a (2 x n ) structure corresponding to 1 ML coverage in those areas, which would thus form a distinct phase coexisting with the bare-Si areas. Instead, STM studies (Mo and Lagally, I991b; Mo et al., 1991; Mo et al., 1992b; Kohler et al., 1992; Iwawaki et al., 1992c; Croke et al., 1991; Butz and Kampers, 1992; Chen er al., 1994; Wu et al., 1995; Wu, 1996) show that dimer vacancies and then ordered vacancy lines gradually form uniformly on the entire surface upon Ge deposition. The intermixing

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affects both the value, n , of the vacancy spacing and the shape of its confinement potential. An experiment by Li et al. (unpublished) demonstrates that it is possible to obtain different n values and distribution functions P,(n) for the same Ge coverage by using different growth and annealing procedures to induce Si/Ge intermixing. STM has, however, so far not been able to separate spectroscopically Si and Ge atoms in close proximity, and thus the atomic-level composition of a mixed Si-Ge layer has as yet not been determined. Such measurements are nevertheless potentially possible (Qin and Lagally, 1998 unpublished).

d. Steps and Morphology at Higher Ge Coverage ( 2 ML and above) The deposition of Ge on vicinal Si(OO1) (that is, a surface that contains steps created by miscutting from a singular surface) significantly influences the monolayer step morphology (Wu et al., 1995; Liu et al., 1997). With increasing coverage, the initially smooth SA step becomes rougher than the initially rough S g step, which actually smoothens. This phenomenon can be used to extract the influence of Ge on step energies. On a strained surface, the step energy contains mainly two contributions. One is positive and local, resulting from bond distortion along the step. The other is negative and nonlocal, resulting from strain relaxation associated with the creation of the step. Both contributions decrease the step energy as the Ge concentration is increased in the uppermost layers. First, because the strength of a Ge-Ge bond or a Ge-Si bond is weaker than that of a Si-Si bond, an overall smaller step energy is expected as Si-Si bonds are replaced by Ge-Ge and Ge-Si bonds. Second, at higher Ge coverage, the surface is more strongly strained, and the elastic energy released by the creation of a step is larger because it relaxes more strained bonds. Figure 21 shows the measured dependence of the step energy of the two types of steps, S A and S B , on the Ge coverage. Both step types show a decrease in energy, although the effect differs in magnitude (Wu et al., 1995; Liu et al., 1997). The measurements of Wu et al. (1995) also show that the stress anisotropy of the surface reverses with Ge coverage from the anisotropy exhibited by clean Si(OO1). The crossover point of zero stress anisotropy occurs at a coverage of about 0.8 ML. The change in step energies and the change in surface stress magnitude and anisotropy with increasing Ge coverage both influence the further evolution of the morphology of the growing Ge film. This evolution is shown for the first three monolayers of Ge in Fig. 22 (Lagally, 1993). Beyond a coverage of -2 ML of Ge, the surface morphology changes to a patchy layered “wedding cake” one. Apparently the increasing stress can no longer be accommodated by increasing the density of vacancy lines. Increasing stress anisotropy also contributes to the breakup of the 2-D layers. Steps are created. These steps relieve stress (Wu, 1996; Liu et al., 1997). This patchy, quasi-2-D morphology represents, at an atomic level, the layer-to-cluster transition predicted by the Stranski-Krastanov model. Clearly the picture is not as simple as a clean, abrupt transi-

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2.5 1

0.5

I

I

I

0

0.5

I

I

I

I

1.o

I

I

I

1.5

2.0

FIG.2 1. Dependence of the energies of SA (circles) and SB (diamonds) steps. The energies are in units of k T and given for a step of length 2a0, where a0 is the distance between true adjacent dimers along a dimer row. (Reprinted with permission from Liu e t a / . , 1997.)

tion from a continuous 2-D layer to clusters. Clusters will form on this patchy template with increasing Ge coverage, as described next.

2.

NUCLEATIONOF COHERENT

‘HUT’-~SLANDS

For pure Ge deposited on Si(OOl), the strain relaxation mechanisms described so far extend the thickness of the wetting layers up to 3 ML (Asai et al., 1985; Gossman et al., 1985; Zinke-Allmang ef al., 1989; Mo eta]., 1990b; LeGoues et al., 1990; Eaglesham and Cerullo, 1990; Mo, 1991; Mo and Lagally, 1991b; Tersoff, 1991; Lagally, 1993) even though by the third ML it is not possible to make a complete 2-D layer. The misfit strain is partially relaxed by the (2 x n ) reconstruction, by the creation and morphological modulation of steps, and by breakup of large terraces into 2-D islands. As one grows Ge on Si(OO1) beyond the first -3 monolayers, strain energy that can not be released in that way will continue to build in the film and the growth mode changes from 2-D to the formation of epitaxial 3-D structures. At a late stage these 3-D structures relax to the Ge (or SiGe if an alloy is deposited or if intermixing occurs in the 3-D structures) lattice constant, with interface dislocations between the substrate and the island. For clarity, we refer to the strained, coherent, epitaxial 3-D structures as 3-D islands and the relaxed structures as clusters. In 1990 Eaglesham and Cerullo showed with cross-sectional transmission electron microscopy (CTEM) that Ge deposited to a thickness beyond 3 monolayers on Si(OO1) initially formed 3-D islands that were coherent with the substrate, that is, without dislocations. They proposed that the islands relieved strain by relaxing outward while at the

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Ge/Si(001) 450°C

FIG.22. Scanning tunneling micrographs (300 nmx300 nm) of the morphology of Ge layers on Si(OO1) for coverages of 1.2, and 3 ML, respectively. The layers were deposited under identical conditions, chosen so that the first monolayer grows in a step-flow mode. Further annealing does not change the morphology. The surface becomes increasingly rough as the Ge coverage increases, a consequence of increasing stress and the concomitant decrease in step creation energy. (Reprinted with permission from Lagally, 1993.)

same time compressing the underlying Si substrate. Also in 1990, Mo et ul. followed the formation of small, faceted islands of Ge on Si(OO1) for deposits beyond 3 monolayers using STM. The 3-D island growth exhibited unusual behavior compared with the usual Stranski-Krastanov growth mode, in that the island density rather than island size increased dramatically with increased coverage. In addition, Mo et al. (1990b) proposed that these islands were coherently strained and grew as an intermediate step before the formation of large dislocated clusters at much higher coverages. The 3-D islands have well-defined facets (Mo et al., 1990; Mo, 1991; Eaglesham and Cerullo, 1990; Lutz et ul., 1994). In particular, STM has identified them as hut-

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like with predominantly a prism shape (with canted ends), in some cases a four-sided pyramid, with perfect { 105) facet planes on all four sides (Mo et al., 1990, Iwawaki et al., 1991 and 1992b, Tomitori et al., 1994). Their principal axes are strictly aligned along two orthogonal (100)directions. The [ 105) facets make a shallow (- 11”) angle with the underlying Si(OO1) plane. An STM image of a Ge hut on Si(OO1) is shown in Fig. 23. The four facets in these so-called “hut” islands (Mo et al., 1990) appear always with perfectly completed layers. This and the observation that the number density of the huts increases rapidly while their size grows slowly as the Ge coverage is increased indicate that the formation of huts is driven by the low surface free energy of { 105) facet planes. Because hut clusters form preferentially at lower growth temperatures (< 500 “C) and because they transform completely to macroscopic dislocated clusters after annealing at higher temperatures (Mo et aZ., 1990), they are believed to be a metastable intermediate phase leading eventually to the formation of these macroscopic dislocated clusters (Mo et al., 1990; Mo, 1991; Eaglesham and Cerullo, 1990; LeGoues et al., 1990). The kinetics of hut-island formation are still unclear. The concentration at low growth temperatures of coherent hut islands is much higher than that of dislocated macroscopic clusters, indicating that huts are much easier to nucleate, with a lower formation barrier. Thus, hut islands define the onset of the transition from 2-D to 3-D growth and provide an easier kinetic path for the ultimate formation of the equilibrium rough surface consisting of dislocated macroscopic clusters. The small formation barrier for huts can result from the low surface energy of their { 10.5) facets (see discussion that follows). It is also suggested that (100) steps (running at 45” to the dimer row direction), formed in the initial Ge layers may lower the hut formation barrier by acting as nucleation sites (Mo et al., 1990b; Chen et al., 1995). Stress relaxation via the formation of 3-D clusters, although the natural route according to the Stranski-Krastanov mechanism, is an unconventional view in the general lit-

Frc. 2 3 . A single coherent “hut” island as “seen” by STM (perspective view). The base dimensions are 40 nrn x 28 nm and the height of the hut is 2.8 n m . (Reprinted with permission from Mo eral., 1990b.)

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erature of heteroepitaxialfilm growth, which mostly discusses dislocation formation in films grown, at sufficiently low temperature, beyond their critical thickness (discussed in detail by Hull in Chapter 3). Theories show that under appropriate conditions, coherent islands can be not only energetically more stable than both strained epitaxial films and dislocated islands (Vanderbilt et al., 1991; Tersoff and Tromp, 1993; Tersoff and LeGoues, 1994) but also kinetically favored over the nucleation of dislocations (Tersoff and LeGoues, 1994). The coherent islands allow the partial relaxation of strain by elastic deformation at the expense of introducing extra surface area. In general, the strain-relaxation energy is proportional to the volume of the island ( V ) , while the increase of surface free energy scales with the surface area ( V213).For a 3-D island of trapezoidal shape with a small facet angle, the total free energy can be expressed as E = aTV213 - bs2V

(11)

where a and b are coefficients related to the island facet angle, V is the volume of the island, E is the misfit, and r is surface free-energy anisotropy between the normal orientation and the beveled edge (Tersoff and LeGoues, 1994). Clearly, for a sufficiently large island (or an equivalent pit), formation of the island (or pit) is energetically favored. Kinetically, the thermal activation barrier is proportional to 1‘3/~-4 for nucleating clusters, but scales as E - ~(LeGoues et al., 1993) for nucleating dislocations (Tersoff and LeGoues, 1994). Thus, for large misfit (large E ) , formation of coherent 3-D islands is kinetically favored over dislocation formation, while for small misfit, dislocation formation is favored. The formation barrier also depends sensitively on surface free energy anisotropy (r).The smaller the value of r, the lower the barrier. In addition to the 3-D hut islands, larger coherent multifaceted 3-D islands with steeper facet angles (referred to as “domes”) have been observed (Mo et al., 1990b; Medeiros-Ribeiro et al., 1998), with a transformation from the huts to the domes with increasing coverage. It is likely that the difference in surface energies between the strained Ge( 100) and (105) faces is rather small, making the 3-D hut islands kinetically favorable over the larger multifaceted islands, which contain other faces with surface energies much higher than that of the strained Ge(100) face. On the other hand, the larger 3-D dome islands are energetically more stable than hut islands by incorporating faces with steeper facet angles to allow more strain relaxation (Lutz et al., 1994; Tersoff and LeGoues, 1994). The energetic argument is consistent with the observation that 3-D hut islands form preferentially at lower temperature and transform to larger islands after annealing at high temperature (Mo et al., 1990b). Also at higher temperature, r becomes generally smaller due to increased entropy; the islands will have multiple facets with less well-defined overall shape and structure (Mo et al., 1990b). Finally, of course, dislocation formation at the interface between 3-D dome islands and the substrate and relaxation of the islands to the Ge or SiGe lattice constants occurs to provide ultimate stress relief.

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In order to grow thicker smooth films, it is possible to delay or suppress 3-D island formation by decreasing E (e.g., by lowering the concentration of Ge in a SiGe alloy that is deposited), by decreasing r, for example, by using surfactants (Cope1 et al., 1989), and/or by growing at low temperature. Surfactants may, however, also change surface diffusion, a kinetic parameter. The strain relaxation in 3-D hut islands has been studied by x-ray diffraction (Steinfort et al., 1996). Profiles through crystal truncation rods show side peaks around the central rod originating from scattering from the { 105) hut facets. The expansion of the lattice parameter in the huts produces an asymmetry in the intensity of these side peaks. By modeling the variation of the lattice constant simply as increasing quadratically with the height of the hut islands and simulating the diffraction profiles, a good agreement with the experimental results is obtained assuming full relaxation (to the Ge lattice constant) at the tops of the huts and a relaxation (from the Si lattice constant) of 0.5% at their bottom. Knowledge of the cluster size is crucial for this evaluation. The model, so far, does not consider the strain field in the Si substrate (Eaglesham and Cerullo, 1990). Recently, there has developed an intense interest (Shchukin et al., 1995; Tersoff et al., 1996; Steinfort et al., 1996; Liu and Lagally, 1997b) in the { 105)-faceted hut islands (Mo et al., 1990b) because of their potential applications as quantum dots (Lagally, 1998). To obtain uniform electrical and optical properties in such quantum dot arrays, it is necessary to develop ways to control the size and size distribution of coherent 3-D islands. For example, one can attempt to optimize parameters that influence the island growth hnetics, such as deposition rate and substrate temperature, in order to narrow the 3-D island size distribution. We briefly describe approaches for such optimization in Section IV.2. Alternatively, one can grow 3-D islands on lithographically patterned substrates. While such an approach gives a well-ordered array, the density is then limited to the resolution of the lithography.

IV. SiGe Alloy Films Silicon and germanium are miscible over the entire binary alloy composition range, showing a nearly ideal solid solution behavior. Because strain can be tuned by changing alloy composition, one expects that the growth of Sil-,Ge, alloy on Si can act as model system to understand the influence of strain on growth. In reality, however, alloy growth is complicated by the presence of surfaces. For example, germanium is well known to segregate to the surfaces of Si and Sil-,Ge, alloys because dangling Ge bonds cost less energy than dangling Si bonds, lowering the surface free energy. In addition, in the presence of a nonuniform surface strain such as produced by clustering (roughening), there is a driving force for lateral concentration gradients (Guyer and Voorhees, 1995). Thus, Ge should preferentially incorporate in regions in which strain has been relaxed while Si will incorporate preferentially in regions that are still lattice

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matched to the substrate. Alloy concentration gradients were confirmed experimentally by Walther et al. in 1997. In addition, during the growth of SiGe alloy in nearly equal concentrations, an ordered phase will form that does not appear in the bulk alloy. The ordering occurs by phase separation of Ge and Si into alternate bilayer { 111) planes. This ordering is discussed by Bean in Chapter 1.

In general, phenomenology similar to that found in the growth of pure Ge on Si(OO1) is observed for the growth of SiGe alloys. During the initial growth of the alloy a (2 x n ) reconstruction forms to relieve the surface stress generated as approximately 1 monolayer of Ge segregates to the surface (Butz and Kampers, 1992).’ As the coverage is increased, monolayer-height steps bunch, relieving additional stress (Teichert et al., 1996). If the film is grown thick enough, stress relaxation occurs through the formation of coherent faceted 3-D islands or through the formation of misfit dislocations. Ultimately, dislocation formation is the dominant stress relaxation mechanism. Dislocation nucleation can be promoted on “rough” surfaces by stress concentration in cusps where nondislocated 3-D islands initially touch (Jesson et al., 1995). The stress state and, hence, thermodynamics of the heteroepitaxial system can be modified by growing SiGe alloys of different compositions. Under given growth conditions (temperature, growth rate, sample orientation and miscut, etc.), the mode of stress relaxation depends critically on misfit strain, that is, the alloy composition during the growth. As discussed in the previous section, the activation barriers for different modes of strain relaxation (nucleation of a dislocation or a coherent faceted 3-D island) scale differently with misfit strain ( F ) . The competing paths for stress relaxation have been confirmed by growth of SiGe alloys on Si(OO1) (Tersoff and LeGoues, 1994). At low Ge concentration with misfits below 1%,dislocations form before noticeable surface roughening, whereas at high Ge concentration coherent 3-D islands appear before dislocations form. Growth temperature will also play a role; alloy films at lower temperature will remain smooth until eventual dislocation formation for higher states of strain (Tersoff and LeGoues, 1994). Understanding the conditions under which dislocation formation relieves strain before clustering occurs is crucial in the growth of relaxed SiGe alloy layers with a low dislocation density at the film surface. The presence of clusters before the formation of dislocations can alter severely the nucleation mechanism of dislocations, yielding an unacceptably high dislocation density (Tersoff and LeGoues, 1994; Jesson et aE., 1995).

‘Surface segregation is suppressed if hydrogen ties up surface dangling bonds. Chemical vapor deposition

from H-containing precursors will leave the surface H terminated at temperatures at which H desorption from the surface is the rate limiting step.

FENGLIU,VOLKMAR ZIELASEK, A N D MAXG. LAGALLY 92 DONALDE. SAVAGE, AND COHERENT 3-D ISLAND FORMATION IN ALLOYS 1. ROUGHENING

The morphologies of Sil-,Ge, alloy films are found to be similar to those observed for Ge on Si(OO1) for a wide range of Ge concentrations (x L 0.15). They have been obtained with a variety of deposition techniques including MBE, CVD, gas-source MBE, and solid-phase epitaxy. While the general features are similar, there are differences that raise questions about the mechanism of the morphological transformation. The SiGe films deposited using gas-source MBE by Cullis et al. in 1992 were described as having ripples. The ripples were observed to extend along [ 1001 and [OlO] directions with slopes -11" from the (001) substrate. In cross-sectional TEM images the waviness appeared somewhat rounded; however, the values of angle and the directions the ripples extend are consistent with those of the (105) faceted coherent 3-D islands observed in pure-Ge growth. Observations of ripple spacing over a wide alloy concentration range (Pidduck et al., 1993) were fitted well with continuum elasticity models of thermodynamic strain relief (Asaro and Tiller, 1972; Grinfield, 1986; Srolovitz, 1989) that predict that strained films are unstable to roughening. In such models the average ripple amplitude ( t ) and wavelength (A) are related to misfit strain ( E O ) and are described with the inequality

where Y is Young's modulus and y is the surface free energy per unit area (Pidduck et al., 1993). A plot of t / A 2 as a function x2 where x is the percent Ge concentration in the alloy, yielded a straight line for x ranging from 0.15 to 0.27, in good agreement with the model. Jesson et al. (1995) deposited alloy films at room temperature and subsequently annealed them at elevated temperatures to allow the film morphology to relax towards local equilibrium. Ge concentrations of 50% in the alloy film were used. The authors observed isolated pyramidal 3-D islands with { 1051facets and under certain conditions pyramid-shaped pits. The authors concluded that their observation of isolated faceted 3-D islands was evidence that they arose through a nucleation process, indicating that 3-D island formation is an activated process. These two very different views of how similar-looking morphologies arise show the difficulty in attempting to understand morphology evolution by looking at the final stage of a process. While the formation of faceted 3-D islands indicates an activated process, the question remains as to what is controlling the separation of islands or ripples. For alloys with lower Ge concentrations it is quite possible that kinetic roughening may be enhanced by strain relaxation, building in a preferred separation between mounds or ripples. At a later stage in the growth these could transform into faceted islands after a critical slope is reached. In higher-Ge-concentration alloys, it appears that strain induced in the substrate causes mounds or islands to repel and so nucleate preferentially away from existing islands.

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Understanding roughening or islanding in alloy films is additionally complicated by lateral as well as vertical concentration gradients (Guyer and Voorhees, 1995; Walther et al., 1997). Any full description of the mechanism must include these effects as well.

2 . MULTILAYER GROWTH The ability to grow strained-layer superlattices of {SiGe alloy/Si} on Si without dislocation formation was demonstrated long ago (Bean et al., 1984). To prevent dislocation formation, the volume strain energy must be kept below a critical value or at least low enough so that kinetics limit the formation of dislocations. In the first case, the films are stable and dislocations will not form. In the second case, the films are metastable with respect to dislocation formation. From the simple thermodynamic arguments about growth modes presented in Section 1.1, one would expect that it would be impossible to grow a strained-layer superlattice. If SiGe alloy initially wets Si, it is expected that Si will not wet the SiGe alloy film. It must be remembered, however, that the arguments for equilibrium growth modes are idealized and contain simplifying assumptions. One factor that helps Si to grow smoothly on a strained alloy substrate is that at least one monolayer of Ge will segregate, reducing the surface free energy of the Si film and allowing it to wet more readily. In films deposited by CVD, for which Ge segregation is suppressed, surface hydrogen reduces the surface energy of the Si film, again helping it to wet the SiGe alloy layer. a. Step Bunching in Multilayers

Headrick and Baribeau (1993), using low-angle diffuse x-ray scattering, demonstrated that interfaces in SiGe/Si superlattices exhibit a 1-dimensional-grating like morphology parallel to the substrate surface that is correlated vertically through the superlattice. The grating-like behavior was attributed to replication of substrate steps. Detailed x-ray scattering measurements by Phang et al. (1994) varying the alloy composition confirmed the presence of the grating-like interfacial morphology; the authors concluded, however, that the morphology arose from step bunching during growth of the alloy layers, with the buried interfaces having a “sawtooth”-like morphology. By determining the substrate vicinality with high-angle x-ray diffraction they showed that no new steps were created to make the interface “sawtooth,” but instead, steps move alternately closer together and farther apart, that is, they bunch. For a fixed alloy layer thickness of 25 A and a Si spacer layer of -100 A, step bunching was not observed for a 30% Ge alloy concentration, but was observed for alloy concentrations of 50% and above, suggesting that strain is causing the bunching. Atomic-force microscopy images of the outer-surface roughness were consistent with the description of the morphology derived from the scattering measurements. A model developed by Tersoff

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et al. in 1995 explained many of these observations; nevertheless there are still open questions. The driving force for step bunching in a strained overlayer occurs through long-range step-step interactions (Tersoff et al., 1995). If silicon is deposited onto a step-bunched SiGe alloy layer, the steps should become more uniformly spaced with increasing Si film thickness, that is, steps should debunch, because the driving force for bunching is removed. Phang et al. (1994) saw little debunching during the growth of 100 8, Si spacer layers. The mechanism for vertical correlation of step bunches is also not fully understood. Phang et al. (1994) suggested that long-range strain fields propagating through the spacer layer caused bunches to line up, but made no calculation. An alternative possibility is that step bunches have vertical correlation simply because they grow in step-bunch flow and that the vertical correlation is a geometric effect dependent only on bilayer thickness and the height of the bunch.

6. Self-organization of 3 - 0 Islands in Multilayers When alloy films that exhibit coherent 3-D islands are grown in a superlattice with silicon spacer layers of sufficient thickness to smooth out the roughness introduced by the islands, experimental observations show a remarkable improvement in the organization of the islands in the top layer (Liu and Lagally, 1997b). The islands become more equiaxed, exhibit a narrower size distribution, and begin to align in an ordered square array, narrowing as well their separation distribution (Teichert et al., 1996). Figure 24 shows AFM images comparing a single 25 A thick, 75% Ge alloy layer and the top alloy layer of a superlattice that consists of 40 such layers separated by 39 1008, thick Si spacer layers. In addition to the increased ordering of the size, shape, and position of the coherent 3-D islands, the average size has approximately doubled. The AFM images after the completion of a Si spacer layer do not show a remanent morphology from the underlying islands. The authors postulated that the organization was caused by an enhanced nucleation of islands on top of buried islands, which occurs because of nonuniform strain propagated through the spacer layer. The observation of 3-D-island correlation from layer to layer in a superlattice has been made in III-V (Xie et al., 1995) and in SiGe/Si/SiGe structures (Rahmati et al., 1996) with CTEM. Recent CTEM measurements on SiGe/Si superlattices show the correlation and, additionally, give insight into the mechanism of organization and embedding of the 3-D islands (Mateeva et al., 1997).

V.

Summary

In this chapter we have explored the fundamental mechanisms of the growth, on the atomic scale, of Si on Si and of Ge on Si. For Si on Si(OO1) quantitative analysis of STM measurements of morphological features, such as 2-D islands and monatomic

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20 I (2.5 am Si,&e,,,

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i 10 am Si)an Sl(OO1)

FIG. 24. Three-dimensional A F M images of coherent hut island distributions illustrating the effect of multilayering on narrowing the size and spacing distribution. (a) Single layer: 3-D view of a 2.5 nm thick film of Si0.25Ge0.75 deposited on Si(OO1). (b) Twenty bilayers of 2.5 nm Si0.25Ge0.75 and 10 nm Si, grown on Si(OO1): the islands have become square pyramids, very well arranged and uniform in size, and about twice as large as in (a). (Reprinted with permission from Teichert er al., 1996.)

steps, makes possible the determination of fundamental properties such as the diffusion coefficient of adatoms, the incorporation mechanisms of adatoms into steps or islands, and the energetics of the atomic steps themselves. The growth of Ge on Si(OO1) is complicated by lattice-mismatch-induced strain. Measurements at initial stages of growth (submonolayer coverage) show phenomena quite similar to those in Si homoepitaxy, that is, similar diffusion, diffusion anisotropy, and incorporation into steps or islands. At later stages in the growth, new phenomena take control: the change in the surface reconstruction to (2 x n) for strain relief, the breaking up of the surface into 2-D patches at higher Ge coverage and, beyond a critical thickness, the formation of coherent 3-D islands. In the growth of 3-D SiGe alloy films, additional phenomena such as lateral and vertical ordering of 3-D islands deposited in superlattices occur. While much is known about the fundamental mechanisms of growth in both SUSi and GeISi, open questions remain. In particular the transition from nucleation to subsequent growth, the influence of strain on submonolayer structure and dynamics, the mechanisms by which coherently strained 3-D islands grow and order, and the morphological transitions that occur when 3-D islands are buried in a matrix material are not fully understood and are topics of active research.

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ACKNOWLEDGMENTS The preparation of this chapter was in part supported by NSF and by ONR. Work described herein that was performed by the authors was supported by NSF, ONR, and AFOSR.

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100 DONALDE.

SAVAGE,

FENGLIU,VOLKMAR ZIELASEK,

AND

MAXG. LAGALLY

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SEMICONDUCTORS AND SEMIMETALS.VOL. 56

CHAPTER3

Misfit Strain and Accommodation in SiGe Heterostructures R . Hull DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING OF VIRGINIA UNIVERSITY

CHARLOTTESVILLE. VIRGINIA

I . ORIGINOF STRAIN IN HETEROEPITAXY. . . . . . . . . . . . . . . . . . . . . . . . . . . 11. ACCOMMODATION OF S T R A I N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Elastic Distortion of Atomic Bonds in the Epitaxial Layer . . . . . . . . . . . . . . . . . 2. Roughening of the Epitaxial Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Interdifision across the Epilayer/Substrate Interface . . . . . . . . . . . . . . . . . . . . 4 . Plastic Relaxation ofstrain by Misfit Dislocations . . . . . . . . . . . . . . . . . . . . . 5. Competition Between Different Strain Relief Mechanisms . . . . . . . . . . . . . . . . . . 111. REVIEWOF BASICDISLOCATION THEORY. . . . . . . . . . . . . . . . . . . . . . . . . . 1. Definition and Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Energy of Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Forces on Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. GlideandClimb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Geometry of Interfacial Misfit Dislocation Arrays . . . . . . . . . . . . . . . . . . . . . . 6. Motion of Dislocations: Kinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Dislocation Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Partial versus Total Misfit Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. EXCESSS T R E S S , EQUILIBRIUM S T R A I N A N D CRITICAL THICKNESS ............ I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Matthews-Blakeslee Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Accuracy of the MB Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Other Critical Thickness Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Extension to Partial Misfit Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Models for Critical Thickness in Multilayer Structures . . . . . . . . . . . . . . . . . . . V. METASTABILITY A N D MISFITDISLOCATION KINETICS. . . . . . . . . . . . . . . . . . . 1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Misfit Dislocation Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Misfit Dislocation Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Misfit Dislocation Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Kinetic Modeling of Strain Relaxation by Misfit Dislocations . . . . . . . . . . . . . . . .

102 103 103 105 105 107 108

109 109 111 112 112 113 116 117 119

120 120 120 124 124 126 128 131 131

133 144 149 152

.. -”., ...?-.--.-

Copynghr @ 1999 by Academic Press A l l irl.rr

.c.O.-.A.”.L..

a,, the strain in the epitaxial layer is compressive and e is positive; for a, < a, the strain in the epitaxial layer is tensile and E is negative. The lattice constants of Si and Ge at room temperature are 0.5431 and 0.5658 nm, respectively; Ge,Sil-, lattice parameters, a@), have been tabulated by Dismukes et al. (1964). They observed slight deviations from Vegard’s law (Le., slight deviations from the relationship a(x) = a ~ i X ( U G ~- asi)). If this deviation from linearity is defined by A = a(x) - [asi +X(UG, - asi) ] , maximum values of A -0.007 nm were found at x 0.5. A parabolic fitting to the data of Dismukes et al. at room temperature (Herzog, 1995) yields

-

+

a ( x ) = 0.5431

-

+ 0.01992~+ 0 . 0 0 2 7 3 3 ~nm~

(2)

In practice, relatively little error (of order 0.1% error in a(x) and 7% error in ~ ( x )is) involved if the room temperature value of a(x) is assumed to follow the linear form

a(x)= 0.5431

+ 0.0227~nm

(3)

‘Note that we are assuming an infinite substrate thickness here, such that all lattice mismatch strain is accommodated by the epitaxial layer. For substrate thicknesses that are not effectively infinite with respect to the epitaxial layer, strain will be partitioned between substrate and epitaxial layer. In practice, typical Si substrate thicknesses are several hundred microns, which is effectively infinite with respect to any reasonable epilayer thickness.

3 MISFIT STRAINAND ACCOMMODATION

103

whence, from Eq. (1) EO(X)

= 0.0409~

(4) The simplified relations of Eqs. (3) and (4) will be used in the remainder of this chapter. In general, materials have temperature-dependent lattice parameters via thermal expansion coefficients (which are themselves temperature dependent). The linear thermal expansion coefficients, a ( x , T ) have been measured as functions of temperature for Si, Ge and Ge,Sil-, alloys (Wang and Zheng, 1995). The values of a(x,T ) are somewhat nonlinear with Ge fraction and temperature, but for the range 0-800 "C, within accuracies of order 10%

+

= (2.7 0.0026T) x low6 a~~ = (5.9+0.0021T) x asi

Linear interpolation for intermediate Ge, Si 1 compositions will generally overestimate a ( x , T ) , especially for higher x and T . Nevertheless a linear interpolation of Eqs. 5(a) and (b) will yield estimates for a @ ,T ) which are accurate to order 30% a ( x , T ) = [(2.7

+ 3 . 2 ~ +) (0.0026 - 0.0005x)TI x

(6)

The thermal mismatch stress, E T S , induced as a function of change in temperature, A T , with respect to a substrate with thermal expansion coefficient, asub(T),is thus

-

For example, considering a Geo.2Sio.s layer grown upon a Si substrate, at 550 O C (a typical temperature for molecular beam epitaxy, MBE, growth), we have E T S 2x that is, just a few percent of the lattice mismatch strain EO. Thermal m i s match strains are thus relatively small compared to lattice mismatch strains. They can, however, become important at large epitaxial layer thicknesses where lattice mismatch strain is largely accommodated by misfit dislocation generation at the crystal growth temperature, and thermal stresses are induced during cooling to room temperature, as will be discussed later in this chapter.

11. Accommodation of Strain

In strained layer epitaxy, the lattice parameter difference between a thin epitaxial layer and an epitaxial substrate can be accommodated by several mechanisms. 1.

ELASTICDISTORTION OF ATOMICBONDS I N THE EPITAXIAL LAYER

This configuration is shown in Fig. l(a). The in-plane lattice parameter of the epitaxial layer uep is distorted to that of the substrate a,. The epilayer lattice parameter

R. HULL

104

a

b

C

FIG. 1. Schematic illustration of mechanisms for accommodation of lattice mismatch strain: (a) elastic distortion of epitaxial layer; (b) roughening of epitaxial layer; (c) interdiffusion; (d) plastic relaxation via misfit dislocations.

perpendicular to the interface, sen, then relaxes along the interface normal, to produce a tetragonal distortion of the unit cell (recall that in their unconstrained states, Si, Ge and Ge,Sil-, have diamond cubic lattices). The magnitude of the tetragonal distortion is given by aen/aep 1 ~ ( 1 ~)/(l - v) (8 1 ‘V

+ +

Here, E is the epilayer strain (which may have relaxed from 60 if any of the relaxation mechanisms in Sections 11.2, 3, and 4 have operated), and u is the Poisson ratio of the epilayer material. For an elastically isotropic cubic crystal, u is derived from the . of c1 1 and c12 appropriate elastic constants by the relation u = c12/(c11 ~ 1 2 ) Values (Landholt-Bornstein, 1982) for Ge and Si then yield u = 0.273 and 0.277 for Ge and Si, respectively. The generally quoted value for u in Ge,Sil-, in the literature is 0.28, which we shall use henceforth. The sense of the tetragonal distortion in Eq. (8) is positive (aefl> aep)for a, > a,, that is, the epilayer lattice relaxes outwards along the interface normal. For a, < u , ~ , the tetragonal distortion is negative (aen < a,), and the epilayer relaxes inwards along the interface normal. The tetragonally distorted epitaxial layer stores an enormous elastic strain energy (of the order 2 x 107Jm-3 for a lattice mismatch strain of 0.01). The stored elastic strain energy in the epitaxial layer, per unit interfacial area, is given by continuum elasticity theory as2 E,i = 2 G 4 ( 1 + u)h/(l - u ) (9)

+

Here h is the epilayer thickness and G is the epilayer shear modulus. As Si and Ge are relatively anisotropic elastic materials, average shear moduli are generally used 2Equation (9) assumes that all strain accommodation is elastic. If any of the lattice mismatch strain is relaxed by the mechanisms discussed in Sections II.2., 3., and 4.. then E, should be replaced by F , the remaining elastic strain.

3

MISFIT STRAIN AND

ACCOMMODATION

105

in strained layer theory, derived by averaging over the appropriate elastic constants, or elastic compliances, denoted, respectively, by the Voigt and Reuss average moduli (Hirth and Lothe, 1982). The Voigt and Reuss methods give for G in Si, Ge values of 6533 GPa and 68,56 GPa, respectively. This use of isotropic elasticity theory combined with these average elastic moduli is a significant approximation, compared to a rigorous application of anisotropic theory. However, the mathematical complexity in calculating the strain fields of dislocations in anisotropic materials is daunting (Hirth and Lothe, 1982), so less precise isotropic theory is generally used. This can lead to errors of the order 20% in subsequent calculations.

2.

ROUGHENING OF THE EPITAXIAL LAYER

As shown schematically in Fig. l(b), roughening of the epitaxial layer surface allows atomic bonds near the surface to relax towards their equilibrium length and orientation. The basic energetic competition in this process is between the surface energy of the epitaxial layer (representing an increase in the system energy as surface roughening increases the total surface area, and hence surface energy, of the epitaxial layer) and elastic energy (which is reduced by roughening, therefore representing a decrease in the system energy). This mechanism will not be treated further in this chapter, as it is dealt with in detail in the chapter by Savage in this volume. INTERFACE 3. INTERDIFFUSION ACROSS THE EPILAYER/~UBSTRATE

As the areal strain energy density, given by E q . (9), varies as E:, lowering of the average strain by interdiffusion will reduce the elastic strain energy stored in a heteroepitaxial system. For example, consider the highly simplified configuration where an initially abrupt interface between a Ge,Sil-, epilayer of thickness h nm and an infinite Si substrate undergoes an interdiffusionalprocess, such that the Ge,Sil -, layer redistributes itself into a layer of thickness h h~ nm, and a uniform Ge fraction of x h / ( h h ~ ) . The initial areal energy density will reduce from k'x2h to k'x2h2/(h h ~ )where , k' is the relevant constant of proportionality from Eq. (9). In the limit that h~ tends to infinity, the strain energy tends to zero. Of course, the abrupt diffusion profile implied by this theoretical experiment is highly unphysical, but the principle of strain energy reduction via interdiffusion will hold for any diffusion profile with a monotonic decay of Ge fraction. Interdiffusion at Ge,Sil-,/Si and Ge/Si interfaces has been studied by several authors. Early studies by Fiory et al. (1985) established the presence of significant interdiffusion at temperaturesof 800 "C and higher in a 10 nm Si/14 nm Ge0.24Si0.76/Si(1~) structure via HeC ion channeling and backscattering studies. As this structure is below the critical thickness criterion for relaxation of strain via formation of a misfit dislocation array, relaxation of strain in this structure was determined to occur via in-

+

+

+

R. HULL

106

FIG. 2. Measurements of interdiffusion at Ge,Sil -,/Si interfaces: Arrhenius plot of the diffusion coefficient of Ge in strained Si/Ge,Sil-,/Si structures for x = 0.07 (circles), x = 0.16 (squares); x = 0.33 (triangles), derived from diffusion in the tails of the diffusion profile (filled symbols) and at the peak of the diffusion profile (open symbols). Solid line is an extrapolation of Ge tracer diffusion in bulk Si (McVay and Ducharme, 1974). Reprinted from Thin Solid Films 183, G.F.A. Van de Walle, L.J. Van Ijzendoorn. A.A. Van Gorkum, R.A. Van den Heuvel, A.M.L. Theunissed and D.J. Gravestein, “Germanium Diflususion and Strain Relaxation in Si/Sil-,Ge,/Si Structures,” pgs. 183-190. 1990, with permission from Elsevier Science, The Boulevard, Langford Lane, Kidlington OX5 IGB, UK.

terdiffusion. A more extensive study by Van de Walle et al. (1990) derived diffusion coefficients for Ge in Si/GexSil-,/Si structures. A summary of their data is shown in Fig. 2. The measured diffusion constant appears to be relatively independent of Ge fraction in the range x = 0.07-0.33. This is in contrast to earlier measurements of the diffusion coefficient measured for Ge in large-grain polycrystalline Ge, Si 1--x material (McVay and DuCharme, 1974), where diffusion was noted to increase rapidly with x up to a maximum at x 0.8. Van de Walle et al. observed that diffusion in the tails of the Ge concentration profiles correlated well with measured diffusion coefficients for Ge diffusion in bulk Si, whereas measured diffusion constants in the peaks of the Ge concentration were an order of magnitude greater. The measured diffusion constants suggest that diffusion lengths of the order of one monolayer at 800°C would take 1 hr in the Ge tail. Thus strain relaxation by interdiffusion is not expected to be a significant factor during growth of relatively dilute (i.e., low Ge fraction) and thick

-

-

3

MISFITSTRAIN

AND

ACCOMMODATION

107

(compared to one monolayer) Ge,Sil-, layers on Si substrates, for techniques such as MBE and ultrahigh-vacuum chemical vapor deposition (UHV-CVD) where growth temperatures are typically less than 800 "C. A configuration where interdiffusion can represent a significant strain relaxation mechanism, even at typical MBE growth temperatures, are the monolayer-scale GeSi superlattices which at one time were widely fabricated in pursuit of efficient optical emission (see chapters by Cerdeira, Campbell, and Shaw and Jaros in this volume). Chang et al. (1990) reported diffusion coefficients in monolayer-scale Ge-Si superlattices that were consistent with the diffusion constants measured for Ge in pure Si, and by Van de Walle ef al. for tail diffusion. Baribeau (1993) and Lockwood et al. (1992) studied similar systems and concluded that for atomically abrupt interfaces, diffusion was indeed of the order of that associated with Ge diffusion in bulk Si, but that existing intermixing or segregation at the interfaces could dramatically enhance diffusion, due to strong increase in Ge diffusivity with increasing x in Ge, Sil Under such conditions, substantial diffusion (enough to homogenize a multilayer structure consisting of alternating layers of 4.5 monolayers of Si and 3.5 monolayers of Ge) was observed for a 20-s anneal at 700 "C.

4.

PLASTIC

RELAXATION OF STRAIN B Y MISFITDISLOCATIONS

As shown schematically in Fig. l(d), another mechanism for strain relief is via generation of an interfacial dislocation array, known as a misfit dislocation array, which allows the epitaxial layer to relax towards its bulk lattice parameter. This is a very prevalent mechanism for strain relief in Ge, Si 1-,-based heterostructures. It is experimentally observed, and theoretically predicted, that the misfit dislocation array forms only in epitaxial layers thicker than a minimum thickness, known as the critical thickness h,. The interfacial dislocation array relaxes elastic strain energy by allowing the average lattice parameter of the epitaxial layer to relax towards its unconstrained value. However, the dislocations have a self-energy &is, manifested by the stress field they produce in the surrounding crystal. Thus the energy of a heteroepitaxial system containing a total line length L of interfacial dislocation is (ignoring surface roughening and interdiffusion) Etot = Eel(L, h ) Edis(L, h ) (10) We know from Eq. (9) that E,) varies linearly with h . As each unit length of dislocation will reduce a finite amount of strain in the epitaxial layer (this will be discussed more fully in the next section of this chapter), we can also deduce that F decreases linearly with L . The energy of the dislocation array will increase with L , and at relatively low values of L (specifically such that the average separation of the interfacial dislocations is less than the epilayer thickness), this increase will be linear as will be discussed in Section 111 of this chapter. At higher dislocation densities (i.e., greater L ) , the increase will no longer be linear, due to the importance of dislocation interactions.

+

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Finally, as we shall also see in Section 111, the self-energy of an individual dislocation varies logarithmically with its distance from a free surface. Thus for low dislocation densities Etot= k l h ( ~ ok3L ln(k4h) (11)

+

In this equation kl through k4 are constants whose magnitudes will be derived in later sections of this chapter. Comparing Eq. (1 1) to Eq. (9), the change in total energy as a result of the introduction of the dislocation array is

AE,,, = k3L ln(k4h)

+ klk?jhL2 - 2 k l k 2 h ~ ~ L

(12)

For h > hc, we would of course expect that AEtot < 0, namely, that introduction of the dislocation array lowers the energy of the system. For h < h,, A EtOt > 0, that is, the dislocation array is not energetically favored. The critical thickness is found by finding that value of h for which the change in total energy A Et,,, for introduction of a single misjit dislocation is zero. Thus we take the limit of Eq. (12) as L --f 0, allowing solution for h = h, h, = k3 ln(k4hc)/2klk2~o (13) For a given epitaxial layer thickness h > h, and residual lattice-mismatch strain E =

(eo - k2L), the minimum energy configuration will correspond to (GEtot/GL)h,s= 0, allowing solution for the equilibrium value of L from Eq. 12:3 k3 ln(k4h) = 2hklkz[eo - k2L]

(14)

Before a more rigorous development of models for the critical thickness and equilibrium misfit dislocation densities (i.e., evaluation of the constants ki in the foregoing equations), we will briefly review the relevant aspects of dislocation theory.

5 . COMPETITION BETWEENDIFFERENT STRAINRELIEFMECHANISMS Of the strain relief mechanisms discussed in the preceding four sections, interdiffusion is significant only at growth or annealing temperaturehime cycles of order 800 "C/ 1 hr or greater (except for the relatively specialized configuration of monolayer scale Si:Ge superlattice structures). Thus, interdiffusion is not a significant mechanism at the growth temperatures typically used during MBE or UHV-CVD growth, although it could conceivably be significant during high-temperature post-growth processing (e.g., implant activation or oxidation processes). Relaxation via surface roughening can occur for any epitaxial layer thickness (see chapter by Savage in this volume). Strain relaxation by misfit dislocations occurs only for layer thicknesses greater than the critical thickness. Both processes are kinetically 3Note that substitution of L = 0 into Eq. (14) reduces this expression to Eq. (13) as expected.

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limited, either by surface diffusion lengths in the case of surface roughening, or by nucleatiodpropagation barriers in the case of misfit dislocations. These two processes may be competitive, such that the strain relaxed by surface roughening (which may occur before a sufficient epilayer has been deposited for misfit dislocations to be energetically favored) reduces or eliminates the driving force for dislocation introduction, or they may be cooperative, as in the observed reduction of energetic barriers for dislocation nucleation associated with surface morphology (Cullis et al., 1994; Jesson et al., 1993, 1995), and surface morphology induced by misfit dislocations (Hsu et al., 1994; Fitzgerald and Samavedam, 1997). Tersoff and LeGoues (1994) modeled the introduction of misfit dislocations into planar epilayers, and into surface islands or pits. They demonstrated that if the energy barrier is essentially zero for dislocation introduction into islands or pits (this should be regarded very much as an approximation, although it is reasonable that the activation barrier is greatly reduced with respect to a planar surface), a temperature dependent critical strain (of order 0.01) exists above which strain relief is dominated by dislocation injection into roughened surfaces, and below which dislocation injection into planar surfaces is favored. This is consistent with general experimental observations that roughening of Ge,Sil-, epilayers is greater for higher Ge concentrations and temperatures. The detailed balance between roughening and dislocation generation, however, is still a topic of active experimental research and simulation.

111. Review of Basic Dislocation Theory We now briefly review the salient properties of dislocations pertinent to understanding their role in relieving lattice mismatch. For a full description of dislocation theory, the reader is referred to the volume by Hirth and Lothe (1982).

1.

DEFINITIONAND GEOMETRY

A perfect or total dislocation is a line defect bounding a slipped region of crystal. A circuit drawn round atoms enclosing this line will have a closure failure as illustrated in Fig. 3(a); this closure failure is known as the Burgers vector of the dislocation. For a perfect or total dislocation, the Burgers vector is a lattice translation vector. Although the line direction of a given dislocation may vary arbitrarily, its Burgers vector is con~ t a n t .A~ total dislocation cannot end within the bulk of a crystal-it must terminate 4Apart from a possible difference in its sign, depending upon the convention used. A widely accepted convention for determining the sign of the Burgers vector is to draw the circuit from start S to finish F in the direction of a right-handed screw, R H-the so-called F S I R H convention (Bilby et al., 1955). Under this convention, the opposite sides of a dislocation loop have opposite Burgers vectors’ signs.

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FIG.3 . (a) Illustration of the Burgers vector of a total dislocation (in this example an edge dislocation, with the line direction u running perpendicular to the page). The dislocation core is at X. A circuit of 5 atoms square, which would close in perfect material, demonstrates a closure failure, the Burgers vector b. when drawn around the dislocation core. Reprinted from R. Hull and J.C. Bean, Chapter 1, Semiconductors and Semimetals Vol. 33, ed. T.P. Pearsall, (Academic Press, Orlando, FL, 1990). (b) Illustration of the misfit dislocation (AB) I threading dislocation (BC) geometry at a Ge,Sil-,/Si interface. Reprinted with permission from R. Hull and J.C. Bean, Critical Review in Solid State and Materials Science 17. 507-546 (1992). Copyright CRC Press, Boca Raton, Florida.

at an interface with noncrystal (generally a free surface, but possibly also an interface with amorphous material), at a node with another defect, or upon itself to form a loop. The geometrical requirement that a dislocation must terminate at another dislocation, upon itself, or at a free surface means that something has to happen with the ends of misfit dislocations-they cannot simply terminate within the interface. If the defect density is relatively low and dislocation interactions thus unlikely, the most obvious place for the misfit dislocation to terminate is at the nearest free surface, which will in general be the growth (i.e., epilayer or cap) surface. This requires threading dislocations, which traverse the epitaxial layer from interface to surface, as illustrated in Fig. 3(b), and in general each misfit dislocation will be associated with a threading defect at each end, unless the length of the misfit dislocation grows sufficiently that it can terminate at the wafer or feature (e.g., mesa) edge, or at a node with another defect. Propagation of misfit dislocations occurs by lateral propagation of the threading arms. These threading dislocations are extremely deleterious to practical application of strained layer epitaxy. For many potential device applications, a high interfacial misfit

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dislocation density is tolerable if the epilayer quality is sufficiently high at some distance from the interface (say, 1 wm or so). Threading dislocations compromise this possibility. Techniques for reducing these threading defect densities will be discussed in Section VI of this chapter. The character of a dislocation is defined by the relationship between its line direction u and its Burgers vector, b. If b is parallel or antiparallel to u, the dislocation is said to be of screw character. If b is perpendicular to u, the dislocation is said to be of edge character. In intermediate configurations, the dislocation is said to be of mixed character. As u may vary along a dislocation but b may not, a nonstraight dislocation will vary in character along its length.

-

2.

ENERGY OF DISLOCATIONS

A dislocation has a self-energy arising from the distortions it produces in the surrounding medium. This energy may be divided into two contributions, those arising from inside and those arising from outside the dislocation core. The distortions of atomic positions inside the core are sufficiently high that linear elasticity theory does not apply (dangling bonds may also exist, producing electronic contributions to the energy). The dislocation core energy is not well known, but depends upon both the material type (predominantly the nature of the interatomic bonding) and the dislocation Burgers vector and character. The dimensions of the core are also uncertain, but theoretical and experimental estimates of its diameter are of the order of the magnitude of the Burgers vector for covalent semiconductors and several Burgers vectors for metals (Hirth and Lothe, 1982). Outside the core, atomic distortions may be modeled using linear elasticity theory and exact expressions for this energy can be derived. The self-energy per unit length of an infinitely long dislocation parallel to a free surface a distance R away is5

In this equation, 8 is the angle between b and u and a is a factor intended to account for the dislocation core energy (a is generally estimated to be in the range 1 4 in semiconductors). The dislocation self-energy thus varies as the square of the magnitude of its Burgers vector. This strongly encourages the Burgers vector of a total dislocation to be the minimum lattice translation vector in a given class of crystal structure. For the diamond cubic (dc) structure of Ge,Sil-,, Si and Ge, this minimum vector is a/2(011). This is indeed the Burgers vector almost invariably observed for total dislocations in these structures. The value of R in Eq. (15) pertinent to calculations of interfacial mis5Strictly speaking this formula is derived for a dislocation within a cylindrical volume of inside radius b/u and outside radius R, but application to a planar free surface a distance R from the dislocation is generally a good approximation. We also continue to use the asumption of isotropic elasticity in this treatment.

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fit dislocation energies for uncapped strained epilayers is generally the epitaxial film thickness h . For interfaces with very high defect densities, a cut-off parameter R , corresponding to the average distance between defects p (if this is less than the distance to the epilayer surface), is more appropriate. Thus if we consider the total energy of an interfacial misfit dislocation array, the energy of the m a y will increase approximately linearly with dislocation density for p > h , as each dislocation will have essentially the same self-energy given by Eq. (15) with R = h. For p 5 h , however, the array energy will increase sublinearly with density, as the energy of each dislocation will be given by Eq. (15) with R p ; the energy per dislocation will then decrease approximately logarithmically as p decreases.

-

3.

FORCESON DISLOCATIONS

The self-energy of a dislocation produces a virtual force pulling it towards an image dislocation on the opposite side of a free surface. The simplest case is for an infinite straight screw dislocation running parallel to a free surface whose image is a dislocation of opposite Burgers vector in vacuu, equidistant from the surface. Other configurations have more complex image constructions. Image effects also exist across internal interfaces between materials with different shear moduli. The stress field around a dislocation produces an interaction force, Fij, between two separate dislocations. The magnitude of this force is again configuration dependent. For the simplest case of parallel dislocation segments, the interaction force per unit length is given by Fj,i = Gkj, (bj . bj)/ R' (16) where R' is the separation of the two segments and kin is the constant of proportionality (equal to 1/2 n for parallel screw segments). This force is thus maximally attractive for antiparallel Burgers vectors, maximally repulsive for parallel Burgers vectors and zero for orthogonal Burgers vectors. The general expressions for FiJ are more complex, but are relatively straightforward to derive (Hirth and Lothe, 1982).

4.

GLIDEA N D CLIMB

Motion of dislocations occurs most easily within their glide planes, which are the planes containing their line direction and Burgers vectors. For a screw dislocation, u is parallel to b and thus any plane is a potential glide plane. For mixed or edge dislocations, there is only one unique glide plane whose normal is given by b x u. Glide also occurs by far the most easily on the widest spaced planes in a given system because the Peierls stress (Peierls, 1940) resisting dislocation motion decreases with increasing planar separation. For diamond cubic, zinc blende and face-centered cubic crystals this corresponds to the { 111] sets of planes, and these are the almost ubiquitously

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observed glide planes in these structures. Glide occurs by reconfiguration of bonds at the dislocation core to effectively move the core one atomic spacing; this process is further aided by nucleation and motion of atomic-scale kinks, which will be discussed shortly. No mass transport of point defects is required in the glide process. Motion out of the glide plane, called climb, however, has to occur by extension or shrinkage of the half plane terminating at the dislocation core, requiring mass transport of point defects. Such diffusion processes are generally very much slower than glide processes in most temperature regimes.

5 . GEOMETRYOF INTERFACIAL MISFITDISLOCATION ARRAYS The resolved lattice mismatch stress a, acting on a misfit dislocation with Burgers vector b is given by the Schmid factor S (Schrnid, 1931) a, = aos = 0 0 cos h cos fp

(17)

where h is the angle between b and that direction in the epilayerhubstrate interface perpendicular to the misfit dislocation line direction, fp is the angle between the glide plane and the interface normal, and 00 is the lattice mismatch stress, given by standard isotropic elasticity theory as 00

+ ~ ) / ( -l U )

= 2C&(l

-

(18)

In the Ge,Sil-,/Si system, a0 9 . 4 ~GPa, an enormous stress! The effective strain relieving component of the misfit dislocation is given by beR = b cos h

(19)

Equation (17) shows that only dislocations gliding on planes inclined to the interface will experience a resolved stress (for fp = 90", cosfp = 0; for fp = 0", h = 90" and cos h = 0). For the Ge,Sil-,/Si(100) orientation, the four possible inclined { 111) glide planes intersect the (100) interface along orthogonal in-plane [Oil] and [Ol-I] directions, with a pair of glide planes intersecting along each direction. The orientation of one of these glide planes, and the accompanying possible a/2( 110) dislocations are shown in Fig. 4. The intersectionsof the glide planes with the interface thus produces a square mesh of interfacial dislocations, as shown experimentally in Fig. 5. In general, only dislocations with Burgers vectors lying within these { 111) planes will be able to move by glide. For a given glide plane three such Burgers vectors exist, for example, for the (-111) plane in Fig. 4, b = a/2[101], a/2[110] or a/2[01-1]. Of these three Burgers vectors, the last is a screw dislocation and will not experience any resolved lattice mismatch stress as cos h = 0. The first two are of mixed edge and screw character and are known as 60" dislocations, corresponding to the angle between b and U. From Eq. (19), only 50% of the magnitude of their Burgers vectors projects onto the inter-

interface. FIG. 4. Schematic illustration of the geometry of misfit dislocations at a Ge,Sil-,/Si(100) One inclined (-1 11) glide plane and consequent interfacial [Ol-11 dislocation direction are shown, together with the possible a/2(110) Burgers vectors orientations, where bl is of edge type and h2 and b3 are of 60" (glide) type. Reprinted with permission from R. Hull and J.C. Bean, Critical Review in Solid Srare and Materials Science 17,507-546 (1992). Copyright CRC Press, Boca Raton, Florida.

11:

1Bc3

FIG. 5 . Schematic illustrations of the symmetries of interfacial misfit dislocations at Ge,Sil-,/Si(lOO), (110) and ( 1 11) interfaces. Solid straight lines show the interfacial misfit dislocations; dashed lines outline intersecting ( 111) glide planes. Also shown are experimental verifications of these interfacial dislocation geometries from plan view (electron beam perpendicular to Ge, Sil -.r/Si interface) TEM.

114

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3 MISFITS T R A I N A N D ACCOMMODATION

facial plane, thus they are only 50% effective at relieving lattice mismatch. Because of their ability to propagate rapidly by glide, these are the general total dislocations associated with strain relief in Ge,Sil -,-based heterostructures. The final possibility to consider is that of edge dislocations, for example, for the configuration of Fig. 4, b = a/2[0-1-1]. Such dislocations have their Burgers vectors lying within the interfacial plane and are 100% effective at removing lattice mismatch. The Burgers vectors do not, however, lie within any glide plane, and thus these defects must move by far slower climb processes. Such edge dislocations are, however, frequently observed at high strains (of order 2% or greater) in the Ge,Sil-,/Si (Hull and Bean, 1989a; Kvam et al., 1990; Narayan and Sharan, 1991) and many other lattice-mismatched heteroepitaxial semiconductor systems. It is somewhat mysterious that such dislocations can be prevalent, because of the requirement for motion by climb. It has been suggested that they are formed by reaction of 60" dislocations on different glide planes (Kvam et al., 1990; Narayan and Sharan, 1991); for example, for an interfacial misfit dislocation line direction u = [0111, an edge dislocation of Burgers vector a/2[01-1] could be formed by the reaction a/2[10-1](1-11) a/2[-110](11-1) (in this reaction the square brackets refer to the dislocation Burgers vector and the curved brackets to the glide plane). Because they are prevalent at low and moderate strains, subsequent discussion will concentrate primarily on 6Ooa/2(101) glide dislocations. The geometry of misfit dislocations will be different on surfaces other than (100). If the dislocations glide on inclined { 11l } planes, the interfacial misfit dislocation line directions will be defined by the intersection of these planes with the relevant interface. The expected geometries for (loo), (110) and (1 11) interfaces are illustrated schematically and experimentally in Fig. 5. At the enormously high lattice mismatch stresses that can exist in strained layer systems, the presumption of dislocation glide on the widest spaced planes in the structure, that is, { 111) planes for the diamond cubic (dc), zinc blende (zb) and face-centered cubic (fcc) structures, may be overcome. As was first observed in highly strained (EO 0.03; a0 5 GPa) (Al)GaAs/Ino.4Gao.6As/GaAs(lOO) zb structures by Bonar et al. (1992), secondary slip systems may operate at these enormous stresses. In the work of Bonar et al., a/2(101) dislocations were observed gliding on { 110) planes, producing (010)misfit dislocation directions in the (100) interface. The same slip system has since been observed in Ge0.86Si0.~4/Si(100)(EO 0.035,ao 8 GPa) structures by Albrecht et al. (1993). The observations of this secondary slip system at these enormous lattice-mismatch stresses may be related to a more efficient Schmid factor, and, therefore, higher a, for a given ao.For the (lOl){lll}slip system, Sill = 0.42. For the (101){110}system, Silo = 0.50. Therefore the extra resolved stress on the 0.08~0 (lOl){llO}system compared to the (101){111}system is cro(S110 - S111) or 0.4 - 0.6 GPa for the structures described by Bonar et al. and Albrecht et al. This more efficiently resolved applied stress may allow a secondary slip system with higher Peierls stress to operate. At lower strains (< 0.03), however, the (1lo){11I} slip system appears to operate ubiquitously.

+

-

-

-

-

-

-

116 6.

R. HULL MOTION OF DISLOCATIONS: KINKS

The glide process is facilitated by nucleation of atomic-scale lunks along the propagating dislocation line, with lateral motion of the kink arms transverse to the dislocation line effectively moving the entire dislocation length. In the absence of kinks, dislocations in semiconductors typically lie along well-defined crystallographic directions corresponding to minima in the crystal potential (known as Peierls valleys). These are the (01I ) directions for the dc structure of Ge, Sil -, . Formation of a kink requires motion of a small length of dislocation line across the potential, or Peierls, barrier between valleys. Subsequent lateral motion of the kink arms also involves motion over a secondary Peierls barrier. This process is illustrated in Fig. 6. In metals the energy required to form and move these kinks is relatively low-typically less than of the order 0.1 eV-because of the low Peierls barriers resulting from the relatively weak metallic bonding. This low kink energy in metals means that the dislocations are not strongly constrained to lying within Peierls valleys, and thus are not very straight. Dislocation motion and configurations in semiconductors, however, are typically dominated by the Peierls barriers. In materials that are purely covalently bonded such as Ge and Si, the glide activation energies are particularly high, for example, 1.6 eV in Ge and 2.2 eV in Si for stresses in the tens to hundreds of MPa regime (Alexander and Haasen, 1968; Patel and Chaudhuri, 1966; Imai and Sumino, 1983; George and Rabier, 1987). These glide activation energies arise from the Peierls barriers that have to be overcome in

I

I

J

c

FIG. 6. Motion of dislocations by kink pairs in a semiconductor crystal. A small length s of a straight dislocation line jumps an interatomic distance q transverse to the line, to from a kink pair. The kinks then run parallel to the dislocation line by successive jumps of interatomic distance a, thereby effectively moving the entire dislocation line a distance q to the right.

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forming and moving kinks. The details of the kink nucleation and propagation process have been derived in some detail by Hirth and Lothe (1982) and corresponding dislocation velocities u as functions of temperature and applied stress calculated. These lead to an expression of the form u = UOD," exp[-E,(a)/kT]

where uo is a prefactor containing an attempt frequency (commonly taken to be of the order of the Debye frequency), kink jump distances and an inverse dependence upon temperature and E , (a)is the glide activation energy. Based upon the double kink theory (Hirth and Lothe, 1982), the prefactor uo and the activation energy &(a) depend upon the propagating dislocation length. (This essentially depends upon whether kinks collide with each other before reaching the end of the propagating dislocation segment. It is generally assumed that they do in bulk samples, whereas for very short propagating dislocation lengths, as may occur in thin epilayers, kinks may reach the end of the propagating segment before colliding with each other.) The activation energy is also predicted to exhibit a stress dependence at applied stresses that are a significant fraction of the Peierl's stress. Consistent with the double kink theory (Hirth and Lothe, 1982), the pre-exponential power m is found experimentally to be of the oriler 1.0 at stresses of the order tens of MPa in very pure Si (Imai and Sumino, 1983). The kink model for dislocation motion is widely accepted, and experimental results are generally well described by Eq. (20). There is some variation in the measured magnitude of m , which is found to vary in the range 1.0-2.0 (Alexander and Haasen, 1968); this variation may arise partly from difficulties in separating pre-exponential and exponential stress dependence of the measured velocities. Also, the prefactors derived from measurements on bulk semiconductors typically are 2-3 orders of magnitude lower than the Hirth-Lothe theoretical predictions (Imai and Sumino, 1983). This may be due to obstacles to dislocation motion (Moller, 1978; Nititenko et al., 1988, Kolar et al., 1996) such as point defects, impurities, inhomogeneities in the dislocation core structure etc., or to entropic effects in kink formation or migration (Marklund, 1985), or to charge states associated with dangling bonds at kinks (this latter model is supported by observations of a doping dependence of dislocation velocity [Hirsch, 19811).

7.

DISLOCATION DISSOCIATION

A final major consideration is that total dislocations may be dissociated into partial dislocations. A partial dislocation is a dislocation whose Burgers vector is not a lattice vector. In fcc, zb and dc materials a very common partial dislocation corresponds to a stacking fault in the cubic ABC stacking sequence of atoms along (111) directions. The partial dislocations bounding these stacking faults have Burgers vectors of a / 6 ( 112) or

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R. HULL

a / 3 ( 111) and are called Shockley and Frank partials, respectively. Only the Shockley partial can glide within (11I} planes. Total dislocations can dissociate if they can lower their energy according to the requirement that C b 2 is less after the dissociation than before (recall from Eq. (15) that the self-energy of a dislocation is proportional to b2). For example, the reaction

+

~ / 2 [ 1 1 0 ]= ~/6[121] ~/6[21-1]

(21)

is energetically favorable. The resulting partial dislocations mutually repel each other and glide apart on the (-1 1-1) plane. This produces a ribbon of stacking fault between them, and at some point the extra cost in energy from the stacking fault balances the interaction energy of the two partials. Typical dissociation widths in unstressed Si and Ge are of the order of a few nm, implying stacking fault energies y of the order 50-80 mJ mP2 (Gomez et al., 1975; Cockayne and Hons, 1979; Bourret and Desseaux, 1979). Similar stacking fault energies have been measured in epitaxial Ge,Sil --I layers (Steinkamp and Jager, 1992; Hull et al., 1993). A high-resolution electron microscope lattice image of the dissociation reaction of Eq. (21) at a Geo,7sSio,25/Si(100) interface is shown in Fig. 7. The existence of partial dislocations, and the possibility of dissociation, can significantly affect the energetics of dislocation motion. For example, the partials may have different core structures and charge states from each other and from the undissociated dislocation. The Peierls barriers for motion of partial dislocations may be different than for motion of a total dislocation, particularly if kink formation and motion on the two

FIG.7. Cross-sectional (electron beam parallel to a Geo,7sSi0,25/Si( 100) interface) TEM lattice image of dissociation of a 60°b = a/2(101) dislocation into h = a/6(21I ) Shockley partials, separated by a region of stacking fault.

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partials are correlated (Heggie and Jones, 1987). The existence of partial and dissociated dislocations may also be of significance in dislocation nucleation and motion, as will be discussed in Section V.

8. PARTIAL VERSUS TOTALMISFITDISLOCATIONS

The dissociation reaction described by Eq. (21) also has significant implications for the microstructure of misfit dislocations. We characterize the different partials in this equation according to the angle 8 between their line directions u and Burgers vectors b. For dissociation from the 8 = 6Ooa/2(101) total dislocation, the two a/6(211) partials have 8 = 30" and 8 = 90", respectively. The resolved lattice mismatch stress, from Eq. (17), on these two partials is very different. In general, the Schmid factors for the three types of dislocations are ordered

The order in which the partials move as the dissociated a / 2 (101) defect propagates is determined by a geometrical construction known as the Thompson tetrahedron construction (Thompson, 1953). This construction is based upon the requirement that the stacking fault bounded by the two partials produces only second-nearest stacking violation in the cubic lattice, that is, faults of the type ABCABCBCABCA, which is a relatively lowcmergy planar fault (-- 50-80 mJ mW2in Si, Ge and Ge,Sil-,, as described in Section 111.7), as opposed to nearest neighbor stacking violation, ABCABCKABCAB, which is a much higher energy planar fault. For compressively strained layers grown on a (100) surface, such as Ge,Sil-,/ Si( loo), the Thompson tetrahedron construction shows that for creation of an intrinsic stacking fault the 30" partial leads and the 90" partial trails as the dissociated a / 2 ( 101) dislocation propagates through the lattice. From Eq. (22), the trailing partial then experiences a greater lattice mismatch stress than the leading partial. The two partials are therefore compressed more closely than their zero-stress equilibrium separation. (In the limit of very high applied stresses, it may not be energetically favorable for the a / 2 ( 101) dislocation to dissociate at all in this configuration.) In this condition, the narrowly dissociated defect can be accurately approximated by a single 60"a/2( 101) dislocation. For other interfacial configurations, for example, tensile strain layers on (100) interfaces (Ge,Sil-,/Ge(100)), or compressively strained layers on (110) or (I 11) interfaces (GexSil-x/Si(l 10) and Ge,Sil-,/Si(ll 1)), the 90" partial leads. In these configurations, therefore, the leading partial experiences a greater resolved lattice mismatch stress than the trailing partial. This will increase the equilibrium separation, and if the net stress on the leading 90" partial is sufficiently greater than on the trailing 30" partial, the restoring stress due to the stacking fault energy between the partials can be

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FIG. 8. Cross-sectional TEM image ([220] bright field near the [I-101 pole) of a 41 nm Ge0,33Si0,67/Si(lIO)structure, showing stacking faults produced by passage of a/6(211) partial misfit dislocations. Reprinted with permission from R. Hull er ul. Appl. Phys. Left. 59, 964, Figure 3(a). Copyright 1991 American Institute of Physics.

overcome, and the dissociation width becomes infinite. The 90°a/6(21 1) partial will then effectively propagate as an isolated partial misfit dislocation, leaving a stacking fault in the lattice as it propagates (Fig. 8). In Section IV we will analyze the conditions under which this can occur, and find solutions in ( h ,x) space for which the partial dislocation is favored.

IV. Excess Stress, Equilibrium Strain and Critical Thickness 1 . INTRODUCTION We will now analyze more rigorously the conditions that define whether strain in a lattice-mismatched heterostructure is accommodated elastically or by misfit dislocations (in the limits where there is no interdiffusion across the epilayer/substrate interface, and where the epilayer surface is planar, that is, we ignore the relaxation mechanisms discussed in Sections 11.2 and 11.3). In particular, we will derive quantitative expressions for the critical thickness for the onset of misfit dislocation relaxation, the equilibrium amount of relaxation for 12 > h,, and the net or effective driving stress acting on a misfit dislocation.

2.

MATTHEWS-BLAKESLEE FRAMEWORK

Perhaps the most intuitive and general framework for analyzing these quantities is that originally developed by Matthews and Blakeslee (MB) (Matthews and Blakeslee, 1974, 1975, 1976; Matthews, 1975), and illustrated in Fig. 9. The original MB treat-

3

FIG.9.

M I S F I T S T R A I N AND

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Schematic illustration of the Matthews-Blakeslee model of critical thickness

ment analyzed the net force on a threading dislocation. We will derive an equivalent analysis in terms of stresses, which enables extension to more general results. The primary stresses acting on the dislocation are shown in Fig. 9. The resolved lattice mismatch stress a, drives the growth of misfit dislocations by lateral propagation of the threading arm. This is because growth of misfit dislocations (up to an equilibrium density) relaxes elastic strain by allowing the epitaxial layer to relax towards its free lattice parameter. The magnitude of a, has already been given in Eqs. (17) and (18). We also know from Section I11 that misfit dislocations have a self-energy, arising from their strain fields in the surrounding crystal. This produces a restoring stress ar (MB referred to the corresponding force as the “line tension” of the dislocation), which acts so as to inhibit growth of the misfit dislocation. The magnitude of this stress is easily derived from the equation for the self-energy per unit length of dislocation, Eq. (1 5). In addition, for partial misfit dislocations, there is a restoring force due to the energy of the stacking fault created by passage of the defect vsf. The net stress (or following the nomenclature of Dodson and Tsao (1987) the “excess stress” ue,) is thus given by

Here, E is the residual elastic strain in the system following partial plastic dislocation relaxation, defined by E = EO - [(bcosh)/p]. Other parameters in Eq. (23) have been previously defined in the text. Note that the generally quoted form of the MB model includes only the forces corresponding to a, and O T . Also, in the original MB framework, the quantity a was generally taken to be of magnitude e , such that they rewrite ln(ah/b) as [ln(h/b) I]. Figure lO(a) shows the dependence of a,, upon epilayer thickness h, using standard values (which we will assume in calculations henceforth, unless otherwise quoted) for (100) epitaxy of u = 0.28, cos8 = 0.5, cosh = 0.5, b = 3.9 nm, G = 64 GPa, E =0.41~ (where x is the Ge fraction in Ge,Sil-,), and a = 2. At very low values of

+

R. HULL

122 a

FIG. 10. Variation of (a) a,, and (b) eey with epilayer thickness h for a Ge0,25Si0,75/Si(IOO)structure. Reprinted with permission from R. Hull and J.C. Bean, Critical Review in Solid Stare andMateriais Science, 17, 507-546 (1992). Copyright CRC Press, Boca Raton, Florida

h , vexis large and negative. This corresponds to the regime where introduction of misfit dislocations increases the energy of the system. With increasing h, ae, becomes less negative, until at h = h, it becomes equal to zero. This defines the critical thickness of the system. For increasing h > h,, a,, becomes increasingly positive (in the absence of plastic relaxation), up to an asymptotic limit of a, - O , ~ Jindicating , that the misfit dislocation array is increasingly energetically favored in the structure. The equilibrium configuration of the system for any h > h , is that aeX= 0. The magnitude of the critical thickness is found by solving Eq. (23) for a,, = 0 and h = h,. For total dislocations (i.e. b = a / 2 ( 101)) where y = 0, this yields6 h , = b( 1 - u cos2 0) 1n(ahC/b)/[8n(1

+ u)s cos h]

(24)

At increasing h > h,, increasingly larger densities of interfacial misfit dislocations are favored, and correspondingly smaller amounts of residual elastic strain E . For h > 12, , the equilibrium residual elastic strain seq is found by solving Eq. (23) for a,, = 0 and E = E , ~ . The variation of E , ~with h is plotted in Fig. lO(b). 'Equation (24) thus effectively yields the values of kl , k z . k i , and k4 in Eq. ( I 3)

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FIG. 11. Predictions of the MB theory for the critical thickness h, in Ge,Sil-,/Si(100) structures for different values of the core energy parameter a. Also shown are experimental measurements of h , for different growthhnealing temperatures from the work of (a) Bean et al. (1984), (b) Kasper et al. (1973, (c) Green et al. (1991), and (d) Houghton etul. (1990).

Equation (24) does not have analytical solutions, but is simple to solve numerically. Solutions to this equation for the Ge,Sil-,/Si( 100) system are shown in Fig. 11. It is seen that the equilibrium critical thickness decreases rapidly with increasing Ge concentration, as the volumetric strain energy density increases as e2. Also shown in Fig. 11 are experimental measurements of critical layer thickness in the Ge,Sil-,/Si( 100) system from different groups, at several different growth temperatures. In the limit of high-growth temperatures (relative to the melting points of the materials, T, = 1412 "C for Si and 940 "C for Ge, with close to linear interpolation for melting temperatures of intermediate alloys [Stohr and Klemm, 1939]), experiment and equilibrium prediction agree well. At lower growth temperatures, experiment and theory are seen to diverge increasingly, in that increasingly larger critical thicknesses are measured experimentally as the growth temperature decreases. We shall discuss in Section V of this chapter that this divergence is due to the thermally activated kinetics of generation of the misfit dislocation array. In brief, as the equilibrium critical thickness is exceeded, plastic relaxation by generation of interfacial misfit dislocations is favored, but activation barriers exist to the nucleation and propagation of misfit dislocations. With decreasing temperature, the nucleation and propagation rates decrease, and plastic relaxation by misfit dislocations lags increasingly behind the equilibrium limit. The "experimental" critical thickness at a given growth temperature then becomes that epilayer thickness at which strain relaxation, or dislocation generation, is first experimentally detected (Fritz, 1987). Dodson and Tsao (1987) first demonstrated convincingly how kinetic modeling of this minimum detectable dislocation density process could accurately predict a "temperature-dependent'' critical thickness.

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ACCURACYOF THE MB MODEL

How accurate are the predictions of Eq. (24), in light of the perspective that there have been many refinements or recalculations of the critical thickness since MB originally developed their model? First, there are several approximations in the original formulation of this equation by MB. It assumes isotropic elasticity theory, whereas as we have already discussed, Si and Ge are relatively elastically anisotropic. The treatment of the dislocation core energy, where linear elasticity theory can no longer be applied, is very oversimplified. This core energy is approximated by assuming that we can apply standard elasticity theory outside of a “core radius” r, = ba, and accounting for the core energy inside a cylinder of radius r, by simply adding on a fixed energy per unit length of dislocation, Ecore: E,,,

= [Gb2(1 - u COS* 0)/471( 1 - v ) ]ln(a)

(25)

We can only ascribe a if we know EcOre. Accurate estimates of this quantity require sophisticated a b initio calculations of the core structure (Nandekhar and Narayan, 1990; Jones et al., 1993). In addition, E,,,,, and therefore a , are invariant with h only for h >> b, and will vary with the character of the dislocation, that is, the value of 8 . Estimates of cy in the literature vary from 0.5 - 4 (Nandekhar and Narayan, 1990; Hirth and Lothe, 1982; Perovic and Houghton, 1992; Beltz and Freund, 1994; Ichimura and Narayan, 1995), with the more recent total energy calculations generally suggesting a 1. We assume a value a = 2 in subsequent calculations. This variation in a affects the critical thickness calculation most significantly at higher E (higher x in Ge,Sil-,/Si), and lower h,. For example, if h = 1 nm (corresponding to h, for EO 0.04), In(ah,/b) varies between 0.9 and 2.3 as a varies between I and 4, a O.Ol), the variation of 160%. However, if h = 10 nm (corresponding to h, for 60 corresponding variation of ln(ah,/b) is between 3.2 and 4.6, or a potential error of 40%. In summary, the MB model in the form of Eqs. (23) and (24) should be regarded as approximate, to an accuracy perhaps 20-50% for critical thicknesses greater than a few nanometers. This makes it a very useful model.

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4. OTHERCRITICALTHICKNESS MODELS Our initial discussion of strain relaxation by misfit dislocations in Section 11.4 introduced the concepts of misfit dislocations and critical thickness qualitatively using energetic arguments. This was the basis of the earliest models of critical thickness developed by Frank and van der Merwe (1949a,b,c), who used a one-dimensional Fourier series to represent interactions between atoms in the epilayer and substrate, and demonstrated the concept of critical thickness. Subsequent development by Van der Merwe and co-workers (Van der Merwe, 1963; Van der Merwe and Ball, 1975; Van der Merwe

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and Jesser, 1988) developed the theme of calculation of the energy of a misfit dislocation array, including dislocation interaction energies, and comparison to strain energy relaxed within the epitaxial layer. Many of these models were mathematically complex, and had analytical solutions only in the limits of very thin and very thick epitaxial layers. Nevertheless, the energy balance approach derived in these papers set the foundations for subsequent development in this field, and enjoyed considerable success in predicting the critical thickness in body-centered cubic metal systems. Formally, the evaluation of critical thickness should be equivalent using either energetic or mechanical constructions, providing equivalent approximations are made in the two approaches (Willis et al., 1990). We now summarize the salient features of some other critical thickness models which have been developed as refinements of, or alternatives to, the MB framework:

(a) The model of People and Bean (1985, 1986), which attempted to reconcile theory with the early MBE measurements of h, in the Ge,Sil-,/Si(100) system (Kasper et al., 1975; Bean et al., 1984). This model assumed the self-energy of the dislocation to be localized within a certain region (of order five times the Burgers vector magnitude) centered on the dislocation core. This is in contrast to the usual elasticity treatment of dislocation self energy, and to subsequent verification that the MB theory describes the Ge,Sil-,/Si(100) system well in the limits of highly sensitive experimental techniques or very high temperatures (Houghton et al., 1990; Green et al., 1991).

(b) The model of Cammarata and Sieradzki (1989), who incorporated the concept of surface stress into the MB framework. For the Ge,Sil-,/Si system they argued that surface stress will be inward along the surface normal, and thus reduce the tetragonal distortion of the Ge,Sil-, epilayer and increase h,. These effects are significant only in the range of high Ge concentration where h, becomes relatively small. (c) The work of Willis et al. (1990), who derived a more precise expression for the energy of an array of misfit dislocations than the original Van der Merwe formulations. Subsequent development of this work using both energy minimization and force balance analyses (Gosling et al., 1992) has enabled refinement of both the Matthews-Blakeslee and Van der Merwe models. (d) The work of Chidambarro et al. (1990) who considered the effect of the orientation of the threading arm within the glide plane, and also analyzed a quasi-static Peierls force on the misfit dislocation. Certain orientations (e.g., screw) of the threading arm were determined to enhance the predicted critical thickness significantly.

(e) Fox and Jesser (1990) have invoked a static Peierls stress as an additional restoring stress upon a misfitkhreading dislocation, thereby increasing the critical thickness. It seems to the present author, however, that the effect of the Peierl’s barrier enters

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into dislocation kinetics, as discussed in a later section, rather than for the static case of the equilibrium critical thickness. (f) Shintani and Fujita (1994) have performed a calculation for critical thickness based upon anisotropic elasticity theory. Of the forementioned treatments, models (c), (d) and ( f ) represent refinements/ improvements of the original MB formulation, but do not radically alter the predicted magnitudes of critical thickness or excess stress. Models (b) and (e) represent additional terms to be considered in the MB analysis; of these models, (b) is significant only at relatively small critical thicknesses (of order a few nanometers or less), and (e) does not appear appropriate to the static critical thickness configuration. Model (a) is radically different from the MB model, but does not have the physical plausibility of the MB framework. In summary, the MB model remains an extremely useful general framework for predicting equilibrium relaxation by misfit dislocations in strained layer heterostructures.

TO PARTIAL MISFITDISLOCATIONS 5 . EXTENSION

So far, our discussion of critical thickness has been restricted to total (b = a / 2 ( 101)) misfit dislocations, which represent the appropriate misfit dislocation microstructure for interfacial configurations where the 30"a/6(21 1) partial leads in the dissociated total dislocation. This corresponds to the Ge,Sil-,v/Si(lOO), Ge,Sil-,/Ge( 110) and Ge,Sil-,/Ge( 1 11) configurations among low index planes. For the interfacial configurations where the 90" partial leads, that is, Ge,Sil-,/Ge(100), Ge,Sil-,/Si( 110) and Ge,Si~-,/Si(lll), we should analyze the excess stress and critical thickness appropriate to the 90°a/6(21 1) misfit dislocation, and compare to the 60°a/2(101) misfit dislocation configuration. To simplify the calculations, we shall consider the 60"a/2(101) misfit dislocation in its undissociated state. (Consideration of the dissociated 60"a/2( 101) configuration with the 30" partial leading will generally lead to lower energies than for the undissociated configuration. Our simplified analysis, therefore, will tend to overestimate slightly the regimes in which the 90" partial is preferred over the 60" total dislocation.) The relevant descriptions of excess stress and critical thickness for the undissociated 60" total dislocation have already been given in Eqs. (23) and (24). For the 90" partial, we apply Eq. (23) with the relevant value of y , and modify Eq. (24) according to h , = Gb2cos@(1-ucos2B)ln(ah,/b)/[(8rrbG(1+

W ) E C O S ~ C O S @ ) - ( ~ ~ ~ ~ ( ~ - U ) ) ]

(26) By comparison of Eqs. (23), (24), and (26), we can then determine which is the favored dislocation type, 60" total, or 90" partial. The magnitudes of the critical thickness and the excess stress for the 90" partial dislocation are very sensitive to the stacking

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fault energy. Here we use the value of y = 65 mJ m-’ that we have previously determined for Ge,Sil-, alloys (Hull et al., 1993). A comparison of critical thicknesses for 90”a/6(211) and 6O0a/2(101) dislocations in the Ge,Sil-,/Si(IlO) system is shown in Fig. 12(a). It is observed that the 90” partial dislocation has a lower critical thickness at higher Ge concentrations, but the 60” total dislocation has the lower critical thickness at lower Ge concentrations. This transition is essentially due to the stacking fault energy associated with the partial dislocation: at zero stacking fault energy the 90” partial dislocation would always have the lower critical thickness, but with increasing

n

E 0

J

Ob!o

0.1

0.2

0.3

0.4

X

’

K

n

E 0,

0

3

1

60

+-. v)

0)

2

v

c

NONE I

O’

‘

1

I

Oll

0.2

0.3

w I

I

0.4

x FIG. 12. (a) Comparison of critical thicknesses for 90°a/6(21 1) and 60°a/2(101) dislocations in the Ge,SiI-,/Si(llO) system, assuming CY = 2 and y = 65 m J m-’. (b) Predicted dislocation microstructure in the Ge,Sil~,/Si(llO) system as functions of epilayer thickness h and Ge concentration x assuming CY = 2 and y = 65 mJ m-2. Regions labeled “NONE,” “60” and “90,” respectively, refer to regions where no dislocations are expected, regions where 60”a/2(101) dislocations are most favored, and regions where 90°a/6(21 1) defects are most favored.

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stacking fault energy the critical thickness for the partial dislocation increases. The effect of the stacking fault energy is increasingly significant in thicker layers (because the total energy of the stacking fault per unit interfacial misfit dislocation length increases). Thus at lower Ge concentrations, where the critical thickness is higher, the effect of the stacking fault energy upon h,(90) is maximized, and the 60" partial dislocation has the lower critical thickness. Thus below a critical Ge concentration, x, hc(60) < h,(90), whereas for x > x, hc(60) > hc(90). These trends are also evident in analysis of the energetically favored dislocation type as functions of epilayer thickness h and Ge concentration x. This is defined by which dislocation has the greater excess stress acting upon it as a function of ( h ,x). The results of this analysis for the Ge,Sil-,/Si(lIO) system are shown in Fig. 12(b). For x < x, the 60" total dislocation is favored for all h. The curve AB corresponds to the plot of hc(60) in this composition range. For x > x,, the 90" partial dislocation is favored for lower epilayer thicknesses (and the curve BC corresponds to the plot of h,(90) in this composition range), but as h increases, the stacking fault energy associated with the partial dislocation increases and at a thickness h,, (x) defined by the curve BD, the 60" total dislocation again becomes energetically favored. The locus of BD is extremely sensitive to the value of y , and we have used the sensitivity of this transition to experimentally determine y (Hull et al., 1993). Thus, there exists a defined area of ( h ,x) space where the 90" partial dislocation is energetically favored. The trends of increasing tendency for 90"a/6(21 1) partial dislocations with increasing Ge concentration x and decreasing epilayer thickness have been experimentally verified in Ge,Sil-,/Si(llO) heterostructures (Hull et al., 1993).

6.

IN MULTILAYER STRUCTURES MODELSFOR CRITICAL THICKNESS

A very common configuration for strained Ge,Sil-, layers is to be confined between a Si substrate and a Si cap. For this geometry, the misfit dislocation configuration may involve interfacial segments either at both interfaces or just the bottom interface, as indicated schematically in Fig. 13. The double interface configuration is more general, and is demonstrated experimentally in Fig. 14. The segment of the dislocation loop at the lower Ge,Sil-,/Si interface allows the lattice parameter of the Ge,Si]-, to be relaxed toward its equilibrium value by increasing the average lattice parameter of the material above this dislocation segment. However, in the absence of the misfit dislocation segment at the upper Ge,Sil-,/Si interface, the Si cap would also have its average lattice parameter increased, thus straining it away from its equilibrium value. The upper misfit dislocation segment thus adjusts the lattice parameter in the Si cap back to its original, unstrained value. The extra interfacial segment increases the dislocation self-energy, but only in relatively thin Si capping layers is this energy contribution greater than the strain energy which would otherwise exist in the Si cap. The ranges of Ge concentrations, epilayer thicknesses and cap thicknesses h,,, which define the

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a

CAP EPI SUB FIG. 13. Schematic illustration of misfit dislocation configurations at capped Si/Ge,Sil-,/Si tures: (a) single interfacial dislocation; (b) double interfacial dislocation.

struc-

two configurations of Fig. 13, have been studied by several groups (Tsao and Dodson, 1988; Twigg, 1990; Gosling et al., 1993). For the double misfit segment configuration, the extra interfacial segment modifies the dislocation self-energy and critical thickness expressions, Eqs. (15) and (24). The self-energy per unit interfacial length of the dislocation dipole is given by the separate energies of the top and bottom dislocations minus the interaction energy between them. For a capping layer thickness hcap and a strained

FIG. 14. Plan-view TEM image of a 300-nm Si/100 nm Geo.2SiO.S/Si(lOO) structure. Closely spaced interfacial dislocation pairs correspond to segments of the same dislocation loop at top and bottom Ge,Sil-,/Si interfaces as illustrated schematically in Fig. 13(b). Reprinted with permission from R. Hull and J.C. Bean ,Appl. Phys. Lett. 54,92, Figure 2. Copyright 1989 American Institute of Physics.

R. HULL

layer thickness h , this yields

The last pair of logarithmic terms in this equation is the interaction energy between the two interfacial dislocations (Hirth and Lothe, 1982). For the limit heap >> h , the entire logarithmic expression simplifies to 2 In(ah/b), or simply twice the energy of the single interfacial dislocation at an uncapped epilayer. The restoring stress for the buried layer q - b is then a factor of two higher than for the single layer (as given by Eq. (23)), and the critical thickness for h, >> b is also approximately a factor of two higher. In fact this approximation is reasonably accurate for all hcap > h if h >> b. This factor of approximately two in critical thickness from capping of strained layers is of great benefit in post-growth processing of practical strained layer devices. Extension of critical thickness concepts to superlattice structures i s complex due to the larger number of degrees of freedom involved (individual layer strains and dimensions, total number of layers, total multilayer thickness, etc.). Experimentally, it is generally observed that providing each of the individual strained layers within the multilayer structure is thinner than the critical thickness for that particular layer grown directly onto the substrate, then the great majority of the strain relaxation occurs via a misfit dislocation network at the interface between the substrate and the first strained multilayer constituent (Hull et al., 1986). If individual strained layers within the multilayer do exceed the relevant single-layer critical thickness, then substantial misfit dislocation densities will generally be observed at intermediate interfaces within the multilayer. Thus, for the configuration where individual layers do not exceed the relevant single-layer critical thickness, the relaxation may be regarded as occurring primarily between the substrate and the multilayer structure taken as a unit. A simple energetic model has been developed (Hull et al., 1986),based upon reduction of the multilayer to an equivalent single strained layer. In this model, a multilayer structure is considered consisting of n periods of bilayers A and B , of thickness dA and d B , compound elastic constants k A and k ~ and , lattice mismatch strains with respect to the substrate of E A and E B , respectively. The amount of strain energy which may be relaxed by a misfit dislocation array at the substratehperlattice interface is found to be:

-

The form of this relaxable energy is equivalent to the average strain energy in the superlattice, weighted over the appropriate elastic constants and layer thicknesses. For k B and that Vegard’s Law applies (i.e., the Ge,Sil-,/Si system, if we assume k A that the strain of Ge,Sil-, with respect to Si varies linearly with x), then the relaxable strain energy simplifies to that in an equivalent uniform layer of the same total thickness

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+

as the superlattice = n(dGeSi dsi), and the average superlattice composition x, = x&esi/(&esi &i). The preceding analysis provides an equilibrium framework for analysis of critical dimensions for the onset of misfit dislocation generation in GeSi/Si superlattice structures. In practice, kinetic effects and dislocation interactions are likely to be very significant in these more complex structures (Hauenstein et al., 1989). It has been found, however, that relaxation kinetics of equivalent single layers at MBE growth temperatures of 550 "Cprovide an approximate guide to kinetic relaxation rates in superlattice structures (Hull et al., 1986).

+

V. Metastability and Misfit Dislocation Kinetics 1. BASICCONCEPTS

a. Introduction To date, we have considered only equilibrium descriptions of the misfit dislocation array. However, it is clear from the comparison of experimental data with equilibrium modeling of critical thickness in the GexSi~-,/Si(1O0) system, as illustrated in Fig. 11, that there are significant kinetic effects associated with generation of misfit dislocation arrays. These arise primarily from the substantial energetic barriers generally associated with dislocation nucleation and propagation, which have to be overcome by thermal activation, and with interactions between different dislocations in the array. In this section, we will consider each of these processes in turn. The primary effect of kinetic barriers in the development of the interfacial dislocation array is that the magnitude of plastic relaxation will lag behind the equilibrium condition. This gives rise to nzetastably strained structures. The definition of a metastably strained structure is that the excess stress on the operative dislocation type aeXis greater than zero. Increasing excess stress corresponds to increasing metastability of the structure. The definition of equilibrium is that aeX= 0. Experimentally, we describe the degree of metastability by a slight modification of Eq. (23) ~

c

+

= x 2GS[&o- (bcosh/p)](l ~ ) / ( l- U ) - [Gbcos@(l - ucos28)/4nh(l - u)]ln(ah/b) - y/b

(29)

Here, as discussed in Section IV, we have transformed E in Eq. (23) to [ ~ - ( cos b Alp)], where EO is the initial lattice mismatch strain (a, - a,)/a,, and (bcos A l p ) is the amount of strain relaxed by the misfit dislocation array. The maximum degree of metastability in a given structure corresponds to an infinite spacing of the misfit dislocations. As development of the misfit dislocation array proceeds, p and a,, decrease

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R. HULL

until equilibrium is reached at a,, = 0 and p = pmjn.The value of pmill is found by solving Eq. (29) for oeex = 0. Kinetic effects are very substantial in GeSi-based heterostructures, as the covalent bonds of Ge and Si lattices are relatively strong. Thus, as described in Section 111, the activation energies for dislocation motion in bulk Ge and bulk Si are of order 1.6 eV and 2.2 eV, respectively. These values are very much greater than kT at any reasonable crystal growth temperature. Dislocation nucleation is also generally associated with significant activation barriers. Thus, particularly at moderate growth temperatures, the actual development of the misfit dislocation array may lag orders of magnitude behind the equilibrium configuration, and substantial excess stresses (up to 1.0 GPa) may develop. This is the essential reason for the ability to grow low misfit dislocation densities far beyond the equilibrium critical thickness at lower growth temperatures, as illustrated in Fig. 11. 6. An Idea of the Numbers Involved in Relaxation by MisJit Dislocations What kinds of numbers of total misfit dislocation length, interfacial spacings, and numbers of individual dislocation loops are we considering in strained layer relaxation? Consider a 10 cm diameter Si(100) substrate. Let a Ge,Sil-, epilayer be grown upon it with a lattice mismatch of 1% with respect to the substrate. Let the residual strain in the structure be close to zero (this will be true for a sufficiently thick epilayer grown at a sufficiently high temperaturc). Let the interfacial misfit dislocations be of the 60" a/2(110) type, such that the Burgers vector magnitude is 0.39 nm. The required interfacial misfit dislocation spacing will be given by the relation EO = b cos A l p , as previously discussed. This yields an interfacial misfit dislocation spacing 20 nm. The equilibrium misfit dislocation density is thus very high for epitaxial layer thicknesses that are significantly greater than the critical layer thickness. This means that dislocation interactions become very important as the structure relaxes plastically towards equilibrium. An average dislocation spacing of 20 nm across a 10 cm wafer requires a total length of the orthogonal interfacial misfit dislocation grid of the order lo6 m (recall that two separate, orthogonal, dislocation arrays have to be created). Thus f o r complete relaxation enormous line lengths of dislocation have to be created (in this example, of order 1000 km over a 10 cm wafer!). To create this line length in a finite time interval propagation and nucleation rates will need to be relatively rapid. So how many misfit dislocations are needed to create this array? Even if each dislocation makes a chord from edge to edge of the wafer, lo7 separate dislocations will be required, or of the order lo5 cm-2 of substrate area. Thus high densities of misfit dislocation nucleation sources are required. However, this estimate should be regarded as an absolute minimum required source density. Let us now consider the implications of finite dislocation propagation velocities (in general, there will not be sufficient time at temperature for the dislocation to grow to be sufficiently long to traverse the entire

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wafer-unless the growth temperature is very high, for example, the growth by CVD of Ge,Sl-,/Si(lOO) with x 5 0.05 at 1120 "C [Rozgonyi et al., 19871). As will be discussed later in this section, typical misfit dislocation velocities in GeSi-based heterostructures at strains of order 1% are of the order 0.1 - l p m s-l at 550 "C. At a typical MBE growth rate of 0.lnm s-l, it takes 1000 s to grow a 100-nm epilayer, by 0.01 is typically > 10% relaxed. Based upon the which time an initial strain of EO foregoing analysis, a 10% relaxation of the original strain requires a total interfacial dislocation length lo5 m. The maximum length of individual dislocations, based upon their propagation velocity, is 0.1-1 mm (the average will obviously be significantly less than this). Thus a minimum total number of 108-109 dislocation nucleation events are required, corresponding to an areal density 106-107 cmP2, and a nucleation rate 103-104 cmP2 sP1. (These numbers again represent a lower limit to the required source density as not all dislocations will nucleate at the start of the relaxation process, propagation velocities will be substantially lower than the number quoted above until the critical thickness is significantly exceeded, and misfit dislocation interactions may also slow propagation.) Identification of plausible mechanisms for generating such dislocation source densities is a critical question in our current understanding of strained layer relaxation.

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2. MISFITDISLOCATION NUCLEATION a. Introduction The precise mechanisms of nucleation of misfit dislocations in strained heteroepitaxial systems remain somewhat elusive and controversial. There are many papers on this topic in the literature, and in this section we will summarize this literature with respect to nucleation in GeSi-based systems. The generic candidates for misfit dislocation nucleation sources are:

(a) Heterogeneous nucleation at specific local strain concentrations, due for example to growth artifacts or pre-existing substrate defects. (b) Homogeneous or spontaneous nucleation of dislocation loops or half-loops. (c) Multiplication mechanisms arising from dislocation pinning and/or interaction processes. These are generally extensions of classic mechanisms such as the FrankRead source in bulk crystals (Frank and Read, 1950). We will now consider each of these generic mechanisms in more detail. b. Heterogeneous Nucleation Sources By heterogeneous nucleation, we mean nucleation of dislocations from sources that are not native to or inherent in the structure.

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The original formulations of Matthews and Blakeslee generally assumed that the required density of defect sources were generated by existing dislocations in the substrate (although they did consider other potential nucleation mechanisms). This may have been a plausible mechanism for the GaAs substrates of the 1970s that they were considering, but contemporary commercial Si substrates typically have defect densities in the range 1-lo2 cm-2. Clearly, these substrates themselves cannot provide sufficient densities of defect sources, based upon the required source densities discussed in Section V. 1. Other heterogeneous features that may develop during epitaxial growth, or which arise from incomplete cleaning of the substrate surface prior to growth, can act as misfit dislocation nucleation sources if there are high local stresses and strains associated with them. Examples include residual surface oxide or carbide after substrate cleaning, particulates on the substrate surface or included during growth, source “spitting,” contaminants, transition metal precipitation, etc. For example, in our experience of Ge,Sil-, growth upon Si substrates by molecular beam epitaxy (MBE), the most generic heterogeneous source we observe are polycrystalline Si inclusions, of order a few hundred nanometers in size, and present at densities of the order lo3 cmP2, as illustrated in Fig. 15. We believe that these sources are associated with flaking of polycrystalline Si from deposits built up on the walls of the growth chamber. Other heterogeneous sources that have been documented in GeSi/Si heteroepitaxy include surface nucleation mechanisms associated with trace impurities (-- l O I 4 cmP3) of Cu (Higgs el al., 1991), and heterogeneous distributions of 1/6(114) diamondshaped stacking faults (Eaglesham et al., 1989) that have dimensions of order 100 nm

FIG. 15. Example of a heterogeneous dislocation source (an inclusion of polycrystalline Si that arises from flaking from the walls of the MBE growth chamber) in a 200-nm Geo.1 5 S i o . ~ ~ / S100) i ( heterostructure. Photo courtesy of F. M. Russ.

3 MISFITSTRAIN AND ACCOMMODATION

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and act as sources for 60°a/2(110) misfit dislocations. (Defects with similar geometries have been correlated with precipitation of metallic impurities, for example, Fe in Si [DeCoteau et al., 19921). Each of the features listed here certainly can provide sufficient source densities if the growth quality is poor enough (i.e., feature density and, therefore, source density is high enough), but each should be controllable in high-quality crystal growth to lo3 cm-2, or better. Of course, a single source may emit more than one misfit dislocation, but each source will only be able to relax strain in the heterostructure over dimensions comparable to the source size (which for isotropic source dimensions must be no greater than the epitaxial growth thickness). In summary, it is difficult to imagine that any of these heterogeneous nucleation mechanisms can generate the high densities of dislocations consistent with the observed relaxation of moderately or highly strained structures.

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c. Homogeneous Nucleation Sources By homogeneous nucleation, we mean nucleation of dislocations from sources that are inherent in the structure. The most obvious homogeneous nucleation source in lattice-mismatched heteroepitaxy is the elastic strain, which if sufficiently high can lead to spontaneous (i.e., zero or negative activation energy) nucleation of dislocation loops or surface half-loops. At lower strains, homogeneous dislocation nucleation is associated with an energy barrier. This situation has been modeled by several authors, for example, Cherns and Stowell (1975, 1976); Matthews et al. (1976); Fitzgerald et al. (1989); Eaglesham et al. (1989); Hull and Bean (1989a); Kamat and Hirth (1990); Dregia and Hirth (1991); Perovic and Houghton (1992); and Jain et al. (1995). The general principle underlying these models is that a growing dislocation loop of appropriate Burgers vector relaxes strain energy within the epilayer Est, but balancing this is the self-energy of the dislocation loop itself El (this is closely analogous to the Matthews-Blakeslee critical thickness criterion for growth of interfacial misfit dislocations). Other energy terms that need to be considered are the energies of steps created or removed in the nucleation process ESP(a 60" a/2(101) dislocation, for example, has a Burgers vector component normal to the surface and must thus always be associated with step creation or removal), and the energy of any stacking fault created E,f either as a result of dislocation dissociation, or as a result of separate nucleation of partial dislocations. This produces a total energy of the form Er = El - Est i= E,, f Esf (30) Note that E,f may either increase or decrease the total energy: a stacking fault clearly increases the system energy, but a 30" partial dislocation, for example, could nucleate along the path of an existing 90" partial dislocation to remove the existing stacking fault and generate a total misfit dislocation. The total system energy will in general pass

136

R . HULL

through a maximum value A E (which represents an activation barrier for homogeneous dislocation nucleation), at a critical loop radius R,. The magnitude of A E as a function of strain depends sensitively upon the Burgers vector of the dislocation, the magnitude of the dislocation core energy assumed, and whether or not ESt and E,f are included in the calculation. Variations between these different terms cause a range of predicted activation barriers at a given strain in calculations by different authors, but consensus exists that activation barriers approach a physically attainable limit (of order a few electron volts or less) for strains of the order 2 4 % (corresponding to x 2 0.5 in Ge,Sil-,) , and are unphysically high (100 eV or greater) at strains below about 1% (corresponding to x 5 0.25 in Ge,Sil-,). A common expression used for the loop self-energy (Bacon and Crocker, 1965) for a complete loop of radius R is El = [Gb2R/2(1

-

+ (1 - u/2)(1 - b:/b2)][ln(2nRa/b)

u)][b:/b2

-

1.7581 (31)

Here b, is the component of the dislocation Burgers vector normal to the loop. The original Bacon and Crocker expression also contained an extra term due to surface tractions; the magnitude of this extra expression is relatively low and is generally omitted by most authors. The strain energy relaxed by the loop is given by Est = [2nR2G( 1

+ u ) E / ( ~- ~ ) ] ( bcos, q5 cos A + b, cos2 q5)

(32)

Here b, and be are the glide and climb components, respectively, of the dislocation Burgers vector. Considering the energy terms in Eqs. (31j and (32) only, the critical radius is found by setting 6Et/6R = 0, yielding

{b2tb;/b2 R, =

+ (1 - u/2)(1 - b;/b2)l[ln(2nRca/b) Sn(l+

- 1.758

+ 2na/b]}

u)E(6~COSq5COSh+b,cos~~)

(33)

Assuming the most common configuration of 6Ooa/2(101) dislocations moving on (11 1) glide planes with a (100) interface, we have b, = be = 0, b, = b = 0.39 nm, simplifying Eq. (33) to cos h = 0.5, cos q5 =

m,

R, =

&b(l - u/2)[1n(2naRc/b) - 1.758 - 2na/b] 4&(1

+ VIE

(34)

This expression may be solved numerically for R, as a function of E and the value substituted back into Eq. (30) to yield A E For a dislocation half-loop nucleating at the epilayer free surface, ESt is halved relative to a full loop, El is approximately halved (this is actually an involved calculation if done rigorously because of the complexity of the image interaction calculation; these

3

137

MISFITSTRAIN AND ACCOMMODATION

complexities are generally ignored in the literature, and a factor of a half used), R, is approximately unchanged, El is approximately halved and A E is approximately halved. This indicates why surface half-loop nucleation is generally assumed to be greatly favored over full-loop nucleation within the epitaxial layer. The value of R, for the surface half-loop is closely analogous to the Matthews-Blakeslee critical thickness for an uncapped epilayer. The small quantitative differences between R, and h, arise because the dislocation configuration is somewhat different in the two cases, thus modifying the expression for dislocation self-energy, and because R, is measured in an inclined { 111) plane, while h, is measured along the interface normal. Evaluation of the activation barrier A E (for either half- or full-loops) shows that it increases approximately as the magnitude of the Burgers vector cubed (this strongly reduces the activation barrier for partial vs total dislocations [Wegscheider et al., 1990]), increases strongly with the magnitude of the core energy parameter a and is approximately inversely proportional to the strain. In Fig. 16 we show the variation of A E with x for surface half-loop nucleation in the Ge,Si~-,/Si(IOO) system for 60°a/2(110) dislocations with removal and creation of surface steps as they nucleate; EStis approximated from the relation ESt= 2Rbx sin3!, (35) where j3 is the angle between the dislocation Burgers vector and the free surface, and x is the areal epilayer surface energy, which, following Cherns and Stowell (19759, we approximate by x Gb/8. Note the great sensitivity of the results for A E in Fig. 16 to the value of a. The foregoing calculations suggest physically accessible activation barriers (of order 5 eV)7 for strains of order 3 4 % or greater. However, quasi-homogeneous processes can provide substantial densities of sites at the epilayer surface, which significantly reduce the homogeneous nucleation barrier. By quasi-homogeneous, we mean features in the crystal that, although arising from inherent physical processes in the crystal growth, represent perturbations in the average crystal structure. For example, we have demonstrated that statistical fluctuations in the Ge concentration of a Ge,Sil-, alloy can produce significant densities of local volumes where the Ge concentration is significantly higher than the average matrix composition (Hull and Bean, 1989a). Local Ge-rich regions have also been implicated by Perovic and Houghton (1992) in dislocation nucleation. Another quasi-homogeneous process that can locally reduce activation barriers for dislocation nucleation is roughening of the epilayer growth surface. We have already considered in the analysis of Eqs. (30)-(35) how removal of monolayer surface steps

-

7Consider the number of surface atomic sites, IOl5 cm-2, available for nucleation, and a nucleation s-’ in Si. We thus have a attempt frequency, which we will approximate by the Debye frequency, lo2* ~ r n - ~ s - ’ .For a crystal temperature of 1000 K, kT 0.086 eV, and for a nucleation prefactor of lo-”, which when multiplied by the prefactor 5 eV activation energy, the Boltzmann factor yields a significant nucleation rate.

-

-

-

-

R. HULL

138

%

U

w Q

FIG. 16. Homogeneous activation barriers A E for nucleation of 60°n/2(101) half-loops at Ge,Sil-,/Si( 100) surfaces, for different values of the dislocation core energy parameter a with removal of surface steps (RS) or creation of steps (CS).

can reduce activation energies. Local stresses associated with surface steps and facets (particularly if they are several monolayers, or more, high) can also significantly enhance nucleation locally. For example, theoretical (Sorolovitz, 1989; Grinfeld and Sorolovitz, 1995) and experimental (Jesson et al., 1993, 1995) studies have postulated and demonstrated the formation of surface cusps during strained epilayer evolution. These cusps are associated with substantial local stress concentrations, and reduced barriers for dislocation nucleation. Similar observations of dislocation injection associated with troughs in surface roughness in the InGaAs/GaAs system have been described by Cullis et al. (1995). In general, the boundary between “homogeneous” and “heterogeneous” source mechanisms can become indistinct, and to some extent no nucleation event will be truly homogeneous within the strained layer: loop nucleation will always be energetically favored at some nonperiodic event, such as a surface step, cusp, or locally enhanced Ge concentration. This may produce a “hierarchy” of misfit dislocation nucleation sources, with the lowest activation energy processes exhausted first, and subsequent activation of increasingly higher activation energy events. d. Dislocation Multiplication

The most intuitively appealing generic candidate for a source mechanism producing high densities of misfit dislocations is a multiplication mechanism, by analogy to deformation experiments in bulk semiconductors. The idea of a regenerative dislocation source goes as far back as the Frank-Read source (Frank and Read, 1950). Probably the first application of this concept to semiconductor strained layer epitaxy was reported by Hagen and Strunk (1978) for the growth of Ge on GaAs. Their proposed mecha-

3 MISFITS T R A I N AND

ACCOMMODATION

139

FIG. 17. Schematic illustration of the Hagen-Strunk mechanism of dislocation multiplication, (a)-(d). (e) shows the expected configuration of intersecting dislocations without the Hagen-Strunk mechanism operating; ( f )shows the expected configuration after operation of the Hagen-Strunk mechanism. Reprinted with permission from R. Hull and J.C. Bean, Critical Reviews in Solid State and Materials Science 17, 507-546 (1992). Copyright CRC Press, Boca Raton, Florida.

nism, illustrated in Fig. 17, relies upon intersection of dislocations with equal Burgers vectors along orthogonal interfacial (011) directions within a (100) interface. The very high energy configuration associated with the intersection is lowered by formation of two interfacial segments with localized climb producing rounding near the original intersection, as shown in Fig. 17(b). This reduces the very high radius of curvature at the original intersection, and lowers the dislocation configurational energy. Local stresses near the dislocation intersection now modify the local energy balance for the dislocation, causing one of the rounded segments of dislocation to move toward the surface, as shown in Fig. 17(c). When the tip intersects the surface, Fig. 17(d), a new dislocation segment is formed, which can act as a new misfit dislocation. This process may repeat many times, producing a regenerative dislocation source. Several authors have since invoked this mechanism as a dislocation source in Ge,Sil-,/Si strained layer epitaxy (e.g., Rajan and Denhoff, 1987; Kvam el aE., 1988). However, the experimental evidence for the Hagen-Stmnk source is often based upon dislocation configurations as shown schematically in Fig. 17(e), where dislocation segments align along (011) directions across the original intersection event. The true “footprint” of the Hagen-Strunk source is as shown in Fig. 17(f) where alignment across the intersection does not occur. The configuration of Fig. 17(e) is simply that of Fig. 17(b) where many orthogonal dislocation intersection events have occurred (Dixon and Goodhew, 1990).

140

R. HULL

Direct evidence for different multiplication mechanisms has been reported by several other authors. Tuppen et al. (1989, 1990) used Nomarski microscopy of chem(x 5 0.15, epilayer thickness 0.9pm) structures ically etched Ge,Sil-,/Si(100) to demonstrate greatly enhanced dislocation nucleation activity associated with dislocation intersections. Two distinct Frank-Read type and cross-slip mechanisms for the multiplication process were proposed. An important requirement for these specific mechanisms, and for most other multiplication mechanisms, is the existence of two pinning points along that segment of dislocation line that acts as the regenerative source. The segment then grows by bowing between the pinning points, and may eventually configure into re-entrant and re-generative geometries, similar to the FrankRead source. In the models described by Tuppen et al. (1989, 1990), dislocation intersections act as these pinning points. Capano (1992) described several multiplicative configurations, not involving dislocation intersections, for a single isolated threading dislocation. These mechanisms generally involved dislocation cross-slip following pinning of segments of the dislocation by inherent defects in the dislocation or host crystal (e.g., constrictions in the partial dissociation along the dislocation line). Capano measured a minimum “multiplication thickness” for these processes of 0.67 p m for Ge0,13Si0,87/Si(100) structures. This is very consistent with the experiments of Tuppen et al. (1989, 1990), who studied 0.5 pm, 0.7 p m and 0.9 p m thick epilayers with Ge concentration x = 0.13, and first observed evidence of multiplication processes in the 0.7 p m layer. Capano also modeled the minimum epilayer thickness required to accommodate the intermediate cross-slip configurations in the multiplication processes he described, and derived minimum epilayer thicknesses an order of magnitude lower than he experimentally observed. The discrepancy was attributed to the density of available pinning points along the dislocation line. A very complete description of a Frank-Read type source in Ge,Sil-,/Si epitaxy has been provided by LeGoues et al. (1991,1992). This mechanism involves dislocation interactions at the interface to provide the required pinning points, and was most generally observed in graded composition layers. Similar mechanisms have also been reported by Lefebvre et al. (1991) for the strained InGaAs/GaAs system. Beanland (1995) described additional multiplication sources in InGaAs/GaAs structures, involving operation of spiral sources operating either from dislocation interactions, or from the tips of pre-existing edge dislocations. Albrecht et al. (1995) demonstrated that dislocation multiplication could be associated with surface roughening (see discussion in Section V.2.c). They used finite element modeling to model stress concentrations at ripple troughs in relatively low Ge concentration (x = 0.03) Ge,Sil-,/Si( 100) heterostructures, which were demonstrated to lead to dislocation injection into the substrate and subsequent Frank-Read type multiplication sources. In summary, it appears that dislocation multiplication mechanisms do occur in strained GeSi layers. However, a significant density of dislocation pinning points is required for these mechanisms to operate efficiently. These pinning points can either

3 MISFITSTRAIN AND ACCOMMODATION

141

occur from dislocation intersections (which requires a significant source dislocation density), or from inherent features of the dislocation or host crystal (constrictions,point defects, etc.) It also appears that minimum epilayer thicknesses are required for multiplication, as intermediate cross-slip or loop configurations have to be accommodated during the regeneration process. Tuppen et al. (1989, 1990) and Capano (1992) measured minimum epilayer thicknesses > 0.5 p m for Ge concentrations of x = 0.13, but LeGoues et al. (1991, 1992) did observe multiplication in graded structures with thicknesses as small as 200-300 nm.

e. Experimental Measurements of Dislocation Nucleation Rates

A powerful insight can be provided into the epilayer thickness and composition ( h ,x) regimes in which different dislocation mechanisms dominate by experimental study of dislocation nucleation rates and activation energies. Unfortunately, relatively little experimental data have been reported for the Ge,Sil-,, or any other strained layer system. The most extensive experimental work to date has been by Houghton (1991), who used direct counting of dislocation source densities via optical microscopy of etched (Si)/Ge,Sil-,/Si(lOO) structures following post-growth annealing. Only the early stages of strain relaxation were studied (due to the resolution limits inherent to conventional optical microscopy), where less than about 0.1% of the initial lattice mismatch strain was relaxed. The number of observed dislocations followed the trend

In this equation B is a constant of the order loi8 s-’. The activation energy for dislocation nucleation, En is of the order 2.5 eV for 0.0 < x < 0.3, and epilayer thicknesses in the range 100-3500 nm. Measured nucleation rates were in the range 10-’-105 cm-*s-l. In the Houghton formulation, NO is an adjustable parameter (determined by experimental inspection) for each structure and represents the number of pre-existing heterogeneous nucleation sites before the anneal is started. Measured values for NO reported by Houghton were in the range 103-105 cm-* and generally increase for higher x. Equation (36) implies that, at least in the early stages of relaxation, a12 misfit dislocations are nucleated from heterogeneous sources. As discussed in Section V. 1 of this chapter, this appears implausible during later stages of dislocation-mediated strain relief. Also note that Perovic and Houghton (1992) later reinterpreted Eq. (36) in terms of “barrierless” nucleation of dislocations, where it was assumed that the activation energy of 2.5 eV measured for dislocation nucleation was essentially the 2.2-2.3 eV activation energy associated with dislocation growth by glide (see Section V.3 of this chapter), that is, the activation energy of Eq. (36) corresponded to the rate at which dislocations grew to be significantly large to be detected by optical microscopy.

142

R . HULL

Some other data for dislocation nucleation rates in GeSi/Si heterostructures have been reported by Hull et al. (1989a) using in situ TEM measurements (these experiments correspond to much later stages of the relaxation process than those reported by Houghton, as TEM imaging covers a much smaller field of view than optical microscopy). Nucleation activation energies of the order 0.3 eV were reported for a 35 nm Geo.25Si0.7s/Si(100)structure, with a prefactor of 2.2 x lo6 cm-2.y-l. The observed dislocation densities were relatively high (-- 107-108 cm-’), therefore strongly suggesting quasi-homogeneous nucleation in these experiments. Although this activation energy is very different to that reported by Houghton, overall nucleation rates at comparable excess stress are of the same order of magnitude (e.g., at a temperature of 650 “C in a 100 nm x = 0.23 structure, Houghton reports a nucleation rate 3 x lo4 cm-’s-l, whereas for the 35 nm, x = 0.25 structure, Hull et al. (1989a) reported a nucleation rate 5 x lo4 cm-2s-’). In capped Si/Ge,Sil-,/Si(100) structures (0.10 < x < 0.30) we have measured activation energies in the range 0.5-1.0 eV (Hull et al., 1997). Nucleation data from the work of Houghton and of Hull et al. is shown in Fig. 18. Other quantifications of misfit dislocation nucleation in the Ge,Sil-,/Si system are the work of LeGoues et al. (1993), relating to the Frank-Read-like multiplication mechanism proposed by that group, and Wickenhauser et al. (1 997), relating to heterogeneous nucleation in Geo.16Sio.84layers. LeGoues et al. (1993) inferred an activation 5 eV, and a total dislocation nucleation rate energy for the former mechanism of l the amount of crystallographic tilt of the epilayer produced of 6 x 10’ ~ m - ~ s -from by differential dislocation densities on different glide planes in Ge,Sil-, layers grown on misoriented Si( 100) substrates. Wickenhauser er al. (1997) determined a heterogeneous source (the physical nature of the source was not identified) activation energy of 2.8 eV.

-

-

-

-

Summary of Misfit Dislocation Nucleation From the discussion of the preceding few subsections it is clear that there is not a universal model for dislocation nucleation in GeSi-based heterostructures, and, further, that we should not expect such a universal model. The very high dislocation nucleation rates associated with strain relaxation in higherstrained systems are consistent with homogeneous, or quasi-homogeneous processes (such as alloy clustering, or epilayer roughening) in this strain regime. Although calculations of true homogeneous nucleation predict that strains of order 3 4 % or higher are required for appreciable nucleation rates, local stresses associated with quasi-homogeneous processes appear to lower this strain threshold down to 2% or even 1%. At strains below this level, it appears that a combination of heterogeneous nucleation and multiplication dominates. The initial heterogeneous stage is severely source limited, thus the metastable growth regime at low strain and low temperature is very large, as indicated in Fig. 11. As the network of dislocations from heterogeneous

3

MISFITSTRAIN AND ACCOMMODATION

a

143

.

10'

-

nn

10'.

"

u- 10' t-

4 U

*

102

0 I$

lo'

d

2

100

10'9

06

I .6

I 1

INVERSE TEMPERATURE, looo/T K - I

1

J

A

i

I lo2 1

L

1 OI6

m A

RHx=OZS,h=35nm R H x=O 30, h=30 nm DCH xdJ.23, h=l OOnm

7

8 l/kT

A10

9

(J-lxlO19)

FIG. 18. (a) Measured misfit dislocation nucleation rates during annealing of (Si)/Ge,Si*-,/Si( 100) heterostructures; A = 20 period superlattice of 32 nm .%/lo nm G ~ o . ~ o S ~ D O .=~ 500 O ; nm Geo.035Sio.965; E = 3000 nm Ge0.035Si0.965; F = 190 nm Ge0.17Si0.83; G = 100 nm Ge0.23Si0.77. Reprinted with permission from D.C. Houghton, Appl. Phys. Lett. 55, 2124, Figure 2. Copyright 1990 American Institute of Physics. (h) Comparison of nucleation rates measured by Houghton (1991) (DCH) and Hull etal. (1989a, 1997) (RH) for Ge,Sii-,/Si(100) structures with similar composition (x 0.2-0.3) and excess stress.

-

sources eventually develops, the required dislocation intersection events generally assumed to be required to fuel multiplication processes can occur. We can thus tentatively map out three broad nucleation regimes: in high strain systems (> 1-2%), relaxation is by homogeneous and quasi-homogeneous nucleation processes. In low strain systems (- 1% or less), heterogeneous sources provide the initial background dislocation density in the low epilayer thickness regime of the order of a few hundred nanometers or less. Multiplication mechanisms then become dominant in the low strain, high thickness regime.

144

R. HULL

Experimental mapping of dislocation nucleation rates and activation barriers have so far provided little additional insight into delineating these different nucleation regimes. The only extensive existing data set from Houghton is apparently consistent with heterogeneous sources in the low strain regime.

3.

MISFITDISLOCATION PROPAGATION

Experimental descriptions of dislocation motion are relatively well developed, and in general follow straightforwardly from treatments of dislocation glide in bulk Si and Ge crystals, as reviewed in Section 111and described by Eq. (20) u = ugmm exp[-E,,(a)/kT]

For misfit dislocations in Ge,Sil-, heterostructures, we shall also use this equation to describe dislocation velocity, using the excess stress for CJ in the prefactor. In the low stress (10-100 MPa) regime for intrinsic, pure crystals, EL, I .6 eV in Ge and 2.2 eV in Si. The prefactors are very similar for the two materials ( u g 3 x 10-'m2Kg-'s) (Alexander and Haasen, 1968) and thus dislocations glide a lot 5000 at 550 "C). Thus we should expect that for faster in Ge than Si (by a factor Ge,Sil-, alloys the glide activation energy will decrease, and the glide velocity will increase, with increasing x. Unfortunately, the dependence of E , ( x ) from bulk crystals is not known (apart from recent measurements very near x = 1.0 (Yonenaga and Sumino, 1996), which scaled well from measurements on bulk Ge), and in general we are restricted to linear interpolation of the values for bulk Si and Ge. The composition dependence of E,(x) in Ge,Sil-, alloys is further complicated by the relationship between x and o:it is predicted that kink nucleation energies (and hence glide activation energies) are reduced at sufficiently high applied stresses (Seeger and Schiller, 1962; Hirth and Lothe, 1982), such as are typically encountered in Ge,Sil-,/Si heteroepitaxy for all but the most dilute Ge concentrations. The stress dependence of the dislocation velocity is still somewhat uncertain in bulk Si and Ge crystals, let alone Ge,Sil-, alloys; undoubtedly part of this uncertainty depends upon how the stress dependence is apportioned between the prefactor and the exponential in Eq. (20). However, there is strong evidence from bulk measurements in Si that the activation energy E , is stressdependent for (T of the order of a few hundred MPa or more (Kusters and Alexander, 1983). In general, these stress effects will also need to be deconvoluted in glide activation energy measurements at the enormous stresses (of order 1 GPa), which can be present in Ge,Sil-, heterostructures. An extensive set of measurements by Imai and Sumino (1983) has yielded a linear stress dependence, nz = 1 .O in Eq. (20), at stresses of the order tens of MPa in Si, and this is also the dependence predicted by the generally accepted microscopic model of dislocation motion, the Hirth-Lothe diffusive double kink model (Hirth and Lothe, 1982).

-

- -

145

3 MISFITS T R A I N A N D ACCOMMODATION

Misfit dislocation propagation velocities in (Si)/Ge, Sil --x /Si( 100) heterostructures have been studied by several groups, using either in situ TEM observations (Hull et al., 1989a, 1991a; Nix et al., 1990) or chemical etching and optical microscopy (Tuppen and Gibbings, 1990; Houghton 1991; Yamashita et al., 1993). In Fig. 19, we plot measured dislocation propagation velocities vs excess stress a,, from these different groups for a temperature of 550 "C (interpolated where necessary from measurements at other temperatures). The data between different groups and different techniques agree relatively well. Note that even the relatively limited vertical scatter of data in this plot is not necessarily due to experimental error, as there are factors other than just excess stress (primarily Ge concentration in the Ge,Sil-, alloy, as discussed previously) which determine dislocation velocity. In our own work we have made hundreds of measurements of misfit dislocation velocities from a wide range of (Si)/Ge,Sil -,/Si( 100) heterostructures (see, for example, Hull et al., 1991a; Hull and Bean, 1993). The data from different structures can be effectively normalized to each other by plotting the logarithm of the quantity v* inverse temperature, where: u* = [v,e-

[0.6x(eV)/kT]

1/sex

(37)

In this expression, v, is the measured dislocation velocity and the quantity e-[0.6x(eV)lkT1 accounts for the 0.6 eV glide activation energy difference between Ge and Si, such that we are assuming E , ( x ) = 2.2 - 0 . 6 ~eV in Ge,Sil-,. Equation (37) therefore effectively normalizes the measured dislocation velocity to an equivalent velocity at an excess stress of 1 Pa in pure Si. In Fig. 20, we plot our measurements of misfit dislocation velocities from a wide range of (Si)/Ge,Sil -x/Si( 100) heterostructures (Hull et al., 1991a; Hull and Bean, 1993), normalized according to Eq. (37).

1

-,

)4

/Si(lOO) heterostructures vs FIG. 19. Measured dislocation Propagation velocities in (Si)/Ge,SlI excess stress oex at 550 "C from Houghton (1990), Hull et al. (1991a, 1993), Tuppen and Gibbings (1990), Nix et al. (1990), and Yamashita et al. (1993).

146

R. HULL

-

-

M -

Y f

-35

.

\4

-33

h

1

~

-31

v

3

B

-

L

-39-

-41

~

-43

-

-45

' 7

"*=

8

9 l/kT (J-1x1019)

10

1

FIG. 20. Normalized dislocation velocities for uncapped and capped (300 nm Si)Ge, Sil -,/Si(lOO) structures. Faint dashed lines either side of the main regression lines correspond to 0.7 confidence bounds.

Note that there is a systematic difference in normalized velocity for capped vs uncapped Ge,Sil --x layers. We have ascribed this difference to different microscopic kink mechanisms for dislocation propagation motion in these two geometries. The regression line fits to the data in Fig. 20 are given for uncapped structures (a) and capped structures (b) by u* = ,-(7.8+l.4),-(2.03+0.10

*=

,-

eV)/kTm2S~g-I

,-1.93+0.10 eV)/kT m 2 s ~ g - I

( 10.4fl.4)

(

(a) (b)

(38)

To calculate the misfit dislocation velocity at a given temperature in a given (Si)/ Ge,Sil -x/Si( 100) heterostnicture, therefore, one simply multiplies the relevant u* by a , , ,iO.WeV)lkTI

Note that Eqs. 38(a) and (b) are still largely empirical, as they ignore further microscopic details of the diffusive double kink model such as the dependence in some regimes of the velocity upon the length of the propagating dislocation line (see Section 111.6) and single vs double kink dynamics (Hirth and Lothe, 1982; Hull et al., 1991a; Hull and Bean, 1993). A stress-independent activation energy is also implied by the form of Eqs. 38(a) and (b), although note that the regression calculations give activation energies 1.9-2.0 eV, which is less than the 2.2 eV activation energy that would be expected from the normalization to equivalent velocities in Si. (The lower value of 1.9-2.0 eV corresponds to an average 0.2-0.3 eV reduction in activation energy due to the stress dependence.) However, from the regression coefficients of Eqs. 38(a) and (b) ( R = 0.93 and 0.96, respectively), it is apparent that the equations offer good semiempirical descriptions of misfit dislocation velocities. There have been other attempts to fit measured dislocation propagation velocities systematically to an empirical model. Houghton (1991) modeled his measurements

3

MISFIT S T R A I N A N D ACCOMMODATION

147

of misfit dislocation velocities using a slightly modified version of Eq. (20): u = uo(oex/G)me(-EL,/kT) with m = 2, uo = (4 i 2) x 10" ms-', and a constant activation energy of E , = 2.25 f 0.05 eV for 0.0 < x < 0.3 in (Si)/GeXSil-,/Si(100) structures. The higher pre-exponential factor, m, may be accounted for by the assumption of the constant activation energy: the higher Ge concentration structures (which in general will correspond to the structures with higher excess stresses) will have enhanced velocities due to the lower dislocation glide activation energy in Ge than in Si. Assumption of a constant value for E , will therefore tend to overestimate the pre-exponential stress dependence of dislocation velocities in higher Ge concentration films, producing an artificially high value of rn. Tuppen and Gibbings (1990) studied misfit dislocation velocities in (Si)/GexSil-,/Si(lOO) structures with relatively low Ge concentrations (typically x i 0.15). They observed a linear pre-exponential dependence of velocity upon excess stress, m = 1 in Eq. (20), and a prefactor consistent with bulk Si and Ge measurements (UO = 2.81 x m2Kg-'s). The measured glide activation energy was E , ( x ) = 2.156 - 0 . 7 ~ eV, which is somewhat lower than predicted from bulk values (perhaps due to the theoretically predicted stress dependence of the activation energy). They also observed in certain structures a dependence of the dislocation velocity upon the threading dislocation length L f i h (this relationship arises from the orientation of the threading arms within the inclined { 111) glide planes), where h is the Ge,Sil-, epilayer thickness, consistent with the predictions of the double kink model (Hirth and Lothe, 1982) for dislocation lengths, L > X.This was not observed by Tuppen and Gibbings, however.) A similar length dependence has been reported by Yamashita et al. (1993). In Fig. 21 we show data from misfit dislocation velocities in GeXSil-,/Ge(100) structures (Hull et al., 1994). These structures are in the low strain (x > 0.8) regime, such that the preferred dislocation type is b = a/2(101) (total dislocation), rather than the b = a/6(211) (partial dislocation) configuration, which would be expected at higher strains (see Section 111.8). Figure 21(a) shows that for comparably strained Ge,Sil-, layers ( E 0.008) grown on Ge(100) and Si(100) substrates, dislocation velocities are much higher for the Ge-rich alloy grown on the Ge substrate than for the Si-rich alloy grown on the Si substrate, as expected from the lower activation energy for dislocation glide in Ge than Si. In Fig. 21 (b) we show how these measurements of dislocation velocities in Ge,Sil-,/Ge( 100) structures follow the same scaling laws as the structures grown on Si substrates, as defined by Eq. 38(a). Studies of misfit dislocation velocities in GexSi~-,/Si(ll0) structures (Hull and Bean, 1993) have enabled comparison of the velocities of b = a/6(211) and b = a/2(101) Burgers vector misfit dislocations. As illustrated in Fig. 22, the partial dislocations actually have lower velocities than the total dislocations. This is somewhat surprising, as we would expect the motion of the total a/2(101) dislocation to be con-

-

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148

13 1

i 1

.-... -.

-t

-1

685A x=O 18, Si(100) 750A x=0.80, Ge(100)

____

A

8

_ _ _ _

10

9

l/kT -34~

i

11 (J-lxlO19)

.

1

I _J

12

I

FIG. 2 1. (a) Comparison of measured dislocation velocities in Ge,Sil-, layers with comparable atrain and excess stress grown on Si(100) and Ge(100) substrates. (b) Normalized dislocation velocities in Ge,Sil-, layers grown on Si(100) and Ge(100) substrates. Reprinted with permission from R. Hull er a/. Appl. Phys. Leu. 65, 327, Figures I and 3. Copyright 1994 American Institute of Physics.

G

-34 -36 -

-3 8 -40 -

-42 -

-44-46;

9 10 l/kT (J-1x1019)

FrG. 22. Experimental measurements of dislocation velocities for 60"a/2( 101) and 9Oou/6(211) misfit dislocations in Ge, Sil-, /Si( 110) heterostructures. Velocities are normalized according to Eq. (37).

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149

trolled by the slower of the two (i/6(211) partials into which it is dissociated, that is, the maximum velocity of the total dislocation would be limited to that of the slower of the two partials. Hull and Bean (1993) suggested that this apparent dichotomy can be resolved by consideration of details of the kink nucleation process (essentially the effect of stacking fault energies within the critical kink configurations). The data o n dislocation glide in bulk Si and Ge also reveals strong dependence upon dopant and other impurities (Hirsch 1981; Imai and Sumino, 1983; George and Rabier, 1987). Some measurements of dopant and impurity effects upon dislocation glide in Ge,Sil-, heterostructures have also been made. Gibbings et rtl. (1992) studied the effect of both p-type (€3) and n-type (As) doping upon dislocation velocities in strained Ge,Sil .-, layers grown upon Si( 100) substrates. Consistent with studies of doping effects upon dislocation velocities in bulk Si, it was found that high n-type doping (1 l o i 7 cm-j) could enhance dislocation motion in the Ge,Sil-., layer, while p-type doping had relatively little effect. The effects of very high (- 10'9-102"~ m - oxygen ~ ) concentrations upon dislocation glide velocities in strained Ge,Sil -.r layer have also been studied (Nix et al., 1990; Noble et al., 1991; Hull et al., 1991b). These studies concluded that misfit dislocation velocities were reduced and critical thicknesses for dislocation introduction increased, presumably by locking effects of the oxygen upon dislocation motion. Finally, Pethukov (1995) has considered the effects of compositional fluctuations within the GeSi alloy upon dislocation propagation.

4.

MIsm

DISLOCATION IKTERACTIONS

Interaction between misfit dislocations is a critical process in the later stages of plastic relaxation. The primary interaction mechanism arises from the force between two dislocation segments, which results from the interaction of the strain fields around them. As described by Eq. (16), this force is generally inversely proportional to the segment separation, and proportional to the dot product of the two dislocations Burgers vectors. Calculation of the exact magnitude, components and spatial variation of this force is complex for the general configuration, but relatively straightforward for simplified configurations (e.g., for parallel screw dislocations, the force per unit length, F / L = Gh2/2n). The most dramatic effect of misfit dislocation interactions is that they can pin motion of propagating dislocations, effectively leading to effects that are analogous to workhardening in metals (Dodson 1988, Hull and Bean, 1989b; Freund, 1990. Gosling etal., 1994; Fischer and Richter, 1994; Gillard and Nix, 1995; Schwarz. 1997), as illustrated experimentally in Fig. 23. To understand this, consider the case of a total dislocation propagating along an (011 ) direction in a (100) interface. and about to intersect a pre-

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FIG. 23. Experimental demonstration of misfit dislocation blocking events in a 300 nm S1/59 nm Ge0,18Si0,82/Si(100) heterostructure.

existing orthogonal interfacial dislocation, as illustrated schematically in Fig. 24. The excess stress driving dislocation motion is o,, = a, - 07. If the Burgers vectors of the two dislocations are parallel, there will be a repulsive interdislocation stress between them, which will act against the excess stress, and whose magnitude will depend upon the longitudinal coordinate along the threading arm (it will be highest at the points of closest approach near the interface, and lowest near the epilayer surface). As the two dislocations come closer, this repulsive stress will exceed the excess stress along greater fractions of the propagating threading dislocation, pinning motion of those segments of the threading arm. If enough of the threading arm is pinned, it will be unable to move past the orthogonal dislocation. This is clearly more likely to occur (because of the l / r dependence of the inter-dislocation force) in thinner epitaxial layers than thicker epitaxial layers. (Note that although the preceding discussion assumes a repulsive interaction, that is, parallel components of Burgers vectors, the discussion is

FIG. 24. Schematic illustration of the forces acting on a propagating threading dislocation ( B C ) when it encounters a pre-existing orthogonal misfit dislocation (D); cr, and oy are the Matthews-Blakeslee lattice mismatch and line tension stresses, respectively; OD is the horizontal component of the inter dislocation stress between D and B C .

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quantitatively the same for attractive interactions, that is, anti-parallel components of Burgers vectors, as the net stress is then reduced as the propagating dislocation attempts to pull away from the intersection event. For simplicity, we will assume repulsive dislocation interactions in subsequent discussion, but the concepts will be the same for attractive interactions.) Thus, dislocation pinning events are most likely in thinner layers. Substantial dislocation densities in thin layers occur more readily in structures that are initially more highly strained (because the critical thickness is lower and dislocation nucleation and propagation kinetics are more rapid than lower strained structures). Thus these pinning events tend to be more critical in growth of higher strain, lower thickness structures. This is one reason why, for a given amount of relaxation, higher strain systems have higher threading dislocation densities than lower strain systems (Hull and Bean, 1989b; Kvam 1990). The pinning process has been modeled in detail by Freund (1 990), Gosling et al. (1994) and Schwarz (1997). These authors evaluated the elastic integrals for this configuration, and modeled the regimes of epilayer thickness and strain ( h ,E ) where this blocking occurs. Results from the work of Freund are shown in Fig. 25. The formula-

-E

0

case

A

A

case

B

C

W J

FIG.25. Plot of minimum strain required for passage of a 60°a/2(101) misfit dislocation past a preexisting orthogonal 60"a/2(101) misfit dislocation at a Ge,Si~-,/Si(100) interface vs epitaxial layer thickness. The solid line marked A corresponds to the case where the misfit dislocations Burgers vectors are inclined at 90' to each other and the solid line marked B corresponds to the case where the misfit dislocations Burgers vectors are parallel to each other. The dashed line corresponds to the minimum strain analog to the critical thickness for misfit dislocation introduction. Reprinted with permission from L.B. Freund, J. Appl. Phys. 68, 2073, Figure 11. Copyright 1990 American Institute of Physics.

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R . HULL

tion of Gosling et al. (1995) is relatively amenable to analytical approximations, and to evaluation of a more general calculation, the mean position-dependent stress field om(I-) experienced by a propagating dislocation. Inspection of Fig. 25 shows that there is a region of ( h ,6) space for which dislocation blocking is possible. The lower bound of this region is defined by the critical , which dislocation motion is not energetically favored (indethickness h , ( ~ ) below pendent of any interaction processes). The upper bound is defined by the curve hb(&) (note that the locus of this curve depends upon the angle between the Burgers vectors of the intersecting dislocations). For intermediate thicknesses hc(&) < h < h b ( & ) , pinning of propagating dislocations will occur. For thicknesses h > hb(&),blocking will not occur, but the propagating dislocation will be slowed during approach to the intersection event (for a repulsive interaction stress), as the local net stress is reduced by the interaction stress. Conversely, as the propagating dislocation moves away from the interaction event, the net stress is increased by the repulsive interaction. Dislocation interactions also inhibit complete strain relaxation in any thickness of strained epilayer (this will have significant ramifications for the reduction of threading dislocation densities, as will be discussed in Section VI of this chapter). This is because as the residual elastic strain tends to zero, the blocking thickness hb(&)tends to infinity. Thus, in the latest stages of strain relaxation, dislocations will find it difficult to propagate past each other in any epitaxial layer thickness, leaving residual threading dislocation densities.

5 . KINETICMODELING OF STRAIN RELAXATION B Y MISFITDISLOCATIONS The processes of dislocation nucleation, propagation, and interaction define the kinetics of relaxation by misfit dislocations. There have been several attempts to combine these processes into predictive models of strain relaxation. Dodson and Tsao (1987) published the first comprehensive kinetic description of relaxation by misfit dislocations in Ge,Sil -n /Si heterostructures. They combined the concepts of excess stress, bulk parameters for dislocation propagation, and dislocation multiplication arising from a pre-existing dislocation source density, into a theory of plastic flow, thereby producing a predictive equation for strain (and hence dislocation density) for finite time at temperature

+

d [ A ~ ( t ) ] / d=r CG2(so- A & ( t )- Ecq)2(Ae(r) E,)

(39)

Here, A s ( t ) is the amount of strain relieved by misfit dislocations, EO is the initial lattice mismatch strain, E, arises from an initial “source” density of dislocations from which multiplication proceeds, eeq is the equilibrium strain in the structure, predicted by solution for E of Eq. (23) with oeX= 0, and C is a constant (C and E, were found to be 30.1 and lop4, respectively, from fitting to available data). Using this model, Dodson and Tsao were able to predict a wide range of experimental measurements of strain relaxation in GeSi heterostructures. In particular, they were the first to demon-

3

MISFITS T R A I N AND ACCOMMODATION

K I N E T I C MODEL ( 5 5 0 0I~

x

.

BEAN

153

E r AL

550'C 0 \

0

s 3 v lo -

-

KASPER

ET AL

750°C

K I N E T I C MODEL ( 7 5 0 ~ ~

0

0.01

0.02

0.03

LATTICE MISMATCH

FIG. 26. Predictions of temperature-dependent "critical thickness" (as defined by the Ge,Sil --x layer thickness at which misfit dislocations are first experimentally detected) from the Dodson-Tsao model and corresponding experimental data in the Ge,Sil -x/Si(lOO) system from Bean et al. (1984), Tg = 550 "C; and Kasper et al. (1975), Tg = 750OC. Reprinted with permission from B.W. Dodson and J.Y. Tsao, Appl. Phys. Lett. 51, 1325, Figure 3. Copyright 1987 American Institute of Physics.

strate convincingly that kinetic modeling of the minimum detectable strain relaxation (or equivalently, minimum misfit dislocation density) accurately predicted temperaturedependent critical thicknesses, as illustrated in Fig. 26. In subsequent work, Tsao et al. (1988) constructed a framework for describing relaxation kinetics by misfit dislocations in Ge,Sil -,/Ge( 100) heterostructures in terms of deformation mechanism maps (Frost and Ashby, 1982). Experimentally, it was found that temperature and excess stress were the critical parameters in determining plastic relaxation rates, consistent with thermal activation of dislocation nucleation and motion, as discussed previously in this section. For example, it was determined that the onset of detectable strain reiaxation (using Rutherford backscattering spectroscopy, with a detectable strain relaxation of 1 part in lo3) occurred at excess stresses of 0.024 G and 0.0085 G at 494 "C and 568 "C, respectively. This is consistent with much more rapid relaxation kinetics at the higher temperature. Dodson and Tsao (1988) subsequently developed scaling relations for relaxation by misfit dislocations in GeSi heterostructures as functions of temperature and excess stress

-

As(gex1,

Ti)/A&(oe,o, To) = (a,-xi/a,,o)2elE(g,exo)/kTo - E ( O ~ I ) / ~ T I(40) I

where A&(ce,1, T I )represents the degree of plastic relaxation for a structure with excess stress u , , ~at a temperature Ti during a growth or annealing cycle, and As(cr,,o, To) represents a relaxation standard for a structure with excess stress ae,0 and temperature

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R. HULL

To. The effective activation energy E(o,,J was determined to be given by (Dodson and Tsao, 1988) where T, is an effective alloy melting temperature obtained by a linear weighting of the melting temperatures of the pure components. Hull et al. (1989b) attempted to model the strain relaxation process in GeSi heterostructures by direct measurement of the fundamental parameters defining misfit dislocation kinetics, and subsequent incorporation into a kinetic model. The relevant measurements were made by direct in situ TEM observations and quantification of misfit dislocation nucleation, propagation and interaction processes, followed by incorporation into the equation'

where A&(t), L ( t ) , N ( t ) and u ( t ) are the degree of strain relaxation by misfit dislocations, total interfacial misfit dislocation length per unit area of interface, number of growing dislocations per unit area of interface and average dislocation velocity at time t , respectively. The integral is evaluated over all time for which a,, > 0, for either growth or post-growth annealing. Experimental descriptions are used for N ( t ) and v(r). The effects of misfit dislocation interactions are incorporated by reducing N ( t ) by the number of dislocations pinned according to the previous discussion in this section, and by incorporating an empirical velocity-stress-temperature relation in a regime where dislocation interactions strongly affect propagation rates (Hull et al., 1989a,b). Comparisons of this model with experiment are shown in Fig. 27. Subsequent models have modified and developed the concepts embodied in Eq. (42); Houghton (1991) applied a version of Eq. (42) to the initial stages of relaxation. In this regime, where misfit dislocation densities are low, dislocation interactions are relatively unimportant, and the integral in Eq. (42) simplifies to the product of the expressions for dislocation nucleation and propagation, which were directly measured by Houghton, and represented by the e q ~ a t i o n : ~

where NO is the initial source density of misfit dislocations at time t = 0. Typical measured values of NO were in the range 103-105 cm-*. Gosling et al. (1994) further *The exact relationship between A s and L ( t ) depends upon the shape of the substrate, and Eq. (42) is strictly true only for a square or rectangular substrate. For a circular substrate, a constant of proportionality 4/71 should be included in the middle expression in Eq. (42). 'Note that the equation's presentation here is identical to its presentation in work by Houghton (1991). The reason that it does not appear to be dimensionally correct is that various constants (e.g., a factor G-"') are combined into the perfactor term of I .9 x lo4.

3 MISFITSTRAIN A N D ACCOMMODATION

155

-

FIG.27. Comparison of the predictive strain relaxation model of Hull et al. (1989b) with experimental data for a 35 nm Ge0.2sSi0.75 layer annealed for 4 min at successively higher temperatures: (a) average distance between misfit dislocations p ; (b) areal density of threading dislocations N ; and (c) average misfit dislocation length 1. Reprinted with permission from R. Hull et al., J. Appl. Phys. 66, 5837, Figure 6. Copyright 1989 American Institute of Physics.

developed the concepts of Eq. (42), using more complete descriptions of misfit dislocation interactions, and a fittable form for dislocation nucleation. They were able to successfully reproduce the experimental data of Fig. 27. In summary, although the different models developed to date for predicting relaxation rates by misfit dislocations in Ge,Sil-, heterostructures may at first sight appear to have different forms, they generally attempt to combine the concepts of misfit dislocation nucleation, propagation, and interaction to construct a framework for predicting relaxation kinetics. In general, the framework of Eq. (42) has been adopted for this kinetic modeling. Quantitative implementation of this framework, however, will depend upon the strain and relaxation regimes under consideration. In general, a universal model for misfit dislocation relaxation kinetics is unlikely to have a simple analytical form due to existence of different mechanistic regimes, and due to the complexity of some of the constituent processes (e.g., interactions, multiplication).

VI. Misfit and Threading Dislocation Reduction Techniques 1.

INTRODUCTION

Silicon substrate wafers can now be routinely grown with fewer than 10 dislocations per cm’, representing a remarkable degree of structural perfection. Homoepitax-

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ial growth of Si can compete with this level of structural quality. If Ge,Sil-,-based strained layer epitaxy is to compete with existing device technologies, either it must offer unique and overwhelming advantages over bulk or homoepitaxial structures, or it must be of sufficient structural perfection to be compatible with existing processing technologies. In this section, we will discuss prospects and techniques for attaining Ge, Sil-, layers (especially supercritical structures) of the required structural quality. The magnitude of defect densities tolerable in device and circuit manufacture is a somewhat subjective (and controversial) topic, but maximum permissible densities of order lO5cmP2 in majority carrier devices, lo3 cmP2 in discrete minority carrier devices, and I0 cmP2 for Si integrated circuit technology are the ranges of numbers typically quoted. The only reliable way to avoid misfit and threading dislocations in strained layer epitaxy is to remain below the equilibrium critical thickness, and many technological applications of Ge,Si 1 -,are evolving towards subcritical layers. This, however, places extremely severe limitations on layer thicknesses, as demonstrated by Fig. 1 1, which will have ramifications for device growth, processing, and doping. An example where such layer dimensions are compatible with these constraints, however, is the Si/Ge,Sil-,/Si heterojunction bipolar transistor (Harame et al., 1995a,b), where a fortuitous combination of strain-induced bandgap lowering and a high valence band offset have allowed useful bandgap variation at relatively low x , thus enabling Ge,Sil -, base layers which can be of practical use, while remaining below the critical thickness. Tolerably low defect levels may also in principle be achieved by growth in the metastable regime, that is, at layer thicknesses greater than the Matthews-Blakeslee equilibrium critical thickness, if the structure is grown at sufficiently low temperatures, strains, and excess stresses that the misfit defect density is still relatively low. Post-growth thermal exposure during device processing will cause further nucleation and propagation of dislocations, however. To prevent further significant degradation, therefore, each time-temperature cycle during processing would typically be restricted to less than that of the original growth cycle. This may be an impractical restraint. In addition, device fabrication processes may enhance plastic relaxation. For example, Hull et al. (1990) have shown that contact implantation and thermal activation in a Si/Ge,Sil-, /Si heterostructure significantly enhances misfit dislocation generation rates compared to unimplanted structures, via formation of high densities of misfit dislocation sources from condensation of point defects into dislocation loops during implant activation.

2.

BUFFERLAYERS

An important technique for attempting to separate device quality material regions spatially from dislocated interfaces is incorporation of sacrificial buffer layers (e.g. Kasper and Schaffler, 1991). In this concept, a thick (of order 1 ,urn) Ge,Sil-, layer is

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grown upon the Si substrate, such that almost complete relaxation of lattice mismatch strain occurs via misfit dislocation generation. This produces a fully developed interfacial misfit dislocation array, with a residual density of threading dislocations traversing the buffer layer to the growth surface. The device-quality material is then grown upon the buffer layer (and generally, closely lattice-matched to it). In this configuration, the density of threading dislocations extending through to the device will be the important metric for structural quality. Several techniques have been developed for filtering these threading dislocations, to reduce their density to acceptable levels.

3.

THREADING DISLOCATION FILTERING

a. Introduction One mechanism for filtering of threading dislocations is for the misfit segments to grow sufficiently long that they terminate at the edges of the wafer. The ideal relaxed epilayer configuration would then correspond to two orthogonal sets of parallel, equally spaced (011) dislocations running across the entire (100) wafer. This would result in no threading dislocations propagating through the buffer layer. In practice, finite dislocation propagation rates and blocking via dislocation interactions prevent this (see Section V of this chapter). Dislocation propagation can be enhanced either by growing at higher temperatures, or by post-growth annealing (the latter may be preferred due to likely surface morphology problems in strained layer growth at higher temperatures). Lateral motion to the edges of a standard Si wafer (i.e., diameter 10-20 cm), however, is still highly improbable because as relaxation by dislocations proceeds towards its equilibrium limit, the excess stress becomes increasingly low causing (i) dislocation blocking to become increasingly prevalent and (ii) propagation velocities to become increasingly low. Dislocation interactions, however, can be exploited to advantage if dislocation annihilation processes can be encouraged. As illustrated in Fig. 28, threading dislocations of opposite Burgers vectors can attract each other and annihilate, transforming two dislocation loops into one, and removing two threading dislocations from the structure. Both thermal annealing (either during growth or post-growth), and growing the buffer layer to greater thicknesses will enhance the total annihilation probability. These processes can be extremely effective at high threading dislocation densities, where such interaction events are statistically likely, but as the density decreases, so does the probability of further dislocation interactions and further defect reduction. This renders the annihilation process virtually ineffective at lower threading defect densities. Typical threading defect densities in uniform buffer layers grown with an abrupt interface to 1 p m for strains > 1% the substrate are of order 107-109 cm-2 after growth of (Kasper and Schaffler, 1991). Lower strain systems may allow perhaps one order of magnitude reduction in this density because of reduced dislocation pinning events.

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R. HULL

158

FIG. 28. Schematic illustrationa of possible mechanisms for dislocation threading arm interactiodannthilation events in a strained layer superlattice. Reprinted from R. Hull and J.C. Bean, Chapter 1 , Semiconductors und Semimetals, Vol. 33, ed. T.P. Pearsall, (Academic Press, Orlando, Florida, 1990).

Note that differential thermal expansion coefficients are significant in this geometry, as they may cause substantial defect generation in structures that are fully relaxed at the growth temperature. Thus in the Ge,Sil-,/Si( 100) system, complete relaxation of the compressive lattice mismatch stress at the growth temperature will result in a tensile strain during cooldown due to the higher thermal expansion coefficient of Ge, Sil --x than Si. This can generate new misfit dislocations or cause extended splitting of the a/6(211) partial dislocations, which constitute a dissociated a/2( 101)total dislocation, as discussed in Section 111.7, leaving a 90" a/6(112) partial at the (100) interface. b.

Graded Layers

A promising technique for minimizing dislocation blocking processes in buffer layers is continuous grading of strain in the buffer layer. Compositional grading of buffer layers in the Ge,Sil-,/Si system (e.g. Fitzgerald et ~ l . 1991; , Tuppen et nl., 1991) has yielded threading defect densities in the range 105-106 cm-* for lattice mismatch strains as high as 3% and buffer layer thicknesses in the range 1-10 pm. The main benefit of such compositional grading is that instead of the misfit dislocations being confined to a single Ge,Sil-,/Si interface, there will be a distribution through the epilayer to compensate for the continuously varying strain field. This provides an extra degree of freedom for misfit dislocations to propagate past each other (as they may be at different heights in the structure) and thus minimize pinning events. The vertical distribution of misfit dislocations can also vary during specimen cooldown after growth, minimizing the effects of differential thermal expansion coefficients. There has been considerable work on modeling and measurement of strain relaxation in such compositionally graded layers (Tersoff, 1993; Shiryaev, 1993; Tongyi, 1995; Mooney et al., 1995; Li et al., 1995). In particular, it is observed experimentally (and predicted theoretically) that dislocation pileups within the graded layers can cause significant surface

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morphology (Shiryaev et al., 1994; Samavedam and Fitzgerald, 1997), with significant ramifications for technological applications of these structures. Such effects can be ameliorated by growing on off-axis substrates (Fitzgerald and Samavedam, 1997) and by intermediate chemical-mechanical polishing stages (Currie et al., 1998).

c. Strained Layer Superlattices The probability of threading dislocation annihilation processes can be substantially enhanced by providing specific directions for threading dislocation motion. This is the underlying concept of strained layer superlatrice filtering, originally proposed by Matthews and Blakeslee (1974, 1975, 1976). This technique consists of growth of a stack of strained layers, generally on top of the relaxed buffer layer. The thickness and strain of each individual layer within the stack is designed to be insufficient to allow significant nucleation of additional dislocations, but sufficient to deflect threading dislocations into being misfit dislocations at the superlattice interfaces (this translates effectively into the criterion that the MB critical thickness be exceeded, but not by too much!). For a (100) interface the interfacial misfit dislocations are constrained to move along the interfacial (011) directions, thereby increasing the probability of their meeting, interacting, and annihilating (compared to random motion of threading dislocations within their slip planes in the absence of the superlattice). Many groups have since claimed successful application of this technique, in a range of different strained layer semiconductor systems e.g. (Olsen el al., 1975; Dupuis et al., 1986; Liliental-Weber et al., 1987). Typically, threading dislocation density reductions from the range 108-109 cm-2 down to 106-107 cm-2 were claimed. However, again as the threading dislocation densities decrease, the probability of interaction and annihilation also decreases. Quantitative analysis of these probabilities (Hull et al., 1989c) suggests that defect densities much below lo6 cm-= are unlikely to be achieved. d.

Limited Area Growth

A very promising approach to reducing threading dislocation densities is limited area epitaxy, that is, growth on mesas or in windows, typically with dimensions in the range 10-100 pm. One potential advantage of the limited area is that the number of heterogeneous dislocation nucleation sites within this reduced growth area may be vanishingly small, thus inhibiting generation of misfit dislocations altogether (at sufficiently high strains, however, quasihomogeneous nucleation at the mesa edges is likely to operate). The most important advantage, however, is in reduction of threading dislocation densities, as the dislocation now only has to propagate a far more limited distance to reach the mesa edge than it would have to reach the wafer edge. The classic original demonstration of the potential of this potential of this technique is that by Fitzgerald et al. (1988, 1989) in the In,Ga~-,As/GaAs(100) system, as illustrated in Fig. 29, and

R. HULL

160 1

3000

I

100

0

200

300

400

500

Circle Diometer (microns)

3000

.-. f

>

b

2500

-

2000

.

1500

-

0

D

2

I

v L 0

-g

O[110]

1000

0

.t

500

_I

0 0

I00

200

300

400

500

circle Diameter (misrona)

FIG. 29. Illustration of the benefits of reduced area growth: linear density of interfacial misfit dislocations vs mesa diameter for 350 nm Ino.osGag.9sAs layers grown onto GaAs substrates with (a) 1.5 x lo5 cm-' and (b) lo4 cmP2 preexisting dislocations in the substrate. Reprinted with permission from E.A. Fitzgerald et al., J. Appl. Phys. 65, 2220, Figures 4(a) and 4(b). Copyright 1989 American Institute of Physics.

subsequently developed by several other groups in a range of strained semiconductor systems (Matyi et al., 1988; Lee et al., 1988; Guha et al., 1990; Noble et al., 1990; Knall et al., 1994). The primary disadvantages of the limited growth area technique are the reduced dimensions for device processing, and in configurations such as mesa growth, a highly nonplanar geometry, which may be incompatible with some processing steps. One at-

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161

tempt to address these shortcomings was described by Hull et al. (1991~)who devised a substrate patterning technique involving a two-dimensional array of oxide dots, in which neighboring dots were slightly offset from each other with respect to the interfacial (011) directions. Thus any misfit dislocation traveling along an interfacial (011) direction must intercept a dot within a path length, A given by simple geometrical analysis as A = L 2 / s , where L is the interdot spacing and s is the offset of neighboring dots along the interfacial (011) directions. The misfit dislocation can then terminate at the crystal/amorphous interface at the dot, thereby annihilating the threading dislocation. Thus the advantages of the limited growth area approach (finite misfit dislocation propagation lengths for threading dislocation annihilation) are retained in this dot array, while allowing connectivity of the structure across the entire wafer, and planar geometries (if the epitaxial layer thickness is approximately equal to the oxide dot thickness). Residual threading defect densities lo5 cm-* were reported for MBEgrown Ge,Sil-, layers 200-800 nm thick with x = 0.15-0.20 on the patterned wafers, whereas growth on unpatterned wafers typically yielded threading dislocation densities one to two orders of magnitude higher. Post-growth annealing of the patterned structures to temperatures as high as 900 “Ccaused the structure to relax almost completely to equilibrium, dramatically enhancing interfacial misfit dislocation densities, but with threading dislocation densities typically remaining < lo6 cmP2.

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VII. Conclusions The following are summaries of the salient points of each preceding section: The lattice constants of Ge,Sil-, may be estimated with reasonable accuracy by linear interpolation of the lattice parameters of Ge and Si. The strain in a Ge,Sil-,based heterostructure arises primarily from lattice parameter differences. Differential thermal expansion coefficients produce a second-order effect. There are four primary mechanisms for lattice-mismatch strain accommodation: (a) elastic distortion of the epilayer; (b) roughening of the epilayer; (c) interdiffusion; and (d) plastic relaxation by misfit dislocations. Of these mechanisms, (c) is only significant at very high-growth temperatures, or for ultrathin layers. Mechanism (d) requires a minimum layer thickness (the “critical thickness”) to operate. Mechanism (b) is prevalent, especially at higher temperatures and strains. Strain not accommodated by mechanisms (b)-(d) is accommodated by mechanism (a). There are extensive and rigorous elastic descriptions of dislocation structure and properties. Atomistic details at the dislocation core are not so well understood. Depending on the predictions of the Thompson tetrahedron construction, we need to consider the possibility of b = a/6(211) partial misfit dislocations, as well as conventional b = a/2( 101) total misfit dislocations in the diamond cubic Ge,Sil-, lattice.

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(IV) The Matthews-Blakeslee model provides an excellent framework for the critical thickness for relaxation by misfit dislocations. Other models generally either fall into the category of a broadly equivalent energetic approach, or into the category of developments/refinements of the MB theory. Accuracies within a factor two (better at lower strains) should be expected for application of the basic MB model. For configurations where the Thompson tetrahedron construction predicts that the lattice-mismatch stress acts so as to increase dissociation of a / 2 ( 101) total dislocations into a/6(211) partials, the partial misfit dislocation configuration will be favored at higher strains and lower epilayer thicknesses.

(V) Finite misfit dislocation nucleation and propagation rates prevent strain relaxation from keeping pace with the equilibrium condition for typical growth temperatures and times. This produces metastable (defined as a,, > 0) regimes of growth in Ge,Si 1 heterostructurep, which become increasingly broad with decreasing growth temperature. Consequently, relaxation by misfit dislocations is often experimentally detected only in Ge,Sil -, layers substantially thicker than predicted by the MB equilibrium theory, the discrepancy increasing with decreasing strain and temperature. Analysis of observed relaxation processes shows that enormous lengths of misfit dislocation need to be generated, and very high source densities are required. Considerable uncertainty remains about the dominant misfit dislocation nucleation mechanisms in different regimes of strain, epilayer thicknesses and temperature in the Ge,Sil-,/Si system. The generic mechanisms for dislocation sources are homogeneous, heterogeneous, and multiplication. True homogeneous nucleation requires high lattice mismatch strains of order 3 4 % , or greater. “Quasihomogeneous” nucleation, that is, nucleation aided by inherent physical properties of the structure, such as random concentrational clustering or surface roughening during growth, can lower this minimum strain threshold down to 1%. Below this threshold, heterogeneous or multiplication mechanisms operate. Heterogeneous sources are necessarily limited in high quality epitaxial growth, and plastic relaxation that relies solely upon heterogeneous nucleation will be very sluggish. Multiplication mechanisms can act as efficient dislocation sources, apparently in any strain regime, but generally require minimum layer dimensions (of order hundreds of nanometers) to operate, and typically require precursor heterogeneous sources. In general, relaxation at low strains is nucleation-limited. Experimentally, there is a paucity of nucleation rate data in the Ge,Sil-. system. Good experimental descriptions of 60”a/2( 101) misfit dislocation propagation velocities exist for the (Si)/Ge,Sil -,/Si( 100) system. Observed velocities follow broadly the same trends as those determined from bulk deformation experiments of Ge and Si. Dislocation velocities depend upon strain, epilayer thickness, and Ge concentration, and monotonically increase with these parameters. Again, the propagation component of relaxation by dislocations is much more rapid in the high

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strain regime. Observations in the Ge,Sil-,/Si( 1 10) system allow propagation velocities of a/2(101) and a/6(211) dislocations to be separately determined. Dislocation interactions are very important in plastic relaxation, particularly in thinner films and in the terminal stages of strain relief, where orthogonal interfacial dislocations can pin each other’s motion. Such pinning processes can stabilize high threading dislocation densities in the structure. Kinetic models of strain relaxation rates, incorporating the concepts of dislocation nucleation, propagation, and interaction rates have been developed, and show reasonable predictive capability. These models are generally based upon the concepts of excess stress, thermal activation of dislocation nucleation and propagation, and interaction blocking events. VI) Many techniques have been developed to reduce threading dislocation densities in Ge,Sil -,/Si structures. These techniques rely on removing threading dislocations by annihilation either with other defects or by propagation to the edge of the epitaxial growth area. Strained layer superlattice filtering relies on threading defects annihilating through interaction, but this interaction probability decreases as the threading defect population decreases, running out of steam for areal densities less than about lo6 cmP2. Thick, compositionally graded layers appear to be promising in producing low threading dislocation densities, probably because the threading dislocations are less subject to interaction pinning events as their accompanying misfit segments are distributed vertically through the graded structure. Substantial surface morphology can develop from dislocation pileups, however. Reduced area (e.g., mesa) growth schemes result in lower threading dislocation densities both because of reduced probability of dislocation nucleation within the reduced area, and because threading dislocations have to propagate much smaller distances to terminate at the edge of the growth area.

ACKNOWLEDGMENTS The author would like to thank a large number of colleagues, past and present, for collaborations and contributions to my understanding of this field. These include: J. Bean, D. Bahnck, J. Bonar, D. Eaglesham, G. Fitzgerald, L. Feldman, M. Green, M. Gibson, G. Higashi, Y. Fen Hsieh, T. Pearsall, R. People, L. Peticolas, F. Ross, K. Short, B. Weir, A. White, Y. Hong Xie (with all of whom I collaborated during my tenure at Bell Laboratories); E. Kvam (Purdue University); B. Dodson and J. Tsao (Sandia); J. Hirth (Washington State University); M. Albrecht and H. Strunk (University of Erlangen, Germany); D. Perovic (University of Toronto); D. Houghton (National Research Council of Canada); C. Tuppen (British Telecomm); D. Noble (Stanford University); B. Freund (Brown University); F. LeGoues, B. Meyerson, K. Schonenberg, D. Harame, R. Tromp and M. Reuter (IBM); P. Pirouz (Case Western); and W. Jesser, E. Stach, J. Demerast and Y. Quan (University of Virginia).

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Fundamental Physics of Strained Layer GeSi: Quo Vadis? M. J. Shaw and M. Juros DEPARTMENT OF PHYSICS THEU N I V E R S I T Y O F NEWCASTLE

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I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . 11. PERFECTSUPERLATTICE SYSTEMS. . . . . . . . . . , . . . . , . . , . . 1. Basic Concepts of Superlattice Bandstructures . . . . . . . . . . . . . . 2. GeSi Bandstructures from Empirical Pseudopotential Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. ELECTRONIC STRUCTURE OF IMPERFECT A N D FINITESYSTEMS . , . . . 1. Bandstructure of Ordered and Disordered Systems . . . . . . . . . . . . 2. Oprical Transitions in a Finite Superlattice . . . . . . . . . . . . . . . . IV. LUMINESCENCE AND INTERFACE LOCALIZATION . . .. ... ...... 1. Experimental Optical Spectra of SiGe Systems . . . . . . . . . . . , . . 2. Impurities at Interface Islands . . . . . . . . . . . . . . . . . . . , . . V. MICROSCOPIC SIGNATURE OF GESIINTERFACES . . . , . . . . . . . . . 1. First-Principles Calculations of Si/Ge Superlattices . . . . . . . . . . , 2. Inte$ace-lnduced Localization at Donor Impurities . . . . . . . . . . . 3. Defect Perturbations to Conduction States . . . . . . . . . . . . . . . . 4. Localization at Ge Impurities in Si Layers . . , . . , . . . . . . . . . . VI. MICROSCOPIC ELECTRONIC STRUCTURE EFFECTS I N OPTICAL SPECTRA VII. CONCLUSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . .

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I. Introduction The GeSi system has two key applications: in electronic switching (e.g., fast transistors) and in optical devices integrable with Si and SiGe circuitry. Whereas electronic switching applications are well established in the market place, the viability of optical applications is still doubtful. The optical response is weak, unstable at higher temperatures and together with other merit parameters (dark current, spectral shape, etc.) uncomfortably sensitive to material preparation. However, both application domains Copyright @ 1999 by Academic Press All rights of reproduction in any farm reserved ISBN 0-12-752164-X

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rest on the common basic physics, that is, on the possibility of making a heterojunction potential barrier at the Si/GeSi interface which has a number of well-controlled tunable properties (e.g., barrier height, transition strengths). In other words, as far as basic microscopic physics is concerned the success or failure of any GeSi technology depends on our understanding of the interaction between excited carriers and the interface. In transport devices this interaction determines the mobilities, channel widths, and lifetimes. In optical devices it also determines the quantum efficiency of absorption and emission, the dark current, and the operational wavelengths. A long list of other parameters could, of course, follow. Furthermore, there is a strong link between optical and electronic processes in that one can serve as a diagnostic tool for applications involving the other. Whereas electrical measurements tend to inform about sums of many different contributions, the optical spectra are often highly selective to specific scattering and excitation processes and it is therefore the latter that figure prominently on the theorist’s agenda. In this chapter we aim, first, to outline briefly the key ingredients and tools required in developing quantitative models of microscopic interactions at interfaces. Second, we set out to identify a research agenda where microscopic physics is an indispensable tool in promoting this class of technologies. We argue there that the latest experimental evidence (particularly optical spectra) points to a radically different class of interactions that may significantly affect the carrier dynamics in this heterostructure system. It would appear that the key features of this behavior do not arise from the particle-ina-box confinement and related interface interference or scattering normally considered in the literature, but instead must be sought in the intrafacial parameter space of the interface-related bonds. One of the most general features of GeSi heterostructures is the strain that arises through the difference in the equilibrium lattice constants of bulk silicon and germanium. While the most commonly studied heterostructure systems, AIGaAs-GaAs, are almost perfectly lattice matched (with mismatch of order 0.1%), silicon and germanium have a lattice mismatch of over 4%. Despite the large lattice mismatch, it is possible to grow high-quality pseudomorphic strained layers, provided suitable growth conditions prevail (Bean et al., 1984; Bean, 1985), and provided the layers are sufficiently thin. In addition to making pseudomorphic growth of layers more difficult, and leading to restrictions on layer dimensions that can be grown, one of the consequences of strain is to rule out one of the simplest and most intuitive of the bandstructure models available for the study of lattice matched systems. The effective mass approximation (EMA) method, detailed in a review by Ando et al. (1982), neglects the microscopic crystal potential variations in the two materials, and represents the heterostructure by assuming a steplike electrostatic potential barrier at each interface. This leads to the simple “particle-in-a-box’’ picture, which provides a good description of the states in latticematched systems such as AlGaAs-GaAs. However, as described in Jaros (1990), the model breaks down for systems with significant strain, such as the GeSi layers of interest here. Clearly, in a strained layer the atoms occupy sites significantly shifted from

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the bulk-like lattice, and the neglect of the microscopic potential variations becomes invalid. It is therefore necessary to use a microscopic formalism, in which the detailed atomic positions and potentials may be taken into account. One such approach is the empirical pseudopotential (EPP) method, described in the literature for bulk semiconductors by Cohen and Bergstresser (1966) and Chelikowsky and Cohen (1976), and extended to superlattice structures by Wong et al. (1986) and Gel1 et al. (1986). In this microscopic formalism, the bulk constituents are described by a pseudopotential chosen such that a number of empirically known bandstructure properties (e.g., bandgaps, effective masses) are reproduced. The case of the superlattice or microstructure may then be treated as a perturbation to one of the bulk constituents, its wavefunction being expanded over a complete set of the bulk eigenfunctions. The superlattice perturbation potential is simply the difference between the host potential and that of the other bulk constituent. As this potential is constructed for each atom in the unit cell of the superlattice, the correct strained positions of the individual atoms (determined from elasticity theory) can be incorporated. As a result the EPP scheme enables us to obtain a good description of the bandstructure of periodic microstructures even where there is a large strain. Because the microscopic variations in potential between the layers are taken into account, the bulk momentum mixing resulting from the scattering of electrons encountering the misplaced atoms is fully described. The EPP scheme still includes an abrupt step in the potential at the interface, the valence band offset. This is found to play an important role in the EPP calculation, and is a parameter of continued experimental and theoretical debate (see review by Franciosi and Van de Walle, 1996). The role of the band offset is discussed in more detail in Section 11. Also, this step-like treatment of the interfaces represents a limitation on the scope of the EPP description. Any physical processes that are governed by the microscopic properties of the interface region itself will not be included. Empirical pseudopotential calculations have been shown to correctly predict many of the observed properties of GeSi layers, and have led to a physical understanding of many optical and transport phenomena. Much of the theoretical work published on GeSi heterostructures assumes ideal, perfectly ordered crystals. The EPP approach can be extended to the case of imperfect systems through the study of larger supercells in which pseudorandom or reconstructed interfaces can be represented. Further approximations are required in this process as the empirical potentials, fitted with regard to the bulk constituents, must be applied to the individual atoms in the disordered layers. Similarly, the prediction of atomic positions using bulk elastic properties becomes less reliable. However, the EPP does enable a microscopic description of the imperfections to be formulated, and for the effect of these to be determined. Where the deviations from the bulk-like structure are too great, for example, in the presence of an impurity atom about which large lattice relaxation takes place, the EPP approach may become unsuitable. In such cases, as in situations where the microscopic interface features are to be studied, it is necessary to consider a more sophisticated microscopic model.

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The local density approximation (LDA) of density functional theory (Hohenberg and Kohn, 1964; Kohn and Sham, 1965) and ab initio pseudopotentials provide a microscopic description that does not make reference to the bulk crystal properties. These nonlocal norm-conserving pseudopotentials, derived to describe the electronic structure of the free atoms themselves (Bachelet et a!., 1982), are fully transferable, describing the properties of a particular atomic species regardless of its local environment. Application of such a scheme is therefore ideally suited to the study of disordered layers and defects, where no reference need be made to bulk-like characteristics, and for studies in which short-range effects are important. A variety of LDA calculations have been used to provide detailed analyses of the electronic structure of short period Si-Ge superlattices (e.g., Froyen et al., 1988; Satpathy et at., 1988; Schmid et a!., 1991). These computationally intensive schemes provide a very accurate description of the valence bands through minimization of the ground-state total energy, and are particularly effective in describing structural properties of the system such as the position of atoms. In addition, the formalism does not require any additional empirical data such as the valence band offset. The microscopic potential variation in the interface region is fully included in the calculation, as compared with the steplike interface represented in the EPP approach. Such LDA calculations are therefore clearly superior to the EPP method for studies of the microscopic properties associated with the interface region of the microstructures. There are many competing factors governing the choice of model to suit a particular problem. The ability of the LDA to predict the structural relaxations of a system accurately, and describe short-range features such as the microscopic interface potential provide it with a clear advantage over the empirical approach. However, such advantages must be balanced against the increased computational effort required. While the EPP can readily be used to study structures with unit cells containing many thousands of atoms, the increased complexity of the LDA calculations restricts the unit cells that may be studied to a few hundred atoms on comparable computers. This represents a very real limitation to the LDA approach, particularly where the dimensions of the unit cell are large in all three dimensions. On a physical note, while the LDA provides a particularly accurate representation of the ground state of the system, and hence gives a very good account of the occupied valence states, the excited states of the system are not so well described. One well-known consequence of this is the tendency for the LDA to underestimate vastly the magnitude of the bandgap (an error of order 50%). As the empirical pseudopotentials are specifically chosen to describe the states at and around the conduction and valence bandedges such a problem does not exist for the EPP method. Both methods therefore have a role to play in developing a full understanding of the physics of GeSi layers. The most appropriate method to use depends in each case upon the nature of the particular system being considered and the specific properties or effects being studied. In this chapter we apply the theoretical models described in the preceding text to a study of some of the essential physical properties of GeSi strained-layer heterostruc-

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tures. The study focuses on the microscopic features of the structures that determine their key electronic and optical properties, and leads in particular to a detailed examination of the properties associated with the heterointerfaces themselves. We choose to concentrate on examples relating to optoelectronic device applications, where the parameter of greatest interest is the optical strength of the direct transition. For effective device design it is essential that the nominal growth parameters of the heterostructure (i.e., its layer widths and alloy compositions) can be related to the bandgap and the strength of the no-phonon transition. In order that this is possible, microscopically, we must identify the origin of this transition, and the degradation which might be expected as a result of structural imperfections, such as disordered layers and impurity defects. A similar understanding is important for the other parameters that determine the performance of the device, such as the carrier masses and mobilities. In addition, while the foregoing discussion has been restricted to the case of the linear interband optical response, there is considerable technological importance attached to the intersub-band response and nonlinear processes such as harmonic generation. As we shall show, while many of the GeSi superlattice properties thus predicted are in good agreement with the observations of experiment, there are also significant discrepancies. In particular, experimental observations of photoluminescence spectra suggest that the origin of the no-phonon transition is different to that predicted by most theoretical models. Clearly, this origin must be identified if the strength of the transition is to be controlled. These issues are addressed in the following sections. Section I1 provides an introduction to some of the basic concepts in superlattice bandstructure physics, such as zone-folding and the band offset. Empirical pseudopotential calculations of perfect Ge/Si superlattices are used to illustrate these concepts, and to demonstrate the link between parameters such as the layer widths and compositions and key physical properties. The effect of interface disorder and reconstruction on the strength of the direct optical transition is studied in Section 111. The case of randomly disordered interfaces is investigated, using the EPP methods. Calculations are also presented for interfaces modeled according to the chemically driven reconstructions that have been observed in these structures. In practice, a finite number of superlattice periods must be grown. Calculations are presented that address the issues raised by this limit to the overall length of GeSi superlattices. Optical experiments on GeSi microstructures have indicated that EPP calculations, even with the inclusion of disorder and imperfections as described in the preceding sections, are not able to predict the response of superlattices satisfactorily. It is apparent that there is an additional physical effect that is playing a key role in the optical behavior. In Section IV the experimental observation of luminescence from SiGe structures is discussed, and the difficulty in providing a satisfactory theoretical explanation of the experimental findings is described. An argument is put forward for the proposal that localization at the interfaces is responsible. Real GeSi superlattice structures are known to exhibit islanding at the interfaces. Such islands modify the behavior of impurities in

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the structures-EPP calculations are presented to provide a qualitative illustration of this process. Section V examines the role that the microscopic properties of the interfaces themselves might play in the anomalous localization of charge at the interfaces, and how this might explain experimental luminescence measurements. The LDA calculations are presented for a number of impurities situated adjacent to the Si-Ge interfaces to study the effect on the impurity levels. These calculations provide a full description of the potential variations within the interface bond region, and the interaction between this and a variety of defects is investigated. In Section VI we focus on how a number of features in the microscopic electronic structure of Si/GeSi superlattices may affect the optical spectra produced. We demonstrate how external electric fields modify the optical response of the structures. We briefly examine some of the microscopic bandstructure features that must be considered in the design of optical detectors, through the calculation of absorption spectra. Finally, we show how manipulation of the higher-lying superlattice minibands may be used to enhance second-order nonlinearities in the optical response of GeSi superlattices. Section VII presents a brief summary of the microscopic physical processes that have been identified in the response of the heterostructures, and the principal conclusions are outlined.

11. Perfect Superlattice Systems 1. BASICCONCEPTS OF SUPERLATTICE BANDSTRUCTURES The natural starting point for any theoretical study of GeSi microstructures is a discussion of the physical properties of the bulk silicon and germanium themselves, and of strained and unstrained Ge,Sil-, alloys. The effects associated with the formation of ordered layers of these materials may then be addressed with reference to their bulk properties. As a result of their wide technological application, both silicon and germanium have been extensively characterized (e.g. Hellwege, 1982). Further, the theoretical description of their electronic bandstructure through the use of empirical pseudopotentials is well-established. There are two features of bulk silicon and germanium that are particularly relevant to the physics of their microstructures, namely, the indirect bandgaps and the difference in lattice constants. Both silicon and germanium are indirect-gap semiconductors, with conduction band minima lying away from the Brillouin zone center. The separation in k-space of the valence band maxima (which occurs at the zone center r) and the conduction band minima prevents optical transitions across the gap from occurring without the assistance of phonons. The bandstructure of bulk silicon, calculated using the empirical pseudopo-

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X

FIG. 1 . Bandstructure of bulk Si plotted along the symmetry lines L - r - X , where I- is the Brillouin zone center and L and X are the wavevectors 2 n / a ( 1 / 2 , 1/2, 1/2) and 2n/a(1,0,0),respectively.

tential approach, and with the particular pseudopotentials of Friedel et al. (1988), is plotted in Fig. 1 between the zone center r, and the edge of the Brillouin zone along the [ 1001 direction X , and along the [ 1111 direction. The conduction band minimum is seen to have wavevector 2n/a(0.8,0,0). The silicon Brillouin zone has six of these minima (the A valleys) lying along the coordinate axes. Note that the effects of spin-orbit coupling are not included in the pseudopotentials of Friedel et al. While this makes a very small change to the Si bandstructure, the effect on the bandstructure of Ge is more significant. The spin-orbit interaction breaks the 6-fold degeneracy at the valence bandedge, raising the energy of the highest state (for a full discussion of the role of the spin-orbit potential, see, e.g., Kittel, 1987). While this has some effect on the absolute magnitude of the bandgap, to a degree which depends on the particular material in question, the electronic structure of the conduction bands is virtually unchanged. Certainly, our discussions concerning the nature of the gap are not affected by the inclusion of spin-orbit coupling. For germanium, whose calculated bandstructure is plotted in Fig. 2, the lowest conduction valleys are the L-valleys, where L labels the wavevectors 2n/a(f1/2, f 1 / 2 , &1/2). Design of superlattices suitable for optical devices therefore focuses on ways to engineer a direct bandgap. In many practical situations the design of suitable structures involves the specification of layers of Ge,Sil-, alloy. The empirical pseudopotential formalism is based upon the concept of a periodically repeating system. While this is appropriate in the case of pure bulk materials, the random distribution of the different species in an alloy

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L

r

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FIG.2. Bandstructure of bulk Ge plotted along the symmetry lines L - r - X , where r is the Brillouin zone center and L and X are the wavevectors 2n/a(1/2. 112, 112) and 2 x / a ( l ,O,O), respectively.

clearly breaks the translational symmetry of the crystal. In theory, then, one cannot define a unit cell for an alloy system. Of course, it is possible to obtain a good description of an alloy by defining a very large unit cell in which the alloy atoms are randomly assigned. However, such a description of alloys, particularly in the treatment of alloy layers in heterostructures, proves costly in terms of computational effort. An alternative approach that is able to provide a good description of many alloy systems, including the Ge,Sil-, alloy of interest in this paper, is available, namely, the virtual crystal approximation (VCA) (Jaros, 1985). The VCA assumes that the physical properties of an alloy, such as its lattice constant, potential, and so on, may be interpolated between the individual constituents. The alloy is then treated as a perfect “virtual crystal” having these interpolated properties. This restores the translational symmetry of the system enabling the empirical pseudopotential technique to be used. The bandstructure obtained for a Geo.sSi0.5 alloy using the VCA with a linear interpolation is shown in Fig. 3. The variation of the indirect-gap with alloy composition is shown in Fig. 4, in relatively good agreement with the findings of Braunstein et al. (1958). Here we have explicitly included the reduction in bandgap associated with the spin-orbit interaction, an effect which increases with the germanium content. While the linear VCA unsurprisingly fails to reproduce the bowing observed experimentally, the essential qualitative features are well represented. In particular, the crossover of the Si A minimum and Ge L minima is clearly seen at x 85% Ge content. For the calculations presented here the VCA is used for alloy layers except where we are particularly inter-

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FIG.3. Bandstructure of unstrained Si0.5Geo.s alloy plotted along the symmetry lines L-T-X, where r is the Brillouin zone center and L and X are the wavevectors 2 x / a ( 1/2, 1/2, 1/2) and 2n/a( 1,0,0), respectively.

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Ge fraction, x FIG.4. The variation in the indirect gaps of Sil_,Ge, alloy with germanium concentration x , as calculated using empirical pseudopotentials and the virtual crystal approximation. The variation of the L- and A-valleys are shown individually (A lies in the crystallographic [ 1001 direction).

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ested in the effects of random disorder (Section III.l), where large supercells are used to simulate the true random alloy. When grown as epilayers on Si substrates, the GeSi layers incorporate a large biaxial strain. The effect of the strain on the alloy is to result in a reduction of the fundamental gap, which remains indirect in nature (Lang et al., 1985; People, 1986). Figure 5 shows schematically the relative alignment of the bandedges in Si and in the particular case of strained Geo.sSio.5alloy. An intuitive description of the strain-induced bandgap reduction may be obtained by the method of People (1985), where the splittings of the band extrema are described in terms of the strain tensor and the appropriate deformation potentials. The strained bandgaps are then obtained by a superposition of these straininduced splittings upon the unstrained alloy gaps of Braunstein et al. (1958). Although this does provide an estimate of the principal strain effects, and leads to the correct prediction concerning the reduction of the bandgap, such a model does not represent a complete description of the real physical processes involved. The importance of the bandgap reduction arising through strain in alloy layers is apparent when the alloy bandedges are compared to the energy levels in Si/Ge microstructures, as in Fig. 5. In a Si/Ge superlattice the alignment between the bands in the different layers is governed by the valence band offset parameter (to be discussed in detail in this chapter). As may be seen from Fig. 5 the offset does itself result in a reduction in fundamental gap. The precise energy of the superlattice states is governed by a multiplicity of factors that are discussed in the following paragraphs. However, the essential point to note is that the range of energies spanned by the indirect gaps of the strained alloys corresponds to the

Si

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Si 4 Ge 4 superlattice

FIG. 5 . Schematic diagram showing the relative bandedge positions in unstrained Si and strained Si0.5Ge0.5 alloy. Also shown is the band alignment of a SiqGeq superlattice. The transition energies between superlattice states are shown to span the same energies as the strained alloy.

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range of superlattice gaps. The gaps of strained alloys and superlattices span the same energy subspace. This highlights one of the principal challenges facing semiconductor theory, that is, how to distinguish and characterize the interface-related effects. In other words, to identify the features that are unambiguously derived from the presence of the superlattice order, and which cannot arise simply through the presence of random GeSi alloy. Section V invokes first-principles microscopic theory to address this issue. First, we must examine in more detail the basic properties of GeSi microstructures. A direct-gap may be achieved in a superlattice through the increased periodicity of the structure. This process may best be understood by the concept of zone-folding (People and Jackson, 1987). As a result of the periodic potential arising from the superlattice layers, the wavevectors of the superlattice minibands are restricted to a volume of k space reduced in the direction of the superlattice period (the small Brillouin zone). The superlattice states may then be viewed as being constructed from the bands of the bulk constituents folded into this small Brillouin zone. Such a picture completely neglects the interactions between the bulk bands, and is therefore not a suitable starting point for quantitative analysis (however, it provides a useful intuitive description of the role of the period in determining the superlattice miniband structure). In particular, the zonefolding picture illustrates how the creation of a superlattice can result in a direct-gap structure. By choosing a suitable length of period, and hence a suitable small Brillouin zone, the indirect conduction minima may be folded onto the small Brillouin zone center. For the silicon minima with wavevectors lying on the r - X axes this folding may be achieved by a [001]-oriented superlattice. This approach is used in the work presented in this chapter to engineer direct gap Si-Ge structures. Of course, it is not sufficient merely to obtain a structure with a direct gap. For the structure to be useful one requires also that the optical transition strength associated with the direct interband transitions is reasonable. In the simple zone-folding picture already described here, the symmetry of the zone-folded state remains essentially X like. Consequently, in the absence of band mixing, the direct transition formed by the folded state will be forbidden. In order that the transition should have a finite oscillator strength it is necessary to achieve a mixing of the bulk states involved. Such mixing processes occur when the interactions between bulk bands are included. However, for many systems (e.g., GaAs-AIGaAs) the degree of band mixing is small, and the folded states remain optically inactive. For strained epitaxial layers, such as those in GeSi structures, the displacement of atoms from the unstrained lattice positions presents a large scattering potential to an electron at an interface. This scattering mechanism ensures that there is a substantial degree of mixing of states of different bulk character. The strength of the direct transition to zone-folded states is enhanced by the strain in the system. The relatively large difference in the equilibrium bulk lattice constants of silicon and germanium also plays a key role in the physics of Si, Ge and GeSi layered structures. Silicon has a lattice constant of 5.43 8, in comparison to the 5.65 A of germanium, a mismatch of 4.1%.Such a large mismatch results in highly strained layers, giving rise

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to a number of physical effects. The precise nature of the strain in the layers depends on the composition of the substrate on which the heterostructure is grown. While for practical reasons the actual substrate used is usually chosen to be pure Si, the strain in the microstructure can be adjusted by creating a “virtual substrate” in which an alloy buffer layer is grown between the substrate and the superlattice (Kasper ef al., 1987). Asymmetrically strained systems may be grown on, for example, a pure Si substrate. In this case, assuming a pseudomorphic growth, the lattice constant parallel to the interfaces in all layers will be that of silicon. The silicon layers are thus unsti dried, while the germanium has a very large biaxial strain. Such systems are restricted to relatively short layers, the critical thickness, beyond which pseudomorphic growth breaks down (People and Bean, 1986; Hull et aZ., 1986). The asymmetric strain field also places a restriction on the total number of periods that may be grown. The symmetrically strained structure, grown on a Sio.sGeo.5 alloy buffer, has both the Si and Ge layers under strain. However, the strain in each layer is reduced, increasing the critical thickness and the number of periods that may be grown before the dislocation density becomes too great. The preceding discussion has focused on the growth of very narrow layers of pure Ge and Si. Structures of larger dimension may be grown involving GeSi alloy layers, where the degree of strain depends upon the concentrations in the alloy. In addition to the effect on the growth characteristics of the layers, the strain has a dramatic influence on the electronic properties, splitting the otherwise degenerate A valleys into two equivalent A 1 minima, and four equivalent All minima. The ordering of the split minima in each material is determined by the nature of the strain in the lcver, that is, whether the parallel lattice constant is smaller or larger than the bulk value. The precise amount of the splitting in each material is critical in determining the nature of the lowest state in the conduction band, and can alter the particular material in which it is localized. This may be illustrated by considering as an example the case of the symmetrically strained system described earlier, where the layers are grown on a Sio sGeo.5 alloy buffer layer. For such a system the parallel lattice constant of the substrate, and hence for pseudomorphic growth, the layers, is larger than that of bulk silicon. The silicon layers have therefore been strained to this larger lattice constant, resulting in the A 1 minima being lowered in energy relative to the All minima. Conversely, the germanium layers are strained to the smaller lattice constant splitting the degenerate A valleys such that the A 1 minima are highest. These conduction minima splittings are illustrated schematically in Fig. 6 (where the relative alignment of the bands in the two layers is fixed by the valence band offset, discussed in what follows). The numerical values are those obtained from empirical pseudopotential calculations. As the magnitude of the splitting of the A valleys is comparable to the conduction band quantum well depths, the strain determines which material acts as a barrier for electrons in these valleys. For the strain configuration discussed, the parallel and perpendicular valleys act to confine the electrons in the germanium and silicon layers, respectively, though the All offset is extremely small. Which of these valleys will give rise to the lowest conduction state in the superlattice? This depends on the other parameters of

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Ge

u 284meV

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(Strained to Sio.sGe0.5) FIG. 6. The alignment of the strained bulk handedges in a SUGe superlattice strained to a Si0.5Ge0.5 alloy substrate. The splitting of the bulk A minima parallel and perpendicular to the interfaces is indicated, with numerical data obtained from empirical pseudopotential calculations.

the superlattice, such as the well and barrier widths, as well as the strain. For, while the AJ- bandedge is clearly the lowest in energy, it is not necessarily the case that the zone-folded state from this well will lie below the nonfolded states originating in the parallel valleys. The energy due to quantum confinement in the conduction well of the A 1 derived zone-center state may be sufficient to lift this state above the nonfolded minima. Although the effective mass approximation, leading to the particle-in-a-box picture, is not sufficient to make quantitative predictions for strained-layer systems, it remains very useful for an intuitive understanding of the effect of quantum confinement and its dependency on the structural parameters. The role of the layer widths and compositions can be deduced from simple particle-in-a-box considerations, provided care is taken to include strain in the relative line-ups of the bands in the two materials. Having obtained well profiles from the strained bandedges the qualitative behavior of the miniband energies can be determined using the familiar effective mass model. One obtains the usual increase in electron and hole confinement energies as the layer widths are reduced and barrier heights increased. Changes in barrier heights correspond to changes in the alloy composition of the layers, as well as the lattice constant of the substrate. Of

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course, the alignment of bands in the effective mass model is dominated by the valence band offset parameter. Much of the physics of heterostructures is determined by the band alignment, usually described by the valence band offset. The value of the offset determines the relative energies of the states in the two constituent materials, and as such controls the quantum well depths, degree of wavefunction confinement, and the very nature of the heterostructure (i.e., type-I, with holes and electrons confined to the same layer, or type-I1 with confinement in different layers). However, despite considerable effort over many years, summarized by Franciosi and Van de Walle (1996) and Capasso and Margaritondo ( 1987), the theoretical prediction and experimental determination of band offsets remains a topical issue. One of the principal questions that must be addressed in theoretical studies of offsets is that of whether the offset is intrinsic, that is, solely dependent on bulk reference levels, or whether it is determined by the particular properties of the interface concerned. Only first-principles methods are able to self-consistently account for charge transfer at the interfaces to enable the relative alignments to be determined (e.g., Massidda er al., 1987; Christensen, 1988). The ab initio pseudopotential calculations of Van de Walle and Martin (1986) enabled the band offset to be deduced from the average self-consistent potential in a Si/Ge superlattice. The potential was seen to become “bulk-like’’ a short distance from the interfaces, allowing the average bulk potentials to be aligned on a common energy scale. Band calculations for the bulk materials provided the relative positions of the individual bandedges, and thus the actual valence offsets. The effects of spin-orbit coupling and strain splittings, which will clearly affect the valence bandedge alignment, were included from simple deformation potential theory (Pollak and Cardona, 1968). The “model solid” theory of Van de Walle (1989) again worked upon the alignment of the average potentials in the bulk materials, this time using a simplified model for the bulk charge densities. This method was found to be successful for a wide variety of materials at nonpolar interfaces. Jaros (1990) showed that a simple intuitive model, based upon empirical values of the bulk optical dielectric constant, yielded values for the offset in good agreement with these more complex methods. The success of this simple model reflects the fact that the principal conclusion of the first-principles calculations is that the offsets are essentially intrinsic. However, it should be noted that the intrinsic nature of nonpolar interfaces is not carried over to polar interfaces, where the microscopic interface properties become critical.

2. GESI BANDSTRUCTURES FROM EMPIRICAL PSEUDOPOTENTIAL CALCULATIONS To obtain a quantitative description of ideal (i.e., defect-free) (001)-GeSi strainedlayer superlattices, and to study how their key properties are affected by the structural parameters, we employ an empirical pseudopotential scheme. The extension of the

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well-established EPP method for the calculation of bandstructures of bulk semiconductors to periodic superlattice systems is performed using a perturbative approach. The superlattice wavefunctions are expanded in a complete set of eigenfunctions of a suitable bulk (“host”) crystal

where @ ( a ,k) are solutions to the bulk Hamiltonian

Ho@(n,k) = E ( n , k)@(n,k)

+

(2)

The superlattice Hamiltonian H may be written H = Ho V, where V represents the perturbation arising from the replacement of atoms of the host by atoms of the other superlattice layers. The perturbing potential is constructed as the difference between the potential of the atoms in the superlattice unit cell and that of the host atoms. Such a potential possesses the periodicity of the superlattice, determining the wavevectors k that appear in the expansion of the superlattice wavefunction (those being the bulk vectors displaced from the superlattice wavevector by a whole number of superlattice reciprocal lattice vectors), and the extent of the reduced Brillouin zone of the superlattice. This is the origin of the zone-folding effect discussed previously. The Schrodinger equation for the superlattice may then be solved by constructing the Hamiltonian matrix and direct diagonalization. For the expansion over bulk wavefunctions to provide a rapidly converging set of basis functions it is necessary that they may be matched to the total length of the superlattice; in other words, that the dimensions of the superlattice unit cell are multiples of the bulk cell dimensions. Of course, as the superlattice consists of strained layers of two different materials this will not be the case if unstrained bulk is used to generate the basis functions. This problem is overcome by calculating the basis functions using a strained bulk cell, with lattice constant in the plane of the interfaces set to the substrate lattice constant, and lattice constant in the growth direction chosen so that the overall length of the superlattice unit cell (determined using simple elasticity theory as in Van de Walle, 1989) is an integral number of bulk (growth direction) lattice constants. In order to construct the perturbing potential, the positions of the atoms in the strained superlattice are determined from the empirical elastic constants of the two materials. As the substitution of the superlattice constituents for the host involves a change in the position of the atoms, the perturbing potential is relatively large (e.g., compared to that which would arise in a lattice-matched superlattice like GaAs-AlGaAs). Consequently, a large number of host bands must be included in the basis to obtain convergence. The computational implementation of the scheme outlined in the foregoing provides us with the eigenvalues corresponding to the miniband energies of the superlattice, and the coefficients A ( n , k) describing the superlattice wavefunctions. The A ( n , k) coefficients describe the contributions to the superlattice states arising from bulk states

184

M. J. SHAWA N D M. JAROS

of momentum k and bulk band index n. This matrix therefore provides us with a valuable tool for analysis of the superlattice electronic structure, indicating the bulk origin of the states. The mixing of states of different bulk momenta or different bulk character will show up in the magnitude and distribution of the A ( n , k) coefficients for a given superlattice state. Having obtained solutions for the superlattice states using the foregoing method, it is also possible to evaluate the transition probability lMjj l2 for optical transitions between states i and j IMij12 = I ( + ~ I P I + ~ ) I ~ (3) We may therefore use this approach to study the strength of the direct transition across the gap as the superlattice parameters are varied. A full description of the application of the empirical pseudopotential method to strained-layer superlattices is available elsewhere in the literature (e.g., Morrison ef al., 1987; Wong et al., 1988). For the empirical pseudopotential calculations presented in this chapter we have used the particular pseudopotentials developed by Friedel et al. (1988). The band offset incorporated into these potentials is itself derived from the theoretical prediction of Van de Walle and Martin (1986). Before we present the results of a systematic study of the superlattice parameters determining the strength of the direct transition, it will be instructive to consider an example structure in detail. For this we shall choose the symmetrically strained (i.e., grown on a Sio.sGeo.5 substrate) superlattice consisting of four atomic layers of silicon and four of germanium. While this structure does not in the event prove to be the most attractive system, it presents a useful demonstration of empirical pseudopotential calculation, and illuminates some of the basic features of superlattice bandstructures. The parallel lattice constant all of the superlattice will, for pseudomorphic growth, be equal to 5.55 A, the lattice constant of a Sio.5Geo.5 alloy. Here we have assumed a virtual crystal approximation for the alloy, where it is assumed that the lattice constant of the alloy may be linearly interpolated between that of silicon and germanium. Applying the method of Van de Walle to determine the lattice constant in the growth direction for the strained layers of Si and Ge we obtain perpendicular lattice constants as( = 5.35 A, and a y e = 5.74 A. Calculations of the strained bulk Si and Ge bandstructures were performed to determine the relative energies of the bulk bandedges. These were shown schematically in Fig. 6, where the key numerical values are indicated. In particular, the valence band offset of 284 meV is shown, its value being fixed for this strain by the Friedel et al. pseudopotentials. For the particular structure described here, the lowest electron states in the superlattice will be confined in the folded A 1 valleys of the Si layers, while the holes are confined in the Ge layers. The calculated bandstructure of the superlattice is shown along some of the key symmetry lines in the reduced Brillouin zone in Fig. 7. It is interesting to note that the minimum of the lowest conduction miniband does not occur at the zone center, but rather lies some way toward the edge of the reduced zone in the growth direction. The

4

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185

FIG.7. The bandstructure of the SiAGe4 superlattice strained to a Si0.5Ge0.5 alloy substrate is plotted along the P-r-XII symmetry lines; P is the point lying at the edge of the superlattice Brillouin zone on the growth axis.

period of two lattice constants of this superlattice results in a reciprocal lattice vector whose length does not exactly map the Si A 1 minima onto the zone center. For this reason we would not expect this structure to present a strong direct optical transition. An additional feature of the particular structure studied here is that the symmetry of the conduction and valence minibands at r is such that transitions to the lowest conduction state across the gap are forbidden. This is a consequence of the point group symmetry of the crystal and the particular period of the superlattice. A full discussion of the point group symmetries of SiGe structures is given by Satpathy et al. (1988). The ordering of the two lowest conduction states changes as the length of the superlattice is varied, with the symmetry-forbidden state lowest in the Si4Ge4 structure. In the systematic study of the Si,Ge, superlattices presented in what follows, it is the transition to the lowest optically active state that is considered (this only affects the n = 4 structure). To investigate fully the parameters affecting the nature of the gap in these structures we have calculated the transition energies and strengths in a series of Si,Ge, superlattices, grown on a variety of substrates. In addition to the question of how the substrate and period affect the diredindirect nature and oscillator strength of the structures, we have also considered the restrictions associated with the critical thickness and the problem of indirect transitions to the substrate band extrema. Let us consider first the choice of substrate used. In addition to the strain effects described in the previous section, which are critical in determining the nature of the gap in the superlattice itself (in an “infinite” superlattice), one must also take into account

M. J. SHAWA N D M. JAROS

186

the possibility of transitions to the substrate when a finite number of layers is grown. For example, if we consider the case of a structure grown on pure silicon, the bandedges of the silicon layers will align exactly with those of the substrate. However, the presence of the germanium barriers results in a confinement energy for the superlattice conduction electrons, shifting the lowest superlattice conduction state above the substrate A valleys. Regardless of the nature of the superlattice-confined electron states, the system is indirect through transitions to the substrate. Similarly, the choice of a pure germanium substrate will result in the valence band maximum of the substrate lying above the maximum in the germanium superlattice layers. In this case, while the valence maximum remains at wavevector r, the transition is indirect in real space, with lowest energy transitions from the substrate valence states. Such considerations indicate that for direct transitions it is necessary to use an alloy substrate. This has the added attraction that the critical thickness that may be grown is increased, and that the quality of the epilayers is consequently improved. The substrate alloy concentration required to obtain both the valence and conduction extrema from within the superlattice depends on the layer widths, through the confinement energies of the conduction and valence quantum wells. Figure 8 represents the restrictions on the substrate/layer-width choice that result from consideration of the substrate, including the critical thickness and the role of the nonfolded minima. Only structures in the unshaded region of the diagram are expected to be suitable for engineering a direct gap.

Ge

indirect t o Lie substrate aJ

+

{n sio.5%J.5

duction minima [owest

3 v)

SI

2

4

6

8 10 12 no. monolayer, n

14

16

FIG.8. The unshaded area indicates the combination of substrate and period for which Si,Ge, systems have both valence and zone-folded conduction extrema within the superlattice. [Reprinted from Marerials Science and Engineering B7,Turron, R. J., Jaros, M., “Optimization of Growth Parameters for Direct Band Gap Si-Ge Superlattices,” 37-42, 1990, with kind permission from Elsevier Science S. A,, P. 0. Box 564, 1001 Lausanne, Switzerland.]

4

187

FUNDAMENTAL PHYSICS

It is now interesting to examine how the variation of the layer widths and substrate composition affect the oscillator strengths of the direct transitions. To compare the strengths for different substrate compositions we have considered the case of the Sio.sGeo.5 substrate and the extreme case of the pure germanium. Although the structures with pure Ge substrates will suffer from the problem of indirect transitions involving the substrate valence bandedge, these will not affect our calculations of the transition strengths within the superlattice. These values will serve to illustrate the effect of the alloy concentration, even though real devices would in fact be indirect. In Fig. 9 the oscillator strengths are compared for the two different substrate compositions, for a number of different layer widths. The variation with layer widths is studied in more detail in Fig. 10 for the case of the alloy substrate. There are two principle features to note from Figs. 9 and 10. First, changing the substrate composition appears to have a generally small effect on the oscillator strengths. Second, the oscillator strength shows a general decrease with period. These trends may easily be explained by considering the factors that contribute to the oscillator strengths. The folding of the A valley on to the zone center to obtain a direct gap is not in itself sufficient to result in a strong transition; the states remain essentially X-like, and are forbidden unless there is some r-state character mixed in. The mixing of states of different bulk momenta into the superlattice states arises as a result of scattering of the bulk-like electrons on encountering the “substituted’ atoms in the barriers. The magnitude of this scattering is strongly affected by the strain in the layers that results in atoms being disturbed from their bulk-like lattice sites. In general, increased strain leads to

. 1.00

3M

8

f: h

3 0.10 .*

.

v

c ( c (

.

v

T

0.01

i

$

4

5

6

no. monolayers, n FIG. 9. Variation of oscillator strength of lowest direct transition for Si,Ge, superlattices grown on Ge (triangles) and Si0.sGq.s alloy (circles) substrates. [Reprinted from Materials Science and Engineering B7,Turton, R. J., Jaros, M., “Optimization of Growth Parameters for Direct Band Gap Si-Ge Superlattices,” 37-42, 1990, with kind permission from Elsevier Science S . A,, P. 0.Box 564, 1001 Lausanne, Switzerland.]

M. J. SHAWAND M. JAROS

188

1.000

f! M

f? s m

7 1

*

0.100-

#

&-i

cr 0 (d

*

* **

* *

4

I . 3

0 0.010-

0 4

0.001

I 12

18

no. monolayers, n FIG. 10. Variation of the oscillator strength with period for Sin&, superlattices grown on Sio.sGe0.s alloy substrates. [Reprinted from Muteriuls Science andEngineering B7,Turton, R. J., Jaros, M., “Optimization of Growth Parameters for Direct Band Gap Si-Ge Superlattices,” 37-42, 1990, with kind permission from Elsevier Science S. A., P. 0. Box 564, 1001 Lausanne, Switzerland.]

an increase in the scattering, and hence in the mixing that occurs. Thus, although the strain distribution is affected by the substrate composition, the overall magnitude of the strain does not change, and we find that the oscillator strengths are relatively unchanged with substrate. Were we to use alloy layers rather than the pure silicon and germanium, the magnitude of strain would be reduced, and consequently the direct transitions weakened. The strength of the scattering also depends on the difference in the potentials associated with the Si and Ge atoms themselves. The relative effect of these potential differences is diminished as the layer widths increases. Increasing the widths of the layers also results in increasingly well-confined states, reducing the overlap in real space between the conduction and valence states (because the type-I1 superlattice confines the holes and electrons in different layers). These effects controlling the dependence of the oscillator strengths on period are largely independent of the choice of substrate, explaining the fact that the oscillator strengths for the two substrates in Fig. 9 follow broadly the same pattern. There are two particular structures for which the direct transition strength in Fig. 10 is seen to be significantly large, namely, the Siz-Gez and Sis-Ges structures. The layer widths involved in the former are simply too short to be grown accurately with existing technology (and indeed it is unlikely that such growth could ever be achieved due to interface reconstructions, see Section 111.1). The Sis-Ges structure is a far better prospect, though again it demands an extremely accurate growth. The origin of its

4 FUNDAMENTAL PHYSICS

189

enhanced transition strength is in the fact that the zone-folding associated with that particular period results in the conduction minima folded almost exactly onto the zone center.

111. Electronic Structure of Imperfect and Finite Systems 1. BANDSTRUCTURE OF ORDERED AND DISORDERED SYSTEMS In the previous section results were presented for a series of SiGe superlattices. These structures were all assumed to be perfect, with no foreign species present in the layers and with abrupt monolayer interfaces. Of course this does not represent the situation in real superlattices. There are numerous imperfections that could cause a deviation from this idealistic model, including the presence of dislocations,the presence of impurity atoms, and an imperfect arrangement of the silicon and germanium atoms themselves. In this section we focus on the latter case, investigating how the presence of such atomic fluctuations might affect the physical properties of the structures. We restrict our attention to structures in which the deviations to the perfect superlattice configuration occurs only in the atomic planes immediately adjacent to the interface. In other words we look at structures in which the interfaces are no longer perfect and abrupt. It is to be expected that the interface region is where the most significant imperfections would occur. At first sight one might expect that the imperfect interface layers should be described as a random disorder of the Si and Ge atoms. However, experimental studies of the interfaces in SiGe structures using scanning transmission electron microscopy (Jesson et al., 1991) indicate that the breakdown of the perfect interfaces does not in fact result in a random alloy in the interface planes. Rather, a number of chemically driven ordered reconstructions of the interfaces have been observed. After these reconstructions a translational symmetry parallel to the interfaces remains, despite the diffusion of atoms across the interfaces. In this section we compare both the case of a random distribution of atoms in the atomic layers at the interfaces and one of the ordered interface arrangements described by Jesson et al. (1991), with the perfect superlattice. In particular, we examine the effect on the optical transitions as a result of these interface structures. In all of the superlattices described in the previous paragraph the translational symmetry parallel to the interfaces has been reduced. Even where the ordered reconstruction takes place, the repeating period parallel to the interface has been dramatically increased. For computational studies of these structures this symmetry breaking presents a considerable practical problem. While the study of perfect structures may proceed with only a single atomic spiral, exploiting the full bulk-like symmetry in the plane, the inclusion of displaced atoms requires the use of a large unit cell in all three dimensions. For the reconstructed interfaces the unit cell must be large enough to represent the full

190

M . J. SHAWAND M. JAROS

period of the reconstruction, while for the random alloy a unit cell must be used that is sufficiently large to allow the random nature of the disorder to be described. The extension of the empirical pseudopotential method for perfect superlattices to the case of imperfect superlattices with extended unit cells in three dimensions is straightforward. The change in periodicity parallel to the interfaces simply results in an increase in the number of the bulk wavevectors that appear in the expansion of the superlattice wavefunction. However, while the conceptual change this represents is very small, it has a dramatic effect on the practical solution of the problem computationally. The number of bulk wavevectors required for a perfect superlattice is proportional to the length of the superlattice period. For the three-dimensional cell the number of terms in the expansion is proportional to the product of the period in the three directions. As a result the number of bulk wavefunctions that can appear in the superlattice wavefunction rises dramatically as the unit cell is increased. Because the dimension of the potential matrix depends on the number of functions in the expansion, the problem rapidly becomes too large to compute, placing a limit on the size of cell we can consider. A complete description of the mathematical formalism and computational considerations required for the results presented below is given by Turton and Jaros (1993). To allow the effects of disorder to be analyzed quantitatively it is necessary to define a measure of the disorder present in a given structure. In this context “disorder” refers to deviations from the perfect superlattice structure, both random and reconstructed. A disorder parameter D may be defined as nmis

D = ~ x - .

ntot

(4)

Here, n,is is the number of misplaced atoms and ntOtis the total number of atoms in the unit cell. Misplaced atoms are defined as those atoms whose species differs in comparison with the idealized perfect superlattice. The factor of 2 ensures that the disorder parameter varies between 0 for the perfect structure, to 1 for a completely random distribution of atoms throughout the whole unit cell, that is, for a random Sio.5Geo.s alloy. The effect of random disorder at SiGe interfaces is illustrated in what follows for the SisGes superlattice grown on Ge substrate. A series of structures was modeled using unit cells containing 8000 atoms, extending 10 lattice constants in directions parallel to the interfaces and consisting of 4 superlattice periods. Within these unit cells, the interface disorder was introduced by randomly assigning the atoms in the interface layers to represent the perfect configuration, encroachment of Si into the Ge layer or of Ge into the Si layer. The disorder parameter is chosen by weighting the number of perfect configurations occurring. The perfect Si5Ges superlattice grown on Ge is direct-gap, with the lowest conduction state derived from the zone-folded minimum. In contrast to the Si4Ge4 case, where transitions to the lowest energy conduction state were symmetry-forbidden, the Si5Ges states are reversed and transitions to the lowest conduction state, derived from

4

191

FUNDAMENTAL PHYSICS

the folded A 1 minima, are allowed. No-phonon transitions to the higher-lying nonfolded All minima are forbidden in the ideal superlattice, where there is no reduction of the in-plane translational symmetry. However, for structures with randomly disordered interfaces the perturbing potential in the plane of the interfaces reduces this symmetry, and the no-phonon transitions to the Ail minima become allowed. Figure I1 shows the variation of strengths of the optical transitions to the A 1 and All states as the degree of disorder is increased. Two effects are clearly identified from this figure. First, the transition to the nonfolded minima, forbidden in the perfect system (calculated to be 12 orders of magnitude smaller than the allowed transition-the “computer zero”), is dramatically increased in strength as the degree of disorder increases. Meanwhile, the direct transition to the folded A 1 minima is weakened by the disorder at the interface. For an equal number of the three interface configurations considered, corresponding to a disorder parameter of 0.267, the strengths of the two transitions become comparable. It is the presence of the in-plane symmetry-breaking potential introduced by the disorder that results in a number of newly allowed transitions, and consequently a reduction in the strengths of the existing transitions. We can see that the existence of a high degree of disorder in very short period superlattices can result in changes to the optical transition mechanisms available. However, it is worth noting that the degree of disorder required for the All transitions to become comparable in strength to the “perfect” transitions is very high. For the very short periods involved the interface layers constitute a significant fraction of the period, and a high degree of disorder can result even where only single-

I

-?

-7 I 01 0

- & A 02

i___

03

disorder FIG.1 1 . Squared optical matrix elements (in arbitary units, plotted on a loglo scale) with x polarization at r as a function of random interface disorder for a SisGes superlattice strained to a Si substrate. The lowest energy transitions to the All minima (circles) and A 1 minima (triangles) are represented. Where appropriate, the error bars indicate the variation over a number of different random supercells. The “forbidden” nophonon transition to the All minima is calculated to be 12 orders of magnitude smaller than that to the AL minima and is not plotted. [Reprinted with permission from the Institute of Physics, Turton, R. J., and Jaros, M. (1993). Sernicond. Sci. Technol. 8,2003.1

192

M. J . SHAW AND M . JAROS

monolayer fluctuations of the interface are allowed. For a smaller degree of disorder, such as that indicated on Fig. 11 where D = 0.04, the original transitions to the zonefolded A 1 minima remain dominant. How does the reconstruction at Si-Ge interfaces observed by Jesson et al. (1 991) affect the optical transitions? To illustrate this difference we compare the case of a perfect Si4Ge7 superlattice with one of the structures identified by Jesson. The reconstructed interface structure we considered was one consisting of alternating phases A and C, where A and C refer to the particular interface reconstructions as labeled by Jesson et al. The disorder parameter for this reconstructed system is calculated to be 0.24. For comparison we also modeled a Si4Ge7 superlattice with randomly disordered interfaces corresponding to a disorder parameter of 0.24. The results of these calculations are summarized in Fig. 12, where the strengths of the transitions to the folded and nonfolded minima are compared for the three systems. Interface reconstruction can be seen to have reduced the effect of the disorder on the transition strengths. The reconstructed superlattice shows a stronger transition to the folded minima, while the enhancement of the transition to nonfolded states is not so great. The optical characteristics of GeSi structures are therefore seen to be strongly affected by the accuracy with which the layers are grown. Random disorder, even restricted to atoms lying in the planes adjacent to the interfaces themselves, can reduce the strength of the direct transition to the zone-folded minima by two orders of magnitude. The presence of such disordered layers also led to the breaking of the selection rules governing transitions to the nonfolded minima. Where the disorder in these interface planes is sufficiently high, and for structures of sufficiently short period, the two transition mechanisms may become comparable. The degradation of the transition to the zone-folded minima is reduced by the chemically driven reconstructions that have been observed experimentally.

FIG. 12. Squared optical matrix elements (in arbitary units, plotted on a loglo scale) with z polarization at r for the three systems considered in the text. Column A corresponds to the perfect SiqGe7 superlattice, column B to the reconstructed interface, and column C to a randomly disordered system. [Reprinted with permission from the Institute of Physics, Turton, R. J., and Jaros, M. (1993). Semicond. Sci. Techno]. 8.

2003.1

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FUNDAMENTAL PHYSICS

193

2. OPTICAL TRANSITIONS IN A FINITE SUPERLATTICE The calculations in the preceding section implicitly assumed that the superlattice is

a periodic structure of infinite extent. The substrate has been considered independently of the superlattice itself, as a possible source of indirect transitions, and in fixing the parallel lattice constant of the superlattice. So far, however, we have not taken into account the fact that any real superlattice is finite in extent. Indeed, for practical considerations, the actual number of periods that are usually grown is relatively few. In particular, for asymmetrically strained structures the number of periods is restricted to a critical length, providing an absolute limit on the length of structure that may be grown pseudomorphically. While the assumption of a truly periodic system allows for a significant simplification of the computational problem, it also introduces a discrepancy between the model and experiment. In this section the effect on the optical transitions of the finite nature of real superlattices is examined. A system for which experimental optical data are available, and which stimulated considerable interest in ultrashort period superlattices, is the five-period SbGe4 superlattice grown on a pure Si substrate. This was studied by Pearsall et al. (1987) who observed a series of strong optical transitions below the energy of the lowest direct transitions in GeSi random alloys. The transitions were initially attributed to superlattice order, but there was considerable speculation as to the microscopic origin of these spectral lines (e.g., Pearsall et aE., 1989; Wong et nl., 1988). Electronic structure calculations on infinite Si4Ge4 superlattices, using models such as that outlined in Section 11.2, were not able to account for the strength and energies of the observed transitions. In particular, the energy of the first direct transition is predicted by such calculations to occur at around 1.2-1.3 eV, not the 0.76 eV of experiment. Only the indirect transitions to the nonfolded Si A 11 minima could occur at around this energy and these are forbidden in a perfect structure by symmetry. A more realistic model of the structure of Pearsall el al. can be achieved by constructing a unit cell containing the five-period superlattice and a thick Si buffer layer (Wong and Jaros, 1988). While this unit cell is clearly much larger than the eight monolayer cell required for the infinite structure, the approach allows the computational advantages associated with periodic boundary conditions to be retained. Provided the length of the Si buffer layers is sufficiently large the calculation ought to describe fairly well the case of an isolated 5-period system grown on Si and with a Si cap layer (i.e., the experimental system). Of course, such a model imposes a periodicity that is absent from the real system and care must be taken to account for this discrepancy. In the real system the Si substrate and cap layers behave essentially as unstrained bulk Si, and give rise to 6-fold degenerate A minima. In contrast, due to the periodic boundary conditions, the Si buffer layers in the model behave as wide Si quantum wells, giving rise to a series of states confined in the buffer layers. The energy of these states is raised by the confinement energy associated with the finite width of the buffer quantum wells. Correcting our

194

M . J. SHAW AND M. JAROS

computed energies to account for this, the lowest conduction states lie 0.76 eV above the valence bandedge. Although the energy of these states compares directly with the lowest observed transition, as mentioned previously, such indirect transitions are forbidden by the symmetry of the system, and would not be expected to be observed. In fact, comparison of the results of the calculations for infinite and five-period structures shows that the energies and transition strengths are virtually unchanged (Wong and Jaros, 1988). The finite nature of the structure does not, therefore, contribute an explanation of the experimentally observed transitions. However, it is clear from the charge densities of the superlattice states shown in Fig. 13 that the detailed form of the electronic wavefunctions is significantly altered by the finite length of the superlattice. In particular, the lowest conduction state confined to the superlattice itself (i.e., not the buffer layer states) is localized at the center of the 5-period system. Clearly, no such localization can be represented in the infinite model. The valence states appear to behave as though they are confined states of a GeSi quantum well sandwiched between the Si buffer layers. The states have the form of the typical envelope functions of a simple square well, again a behavior that cannot be obtained in the infinite structure. f

>

A

>A -40

-30

-20

-10

0

10

20

30

40

FIG. 13. A plot of the charge densities along the growth direction of the five-period superlattice. The broken lines indicate the positions of the interfaces. At the bottom of the figure the dark blocks indicate the Ge superlattice layers.

4 FUNDAMENTAL PHYSICS

195

To summarize, the fact that in practice only a limited number of superlattice periods can be grown does not greatly affect the energies and momentum matrix elements. Although the precise nature of the localizations in the system is significantly affected by the finite length, the prediction of optical properties due to superlattice states using infinite systems remains valid. The origin of the observed transitions in the 5-period Si4Ge4 structures remains to be conclusively identified, although it is now generally accepted that the transitions are indirect and result from phonon-scattering or lattice imperfection (e.g. People and Jackson, 1987; Froyen et al., 1987; Hybertsen and Schluter, 1987).

IV. Luminescence and Interface Localization 1. EXPERIMENTAL OPTICAL SPECTRA OF SIGE SYSTEMS In recent years numerous experimental studies of optical phenomena in SiGe heterostructures have been reported. Much attention has focused on the photo- and electroluminescence from very short period superlattices (Pearsall et aL, 1987; Zachia et al., 1990; Presting et al., 1992). The rationale behind the design of such structures was that the zone-folding effect, related to the long-range superlattice periodicity, could result in allowed direct transitions. However, the available experimental data does not support the theory that this mechanism is responsible for the luminescence observed. Just as the observed transitions of Pearsall et al. (1987) could not be reconciled with theoretical predictions (as discussed in Section 111.2), so the experimental results of Zachia et al. were at odds with the theory of zone-folded quasi-direct superlattice transitions (Schmid et al., 1990). The dependence of the luminescence on temperature and external fields is, rather, suggestive of an alloy-scattering origin (Ting and Chang, 1986), showing similarity to the behavior of SiGe alloy (Noel et al., 1990; Robbins et al., 1991) and alloy quantum well systems (Sturm et al., 1991; Northrop et al., 1992). It has been shown in Section I11 that random disorder, and the interface reconstructions observed, are capable of introducing an alloy-scattering process comparable to the theoretical zone-folded transition mechanism. This was demonstrated even for systems in which interface imperfections were restricted to a single atomic plane on either side. The evidence at present therefore suggests that in very short-period superlattices the observed luminescence arises primarily through alloy effects, rather than from the zone-folding mechanism. Effects arising through the formation of alloys at the GeSi interfaces can be reduced by choosing systems with wider layers. The extent of the disorder in the vicinity of the interfaces that would be required to result in a dominant alloy-scattering luminescence process in these larger systems is far greater than that which is present in high-quality MBE samples. Such reasoning led to the proposal by Jaros of double-well structures, studied experimentally by Gail et al. (1995) and Engvall et al. (1993, and illustrated

196

F I G . 14. emission.

M. J. SHAWAND M. JAROS

Schematic diagram of a typical double-well SiGe structure proposed for room-temperature

schematically in Fig. 14. These structures are designed to result in the lowest conduction state being confined in the central Si well. Full-scale pseudopotential calculations for these structures (Turton and Jaros, 1996) give energy gaps in good agreement with the experimental luminescence energies reported. The calculations predict confined A 1 and All states, giving rise to strongly allowed and forbidden transitions, respectively, at similar energies. The luminescence observed from these structures is stable at room temperature as might be expected from the large potentials that are confining the conduction wavefunctions. In the absence of experimental data one would expect that it is the zone-folded AL state that would luminesce. However, further experimental studies of the pressure dependence of the optical spectra conclusively show that it is the All states that are the source of the photoluminescence (Gail et al., 1996). As we have shown, the breakdown of the selection rule forbidding transitions from the nonfolded minima cannot reasonably be assigned to the alloy effects of interface disorder. For such an effect to allow comparable transitions the quality of the samples would have to be considerably poorer than is believed to be the case. It is also reasonable to ask whether the luminescence may originate from the alloy-cladding layers, though this could only explain the low-temperature behavior. In any case the computed wavefunctions are found to penetrate only a very short distance into the cladding layers. It is clear then that there must be some other mechanism enabling the room-temperature luminescence. One possible mechanism is that of localization at the interfaces of the heterostructure. In the following sections we study in detail the role interface localization may play in the luminescence spectra, and the possible sources of such localized features. First, we use an empirical technique to study impurity atoms situated in interface islands. Then we study in detail the effect of the microscopic interface potential, the microscopic signature of the interface, in the presence of substitutional defects using ab initio pseudopotential methods.

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197

2 . IMPURITIES AT INTERFACE ISLANDS In the preceding section we have argued that the room-temperature luminescence cannot be ascribed to the alloy-scattering mechanism commonly used to explain low temperature luminescence in SiGe systems. Rather, we suggested that anomalous localization at the interfaces of the Si and Ge layers could be the source of the luminescence. In general, luminescence features are found to be insensitive to the microscopic details of the interfaces, except for ultrathin layers. The confinement of electrons and holes in the quantum wells results in wavefunctions peaking at the center of the wells, with only a small fraction of charge sampling the interface regions. Interface effects would only be expected to dominate optical spectra if there were a mechanism for localization of the wavefunctions in the interface region. Here we investigate the possibility of localization occurring at these interfaces using the empirical pseudopotential method. Despite the limitations of the EPP method in describing microscopic interface effects, principally due to the inclusion of a step-like valence band offset, it is still possible to extract qualitative information concerning the physical processes involved from such calculations. The role of disorder has been shown to be significant only when that disorder comprises a large fraction of the crystal. For typical, high-quality MBE interfaces this is only true of ultrathin layers. Another type of interface imperfection that is thought to occur in SiGe layers is that of interface islands, by which we mean an incursion of one material across the interface into the other layer, extending over many atoms in the plane of the interface. Could such interface islands result in a localization at the interfaces that is capable of driving the observed luminescence? As in the case of the random disorder, we shall restrict ourselves to consideration of islands that extend only one monolayer across the interface. Further, we limit the size of the islands so that they do not represent changes in the effective layer widths. However, calculations for a number of material systems and for a variety of island geometries and sizes have shown that for islands only one monolayer deep, no localized states were formed. The formation of interface islands is not in itself sufficient to explain the origin of the luminescence. However, there remains the possibility that the existence of interface islands could affect the behavior of an impurity atom situated at the interface. An intuitive view of the binding energy of impurity atoms in quantum wells holds that the binding energy will be greatest for impurities situated in the center of the well; essentially this results from the localization of the ground state electron and hole wavefunctions at the center of the well. Consequently, the electron-hole recombination processes in quantum wells are governed by impurities near the center of the-wells. However, it is possible that the interface island potential could increase the binding energy of the impurity level for an atom located in the interface island such that it drops below the central site level. Under such circumstances one could explain the observed luminescence in terms of recombination processes localized at the interfaces of the heterostructures. The calculations

198

M. J. SHAWAND M. JAROS

described below set out to determine whether such a mechanism is plausible, and the approximate size of interface island necessary to sufficiently lower the impurity level. Calculations were performed to determine the change in a typical shallow donor level as the spatial extent of the interface islands was varied. This was compared to the binding energy at the center of the well. The details of the calculation are reported elsewhere (Jaros and Beavis, 1993), but essentially involve the inclusion of a model potential representing the impurity atom. The potential was adjusted to reproduce the correct behavior in bulk, before being included in empirical pseudopotential calculations of the quantum well systems. The calculated binding energies are determined at the center of the quantum well and at the center of the interface islands, and their ratio computed. The results for a number of different island configurations are shown in Fig. 15. Ten different rectangular island geometries were studied and are labeled in order of increasing area. The actual island dimensions are listed in Table I. Figure 15 shows the variation with island size of the ratio of the binding energy of a donor at the interface to one at the center of the quantum well. Results are shown for the SiGe system of interest here, and for comparison the results for GaAs-AIGaAs and ZnCdSe-ZnSe systems are also shown. In all cases it can be seen that as the cluster size increases, the binding energy at the interface increases relative to the well-center value. For the SiGe system

:

O 6 t :

0 4

0

1

f

2

~,, ~, ; f

3

b

5

6

7

8

9

10

[Luster reference numbers

FIG. 15. For the interface islands listed in Table I, the ratio of the binding energy of a substitutional donor positioned at the interface to that in the center of the quantum wells is shown. The binding energy at the interface is calculated with the donor in the middle of the island, and results are shown for Si0.8Ge0.2-Si. GaAs-Gao~A103As, and Zn0,7&&.24Se-ZnSe quantum-well systems. [Reprinted with permission from Jaros, M., and Beavis, A. W. (1993), Appl. Phys. Left. 63, 669. Copyright 1993 American Institute of Physics.]

4

199

FUNDAMENTAL PHYSICS

TABLE1. Lateral Island Dimensions

Dimension Island Index 1 2 3 4 5

6 7 8

9 10

(a0

1 1 1 1 3 3 3 5 5 7

1

x 1 x 3 x 5 x 7 x 3 x 5 x 7 x 5 x 7 x 7

Area (a;, 1 3 5 7

9 15 21 25 35 49

the ratio becomes greater than unity when the island increases to 3 x 3; this is the smallest island size for which the impurity levels are lower at the interface site. The preceding results demonstrate that it is indeed possible for sufficiently large islands of Si, penetrating just a single monolayer into the Ge layers, to cause localization sufficient for the recombination properties of SiGe quantum wells to be dominated by impurity atoms situated at the interfaces rather than at the well center. As a result the breaking of translational symmetry parallel to the interfaces is sampled strongly by the carriers, and the breakdown of the selection rules governing the All minima becomes significant. This supports the hypothesis that the origin of the room-temperature luminescence may lie in the presence of such interface localization sources. However, it should be noted that quantitative data obtained from the present empirical pseudopotential scheme are not expected to be reliable.

V. Microscopic Signature of GeSi Interfaces In Section IV we have demonstrated the importance of the Si-Ge interfaces in determining the optical properties of the GeSi heterostructures. In particular, the difficulty of interpreting the experimentally observed optical spectra in terms of conventional bandstructure theory has been discussed. However, the calculations presented so far have all been based upon a semiclassical model of the interface. That is, the microscopic variation in the potential across the region of the interface bonds has been replaced by an abrupt steplike change in potential. While such a picture of the interface is sufficient to allow a relatively good description of the quantum-confined states in the superlattice wells, it is essentially a first-order approximation, and is unable to describe higher-order interface effects. Thus, although the EPP calculations are able to show the importance the interfaces may have on the optical spectra, in order to obtain the

200

M. J. SHAWA N D M. JAROS

microscopic signature of the interfaces it is necessary to go beyond the semiclassical picture. To this end we present a study of Si-Ge interfaces in the presence of impurity atoms using ab initio pseudopotential calculations (Shaw et al., 1996). These provide a complete description of the short-range potential variations within the region of the interface bonds themselves (what might be termed the “intraface” properties). This presents a whole new framework within which to describe the heterostructure systems; the intrafacial properties provide a fresh basis for our understanding of the physical behavior, for example, the optical spectra, of the system. The development of such a microscopic signature of the interfaces opens the way for an unambiguous interpretation of the observed spectra. The mechanism that we are proposing to explain the origin of the luminescence in SiGe heterostructures is closely analogous to the bandstructure enhancement effect invoked to explain the luminescence observed in the familiar case of GaP:N, reviewed, for example, by Jaros (1982). The isovalent nitrogen substitutional defect is characterized by a strong short-range impurity potential; although this potential is not sufficient to introduce deeply localized levels in the forbidden gap, it does alter the nodal character of the exciton wavefunction near the impurity site. This breaks the selection rule for indirect GaP and greatly enhances the oscillator strengths of excitonic recombination at nitrogen. The coupling between the impurities and the lattice provide an explanation for the wealth of experimental luminescence and absorption data available (e.g., Mertz et al., 1972). In the case of antimony in SiIGe heterostructures, however, it is known that antimony defects themselves are not able to achieve such an effect in bulk Si, and we propose that it is the interaction between the defects and the interfaces that gives rise to the luminescence.

1.

FIRST-PRINCIPLES CALCULATIONS

OF

SI/GE SUPERLATTICES

The first-principles calculations presented here are founded on the well-established methods of density functional theory described extensively in the literature (e.g., Dreizler and Gross, 1990). Using the local density approximation and the ab initio pseudopotentials of Bachelet et al. (1982) we determine self-consistent charge densities for the superlattice supercells. In addition, the nuclear coordinates of all of the atoms are fully relaxed to minimize the total energy. Our calculations involve expansion of the wavefunctions over a basis set of Gaussian orbitals, with s- and p-like character imparted through multiplication by appropriate spherical harmonics. The basis included 16 of these functions centered on each atom and 8 centered on the middle of each bond. The particular formalism used is described in further detail in Jones ( I 988) and Briddon (1991). The successful application of this particular implementation of the LDA to heterostructure systems, and specifically to the study of the microscopic properties of heterointerfaces, has been verified for a series of perfect AISb/InAs superlattices by Shaw et al. (1995).

4

FUNDAMENTAL PHYSICS

201

FIG. 16. A schematic diagram of the @-atom unit cell of the Si-Ge superlattices. The positions of the atomic planes are indicated, and the site of the substitutional donor is highlighted. The planes used for the contour plots are shown: plane A parallel to the interfaces and plane B perpendicular to the interfaces, each passing through the defect atom.

The calculations were performed on 64-atom unit cells, as illustrated schematically in Fig. 16. The cells consist of an 8-atom period of the superlattice, with the primitive unit cell repeated 8 times in the interface plane to form a near cubic unit cell. The systems studied were Si4Ge4 grown on Sio.sGeo.5(virtual) substrate, and bulk Si strained to the same substrate. The dimensions of the unit cell in the plane parallel to the interfaces were held fixed to a size determined by the lattice constant of the alloy substrate. This substrate constant was determined using a virtual crystal approximation with the calculated bulk equilibrium lattice constants. The overall lengths of the superlattice and strained bulk unit cells in the growth direction were determined by calculation through minimization of the total energy. The substitutional defects were introduced by replacing one of the atoms in the layer of Si forming one side of the superlattice interface at the center of the unit cell (see Fig. 16), and at an equivalent point in the strained bulk Si cell. For each calculation the position of ail of the atoms in the unit cell was fully optimized. The charge density in the 64 atom cells was represented by the contribution fromjust the single zone-center wavevector. This was found to provide a close approximation to the calculation using the complete set of special k-points, given by Ren and Dow (1988), which are equivalent to the set of 10 points frequently used to describe the primitive diamond unit cell (Chadi and Cohen, 1973). To assist in the interpretation of the results of the full-scale calculations for structures containing substitutional defects, it is helpful to develop a simple qualitative picture of

202

M. J. SHAWAND M.JAROS Perfect Crystal

Crystal with Defect

AlB

Vacancy States

Free Defect Atom

FIG. 17. Schematic diagram representing the simple defect molecule model for a substitutional defect in a bulk crystal. [Reprinted with permission from the American Physical Society, Shaw, M. J., Briddon, P. R., and Jaros, M. (1996). Phys. Rev. B54, 16781.1

the states induced by a substitutional donor. The defect molecule model (Jaros, 1982) provides us with just such a description, and is illustrated schematically in Fig. 17. Consider first the case of a substitutional defect in a bulk crystal. First, an atom is removed from the perfect crystal creating a vacancy, and with it a series of vacancy states. The vacancy has four unbonded sp3 orbitals associated with it, and these will symmetrize to form a singlet A1 state and triplet T2 states. Next, consider the freedefect atom, with its s (A1) and p (T2) orbitals being placed at the vacancy site. The free-atom and vacancy states of the same symmetry interact to give bonding and antibonding resonances: A1 bonding (AlB) and antibonding (AIA) near the bottom of the valence and conduction bands, respectively, and T2 bonding (T2B) and antibonding (T2A) deep inside the valence and conduction bands. The model applies also to the case of superlattices, although the symmetry labels ought to reflect the lower point group symmetry of the superlattice crystal. For the purposes of the present work such a distinction is not important, and we shall retain the bulk labeling for simplicity. It must be stressed, however, that the defect-molecule model is an extremely basic model that takes no account of the interaction between the defect and the lattice, and as such makes no quantitative prediction concerning the energies of the resonances. It does, however, provide us with a useful framework and language for the interpretation of the results of the ab initio calculations. The defect-related states in which our primary interest lies are the localized resonances, whose features reflect the microscopic interaction of the defect with the lattice. We do not concern ourselves with the extended shallow donor state, bound by the Coulomb potential of the ionized donor. The restricted size of the unit cell that can be

4

FUNDAMENTAL PHYSICS

203

studied using ab initio techniques makes them unsuitable for studies of extended features, which can, in any case, be well-accounted for by simple models. The interesting physics underlying the behavior of the defects is contained in the localized resonances. The projection of such effects onto the extended shallow donor and excitonic wavefunctions would provide a direct link to experimental spectra, but is beyond the scope of the present article.

2.

INTERFACE-INDUCED

LOCALIZATION AT DONORIMPURITIES

One of the most interesting impurities in SiGe heterostructures is that of substitutional antimony. The inclusion of Sb layers as a surfactant in the MBE growth process is found to improve greatly the quality of the heterostructures. However, the use of Sb in this way inevitably leads to the presence of Sb defects, particularly in the Si layers, where the tensile strain favors the accommodation of the larger Sb atoms. We therefore concentrate initially on the behavior of substitutional Sbsi defects at the interfaces of SiGe superlattices. The ab initio calculations described above were applied to a Si4Ge4 superlattice (grown on a Sio.sGe0.5alloy substrate), in the presence of the antimony defects. In order to identify the effect of the interface potential on the defect-relatedstates in the superlattice we also compare with calculation of substitutionalSb in bulk Si, with the Si strained to the same alloy substrate as the superlattice. Figure 18 shows the computed charge density associated with the A1A resonance (lying close to the conduction bandedge) for the Sbsi defect in the superlattice. The charge density in Fig. 18a, b is plotted in the planes A and B, respectively, where A and B are the planes indicated in Fig. 16. Plane A lies parallel to the interface and passes through the defect atom, while plane B is perpendicular to the interface, again passing through the defect atom. The positions of the atoms that were situated in the plotting planes prior to relaxation, and which moved only a small distance from the plane on relaxation, have been projected onto the plotting planes. For comparison,Fig. 19a, b show the charge density of the A l A resonance in bulk Si, again through planes A and B, respectively. These plots demonstrate the near-spherical distribution of the localized AIA resonance associated with the Sb defect in strained bulk Si. Both planes show a highly symmetrical charge density around the defect atom. This contrasts sharply with the case of the superlatticeillustrated in Fig. 18. In the plane parallel to the interface, the defect resonance has been strongly perturbed, taking on an axial shape. Similarly, in the plane perpendicular to the interface, the symmetry of the charge distribution has been lowered. The changes in the chxgeaensity distributions between Figs. 18 and 19 indicate a strong coupling between the Sbsi defects and the Si-Ge interfaces. The introduction of the interfaces has dramatically affected the nature of the localized A1A resonance. The detailed form of the interface-relatedresonance in the superlattice is illustrated in Fig. 20, where the charge density is plotted on a series of slices through the superlattice parallel to the interfaces. One can see that the

204

M. J. SHAWAND M. JAROS

~

b) Plane B

-

0

I High

1

FIG. 18. The charge density (arbitrary units) of the AIA resonance of a substitutional antimony defect in the Si4Ge4 superlattice, plotted in (a) plane A, parallel to the interface, and (b) plane B, perpendicular to the interface. The circles represent projections of the Si (solid) and Ge (open) atoms that lay in the plotting plane prior to relaxation, and the open box shows the position of the antimony atom.

interface-induced charge localization occurs most strongly on the Si side of the defect ion. From Fig. 20 it is apparent just how strongly the defect-interface interaction alters the spatial charge distribution of the A1A resonance. At this point it is worth recalling the expectations of the defect-molecule picture. This simple model predicts the formation of bonding resonances (A1B and T2B, see Fig. 17) in addition to the A l A resonance observed so far. Are these predictions verified by our full-scale calculations? Figure 2123 shows the charge density of the lowestenergy occupied level in our calculation, lying below the bottom of the valence band in the unperturbed superlattice. This highly localized state is clearly of A1 symmetry, and corresponds to the A1B resonance. Figure 21b shows the charge density of one of the T2B resonances lying around the middle of our valence band, the p-like symmetry apparent. Our ab initio calculations therefore support the qualitative picture provided by the intuitive defect-molecule model. These lower-energy resonances describe the

4

FUNDAMENTAL PHYSICS

205

a) Plane A

High

I I I

S

l

5m

g

e

€3

0 0 LOW

b) Plane B High

I

I

0 0 0 Low

FIG.19. The charge density (arbitrary units) of the AIA resonance of a substitutional antimony defect in bulk Si strained to a Sio.5Geo.5 alloy substrate, plotted in (a) plane A, parallel to the substrate, and (b) plane B, perpendicular to the substrate. The circles represent projections of the Si atoms that lay in the plotting plane prior to relaxation, and the open box shows the position of the antimony atom.

modification to the charge associated with the bonding between the defect atom and its neighbors in the region of the interface. That is, they reflect the changes to the interface bonds themselves. It is now interesting to contrast the behavior of the antimony defect with that of substitutional arsenic (Assi). We return to the study of the A1A resonance close to the conduction bandedge. The calculated charge density of the Assi AIA resonance is plotted parallel and perpendicular to the interfaces of the SkGe4 superlatticein Fig 22a, b. The Assi defect is seen to result in a near-spherical localized AlA charge density, qualitatively very similar to that of Sbsi in bulk Si. In other words, in contrast to the strong coupling between the antimony and the interfacial potential, the arsenic defect is largely unaffected by the presence of the interfaces. From the foregoing discussion it is apparent that there is a significant difference between the behavior of the antimony and arsenic defects. Specifically, the defect-

M. J . SHAWA N D M. JAROS

206

Hieh

SbSi,

FIG.20. The charge density (arbitrary units) of the A l A resonance o f a substitutional antimony defect in the Si4Ge4 superlattice, plotted on a number of planes parallel to the superlattice interface. The planes shown lay in the immediate vicinity of the interface at which the defect is placed, from the plane of Ge atoms forming one side of the interface, through Plane A containing the Sb defect, to the next plane of Si atoms. The solid circles represent projections of the atoms laying in the planes prior to relaxation, for the three planes that coincide with atomic planes. The text at the right-hand side of the diagram indicates the atoms present in the unit cell at each of these layers.

interface coupling has been found to be far greater in the case of the antimony compared to that of the arsenic. What is the origin of this difference? It is not clear from the forementioned discussion whether the contrasting behavior originates primarily through a size effect, that is, where the difference arises mainly through the differing degrees of lattice relaxation for the two defects, or whether the difference is essentially a chemical effect, determined by the microscopic nature of the atomic species. Certainly, the larger Sb atom induces a relaxation in the lattice of around two times that caused by the As defect, and it could reasonably be expected that this could account for the difference in behavior. The theoretical method we have employed allows us to isolate these effects by “freezing” the atoms at nonequilibrium positions. In particular, we can place, for example, the Assi defect in a unit cell whose positions have been relaxed for an Sbs; defect, and then calculate the self-consistent charge density. The charge density of the A1A resonance for just this situation (Assi in a cell with Sbs; positions) is shown in Fig. 23. The resonance is clearly very similar to the relaxed Ass; resonance in Fig. 22a suggesting that the different degree of relaxation in the lattice is not the primary cause of the difference between the antimony and arsenic defect resonances. The strong defect-interface coupling, which occurs for the antimony defect, is thus seen to arise through its microscopic “chemical” properties, and not due to the large

4 FUNDAMENTAL PHYSICS

207

1

High

FIG.2 1. Charge densities (arbitrary units) in plane A of (a) A1B and (b) T2B resonances of a substitutional antimony defect in the Si4Geq superlattice. The circles represent projections of the Si atoms that lay in the plotting plane prior to relaxation, and the open box shows the position of the antimony atom.

perturbation to the lattice that it induces. This is verified by calculations of the reverse case, where the Sbsi defect is placed in the lattice relaxed for Assi. In this case the resonance remains strongly coupled to the interface, although its energy relative to the conduction bandedge changes.

3.

DEFECTPERTURBATIONS T O CONDUCTION

STATES

The introduction of a substitutional defect such as Sbsi or Assi has been shown to introduce localized resonances that in the case of Sbsi interact strongly with the Si-Ge interfaces. In addition, however, the presence of these defects, and the localization of charge associated with them, will perturb the conduction band states of the perfect

M. J. SHAWAND M. JAROS

208

b) Plane B

, -, 0

0

i-J

LOW

FIG. 22. The charge density (arbitrary units) of the A1A resonance of a substitutional arsenic defect in the Si4Ge4 superlattice, plotted in (a) plane A, parallel to the interface, and (b) plane B, perpendicular to the interface. The circles represent projections of the Si (solid) and Ge (open) atoms that lay in the plotting plane prior to relaxation, and the open box shows the position of the arsenic atom.

superlattice. In this section we shall study the effect on the conduction states due to the presence of the Sbsi and Ass; defects. First, let us examine the lowest two conduction states in the perfect superlattice. The charge density of these states, integrated in the plane parallel to the interfaces, is plotted as a function of position in Fig. 24. Inset is a schematic diagram showing the selection rules for the transitions across the fundamental gap. Note that for the particular superlattice structure studied here, all transitions between the upper valence bands and the lowest conduction band are symmetry-forbidden. The lowest energy allowed transitions across the gap are to the second conduction state. In Fig. 25 the integrated charge densities are plotted for the lowest conduction band in the structures with Sbs; and Assi defects. These are compared to the charge density of the unperturbed superlattice. It is clear from this figure that the symmetry of the conduction state has changed. This is reflected in the selection rules of the perturbed

4 FUNDAMENTAL PHYSICS

209

FIG.23. The charge density (arbitrary units) of the AIA resonance of a substitutional arsenic defect in the SiqGeq superlattice where the atomic positions are frozen at those of the antimony defect. The charge density is plotted in plane A and the circles represent projections of the Si atoms that lay in the plotting plane prior to relaxation, and the open box shows the position of the arsenic atom.

systems illustrated in the inset to Fig. 25. The presence of the defects lowers the wavefunction symmetry and results in allowed transitions to the lowest conduction band. It is also clear that the strong coupling of the Sbsi defect, which played such a large role in determining the form of the resonances, also results in an increased perturbation to

I'

0 0

Growth Direction

FIG.24. The charge density of the lowest two conduction states in a perfect SiqGe4 superlattice, integrated in the plane parallel to the interfaces, are plotted along the growth direction. The solid and open circles at the bottom indicate the positions of the planes of silicon and germanium atoms, respectively. The inset shows the selection rules for optical transitions across the gap. The symbols 11 and Iindicate the polarization of the incident light.

210

M. J. SHAWAND M . JAROS

FIG. 2 5 . A comparison )f the charge densities, integrated in the plane parallel to the interfaces, of the Si4Ge4 superlattice with Sb and As defects. Also shown is the charge density of the perfect stmcture. The positions of the atomic planes are indicated at the bottom of the diagram (solid-Si planes, openGe planes), and the plane in which the defect occurs is shown. The inset shows the selection rules in the perturbed systems, with the symbols (1 and Iindicating the polarization of the excitation. [Reprinted with permission from the American Physical Society, Shaw, M. J., Briddon, P. R., and Jaros, M. (1996). Phys. Rev. B54,16781.1

the conduction-band wavefunctions. Figure 25 shows that the conduction states are perturbed to a far greater extent by the Sbs, defect than by ASS,. The modification of the selection rules suggests that the alteration to the electronic structure associated with the presence of the defects in the superlattice provides a mechanism for changes to the optical response of the systems. Of course, it should be remembered that experimental studies of the optical spectra of such structures will be dominated by the extended features of the system, such as the shallow donor and excitonic states. The microscopic approach, which has been applied here, is not appropriate for the study of such extended features. However, we have demonstrated that the microscopic interactions between the defects and the Si-Ge interfaces result in changes to the electronic wavefunctions that can affect the optical properties of the superlattice. Further, these interactions are shown to distinguish the chemical nature of the defect. The large perturbation to the form of the conduction states that results from the defect-interface coupling will clearly also modify the transport properties of the system. Again, a full evaluation of the effect on the mobilities and carrier lifetimes, and so on, does not lie within the scope of this article. It is, however, clear that the localized interface features identified will play an important role in determining both the optical and transport characteristics of SiGe structures.

4 FUNDAMENTAL PHYSICS

4.

211

LOCALIZATION AT GE IMPURITIES IN SI LAYERS

In most practical applications of SiGe-strained layer systems the formation of layers containing mixtures of Si and Ge occurs. This may be intentional, where one attempts to grow an alloy layer or substrate buffer, or may occur naturally through disorder or reconstruction at interfaces. It is therefore essential to understand how Ge atoms behave in Si layers, namely, is it appropriate to consider the system as that of a simple alloy? In most cases it is assumed that layers containing Si and Ge atoms can be very well described as a simple alloy. Indeed, the use of the virtual crystal approximation in theoretical studies of SiGe is widespread. However, the model used to describe the behavior of substitutional donors in the foregoing text can also be used to examine the effect of a substitutional Gesi defect, effectively the situation in a GeSi alloy. As expected, the effect of the isovalent defect is generally far smaller than that of the group-V donors considered so far. The wavefunctions obtained from our calculations show that the lowest conduction band is only very slightly perturbed from the perfect superlattice case, supporting the assumption that the alloy description is reliable. However, the second conduction state, whose charge density is plotted in Fig. 26, shows a rather surprising feature. There is a considerable degree of localization around the Ge atom, a feature that is contrary to the predictions of a simple alloy model. This result suggests that when the full microscopic properties of the interfaces are taken into account, the Ge atom exhibits a behavior that is not entirely consistent with simple alloy models. While this is clearly a secondary effect, and while the alloy model does pro-

High

FIG.26. The charge density (arbitrary units) of the second conduction state of a germanium defect in the SiqGeq superlattice, plotted in the plane parallel to the interfaces. The solid circles represent projections of the Si atoms that lay in the plotting plane prior to relaxation, and the open box shows the position of the defect atom. [Reprinted with permission from the American Physical Society, Shaw, M. J., Briddon, P. R., and Jaros, M. (1996). Phys. Rev. B54, 16781.1

212

M. J. SHAWAND M. JAROS

vide a good description of most of the properties of GeSi, our predictions do indicate that the applicability of the alloy model is limited.

VI. Microscopic Electronic Structure Effects in Optical Spectra In the previous sections we have shown how the microscopic features associated with the Si-Ge interfaces themselves are reflected in the luminescence spectra observed from interband transitions in GeSi-strained layer heterostructures. The microscopic models described in this chapter are also able to predict effects on a number of other optical phenomena, including absorption and nonlinear optical spectra. Use of these models can provide a physical understanding of the microscopic processes underlying the behavior, and to enable the design of optimum structures for particular applications. In the present section we shall briefly review the essential physics behind some of these effects. One of the applications of SiGe structures which has generated great interest in recent years has been the possibility of infrared detector development (Wang and Karunasiri, 1993; Robbins et al., 1995). To achieve an absorption at infrared wavelengths in the 3-5 p m and 10-15 prn ranges, p-doped Si-Si,GeI-, superlattices are used. Absorption from occupied to unoccupied valence minibands results in an intravalence band contribution to the absorption that may be resonantly enhanced at the photon energies of interest. The infrared photon energies are not sufficient to allow intertiand absorption to take place. The empirical pseudopotential method enables the origin of the dominant intravalence band transitions to be identified. It is then possible to identify key design parameters such as alloy and doping concentrations, layer widths, and so on, which determine the strength and angular properties of the absorption, and allow the response to be tuned throughout the infrared spectrum. Such parameters are necessary for the design of efficient infrared detector devices. Many calculations of absorption spectra for p-type SiGe infrared detectors are described in detail in the literature (e.g., Corbin et al., 1994a, 1994b). Here we shall provide a brief overview of some of the principal physical insights obtained from the microscopic theory. In the design of suitable structures one of the most important factors to consider is the angular dependence of the absorption response. For many detector applications a large response to light incident normal to the interfaces is most favorable. However, such a response is made possible only through mixing of the valence minibands, and consequently cannot be described without invoking a microscopic theory such as that applied by Corbin et al.. In addition, the empirical pseudopotential approach enables the minibands involved in the dominant absorption processes to be identified. For the case of a typical p-doped Si-Si,Gei-, quantum well (20-monolayer well with 15% germanium), the normal incidence response is found to originate from transitions between the ground heavy-hole state (HH 1) and the ground split-off state (Sol). A larger parallel incidence response can be identified with the HHl to first

213

4 FUNDAMENTAL PHYSICS

->,

+ 15% Ge

200-

9309. Ge

-. r sepaotion for ......

E

15% Ge

W

C 0

150-

0)

0

Q Y

o

W

a

100-

1

20

I

I

I

I

I

I

25

30

35

40

45

50

55

Well width (monolayers) FIG.27. The variation of the energy (meV) of maximum parallel incidence absorption with well width (monolayers) for p-doped Si0.85Ge0.15 and Sio.7Geo.3 quantum wells. Also shown is the zone-center (r) separation of the ground and first excited heavy-hole minibands, transitions between which dominate the parallel incidence absorption response. [Reprinted with permission from the American Physical Society, Corbin, E. A,, Wong, K. B., and Jaros, M. (1994). Phys. Rev. B50.2339.1

excited heavy-hole (HH2) transitions. Variation of the well width and/or alloy concentration results in a change in the energy of the maximum absorption response, as shown for parallel incidence absorption in Fig. 27. Judicious choice of these growth parameters enables the principal response wavelength to be selected. However, the absorption spectrum includes contributions from throughout the volume of the Brillouin zone that is occupied by the hole carriers. As a result the energy at which the maximum response occurs does not correspond to the zone-center energy separation of the minibands involved. Rather, the precise energy of maximum absorption depends on the microscopic properties of the minibands throughout wavevector space. The discrepancy between the zone-center miniband separations and the energy of the absorption peak is illustrated in Fig. 27. A further property that plays an important role in device application is that of the lineshape, and it is important to consider some of the factors that determine the shape, and particularly the width, of the absorption peak. For example, the absorption spectrum is plotted for a number of different doping concentrations, distinguished by the Fermi level, in Fig. 28. The lineshape of the absorption is found to depend on the properties of the minibands throughout wavevector space, and is determined by a number of design parameters including the doping level. Clearly, the task of tuning

214

M. J. SHAWAND M. JAROS

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Wavelength (m) FIG.28. The imaginary part of the first-order susceptibility (arbitrq units), representing the linear absorption, is plotted against photon wavelength (m) for several different Fermi energies in p-doped Si0.7Geo 3 quantum wells. The Fermi levels studied, given relative to the energy of the valence bandedge, describe systems of different doping concentrations. [Reprinted with permission from the American Physical Society, Corbin, E. A,, Wong, K. B. and Jaros, M. (1994). Phys. Rev. B50,2339.]

the absorption energy, and of optimising structures for particular applications, must be addressed using a full-bandstructure description of the heterostructures, accounting for the dispersions of the key minibands. The microscopic description of the electronic structure provided by the empirical pseudopotential calculations also enables us to develop an understanding of a wide variety of physical processes that limit the performance of infrared detectors and other optoelectronic devices. For example, while the absorption process itself is clearly essential to the performance of an infrared detector device, the dynamic properties of the photoexcited carriers are critical in determining its performance. The carrier lifetime is one such property, and in many devices it is limited by nonradiative, Auger recombination (Landsberg, 1991). A typical Auger process is shown in Fig. 29, where the photoexcited carrier in the SO1 band recombines nonradiatively with an electron in the ground lighthole band (LHl), the excess energy exciting a second lighthole electron into the HH1 level. Clearly, such a process removes the photoexcited carrier from the SO1 band from which it would be collected, resulting in a degradation in detector efficiency. However, it is possible to design the heterostructure such that the energy separations of the minibands prevents the forementioned process from taking place. That is, by setting the HH1-LH1 separation greater than that of LH1-Sol, so that the

4 FUNDAMENTAL PHYSICS

215

Intersubhand Absorption

Auger Recombination

Electron 2 does not have

FIG.29. Schematic diagram of a typical Auger recombination process by which a photoexcited carrier in the split-off miniband recombines with an electron in the light-hole miniband. Also shown is the condition for which this process becomes forbidden. [Reprinted with permission from the American Physical Society, Corbin, E. A,, Cusack, M., Wong, K. B., and Jaros, M. (1994). SuperlatticesandMicrostructures 16,349.1

energy released by the recombination is not sufficient to allow excitation from LH1 to HH1, the process is energetically forbidden (see Fig. 29). If such a condition may be satisfied throughout a substantial fraction of the active region of the Brillouin zone then an increased lifetime may be achieved. In practice, the elimination of the process over a sufficiently large volume of the zone has proven difficult to achieve. Furthermore, this process is just one of a number of similar Auger recombination mechanisms that can degrade the device performance, the elimination of which requires a considerable design effort (see Corbin et al., 1996) based upon the microscopic bandstructure of the heterostructures. For many applications an important consideration is the behavior of the heterostructure in the presence of externally applied electric fields, which arise, for example, through the operating bias of the device. The perturbations to the electronic structure induced by such fields can significantly modify the response that would occur with no such field present. Including the electric field as a perturbation to the zero-field superlattice potential allows the field-induced properties to be calculated from the results of empirical pseudopotential calculations (Jaros et al., 1995). Consider, for example, the case of Si-Ge double-well emitters, which have received considerable attention in the literature (Engvall et al., 1995; Gail et al., 1995, 1996). The bandedge diagram for one such structure is shown in Fig. 14, where the central Si layer confines the lowest conduction level and the valence bandedge states are localized in the narrow Ge layers. Both Ge layers are 4 monolayers wide, and are separated by 20 monolayers of Si. The calculated charge densities for the levels close to the bandedges are plotted in Fig. 30 for external electric fields of 0, 1 and 4 x lo5 V/cm-'. With no external applied field the conduction and valence bandedge states are localized as predicted in the foregoing.

216

M. J. SHAW AND M. JAROS Charge Densities: alloy substrate with doping of 5 x ; 1 cm3 c2 CI

v1

VI

v2

v2

v3

u

v3

v4

v4

FIG.30. The charge densities associated with the confined levels at the conduction and valence bandedges of the double-well structure shown in Fig. 14. Results are presented for zero field, and for external electric fields of 1x lo5 V/cm-‘ and 4x LO5 V/cm-’. [Reprinted from Journal of Crystal Growth 157, Jaros, M., Elfardag, G., Hagon, J. P., Turton, R. J., and Wong, K. B., “Optimisation and stability of optical spectra of novel Si-Ge quantum well structures in an external electric field,” 1 1-14,1995,with kind permission from Elsevier Science-NL, Sara Burgerhartstraat 25, 1055KV Amsterdam, The Netherlands.]

With an applied field it can be seen that the conduction state remains well-localized to the Si layer, despite being confined only by the narrow Ge layers. In addition, the ground-hole states remain strongly localized in the Ge, though their symmetry has been modified to result in localization in a single well. Calculations of the transition probabilities for cross-gap emission processes show that up to fields typically present in experimental conditions (up to x 1 x lo5 Vkm-’), there is no significant degradation in the emission strength. The design of this structure was performed with such stability in mind, and experimental studies of such structures show that the emission does indeed remain stable in the presence of external fields. So far, we have examined some of the physical properties of superlattices that affect the electronic structure of SiGe superlattices, and how these in turn can affect the linear optical response (i.e., absorption). There is also great interest in the nonlinear optical response of semiconductor heterostructures under excitation by intense laser excitation. Noniinearities in the response of a crystal can give rise to effects such as harmonic generation, difference frequency generation and an intensity-dependent refractive index, with huge potential for application as optical modulators and optical signal processing components (e.g., Shen, 1994). Calculations of the nonlinear optical susceptibilities can be achieved by evaluation of microscopic expressions derived from density matrix theory, using empirical pseudopotential bandstructures. Such calculations are described in considerable detail in the literature (e.g., Shaw et al., 1984). As

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FIG. 3 I . Schematic diagram of the virtual excitation processes that can be resonantly enhanced in microstructures to achieve large second harmonic generation.

in the case of the linear absorption calculations, the microscopic origin of the contributions to the spectral response can be identified, opening the way for optimization of the nonlinearity. Just as p-type SiGe superlattices have been used to exhibit an absorption in the 10-15 p m infrared region of the spectrum, so similar structures can be designed to exhibit an enhanced second-order nonlinear response at these frequencies. By choosing structures in which there are three equally spaced levels it is possible to resonantly enhance the second harmonic generation processes indicated in Fig. 3 1. Such processes, consisting of three virtual transitions, occur on ultrashort timescales and lead to the creation of second harmonic radiation. Of course, as the overall response will consist of contributions from across the populated region of the Brillouin zone, exact achievement of this enhancement is not possible. A third layer is inserted into the quantum wells to lower the symmetry of the states. For the symmetric well structures designed for the study of absorption, all of the components of the second-order susceptibility tensor are zero. The asymmetric stepped well structures have a lower symmetry and as a result exhibit five independent nonzero components. The second-order susceptibility describing the second harmonic generation process, written x g B ( - 2 w ; w , w ) (where a and j3 are the polarizations of the incident photons of frequency w and p is the frequency of the second harmonic, 2w response), was calculated for the p-type (001) 18Sio.gsGeo.15/2Si0.925Ge0.075/40Si superlattice (where 40Si refers to 40 monolayers, 10 lattice constants of Si). The frequency dependence of the five nonzero components is plotted in Fig. 32, where the doping concentration is such that the Fermi level lies 26 meV below the valence bandedge. The full microscopic expression for the susceptibility, and further details of the calculations, are described in Shaw et al. (1993). By evaluating specific terms in the expression for the susceptibility

218

M. J. SHAWAND M. JAROS x10’

1 .o Component

__

0.09

0.095

0.1

0.105 0.11 0.115 Photon Energy (eV)

u x

0.12

0.125

0.13

FIG. 32. The magnitude of the five independent components of x:dp(-2w; w , w ) in esu, plotted against the photon energy in electronvolts, for the p-type (001) 18Si0,85Ge0.1~ /2Si0,925Ge0,07~/40Sisuperlattice at 0 K. [Reprinted with permission from the American Physical Society, Shaw, M. J . , Wong, K. B., and Jaros, M. ( 1993). Phys. Rev. B48,200 I .I

it is possible to identify the particular excitation sequences that dominate the response. (2) at around 100 meV in Fig. 32, the dominant processes For the principal peak of xzzz are found to be C+SO+HHl+C and SO+HHl-+C+SO (where HH1 refers to the ground heavy-hole state, SO refers to the spin split-off state and C refers to states lying in the continuum). These processes correspond to those illustrated schematically in Fig. 3 1, which can be resonantly enhanced if the miniband separations are approximately equal. We note that, as in the case of the linear absorption, the maximum of the second-harmonic response did not in fact correspond to the zone center separation of the minibands involved. For example, while the HHl-SO1 separation is 107 meV at the zone center, the peak in absorption occurs some distance from this. This is a result of the contribution from wavevectors away from the zone center, and the dispersion of the superlattice minibands. The energy shifts are more prominent for the peaks of components and x !: for which the strength of the key transitions depends upon the momentum mixing of the minibands. As the momentum mixing is only strong at wavevectors lying away from the zone center, these components are dominated by such contributions, and the peak energy is not determined by the zone-center separations.

x:zi

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It is clear then that the frequency and angular dependences of the nonlinear response are governed by the properties (e.g. dispersions, mixing) of the minibands throughout the Brillouin zone. The design of suitable structures therefore involves a consideration of the bandstructure properties throughout k-space, and not simply at the zone center. In particular, the angular dependence of the second-harmonic response is important in the design process, as this determines the geometry of any device. Specifically, it is desirable to have a device that operates with normal-incident light, a geometry more easily realized in practice. This corresponds to light polarized in the x - y plane, and ( 2 ) component. to, for example, the xzxx These examples demonstrate the essential role played by the microscopic bandstructure features in the optical spectra of SiGe heterostructures. The principal features in the linear and nonlinear spectra can be understood in terms of the microscopic transition processes, and in turn through the properties of the minibands themselves. VII. Conclusion The properties of strained layer GeSi heterostructures cannot be well described using a simple effective mass approximation. While such a model is adequate for understanding many of the features of unstrained structures (e.g., AlGaAdGaAs), its neglect of the microscopic potential variations is no longer reasonable for strained systems, where the atoms are displaced from the regular lattice positions. It is necessary to use more sophisticated techniques to capture the microscopic physics that underlies these structures. One such method is the empirical pseudopotential method in which a microscopic pseudopotential, fitted to reproduce particular empirical data, is included. This approach provides a good description of most of the properties of ideal systems, and can be extended to include a perturbative description of features such as disorder and so on. The computationally intensive density functional theory approach using ab initio pseudopotentials provides a complete microscopic description, and allows a detailed study of short-range features of the system unable to be described by the empirical pseudopotentials. Such a model enables the microscopic signature of the Si-Ge interfaces to be studied, opening the way for definitive distinction between microstructure and strained alloy systems. These two theoretical techniques together provide a means to obtain a complete description of the GeSi structures. The bandstructures of perfect GeSi heterostructures, for example, superlattices, are dominated by the effects of strain and of zone-folding due to the superlattice long-range order. The precise choice of substrate and layer widths determines the very nature of the structure, that is, direct or indirect, and as such the suitability for optical applications. Of course, it is not possible to grow “perfect” structures, and as one might expect the properties of the structures depend on the quality of the growth process. A study of random disorder at interfaces and an ordered reconstruction of the interfaces (such as is observed experimentally) shows that in both cases the strength of the direct transition

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is reduced, while the indirect transition to the in-plane minima is enhanced relative to the perfect structure. The effect is sufficiently strong in the randomly disordered case that the direct and indirect transitions become comparable. The optical properties of “real” structures are therefore seen to differ from those of an idealized system. Although the empirical pseudopotential calculations used have been shown to agree well with many of the experimentally observed phenomena, there remains a discrepancy with regard to some optical spectra. Experimental observations of luminescence spectra indicate that the in-plane minima dominate the spectra. The extent of random disorder required to produce sufficiently strong in-plane transitions is incompatible with what is known about the samples concerned. A mechanism that provides a possible explanation involves the role of interface islands. Calculations indicate that in the presence of sufficiently large islands the optical recombination will be dominated by impurity atoms at the interfaces, and the breaking of the inplane symmetry at the interface could enhance the indirect transitions to the observed level. It is clear then that the interfaces play a key role in determining the optical response of the structures. In many calculations, the interfaces are represented by an abrupt semiclassical step-like potential, neglecting the microscopic variations of the potential in the region of the interface bonds themselves. The ab initia pseudopotential calculations presented here include a complete microscopic description of the interface region, the “intrafacial” properties. These intrafacial parameters govern the behavior of certain impurities in the vicinity of the interfaces, modifying the optical and transport properties of the structure. In particular, interface-induced localization occurs at substitutional antimony defects situated adjacent to the Si-Ge interfaces. This localization is primarily dependent on the chemical nature of the impurity (rather than, say, its size) and is the result of the microscopic defect-interface interaction. Such interface localization effects provide a possible foundation for an understanding of the observed luminescence spectra. While the interband transition spectra are governed by transitions weak or forbidden in the perfect case, and hence require an additional description of disorder and impurity effects, the intraband optical processes of doped GeSi structures are well described by the “perfect” calculations. These processes are technologically important in optical device applications, and show linear and nonlinear optical responses governed by the details of the superlattice bandstructure. The microscopic origin of the optical response can be identified, enabling the specific features of the superlattice to be tuned to give optimum performance. For GeSi heterostructures to fulfill their enormous potential it is essential to gain an understanding of the microscopic physical processes underlying their behavior. While these materials have many inherent advantages with regard to applications, there are several challenges that must be overcome if their use is to become widespread. Primarily, for optoelectronic applications, upon which we have chosen to focus in this chapter, one must address the issue of the indirect nature of the materials. Bandstructure en-

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gineering techniques can be applied to obtain direct-gap heterostructures in which the optical response is improved. However, there remains the difficulty of growing highquality layers in the presence of such high strain. As the calculations of this chapter show, the optical properties suffer a severe degradation through the existence of disorder and reconstruction, common at the interfaces of these strained systems. Perhaps most significantly, however, it is necessary to be able to characterize and distinguish between microstructure and alloy-related features. To achieve this we have demonstrated that a full microscopic description of the heterointerfaces themselves, the “intrafacial” parameters, provides us with a microscopic signature of the interfaces. Indeed, our theory indicates, in agreement with experimental data, that some of the key optical and transport properties of SiGe systems are dominated by the microscopic properties of the interfaces. The future development of strained-layer GeSi devices depends, both in the case of switching applications (e.g., through carrier lifetime) and optical applications (e.g., through transition strength), on our understanding of the physics associated with the heterointerfaces themselves. As we have shown in this chapter, this problem cannot be addressed using the conventional physical models usually applied to heterostructures. Rather, a microscopic treatment of the intrafacial parameter space is required. This defines a clear role for fundamental physics that must be fulfilled to enable continued advances in strained layer GeSi device technology.

ACKNOWLEDGMENTS We would like to thank the U. K. Engineering and Physical Science Research Council, D.E.R.A. (Malvern), and the Office of Naval Research (USA.) for financial support. Work on GeSi has been carried out at the University of Newcastle upon Tyne for a number of years, and we would like to thank those involved, in particular, R. J. Turton, P. R. Briddon, K. B. Wong, J. P. Hagon, and E. A. Corbin for many helpful discussions.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 56

CHAPTER 5

Optical Properties Fernando Cerdeira INSTITUTO DE F ~ S I C A UNlVERSlDADE ESTADUALDE CAMPINAS, UNICAMP

SAo PAULO,BRAZIL

I . INTRODUCTION . . . . . . . . . . . . . . . . . . . . 11. FORMSOF DIFFERENTIAL S P E C T R O S C O P Y BASEDO N REFLECTIONO R ABSORPTION O F LIGHT. . . . . . . 1. General Considerations . . . . . . . . . . . . . . . 2. On Pseudo-direct Optical Transitions . . . . . . . . 3. Other Optical Transitions in Si/Ge,Sil --x and

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Ge/Gex Si 1 Microstructures 4. Other Optical Transitions in Ge,Sim Quantum Wells and Superlattices . . . 111. RAMANSCATTERING ............ ......... 1. General Considerations . . . . . . . . . . . . . . . . . . . 2. Raman Scattering in Bulk GexSil-, Random Alloys . . . . 3. Raman Scattering by Optic Modes in Ge,Sim QWS and SLs 4. Raman Scattering by Acoustical Phonons in Si/Ge Microstructures ... 5. Resonant Raman Scattering . . . . . . . . . . . . . . . . . 6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . .

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I . Introduction. . . . . . . . . . . . . . . 2. PL from Bulk Ge,Sil-, Alloys . . . . . 3. P L from Si/Ge,Sil_, Microstructures . 4. PL from Ultrathin Ge,Si, QWs and SLs V. CONCLUDING REMARKS . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . .

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I. Introduction The optical properties of semiconductors have provided rich information on such diverse aspects of their physical properties as their electronic and vibrational states and the existence and nature of defects and impurities. In the particular case of seniiconductor heterostructures, some optical techniques have provided information about their structure (super-periodicities, layer thicknesses, etc.) and that of their interfaces. Light incident on a semiconductor surface is partly reflected and partly transmitted. The reflected light carries information about the electronic states of the material. Part of the light that enters the semiconductor is absorbed or scattered while the remainder is transmitted if the sample is thin enough. The energy from the absorbed radiation can be dissipated (absorption) or re-emitted as photons of different frequencies (photoluminiscence). Photons can also be inelastically scattered by creating or annihilating elementary excitations within the semiconductor (Brillouin or Raman scattering). By now, so much information has accumulated about these forms of interaction of electromagnetic radiation with semiconductors and other materials that good accounts of the basic physics and experimental details involved in this interactions can be found in many textbooks and review articles (Yu and Cardona, 1995; Haug and Koch, 1990; Cohen and Chelinkowsky, 1989; Bassani, 1975). We shall not attempt to duplicate this work. Rather, we shall give brief introductory descriptions of the optical techniques that have contributed most to the understanding of the properties of Si/Ge heterostructures. These brief descriptions will be provided in any of the sections of this chapter that contain a discussion of the results obtained by a given technique. Thus, Section I1 is dedicated to discussing techniques based on reflectivity or absorption of light; Section 111 describes the results of inelastic light scattering; Section IV is devoted to photoluminescence. Finally, in Section V we attempt to summarize the main points developed in the previous sections. Because several techniques have sometimes contributed to an understanding of a given issue, this division into sections is not ironclad and the results from several techniques must be discussed together. In doing so, the results from techniques that have not yet been introduced are summarized, postponing more detailed discussions to the appropriate subsection.

11. Forms of Differential Spectroscopy Based on Reflection or Absorption of Light 1.

GENERAL CONSIDERATIONS

The quantities experimentally determined by these techniques are related to the real ( w ) ] and imaginary [ ~ 2 ( w )parts ] of the dielectric constant. The latter is sensitive to processes in which a photon is absorbed, lifting an electron from the valence into the [EI

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OPTICALPROPERTIES

227

conduction band. In these processes the total crystal momentum is conserved. Since the wave vector of the light is very small, compared to electronic wavevectors inside the Brillouin Zone (BZ), such transitions are essentially vertical and connect conduction and valence band states of virtually the same k-vector. Peaks and shoulders ap) the joint density of states of the bands involved in the transitions pear in ~ ( wwhen have singularities. These peaks and shoulders can be correlated to similar structures appearing in the reflectivity R ( w ) or the absorption coefficient a ( w ) of the material. The photon-energy at which these structures appear give precise values for the energy difference between valence and conduction band states at important symmetry points (or along symmetry axes) of the BZ, at which the joint density of states is singular (van Hove singularities) (Yu and Cardona, 1995; Haug and Koch, 1990; Cohen and Chelinkowsky, 1989; Bassani, 1975; Cardona, 1969). As an example we show in Fig. 1 the bandstructure of bulk Ge. In this figure the various electronic transitions responsible for structure in the optical properties are indicated. The most prominent structures in the optical coefficients are given names such as Eo (direct transitions at the BZ center), El (direct transitions along the (111) axis in the BZ), etc. Table I lists their transition energies for bulk Si and Ge (Yu and Cardona, 1995). Notice that in both these materials the fundamental gap is indirect, so that optical transitions across this gap must be assisted by large-wavevector phonons in order to conserve crystal momentum. Hence, these transitions provide only weak contributions to the optical constants. These show clear structures only for direct transitions (Fig. 2). In the upper curve of Fig. 2 we display the reflectivity of this material. As we can see, not all

FIG. 1. The bandstructure of bulk Ge showing the various direct transitions responsible for the structure in the optical spectra of Fig. 2. Adapted from Yu and Cardona (1995) with permission. To produce this figure, the authors of this textbook used data from Cardona and Poll& (1966).

228

FERNANDO CERDEIRA TABLEI. Measured energies (eV) of prominent structures in the optical spectra of bulk Si and Ge.

Transition

Si, hw(eV)

Ge, hw(eV)

EO

4.185 4.229 3.45

0.898 1.184 2.222 2.41 3.206 3.39 4.49 5.65

Eo + A0 El El

+A1

-

Eb E;, A;,

3.378

E2

4.330 5.50

+

E’1

-

All data refer to low temperature measurements, except for the Eo transition of Si, which has been taken at room temperature, compiled from data listed in Yu and Cardona’s book Fundumenruls of Semiconduclors ( 1995).

the vertical transitions indicated in Fig. 1 show up clearly in the reflectivity spectrum of Fig. 2(a). During the sixties, several techniques were developed for modulating either some sample parameter or the incoming or outgoing beams. These modulations produce spectra that are related to some derivative of the dielectric function. The process of differentiation suppresses uninteresting backgrounds and produces sharp structures in the photon-nergy region of the optical singularities. This point is illustrated in Fig. 2(b), where the electroreflectivity spectrum of bulk Ge is shown. In this technique an ac electric field modulates the optical properties of the material and the resulting spectrum is related to the third derivative of the dielectric function (Aspnes, 1973; Aspnes, 1980). Bumps and shoulders in R ( w ) (upper curve) are highlighted in the modulated reflectivity spectrum (lower curve). The latter gives good resolution of critical points, which are almost invisible in the plain reflectivity spectrum. Because of this advantage, modulation spectroscopy had a decisive influence in understanding the bandstructure of bulk semiconductors. Most of the work in this area was performed in the 1960s and early 1970s and has been extensively reviewed (Cardona, 1969; Aspnes, 1980). With the advent of semiconductor microstructures, there was a revival of interest in these techniques. Their applications to semiconductor superlattices and quantum wells have been recently reviewed by several authors (Pollak, 1989; Pollak 1991; Pollak and Shen, 1993; Cerdeira, 1993). Of particular importance have been the techniques of photo- and electromodulated reflectivity, in which an electric field is modulated within the sample by either depositing a semitransparent metal layer on the sample surface and applying an ac voltage between the front and the back of the sample or by photoinjecting carriers by a modulated secondary beam. The measured quantity is the ratio between the modulated ( A R ) and the dc parts of the reflectivity ( R ) . This is related to the third derivative of the dielec-

5

229

OPTICAL PROPERTIES

Photon Energy ( eV )

a8

I II 0.5

L\lll*

1

bulk Ge

1.0 1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy ( eV )

FIG. 2. (a) Reflectivity (adapted from Yu and Cardona (1985)with permission). To produce this figure, the authors of this textbook used data from Philipp and Ehrenreich (1967). (b) Electroreflectance (adapted from Pearsall er al. 1989a with permission) of bulk Ge. Peaks in the latter are identified according to the optical transitions of Fig. 1.

tric constant and is well represented by a, now, standard lineshape function (Aspnes, 1980):

where each term in the sum corresponds to a critical point of energy (lifetime broadening) E j ( r j ) ;C , and 4, are amplitude and phase factors, respectively, of the transition. The exponent n depends on the type of critical point. Choosing a value of this parameter for SLs and QWs has been the subject of much debate (Cerdeira, 1993). However, the value obtained for the critical energies by fitting the experimental data with Eq. (1)

230

FERNANDO CERDEIRA

is remarkably independent of this choice. The usefulness of this technique depends greatly on this feature of ER and PR lineshapes. An oblique angle of incidence technique that has been very useful in the last decade or so is that of spectroscopic ellipsometry. Its name refers the fact that when linearly polarized light, which is neither polarized parallel nor perpendicularly to the plane of incidence, is reflected obliquely from the semiconductor surface it emerges elliptically polarized. By determining the orientation and the ratio of the polarization ellipse axes, the real and imaginary parts of the dielectric constant can be obtained. Because of present-day accuracy in these measurements, numerical differentiation of E ( W ) can be performed that produces similar results to those of modulation spectroscopy (Yu and Cardona, 1995; Aspnes, 1980). This is illustrated in Fig. 3, where the third derivative of E ~ ( w )taken , from ellipsometric data is compared with electroreflectance results (Aspnes, 1983). Ellipsometric measurements have provided excellent values of dielectric constant and refractive indices of a large variety of bulk semiconductors (Aspnes and Studna, 1983). The accurate information about critical point energies obtained by the methods described in the foregoing paragraphs have had a symbiotic relationship with bandstructure calculations in the physics of semiconductors. In the following subsections we discuss the application of differential optical techniques to the determination of critical points in the electronic transitions of Si/Ge microstructures. When interpreting experi-

-

Photon Energy ( eV )

FIG. 3. (a) Real and imaginary parts of the dielectric constant for bulk Ge, (b) E - 2 d ' / d E 3 [ E 2 ~ l , from numerical differentiation of the curve in (a), and ( c ) A s from ER measurements. Adapted from Aspnes (1980) with permission.

5

OPTICALPROPERTIES

231

mental data we shall use simple concepts such as those of zone-folding or confinement of electronic states that can be derived from those of the bulk components. This method gives a good intuitive understanding of some results but is not applicable to all cases, so the reader is advised to read Chapter 4 of this volume, where the electronic structure of these materials is described in great detail.

2.

ON PSEUDO-DIRECT OPTICAL TRANSITIONS

It is expected that superlattices (SL) alternating n-monolayers of Ge with m-monolayers of Si (Ge,Si,), should produce, through zone-folding, a direct bandgap material with appropriate choices of n , m and the amount of strain in each type of layer. The strain can be controlled by the choice of substrate (Si or Ge) and buffer layer on which the superlattice is grown (see the chapter by Bean). In these superlattices the conduction band edge is formed from bulk-Si A states, while the top of the valence band originates in bulk-Ge r-point states. The A-conduction band of bulk Si forms a degenerate sextuplet, one for each (100) equivalent direction. In the SL the multiplet splits into a doublet ( A J and a quadruplet (All), for the valleys perpendicular and parallel to the plane of the layers, respectively. Choosing the SL period appropriately, the A 1 can be folded into the Brillouin zone center. This results in a direct gap material if the 2-fold A 1 minima are lower in energy than the 4-fold A 11 ones. This could be achieved by subjecting the Si layers to a tensile strain. Hence, we should not expect to find direct gaps in SL-grown lattice matched on Si. Paradoxically, it was a report of a strong optical transition at very low photon energies in such a material that produced a flurry of activity on the subject. Room-temperature electroreflectance measurements in a Ge4Si4 5-period SL exhibited a very strong line at 0.76 eV, which was tentatively identified as a direct transition between the valence band and the Al-folded conduction band (Pearsall et al., 1987). The spectrum, shown in Fig. 4(a), exhibits several other lines that can be attributed to direct transitions and in which zone-folding plays no role. The fact that the line at 0.76 eV (labeled “1” in Fig 4(a)) has an intensity that is comparable to those of these other lines was interpreted as a signature of a quasi-direct transition (i.e., a transition made direct through zone-folding). Although a tight binding band calculation by Brey and Tejedor (1987) gave support to this interpretation, the majority of calculations predicted an indirect gap (ie., they predicted that the lowest conduction-bands minima were produced by All states) (Wong et al., 1988; Hybertsen et al., 1988). Even for a pseudo-direct transition, the calculated oscillator strength is much smaller than the observed one. Subsequent measurements of photocurrent and electroreflectancein the same sample, interpreted with a first-principles band calculation, established the existence of two indirect absorption edges, at 0.78 and 0.90 eV, respectively, but not of a direct one (Hybertsen et al., 1988). The photocurrent measurements are shown in Fig. 4(b). The anomalous oscillator strength of these indirect transitions remained

-

,.,

-

232

FERNANDO CERDEIRA

Photon Energy (ev)

I " " "

0.2

0.4

'

06

0.8

1.0

" " I

1.2

1.4

16

Photon Energy (ev)

FIG. 4. (a) ER spectrum of a GeqSi4 SL with fitted critical point energies indicated by arrows. (b) Photocurrent signal for the same sample; the dashed lines show a fit with two indirect absorption edges and background. Adapted from Hybertsen ef al. (1988) with permission.

unexplained, although Hybertsen et al. (1988) mention end effects (their SL is only 5 periods long) and interface roughness as probable causes. The other lines in the ER spectrum of Fig. 4(a) were discussed in more detail in a later paper by the same group (Pearsall et al., 1989a) and their interpretation includes other transitions from the valence band to folded conduction band states whose intensity exceeds greatly that of the predictions of band calculations. These results will be discussed in Section 11.4, in the context of higher-energy direct transitions in Ge, Si, SLs. Next, electroreflectance measurements performed on two Ge,Si, ( n m = 10) SLs grown commensurately on Ge substrates are reported by Pearsall et al. (1989b). These SLs should have pseudo-direct bandgaps, produced by the folding of the A 1 conduction band edge, because they satisfy both the periodicity and strain conditions previously explained. Their spectra show a rich pattern of strong structures at photon

+

5

OPTICALPROPERTIES

233

energiesjust above that of the direct Eo peak of bulk Ge, which they attribute to pseudodirect transitions. First-principles band calculations show that such pseudo-direct gaps exist in this photon energy region, although the transitions associated with them should have negligible oscillator strength (Schmidt et al., 1991). Hence, the existence of a pseudo-direct gap does not necessarily explain the structure observed in the spectra of Pearsall et al. (1989b). This assignment is even less firm when we take into account the actual structure of the samples used in the experiments. In addition to the thick Ge buffer layer, each sample contains 20 repetitions of the basic 5-period Ge,(SimSL separated from one another by 25-nm-thick Ge layers. These thicker Ge layers contribute to the total spectrum with their own Eo transition and a strong pattern of Franz-Keldysh oscillations induced by the applied electric field (Aspnes, 1980; Cerdeira, 1993). These contributions fall into the same photon energy range as that of the pseudo-direct transitions from the Ge,Si, parts of the sample. In order to overcome the problem of the Franz-Keldysh oscillations, Yin et aE. (1991) performed a piezoreflectance study on a series of Ge,Si, SLs, including those previously studied by Pearsall et al. (1989b). Their piezoreflectance results show that the spectral features that had been identified as due to pseudo-direct transitions from the SL parts of the samples are, instead, quantumconfined Eo transitions originating in the 25 nm Ge spacer layers. However, the search for pseudo-direct transitions continues. Pearsall et al. also reported measurements of differential transmission on these samples that seem to support the idea of anomalously strong optical absorption at the pseudo-direct bandedge (Pearsall, 1992; Pearsall et al., 1995). While the controversial results of the modulated reflectivity work were being actively discussed, new evidence from photoluminiscence (PL) work performed on Ge, Si, SLs was added to the debate. Zachai et al. (1990) reported photoluminiscence experiments performed on a series of Ge,Si, SLs with different periods and states of strain. The strain variations were achieved by using either Si or Ge substrates and buffers of partially relaxed Si-Ge alloys. In all cases their SLs have many periods (total SL thicknesses of 200 nm), so end-effects cannot be invoked here. On the other hand, both the density of misfit dislocations and interface roughness should be larger here than in the shorter SLs used in the electroreflectance work (see the chapter by Bean). Figure 5 summarizes the results of Zachai et al. (1990). A very broad and inhomogeneously broadened peak at -0.84 eV appears in a strain-symmetrized sample with n + rn = 10. This sample has the right period and strain to have a pseudo-direct gap. This peak is either absent or very weak in samples that do not meet these criteria (i.e., samples with indirect gaps). Hence, these authors identified the PL line as a direct recombination, at the BZ-center, from the bottom of the folded A 1 conduction band to the top of the Ge-like valence band. This interpretation was hotly disputed by Schmidt et al. on the basis of their comparison of the photon-energy position of the PL peak and the value of the pseudo-direct gap obtained in their ab initio calculation for the SL used in the PL experiment (Schmidt et al., 1990). Also, the calculated oscillator strength for this pseudo-direct recombination is orders of magnitude smaller than that which would be

-

FERNANDO CERDEIRA

234 1

1

1

Si I Ge

1

1

1

1

,*Ge8

7 0.7

1

1

IW/crn2 urc -

-

I00W/ cm2

-

Xo.1 ,

1

IW/ cm2

Si, Ge2 ( alloy )

Si

~

T = 5 K hL=457.9 nm

.

l

0.8

,

l

0.9

, ,

l

1.0

,

A

l

,

1.1

Photon Energy (eV) +

FIG. 5 . The PL spectra of several strain-symmetrized Ge,Si,, SLs with n rn = 5 , 10, and 20. All have a common thickness ratio rn/n = 1.5 and biaxial strain €11 E I .4% (€11 2 2.7%) in the Si (Ge) layers. The Ge2Si3 structure has a more alloy-like behavior. Adapted from Zachai et al. (1990) with permission.

required to observe this strong emission. They suggest that the emission line is associated with defects (the samples in question are known to have dislocation densities of between los and 1010cm-2) and point out that remarkably similar emission lines were observed by other authors in samples where the active region was composed of a homogeneously strained layer of Ge,Sil-, alloy (Noel et al., 1990). In these samples the gap is definitely indirect and no zone-folding can be invoked. To counter this criticism, Meczingar et al. (1993) studied the absorption (via photocurrent) and PL spectra of two Ge,Si, superlattices with n m = 10. These samples were grown in conditions that guaranteed a very low dislocation density. Figure 6 reproduces their PL and absorption spectra for a Ge4Si6 SL (upper curves) and a Geo.4Sio.6 alloy grown under the same conditions. The onset of the SL absorption is shifted towards lower photon-energies, by 100 MeV, in relation to that of the alloy. Comparison between the absorption and the PL features in the former sample supports the interpretation that the latter originates in a no-phonon recombination across the gap that produces the absorption edge (see Section IV).

+

-

5

OPTICAL PROPERTIES

10K

235

- 102

h

v)

c

.-

C

5K

= l

Y

-

step graded

-.I

n

I

0.031xM.4

1%..f

m

-E

I

i

0.4

10’ 5K

I 0.7

I

I

I

1.0 Photon Energy (ev)

0.8

0.9

1.1

FIG. 6. PL and absorption spectra of a GeqSi6 SL and a Ge0.4Si0.6 alloy. Adapted from Meczingar et ~ l (1993) . with permission.

Combining both results we conclude that the PL of the SL sample is due to a nophonon recombination that takes place in the part of the sample containing the Ge4Si4 SL and not in the alloy buffer layer. This seems to support the interpretation of Zachai et al. (1990). However, this interpretation is not unique. First we notice that the similar PL features observed by Noel et al. (1990) in Ge,Sil-, quantum wells are also due to a no-phonon recombination process across the alloy indirect energy gap, that is, to explain this line no direct gap is necessary. Second, the buffer layer is not the only place in the sample that contains alloy layers. The results from Raman scattering experiments in Ge,Si, SLs show that alloy layers form spontaneously at the Ge/Si interface (see Section III.5.C). Thus these superlattices contain a certain amount of Si-Ge alloy even when it has not been intentionally included in the sample. Hence, the PL peak could be equally well interpreted as due to recombination in the alloy regions of the sample located around the Si/Ge interfaces of the Ge4Si6 SL. The preceding discussion shows that, although zone-folding does result in pseudodirect gaps for samples of appropriate periods and strain, no clear evidence exists that

236

FERNANDO CERDEIRA

the strong optical structures observed in reflectivity, absorption or PL spectra of some Ge,Si, superlattices are associated with transitions across this gap. This is made especially plain by the fact that these strong spectral features also appear in samples where the gap is clearly indirect. Thus, zone-folding does not appear to be the main reason behind these strong features in the optical spectra, but rather other components of the sample, which appear unintentionally during growth, might be responsible for them. This view is supported by recent theoretical calculations showing that if a disordered layer exists, extending only f l monolayer (ML) at the Si/Ge interfaces of a 10-ML period superlattice, alloy scattering becomes the dominant mechanism for recombination (Turton and Jaros, 1996). This point is thoroughly discussed in the chapter by Shaw and Jaros, so we need not elaborate any further here. One additional remark is in order about the interpretation of the results from the type of optical experiments discussed so far. Most of the uncertainties when interpreting spectra arise from the failure to answer the following question: Which part of the sample is responsible for the observed spectral feature? The optical spectra results from the response of the whole sample, which, aside from the actual Ge,Si, SL, includes buffer and spacer layers as well as thin layers of disordered material at the interfaces. In some cases the technique of resonant Raman scattering is able to give an experimental answer to this question (see the discussion in Section 111.5). However, it is not always possible to perform such experiments. In these cases theoretical studies must be used to answer this question (for more information see Chapter 4).

3.

TRANSITIONS I N SI/GE,SII-, GE/GE,SI~-, MICROSTRUCTURES OTHER OPTICAL

AND

The early optical work in Si/Ge microstructures was conducted on quantum wells (QWs) and superlattices obtained by alternating relatively thick (2.5-25 nm) layers of Si and Ge,Sil-, alloys grown lattice matched on Si (001) substrates (Bean et al., 1984). In these structures the quantum wells are composed of a disordered, strained material. In order to describe the electronic states of the SLs it is necessary first to understand those of the strained alloy. Experience shows that these can be described fairly well in the spirit of the virtual crystal approximation (Therodorou et al., 1994). Within this framework we can attribute to the alloy a bandstructure, which is a weighted average of those of Si and Ge and that responds to strain similarly to those of the constituent materials (Abstreiter et al., 1985; Zeller and Abstreiter, 1986; People, 1985; Lang et al., 1985). Figure 7 shows a schematic representation of a biaxially compressed Geo.5Sio.5 alloy derived using the approximations just described (Pearsall et al., 1989a). A comparison between Figs. 1 and 7 shows the similarities between the bandstructures of the alloy and those of the constituent materials. Figure 7 also shows the optical transitions responsible for the main features in the modulated reflectivity spectrum. These transitions are clearly seen in the ER-spectra of bulk, unstrained alloys. The

5

OPTICAL PROPERTIES

237

WAVE VECTOR

FIG.7. Schematic bandstructure of a Ge0.5Si0.5alloy subjected to uniaxial tension along the (001) axis. The two nonequivalent (100) directions are shown. Adapted from Pearsall ef al. (1Y8Ya) with permission.

evolution of the transition energies as alloy composition changes is illustrated in Fig. 8 (Kline et al., 1968). This figure shows that the optical transitions in the Ge,Sil-, alloy evolve continuously, and indeed linearly in most cases, from those of Si into those of Ge as x varies from 0 to 1. Disorder seems to affect optical spectra only by introducing extra broadening in the observed lines. This could be interpreted, within the virtual crystal approximation, as a disorder-induced relaxation of the conservation of crystal momentum in the optical transitions. Hence it is possible to think of the states of the quantum well as resulting from confined alloy bulk states, in the same manner as if the material of the QW were pure Si or Ge (Therodorou et al., 1994). These ideas, however, needed to be put to the experimental test. To the best of our knowledge, the first observation of optical transitions attributable to confined states in Si/Ge,Sil-, SLs were the resonant Raman scattering measurements of Cerdeira et al. (1985). The Raman spectrum of these materials is discussed in detail in Section 111. Here we merely remark that the intensity of a given Raman peak is enhanced when the incoming or scattered beams have a photon-energy that coincides with that of a direct electronic transition involving states confined within the same layer as that in which the vibration originating the peak is confined. Hence, plotting the intensity of a ) given Raman line as a function of the photon-energy of the incoming laser ( l i w ~one obtains a curve that has peaks whenever l i w ~coincides with such a transition. Cerdeira et al. (1985) report a resonant enhancement in the cross section of an alloy phonon, which can be attributed to vibrations of the Si-Ge bond (see Section 111.2), at photon

FERNANDO CERDEIRA

238

" I

1

-*.+-*-*-*-

4

*-*-*-*-+-

E2

0.4 1.0 Ge

0.8

0.6 X

0.4

0.2

(

3

Si

FIG. 8. Evolution of the critical point energies for the main optical transitions in Ge,Sil-, the ER-spectra of Kline et a/. (1968) with permission.

-

alloys: from

energies in the range no, 2.0-2.6 eV , in a series of Si/Ge,Sil-, SLs with a variety of QW-widths d and alloy compositions x (see Fig. 9). This signals the presence of an optical transition (or a family of closely spaced optical transitions) between states confined within the alloy QW. These transitions were tentatively identified as the strainsplit Eo doublet of the alloy layers, modified by stress and confinement (see Fig. 7). Encouraging as this first indication of quantum confinement in this type of materials was, the resonant Raman experiments did not provide accurate transition energies for the optical transitions involved. Indeed, even their identification as Eo-like transitions is not unequivocal, because of the proximity of El transitions of the alloy layers. More detailed information about optical transitions in these materials was later reported by Pearsall et al. (1986). These authors reported electroreflectance measurements in Si/Ge,Sil-, SLs in a wide photon-energy range (2.0-4.0 eV). A typical ER-spectrum is shown in Fig. 10, where the arrows indicate assignments of spectral features to transitions between electronic states in the SL derived from bulk-alloy electronic states modified by strain and confinement. These assignments are complicated by the fact that two multiplets overlap in energy: the Eo(1) and Eo(2) strain-split doublet and the

239

OPTICALPROPERTIES

5 I

I

I

I

I

G e , Si,,/Si T = 300 K

-

o X=075(d=25i) 0

X=0.65(d=33i)

A X=0,40(d=75A)

I

I

1

i

I

2.4 hOL ( e V )

2.2

2.6

for Si/Ge,Sil-, FIG.9. Raman cross section of the Si-Ge peak vs h o ~ and molar compositions; from Cerdeira et al. (1985) with permission.

4.00

3.50 I

PHOTON ENERGY ( eV) 2.75 2.50

3.25 3.00 I

I

E,+ ,

A

’ E,

I

I

2.25

SLs with different QW-widths

2.00

I

(b)

0

FIG. 10. ER spectrum (77 K) of a 7.5 nm SiIGe0.45Si0.55 QW, from Pearsall et al. (1986) with perrnission.

240

FERNANDO CERDEIRA

+

and El A1 of the bulk alloy (see Fig. 7). Also, the spectral lines for this strained and disordered QW-material are rather broad, as can be seen in Fig. 10. Even so, the assignments in these figures for the Eo doublet are in good agreement with calculations made on the basis of the well-known behaviors of these gaps with strain, alloy composition, and a simple Kronig-Penney-type model, with constant effective masses, to account for the effects of quantum confinement (Bastard, 1981). The quantum wells were constructed using band alignments at the Si/Ge interface proposed by Van de Walle and Martin (1986), which involve very shallow wells for holes and deep QWs for electrons (as much as 1.8 eV for some of the samples from Pearsall et al., (1986). These deep QWs should produce a multiplet of transitions associated with each of the strain-split Eo gaps. The width of the ER lines in the spectrum of Fig. 10 does not allow resolving the members of these multiplets produced by quantum confinement. As the El -multiplet confinement cannot be included in a straightforward way, it was ignored by Pearsall et al. (1 986). Even so, fairly good agreement is found between predictions made on this basis and optical structures in their ER spectra. The pioneering work already described here proved that optical spectra in these structures could be interpreted successfully on the basis of direct optical transitions in the bulk-QW material, modified by the effects of strain and confinement. These effects were reasonably well-described for zone-center transitions by elastic theory and very simple Kronig-Penney-type models, respectively. In order to obtain more accurate information for comparison with theoretical models, it would be necessary to produce materials in which the EO and El multiplets were not overlapping. A better-quality QW-material also would produce sharper spectral lines. This was accomplished by growing the structures commensurately on Ge substrates and alternating alloy with Ge layers, that is: Ge/Ge, Si 1--x quantum wells and superlattices. In these structures the QW-material is pure, unstrained Ge while the strain and disorder appears only in the barrier (alloy) material. An additional advantage is that in bulk Ge the Eo and El transitions are well separated in energy (-- 1.4 eV, as can be seen in Table I), so the multiple transitions associated with the Eo optical gaps in the QWs do not overlap in energy with the structures associated with the bulk El gaps. Optical multiplets associated with the Eo transitions of bulk-Ge were first observed by piezoreflectance in the thick (29143 MLs) Ge QWs formed in the Ge-spacer layers separating thin Ge,Si, short-period SLs (Yin et al., 1991). These results were already discussed in the previous subsection. The observed multiplets were described qualitatively by a Kronig-Penney-type model using constant effective masses. However, predictions differ from actual peak positions by as much as 110 MeV in some cases. These predictions can be made more accurate by including the effects of nonparabolicities in the conduction band. These effects are not negligible in cases such as these, where the confinement energy can be comparable to, or even larger than, the Eo gap in the bulk material. The matter was later taken up by Rodrigues et al. (1992), who reported photoreflectance (PR) mea10 nm), unstrained, Ge surements on two GelGeo.7 Sio.3 SLs with relatively thick( quantum wells. A typical spectrum from one of these samples is shown in the upper El

-

ER T = 7 7 K

1' +

Ge-bulk

c

1

1 .o

241

OPTICALPROPERTIES

5

1

1

,

,

1

1

I

d 2.5

/

1.5 Photon Energy (eV)

FIG. 1 1. PR spectrum of a Ge/Ge0,3Si0,7 SL (upper curve) and ER spectrum of bulk-Ge (lower curve).

curve of Fig. 11. For comparison, the PR spectrum of bulk Ge is shown in the lower curve of this figure. The multiplet associated with the bulk Ge Eo transitions is clearly seen in the spectrum of the Ge-QW of Fig. 11. The lines associated with bulk-Ge El transitions are also clearly seen, but they appear at much higher photon energies. We discuss first the SL spectral features associated with the Eo gap, which are shown in greater detail in Fig. 12. Eight lines (labeled A through H, in order of increasing photon energy) are clearly identified in this multiplet. These lines were interpreted in terms of the predictions of a simple Kronig-Penney-type model, using the offset of the average valence bands ( A E u , a uas ) an adjustable parameter. The results of these calculations are shown in this figure as solid (dashed) curves for parity-allowed transitions at the minizone center (edge), while experimental transition energies are represented by horizontal dotted lines. The figure on the left-hand side of the spectrum was calculated with constant effective masses, while that on the right-hand side was produced by energy-dependent masses calculated with the Kane model (Rodrigues et al., 1992; Kane, 1966). For constant masses the agreement is poor for all but the lowest photonenergy lines, regardless of the choice of band offset. In contrast, excellent agreement is obtained when nonparabolicities are included (Fig. 12(c)) for a value of the band offset of AE,,+ 2: 0.14 f 0.03, which agrees with that proposed by Van de Walle and Martin (1986). Table I1 compares experimental and calculated values for the transition energies. In these assignments not only the lines associated with heavy ( h )or light hole (I) transitions are identified, but also the effects of miniband dispersion are brought into focus as the structures produced by singular points at the minizone center (r)and edge (n)become progressively resolved when the transition index (n) increases.

242

FERNANDO CERDEIRA Parabolic Bands

%

Ge'Geo,,Sio

111/32 A

3

Non-parabolic

Bands

1.46

1.46

-2

;

F a,

P a,

w

w

r

C

c

1.18

0

1.18 :?

ln C

F

k

Flc. 12. Comparison between the calculated transition energies of the Eg multiplet of a (11.1/3.2 ef al. (1992)). (a) Full (dashed) lines show calculations, using constant effective masses, for zone-center (zone-edge) transitions as a function of the valence band discontinuity. (c) Same as (b) but using energy-dependent effective masses. (b) Experimental PR spectrum; arrows indicate critical points; horizontal dashed lines are the prolongation of these arrows into the (a) and (b) panels.

nm) Ge/Ge0,3Si0,7 SL and those obtained from the PR spectrum (see Rodrigues

The foregoing discussion vindicates the use of simple models based on confinement in square wells for the optical structures associated with the Eo gap. This is a nontrivial conclusion, as the conduction minima at r, in bulk Ge, is higher in energy than other conduction bandstates (see Fig. 1) and intervalley mixing could occur (see the chapter by Shaw and Jaros). The nagging question remains as to whether the same would hold for SLs with ultrathin layers. We tackle this question in the following section. Before coming to that, let us examine the part of the spectrum of Fig. 11 associated with the El and El A1 transitions. No multiplets are observed here. In fact the spectrum of the SL and that of bulk Ge are almost identical, except for a small shift in the lines of the former towards higher photon energies, which increases as the width of the Ge-QW (L) decreases (52 MeV for d = 11.1 nm and 72 MeV for d = 10.2 nm) (Rodrigues et al., 1993a). This argues in favor of confinement effects, even for optical gaps such as those that extend through a large portion of the BZ (Yu and Cardona, 1995). The actual confinement of the electronic states is confirmed by resonant Raman results, which shall be discussed in Section 111.5. However, it is far from obvious how this concept applies to electronic states with such a large energy-width that they overlap with many other states in the BZ. This complex situation precludes the use of square-well models to treat this confinement. In fact, the very concept of confinement becomes dubious,

+

5 OPTICALPROPERTIES

243

TABLE11. Transition energies obtained both for experimental ER data and from an envelope-function calculation (including nonparabolicities in the conduction band) for the Ge/Ge,Sil-, .. SL of Fig. 12, with AE, z 0.14 eV. ~

Line A

~

~~~~

Assignment

0.953

1 hr

0.957 0.962

1 hl7 1 lr

0.978 1.099

1 hn

0.948

B

0.963

C

1.102

D E

1.136 1.176

F

1.324 1.547 1.595

G H ~~

Transition energy (eV\ Experimental Theory

1

zn

1.111 1.136 1.177 1.308

3 hT

1.330

3 hn

1.548 1 .595

4 hn 4 hr

2 hr

zn 2 zr

2

~

Here nh(nl) denotes the transition between the nth confined level of the heavy (light) hole band and the corresponding level at the conduction band. The label r(n)corresponds to transitions at the minizone center(edge). Adapted from Rodrigues et af. (1992).

especially for SLs with very thin layers. This discussion will be taken up in the next section, devoted to optical results in Ge,Si, SLs.

4.

OTHER OPTICAL TRANSITIONS IN G E ~ S I ,QUANTUM WELLS A N D SUPERLATTICES

In Section 11.2 we discussed some aspects of the ER-spectra of ultrathin Ge,Si, SLs ( n , m 5 5 ) , namely, the existence of low photon-energy spectral lines that had been attributed to pseudo-direct transitions at the folded fundamental gap. A representative ER-spectrum from a Ge4Si4 (Hybertsen et al., 1988) is reproduced in Fig. 4(a). Besides the line assigned to this pseudo-direct transition, other strong ER-lines appear at higher photon-energies. These are assigned to direct transitions between electronic states originating in bulk-Ge states modified by the superlattice potential. A more com-

244

FERNANDO CERDEIRA

plete study of ER in this type of materials was later reported by Pearsall et al. (19894. In this work the spectra of Ge,Si, SLs (grown commensurately on Si substrates) with n = m = 1 , 2 and 4 are discussed in detail. The spectrum of Fig. 4(a) is representative of those of these samples. The sample with n = m = 4 shows several lines that are attributed to Eo or El transitions. Because the Ge layers are biaxially compressed two EOlines are expected, corresponding to transitions between the strain-split heavy and light hole valence bands and the confined state (only one for very thin layers) of the conduction band. The members of this doublet are called Eo(1) and Eo(2), in order of increasing energy. This doublet (at 2.20 and 2.38 eV, respectively) is identified in the ER spectra of Pearsall et al. (19894. Also present in their spectra are two doublets, one strong (at 2.60 and 2.82 eV) and one weak (at 3.04 and 3.22 eV), which are assigned to El and El A ] , respectively, modified by the superlattice potential. The nature of these modifications is not made clear by Pearsall et al. They also discuss the spectra for samples with n = m = 1 , 2 , assigning spectral lines with the assumption of perfect interfaces. In view of the fact that interface roughness extends at least one monolayer on each side of the interface, these assignments are not likely to be reliable. Photoreflectance (PR) measurements by Dafesh et al. (1990) and Dafesh and Wang (1992), performed on a strain-symmetrized 60-period Ge32Sis SL, are shown in Fig. 13. The thick Ge-QW should produce a multiplet for each one of the two strain-split Eo gaps, in a manner analogous to that of the upper curve in Fig. 11. Instead, only two strong lines, associated with the n = 1 transitions of Eo( 1) and Eo(2), respectively, appear in the spectra of Fig. 13 (lines B and C, respectively). A series of weak structures (D through P) also appear in the spectra. They are identified as higher transitions of

+

, I . . I I . I I I I I I . 1 . , . . I . . . .

0

1.00

1.50 2.00 2.50 Photon Energy ( eV )

3 I0

FIG. 13. PR spectrum of a strain-symmetrized Gej2Sig SL. The inset shows an enlargement of the structures labeled B and C. The label A designates a photon energy region where indirect transitions could, in principle, be observed. Adapted from Dafesh et al. (1990)with permission.

5 OPTICAL PROPERTIES

245

+

the Eo multiplets, El and El A 1 transitions from the Ge layers or transitions in the thick, strained-relaxed, alloy buffer layer. The label A in Fig. 13 designates a photonenergy region where indirect transitions might appear. None are reported by the authors (Dafesh et al., 1990). The assignments are made exclusively on the basis of the photon energy of a given line. It is not clear, for instance, why the line attributed to the El transition is so weak, knowing that this transition is responsible for the strongest line of the optical spectrum of bulk Ge in this photon-energy range (see Fig. 2). On the other hand, SLs with such thick Ge-layers may have poor interfaces (see the chapter by Bean), so it would not be surprising if these weaker lines are related to defects rather than to the interband transitions of a perfect structure. In any case, there are a good number of these lines in a photon-energy range where different electronic transitions overlap, so a more detailed knowledge of the bandstructure of the SL would be required in order to make reliable assignments of optical structures. The forementioned combination of detailed band calculations with a sensitive optical technique is present in the work of Schmidt et al. (1990). These authors report ellipsometric measurements, both at room temperature and at T = 10 K, performed on a Ge4Sis strain-symmetrized SL. They compare the second derivative of E ~ ( w ) , obtained by numerical differentiation of experimental data, with that generated by a linear-muffin-tin-orbital (LMTO) ab inirio calculation. In Fig. 14a and b, respectively,

h

3

-400 2

,

,

........................... 3 4 Photon Energy ( eV )

5

FIG. 14. Experimental and theoretical results for a strain-symmetrized Ge4Si6 SL. (a) Second derivative of the imaginary part of the dielectric constant [numerically obtained from ellipsometric measurements of q (o)]: lowest (second lowest) curve for T=10 K (300 K). Theoretical simulations with different broadenings: top and second-from top curves. (b) Calculated electronic structure. Adapted from Schmidt er al. (1990) with permission.

246

FERNANDO CERDEIRA

we show the comparison between their experimental and theoretical optical spectra and their results for the bandstructure calculation. Each interband transition indicated in Fig. 4(b) produces a peak in the theoretical optical spectra of Fig. 4(a) (arrows). Comparison between the experimental and theoretical optical spectra is excellent, once the theoretical photon energy is given a uniform 0.1 eV shift to account for a systematic artifact of the calculation (Schmidt et al., 1990). Also, note that experimental spectra can only be obtained after the sample has become opaque to the incoming light (hw 1 2.7 eV). At lower photon energies the optical spectra are dominated by interferences produced by multiple internal reflections. This is a feature that affects most optical measurements based on reflectivity to a larger or lesser degree. Several techniques have been developed to remove the effects of these interferences (Rodrigues et al., 1993a), but it is always an ultimate limiting factor to the accuracy of reflectivitybased measurements in multilayer systems. Taking these limitations into account, we can summarize the main conclusions of this work as follows: 0

0

0

0

The lowest direct energy gap occurs at the r-point (- 1.1 eV). This gap appears as a result of zone-folding (see Section 1.2), but gives no significant contribution to the optical spectra because of its negligible oscillator strength.

-

Strong absorption starts at 2.3 eV and it is associated with transitions along the r - N line in the mini-Brillouin zone. This is a multiplet that originates in bulk El transitions, modified by the effects of the superlattice potential through zone-folding and confinement. They are named EY(a = a , b, c and d ) . The first transition at the r-point of the mini-zone that gives a significant contribution to the optical spectrum occurs at 2.6 eV and originates in bulk-Ge Eo transitions, shifted to this high energy by the effects of quantum confinement.

In addition to the bulk-like features already discussed here, Fig. 14a shows a series of weak peaks, labeled S i ( i = 1 - 6). These are attributed to transitions from the bulk-like valence band to folded conduction band states.

Subsequent theoretical (Schmidt et al., 1991) and ellipsometric (Schmidt et al., 1992) work confirms these results and traces the evolution of these optical structures for different sample parameters. The foregoing discussion exemplifies the importance of having a reliable band calculation when interpreting the optical spectra of Ge,Si, SLs. In this spirit, subsequent ER-measurements (Rodrigues et al., 1993b) in a series of strain-symmetrized SLs were examined within the general scheme of optical transitions illustrated in Fig. 14b. In Fig. 15 we display their ER-spectra, taken at T = 77 K, for samples with different layer thicknesses. Each spectrum shows a large number of structures, which result from a variety of transitions with overlapping critical energies. The authors assumed that the number of critical points were those of the LMTO calculation for the n = m = 5

5 OPTICALPROPERTIES Ge,Si,

I

.5

'

,, , '

E, a E O

2.0

247

,L,d

E,bA%C

2.5

3.0

Photon Energy (eV) FIG. 15. ER spectra of strain-symmetrized Ge,Si, SLs. Circles represent experimental data while the continuous line is the best fit with Eq. (1) for seven critical points (A through G). Component lines of a given fit are shown below each spectrum. Critical energies from the LMTO calculation of Schmidt (1991). for n = m = 5 , are shown with arrows on top. Also indicated are the Eo critical points given by an envelopefunction calculation. Adapted from Rodrigues et al. (1993b).

case (Schmidt et al., 1991) and fitted their experimental data with this number of standard ER-lineshapes [Eq. (l)]. The continuous lines in Fig. 15 represent the best fit to the data (open circles). The individual lineshapes composing each fit are shown below each spectra and the arrows indexed A, B, . . . , etc., are the critical energies obtained from these component lines. The upper arrows indicate the critical energy and assignment of the LMTO calculation for a GesSiS SL (Schmidt et al., 1991). Also indicated in Fig. 15 are the calculated positions of the strain-split Eo doublet, calculated by a

248

FERNANDO CERDEIRA

TABLE111. Critical point energies of Ge,Si,, strain-symmetrized SLs from the fittings of the ER spectra (77 K) with Eq.(l); assignments of the LMTO calculation by Schmidt er al. (1991) and the envelope calculations for the & optical gap.

Sample

Assignment

Experimental

Cj

r, E j ( e V ) Eabs(eV)

GeqSi4

0.49 0.10 2.31 0.59 0.12 2.42 0.59 0.15 2.58 0.69 0.14 2.80

2.30

E: Ef

1.OO 0.16 3.03 GesSig

Ge(jSi6

0.50 0.20 2.30A

E" EO

2.43

E? Ey ,Eb E4

0.69 0.10 2.50B 0.69 0.10 2.55C

Eo(hh)

1.13 0.17 2.64D 0.81 0.12 2.82E 1.00 0.15 3.05F 0.64 0.16 3.36G 0.27 0.20 2.30

E: Ef Ef

Eo U h )

Theoretical

LMTO Ej (eV) 2.31 2.35 2.48 2.68 3.01 3.26 2.23 2.25 2.3 1 2.72 2.79 2.93

EF EO(eV)

2.3 I

2.25

Eb

1.130.102.60 0.93 0.10 2.66

E" EOW) EoQh)

1.43 0.17 2.73 I .20 0.12 2.94 1.000.15 3.07

Ei E; Ef

0.53 0.14 3.37

E:,

2.59

2.30 2.55 2.60 2.75 3.00 3.1 I

2.56

Eabs is the onset of strong absorption in these samples determined from the interface pattern. Adapted from Rodrigues er al. (1993b).

simple Kronig-Penney model with energy-dependent effective masses (Rodrigues et al., 1992). Table 111 summarizes the numerical results of these assignments for the samples with short periods ( n + m 5 10). Here we also list the onset of strong absorption (EabS) in these samples, obtained from the exponentially decaying envelope of the interference oscillations that precedes it, in the manner explained by Rodrigues et al., (1993b). Extending the same analysis to samples with larger periods, the evolution of these optical transitions as a function of period-length can be studied. The main results can be summarized as follows: 0

The spectra always contain a feature whose origin can be traced to confined bulkGe Eo transitions. This feature is very sensitive to the thickness of the Ge layer

249

5 OPTICAL PROPERTIES

3.9

3.6

3.3

3.0

2.7

2.1' '

'

'

" ' ' I ' " 5 10 15 Number of Ge monolayers (n) I

'

I

'

' 1

20

FIG.16. Dependence of the critical point energies of the El multiplet with the thickness of the Ge layer. Arrows indicate positions of critical points for strained bulk Si and Ge. The continuous lines are guides for the eye. The inset shows the evolution of the Q critical point. Adapted from Rodrigues ef al. (1993b) with permission.

and its position is wellkxplained by simple Kronig-Penney-type models. This is illustrated in the inset of Fig. 16, where the experimental transition energies from ER-spectra (open circles) are plotted against the predictions of such a model (open diamonds and continuous line) and those of the LMTO calculation (full diamonds). For n + m 2 10, this transition defines the onset of strong absorption in these materials. For smaller periods, the Eo transitions move up in energy and fall among the members of the El-multiplet (to be discussed next). In this case one of the members of this multiplet defines the onset of strong absorption.

As already discussed, the El -transitions of the bulk materials originate a multiplet as a result of the modifications imposed on them by the superlattice potential. The evolution of the members of the multiplet as the thickness of the Ge layer increases is shown in Fig. 16. This figure suggests that this multiplet is composed mainly of a Ge-like doublet (ET and E;) and a Si-like one (EF and Ef), which evolve towards the El and El A1 transitions of bulk Ge and Si, respectively, as the Ge layers become thicker.

+

250 0

FERNANDO CERDEIRA

The E7-transition of thin-layered SLs ( n 5 6) is responsible for the most intense line of the ER-spectrum and constitutes the onset of strong absorption in these SLs. As the Ge layer thickness increases this line evolves continuously towards the bulk-Ge E I transition, but it always occurs at a higher photon energy than the latter. This is true even for very thick Ge layers, such as those of the Ge/Ge,Sil--x SLs discussed in the previous subsection. Although this might suggest confinement of a bulk-Ge state, this energy increase could also result from an admixture of Si-like states, which diminishes progressively as the thickness of the Ge layer increases. With the data discussed so far it would not be possible to distinguish between these two alternatives.

The last point in the foregoing discussion could be clarified by studying how the

EI multiplet is generated as the number of Ge-quantum wells increases from a single QW to a full superlattice, for fixed thicknesses of the Si and Ge layers. In the case of admixture of Si and Ge wavefunctions we would expect a weak dependence of these structures on the number of periods, as this admixture depends mostly on the relative thicknesses of the Si and Ge layers. On the other hand, confined states would develop into multiplets with the wavefunction of its members still mainly confined in one or the other layer. An experiment of this type was attempted by Rodrigues et al. (1993a), who report PR measurements on three samples containing one (1 QW), two (2 QW) and six (6 QW) Ge quantum-wells. The samples were grown lattice-matched on Si (001) substrates. The Ge QWs have a thickness of five monolayers. In the samples with multiple QWs these are separated by 5 MLs of Si. Each structure is repeated between 10 and 25 times and each unit is separated from the next by a 30-nm thick Si spacer-layer. Low-temperature (77 K) PR and room-temperature resonant Raman scattering (RRS) experiments were performed on these samples. Their PR-spectra are shown in Fig. 17a, where open circles represent expenmental data and the solid curve is a fit with the standard lineshapes of Eq. (1). Each line composing a given fit is shown below the respective spectrum. We see a continuous evolution in the spectra of the NQW samples, from one line for N = 1, to two for N = 2 and four for N = 6, respectively. If we identify the spectral line in the single-QW as El, then the splitting of this feature into two components for the double-QW (A and B in Fig. 17a) is analogous to the splitting of a given electronic state into a symmetric and an antisymmetric component by the double well, while the multiplet generated by a fully periodic superlattice would already appear for 6 QWs. This assignment coincides with that made by Freeouf el al. on the basis of ellipsometric and RRS experiments performed on thin (- 0.7-nm) Ge-layers buried in a Si matrix (Freeouf et al., 1990). The evolution of this structure as the number of Ge QWs increases is illustrated in Fig. 17b, where the data for the strain-symmetrized Ge5Si5 SL from Rodrigues et al., (1993b) was included ( N = 150). The arrows at the side of this inset indicate the El and El + A1 transitions of biaxially strained bulk Ge and strain-free bulk Si, respectively. There is a remarkable agreement between the multiplet of the 6 QW sample and that of

251

5 OPTICAL PROPERTIES

I a,

t

- 1

ER T d 7 K

.... ............................

........ JL.... '., '

i1

Si-bulk E, unstrained E',

3.3

-

t

-I

v

c

W

Ge-bulk strained

2.4

2.1 1.5

2.0 2.5 3.0 Photon Energy (eV)

0 2 4 6 150 180 Number of Ge quantum wells (N)

FIG.17. (a) ER spectra (open circles) of the NQW-samples fitted with the lineshapes of Eq. (I), continuous line. Arrows indicate critical-point energies from the fit. (b). Critical energies for El -like transitions vs N. Arrows indicate the value for this critical points in strained (unstrained) Ge (Si). Adapted from Rodrigues er al. (1993a) with permission.

the SL. This agreement is even more impressive when we consider that both samples have different strain profiles. In order to say something about the actual confinement of the electronic states involved in these transitions, we turn to the RRS results. The exact manner in which this technique gives information about wavefunction confinement will be described in Section 111.5. Here we mention only that the Raman cross section of a vibration, known to be localized in a given layer, is enhanced only when the incoming (or outgoing) beam is in resonance with an electronic transition among states localized in the same layer. In Table IV we list the photon energy and assignments of the lines in the PR-spectra, as well as the degree of confinement of the electronic states derived from the resonant Raman experiments. These results support the idea of wavefunction confinement for the electronic states involved in the El transitions. Those parts of the discussion in the last two sections that were centered around spectral features in Ge single and multiple quantum wells attributable to either & or El transitions of the bulk materials can be summarized as follows: 0

Multiplets associated with the Eo transitions are clearly observed in QWs and SLs with relatively thick Ge layers (- 10 nm) and alloy barriers. As these layers become thinner, this rich multiplet structure becomes obscured. This happens

252

FERNANDO CERDEIRA TABLEIV. Transition energies (Ej) and broadenings

(rj)of the

lines in the ER spectra of NQW samples.

Sample

ER(77 K)

Assignment

Confinement

Mostly Ge

E j (rj) (in eV)

1 QW 2 QW

2.83(0.11)A 2.72(0.17) A 2.98(0.18) B

El E:

Ge

EL

Mostly Si

6 QW

2.43(0.12)A

E;"

Mostly Ge

2.59(0.10) B

El;

Mostly Ge

2.74(0.15) C

EE

Mostly Si

2.97(0.12) D

E!

Mostly Si

Assignments are shown in the third column while the last column lists the degree of confinement of the electronic states participating in the transition from RRS data. Adapted from Rodrigues et al. (1993a).

both because narrower wells have fewer confined states and also because interface imperfection becomes more important in thinner wells, leading to broader spectral lines. Another complicating factor is that confinement shifts these peaks into the region of the stronger El -multiplets. However, in all cases the lines identifiable as Eo transitions have a strong dependence on layer thickness that can be quantitatively explained with simple square-well models. 0

In single Ge-QWs confinement of the A-line states of bulk Ge occurs. This is not obvious, as these states cover a wide range of energies that overlaps (although at different k-vectors) with states along the same line in the barrier material. In a superlattice, these lines split into two doublets with wavefunctions mostly confined into the Ge (Si) layers for the doublet at lower (higher) photon energy. These doublets appear as a consequence of zone-folding and the manner in which this happens cannot be described by simple square-well models.

The results of this section were discussed within the framework of electronic calculations performed for microstructures with perfect interfaces. As we shall see in Section 111.5, actual interfaces always have disordered layers that affect at least fl ML around the Ge/Si interface, and frequently present larger-scale roughness in the form of terracing an island formations. These real interfaces might have a decisive influence on the optical spectra which might, in turn, lead us to revise the previous assignments. The subject of electronic states in imperfect structures, and their influence in their optical properties, is amply discussed in the chapter by Shaw and Jaros.

5

OPTICALPROPERTIES

253

111. Raman Scattering 1. GENERALCONSIDERATIONS Inelastic light scattering by phonons has been used for several decades to obtain information about the electronic and vibrational states of semiconductors. Among the numerous reviews on the subject, we cite two representative examples: that of Cardona (1982) for bulk semiconductors and that of Jusserand and Cardona (1989) for semiconductor quantum wells and superlattices. In what follows we shall give a brief summary of the elementary concepts and equations that we shall use throughout this section to describe the applications of this technique to GelSi microstructures. The scattering event consists of an incoming photon of well-defined energy ( h w ~ ) and momentum (hkL), which is scattered inelastically into another photon ( hws, hks) by creating or annihilating a phonon of energy ho and crystal-momentum fiq. Let us focus on the process of creation of a phonon (Stokes line). Energy and crystalmomentum conservation require that

Experiments are usually performed with lasers emitting in the visible or near infrared parts of the spectrum so, normally: OL 2: u s >> w. In opaque semiconductors most experiments are performed in backscattering (kL 2 - ks), which results in a phonon wavevector given by q = -4nrl (3) 1L

-

where q is the refractive index of the material and h t ( 500 nm) the incident laser wavelength (in vacuo). Phonon wavevectors are measured in terms of the length of the Brillouin zone (lT/L, for a superlattice of period L ) , so, for most cases of interest, q 2 0. Because acoustical phonons in bulk materials, at these small wavevectors, have very small frequencies, scattering by these phonons (Brillouin scattering) is not observable in normal Raman scattering experimental arrangements. Hence, first-order Raman scattering in bulk semiconductors probes only the q E 0 optical phonons. When dealing with superlattices with a periodicity L , it is often useful to define a reduced wavevector 4rlL Q=--4 - (4) qmax AL which is measured in terms of the BZ-length along the growth direction. By an appropriate selection of L and L L , it is possible to probe both the optic and acoustic branches at arbitrary points along this BZ-axis. The incoming and scattered photons are closely correlated, both in polarization and in energy. The intensity of a Raman line, associated with the creation of a given phonon

254

FERNANDO CERDEIRA

of the o;-branch is given by

where e L (es) is a unit vector in the direction of the polarization of the incoming (scattered) light and Rj is the Raman tensor (a tensor determined by the symmetries of the material and that of the j t h vibrational mode). For Si, Ge and their alloys the triply degenerate q 2 0 optical modes have Raman tensors given by

0 0 0

O O d

O d O

In Eq. (6) d is a constant and x, y and z define the direction of the vibrational eigenmode in terms of the cubic axes. Thus, for QWs and SLs grown along the (001) direction ( z ) , the first and second tensors correspond to in-plane vibrations, while the last one corresponds to vibrations along the growth axis. Raman scattering configurations are usually specified in the notation: x1 (x2, x3)x4, where the first (last) xi designates the direction of the incoming (scattered) photon, while the first and second letters in the parentheses define the polarization of the incoming and scattered beams, respectively. Inspection of Eq. (6) reveals that the combination of polarizations ( x y ) selects scattering events by phonons vibrating along the growth axis while in-plane phonons are visible in configurations (x,z) and ( y , z ) . In archetypal GaAs/AlAs SLs acoustical branches are very similar in both materials, while optical branches do not overlap in frequency. Here the dispersion relations for the SL-phonons can be visualized by folding the average bulk acoustic branches into the reduced Brillouin zone of the SL and confining the optical vibrations within each layer. This procedure is schematically shown in Fig. 18 for the longitudinal branches of a hypothetical A2B2 SL, made up of two zinc blende or diamond-type bulk semiconductors A and B . The optical branches of an A , B , SL are virtually dispersionless and obey the confinement conditions

In Eq. (7) 6 accounts for the fact that the atomic displacement, instead of vanishing at the last A or B atom of a given layer, has a small penetration into the adjacent layer. Notice that the confined optical mode vibrating along the growth axis (perpendicular to it) is always derived from the dispersion relation of the bulk LO-modes (TO-modes), irrespective of the direction of propagation of the phonon. This happens because these vibrations are longitudinal or transverse in relation to the quantized q-vector defined in Eq. (7b), which is more important in defining the T or L-character of the phonon

255

LOB(1) LOB(2) h

LOA(1)

0-

LOA(2)

v

3

M(4) M(3) M(2) M(1)

0

“la 0

“la

0

=14a

9 FIG.18. Schematic representation of the folding of the phonon branches in the mini-BZ for hypothetical A2 B2 SL grown along the (001) direction.

‘

I

than the small propagation wavevector. The first experimental demonstration of this, for GaAdAlGaAs, was given by Zucker et al. (1984a) for SLs. The acoustic modes of the A,, B, SL are obtained by zone-folding of the average bulk acoustic branches. The difference between both materials manifests itself at the minizone edge and center, where gaps appear when these folded branches cross (see Fig. 18). For a given laser wavelength, several peaks appear in the Raman spectrum at the points of the dispersion satisfying Eq. (3). This is illustrated in Fig. 18(c) by a dashed vertical line at this q-value. Symmetry allowing, each intersection of this line with the dispersion relation of the SL (open circles) generates a peak in the Raman spectrum. Various models can be used to calculate the lattice vibrations of the SL. The most general type consists of building a cubic supercell (SC) containing several periods of the A,B, structure and building up the dynamical matrix of this supercell by using force constants between the different types of atoms’. This dynamical matrix is then diagonalized, yielding eigenvectors and eigenvalues, which can then be placed in a minizone scheme such as that of Fig. 18. The force constants are chosen so as to reproduce the dispersion relations of the bulk material, when the atoms of the supercell are either all A or all B . These calculations yield accurate results, but they can be very complex. An alternative for obtaining dispersion relations and eigenmodes for longitudinal vibrations, for SLs grown along the (001)-direction, is to treat each plane as an “atom” of mass mA or me and use interplanar force constants so as to reproduce the bulk dispersion relations along the growth axis. These linear-chain (LC) models give very good results and are easy to handle. These models are wellkiescribed by Jusserand and Cardona (1989). More details about them shall be given when discussing actual results for Ge/Si SLs.

256

FERNANDOCERDEIRA

200 100

r

X

r

X

r

X

Wavevector FIG. 19. Dispersion relations, along the T - X axis, for longitudinal modes in bulk Ge (right), Ge,Sif ~x (center) and Si (left). Adapted from Schorer et al. (1994a) with permission.

The description given here of the vibrational modes of SLs is appropriate for systems in which the optic branches of one of the bulk constituents do not overlap with any of the branches of the other. In the Ge/Si system this is not exactly the case. In Fig. 19 we reproduce the bulk dispersion relations of Si, Ge and of a Geo.5Sio.s alloy for longitudinal modes (Schorer et al., 1994a). This figure shows that, although the Sioptic branch is truly isolated, that of Ge has a region of overlap with the longitudinalacoustic branch of Si. Thus, it is not clear that the concept of confinement, exemplified in Eq. (7), applies to all the optic modes of SLs made up of layers of Ge alternating with those of Si or Ge,Sil-,. We shall examine this question in more detail in the following subsections.

RAMANSCATTERING

2.

IN BULK

GE,SIj-,

RANDOMALLOYS

Experimental results reported by several authors (Feldman et a/., 1966; Renucci et al., 1971; Brya, 1973; Lannin, 1977; Alonso and Winer, 1989), show that the Raman spectrum of a random Ge,Sil-, alloy is composed of three main peaks, which, for x 0.5, appear at frequency shifts of 290 cm-'(Ge - Ge), 407 cm-'(Si -Ge) and 480 cm-l(Si - Si). Subsidiary, weaker structures are seen between the last two main peaks. These spectra obey the same selection rules as those of bulk Si or Ge and the main peaks shift as a function of strain in a manner similar to the peaks of their bulk constituents. In fact, Cerdeira et al. (1984) used the shift of the Si-Ge peak to determine quantitatively the biaxial strain in alloy layers deposited by MBE on Si substrates. A representative spectrum of a bulk, 50% alloy is shown in the lower curve of Fig. 20(a). Several theoretical models have been used to describe the Raman spectrum of random Ge,Sil-, alloys (Alonso and Winer, 1989; Lockwood et al., 1987; Wilke et al.,

-

-

5 OPTICAL PROPERTIES I

I

I

Si, Ge, expt.

257

1

W

Si, Ge, rough U

f

I

500

300

o(cm-’> FIG.20. (a) Raman spectra of bulk Geo.sSio.5 (A) experimental and (B) calculated. Curves C and D are calculated spectra of a GeqSi4 SL with rough and perfect interfaces, respectively, while curve E shows the experimental spectrum of a strain-symmetrized GeqSiq SL. (b) Calculated eigenvibrations for this SL. Adapted from Alonso et al. (1989) with permission.

1990; Gironcoli and Baroni, 1992; Keating, 1966). The most consistent descriptions of the spectra are given by supercell calculations (Alonso and Winer, 1989; Gironcoli and Baroni, 1992). Alonso and Winer use a 216-atom supercell (a0 = 1.62813 nm) of Si and randomly place Si or Ge atoms at the different sites with an abundancy ratio dictated by the alloy composition. Their force constants are derived from the Keating model (1966). Diagonalization of the dynamical matrix yields the eigenvalues and eigenvectors of the vibrational modes of this supercell. The latter are used, in conjunction with a bond-polarizability model (Alben et al., 1975), to generate the Raman spectra numerically. These spectra are compared by Alonso and Winer with experimental ones, obtained from thick (1- 5pm) alloy layers grown by liquid-phase-epitaxy (LPE) on Si (1 11) substrates. This comparison is illustrated in the two bottom curves of Fig. 20(a), taken from Alonso et al. (1989). The calculation gives a good reproduction of the three main Raman peaks, as well as of the subsidiary structures appearing between the Si-Ge and Ge-Ge peaks. Although these subsidiary structures were taken by Lockwood et al. (1987), to be signatures of partial ordering in these alloys, Alonso and Winer show that, on the contrary, they are a signature of randomness. In fact, these

258

FERNANDO CERDEIRA

structures arise from localized vibrations of the Si-Si bond when surrounded by Ge atoms, as the later calculations of de Gironcoli and Baroni (1992) prove conclusively; in the same way, they also show that the three main peaks arise from the vibrations of Ge-Ge, Si-Ge and Si-Si bonds.

3.

RAMANSCATTERING BY OPTICMODESIN GE,SI, QWs A N D SLs

The discussion in Section 111.1 would lead us to expect that the contribution of the optic modes to the Raman spectrum would be composed of lines around 300 cm-' (500 cm-l) originating in vibrations confined within the Ge (Si) layers with a possible extra peak between these two, due to vibrations localized around the Ge/Si interface. Such spectra were first reported by Menendez et al. (1988) in Ge4Sij SLs grown commensurately on Si (001) substrates. These authors observe thee peaks in their spectra at 313, 421 and 509 cm-', respectively. The first (last) peak is attributed to an optical vibration confined into the Ge(Si) layer with a downward shift, of 9 cm-' (12 cm-') due to confinement [Eq. 71 and an upward shift of 17 cm-' due to the biaxial strain in the Ge layers. The middle peak, however, bears a remarkable similarity to the Si-Ge peak of a Ge,Sil-, random alloy. This led the authors to suspect that interdiffusion could produce a thin alloy layer ( f l ML) around the Ge/Si interface. Other authors report similar results (Friess et al., 1989; Brugger et al., 1988). These suggestions were firmed up by Alonso et al. (1989), who measured and calculated the Raman spectra of several strain-symmetrized GertSi, superlattices. Their measurements were performed in backscattering with light propagating along the (001)-growth axis, so their spectra contain only longitudinal vibrations. Figure 20(a) shows the experimental spectrum of a Ge4Si4 (curve E), and compares it with the spectrum simulated by a supercell model similar to those previously used for calculating the spectra of random alloys (Alonso and Winer, 1989) (curve D). The eigenvibrations of the modes producing the three theoretically predicted lines are shown in part (b) of this figure. We see that the first (last) peak in curve D of Fig. 20(a) are produced by optic modes confined in the Ge (Si) layers. The agreement between the calculated and experimental spectra for these lines is good. This is also true of the spectra of the other samples measured and calculated by Alonso et aZ. (1989). There is, however, a large disagreement between theory and experiment when it comes to the middle line of the Raman spectrum (- 410 cm-' in curve E). Theory predicts a mode at much lower frequency shifts (- 358 cm-I), in which Si and Ge atoms vibrate in opposition across the interface [Fig. 20(b)]. The peak in the experimental spectrum coincides, both in shape and position, with that produced by the Si-Ge vibrations of a random alloy (curve A in the same figure), which seems to reinforce the idea that a region of alloying exists around the interface. To test this idea Alonso et al. (1989) included disorder in the two layers at each side of the Si/Ge interface. This was done by exchanging Si and Ge atoms in these two layers to obtain an average Geo.5Sio.scompo-

5

OPTICAL PROPERTIES

259

sition. The resulting spectrum (obtained by averaging several calculations for different random configurations in the interfacial layers) is shown in curve C of Fig. 20(a). This calculated spectrum is in much better agreement with the experimental one (curve E) than that calculated for perfect interfaces (curve D). Thus, the idea that roughness on the atomic scale exists at the GeISi interface, in the form of disordered alloy layers spreading on both sides of it, was vindicated. This notion was later reinforced by Schorer et al. (1991), who showed that the alloy Raman peak increases pronouncedly its intensity when the interfaces are smeared by annealing. The most complete proof of the issue discussed here was given by de Gironcoli et al., who compare thorough experimental Raman results with an accurate supercell calculation, which uses first-principles force constants (de Gironcoli et al., 1993). The Raman microprobe technique is used to obtain spectra of both longitudinal (along the growth axis) and transverse modes (in-plane vibrations), by performing backscattering experiments both from the sample surface and from one of its cleaved or polished edges. In the calculation, an alloy plane is included at each side of the Si/Ge interface. Their calculation is explained in great detail in a previous publication (de Gironcoli, 1992), where it is also shown that the exact composition of the alloy layers has little effect on the main results. Their results for 50% alloys are very similar to those already shown in Fig. 20(a). However, two notable differences must be pointed out:(i) the Tpolarization is also obtained, and, (ii) the contribution of the individual atomic layers to each feature in the Raman spectrum (local density of states) is calculated for a GesSis SL. The latter is shown in Fig. 21 for both longitudinal (left-hand side) and transverse (right-hand side) modes. The longitudinal Si-Ge mode is seen to be localized in almost one single interfacial alloy layer. In contrast, the TO-mode leaks into both the Ge and Si layers. This happens because in this case, the line is a superposition of an alloy mode with an interfacial mode, which occurs for the TO-polarization in a SL with perfect interfaces. This mode for a perfect interface does not exist for the L-polarization. Therefore, the appearance of this line in the experimental spectra can be taken as a signature for the existence of atomic-scale roughness at the GeISi interface. Two additional pieces of information can be obtained from Fig. 20: (i) the Si mode, originating the Raman peak close to 500 cm-‘, is strictly confined within the Si-layers; and (ii) the Ge LO-modes are very nearly confined within the Ge layers, so the overlap of the bulk Ge optical and the Si acoustical modes for L-vibrations does not produce a significant leak of this mode into the Si layers (no such overlap exists for the Tpolarization, so Ge TO-modes are strictly confined). In a subsequent publication by the same group (Schorer et al., 1994) these points receive confirmation. Here they also study the Si-confined modes in detail in samples with several layer thicknesses and successfully “unfold” these modes according to Eq. (7). Similar results were reported by other authors, interpreted with a much simpler linear-chain model (Dahrma-Wardana et al., 1990; Araujo Silva et a!., 1996a). Alloying at the interfaces was introduced by substituting the masses of Si and Ge planes on both sides of the interface by weighted averages of both. Similar averages of the

260

FERNANDO CERDEIRA

8 9

300

400 w ( cm-l)

50CI

Si Ge Si Ge Ge Ge Ge Ge Ge Ge SiGe SiGe Si Si Si Si Si Si 300

400

500

w ( crn-l)

FIG.21. Local density of states (LDOS) for L and T modes on the atomic planes along the (001) axis of a GegSig SL with two intermixed Ge0.5Si0.5 atomic layers at the interfaces. Reprinted from Gironcoli et at. (1993) with permission.

force constants were taken, thus creating an “alloy atom” (or plane) at each side of the interface. Although this procedure reproduces the results of the more complete SC-model for the Si and Ge mode, the exact symmetries it presupposes makes it inadequate to represent disorder. Consequently it does not reproduce the Si-Ge Raman peak either in position or lineshape (Araujo Silva et al., 1996a). On the other hand, when its limitations are well understood, the LC-model can be a very useful tool for interpreting experimental spectra of features that are not induced by disorder. In particular, Araujo Silva et al. (1996a) use it to prove confinement, according to Eq. (7), in both the Si and the Ge optical vibrations. More shall be said about this in Section 111.5.

4.

RAMAN SCATTERING BY ACOUSTICAL PHONONS I N SI/GE MICROSTRUCTURES

As previously explained (Section 111.l), the acoustic branches of a superlattice can be obtained by folding the average bulk dispersion relation into the mini-Brillouin zone (Fig. 18). Quantitative results can be obtained by an elastic continuum model, originally developed by Ryotov (1956) to explain the propagation of sound waves in a layered medium. For a two-component SL made up of alternating layers of A and B

5

261

OPTICAL PROPERTIES

layers (of thicknesses dA and d g , respectively, and period L = d A + d g ) , the dispersion relation, w (q),of these superlattice acoustic modes is given by Jusserand and Cardona (1989) cos ( q L ) = cos where and

U A (PA)

and

UB

($)

cos

($1

-

2Y

sin

(%)

sin

($1

(8)

( p ~ are ) the sound-velocities (densities) of the bulk materials y=- P B ~ B

(9) P A UA Raman-scattering experiments using different laser wavelengths (AL) probe these branches at different q-values [see Fig. 18 and Eqs (3) and (4)]. A large variety of Raman experiments performed by different authors in Si/Ge,Sil-, SLs allowed quantitative mapping of the folded acoustic branches (Brugger et al., 1986; Dahrma-Wardana et aE., 1986; Zhang el al., 1992a). These experiments were well explained by the model of Eq. (8). One of the most impressive results was the observation of unklapp processes (Dahrma-Wardana et al., 1986), made possible by choosing h~ and L in such a way as to obtain reduced wave vectors [Eq. (4)] Q > 1 . The Ryotov model assumes an infinite number ( N -+ m) of superlattice periods and phonon wavelengths much larger than the thickness of the layers. The first condition is not always met in highly strained structures. In addition, the use of bulk sound velocities and densities in Eq. (9) only gives good results for relatively thick layers. In Ge,Si, SLs these quantities must be considered adjustable parameters in order to obtain good agreement between the predictions of Eq. (8) and experiment (Zhang et al., 1992a; Zhang et al., 1992b). Also, high-resolution Raman spectroscopy shows additional spectral features, appearing in the spectra of thick-layer Si/Ge,Sil-, SLs, which are not predicted by Eq. (8) (Zhang et al., 1992b; Lockwood, 1992; Zhang et al., 1993; Dahrma-Wardana et al., 1993). In order to explain these features, Dahrma-Wardana et aZ. resorted to a linear-chain model with first-principles interplanar force constants and up to fourth-neighbor interaction (Dahrma-Wardana et al., 1993). This model contains no adjustable parameters and translational invariance (ie., N + 00) is not assumed. They simply diagonalize a dynamical matrix of dimensionality Ntot = Nsubs N ~ LNcap,where N S L is the total (Ncap)are the number of these number of atomic planes of the superlattice and Nsubs planes in the substrate (capping layer). The authors compare the predictions of both the Ryotov and the LC models with their experimental results in the frequency-shiftregion w d 50 cm-' for a Si/Ge0.48Si0.52(20.5nm/4.9 nm) SL with N = 15 repetitions, using several laser lines. This comparison is shown in Fig. 22(a), where the positions of the main peaks in the Raman spectrum (full circles) and the LC-model calculations (crosses) are plotted on the dispersion relation predicted by the Ryotov model (continuous lines). Both models reproduce well the experimental results for the main Raman peaks, but the latter uses several adjustable parameters while the former uses none.

+

+

262

FERNANDO CERDEIRA

FIG. 22. (a) Comparison of experiment and theory for the positions of the major Raman peaks, for different A L S , in the folded acoustic modes of a Si/Ge0,48Si0,52SL: Full circles are experiment, crosses are results of the LC-model while the solid curves are calculated with the Ryotov model. (b) Raman spectra, simulated with the LC-model, of the same SL for a finite number of periods (N). Reprinted from DahrmaWardana rt ui. (1993) with permission.

Most importantly, the Ryotov model predicts only these main Raman peaks, whereas the LC-model also predicts subsidiary structures that appear in the experimental spectra. These additional peaks result from the finite character of the sample. In Fig. 22(b) we reproduce the spectra generated by Dahrma-Wardana et al., with the LC-model, for samples containing different repetitions of its basic period ( N ) . The spectrum evolves towards that of an infinite superlattice (coinciding with the Ryotov model) as N increases. The final folded modes are produced by the accumulation of a high density of states at the Ryotov positions with increasing N . The lower curve (N = 15) corresponds to the sample used in their experiment. This curve shows, besides the main Ryotov peaks, fine structure appearing in the experimental spectra (not shown). Hence, the LC-model gives a better description of the spectra, while maintaining a relatively simple calculation scheme. Recently, a numerical variation of the elastic-continuum model has been proposed, which can account for finite size and capping layer effects by imposing appropriate boundary conditions (Pilla et al., 1994). Many subsidiary peaks, as well as structure appearing within the forbidden gaps of the dispersion relations, observed in the spectra of Si/Ge,Sil-, SLs, are explained with this model (Lemos et al., 1995). However, the model uses several adjustable parameters. For ultrathin Ge,Si, SLs the elastic continuum model is not adequate, both because of the thinness of the layers and also because they frequently contain a very small number of periods. Moreover, the Ge,Si, portions of the sample are nested within more complex structures containing buffer, spacer and capping layers. These structures contain Raman peaks in the low-frequency side of the spectrum that are unrelated to the folded modes of the G e n s & SL. The LC-model is able to deal with this complexity, without losing its simple calculational structure. This is illustrated in the examples reported by Lockwood et al. (1988) and Araujo et al. (1996b). In the latter,

5

263

OPTICAL PROPERTIES

high-resolution Raman spectroscopy was used to study the low-frequency part of the spectrum (w 5 100 cm-I) and ordinary Raman spectroscopy was used for the remaining parts of it. The samples, grown by MBE on Si (001) substrates, had a complicated structure, which can be described by: [(Gen S i m ) ~ - l G e S n ~ Mx] p. Here n , m and M are layer thicknesses in monolayers (ML) and N and p are the numbers of repetitions of a given unit. The samples used in the experiments had 12 2: 5 , m 2 5 or 7, M = 200 and p 2 10 - 20. Thus, they contained two periodicities: the smallest period ( n m ) is that of the GenSi, unit, while the largest ( D = N x n ( N - 1) x m M )is that of the unit in square brackets. The lower-frequency part of the spectrum (o5 100 cm-') contains peaks that arise from this larger period, the structure in the intermediate part of the spectrum (100 cm-' 2 o 5 250 cm-') arises from the smaller periodicity and the high-frequency part of the spectrum originates in the confined optic modes. By applying the LC-model to these structures Araujo et al. (1996b) were able to determine in which parts of the sample the vibrational amplitude of a given mode is confined. They find that the vibrations originating in the low-frequency part of the spectrum spread throughout the whole structure, while those giving rise to the intermediatefrequency part of the spectrum are concentrated within the Ge,Si, strings and are, in fact, the folded acoustic modes of an infinite Ge,Si, SL. Finally, for high frequencies the optic modes dominate the spectrum. This part of the spectrum is totally insensitive to variations in N or M , that is, these complicated samples yield the same spectra, in the optical phonon region, as that of infinite Ge,Si, SLs already discussed in the previous subsection. In Fig. 23 we show the calculated (a) and experimental Raman spectra (b) of these samples in the low-frequency region. This part of the spectrum is very sensitive to variations in N or M , as both alter the greater period D. The latter controls peak positions, as shown in Fig. 23(c), thus providing a good way to determine this structural

+

[

10 1

(a )

C

+

1

( b ) Experiment

Calculation

+

2 QW

mC

a

1 QW 0

10

20

30 40

o (cm-')

50

Q 60 0

10

20

30 40

50

60

w(m-')

FIG.2 3 . (a) Calculated and (b) experimental spectra for NQW-samples; (c) calculated dispersion relations (lines) compared to experimental peak positions (circles) for the 1 QW sample and AL = 496.5 nm and A L = 514.5 nm. Reprinted from Araujo Silva er al. (1996b) with permission.

FERNANDO CERDEIRA

264

( b ) Experimental Results

( a ) Linear Chain model

kL=514.5 nm = 10 cm-'

r

.-d

c

v)

Y .c 3

3

Pm

. 2

Pm

. .0

In c

0)

Ie n

I

C .c

9

.-C

m

E

E

m

w

E,

z

I 3

150

200

250

300

350

100

150

200

250

300

350

o ( cm-') FIG. 24. Intermediate frequency region of the Raman spectrum: (a) calculated, (b) experimental. Reprinted from Araujo Silva et at. (1996b) with permission.

parameter. In Fig. 24 the same is done for the intermediate-frequency part of the Raman spectrum. In Fig. 24(a) the calculations produce a Raman peak originating in the folded acoustic modes of the Ge,Si, SL. The position of this peak is insensitive to variations of both N or M , but its intensity depends strongly on the former. The same trend is observed in the experimental spectra [Fig. 24(b)]. The shift in the lower curve ( N = 100) is due to the fact that this is a strained symmetrized SL and, therefore, has a different strain profile than the other samples (commensurately grown on Si). The interesting aspect of Fig. 24 is that the folded acoustic mode is present in the spectrum, although weakly, even when the basic Ge,Si, unit appears only three times. Raman scattering by folded acoustic modes was observed in strain-symmetrized Ge,,Si, samples containing many periods (Schorer et al., 1994; Alonso et al., 1989). A representative example of these results is shown in Fig. 25. The left-hand side of this figure shows the dispersion relations for the longitudinal and transverse acoustic modes of a Ge4Si4 SL, calculated with the SC-model (Alonso et al., 1989). The circles on four of these curves correspond to the modes observed in the Raman spectrum [Fig. 25(b)]. The most prominent feature in this spectrum is the peak produced by the LJ = f l folded LA modes. Higher-order folded LA-modes are observed in the other SLs [see Fig. 2S(b)]. In all cases simulated spectra are in good agreement with experimental ones. The asymmetry in the Raman peak of the lowest curve in Fig. 25(b) is produced by the appearance of the forbidden Raman peak originating in

5

OPTICALPROPERTIES

265

! NZiL

0

I00

I

200

FIG.25. (a) Dispersion relations of a GeqSiq SL for L-(solid lines) and T-acoustic modes (dotted lines). Circles are peak positions in the Raman spectrum. (b) Experimental (upper curve) and calculated spectra for several Ge,Si, SLs ( T = 300 K and A L = 568.2 nm). Reprinted from Alonso etal. (1989) with permission.

the B1, mode. This peak is forbidden for q = 0. The nonzero value of q in the actual experiment [Eq. ( 3 ) ]weakly induce the appearance of this peak (Alonso et al., 1989).

5.

RESONANT RAMANSCATTERING

a.

Introduction

The subject of resonant Raman scattering in semiconductors is exhaustively reviewed by Cardona (1982), who discusses in-depth its usefulness and the subtleties of the interpretation of the experimental results. The Raman cross section is also didactically explained in chapter 7 of the textbook by Yu and Cardona (1995). For a good understanding of the subject we refer the reader to these general references. Here we

266

FERNANDO CERDEIRA

shall briefly sketch the aspects of this technique that are relevant to the analysis of the results reported for Si/Ge microstructures. The Stokes Raman cross section results from an infinite sum of terms originating in processes that involve the virtual absorption of a photon ( h w ~ )creating , an electronhole pair, the emission of a phonon ( h w ) via electron-phonon interaction at the initial or final state of this transition, and a recombination of the resulting electron-hole pair with the emission of a photon ( f i w ~in) such a way that the conservation laws of Eq. (2) are satisfied. One of these processes is shown schematically in Fig. 26(a) and its contribution to the Raman cross section is given by

c(

IF;:

( u I H e - r I c')(c' I H e - p I

C)(C 1 ~ e - t

Iu)

[fiwr. - (EL - E d ] [hws - (E'! - E " ) ]

+. . I

2

(10)

In Eq. (10) He-,. and He-pare the Hamiltonians of the electron-radiation and electronphonon interactions respectively, while E, ( E , ) is the energy of the electronic conduction (valence) band state. In the cases where the photon energy of either the incoming or outgoing beams coincides with that of an interband transition with a significant joint density of states (i.e., one of the singular points in the optical spectra discussed in Section II), one, or both, of the energy denominators of Eq. (10) vanishes and the contribution from this particular term dominates the Raman cross section. This results in an enhancement in the intensity of the Raman peak. Thus, one might expect that plotting the intensity of the Raman peaks as a function of the photon energy of the incoming beam, spectra similar to those obtained by modulation spectroscopy should be obtained. Here the modulating agent is one of the vibrational modes of the material. Even if this naive interpretation were invariably true, the process of data gathering is

( a ) A typical Ramam process

( b ) A typical

PL-process

FIG.26. Schematic representation of: (a) a two-band term in the resonant Raman cross section; and (b) a PL process involving band-to-band recombination in a direct gap semiconductor.

5

OPTICAL PROPERTIES

267

cumbersome, as many individual Raman experiments must be performed for different laser wavelengths. The data also have to be normalized to correct for changes in alignment or laser intensity between these successive experiments, as well as to account for the fact that both the incoming and scattered beams are partially absorbed as they traverse the material (Cardona, 1982). Returning to Eq. (lo), we note that each matrix element in this equation represents a selection rule that must be obeyed if the scattering process is to have nonzero probability. In particular, the element ( c He-pl c’) corresponds to electron-phonon interaction involving the electronic states that mediate the scattering event. Hence, the electronic and vibrational states involved must have spatial overlap for this matrix element to be different from zero. This is of crucial importance in an A / B SL, where both the electronic and the vibrational states may be confined in either the A or B layers. In this case, a phonon localized in layer A cannot receive a contribution to its Raman cross section from optical transitions between states localized in layer B, and vice versa. Hence, no resonance effect will be observed in the cross section for this phonon when ~ W isL in resonance with such a transition. On the other hand, resonant enhancements will occur when both the electronic states and the phonon are localized in the same layer. In the same way, vibrational modes that extend through both layers will have enhanced cross sections for resonance with any electronic transition and an electronic transition between extended electronic states will provoke enhancement in all Raman lines. These facts were first demonstrated by Zucker et al. (1984b) in resonant Raman scattering (RRS) experiments performed in GaAs/AlGaAs SLs. This characteristic makes RRS a very useful complementary technique to the forms of differential spectroscopy reviewed in Section 11. While the latter provide very accurate information about the energy of critical points, RRS furnishes information about the localization of the electronic states participating in a given optical transition. One cautionary note must be made concerning the analogy between RRS and modulated spectroscopies: The photon-energy position of the maxima in the RRS cross section often differs significantly from those of the singular points in the joint density of states that originate them (and, consequently, from the position of the corresponding peaks in the optical spectra), even for scattering processes involving only two bands, as is the case for the one illustrated in Fig. 26(a) (Cardona, 1982). The exact origin of these discrepancies (which could be as much as 50 MeV) are not fully understood, but the Raman cross section depends on the exact nature of the electron-phonon interaction which, in turn, cannot be exactly formulated in most cases of interest. This discrepancy becomes serious when the phonon has a symmetry such that it can couple two bands that lie close in energy. The contribution from these three-band processes can lead to complex lineshapes with maxima and minima (resulting from interferences between two- and three-band terms), which bear no easy relationship to the energy position of the associated critical points. As an example of this, the resonant Raman cross section of bulk Ge, in the region of the El and El + A 1 critical points, is shown in Fig. 27, from the data of Cerdeira et al. (1972). In this figure the full symbols represent experimental

I

FERNANDO CERDEIRA

268

-

T=3OO”K

19

2.0

2.1

2.2

23

2.4

2.5

26

2T

FIG. 27. Resonance in the room-temperature Raman cross section for bulk-Ge (full circles and triangles). The dashed curve is a guide for the eye while the solid one is a phenomenological representation of the contribution of three band terms. Adapted from Cerdeira et al. (1972) with permission.

data, the dashed line is meant to guide the eye, and the arrows represent the positions of these two critical points, as given by measurements of modulated reflectivity. The Raman cross section presents only one, very broad peak at a photon energy more or less midways between the two ER-peaks. This happens because, in this case, the cross section is dominated by three-band terms, resulting from the coupling that the phonon introduces between the closely spaced valence bands of Ge along the A-axis of the BZ. The solid curve is a phenomenological estimate of this contribution. The good agreement shown in the figure was obtained by shifting this theoretical curve by 45 MeV towards higher energy. The q ? 0 optical phonon of Ge also couples the strain-split valence bands at the zone-center, when the strain has a symmetry axis along the (001) direction, as is the case of Ge layers grown lattice-matched on Si (001) substrates. In that case Eo transitions could produce resonant Raman cross sections very similar to those of Fig. 27. The coupling already described here results from the r15 symmetry of the zonecenter phonon. A phonon of symmetry, for instance, would not produce this coupling. The cross section of this phonon would show two distinct peaks, one for each critical point. Such a phonon exists in the folded acoustic branches of a GeISi SLs or in the totally symmetric part of the two-phonon spectrum of bulk Ge. This is indeed seen in the Resonant cross section of the totally symmetric part of the 2TO(L) spectrum of bulk Ge (Renucci et al., 1974). But even here the peaks in the Raman cross section are shifted in relation to the positions of the El and El A1 critical points. The foregoing discussion should warn us against assigning optical structure on the basis of the positions of peaks in the resonant Raman cross section alone. This is particularly true when several transitions fall in the same photon-energy range. In this case the coupling introduced by the phonon between the states participating of these transitions can result in complicated resonant lineshapes with maxima and minima that bear

+

5

269

O P T I C A L PROPERTIES

no immediate relationship to the energy position of the individual critical points. On the other hand, RRS has the unique property of giving direct experimental information about the localization of the electronic states participating in a given optical transition (or group of transitions). b.

Resonant Raman Scattering in Si/Ge Quantum Wells and Superlattices

The first observation of RRS in this type of structure was made in Si/Ge,Sil-, SLs of relatively large periods (Cerdeira et al., 1985). These results, displayed in Fig. 9, were already discussed briefly in section 11.3. This figure shows broad single peaks in the resonant cross sections, in the general photon energy region where the El and El +A1 critical points of the unstrained alloy should be. Moreover, the general shape of the resonant peaks is similar to that of the El resonance in bulk Ge (Fig. 27). However, strain and confinement should produce another doublet in this photon-energy region [Eo(1) and Eo(2)], which would also be coupled by the phonon, giving rise to a similar peak in the Raman cross section. On the basis of the dependence of this peak with layer thickness, Cerdeira et al. (1985) attributed this resonance to the &-doublet. This assignment proved to be controversial and similar structures in the resonant Raman cross section of related Si/Ge materials were attributed alternatively to either one or another of these two doublets (Cerdeira et al., 1985; Rodrigues et al., 1993a; Cerdeira et al., 1989; Schorer et al., 1994b; Schorer et al., 1995). In Fig. 28 we display RRS results for the LO and LA modes of several strainsymmetrized Ge,Si, SLs (Cerdeira et al., 1989). For the SLs with larger periods, two distinct peaks are observed in the Raman cross sections of these modes at f i o ~ 2.3 and 2.9 eV respectively. The lower photon-energy peak is produced by electronic transitions between states confined in the Ge layers. This can be deduced from the fact that, at this photon energy, only the cross sections of the Ge-optic mode (confined in the Ge layers) and that of the folded LA-mode (extending through the whole SL) show enhancements, while that of the optical mode confined in the Si layers does not. In contrast, at the higher photon energy all modes are enhanced, that is, this transition (or group of transitions) involves electronic states with nonvanishing components in both layers. As the layer thickness decreases both peaks show a tendency to merge. The first group of optical transitions could either be associated with states derived from the bulk Ge El or EOdoublets. Cerdeira et al. (1989) favor the first choice, without totally discarding the second. More recently, Schorer et al. (1994b and 1995) performed very careful RRS experiments, where both longitudinal and transverse modes could be studied by exploiting the micro-Raman technique in order to perform backscattering experiments from the cleaved or polished sample edges. Their main results are summarized in Fig. 29, in which the resonant cross sections of the first Ge and Si confined modes are displayed together with that of the alloy-like Si-Ge mode. In all cases a strong resonance is ob-

-

270

FERNANDO CERDEIRA

A

3.0 FIG.2 8 . Raman cross section for LO and LA modes of several Ge,Si, energy. Adapted from Cerdeira ef ul. (1989) with permission.

as a function of laser photon

served in the cross section of the Ge-modes, which is absent in that of the Si-modes, in the photon-energy range around 2.2 eV, signaling the presence of electronic transitions between states confined in the Ge layers. This resonance is more pronounced in the L-modes, involving light polarized in the plane of the layers, than in the Tmodes, involving light polarized perpendicular to the layers. These anisotropies are in agreement with the results of a dielectric function calculation based on a tight binding approach (Tserbak et al., 1991). These authors calculate the dielectric constant for light polarized both in the layer planes E I (~w ) and perpendicular to them EL ( w ) separating the contributions from Ge and Si bulk states to this response function. This decomposition is shown in Fig, 30, where it is clear that in ~ 2 1 the 1 Ge and Si contributions are well separated in energy while this separation is blurred for ~ 2 1 The . most prominent contribution to the in-plane dielectric constant, in the photon-energy region being discussed, comes from the El states of bulk Ge. Thus, there is a striking analogy between the calculations of Q ( W ) and the results of RRS for L- and T-modes. This analogy also favors the interpretation of the RRS results in terms of bulk-Ge El transitions, even if

5

271

OPTICAL PROPERTIES

150

100

50

0

L

f

8W

600

(P

tY

4w

400

200

200 0 1.6

2.0

2.4

28

0

1.6

2.0

2.4

2.8

FIG. 29. Raman efficiency of Gel (squares), Sil (circles), and Si-Ge modes (triangles) of several GenSim SLs and one Ge7Si3 SL for in-plane backscattering geometry from polished (1 10)-sample edges. Full symbols denote y’ (x’x’)y’ (light polarized Ito the layers). Adapted from Schorer et al. (1995) with permission.

in their first report Schorer et al. (1994b) were inclined to attribute this resonance to Eo-like states. Finally, resonant Raman results, combined with those of modulation spectroscopy, performed on single and multiple Ge5 QWs reinforce the notion that the most important contributions to the optical response functions in this photon-energy range originate in confined electronic states traceable to the bulk Ge E l transitions (Rodrigues et al., 1993a; Araujo Silva et al., 1995). The origin of these discrepancies in the interpretation of RRS results lies in the fact that the position of the maxima in the broad features of the resonant Raman cross sections (produced by scattering processes involving 2- and 3-band terms) are insufficient for making an identification of the optical transitions involved in the resonance.

272

FERNANDO CERDEIRA

FIG.30. Calculated E2(w) for a strain-symmetrized GegSig SL, decomposed into contributions from Ge (Ge-Ge) and Si (Si-Si) atoms. Solid lines are ~ 2 1(w) 1 and dashed ones E ~ L ( w )Adapted . from Schorer et al. (1995) with permission.

The preceding discussion was centered mainly on the resonant cross sections of optic modes. Schorer et al. (1994b) report in detail RRS results from several orders ( u = 1,2, 3 and4) of folded LA-modes in a GelzSil2 SL (see Fig. 31). Because these modes transform according to totally symmetric representations of the SL pointgroup, 3-band terms should not contribute to their resonant cross sections. Hence, two well-resolved peaks should be observed when the resonance is produced by a doublet. This effect is indeed seen in the cross section of the LA1-modes displayed in Fig. 31 as full triangles, which shows two distinct, albeit broad, peaks at ~ W L 2.1 and 2.4 eV, respectively. The resonant cross sections of higher-order TAU modes show one main peak, followed by a shoulder, which shifts towards higher photon-energies as the folding index u increases. Qualitatively, this could be explained by assuming that the resonance is produced by a multiplet which results from confined electronic states with different confinement indices, and that resonances are stronger when both confinement indices (that of the phonon and that of the electronic states involved in the transition) are equal. In this case, higher-order folded phonons resonate preferentially with higher confined electronic transition, thus explaining the energy shift of Fig. 3 1. This explanation, attractive as it sounds, has no theoretical underpinning, as both the nature of the electronic transition and the details of the electron-phonon interaction are not known. All of the preceding discussion was centered on interpretations based on perfect superlattices. As we shall see in the following subsection, this technique is also useful in establishing the presence of certain types of interface roughness.

-

5

OPTICAL PROPERTIES

273

FIG. 3 1. Resonant cross sections of LA-modes in a Gel2Sil2 SL (300 K). Adapted from Schorer et al. (1994b) with permission.

c. Detecting Long-Range Inter$ace Roughness by Resonant Raman Scattering In Section 111.3 we discussed the role of Raman scattering in determining atomic scale roughness in the SifGe interfaces of Ge,Si, SLs, in the form of random-alloy layers, existing in a region of f l ML about each interface. There is another type of roughness (terracing) that has been observed at the interfaces of some SLs composed of 111-V materials (Gammon et al., 1991; Brasil et al., 1993). These terraces, having lateral dimensions of the order of 10 nm or more, produce splittings in the luminescence line produced by exciton recombination at the direct gap of these materials. It would be difficult to use luminescence to detect such terraces in SifGe systems, due to their indirect gaps and the resulting complexity of the luminescence spectra (see Section IV). However, resonant Raman measurements have recently provided evidence of terracing in Ge,Si, SLs (Brafman et al., 1995). The samples used in the experiments of Brafman et al. (1995) were already discussed in Sections 111.3and 111.4. They consist of N-Ge5

-

214

FERNANDO CERDEIRA

quantum wells separated from one another by 5 MLs of Si. Each sample contains up to 20 repetitions of a basic unit (with thick Si-spacer layers between them) which has N = 1,2, or 6 and is designated by NQW. The Raman spectra of these samples are studied, both for L- and T-modes, using several discrete lines of argon- and krypton-ion lasers. In Fig. 32 we show their results for the longitudinal Ge-confined optic mode. The upper part of the figure [Fig. 32(a)], displays the off-resonance spectra of the three samples, while part (b) of the figure shows the same part of the spectrum of the sextuple QW taken with laser lines of different photon-energies. We see that in the offresonance spectra, the position and lineshape of this mode are different for each sample. This is surprising, as this line originates in a mode entirely confined within the Ge layers (see Section 1111.3) and, therefore, insensitive to the number of layers-that is, all three lines should be identical. Moreover, Fig. 32(b) shows that this line, for the same sample, changes in position and lineshape as the wavelength of the incoming laser is changed. This means that we are in the presence of a resonant effect. These changes occur because the observed line is a superposition of Raman lines produced by phonons confined in Ge quantum wells of different thicknesses. These QWs are produced by terraces within a given Ge layer. To produce the effect of Fig. 32(b), the lateral dimen-

250

300 o (cm-1)

350

FIG. 3 2 . (a) Off-resonance spectra of the Gel LO-mode of the three NQW samples and (b) the same spectrum for the 6QW sample taken with different laser lines. Reprinted from Brafman et al. (1995) with permission.

5

OPTICALPROPERTIES

275

sions of these terraces must be at least of the same order as the radius of the exciton involved in the resonance-that is, d 2 10 nm. Thus, the laser beam ( D 2 1 p m ) samples a large number of these terraces-that is, a large number of QWs of different widths. Each one of these QWs contributes to the Raman spectrum with a line centered around a different frequency [Eq. (7)],in such a way that wider wells contribute to the higher-frequency part of the composite line and vice versa. For low values of AWL, resonant conditions are met for the wider wells, increasing the intensity of the highfrequency side of the composite Raman line, which causes an apparent shift towards higher energy. As the laser photon-energy increases narrower wells meet the resonance condition, causing the low-frequency part of the composite line to increase its intensity, which produces the asymmetric broadening and shift of its maximum towards the lower frequencies seen in Fig. 32(b). Why does this happen in the 6QW sample and not in the others? Because terracing becomes more pronounced as the number of quantum wells increases. This explains the differences observed in the off-resonance spectra of the different samples [Fig. 32(a)]. The preceding conclusions were put on a more quantitative basis by comparing the experimental spectra with those generated by a linear-chain model, in which terracing was simulated by superimposing the Raman lines of QWs with different widths (Araujo Silva et al., 1996a). In Fig. 33(a) we show the result of fitting the experimental Raman line, for a given laser line, of the 6 QW sample with a simulation using terraces with three different Ge thicknesses (3,4 and 5 MLs). By performing such a fit for each laser line, the resonant cross section of each terrace, (Y, ( w L ) , is obtained. This is shown in

o 70

L ~r,( = 12.0 m-l)

0.01 L ~r ,(

= 9.0 m-1)

0 5 1 L ~r ,( = 7.0 ~ m - '

I

I

1

I

1

260

280

300

320

340

5

o ( cm-') FIG. 33. (a) Raman spectrum of the Gel TO-mode in the 6 QW sample fitted with contributions from wells of different thicknesses (3,4, and 5 MLs) and (b) the resonant cross section an(o[,)for each of these contributions (circles, squares and diamonds) fitted to Lorentzian lineshapes (lines). The inset shows the position of these Lorentzian lines vs Ge layer thickness (circles) compared to an envelope-function calculation (line) for Eg-like states. Reprinted from Araujo Silva ef a[. (1996a) with permission.

276

FERNANDO CERDEIRA

Fig. 33(b), where the dots, squares, and diamonds represent the Raman cross-sections of the phonons confined within the QWs of 3, 4, and 5 MLs, respectively, and the curves (dashed, dotted, and solid) are least-square fits to these points with Lorentzian lineshapes. The results are consistent with the previous analysis, as they predict optical transitions that decrease in photon energy and linewidth as the QW becomes wider. This is consistent with the confinement of the electronic states involved in the transition (higher transition energies for narrower wells) and with the fact that microroughness is more important in broadening the line as the well becomes narrower. Finally, the change in the transition energy is plotted (full circles) as a function of QW-width in the inset of Fig. 33(b) and compared with the predictions of an envelope-function calculation (solid line) for an Eo optical transition (section 11.4). The experimental confinement shifts are much smaller than those predicted by theory, which lends support to the El (rather than Eo) assignment for the optical transitions responsible for this resonance. The method outlined here was recently used to study the evolution of short and long range roughness in Ge, single quantum-wells of different thicknesses ( n = 3 , 4 , 5, and 6), separated by 70 MLs of Si (Narvaez et al., 1997). These authors find that alloying at the Si/Ge interface occurs always, regardless of the Ge layer thickness. For n 5 5 the alloy layer has an average Ge molar fraction that grows steadily as n increases until it stabilizes at x 0.5 for n 2 5. This is probably due to Ge segregation occurring at low values of n, which results in terrace formation. This terracing is visible in the dependence of the confined Ge Raman line on the wavelength of the exciting laser for the samples with n = 3 and 4, but absent in the samples with n = 5 and 6. Thus, a transition from terracing to layers of uniform average thickness seems to occur in these samples at some value between 4 and 5 MLs. The foregoing discussion shows yet another application of Raman scattering to the structural characterization of quantum wells and superlattices.

-

6.

SUMMARY

The preceding discussion shows that, when the results of experiments are complemented by lattice dynamical calculations, Raman scattering can provide important information about vibrational and electronic states. It also gives quantitative estimates for several structural parameters (such as strain, period length, layer thicknesses, etc.) as well as detecting short- and long-range interface roughness. While the best picture of what goes on in a given microstructure is always given by the rather complex supercell calculations, simpler models, such as linear-chain or elastic continuum ones, are often sufficient to give an enlightening interpretation of the experimental data. Resonant Raman scattering has the unique property of giving direct experimental information about the localization of the electronic wavefunction at critical points in the Brillouin zone. This aspect makes RRS a supplementary technique to those discussed in Section 11. However, its limitations must be understood in order not to incur misinterpretations.

5

OPTICAL PROPERTIES

277

One of these limitations is that the peaks in the Raman cross sections do not always coincide with the energy of the critical point that originates it. The mechanism by which the phonon interacts with the electronic states involved in the transition must be known before conclusions are drawn on the basis of the photon-energy position of peaks in the Raman cross section.

IV. Photoluminescence 1. INTRODUCTION In a photoluminescence (PL) experiment an electron-hole pair is created by the absorption of an incoming photon, the created electron and hole thermalize rapidly to energy minima and recombine from there by emitting a photon of lower energy. Because the emission occurs after a multiple scattering process, there is usually no correlation between the polarizations of the incoming and emitted photons. The idealized process of PL by band-to-band recombination is shown schematically in Fig. 26(b), for a direct bandgap semiconductor. This process bears a certain superficial resemblance to that of resonant Raman scattering, shown schematically in part (a) of this figure. In the latter, however, both the photon absorption and emission are virtual processes and no loss of correlation between them occurs. Also, in the Raman process the frequencies of the incoming and outgoing photons are related to one another through Eq. (2), while in the PL process of Fig. 26(b) the outgoing photon always has the energy of the bandgap, regardless of the energy of the incoming photon (as long as it is greater than the bandgap). In an indirect bandgap semiconductor, such as Si and Ge, recombination must be assisted by large wavenumber phonons in order to conserve crystal momentum. Hence, the intensity of the emission lines in indirect gap semiconductors is always much smaller than those in direct gap ones. In real semiconductors, especially at low temperatures, the recombination energy may not coincide with the bandgap. First, electron-hole interaction (excitons) modifies this. Second, excitons can be localized by impurities and defects and recombine from there, producing a rather complex PLspectrum. This complexity is increased by the fact that the intensity of a given PL line depends much more on the efficiency of the recombination channel than on the contribution of the recombination centers to the overall density of states. Thus, emission lines from electronic states with a very small density of states can, in certain cases, be the dominant features of the PL-spectrum. A technique related to PL is that of photoluminescence excitation spectroscopy (PLE). Here, the spectrometer is set at the maximum of a given PL-line while the photon energy of the incoming radiation is varied in a continuous manner around the region of the absorption edge. As the number of electron-hole pairs created at a given incident photon-energy (Ti@,) is proportional to the number of absorbed photons, the

278

FERNANDO CERDEIRA

intensity of the resulting PL line will be roughly proportional to the absorption coefficient ~ ( w L ) In . microstructures composed of direct bandgap semiconductors PLE spectra show very sharp structure related to transitions between quantum-confined levels associated with the direct bandgap (Liu et al., 1989). For indirect bandgap systems, such as the ones in which we are interested, the PLE spectrum does not show peaks, but rather an absorption edge below which the response is zero and above which it increases monotonically (Sturm et al., 1991). In the following subsections we discuss the application of this techniques to bulk Ge,Sil-, alloys and to QWs and SLs obtained by alternating layers of Si, Ge, or alloy with one another.

2.

~ PL FROM BULKG E , S I ~ -ALLOYS

Well-resolved free-exciton (FE) and bound-exciton (BE) PL have been observed in bulk Ge,Sil-,r alloys by several groups (Benoit B la Guillane et al., 1974; Gross et al., 1973; Rentz and Shlimak, 1978; Mitchard and McGill, 1982; Lyutovich ef al., 1985; Dismukes et al., 1964) culminating in the comprehensive work of Weber and Alonso (1989). In Fig. 34 we display their low temperature (4.2 K) PL-spectra of bulk alloys with different compositions. The spectra exhibit several lines assigned to recombination of excitons bound to shallow donors and acceptors. The lines are labeled X:, where j indicates whether the recombination is phonon assisted or not (NP) and i specifies the nature of the phonon when it is. The phonons of the alloy are labeled as Ge-Ge, Si-Ge or Si-Si, according to the classification explained in section 111.2. They also observe free exciton lines in the PL-spectra taken at higher temperatures. The most prominent feature of the spectra in Fig. 34 is the no-phonon recombination line ( X N P ) , which appears as a consequence of a disorder-induced process and does not conserve crystal momentum. The ratio of the intensities of the no-phonon line to that of the phonon-assisted ones scales approximately as the number of Si-Ge pairs in the alloy INP

-

x(1

-

(11)

x)

and the relative intensities of the phonon-assisted lines are given by

-

The full-width at half-maximum (FWHM) of the X N P lines also depends on x , varying from 4 to 8 MeV (in the best samples), as opposed to 0.3 MeV for the same line in bulk Si. Finally, the position of this line as a function of x allows Weber and Alonso (1989) to obtain an accurate expression for the dependence of the indirect energy gap

5

OPTICALPROPERTIES

279

Ge, x = 0.93

x = 0.08 I

I

I

Photon Energy (eV ) FIG. 34. Near-bandgap PL-spectra for bulk Ge,Sil-, alloys. The optical transitions are labeled X: where j = N P when the transition is not phonon-assisted and nothing when it is and i specifies the type of phonon. Reprinted from Weber and Alonso (1989) with permission.

as a function of Ge molar fraction and to determine the cross-over (from A to L) of the conduction bandedge at x = 0.85. Another interesting feature is observed in the PL spectra of some lower-quality samples: a broad feature on the low-energy side of the X N P line (Weber and Alonso, 1989). This line had been previously labeled as the “L-line” by other authors (Mitchard and McGill et al., 1982), who interpreted it as a bound-exciton recombination at an Inacceptor. This interpretation is revised by Weber and Alonso (1989), who attribute this broad PL-line to recombination occurring in a dense electron-hole plasma gathering in potential wells formed by large compositional fluctuations (probably in the vicinity of dislocations or other defects). A similar line is observed in the PL-spectra of some MBE-grown Si/Ge,Si I-, QWs. We shall discuss this in the following subsection.

280 3.

FERNANDO CERDEIRA

PL FROM SI/GE,SI~-, MICROSTRUCTURES

First reports of PL measurements in MBE-grown Si/Ge,Sil -, structures show spectra that are significantly different from those of bulk alloys (Noel et al., 1990). The low-temperature spectra of these samples show a broad PL structure near the alloy bandgap, rather than the sharp phonon-resolved structures of Fig. 34. By comparing PL and PLE measurements for their samples, Noel et al. (1990) determined that the center of this broad PL structure lies slightly below the indirect absorption edge of the alloy and tracks this gap as x varies. This is illustrated in Fig. 35, where the low temperature (4.2 K) PL-spectra of three samples with different compositions and layer thicknesses are displayed. Observation of phonon-resolved near-bandedge PL from strained Si/Ge, Si 1-,y layers were later reported both in MBE-grown samples (Terashima et al., 1990) and in samples grown by rapid-thermal-chemical deposition (RTCVD) (Sturm et al., 1991). The spectra of Sturm et al. (1991) are dominated by no-phonon recombination, attributed to the annihilation of excitons bound to shallow impurities at T ^" 2 K, and to free exciton recombination at higher temperatures. As in the bulk case, peaks due to phonon-assisted recombinations are also observed. In fact, their spectra are almost identical to those of bulk alloys (Fig. 34), except for photon-energy shifts, which can be quantitatively related to strain and quantum-confinement. They also perform PLEmeasurements to determine the absorption edge of the alloy QWs and use the difference in position between this and the PL line to determine the binding energy of the excitons. Both these measurements and those of the decay times (- 0.4 ps) of the main PL peak

T = 4.2 K

x = 0.47 d = 5.0 nm 3

-

1, = 514.5 nm

QE=5%

d=Z3nm

x

.E v)

c c

K

$

x = 0.12 d=l30nm

A

650

750 850

x

4

I

950 1050

Photon Energy ( eV ) FIG. 35. The PL-spectra at 4.2 K, after rapid thermal annealing, of Si/Ge,Sil-, widths (d) and compositions (x). Adapted from Noel et af. (1990) with permission.

QWs of different

5

OPTICAL PROPERTIES

281

at 2 K are consistent with the assignment of this line (recombination of excitons bound to shallow impurities). These authors also use the relative intensities of the phononassisted lines [Eqs. (1 1) and (12)] to draw conclusions as to the actual confinement of these excitons. They determine that, when the width of the QW (d) is larger than the exciton radius (aexc 4 nm), the wavefunction is entirely contained within the alloy layer while, when d 5 aexc,the exciton wavefunction penetrates into the Si-bamer region. Similar results were reported later by other authors in samples grown by MBE or CVD (Fukatsu et al., 1992; Usami et al., 1992; Xiao et al., 1992). The clearest demonstration of quantum confinement in these QWs was given by Xiao et al. (1992), whose results we reproduce in Fig. 36. The left-hand side of this picture shows their PL spectra at 4 K for QWs of different well-widths ( d ) ,while part (b) of this figure shows a plot of the position of the no-phonon PL-line for two different temperatures (full triangles and squares) compared to the predictions of an envelope-function-type model (solid lines), which include the effects of strain and confinement in the valence band states of the alloy and assume negligible confinement for the conduction band electrons (Van de Walle and Martin, 1986; People and Bean, 1986). The excellent agreement between theory and experiment confirms the assignment of this PL-line. The preceding discussion shows that two distinct types of behavior are seen in the PL spectra of Si/Ge,Sil-, QWs and SLs: well-resolved luminescence of the same type observed in bulk alloys (Fig. 36) and a broad PL-line, also associated with the indirect bandgap of the alloy-layer (Fig. 35). The broad PL-line seems to be present only in some (but not all) of the samples grown by MBE (Usami et at., 1992; Terashima et al., 1991; Spitzer et al., 1992; Noel et al., 1992; Glaser et al., 1993; Wachter et al., 1993; Brunner et ~ l . 1992), , but not in those grown by CVD (Sturm et al., 1991; Dutrarte et

-

- theory n m

-

'0 c

n m

FIG. 36. (a) PL spectra, at 4 K, of four Si/Ge0,8Si0,2 QWs of different widths ( d ) and, (b) bandgap vs d at 4 K (triangles) and 77 K (squares). The solid line is an envelope function calculation for each case. Reprinted from Xiao er 01. (1992) with permission.

282

FERNANDO CERDEIRA

al., 1991; Robbins et al., 1992). Several authors tried to correlate the appearance of this line with growth parameters such as layer-thickness, Ge-molar fraction, number of repetitions of the QWs, and growth temperature. This gave a rather confusing picture, where contradictions abound. Rowell et al. (1993) give a good review of these attempts. The main findings about the appearance of this broad PL-feature can be summarized as follows (we discuss low-temperature PL measurements, T 5 4K, unless otherwise specified): 0

The maximum of this broad (- 80 MeV FWHM) PL peak lies at lower energy than the NP-line in the sharp, phonon-resolved, spectrum, but it tracks the indirect gap of the alloy (always 10 MeV below) as alloy composition or QW-widths change. This shows that this feature is also related to a no-phonon emission process across the fundamental gap (Noel et al. 1990).

-

0

Terashima et al. (1991) studied the evolution of the PL-spectrum of QWs grown by MBE at low-growth temperature (TG 2 400 "C) as a function of annealing temperature. Initially their samples exhibit the broad PL-feature we have been discussing. Upon annealing in a N2 atmosphere at temperatures TA 600 700 "C, this line increases its intensity by factors of between 5 and 10. Annealing at higher temperatures (TA = 800 "C) transforms the PL-spectrum into a sharp phonon-resolved one similar to that observed in bulk alloys or in CVD-grown QWs (although greatly reducing the overall PL-intensity). The NP-line of this new spectrum lies at slightly higher photon energies than that of the maximum of the broad PL-line.

-

0

Spitzer et al. (1992) report PL measurements in samples of different alloy compositions grown by MBE at low temperatures (TG = 325 - 450 "C). The thicknesses of these coherently strained Ge,Sil-, layers (up to 500 nm) greatly exceeded their equilibrium values (see the chapter by Hull). While some as-grown samples present the broad PL line, others exhibit sharp phonon-resolved spectra. No correlation was found between layer thickness and the type of PLpresented by the as-grown samples. The broad PL-line disappears upon annealing at TA ? 600 "C, when strain-relaxation sets in. After annealing both types of samples show narrow phonon-resolved PL-spectra. Noel er al. (1992) and Rowell et al. (1993) present some results that conflict with those of the previous item. They grew, by MBE, Si/Ge,Sil-, MQWs designed to be metastable at the growth temperature (TG = 600 "C). Their samples had three different QW-thicknesses (d = 2.7, 5.2, and 6.8 nm, respectively) and two different molar fractions (x = 0.15 for the first two and x = 0.19 for the last one). Their results are displayed in Fig. 37, which shows a steady increase of the broad PL-line over the phonon-resolved PL as the QW-thickness and Ge molar fraction increase. Observation of images by transmission electron (TEM)

5

OPTICAL PROPERTIES


l V (0.57 eV)

-0.1 V / (0.63 eV)

27

29

31

33

35

I l k 1 (eV”)

FIG. 22. Arrhenius plot of the reverse current measured as a function of temperature for a heteroepitaxial Ge diode grown on a graded GeSi/Si substrate, for various values of applied reverse bias. Activation energies are in parentheses. Reprinted with permission from Grillot et al. (1996).

6 ELECTRONIC PROPERTIES AND DEEPLEVELS

325

reverse biases that incorporate only the 100%Ge top layer within the depletion region, an activation energy of the Ge bandgap is observed. As the bias voltage is increased, the activation energy decreases and approaches the E(0.42) DLTS electron trap energy observed in the high Ge content layers, which is close to midgap for x > 85% (i.e., the constant composition cap plus the top few layers of the graded buffer), consistent with the dominant midgap trap for low Ge content layers. This indicates that the leakage current is dominated by generation via deep states within the depletion region for reverse biases in excess of 4 v. This interpretation was confirmed by considering Fig. 23, which demonstrates a linear dependence of the square of the reverse current on reverse bias for voltages beyond 4 V as expected for generation-dominated current according to the first term of Eq. (12). No such voltage dependence is expected for the ideal diode saturation current term. The physical reasons are clear from the cross-sectional TEM micrograph of Fig. 24 that shows the 2pm Ge cap layer, in which the doping concentration was 5 x 1014cm-3 yielding a zero bias depletion width of l p m . As the reverse bias increases to 1 V, the Ge layer is nearly fully depleted, and for voltages greater than 4 V, the depletion region extends well into the graded buffer. Hence, with increasing reverse bias, regions of higher bandgap and higher defect density are simultaneously incorporated within the depletion region, which from Eq. (12) has the dual effect of reducing the contribution from the ideal saturation current term due to the increasing bandgap, while simultaneously increasing the contribution from generation centers through increased trap density. It is interesting to realize from this that even though the relaxed Ge layers have a higher threading dislocation density than the low Ge content layers due to the higher lattice mismatch, the substantial decrease in bandgap beyond a Ge content of 85% is a more dominant current source. Thus. the constraint on the

-

Diode bias (4)

FIG. 23. The square of the reverse current of this figure is found to vary linearly with respect to the applied reverse bias for voltages in excess of 4 V,indicating that deep generation centers within the depletion region dominate the reverse current in this voltage range. Reprinted with permission from Grillot et al. (1996).

326

STEVEN A. RINGELAND PATRICK N. GRILLOT

FIG. 24. The TEM cross section of a relaxed, Ge/graded GeSi/Si heterostructure. The 2-hm thick Ge cap layer has an n-type doping concentration of 5 x 10’4cm-3.

critical defect density above which defects dictate reverse leakage currents is relaxed for Ge, and Ge layers on GeSi/Si appear more “defect-tolerant.’’ This may have implications for building Ge devices such as 1.55pm infrared photodetectors directly on Si as a simpler alternative to GeSi quantum well detectors (which involve considerably more complexity) because somewhat higher defect densities may be tolerated.

IV. Carrier Transport Properties of Ge,Sil-, The ability to control defect introduction and maintain high-quality interfaces in GeSi/Si heterostructures has allowed the realization of theoretically predicted performance enhancements over conventional Si electronics by virtue of engineering band offset energies, strain energy, and alloy composition. The most important transport property benefiting from these enhancements is the carrier mobility, and the demonstration of record high electron and hole mobilities in GeSi/Si heterostructures is largely attributed to advances in epitaxial growth and defect control in lattice-mismatched systems since the late 1980s and early 1990s (Bean, 1992; Kasper and Schaffler, 1991; Ismail et al., 1995; Fitzgerald, 1995; Kasper et al., 1994; Jain, 1994; Stoneham and Jain, 1995; Fitzgerald et al., 1992; Fitzgerald, 1989). High mobilities have translated into the development of high-speed heterojunction bipolar transistors (HBTs), and n-channel and p-channel GeSi/Si MODFETs. For the usual npn GeSi HBT that utilizes a p-type pseudomorphic GeSi base, increased hole mobilities reduce the RC time constant, which yields higher operation frequency. For MODFETs the speed of operation is determined to a large extent by the speed at which carriers can cross from

6 ELECTRONIC PROPERTIES AND DEEPLEVELS

327

the source to drain through a two-dimensional channel. The obvious importance of carrier mobilities in every electronic device has therefore led to detailed considerations of scattering mechanisms, both fundamental and otherwise, that limit carrier mobilities so that the ultimate performance of GeSi/Si devices can be realized (Chun and Wang, 1992; Monroe et at., 1993; Krishnamurthy and Sher, 1985). Carrier scattering in GeSi crystals can generally occur via interactions with the lattice (acoustic and nonpolar optical phonons), neutral and ionized impurities, alloy fluctuations, and strain distribution. For twdimensional transport, interface roughness is a concern as are threading dislocations when using relaxed GeSi buffer layers in MODFET structures. This section provides an overview of mobility results in both bulk GeSi (relaxed and strained) and two-dimensional carrier gases in Ge-Si and concludes with a brief overview of carrier lifetime and diffusion coefficients due to their importance in the operation of both HBTs and photodiodes.

1.

CARRIER MOBILITIES IN STRAINED AND UNSTRAINED BULKGe,Sil-,

a. Bulk Hole Mobility Bulk GeSi includes relaxed (i.e., unstrained) and strained material where transport is three-dimensional. For relaxed GeSi, the bulk carrier mobility is isotropic, whereas the mobility in strained GeSi has two components, one in the growth plane (the so-called in-plane or transverse mobility), generally labeled pxx = pyyand one perpendicular to the growth plane (i.e., in the growth direction or so-called longitudinal direction), which is denoted as pzz.We first consider the hole mobility, which for strained layers can be expressed in its tensor form according to

The components are shown in the diagram of Fig. 25 (an analogous expression can be written for the electron mobility). For relaxed GeSi when no strain is present, p x x= pyy= pzz= p p . As a starting point, it is useful to review what is known of carrier mobilities in bulk, relaxed GeSi alloys. To provide a reference for GeSi camer mobilities, room-temperature mobility and effective mass values for bulk Si(x = 0) and Ge(x = 1) are listed in Table IV. Complete information on the temperature and doping dependence of mobilities in Si and Ge can be found in other publications (LandoltBornstein, 1982, 1989; Klaassen, 1992a, 1992b). In contrast, very little information on transport properties of bulk, relaxed GeSi currently exists. This is due to two factors: (1) the dominant technological interest in pseudomorphic strained layers, and (2) the fact that bulk GeSi crystal growth with homogeneous Ge content and uniform doping

STEVEN A. RINGELAND PATRICKN.GRILLOT

328

FIG. 2 5 . A schematic illustration of the mobility components in a GeSi layer on Si. The terms

wyl corresponds to the in-plane (transverse) mobility; pLzz corresponds to perpendicular (longitudinal) mobility components. pcxx=

remains a significant challenge. Earlier in this chapter, Fig. 21 showed how the Hall hole mobility varied with temperature for a p-type, relaxed 30%GeSi layer grown at low temperature, which was found to contain a background of conductivity-controlling shallow acceptor defects. In that case, the high-temperature mobility exponent of 1.69 indicated that factors such as alloy scattering or possible defect participation may be important, which was also consistent with the low hole mobility reported for that sample. In a recent systematic study of transport in bulk p-type GeSi single crystals and polycrystalline material grown by the Czochralski method, hole Hall mobilities were measured as a function of Ge content up to 50% (Mchedlidze et al., 1995). The temperature-dependent Hall mobility decreased as a function of increasing Ge content for the range of compositions tested. Fitting of this data led the authors to conclude that alloy scattering influenced the mobility even at room temperature, as the measured dislocation densities (< 105cm-*) in these wafers were too low to influence the mobility. However, they also noted the presence of shallow, acceptor-like levels that controlled the undoped conductivity of these bulk crystals, whose concentration increased with

) hole ( L L ~ drift ) mobilities for intrinsic, bulk Ge and Si at 300 K along with TABLEIV. Electron ( b e and

effective mass data Ile

Ilh

(cm*/V-s)

(cm2/ V-s)

Ge

3900

1800

0.082

1.59

0.284

0.044

$ * 0/m o 0.095

Si

1450

505

0.191

0.916

0.537

0.153

0.234

mt

* /mo

m l * /mo

mhh

* /mo

mih

* /m o

~

The terms mt*,mi*,mhh*, mlh* and m,,* refer to the transverse electron, longitudinal electron, heavy hole, light hole and split off effective masses, respectively, and mg is the free electron rest mass (LandoltBfirnstein, 19821989).

6 ELECTRONIC PROPERTIES AND DEEPLEVELS

329

Ge content and probably appeared as a consequence of cooling the CZ GeSi crystal after growth. The presence of these additional defects is consistent with the discussion of acceptor-like point defect complexes in relaxed, heteroepitaxial GeSi layers grown at low temperatures (discussed earlier in this chapter). It is quite possible then that point defects may have limited the mobility in these samples. The trends observed in this recent study of bulk crystals agree with the very early experimental transport studies that were done on polycrystalline bulk GeSi material where the Hall mobility was not only found to degrade strongly as a function of Ge composition up to a mol fraction of 30% for both n and p-type material, but exhibited a general U-shaped mobility dependence on alloy composition where the mobility increases for Ge concentrations in excess of 80% (Levitas, 1955; von Busch and Vogt, 1960; Braunstein, 1963). However, neither the absolute values for the measured mobilities nor the dependence on alloy composition for these early measurements agree with theoretical calculations that predict an expected increase in hole mobility for GeSi as compared to Si due to the lower effective hole mass and lifting of the heavy and light hole band degeneracy (Takeda et al., 1983; Manku and Nathan, 1991). The disagreement between early experiments and theory has been variously attributed to alloy scattering, grain boundary scattering as well as scattering via other uncontrolled defects present in these relaxed, polycrystalline materials (Schaffler, 1995). The possible role of point defects is supported by a recent report in which the hole mobility was found to increase as growth temperature increases, implying a point defect annealing process may be present (Smith et aZ., 1991). Similar discrepancies between experiment and theory exist for bulk hole mobility in strained GeSi layers, where theoretical work has argued that the large reduction in the hole effective mass due to both increasing Ge content and strain should increase mobility with increasing Ge composition (Chun and Wang, 1992). In fact, based on Monte Car10 calculations it was predicted that the bulk hole mobility within strained GeSi layers should reach the bulk Ge value at a composition of only 40% Ge within the strained alloy (Hinckley and Singh, 1990). However, much like the case for relaxed alloys, significant differences exist when theory is compared with early experiments, indicating that more work needs to be done on high-quality materials having a wide variety of compositions with varying amounts of strain to reconcile these differences. For instance, Manku et al. (1992) first calculated the doping dependent hole drift mobility values over a limited composition range based on a measurement of sheet resistance from the SiGe base of a single HBT. From this single data point, they predicted that a monotonic decrease in the hole drift mobility as a function of Ge content could be expected as the Ge content in the base was increased from 0% to 10% over a wide doping range. However, this result is contradicted by a later, but far more systematic experimental study by the same group using a similar approach to extract hole drift mobility but now using sheet resistance measurements made on a statistically much wide range of HBTs with Ge content ranging from 0% to 30% (Manku et al., 1993). In that work a monotonic increase of the in-plane hole drift mobility for low Ge content lay-

330

STEVEN

A. RINGELAND PATRICK N. GRILLOT

ers as compared with Si was measured, for a doping concentration of 2 x 10'9cm-3, which now agrees with the theoretically predicted trend. In general, the higher hole drift mobility in these strained layers has been attributed mainly to the reduced hole effective mass as a result of strain-induced compression of the valence band, which is now consistent with the earlier models. Moreover, as the compression is anisotropic, the in-plane mobility component was found to be larger than the component in the growth direction, although both directional mobilities are increased with respect to relaxed alloy layers (Chun and Wang, 1992; Manku et al., 1993). An increase in hole drift mobility was also predicted and experimentally observed for relaxed layers, although the enhancement over Si was less than in the strained layer case because there is no strain-induced change in the valence band for the former. These general conclusions can be summarized by Fig. 26, which shows the dependence of the directional mobilities of strained GeSi layers on doping concentration for a range of alloy compositions at room temperature. Also included are the calculated and measured bulk Si and Ge mobility data of Chun and Wang (1992) and references therein, from which the mobility enhancement of the GeSi layers are clear. Similar mobility dependencies were calculated by Manku et a/. (1993) using a different approach to calculate the drift mobility with both approaches leading to the conclusion that at room temperature, alloy scattering does not appear to limit the hole drift mobility in GeSi and phonon scattering is dominant [although alloy scattering can be expected to become important at lower temperatures (Chun and Wang, 1992)l. This however, contradicts other studies where alloy scattering was proposed as the dominant scattering mechanism (Venkataraman et a/., 1993; Li eta/., 1993) as well as the early measurements on polycrystalline bulk material (Levitas, 1995) for which the low mobilities were attributed to alloy disorder (although grain boundary scattering clouds quantitative conclusions from those materials). Some of the early discrepancies may also be related to the different methods used to extract experimental mobility values as most measurements made on bulk crystals were by the Hall technique, whereas most theoretical calculations as well as measurements on HBTs are concerned with the in-plane drift mobility. The differences between Hall and drift mobility have recently been considered by a few groups. McGregor et al. (1993) reported that for heavily doped p-type, strained GeSi, the measured hole Hall mobility decreases with increasing Ge mol fraction up to 20%, whereas the measured drift mobility (derived from sheet resistance measurements) increases over the same compositional range. Thus the Hall scattering factor given by w(Hall)/w(drift) is not a constant for GeSi and decreases strongly with increasing Ge content. For strained layers, the Hall scattering factor was found to reduce from around 0.7-0.8 for GeSi layers with less than 10% Ge down to 0.3-0.4 for Ge contents near 25%. This discrepancy was also reported and analyzed in detail in a more recent work by Carns et a/. (1994), where the same divergent behavior for the drift and Hall mobilities was measured as a function of Ge content over a doping range of 10'8cm-3-1020cm~3. These results were compiled together with the experimental and theoretical mobility work of other

6

Old'

ELECTRONIC PROPERTIES AND DEEP LEVELS

Id' lo" Id' LO'* Doping CQncentratlan (cm-')

Id' Id'

331

Id'

FIG.26. Room temperature hole mobility of strained GeSi grown on (001) Si as a function of carrier concentration for (a) the in-plane component and (b) the perpendicular component. Also shown in (c) are the bulk unstrained hole mobilities for Ge and Si (and references therein). Reprinted with permission from Chun and Wang ( 1992).

groups and it was found that the compiled room temperature, in-plane hole drift mobility could be reasonably well fitted by the usual empirical doping dependence for Si mobility given by (Arora et al., 1982)

where a = 0.90, Pref = 2.35 x 10'7cm-3 (assumed to be the same as bulk Si for this composition range), and p p is the in-plane hole drift mobility. The terms Vfin and /IO depend on Ge mol fraction ( x ) and are expressed as (Carnes et al., 1994)

332

STEVEN A. RINGELA N D PATRICK N . GRILLOT vmin

+

= 44 - 2 0 ~ 8 5 0 ~ ~

po = 400

+ 29x + 4 1 3 7 ~ ~

While the scatter in the actual data is large due in part to the difficulty in obtaining accurate drift mobility measurements, this nevertheless provides a means to estimate the in-plane hole drift mobility behavior in p-type strained GeSi that is confirmed experimentally and follows the theoretically predicted characteristics. However, compared to theoretical values, the experimental drift mobility values are still somewhat low, and this may be due to uncertainty in determining the exact alloy scattering potential as well as the lack of consideration of heavy doping effects in the theoretical calculations. The dependence of the room-temperature hole Hall mobility on doping and Ge mol fraction up to 20% was compiled in a similar fashion. For Hall measurements there is considerably less measurement uncertainty compared to drift mobility measurements and Carns et al. (1994) obtained fits to Eq. (13) with Vmin and po now given by urnin

= 37 - 6 1 ~

go = 440 - 6 3 2 ~

In this case, p p in Eq. (14) is the hole Hall mobility. From the drift and Hall mobility results, the strong decrease in the Hall scattering factor rh as Ge content increases is apparent within the GeSi composition range (0-2.5% Ge) considered. However, the fundamental reason for this decrease in rh is not yet clear but may be a consequence of strain-induced changes in the valence band structure and density of states, which may have different effects on Hall and drift mobilities. More accurate determination of the valence bandstructure and factors affecting the scattering times as a function of both GeSi composition and strain are needed for full understanding of the hole mobility behavior. b.

Bulk Electron Mobility

Compared with the hole mobility, somewhat less work has been done on electron transport in relaxed or strained bulk GeSi due largely to the significant valence band offset and negligible conduction band offset for compressively strained GeSi layers grown on Si that has made p-type GeSi the material of choice for the GeSi HBT structures. The most obvious effect of GeSi composition on the electron mobility for unstrained alloys is due to the crossover from Si-like conduction bandstructure with 6 equivalent minima near the X-point to a Ge-like conduction with eight equivalent L-point minima for alloy compositions above 85% Ge (Braunstein et al., 19.58). For strained layers, however, the alloy may remain Si-like up to 100%Ge (Van de Walle and Martin, 1986). The major effect of the bandstructure crossover, which is qualitatively supported by experimental data, is the lower electron mobility for compositions below 85% Ge compared with alloys of higher Ge compositions due to the sharp increase

6 ELECTRONIC PROPERTIES AND DEEPLEVELS

333

in the electron effective mass as the dominant conduction bandedge becomes Si-like. However, within the Si-like bandstructure range itself, that is, below 85% Ge, the trend is less clear. For compositions ranging from 0% to 30% Ge, Monte Carlo simulations (Hinckley et al., 1989; Pejcinovic et al., 1989; Kay and Wang, 1991) and analytical calculations (Manku and Nathan, 1992) all indicate a gradual decrease in the bulk electron mobility with increasing Ge content relative to Si for relaxed alloys, which results from the increase in alloy scattering. For strained layers a similar decrease in the in-plane electron mobility in strained GeSi layers compared with Si was also found, while the perpendicular mobility was enhanced (Hinckley et al., 1989; Pejcinovic et al., 1989; Kay and Wang, 1991; Manku and Nathan, 1992). One of these studies also considered the dependence of these trends on doping concentration, from which it was found that the perpendicular drift mobility component for the strained layers was slightly higher than the Si mobility only for doping concentrations in excess of 10'7cm-3 (Manku and Nathan, 1992). For lower doping concentration, both components are reduced in comparison to Si and these findings are summarized in Fig. 27. Also shown are results of Monte Carlo simulations indicating a general agreement for these trends. The reduced mobility observed for low doping was attributed to the dominance of alloy scattering,

'si 1500t

,

1 , 0 0 0 1

,@pq -.---

aio 0.15 0.20 Ge FRACTION, x

0.00 0.05

Ge FRACTION, x

FIG. 27. Calculated room temperature electron mobility components as a function of GeSi alloy composition for a donor concentration of (a) 10i5cm-', (b) 10'7cmp3, (c) l O ' * ~ m - and ~ (d) 10'9cm-3. The solid lines are the unstrained bulk electron mobilities, the dot-dashed line are the perpendicular mobilities and the dashed lines are the in-plane mobilities as calculated from (Kay and Wang, 1991). The symbols represent the calculations of the same mobility components by Monte Carlo methods (Kay and Wang, 1991). Reprinted with permission from Manku and Nathan (1992).

334

STEVEN A. RINGEL A N D PATRICK N. GRILLOT

whereas for higher doping impurity scattering limits mobility is relatively independent of alloy composition. While the various models for mobility trends may differ in some basic assumptions regarding details of the scattering mechanisms, there is a general agreement between the various methods.

2.

TWO-DIMENSIONAL CARRIER TRANSPORT IN GeSi/Si HETEROSTRUCTURES

The utilization of modulation doping in which a SiGeISi heterojunction is used to separate the mobile carriers from their parent dopant atoms has resulted in extremely high two-dimensional mobilities within MODFET structures. In MODFET structures, carriers are confined to a narrow channel defined by an appropriate heterojunction pair and both two-dimensional electron gases (2DEG) and hole gases (2DHG) are possible, enabling n-channel and p-channel MODFET devices, respectively, and the potential for complementary, CMOS-like functionality. For 2DEGs, the channel is typically within a strained Si layer with barriers consisting of relaxed GeSi, which places the Si in tension (Abstreiter et al., 1985). For 2DHGs the channel is within a compressively strained GeSi (or Ge) layer with either lower Ge content GeSi or possibly Si barrier layers (Pearsall and Bean, 1986). Note that while strain is needed to develop a large enough conduction band offset to achieve electron confinement in these structures, this is not a necessary condition for hole confinement within the lower bandgap GeSi layer due to the large valence band offset in GeSi/Si heterostructures, although pseudomorphic channels are typically employed to exploit the favorable strain-induced valence band deformation and to minimize the presence of dislocations. In contrast to the HBT case discussed in the previous section where bulk mobilities are critical, MODFETs rely on the transport of charge in a two-dimensional sheet that is confined within a narrow region of the strained layer in close proximity to a heterojunction. Carrier transport occurs parallel to the growth plane within quantized states confined by the band bending within the channel and the heterointerface. Extremely high electron and hole mobilities are made possible by the combination of both quantization effects and the physical separation of the mobile carriers from their parent dopant atoms. Figure 28 shows representative schematics of high mobility 2DEG and 2DHG structures with the 2D carrier gas regions identified. Critical to the success of these structures are (1) extremely low defect density, relaxed buffer layers used to provide the desired lattice constant on which to commence pseudomorphic growth of the MODFET structure, as discussed earlier in this chapter and elsewhere in this volume, and (2) appropriate doping setback or spacer layers to control the distance between the doping spikes and the conducting channel in order to optimize the tradeoff between maximizing carrier transfer to the channel and minimizing ionized impurity scattering. As two-dimensional transport is in the growth plane, a critically important issue is interface roughness, which introduces an additional scattering mechanism for these lateral transport structures.

6 ELECTRONIC PROPERTIES AND DEEPLEVELS

Si substrate

Si substrate

2DEG structure

2DHG structure

335

FIG. 28. Representative schematics of typical 2DEG and 2DHG structures in GeSi/Si (not to scale). The degree of shading represents the Ge mol fraction, except for the strained channels and the delta-doped regions. Note that the 2DHG is at the bottom interface of the Ge channel. From Xie et al. (1993) with permission.

Historically, the initial work on 2DHG structures took advantage of the favorable valence band offset for low (30% or less) Ge content GeSi/Si heterojunctions and consisted of psuedomorphic GeSi channels grown directly on Si, which do not require graded buffer layers to provide additional strain adjustment (Fitzgerald, 1995). These structures relied on both their simplicity and the expected increase in hole mobility due to strain to achieve high-performance devices. However, as the graded, relaxed, GeSi buffer layer technology has matured to the point where very low threading dislocation density layers on Si became a reality, this opened the possibility of utilizing high Ge content alloys and even pure Ge as the transport channel (with the additional advantage of an intrinsically lower hole effective mass and in which even higher mobilities can be expected). Measured mobilities for both types of structures are shown in Fig. 29. For structures utilizing the low Ge content GeSi channel, while gradual improvements in low-temperature mobility are evident in the figure due to improvements in growth methods, room-temperature mobilities are well below those of undoped Si. In contrast, extremely high hole mobilities have been achieved using strained Ge channel structures grown on graded GeSi buffers on Si as seen in Fig. 29. Xie et al. (1993) have reported 2DHG mobilities as high as 55,000 cm2/ V-s at 4.2 K. This improvement was explained as resulting from two important findings. First, temperature-dependent Shubnikov-de-Haas (SdH) measurements revealed a concentration-dependent hole ef~ the strained Ge layer, which is substantially lower fective mass of less than 0 . 1 for

336

STEVEN

A.

R I N G E L AND PATRICK N.

0

Gechannel

0

0 0

V 0

0

0

GRILLOT

0

-

D VV" 0

0 .

GeSi channel 0

v

0

o

after[86] after[87] after1881

V 0 0

0

afteriegj

FIG. 29. Representative measurements of two dimensional Hall hole mobility vs temperature of p-type MODFET structures using strained Ge (Xie et al., 1993; Konig and Schaffler, 1993) or GeSi (Wang et al., 1989; Whall et al., 1993) channels for the 2DHG transport.

than the hole density of states effective mass for Ge of 0.29mo (Xie et al., 1993), consistent with the theoretically expected lighter mass due to valence band deformation under strain. Second was the key observation that the interface between the upper GeSi cap and the strained Ge channel was rough, which is depicted by the TEM image shown in Fig. 30. Undulations having a period on the order of hundreds of angstroms are evi-

FIG. 30. Cross-sectional TEM image of a strained Ge channel grown between Ge0.60Si0.40 barrier layers on (001) Si, where the undulation at the top interface due to compressive strain is apparent. From Fitzgerald (1995) and Xie et al. (1993) with reprint permission from Fitzgerald.

6 ELECTRONIC PROPERTIES AND DEEPLEVELS

331

dent at the upper interface, which were explained to be short enough to cause effective hole scattering and likely limit the mobility of these structures (this is not the same as the well-known cross-hatch undulations which occur at a period on the order of 1pm and hence do not interfere with carrier transport). This realization prompted Xie et al. (1993) to move the 2DHG region to the smoother, bottom interface, and after sufficiently increasing the Ge channel width to increase the separation between the 2DHG and the rough interface (but so thick as to cause strain-relaxation), the highest mobilities were achieved. The highest hole mobilities at room temperature of 1300cm2/ V-s were also achieved using a similar, graded buffer scheme and a strained Ge layer to supply a 2DHG region (Konig and Schaffler, 1993). This value approaches that of bulk, intrinsic Ge and additional improvements can be expected because the saturation of the mobility at lower temperatures implies the presence of additional scattering, such as by interface roughness or other unintentional scattering mechanisms. In contrast to the 2DHGs, the situation for achieving similar 2DEGs within GeSi/Si heterostructures was initially complicated by the lack of a natural conduction band offset between low Ge content (30% Ge or less) GeSi and Si. To achieve a useful conduction band offset for electron confinement required placing a Si layer in biaxial tension to achieve the necessary type I1 band alignment. Relaxed GeSi buffer layers can be used to achieve this condition by providing lattice constant larger than that of Si for subsequent Si growth. This was first reported by Abstreiter et al. (1985) where a thin, strained Si layer was sandwiched between two partially relaxed GeSi layers of uniform composition. This structure suffered from a high density of threading dislocations as a result of the lattice relaxation and the low-temperature 2DEG mobilities in the Si channel were low. It was only after substantial reductions of threading dislocation density were achieved via the advent of well-controlled, compositionally graded GeSi buffers on which fully relaxed, uniform composition GeSi layers could be grown that high mobility 2DEGs within strained Si layers were possible. The impact of improved buffer layers and dislocation reduction on the 2DEG mobility is apparent from Fig. 31. Threading dislocation densities were reduced from above 1 x 10' cm-2 for single step (i.e. uniform composition) GeSi buffer layers grown on Si, to less then 1 x 106 cm-* using compositionally graded buffers (Kasper and Schaffler, 1991; Ismail et al., 1995a; Fitzgerald, 1995; Fitzgerald et al., 1992; Fitzgerald et al., 1991; Tuppen et al., 1991). The reduction in defect density translated into dramatic increases in the low-temperature 2DEG mobility over a few year window of optimization in the early-mid 1990s, starting at 17,000-19,000 cm2/ V-s (Ismail et al., 1991; Schuberth et al., 1991), reaching 96,000-125,000 cm2/ V-s in 1991 (Mii et al., 1991), and eventually reaching the 170,000-180,000 cm2/ V-s range by various groups (Fitzgerald et al,, 1992; Schaffler et al., 1992) with the highest report of 520,000 cm2/ V-s occurring in 1995 (Ismail et al., 1995a, 1995b). The significance of these results is apparent upon comparison with the highest 4.2 K electron mobility ever reported for a Si MOSFET of 41,000 cm2/ V-s (Kukushkin and Timofeev, 1988), which is about an order of magnitude lower than the GeSi/Si 2DEG mobility. The fundamental mechanism for this

-

338

STEVEN A .

RINGELA N D PATRICK N.GRILLOT after (5,9] after (951 after1951 after[96]

~7

0

o o

v vcV P

Q

with graded buffers

V

A

0

J

vF

7

0

9

with single step buffer

01

1

0 2

10

ka

0

100

1000

Temperature (K)

FIG. 3 1. Two-dimensional Hall electron mobility vs temperature of n-type MODFET structures using strained GeSi channels for 2DEG transport. Also shown is a comparison between data from stmctures using a single step buffer (open circles) and graded buffers.

improvement is primarily from the substantial reduction in the electron effective mass and the population of only two electron valleys (as compared with 6 degenerate conduction band valleys for bulk Si) due to strain-induced band ordering, which reduces intervalley scattering, in addition to the reduction in ionized impurity scattering via the use of modulation doping in the GeSijSi heterojunction system. The mobility enhancement is maintained at room temperature, where room temperature mobilities of up to 2600 cm2/ V-s were reported (Nelson et al., 1993), as compared with MOSFET mobilities of about 1000 cm2/ V-s. These results have prompted considerable interest in identifying the mobilitylimiting mechanisms of the high mobility 2DEG GeSi/Si structures. Scattering sources, such as remote dopants, impurities, interface roughness, alloy scattering, strain fluctuations, cross-hatch morphology, misfit, and threading dislocations have all been considered. As mentioned here, the well-known crosshatch pattern present in high-quality, relaxed graded buffers does not impact carrier transport due to the small wavevector of these undulations (- 1 pm) as compared with the Fermi wavevector of 2DEGs, resulting in negligible large angle scattering (Xie et al., 1994). Monroe et al. (1993) have concluded from both theoretical calculations and comparison with experiment that scattering from remote dopants, interface roughness, background impurities and alloy fluctuations are the remaining possible limitations on the 2DEG mobility, and for Si layers in excess of the Matthews-Blakeslee critical thickness, Ismail et al. (1994) have shown that the formation of in-plane misfit dislocations at the lower Si/GeSi interface is an important mobility-limiting factor. It is clear that spacer thickness and channel po-

6 ELECTRONIC PROPERTIES AND D E E P LEVELS

339

sitioning are critical, and theoretical calculations support the possibility of long-range impurity scattering as being the limiting factor for optimally designed structures.

AND DIFFUSION COEFFICIENTS 3 . MINORITYCARRIER LIFETIMES

Compared to carrier mobilities, little information is explicitly available on minority carrier lifetimes in GeSi materials and the first direct measurements have only occurred since 1990 in spite of the use of GeSi within minority carrier devices such as HBTs and photodiodes. Nevertheless, the minority carrier lifetime is of great importance for minority carrier devices that invariably depend on the collection efficiency of minority carriers and are, therefore, extremely sensitive to defects via Shockley-Read-Hall (SRH) recombination. In fact to obtain device-quality Si with even modestly long lifetimes of SO ps, deep level concentrations must be less than 1 part in 10" (Higashi et al., 1990) which highlights the extreme sensitivity of minority carrier lifetime to material quality and SRH recombination. Direct comparisons between GeSi-based HBTs and similarly fabricated Si homojunction bipolar transistors indeed show evidence of increased base recombination effects within the GeSi HBT (King et al., 1988). Based on earlier reports showing significant oxygen incorporation within CVD-grown strained GeSi layers as compared to Si layers [41], King et al. (1989) investigated the dependence of the minority carrier recombination lifetime within GeSi on oxygen content. The measured I-V characteristics of p + n and p + in GeSi test diodes containing various concentrations of oxygen as determined by SIMS were fitted using a device model by including the minority carrier lifetime as an adjustable fitting parameter, from which a strong, inverse correlation between lifetime and oxygen content was observed for a given Ge content. Moreover, the lifetime was found to be only weakly dependent on Ge content for oxygen-containing layers, which indicates the extreme sensitivity of lifetime to oxygen content. These results are summarized in Fig. 32, which also includes lifetime values extracted from simulations of GeSi HBTs for comparison. This data clearly shows the necessity of minimizing the oxygen content within GeSi devices as the minority carrier lifetime is reduced from 10 ns for an oxygen concentration of 10'' cm-3 down to the ps range for oxygen concentrations in excess of lo2' cmp3. Another study of minority carrier lifetime was done in MBE-grown Si/GeSi heterostructures in which the minority carrier lifetimes were directly obtained using a contactless photocarrier lifetime measurement (Higashi et al., 1990) instead of being obtained by parameter-fitting. For this case, the minority carrier electron recombination lifetime was found to degrade from SO-100 ps for a Si layer grown on an optimally cleaned Si substrate, to 100 ns for a fully processed GeSi HBT device. It should be noted, however, that the lifetime values for the MBE-grown Si layer were obtained directly from the contactless probe, whereas the lifetime after HBT processing was calculated from the zero bias current of the emitter-base junction. The degradation

-

-

-

-

340

STEVEN A.

RINGEL AND PATRICK N . GRILLOT

T--------

-

1 0 - ’ 2 L

1Oq8

10’’

1oZ0

lo2’

oxygen concentration ( ~ r n - ~ )

FIG. 32. Minority carrier lifetime as a function of oxygen content in GeSi layers for x = 0.15 - 0.31 indicating a strong (but scattered) dependence on oxygen concentration. The two endpoints were measured from GeSi pin diodes and the other data points were extracted from simulations of HBTs. Reprinted with permission from Ghani et al. (1991).

was attributed to the presence of the GeSi layer or to processing steps used in HBT fabrication, although oxygen impurities may have played a role (as already described herein). Another method of obtaining the minority carrier lifetime is the pulsed MOS capacitor technique where the recovery of the device capacitance after pulsing into deep depletion can be related to the carrier generation lifetime (Schroder and Guldberg, 1971). To accomplish this, Schwartz and Sturm (1989) fabricated an MOS capacitor on Si in which a thin, strained GeSi layer was sandwiched between Si layers, beneath Si02. Following Shockley-Read-Hall (SRH) theory, as outlined earlier in this chapter, the rate of carrier generation (G) from within a depletion region via a single, midgap trap level can be simply approximated as

where tg is the generation lifetime. Under these approximations tg = 2t0 where to = ( ~ N uth)-l T is the low-level injection minority carrier lifetime. Hence, the characteristic response time of the capacitance transient after pulsing into deep depletion as well as the total recovery time can be related to the carrier lifetime. However, because in this structure the GeSi is within the Si depletion region, the smaller bandgap and larger intrinsic carrier concentration of the GeSi layer must be accounted for in the Zerbst analysis, which effectively derives the generation lifetime from the relation

6

ELECTRONIC PROPERTIES AND DEEPLEVELS

341

between the generation rate and the generation volume (i.e. the recovery time). Hence by properly accounting for the generation volume within the GeSi layer, a generation lifetime of 1 p s was obtained for a strained, 18% Ge layer. This was similar to comparably processed all-Si MOS capacitors, which led to the conclusion that for these CVD-grown samples, the GeSi and Si layers have comparable trap densities and properties, thereby implying the favorable application of GeSi materials for minority carrier applications. Note that the relation between generation lifetime and actual minority carrier recombination lifetime depends upon the deep level characteristics (trap energy, cross section and density), which can be obtained via DLTS-type measurements. In the simplest case of midgap trap, however, the recombination lifetime would be half of the generation lifetime as just described. In addition to carrier lifetimes, the diffusion coefficient is also an important transport parameter for minority carrier devices. The predicted increase in the perpendicular mobility component over that of bulk Si as described in the previous section suggests a higher diffusion coefficient can be expected for strained GeSi HBTs as compared with Si bipolar transistors. Patton ef al. (1988) however, found that the diffusivity of electrons through the p-type GeSi base is instead reduced by 2630% for strained 12% Ge layers based on analysis of the HBT I-V characteristics. This reduction was supported by the work of King et al. (1989) who, by measuring the effect of changing the base width on the collector current of HBTs, were able to extract the diffusion coefficient. They obtained an electron diffusivity (D,)of 4.4 cm2/s, 6.2 cm2/s, and 7.1 cm2/s, for 31% Ge, 21% Ge and 0% Ge (i.e. pure Si) GeSi layers, respectively. This surprising decrease was attributed either to a large concentration of oxygen within the Ge-containing layers or to alloy scattering. Later however, Grivickas et al. (1991) measured the ambipolar transport properties of strained, p-type GeSi layers for 0% to 50% Ge using an optical transient grating method which measures only in-plane transport. The ambipolar diffusion coefficient in this case was found to increase systematically with increasing Ge content as compared with bulk Si, as shown in Fig. 33. For 50% Ge alloys, the diffusion coefficient is increased by approximately 50%, consistent with the theoretically predicted enhancement of the in-plane mobility.

V.

Conclusions

In this chapter, the electronic properties of relaxed and strained GeSi materials and heterostructures were reviewed with an emphasis on the properties and sources of deep levels within GeSi materials and their impact on electronic transport properties. The presence of deep levels and their association with dislocations were described in some detail for both n and p-type, relaxed GeSi materials grown by a variety of methods. Using DLTS, traps associated with the dislocation core were identified, as were deep levels, which result from other extended defects, such as point defect clusters introduced either by dislocation interactions during relaxation or by extrinsic impurities that are

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, I

6 1

0

I

0.1

0.2

I

0.3

I

0.4

I

0.5

0.6

Ge mole fraction ( x )

FIG.3 3 , Ambipolar diffusion coefficient as a function of Ge mol fraction for MBE-grown GeSi samples with moderate doping concentrations. The vertical bars represent the range values including measurement error. Reprinted with permission from Grivickas, et al. (1991).

associated with the dislocation core. Many of these deep levels were detected in GeSi materials prepared by a wide range of methods and in GeSi layers of various compositions. There appears to be a general consistency throughout the full range of GeSi alloy compositions for both electron and hole traps that correlates with deformation-induced states in plastically deformed bulk Si and Ge. The most dominant deep levels for highquality (threading dislocation densities < lo6 cm-2), relaxed material appear to be a series of shallow acceptor-like states present for relaxed GeSi layers grown at temperatures below 700 "C, which cause significant dopant compensation and even type conversion for lightly doped materials. These levels are not due to the dislocation core but instead result from point defect complexes associated with the dislocation core, which indicates that defects other than threading dislocations must also be considered in the pursuit of optimum relaxed material quality. However, for high Ge content alloys such that the energy bandstructure is Ge-like, the constraint on maximum threading dislocation density is significantly reduced by the small Ge bandgap and it was shown that reverse bias diode currents of relaxed Ge p-n junction diodes grown on graded GeSi/Si substrates were dictated by intrinsic generation for layers having threading dislocation densities as high as 8 x lo6 cm-'. This indicates the potential of relaxed Ge layers on Si as an active device material in its own right for applications such as I .55 wrn photodetectors. Carrier transport properties in strained and unstrained bulk GeSi, as well as twodimensional GeSi/Si heterostructures were also reviewed. For bulk transport in relaxed material, the hole mobility is generally observed to decrease initially with respect to

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bulk Si as Ge content increases due to alloy scattering andor the contribution of defects, but then increases at high Ge compositions due to the significant reduction hole effective mass. For bulk strained layers, the hole mobility increases with Ge content; however, the enhancement is more pronounced for the in-plane directional component than the perpendicular component due to the anisotropic compression of the strained layer. Various groups have attributed the limiting scattering mechanisms for hole transport in the strained bulk layers to either phonon scattering at room temperature or alloy scattering. It was also noted that there are differences between the hole Hall vs drift mobility behavior with alloy composition, with the Hall scattering factor decreasing dramatically with increasing Ge content. For the bulk electron mobility, the in-plane mobility is reduced with respect to bulk Si, whereas the perpendicular component is increased with increasing Ge content for layers having a doping concentration in excess of l O I 7 ~ m - At ~ .lower doping concentrations, alloy scattering immediately limits electron mobility. For twdimensional carrier gases, extremely high 2DEG electron and 2DHG hole mobilities have been achieved by appropriate engineering of the relaxed buffer layers and band offsets. For holes, the highest mobilities reported were 55,000 cm2/ V-s at 4 K (Wang et al., 1989) and for electrons, the highest reported value is 520,000 cm2/ Vs at 0.4 K (Ismail et al., 1995b). The high hole mobility is due primarily to the very small 2DHG hole mass, whereas the high electron mobility results from the reduced intervalley scattering and reduced ionized impurity scattering. Both achievements are only possible due to the low defect density relaxed barrier layers necessary to provide the appropriate band lineups. Finally, although little information is available, carrier lifetimes and diffusivities in GeSi were briefly reviewed.

ACKNOWLEDGMENTS The authors gratefully acknowledge E.A. Fitzgerald (MIT) and Y.H. Xie (Lucent Technologies) for many stimulating discussions and their valuable input. This work was supported by NSF grant DMR9458406 and ARO grant DAAG55-91-0111. REFERENCES Abstreiter, G., Brugger, H., Wolf, T., Jorke, H., and Herzog, H.J. (1985). Phys. Rev. Lett., 54,2441. Alexander, H. (1989). In Point and Extended Defects in Semiconductors, G. Benedek, A. Cavallini, and W. Schroter, eds., 5 1, New York Plenum Press. Arora, N.D., Hauser, J.R., and Roulston, D.J. (1982). IEEE Trans. Electron. Dev., 29, 292. Baumann, F.H. and Schroter, W. (1983). Philos. Mag., B 48, 55. Bean, J.C. (1992). Proc. IEEE, 80,571. Braunstein, E. (1963). Phys. Rev., 130, 869. Braunstein, R., Moore, A.R., and Herman, F. (1958). Phys. Rev., 109,695. Bremond, G., Soufi, A,, Benyattou, T., and Dutarte, D. (1992). Thin Sol. Films, 222,60.

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Brighten, J.C., Hawkins, E.D., Peaker, A.R., Kubiak, R.A., Parker, E.H.C., and Whall, T.E. (1994). J. Appl. Phys., 76,4237. Broniatowski, A. (1983). J. Phys., 44, C4-339. Caldas, M.J., Fazzia, A., and Zunger, A. (1984). Appl. Phys. Lett., 45,671. Carns, T.K., Chun, S.K., Tanner, M.O., Wang, K.L., Kamins, T.I., Turner, J.E., Lie, D.Y.C., Nicolet, M.A., and Wilson, R.G. (1994). IEEE Trans. Electron. Dev., 41, 1273. Chun, S.K. and Wang, K.L. (1992). IEEE Trans. Electron Dev., 39,2153. Fitzgerald, E.A. (1989). J. Metals, 41,20. Fitzgerald, E.A. (1995). Ann. Rev. Muter. Sci., 25,417. Fitzgerald, E.A., Xie, Y.H., Green, M.L., Brasen, D., and Kortan, A.R. (1991). Proc. Mate,: Res. Soc. Symp., 220,211. Fitzgerald, E.A., Xie, Y.H., Monroe, D., Silverman, P.J., Kue, J.M., Kortan, A.R., Thiel, F.A., andweir, B.E. (1992). J. Vuc. Sci. Technol., B10, 1807. Ghani, T., Hoyt, J.L., Noble, D.B., Gibbons, J.F., Turner, E., and Kamins, T.I. (1991).Appl. Phys. Lett., 58, 1317. Grillot, P.N. (1996). Ph.D. dissertation, The Ohio State University. Grillot, P.N. and Ringel, S.A. (1996). Appl. Phys. Lett., 69,2110. Grillot, P.N., Ringel, S.A., Fitzgerald, E.A., Watson, G.P., Fitzgerald, E.A., and Xie, Y.H. (1995b). J. Appl. Phys., 77,3248. Grillot, P.N., Ringel, S.A., and Fitzgerald, E.A. (1996~).J. Electron. Muter., 25, 1028. Grillot, P.N., Ringel, S.A., Michel, J., and Fitzgerald, E.A. (1996b). J. Appl. Phys., 80,2823. Grillot, P.N., Ringel, S.A., Watson, G.P., Fitzgerald, E.A., and Xie, Y.H. (1994). Proc. Muter. Res. Soc. Symp., 325, 159. Grillot, P.N., Ringel, S.A., Watson, G.P., Fitzgerald, E.A., and Xie, Y.H. (1995a). J. Appl. Phys., 77, 676. Grivickas, V., Netiksis, V., Noreika, D., Petrauskas, M., Willander, M., Ni, W.X., Hasan, M.A., Hansson, G.V., and Sundgren, J.E. (1991). J. Appl. Phys., 70, 1471. Higashi, G.S., Bean, J.C., Buescher, C., Yadvish, R., and Temkin, H. (1990). Appl. Phys. Lett., 56,2560. Hinckley, J.M., Sankaran, V., and Singh, J. (1989). Appl. Phys. Lett., 55,2008. Hinckley, J.M. and Singh, J. (1990). Phys. Rev. B 41, 2912. Ismail, K., Arafa, M., Saenger, K.L., Chu, J.O., and Meyerson, B.S. (1995a). Appl. Phys. Lett., 66, 1077. Ismail, K., Arafa, M., Stern, F., Chu, J.O., and Meyerson, B.S. (1995b). Appl. Phys. Lett., 66, 842. Ismail, K., LeGoues, F.K., Saenger, K.L., Arafa, M., Chu, J.O., Mooney, P.M., and Meyerson, B.S. (1994). Phys. Rev. Lett., 73,3447. Ismail, K., Meyerson, B.S., and Wang, P.J. (1991). Appl. Phys. Lett, 58, 21 17. Jain, SC. (1994). Germainium-Silicon Strained Layer Heterustmctures, Supplement 24 in Advances in Electmnics and Electron Physics. Boston: Academic Press. Kasper, E., Kibbel, H., Herzog, H.J., and Gruhle, A. (1994). Jpn. J. Appl. Phys. 33, 1365. Kasper, E. and Schaffler, F. (1991). In Semiconductors and Semimetals, 33,T.P. Pearsall, ed. Boston: Academic Press, 223. Kay, L.E. and Wang, T.W. (1991). J. Appl. Phys., 70, 1483. Kimerling, L.C. and Patel, J.R. (1979). Appl. Phjs. Lett., 34,73. Kimerling, L.C. and Patel, J.R. (1985). In VLSI Electronics 12, N.G. Einspruch, ed., 223 New York: Academic Press. Kimerling, L.C., Patel, J.R.. Benton, J.L., and Freeland, P.E. (1981). Insr. Phys. Con$ Ser., 59,401. King, C.A., Hoyt, J.L., and Gibbons, J.F. (1989). IEEE Trans. Electron Dev.,36,2093. King, C.A., Hoyt, J.L., Gronet, C.M., Gibbons, J.P., Scott, M.P., andTurner, J. (1988). IEEEElecrron Dev. Lett., 10, 52. Kisielowski-Kemmerich, C., Weber, G., and Alexander, H. (1985). J. Electron. MateE, 14, 387. Klaassen, D.B.M. ( 1 992a). Sol. St. Electron., 35,953. Klaassen, D.B.M. (1992b). Sol. St. Electron., 35, 961.

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Optoelectronics in Silicon and Germanium Silicon Joe C. Campbell UNIVERSITY

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I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. PHOTODETECTORS ....................................... 1. Avalanche and p-i-n Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Resonant-Cavity Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Metal-Semiconductor-Metal Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Integrated Optical Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. LIGHTEMITTERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Porous Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Erbium-doped Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Si~-,Ge, Quantum Wells and (Si),(Ge), Strained Layer Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. GUIDED-WAVE DEVICES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Integrated and Active Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I.

347 348 348 352 356 362 363 363 367 369 371 37 1 375 380 380

Introduction

Photonics technology relies on optoelectronic devices to generate, modulate, switch, and detect optical signals. To date, essentially all optoelectronic devices and circuits have been fabricated from 111-V compounds while Si has been the dominant material for electronic circuits. The goal of combining Si-integrated circuit technology and optoelectronics has been a tantalizing and, to a great extent, elusive objective for decades. However, the current course of technological evolution is making this quest more urgent and, simultaneously, providing the technological tools for its realization. Silicon has not been widely used for optoelectronic applications for the following reasons: (1) Si has an indirect band structure, which severely restricts its application Copyneht . . . . 0 1999 by Academic Press All nghts of reproduction m any form reserved. ISBN 0-12-7521M-X 0080-8784/99 $30 00

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for emitters such as lasers and LEDs; ( 2 ) Si does not exhibit an electro-optic effect; and ( 3 ) the bandgap of Si is too large for photodetection in the wavelength range ( k 2 1.0 pm) for long-haul fiber optic transmission systems. Recent advances in the synthesis of Ge, Sil-, epitaxial layers (both single layers and superlattice structures) on Si substrates have opened the possibility of fabricating long-wavelength photodetectors, active waveguide devices such as modulators and switches, and light-emitting devices. The addition of Ge to Si reduces the bandgap and thus extends the sensitivity range for photodetectors to approximately 1.6 pm. Furthermore, this reduction of the bandgap energy can be enhanced by incorporating strain. Most of the early work on waveguide modulators, switches, and active filters employed the electro-optic effect to change the phase of the propagating wave. However, for many applications, especially those where speed is not a driving factor, other effects such as the themo-optic effect and plasma dispersion can be used to realize Si-based modulators and switches. The most promising approaches for practical light emitters appear to be nanostructures and impurity incorporation, for example, Er doping. Numerous nanostructures, including Sil-, Ge, quantum wells and superlattices and porous Si/Sil -,Ge,, have demonstrated room-temperature electroluminescence.

11. Photodetectors

In the area of Si/Sil -,Ge, optoelectronics, photodetectors are the most advanced and widely deployed devices. Several types of Si and Si/Si1-,GeX photodetectors, including p-i-ns, metal-semiconductor-metal (MSM) photodiodes, and avalanche photodiodes have been reported. Due to their low dark current, favorable ionization coefficients, and compatibility with Si integrated circuit technology, Si photodiodes are the most widely used photodetectors for applications in the wavelength range h 5 1 pm. On the other hand, the bandgap of Si renders it transparent at the wavelengths where optical fibers exhibit minima in material dispersion and attenuation, namely, 1.3 pin and 1.55 Fm. To address this deficiency, photodiodes with Sil-,Ge, absorbing layers have been developed. 1.

AVALANCHE AND P-I-N PHOTODIODES

A p-i-n photodiode consists of a single p-n junction designed to respond, without gain, to photon absorption. It has become the most ubiquitous photodetector because of its ease of fabrication and excellent operating characteristics. Avalanche photodiodes are, in many respects, similar to p-i-ns, except that they are operated near breakdown where gain, or multiplication, is achieved by impact ionization. With regard to responsivity, in an ideal photodiode, each incident photon would result in the charge of one electron flowing in the external circuit. In practice, there are several physical

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effects, such as incomplete absorption, recombination, reflection from the semiconductor surface, and contact shadowing that tend to reduce responsivity. In the absence of recombination and to the extent that band-to-band absorption dominates, the external quantum efficiency is given by qe = (1 - R) x (1 - e-OLd),where CY is the absorption coefficient, d is the length of the absorbing region, and R is the reflectivity at the detector surface. Owing to their relatively high index of refraction, semiconductors reflect approximately 30% of the incident light. However, antireflection (AR) coatings consisting of single or multiple dielectrics such as SiN, Al2O3, Pb2O3, ZnS, or MgFz can routinely reduce this optical power loss to less than 5%. As a result, the quantum efficiency of most p-i-n photodiodes is determined by a and d. For a photodiode in which diffusion has been minimized, the bandwidth is determined by the RC time constant and the time it takes for the carriers to traverse the depletion region, referred to as the transit time. By proper scaling of the detector area, it is possible to optimize the tradeoff between the RC and transit-time limits. In essence, this is accomplished by reducing the depletiodabsorption layer thickness to achieve the requisite transit time; the device diameter is then constrained by the condition that the RC time constant should not exceed the transit time. A reduction of the transit time through the use of very thin absorption layers, however, usually results in a significant penalty in quantum efficiency because a large fraction of the light is transmitted without being absorbed. Unfortunately, the absorption coefficients of indirect bandgap semiconductors such as Si and Ge are much smaller (-lox) than those of direct bandgap 111-Vcompounds. As a result, in order to achieve high quantum efficiency, Si-based materials require long absorption thicknesses. This leads to long transit times and low bandwidths. The most successful approach to improving the speed has been to develop structures that increase the optical path while maintaining a narrow depletion width and, consequently, a short transit time. Two such structures that decouple the transittime component of the bandwidth from the responsivity are the waveguide photodiode and the resonant-cavity structure. Figure 1 shows generic, schematic cross sections of these two structures. a.

Waveguide Photodiodes

In the waveguide photodiode light is incident from the edge and propagates parallel to the heterojunction interfaces. The photogenerated carriers, on the other hand, travel perpendicularly to the optical signal across a thin depletion region. In order to optimize the performance there are several design considerations that must be addressed. If the input coupling loss is to be maintained at an acceptable level, the waveguide must be designed with a large enough optical mode to facilitate coupling from a lens or optical fiber. The length of the device is selected to be long enough to absorb essentially all of the input signal, which is determined, to a great extent, by the optical confinement factor, but no longer than necessary so as to keep the capacitance low.

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FIG. I. Schematic cross sections of (a) waveguide and (b) resonant-cavity photodiodes

The waveguide-type structure that has achieved the best overall performance to date is the Ge,Sil-,/Si rib waveguide avalanche photodiode (Pearsall et al., 1986; Temkin et al., 1986). A schematic cross section of this device is shown in Fig. 2. The wafers from which these devices were fabricated were grown by molecular beam epitaxy. The structure is that of a Ge,Sil-,/Si strained-layer superlattice (SLS) absorbing region beneath a Si avalanche photodiode. The SLS absorbing region, which also served as the waveguide core, consisted of 20 pairs of Geo.&0.4(30 A) and Si(290 A). The bandgap of strained Geo.6Sio.4 layers would permit absorption to wavelengths as long as 1.7 p m but, to date, all of the work on these devices has been carried out at 1.3 pm. Light was coupled from the edge into the SLS region where it was absorbed as it propagated along the waveguide. The photogenerated electrons were injected into the p-type Si layer above the SLS where gain was achieved by impact ionization. This approach has the potential for low-noise gain and high gain-bandwidth products because of the favorable ratio of ionization coefficients in Si. The responsivity of these photodiodes is the product of the input coupling efficiency, typically < 25%, the internal quantum efficiency, and the avalanche gain. In the absence of significant scattering or other

7

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GERMANIUM SILICON

351

METALLIZATION

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,ABSORPTION REGION

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FIG.2. (a) Schematic cross section of SilPxGex/Si strained-layer-superlattice photodetector. (b) Lightcoupling geometry for single-mode optical fiber input. Reprinted with permission from Temkin er al.( 1986).

distributed losses, the internal quantum efficiency is given by (1 - e-rrL)where e is the effective absorption coefficient and L is the device length. It was found that a was in the range 50-100 cm-', which gave internal efficiencies in the range 20% to 70% for lengths of 100 pm and 500 pm, respectively. The maximum gains observed before the onset of microplasmas were in the range 12-17. As the depletion layer thickness in this type of structure can be much thinner than that of conventional normal-incidence photodiodes, higher bandwidths would be projected. The highest speed achieved to date was 8 GHz at M = 6. A transmission experiment utilizing these APDs achieved a receiver sensitivity of P = - 26.4 dBm at 800 Mbitsh over 45 km of single-mode optical fiber. A normal-incidence version of this photodiode, which had a Geo,sSio,s SLS, was reported by Huang et al. (1995). The measured quantum efficiency was 17% at 0.85 p m and 1% at 1.3 Fm. The lower efficiency of the normal-incidence structure is due to the shorter optical length.

352

JOEC. CAMPBELL

2 . RESONANT-CAVITY PHOTODIODES The resonant-cavity structure (Fig. lb) increases the absorption through multiple reflections between two parallel mirrors in a Fabry-Perot cavity whose length is usually less than one wavelength (Chin and Chang, 1991; Unlu et aZ., 1990). The lower mirror is typically an integrated Bragg reflector consisting of alternating k / 4 “high” and “low” refractive index layers. It is common for these Bragg reflectors to have a reflectivity > 99%. The top mirror is usually a high-reflectivity dielectric stack that can be deposited after fabrication and initial characterization. In 111-V compound semiconductor systems, the mature materials technologies combined with clever designs and the availability of a wide variety of lattice constants and refractive indices has enabled the fabrication of high-reflectivity (> 95%), wide bandwidth (-50 nm) epitaxial mirrors. However, for Si-based materials, it has been much more difficult to fabricate high-quality mirrors. One approach, reported by Kuchibhotla et aZ.(1993), used alternating layers of GeSi (high index layer) and Si (low index layer). A difficulty with this approach is that the lattice mismatch between Ge and Si imposes severe constraints on how thick the layers can be grown. In fact, if the GeSi layer is grown to h / 4 thickness, the layer relaxes and the resulting high density of dislocations results in very poor reflectivity. An asymmetric mirror (Murtaza et al., 1994) has been developed to overcome this problem. In this mirror every other reflection is perfectly in phase with the first one from the semiconductodair interface, but the intermediate reflections are slightly out of phase depending upon the deviation from the quarter-wavelength thickness. Such mirror structures have a lower peak re-

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8)

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OPTOELECTRONICS IN S I L I C O N AND

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flectivity as well as a smaller bandwidth than a conventional quarter-wave stack with the same number of periods. Nevertheless, mirrors with reflectivity in excess of 90% have been achieved. Figure 3 shows the simulated and experimental reflectivity of a GeSi/Si mirror designed to operate at 800 nm. When these mirrors are used for visible and near-infrared, the reflectivities are reduced somewhat due to absorption. On the other hand, this absorption in the mirror can be more than compensated by the larger refractive index step available at the shorter wavelengths. A mirror similar to that shown in Fig. 3, except peaked at -600 nm, was incorporated into a resonant-cavity photodiode (Murtaza et al., 1996). The lower Bragg reflector had 40 Geo.3Sio.7(225 A)/Si(570 A) periods. The absorbing region was a 1.03 pm, intrinsic Si layer. On top of this was a 0.2 pm, p-doped (1 x lo1*cmP3) Si layer followed by a 200 A, 5 x lo'* cm-3 p-type Si contact layer. The peak quantum efficiency was found to be 67% at 608 nm. In order to achieve the same quantum efficiency with a conventional Si p-i-n structure, approximately 6 p m absorption region thickness would be needed. This would, in turn, reduce significantly the bandwidth. The point corresponding to the measured efficiency and the designed normalized absorption coefficient (ad 0.8) is shown in Fig. 4. The frequency response of a GeSi/Si photodiode that had a resonance of 780 nm and an n-doped mirror is shown in Fig. 5. The bandwidth was approximately 15 GHz, a significant improvement (-lox) compared to commercially available Si p-i-n photodiodes. The resonant-cavity photodiodes with GeSi/Si mirrors demonstrated the performance advantages that can be achieved with the resonant-cavity approach. This has led to the

I""

Normalized Absorption Coefficient (ad) FIG.4. Calculated quantum efficiency vs the normalized absorption coefficient a d for resonant cavity photodetectors with different top (R1) and bottom (Rz) mirror reflectivities. The data point was obtained for a Sil-,Ge,/Si resonant-cavity photodiode where cud was estimated to be 0.8, R1 0.35, and R2 * 0.9. Reprinted with permission from Murtaza ef al.( 1996).

-

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resonant-cavity photodiode. Reprinted with permission

development of a photodiode that is more compatible with standard Si IC processing. The structure, shown in Fig. 6, consists of an interdigitated, polysilicon p-i-n that is grown by MBE on top of the Sit302 layer. Conventional polysilicon deposition techniques yield photodiodes that exhibit high dark current (typically > 1 pA at 1 V) and low quantum efficiencies (Diaz et al., 1996). Bean et al. (1997) have developed a new MBE procedure for growth directlyon Si02 that yields superior device-quality polysilicon films. The p-i-n photodiodes fabricated from this polysilicon have exhibited a 1OOx decrease in dark current and an improvement in peak external quantum efficiency to 50%. Figure 7 shows the dark current vs bias voltage. At bias voltages of - 10 and -25 V, the dark current was 60 nA and 500 nA. It may be that even lower dark current and higher quantum efficiencies will be achieved by post-growth defectpassivation techniques such as hydrogenation. The bandwidth of a 12 p m x 18 p m Si/SiO2 photodiode with a 0.5-pm thick absorbing layer was determined by analyzing the photocurrent spectrum produced by excitation with a mode-locked Timpphire laser that was tuned to the peak of the responsivity. A bandwidth of approximately 10 GHz was observed (Fig. 8). To date, these structures have been demonstrated €or an absorbing layer of polysilicon. However, as the “substrate” is amorphous Si02, it should

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be straightforward to incorporate Ge into the p-i-n in order to extend its operation to longer wavelengths. Ishikawa et al. (1996) have developed a novel technique for fabricating Si/SiO2 Bragg reflectors by multiple separation-by-implanted oxygen (SIMOX). This approach has the advantage that the Si layers, including the top layer of the mirror, are single crystalline. The finished mirror is "epitaxy-ready" for additional crystal growth or device fabrication on top of the mirror. The SiO2 layers were created beneath the Si surface by low-energy oxygen ion implantation. After each implant, the wafer was annealed to form the Si02 layer. This was followed by growth of an additional Si layer by MBE, which was subsequently implanted. This process was repeated until four or five Si/SiOz pairs were formed. The highest reflectivity reported was 92% with a stopband > 3000 cm-l.

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356 3.

JOE C . CAMPBELL

METAL-SEMICONDUCTOR-METAL PHOTOPIODES

The metal-semiconductor-metal (MSM) photodiode (Sugeta et al., 1980) has developed into one of the most promising photodetectors for arrays and optoelectronic integrated circuits (OEICs). Structurally, it is a planar device with two interdigitated electrodes on a semiconductor surface (Fig. 9). These electrodes are deposited so as to form back-to-back Schottky diodes. Light is usually incident from the top and absorption occurs between the electrodes. The positive attributes of MSMs are nui.lerous. The principle advantage, which derives from the simplicity of the planar contact configuration, is its compatibility with transistor circuitry. In addition, MSM photodiodes are relatively easy to fabricate, they do not add significantly to the complexity of circuit, and, typically, they exhibit very low capacitance per unit area. The low capacitance is important because: (1) it permits relatively large-area devices, which facilitates coupling to optical fibers; and (2) its contribution to the total front-end capacitance of an optical receiver is negligible. The bandwidth can be very high for sufficiently narrow electrode spacing, if there is no photoconductive gain. The two fundamental limiting factors in the performance of MSMs are dark current and quantum efficiency. It has frequently been difficult to obtain low dark current in an MSM because the lateral current flow can be significantly influenced by the semiconductor surface. For Si MSMs this is not a concern because excellent passivation techniques and a mature Schottky technology are available. For SiGe structures, on the other hand, passivation and Schottky contacts may require further development. In recent years there have been several studies of Schottky contacts on P-type Sil-,Ge, layers. One of the more thorough investigations, conducted by Nur et at. (1996), included measurements of the electrical properties of Pd, Pt, Ir, and Fe contacts for Ge concentrations in the range 0 5 x 5 0.24. It was found that the Schottky barrier height for each metal decreased with increasing Ge fraction. The energy vs concentration, x , slope was the same for all metals and the change in barrier height with x directly correlated to the valence band discontinuity at the Si/Sil -,Ge, heterojunction. Recently, very similar results have been reported for A1 on Sil-,Ge, (Jiang et aE., 1996). The

I

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FIG.9. Schematic diagram of a generic MSM photodiode.

I/

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OPTOELECTRONICS IN SILICONA N D GERMANIUM SILICON

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degradation in the quantum efficiency of MSMs that is caused by electrode shadowing can not be completely eliminated. There are, however, fabrication techniques such as the formation of submicron electrodes that can reduce the effect of contact shadowing. The indirect bandgap of Si poses an additional challenge in that it gives rise to low absorption coefficients and, consequently, long absorption lengths. For example, at wavelengths of 800 nm, 830 nm, and 850 nm the absorption lengths are 9 pm, 13 pm, and 15 pm, respectively. Numerous techniques have been adopted to deal with this problem. The most straightforward solution is to operate at short wavelengths (-400 nm) where the absorption length is only 100 nm. In this wavelength regime, the transit-time component of the bandwidth is determined by the spacing between the fingers instead of the absorption depth. Liu et al. have reported bandwidths as high as 110 GHz with “short-wavelength” Si MSMs that had finger separation and width of 200 nm. The quantum efficiency of these MSM photodiodes was approximately 12% (Liu et al., 1993). The operation of Si MSMs can be extended to wavelengths in the near infrared by using SO1 substrates (Canham, 1993; Richter et al., 1991). The motivation is to prevent carriers generated out of the shallow depletion region from slowly diffusing to the junction where they contribute to the optical signal but they also greatly reduce the bandwidth. In effect, this approach trades off responsivity for speed. Wang et al.(1994) reported Si MSMs with finger width and spacing down to 200 nm that were fabricated on silicon-on-sapphire substrates. They observed that the pulse response was relatively independent of wavelength but that the quantum efficiency decreased from approximately 20% at A = 400 nm to < 1% for h x 900 nm. Liu et nl. (1994) fabricated similar photodiodes on SIMOX substrates; the top Si layer was thinned to 100 nm. These photodiodes achieved a record bandwidth of 140 GHz at 780 nm but, again, the efficiency was low (-2%). Another approach that has proved successful in increasing the speed of Si MSM photodiodes has been to decrease the carrier lifetime through ion implantation. Sharma et al. (1994) reported that both the quantum efficiency and the bandwidth of Ni-Si-Ni MSMs could be significantly enhanced by using ion implantation of 19F+ to create a damaged, highly absorbing region approximately 1 p m below the Si surface. The quantum efficiency at 860 nm and 1060 nm was 64% and 23%, respectively. It was not clear whether photoconductive gain played a role in the responsivity. Compared to unimplanted devices, the pulse response decreased by approximately a factor of 6 to 100 ps (FWHM). Dutta et al. (1997) have used a similar approach and have obtained bandwidths as high as 6 GHz, compared to 300 MHz for similar unimplanted photodiodes, albeit with approximately 3 to 5 times lower quantum efficiencies (-10%) than the unimplanted devices. Textured surfaces provide a novel and effective method to increase the optical path length for absorption while maintaining short carrier transit distances. The basic idea is to use scattering to “trap” light inside the semiconductor. Yablonovitch and Cody (1982) first used this technique to enhance the conversion efficiency of solar cells. More recently, Lee and Van Zeghbroeck (1995) applied texturing to photodiodes designed to

358

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c. CAMPBELL

be incorporated into optical receivers. A schematic cross section and a photomicrograph of this device is shown in Fig. 10. The membrane was formed by etching the wafer from the back to thicknesses in the range 3-7 pm. Texturing was accomplished in an Ar/CF4 plasma. It was determined from transmission experiments at 830 nm that the effective reflectivity of the black-textured surface was 86%. For comparison, untextured and ideally textured surfaces should have reflectivities of 30% and 98%, respectively. The internal and external quantum efficiencies were 61% and 25%, respectively. Prior to formation of the textured membranes the bandwidth was limited to -300 MHz by the light penetration depth. After forming the thin membrane, the bandwidth was > 3 GHz. Levine et al. (1995) have used texturing in conjunction with an SO1 substrate to fabricate a CMOS-compatible Si MSM. The SO1 prevented carrier diffusion from deep within the substrate and a textured surface provided light trapping that enhanced the efficiency by a factor of 3.6 to 27% compared to an untextured surface. A structure that uses a vertical array of “membranes” or ridges has been developed by Ho and Wong (1996a, 1996b). They have employed reactive ion etching to form Si ridges with electrodes inside the interdigitated trenches. A cross-sectional view and an SEM micrograph are shown in Fig. 11. An SO1 substrate was used to eliminate carriers generated below the ridges. Light is absorbed in the ridges; the electrodes on the sides ensure that the field is relatively uniform throughout the absorbing regions and that the transit distance is short enough to allow high speed, even for those carriers generated several microns below the surface. The responsivity was 0.12 A/W at 800 nm, cor-

FIG. 10. (a) Cross-sectional diagram of a textured Si MSM photodiode. (b) SEM photomicrograph of the textured back surface. Reprinted with permission from Lee and Van Zeghbroeck (1995).

7

OPTOELECTRONICS IN SILICON AND

SW2W nm TiWiAu

Si Rdgc

si

GERMANIUM SILICON

359

Si Trench

r--pq

2.75 urn 1.25 urn

6

FIG. 11. (a) Cross section of an SO1 MSM formed with Si trenches. (h) Edge-view SEM photomicrograph of the photodiode. The trenches are 6 ,urn deep, 2.75 brn wide, and spaced 2.75 wm apart. Reprinted with permission from Ho and Wang (1996b).

responding to an internal quantum efficiency of -90% and an external efficiency of -20%. An instrument-limited bandwidth of 2.3 GHz was reported. a.

Infrared Photodetectors

For long-wavelength infrared (LWIR) applications, Si and SiGe photodiodes have been widely accepted. Technologies that have been developed include PtSi/Si (Ho and Wang, 1996b) and IrSi/Si Schottky-barrier photodiodes (Pellegrini et al., 1982), SiGe/Si heterojunction internal photoemission (HIP) photodetectors (Lin and Maserjian, 1990; Lin et al., 1991; Tsaur et al., 1991; Park et al., 1994; Jimenez et al., 1995), SiGe/Si quantum well infrared photodetectors (QWIPs) (People et al., 1992; Park et al., 1992; Karunasiri et al., 1992; Robbins et al., 1995; Carline et al., 1996; Kruck et al., 1996), and doping-spike PtSi/Si detectors (Lin et al., 1993; Lin et al., 1995). The best overall device characteristics, including detectivity, have been obtained from narrow-bandgap semiconductors such as InSb and HgCdTe. However, it has been difficult to fabricate large, uniform two-dimensional arrays from these materials. For array applications (1024 x 1024 elements), silicide Schottky-barrier devices such as IrSi and

360

JOE C. CAMPBELL

PtSi have been implemented. Unfortunately, however, these photodiodes have a longwavelength cutoff of -5 prn. Strained Sil-,Ge, has been used to extend the response of this type of photodiode to the 8-10 E;c.rnwavelength range. b. SiGe/Si Heterojunction Internal Photoemission Photodetectors The operation of the SiGe/Si heterojunction internal photoemission (HIP) photodiodes is illustrated and contrasted to the PtSi/Si Schottky barrier in Fig. 12. It can be seen that the response of the PtSi/Si photodiode is determined, to a great extent, by the height of the hole barrier. Lin et al. (1993; 1995) have used p-type doping spikes to lower the effective barrier height, through the image-force effect and the electric field due to ionized dopants in the depletion region, to extend the cutoff to -7.3 Wni. The concept of using a HIP structure in place of the PtSi/Si Schottky barrier was first proposed by Shepherd et al. (1969). The first Sil -,Ge,/Si HIP was reported by Lin and Maserjian (1990). The structure consisted of P+-Sil-,Ge, layers grown by MBE on p-type Si substrates. The operating principle involves absorption in the degeneratedly doped Sil _,Ge, layer, primarily by free carrier absorption, and subsequent internal photoemission of photoexcited holes over the Sil -,Ge,/Si heterojunction barrier into the Si substrate. The effective barrier height is determined by the Sil-,Ge,/Si valence band discontinuity A E , and the Fermi level in the Sil-,Ge, layer. By tailoring the Ge concentration to modify A E, and the doping to alter the position of the Fermi level, the barrier height, and thus the cutoff wavelength, can be tailored over a wide range of infrared wavelengths. Lin and Maserjian (1990) achieved cutoff wavelengths between 2 ,um and 10 p m for Ge concentrations in the range 0.2-0.4, respectively, and for a p doping level of -lo2' crnp3. The efficiency decreased from -3% to 1 % with increasing wavelength in initiaI devices. In subsequent work, optimization of the thickness and doping of the Sil -,Ge, layers yielded efficiencies of 3-596 in the wavelength range 810 Wm (Lin et al., 1991). Tsaur et aL(1991) extended this technology by fabricating I

PtSi

FIG. 12. Energy level diagrams of (a) a PtSi/Si Schottky barrier and (h) a P+: SiGeRSi heterojunction internal photoemission photodetector.

7

OPTOELECTRONICS I N S I L I C O N AND

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400 x 400 focal plane arrays of Si0,5&e0.~/SiHIP photodiodes with a cutoff wavelength of 9.3 p m and monolithic CCD readout circuitry. These arrays exhibited a high degree of pixel-to-pixel uniformity (< 1% rms variation) and the overall performance at 50 K was reported to be superior to that of IrSi arrays. The external quantum efficiency of HIP photodetectors is determined by the amount of absorption in the Sil-,Ge, layers and the efficiency with which the photogenerated holes surmount the heterojunction barrier. There is a tradeoff involving the thickness of the Sil-,Ge, layers. Thin layers yield improved barrier transport because scattering is less detrimental but there is also less absorption in thin layers. Park et al. (1994) proposed to use stacks of thin ( 5 5 0 A) Sio.7Geo.3 layers to enhance the absorption without degrading the transport efficiency. Strong response in the wavelength range 2-20 p m was achieved; the quantum efficiencies were 4% and 1.5% at 10 p m and 15 pm, respectively. Using a PtSi/SiGe/Si HIP, Jimenez et al. (1995) have demonstrated a tunable response. The relative heights of the two barriers, the PtSi/SiGe Schottky barrier and the SiGe/Si heterojunction barrier, are very sensitive to the applied voltage. It was found that the effective barrier height could be varied from 0.3 eV at zero bias to 0.12 eV at 2.4 V bias for a 450-A thick Sio.gGeo.2 layer. The tunability is achieved at the price of reduced quantum efficiency at the shorter wavelengths because the carriers must traverse the Sio.gGe0.2 layer prior to being collected. Nevertheless, the tunability may permit spectral analysis of infrared images by altering the bias condition. c.

SiGe/Si Quantum Well Infrared Photodetectors

An alternative approach to HIP photodiodes is the quantum well infrared photodetector (QWIP) (People et al., 1992; Park et al., 1992; Karunasiri et al., 1992; Robbins et al., 1995; Carline et al., 1996; Kruck et al., 1996). GaAs/AlGaAs QWIPs have exhibited detectivities comparable to those of HgCdTe (Levine, 1993). These devices rely on intersubband absorption in conduction band quantum wells. Figure 13 illustrates the bandstructure and the detection process for QWIPs. Unfortunately, for these devices, a quantum mechanical selection rule prohibits intersub-band absorption for light polarized perpendicular to the growth direction (i.e., normal incidence). This complicates input coupling and restricts available device architectures. Extending the QWIP approach to Sil-,Ge,/Si quantum wells would have the advantage that the detector arrays match thermally with Si readout electronics and can be flip-chip bonded to Si multiplexer circuits. Furthermore, for p-type Sil-,Ge,/Si QWIPs normal incidence absorption is strong because strong mixing of heavy and light hole states enables hole intersub-band transitions. To date, however, the performance of Sil -,Ge,/Si QWIPs has been limited by relatively low responsivities and high dark currents. Kruck et al.( 1996) have reported a normal-incidence QWIP that operates in the wavelength range 3-8 p m with a peak responsivity of 76 mAlW and a detectivity as high as D* = 2 x 10" cm(Hz W)'I2. As this material system becomes more mature

362

JOE C. CAMPBELL

CONDUCTION BAND (n-DOPED)

I

I

Eg (WELL)

I Eg

(BARRIER)

I VALENCE BAND (p-DOPED)

FIG.13. Quantum well bandstructure. This diagram illustrates both electron (for N-type) and hole (for P-type) interband absorption. Reprinted with permission from Levine (1993).

and new processing techniques evolve, it is anticipated that the Sil -,Ge,/Si prove to be a practical imaging device.

4.

QWIP will

INTEGRATED OPTICAL RECEIVERS

Optical receivers for long-haul transmission systems that require high speed and high sensitivity have primarily been implemented in the 111-V material systems. However, there are many high-volume applications that require low-cost, high-reliability components with proven manufacturability. Integration of an optical receiver on Si using the well-established Si transistor fabrication technology for use with 870-nm laser transmitters can fulfill these requirements. There have been several reports of Si-MOS receiver circuits with hybrid photodiode interconnection techniques such as wire-bonding or epitaxial-liftoff demonstrating that optimized Si-MOS preamplifiers can provide the required performance for short-distance optical data links (Fraser et al., 1983; Abidi, 1984; Steyaert et al., 1994; Lee et al., 1996). Ultimately, it will be advantageous in terms of cost and performance to integrate optoelectronic devices and electrical circuits. Lim et al. (1993) and Kuchta et al. (1994) have reported an integrated optical receiver with a CMOS preamplifier and a vertical Si p-i-n photodetector fabricated using a Bi-CMOS manufacturing process. That receiver had an optical sensitivity at bit error rate (BER) of - 14.8 dBm at 531 Mb/s with 850 nm optical input. The photodiode structure in that work used an N- absorption layer that was much thinner than the optical absorption depth at the operating wavelength. The authors cited the advantage that the device can be depleted with a low bias voltage while maintaining hig-speed performance. However, another result of the thin

7

OPTOELECTRONICS IN SILICON AND

f

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GERMANIUM SILICON

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FIG. 14. Bit error rate (BER) vs average received optical power, qP,at 155 Mbit/s and 300 Mbit/s for Si NMOS integrated receiver. The inset shows an eye diagram at 250 MBids. Reprinted with permission from Qi et al.( 1997).

absorption layer is that the photodiode had a low responsivity of 0.7 A/w. A recent integrated receiver implemented in a silicon bipolar process using epitaxial layers to integrate a p-i-n photodiode, while demonstrating high bandwidth, also demonstrated low photodiode efficiencies (Wieland et al., 1994). Qi et al. (1997) have achieved an overall improvement in performance using a novel approach to integrate a Si-NMOS preamplifier with a planar p-i-n Si photodiode structure that ameliorates the design tradeoff between the efficiency and bandwidth of the photodiode while causing far less disruption to a standard silicon MOS fabrication process. The p-i-n photodiode was a planar interdigitated structure that exhibited a dark current of 0.1 nA at 5 V and quantum efficiencies of 84% and 74% at 800 nm and 870 nm, respectively. Both depletionand enhancement-mode MOSFETs were used in the preamplifier; the effective channel length of the MOSFETs was 0.6 pm. A transimpedance of 6.5 kR and a bandwidth of 130 MHz was obtained from the preamplifier circuit. Figure 14 shows the BER vs were -33 dBm average received optical power. The sensitivities for a BER of and -25.5 dBm at bit rates of 155 MBit/s and 300 MBit/s, respectively.

111. Light Emitters

1. POROUS SILICON Owing primarily to the dominance of Si in integrated circuit technology, there has long been a desire for a practical Si-based light emitter to provide an interface between microelectronics and optoelectronics. Consequently, light emission from Si, Sil-,Ge,,

364

JOE C. CAMPBELL

and SiGeC has been the subject of intensive research for several years. Many of these topics have been reviewed by Canham (1993). It is clear from this that light emission from Si-related materials is actually quite common. Unfortunately, the efficiency of essentially all of these mechanisms is still relatively low. There are, however, a few exceptions including hydrogenated amorphous Si, siloxene, and porous Si. In this section, we will describe some of the more promising approaches for practical electroluminescent devices in Si-based materials. The technology that has achieved the highest performance as an LED is porous Si, a form of Si that is formed by anodization in an HF solution. It has nanometer-sized columnar crystallites separated by pores of similar dimensions. Photoluminescence efficiencies, for red light emission, in excess of 10% have been widely reported. There have been numerous reviews that detail the fabrication procedures and the luminescence characteristics of porous Si. In addition there are numerous papers that address the physical effects responsible for the luminescence, namely, whether quantum confinement is the dominant physical effect and the role of surface states. These topics are beyond the scope of this chapter, which will concentrate on recent progress in electroluminescent devices. While very high photoluminescence (PL) efficiencies have been achieved with porous Si, the extension to practical electroluminescent (EL) devices has not been straightforward. The most serious difficulty has been that the EL efficiencies are at least 100 times lower than the best PL results. In addition, initially, the EL was unstable, degraded in periods of minutes to days, and was very sensitive to environmental conditions. Passivation techniques have been developed that have solved these latter problems but the issue of low EL efficiency remains. The first porous Si EL devices were relatively simple structures consisting of a top electrode, such as Au, Al, ITO, or conducting polymers, placed directly on top of the porous Si layer and a bottom electrode on the Si substrate (Richter er al., 1991; Koshida and Koyama, 1992; Maruska et a/., 1992; Koshida et al., 1993). These devices exhibited very high series resistance, had lifetimes of only a few minutes, achieved quantum efficiencies -lop6 and had high threshold voltages ( 2 10 V) and current densities (< 10 mA/cm2). Threshold is defined as the bias condition at which EL is detectable. Furthermore, light emission was frequently observed for both forward and reverse bias. There are several reasons for the low efficiencies of these structures. The first is related to charge transport. The porous Si structure is a honeycomb of crystalline nanostructures. The top electrical contact connects directly to only a small fraction of these crystalline clusters that are at the top of the film. There is a strong impediment to transporting through the film to the lower regions as evidenced by the low carrier mobility (c m 2 N s). Another factor is that the low thermal conductivity of porous Si leads to severe heat dissipation problems. A significant increase in emission efficiency was achieved with a p-n structure developed by Steiner et al. (1993) and Lang et al. (1993). This device utilized the fact that the structural and luminescence characteristics of porous Si are strongly influenced by

7

OPTOELECTRONICS I N S I L I C O N AND

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resoporous p+ layer 1 5pm ranoporous nsilicon l o r n macroporous

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voltage (V) FIG. 15. Schematic cross section (inset) and current-voltage characteristic of porous Si light-emitting diode. Reprinted with permission from Steiner et aL(1993).

the carrier type and the carrier density. The device had a "double-heter0structure"-type configuration in which the n-type nanoporous emitting region was sandwiched between a pf mesoporous cap layer and a macroporous n-type substrate. Figure 15 shows the current-voltage characteristic and a schematic cross section of the structure. In order to achieve the three different types of porous Si regions, an n+ substrate was initially implanted with boron and annealed. This produced a 1.5-pm thick p+ layer at the top with a thin, compensated n-type layer near the p-n junction on top of the underlying n+ substrate. When anodized the pf region became mesoporous with crystalline regions having dimensions on the order of 50 to 100 nm. This region did not contribute to the luminescence but it did provide: ( 1 ) an improved interface for the top electrode; (2) lower resistance; ( 3 ) better heat dissipation; and (4) displacement of the porous Si region beneath the surface, which has both mechanical and environmental advantages. The nanoporous light emitting region was formed in the n-type layer underneath the pf layer. Under forward bias, electrons and holes are injected into this layer from the adjacent regions. This approach has resulted in quantum yields as high as Unfortunately, these devices exhibited rapid degradation. The potential of this type of structure for high luminescence efficiencies, however, was demonstrated under pulsed conditions by Linnros and Laic (1995). Using a structure with an optimized p+ layer and an improved ohmic contact they achieved peak efficiencies of -0.2% with 20-V pulses of 200 ps duration and with a period of 4 s between pulses. Loni et al. (1995) reported cw efficiencies of 0.1% with a structure consisting of an IT0 contact deposited directly on the porous Si layer. This device demonstrated record low threshold current density (10 A/cm2) and voltage (2.3 V). Degradation remained a problem, however, in that these results were achieved with the devices under vacuum.

366

JOE C. CAMPBELL

When exposed to air, the efficiency dropped by more than a factor of 100 in a few minutes. Recently, stability has been greatly improved with a passivated p-n emitter developed by Fauchet et al. (1996; Tsybeskov et al., 1996). This device was fabricated as follows: First a p+ layer was diffused into a p-type Si substrate. The wafer was then anodized to form a porous Si layer approximately 0.5 p m thick. The porous Si emitting region was successfully passivated by annealing at 800-900 "C in an inert atmosphere (N2) or in oxygen, The anneal effectively replaced the hydrogen that covers the surface after anodization with a low-defect Si02 interface. After anodization, an n-type poly-Si film was deposited on the wafer and A1 contacts were formed. The threshold of these devices was 2-3 mA/cm2 at 1.5 V and the quantum efficiency was estimated to be approximately 0.1 %. The passivation resulted in stable operation over a time period of weeks (at the time of publication) and a faster pulse response. Devices with a rise time of less than 100 ns and a fall time of -2 p s were demonstrated. As an illustration of the performance of these passivated LEDs, Fig. 16 shows a 7-segment display in room light. The number 2 is clearly visible (Collins et al., 1997). These LEDs have also been integrated with a Si bipolar drive circuit (Hirschman et al., 1996). Figure 17(a) shows a schematic cross section of the LEDhipolar transistor combination, an equivalent circuit, and a photomicrograph of the fabricated structure. The circular LED region has a diameter of 400 p m . The emitter (E), base (B), and collector (C) terminals

FIG. 16. An array of porous Si displays, each composed of seven elements. The height of each display is 4 mm. Reprinted with permission from Collins et al.( 1997).

7

OPTOELECTRONICS IN S I L I C O N AND

GERMANIUM SILICON

367

FIG. 17. (a) Micrograph and schematic of an integrated porous Si LED and bipolar transistor structure. The 400 pm-diameter LED is in the center of the structure. (b) Luminescence of an LEDhipolar transistor. Reprinted with permission from Hirschmann et al.( 1996).

surround the LED. The photograph in Fig. 17(b) demonstrates the luminescence of the LEDhipolar transistor. The emission is relatively uniform over the active LED surface. While porous Si EL devices are not yet in position for widespread deployment in circuits and systems, significant progress toward practical devices has been achieved and there is basis for optimism. Useful efficiencies have been demonstrated, passivation techniques have been developed, and response times have been reduced. Future research will undoubtedly focus on further improving performance in these areas.

2. ERBIUM-DOPED SI Another area that has demonstrated potential for practical EL devices is rare-earthdoped Si and Sil-,Ge,. The rare-earth element that has emerged as the clear favorite is erbium (Er). This is due in part to its relatively narrow emission near 1.5 pm, an important wavelength for communications applications. The Er atoms are incorporated into Si in a 3+ charge state. In this state a transition from the excited 4 1 1 3 p state to the 4115p level results in emission at 1.54 pm. Ennen et al. (1983; 1985) first reported the incorporation of Er in Si and its associated PL and EL. At 77 K they observed sharply structured PL spectra from ion-implanted structures and EL from forward-biased erbium-doped Si junctions that were grown by MBE. Much of the subsequent work on Er-doped Si has focused on PL of the recombination lifetime, thermal quenching, and power saturation. In general, it has been found that co-doping with oxygen improves the luminescence characteristics because it increases the solubility of Er (Coffa et al., 1993), inhibits Er segregation (Coffa et al., 1993; Custer er al., 1994), increases the luminescence efficiency (Michel et al., 199 1 ;Favennec et al., I990), and

368

JOE C. CAMPBELL

reduces thermal quenching (Yablonovitch and Cody, 1982). For example, the PL from samples without oxygen typically decreases by three orders of magnitude as the temperature is raised to room temperature. In the oxygen-doped samples, on the other hand, the decrease is only about a factor of 10 to 50 (Coffa et a/., 1994). While there is a consensus on the physical mechanism responsible for PL, namely, bound exciton recombination with transfer of energy to the Er atom, there are still several competing models to explain the thermal quenching (Coffa et al., 1994; Priolo et al., 1995; Anderson, 1996). Recently, it has been demonstrated that it may be possible to avoid thermal quenching with EL structures. The first room-temperature electroluminescence from an Erdoped Si light emitting diode was an oxide passivated mesa structure with an emission region formed by coimplantation of Er and 0 (Zheng eta/., 1994). Under forward bias these devices exhibited the same thermal quenching as PL (-5Ox lower at room temperature than at 100 K). Subsequently, it was shown by Franzo et al. (1997) that much higher intensities (> 20) could be achieved by operating the devices under reverse bias. The reason for the higher output is that in forward bias, excitation occurs by electronhole recombination at an Er-related level in the Si bandgap. DLTS measurements show that only a fraction (- 1/10) of the Er atoms participate in this type of recombination, thus severely restricting the number of luminescent sites. Furthermore, nonradiative processes such as auger de-excitation reduce the carrier lifetime in forward bias. In reverse bias the Er atoms are excited by hot carrier impact. All of the atoms in the depletion region are excitable and Auger-type processes are inhibited. Stimmer et a/. (1996) have observed similar differences between forward and reverse bias operations in Er-0-doped diodes grown by MBE. Figure 18 shows the luminescence intensity for T (K) 300 250

:

200

150

y

Forward Elas 9 5 A i m 2 0

3

4

5

6

7

Reverse Bias, 8 5 A/cm2 8

9

1

0

1

1

1 O O O R ( 1/K)

FIG. 18. Electroluminescence intensity vs temperature for an Er-doped Si light emitting diode. The forward bias curve (square data points) is multiplied by a factor of 30. Reprinted with permission from Stimmer et aZ.( 1996).

7

OPTOELECTRONICS IN SILICON AND GERMANIUM SILICON

369

forward and reverse bias vs temperature. Under forward bias the intensity was 30x lower than under reverse bias at low temperature and exhibited strong thermal quenching. However, at reverse bias, essentially no thermal quenching was observed between 4 and 300 K. The estimated external quantum efficiency of these devices was >

3.

S I I - ~ G E ,QUANTUM WELLS AND (SI),(GE), SUPERLATTICES

STRAINED LAYER

In recent years Sil -xGex quantum wells and (Si),(Ge), strained-layer superlattices

(SLS) have attracted a great deal of attention. The original motivation for studying (Si), (Ge), SLS was to create a quasi-direct bandstructure by using the periodicity of the superlattice to fold the Brillouin zone (Gnutzmann and Clausecker, 1974; Pearsall et al., 1987). If the period of the superlattice is approximately 10 monolayers, the 2fold degenerate A minima that are perpendicular to the epitaxial layer planes, which are at 0.85 in the r-X direction of the Brillouin zone in Si, are folded back to the r position. Compared to the indirect bandgap transition in bulk Si, the quasi-direct transition between the folded A states and the valence band is projected to have an enhanced oscillator strength. In the initial stages of this work, defect-related emission that was linked to the very high densities of dislocations masked bandgap luminescence from the (Si),(Ge), SLS (Zachai et al., 1990). By using Sil-,Ge, buffer layers with graded Ge concentrations and utilizing a monolayer of Sb to suppress segregation of the Ge atoms during growth by MBE, well-defined bandgap PL (Menczigar et al., 1993) and EL (Engvall et al., 1993) were achieved. The PL of wafers grown in this way have demonstrated several intriguing characteristics. Figure 19 shows low-temperature PL spectra for a (Si)6(Ge)4 SLS wafer at different annealing temperatures. The as-grown spectrum exhibited two strong emission peaks; the strongest signal was identified as a no-phonon, interband transition and the other was a phonon replica (labeled LEN‘ and LET’, respectively, in the figure). The total luminescence intensity was much greater than that of an “equivalent” Sio.sGe0.4random alloy. As the (Si)6(Ge)4 SLS wafer was annealed to higher and higher temperatures to create more intermixing of the Si and Ge layers, the as-grown (Si)6(Ge)4 SLS spectra evolved into that of the Sio.6Geo.4 alloy. Unfortunately, similar to the luminescence from Er-doped Si, there is significant drop in intensity with increasing temperature. While these results clearly show that the (Si),(Ge), SLS can achieve enhanced luminescence at low temperature relative to a Sil-,Ge, alloy, the oscillator strength is still two to three orders of magnitude lower than that of direct-bandgap 111-V compounds such as GaAs. Further, there is still uncertainty whether the enhancement is caused by zone folding or symmetry breaking due to the presence of the Si-Ge interfaces. Turton and Jaros (1990) have proposed that the rapid change of the microscopic potential at the interface breaks the bulk nodal structure of the wave function. This, in turn, alters the selection rule and thus creates an allowed transition across the bandgap.

JOE C . CAMPBELL

370

3,Ge,

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a

0

C

c:

Y

2 0.75

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0.85

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Energy (eV) FIG. 19. Photoluminescence spectra ( 5 K) for a (Si)h(Ge)4 strained-layer-superlattice. Spectrum (a) was obtained on the as-grown sample and spectra (h), (c), (d), (e), and (f) correspond to one hour anneals at 550 OC, 600 O C , 650 O C , 700 OC, and 750 OC, respectively. Spectrum ( 9 ) shows the emission after a complete anneal. Reprinted with permission from Menczigar et uI.( 1993).

Strong PL and EL have also been observed from pseudomorphic and Sil_,Ge, quantum wells. There was some ambiguity in the interpretation of initial SiGe quantum wells because the emission energies were below the projected bandgaps and, in some instances, the emission peaks were close to those identified with dislocations. Recent advances in crystal growth techniques have led to significantly improved luminescence characteristics. Sturm ef al. (1993) have observed well-resolved bandedge luminescence in strained Sil-,Ge, quantum wells grown on Si(100) by rapid thermal chemical vapor deposition. A schematic cross section of this structure is shown in Fig. 20(a). The luminescence was identified as due to shallow-impurity bound excitons at low temperatures and to free excitons or electron-hole plasmas at higher temperatures. Electroluminescence was achieved above room temperature but for high temperatures ( 5 200 K), the luminescence intensity decreased exponentially with an activation energy close to that of the valence band offset. Figure 20(b) shows the EL spectrum at 300 K. At room temperature, the estimated internal quantum efficiency was approximately 2 x 1Ow4. Another type of Si 1-,Ge, heterojunction has achieved room-temperature photolumiquantum wells nescence (Gail et al., 1995). These structures consist of Ge,Si,Ge,

7

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OPTOELECTRONICS IN S I L I C O N A N D ~

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embedded in Sil-,Ge, alloy. For m = 4 and n = 20 the drop in the luminescence intensity from 77 K to room temperature was only about 20%. While there are still questions regarding the physical mechanisms that are responsible for the luminescence (Turton and Jaros, 1996) and electroluminescence has yet to be demonstrated, temperature stability is encouraging.

IV. Guided-Wave Devices Both active and passive Si-based guided-wave devices, including Sil-,Ge, structures, have been reported. Soref (1993) and Schuppert et al. (1996) provide good reviews of work in this area. The passive structures usually contain straight sections branches. These of waveguides with some combination of bends, couplers, andor '3"' "building blocks" have been used to fabricate directional couplers, star couplers, grating feedback elements, multimode interference couplers, Mach-Zehnder interferometers, optical power dividers, and spatial multiplexers.

1. WAVEGUIDES The insertion loss for guided-wave structures is determined primarily by four factors: (1) proper preparation of the end facets; (2) Fresnel losses at the input and output facets; (3) attenuation in the waveguide; and (4) the mode mismatch between the waveguide and that of the VO components, for example, optical fibers, End preparation is more difficult for Si-based waveguides than for their 111-V compound counterparts because

i

~

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Si does not reproducibly cleave with smooth, vertical facets. Consequently, the ends are typically polished, a time-consuming process that might be difficult to adapt to mass production. Nevertheless, optical quality facets can be obtained. Antireflection coatings with net reflectivity of less than 5% are routinely deposited by evaporation. From a materials perspective, the passive waveguides can be grouped into three broad categories: lightly doped Si on heavily doped Si (Soref and Lorenzo, 1985; 1986; Splett and Pettermann, 1994), Sil-,Ge, on Si (Soref et al., 1990; Schmidtchen et al., 1994; Splett et al., 1990; Namavar and Soref, 1991b; Pesarchik et al., 1992; Schmidtchen et al., 1992; Meyer et at., 1991), and Si on insulator (Soref et al., 1991; Schmidtchen et al., 1991; Zinke et al., 1993; Rickman et al., 1994; Evans et al., 1991; Emmons et al., 1992; Namavar and Soref, 1991a; Trinh et al., 1995; Rickman and Reed, 1994; Fisher et al., 1996). Structurally, the two principal waveguide types are: the rib waveguide and the diffused Sil-,Ge, buried channel. Schematic representations of these structures are shown in Fig. 21. The use of lightly doped Si on heavily doped Si relies on the fact that the free carrier contribution to the refractive index is negative. For n-type doping, which is most common for this type of waveguide, the change in the refractive index achieved by heavy doping is given by the expression

Si

N+:Si

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7

OPTOELECTRONICS IN SILICON AND GERMANIUM SILICON

373

where q is the charge on the electron, n is the refractive index of pure Si, EO is the permittivity of free space, and N is the electron carrier concentration. These waveguides are easy to fabricate and they are very compatible with conventional Si processing techniques but the optical attenuation tends to be quite high (- a few dB/cm) due to free carrier absorption of the evanescent field in the cladding region. Splett and Petermann (1994) showed that this loss mechanism could be reduced by using thick (-20 pm) N - layers. Waveguide losses in the range 1.2 to 1.5 dB/cm for both TE- and TMpolarization at wavelengths of 1.3 p m and 1.55 p m were reported. The addition of Ge to Si increases the refractive index, thus making epitaxial layers of Sil -,Gex attractive candidates for Si-based waveguide devices. Assuming a linear relationship between the refractive indices of Si and Ge (3.5 and 4.3, respectively, at 1 = 1.3 pm), the refractive indices for small Ge concentrations is given by the relation nS,Ge 3.5 0 . 8 ~(Soref et al., 1990; Schmidtchen et al., 1994). It has also been determined empirically (Soref and Lorenzo, 1986), that for strained layers, IZSiGe X 3.5 0 . 3 ~ 0 . 3 2 ~ From ~ . these relations it is clear that Sil-,Ge, waveguiding layers can be formed with only a few percent of Ge. The upper limit on x is probably determined by the fact that the bandgap decreases with increasing Ge content and the bandgap energy of the waveguiding layer needs to be greater than the photon energy of the optical signal. Sil-,Ge, rib waveguide structures have been fabricated from epitaxial layers grown by MBE and by CVD. The lowest loss reported to date, for this type of waveguide, was 0.6 dB/cm (Pesarcik et al., 1992). The core region, a 6.5-pm thick Sio.9xxGeo.olz layer, was clad on both sides with Si, below by the Si substrate and above by a 3 wm Si epitaxial layer. The mode size was approximately 8 p m in height with a width of 14 pm. As this profile is well matched to that of a single-mode fiber, low insertions losses would be expected. A diffusion technique, similar to that employed for Ti:LiNbOs, has been developed. This approach has the advantage of utilizing conventional processing on commercial Si substrates without the added cost and complication of epitaxial growth. In this case, Ge is diffused from a Sil-,Ge, source that has been evaporated onto the surface and patterned into the desired channel configuration. Typical diffusion conditions are 65 h at 1200 "C. As this fabrication technique has been developed, the losses have continued to decrease; the champion values are currently in the range 0.3 dB/cm at 1.3 p m and 1.55 p m for TE- and TM-polarizations. The diffusion process creates a refractive index profile that is relatively well-matched to a single-mode optical fiber. Using the approximation of Gaussian mode profiles an overlap-integral calculation predicted coupling losses of approximately 1 dB per facet. Another approach for Si-based optical waveguides that has been very successful is silicon-on-insulator (SOI) (Fig. 21c). One of the first structures of this type was silicon

+

+

+

374

JOE C. CAMPBELL

on sapphire (Namavar and Soref, 1991a). More recently, SO1 prepared by zone melting recrystallization (ZMR), separation by implantation of oxygen (SIMOX), or bond and etchback (BE) wafers have been used. Optical confinement in the vertical direction is achieved because of the large refractive index differences between silicon and air (on the top) and the Si02 layer (on the bottom). Figure 22 shows reported losses for different SO1 materials (Zinke et al., 1993). As a result of the fact that they tend to have lower defect densities, SIMOX and BESOI appear to be better suited than ZMR for this application. The rib height and the roughness of its edges also significantly affect the waveguide losses. By developing processing procedures that yield very smooth rib edges, losses < 0.2 dB/cm have been reported for reactive ion etching (Trinh et al., 1995; Rickman and Reed, 1994) and isotropic chemical etching (Fischer el al., 1996). In order to attain low insertion losses, it is advantageous to maintain single-mode operation. Fischer et al. (1996) have determined that the conditions for single-mode profiles in the horizontal and vertical directions are

r

= -t > 0.5 h -

and

r

W

- 0.01 and especially PL measurements on coupled quantum wells (Brunner et al., 1996c), indicate a constant or slightly increasing valence band offset in SVSiGeC. This is confirmed in X-ray photoemission spectroscopy (Powel et al., 1994; Kim and Osten, 1997). On the other hand, there are a number of reliable experiments like intersubband absorption (Boucaud et al., 1996; Warren et al., 1997), admittance spectroscopy (Stein et al., 1997) and capacitance-voltage measurements on p-type MOS structures (Rim et al., 1995), and pf Sil-,-,Ge,C, / p- Si unipolar diodes (Chang et al., 1997), which clearly indicate a significant decrease of the valence band offset in Si/Sil-,-,Ge,rC, heterostructures. Chang et al. (1997) have reported a value for the valence band offset reduction between 20-26 meV per percent carbon. This means that the bandgap shift in Sil-,-,Ge,C, alloys due to carbon incorporation would be almost completely in the valence band. Figures 16 and 17 summarize and compare the effects of substitutional carbon on the bandgap and band alignment in Si/Sil-,C, and Si/Sil-,-,Ge,C, heterostructures. Figure 16 shows the calculated bandedge energies in strained Sil-,Cy, (a) and (Si0,7Ge0,3)1-~C, (b) on Si( 100) using a deformation potential approach (Brunner et al., 1997). In Fig. 16a the energy shifts caused by lateral strain of 6 = 0 . 3 5 ~in Sil-,C, on Si are taken into account. The intrinsic influence of C is neglected. The tensile strain splits and shifts the electronic levels as already discussed in the previous section. The A(2) states are strongly decreasing and the lh states are slightly increasing in energy. They form the bandedges and the observed PL in Fig. 12 is attributed

.

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0

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LATTICE CONSTANT a (A) FIG. 17. Bandgap in strained and unstrained Sii-yCj,, Sil-,Ge, and Sil-,-yGe,Cy. The PL results from strained SiI-,C, layers are shown by a dashed line. The bandgap for unstrained Sij-,CY is indicated by the solid line. The thin full line and the thin dashed line show the bandgap for unstrained and pseudomorphic Sil-,-rGe,Cy layers, respectively.

to spatially direct type I transitions within the Sil-,C, quantum well. The bandgap reduction deduced from PL is attributed mainly to strain effects. For (Sio.7Geo.3)1 -yCl, the strain-mediated influence of carbon on the bandedges is different from pseudomorphic Si1-&,. Compensation of strain reduces the level splitting and opens the bandgap by about A E = y x 3.8 eV when neglecting the intrinsic influence of C. At a carbon content of y = x / 8 . 2 where perfect strain symmetrization is achieved, the A(2) and A(4) as well as the lh and hh states recover degeneracy as in unstrained Si. This is achieved for y = 3.4% in the example shown in Fig. 16b. For higher carbon concentration the (Si0.7Ge0.3)1-,C~alloy is under tensile strain and bandgap reduction is similar as for the case of Sil-,Cy alloy layers on silicon. Figure 17 shows the bandgap vs lattice constant for strained and unstrained Sil-yCy, Sil-,Ge, and Sil-,-,Ge,C,. The solid curve between Si and Ge indicates the bandgap for unstrained SiGe alloys with the characteristic kink at about 85% Ge, which is due to the crossover from the Si-like 6-fold A minima to the Ge-like 4-fold L minima in the conduction band (CB). The dashed line towards Ge shows the reduction of the bandgap for pseudomorphic SiGe on Si, which is determined by the strain-degenerate 4-fold A minima in the CB and the heavy holes (hh) in the valance band (VB). The PL results from strained Sil-,C, layers are shown by a dashed line starting from Si

408

KARLEBERL,KARLBRUNNER A N D O L I V E R G. SCHMIDT

towards smaller lattice constants. The bandgap for unstrained Si1-,C, is indicated by the solid line. For SiGeC alloys we find a very similar downwards bowing of the intrinsic energy gap such as for Sil-,C, as already discussed here. When starting from a certain unstrained SiGe alloy composition and adding substitutional C into the layer, the energy gap goes down by about 10-20 meV per percent C for unstrained alloys, at least for small C concentrations. In pseudomorphic layers the carbon reduces the strain in the films and increases the bandgap by about A E = y . (0.24 eV); however, this increase is only part of the one that would be obtained by reducing the Ge content in order to achieve similar strain reduction. The latest experimental data demonstrate that SiGeC layers can be prepared on Si, which have small and adjustable lateral strain, a smaller bandgap and a substantial band offset in the valence band (Schmidt and Eberl, to be published). 3.

SI/GE/SII-, C ~ QUANTUM WELLS

In order to increase the light output from Si-based heterostructures it is necessary to achieve strong confinement for both holes and electrons. Based on Si/Sil -x-pGexCv heterostructures this is possible by putting a Sii-,Ge, layer right next to a Sil-,jC, quantum well directly on Si. Similar concepts have been realized on a strain-relaxed Sil-,Ce, buffer layer with a tensile-strained Si layer next to a compressively strained Sil-,Ge,, quantum well with x < y (Usami et al., 1995 and 1996). Figure 18 shows a cross-sectional TEM micrograph of a 25-period 4 nm Sio.84Ge0.16/3.3nm Sio.988 C0.012/17 nm Si double quantum well structure on Si (100). The PL spectra of 3.3 nm siO.986cO.014, 4 nm Si0.84Ge0.16,and 4 nm Sio.832Geo.16 c0.008 single quantum wells (SQWs) are shown in the lower part of Fig. 19. The upper part shows PL spectra of coupled Sil-,-,Ge,C, /Sil-& double quantum well structures (DQWs) with x = 0.16, y = 0 or 0.009, and z = 0.012. The excitonic nophonon and TO-phonon PL lines originating from alloy layers are marked by QW-NP and QW-TO, respectively. The DQWs reveal PL lines at lower energy than the corresponding single QWs. They are attributed to spatially indirect transitions of A(2) electron and heavy hole states localized within the neighboring siO.988CO.012 and Sio.84Geo.16 layers, respectively. The band alignment is schematically illustrated in the insert of Fig. 20. The no-phonon line is strongly enhanced compared to the TO-phonon line. There is a significant intensity gain observed for the DQW with respect to the corresponding single QWs. For optimized QW thicknesses with respect to maximum overlap of the wave functions for electrons in siO.988CO.012and holes in Sio.84Geo.16 we achieve a three-ordersof-magnitude intensity increase as shown in Fig. 20 (Brunner et al., 1996c; Brunner et al., 1997). The strong dependence of the DQW PL on the spatial separation of carriers is also demonstrated by the 40% intensity decrease observed for a DQW structure with a 0.4-nm thick Si layer in between the Si0.84Ge0.16and siO.988cO.012 layers shown in Fig. 19.

8

S I I - , ~ , AND S I ~ - ~ - , G E ~ALLOY C ~ LAYERS

409

FIG. 18. Cross-sectional TEM micrographs with moderate (a) and high resolution (b) of a 25-period 4 nm Si0.84Ge0.~5/3.3nm si-O.988cO.O~2/17nm Si double quantum well structure on Si (100).

Adding C into the Sio.84Geo.16 layers results in a further PL intensity enhancement. A slight downwards shift in energy of about -10 meV/%C is observed for the Sio.84-,Geo,l6Cy/Sil-~C~double quantum wells with respect to corresponding Sio,84Geo,~6/Sil-~C~ DQW structures. This can be assigned to an increase of the hh valence band offset in a 4-nm Si0.84-,,Ge0.16Cy quantum well by C incorporation relative to Si. However, more detailed studies are needed to get a reliable picture of the quantitative change of the valence band offset, as other groups found a slight decrease as already mentioned in the last section. One has to keep in mind that confinement effects, a modified excitonic binding energy in DQWs, inhomogeneities within the layers or impurities, may affect the quantitative PL shifts with C content. In conclusion, we can describe the energy shifts of the PL lines for Sio.84Geo.16/ Sil-,C, and Si0.84-~Geo.l6C,/Sil-~C~ DQWs considering strain and intrinsic effects of C on the alloy layers within the picture of the CB and VB alignments shown in the inset of Fig. 20. An improved PL efficiency of the DQWs embedded in Si is observed

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1.10

1.15

ENERGY (eV) FIG.19. PL spectra of 3.3 nm Si0.986C0.014,4 nm Si0.84Geo 16 and 4 nm Si0.832Ge0.&0.008 single quantum wells (SQWs) are shown in the lower par; PL spectra of coupled Si~-,,_,Ge,C,/Sil~,C, double quantum well stmctures (DQWs) with x = 0.16, y = 0 or 0.009, and z = 0.012 are shown in the upper part. The Sil-,_yGe,Cy and the Si1-,C, layers are 4-nm and 3.3-nm thick, respectively. The quantum wells are repeated 25 times with 17-nm thick Si layers in between. The excitonic no-phonon and TO-phonon PL lines originating from alloy layers are marked by QW-NP and QW-TO, respectively. A 0.4 nm thin Si spacer sample separates the electrons in the Si0.988C0.012 layer from layer in the Sio,8~Geo,~6/Si/Sio,988CO,012 the holes in the Si0.84Ge0.16 layer and thus causes a 40% reduction of PL intensity.

compared to single QWs. Further enhanced no-phonon transitions and even more efficient capture of excited carriers may be expected for larger Ge and C contents.

4.

CARBON-INDUCED GE QUANTUM DOTS

The Ge islands appear during Ge deposition on Si (100) according to the StranskiKrastanov growth model (Apetz et al., 1995; Sunamura et al., 1995; Abstreiter et al., 1996). The island formation is observed after growth of a wetting layer, which is about 3 to 4 monolayers (ML) thick. However, the Ge islands are rather large (> 50 nm) and size reduction is only possible by low temperature growth, which, on the other hand,

411

40A

0.90

A L R , 0.95

1.00

1.05

1.10

1.15

ENERGY (eV) DQW structures with varied layer widths FIG. 20. The PL spectra from d ~ = 1.2dsic i ~ in Si. ~ The inset shows a schematic diagram of the conduction (CB) and valence bandedge (VB) for a pseudomorphic Sil-,Ge, layer next to a Sil- C film on Si (100). Within the Sil-,Ge, and y ' i the SiI-,C, layer the thicker lines indicate the 2-fold A(2) minima and the heavy hole bandedge in the CB and the VB, respectively. The thinner lines indicate the 4-fold A(4) minima and the light hole bandedge. The arrow indicates the PL transition from the A(2) CB states in the Sil-,C, layer to the hh VB states in the Si 1 Ge, layer.

-,

results in a low PL output due to point defects. We reported on the formation of carboninduced Ge islands (Schmidt et al., 1997). A small amount of predeposited carbon causes the formation of very small and optically active Ge quantum dots. Figure 21a shows an atomic force microscopy (AFM) image of 0.2 ML C / 2.16 ML Ge islands on a Si (100) surface. The carbon-induced Ge islands have a diameter of about 10 nm and a height of 1 nm. The island density is 1 x 1011cm-2. The cross-sectional TEM image in (b) shows the planar growth of pure 4 ML Ge deposited at Ts = 550°C without predeposited carbon. This is in clear contrast to the structure shown in Fig. 21c, which is a cross-sectional TEM image of 3 ML Ge on 0.2 ML carbon. The carbon-

412

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EBERL,KARLBRUNNER AND OLIVER G. SCHMIDT

FIG. 21. Atomic force microscopy (AFM) image of 0.2 monolayers (ML) C / 2 ML Ge islands on Si (a). The carbon-induced Ge islands have a diameter of about 10 nm and a height of 1 nm. The island density is 1 x 1011cm-2. The cross-sectional TEM image in (b) shows the planar growth of 4 ML Ge deposited at TS = 550 'C without predeposited carbon. (c) shows a cross-sectional TEM image of 3 ML Ge on 0.2 ML carbon. The carbon-induced 3 ML Ge dots have a diameter of 14 nm and a height of about I .S nm. The samples in (b) and (c ) have a 150-nm Si cap layer on top of the Ge layer.

induced 3 ML Ge dots have a diameter of 14 nm and a height of about 1.5 nm. The samples in (b) and (c) have a 1 5 S n m thick Si cap layer on top of the Ge layer. The 0.2 ML carbon deposited on Si can be regarded as a thin delta-like Sil-,C, layer with considerable surface roughness, which is induced by strong local strain surrounding the carbon atoms. The Ge deposited on this surface has a reduced surface mobility and thus forms a high density of small islands after more than 1.6 ML Ge growth (Schmidt et al., 1997; Schmidt et al., 1998). The expected bandedge alignment across the Ge dots is illustrated in Fig. 22. Spatially indirect recombination of electrons confined in the underlying carbon-rich layer and heavy holes localized in the Ge-rich upper region of the Ge islands are expected. We assume a gradual variation of the alloy composition across the carbon-induced Ge quantum dots, as only very small amounts of carbon and Ge are deposited. The situation is similar to spatially indirect structures discussed in the previous section with additional lateral carrier localization. DQW structures with Figure 23 shows PL spectra from Sio.s4Geo.l~/Sio.sssC0.0~2 dSiGe = 1.2 X dsic = 3.2 nm, a single layer of 0.2 ML carbon-induced 2.2 ML Ge quantum dots embedded in Si, and a 50x stacked 0.2 ML C / 2.4 ML Ge sample. The Si spacer layer thickness in the stacked sample is 9.6 nm. The NP-PL intensity of the dot samples is significantly higher than Sil-,Ge, and Sil-,C, quantum well samples,

CB

A2

HH _I__,

Growth direction

FIG.22. Schematic illustration of the C-induced Ge island structure and the expected band alignment in the growth direction. Spatially indirect recombination of electrons confined in the underlying carbon-rich layer and heavy hole states localized in the Ge-rich upper region of the Ge islands are assumed. Gradual variation of the alloy composition across the carbon-induced Ge quantum dots is expected.

which may be explained by strong carrier localization effects. The integrated PL intensity of the single dot-layer sample is even higher than the 25-period coupled quantum well structure. The energy position of the 50x stacked sample is red-shifted by about 50 meV. This is due to the larger dot size for 2.4 ML Ge and partly by electronic coupling between the dot layers. It is important to note that the DQW structures presented in the previous section as well as the carbon-induced Ge dot structures can be designed as nearly strainsymmetrized layer sequences. This means that there are no strong overall thickness limitations for the superlattice or stacked dots, which makes both concepts interesting for future applications in waveguides, infrared detectors, modulators, and electroluminescence devices grown directly on Si without the need of relaxed SiGe buffer layers.

VI.

Electrical "ransport Properties

Pseudomorphic Si1-,C, and Sil-,-,Ge,C, alloy layers on Si are interesting for transistors, because strain influences the charged carrier transport properties significantly. Ershov and Ryzhii (1994) published a theoretical study of electron transport in strained Sil-,C, and predicted an increase of the mobility for reasonably small alloyscattering potentials. The first experimental results from Sb-doped Sil-,C, alloys were reported by Faschinger et al. (1995). We have prepared 0.5k.m thick Sio.996Co.~4and Si reference layers with nominally the same phosphorus doping of about 3 x 1017 cm-3 (Eberl et al., 1997; Brunner et al., 1996d). The total thickness of 0.5 wm was chosen relatively thick for the doping level of 3 x lo" cm-3 in order to avoid misinterpretation caused by surface-depletion effects. The Si0.996Co.004layer is fully strained as measured by XRD. The critical thickness for pseudomorphic growth is significantly beyond O . 5 ~ mfor the small C content used in this case. The layers described in Figs. 24-26 were grown on an n-

414

KARLEBERL,KARL B R U N N E R AND OLIVER G. SCHMIDT

0,8

or9

1,o

Photon Energy (eV) F I G . 2 3 . The PL spectra from Si0.84Ge0,16/siO,9ggc0.012 DQW structures with d s i =~ 1.2 ~ x dS,C = 3.2 nm, a single layer of 0.2 ML carbon-induced 2.2 ML Ge quantum dots embedded in Si, and a 50x stacked 0.2 ML C / 2.4 ML Ge sample. The Si spacer layer thickness in the stacked sample is 9.6 nm. The NP-PL intensity of the dot samples is significantly higher than for Sil-nGe, and SiI-yCy quantum well samples, which may be explained by strong carrier localization effects. The energy position of the 50x stacked sample is red-shifted by about 50 meV. This is due to the larger dot size for 2.4 ML Ge and partly by electronic coupling between the dot layers.

Si (100) substrate with a resistance of above 5000 s2 cm. A 200-nm thick undoped Si buffer layer is deposited at 700°C before growing the doped layer. A careful chemical precleaning is performed to keep the boron doping at the substrate interface below 5 x 10'0cm-2. The electron density and Hall mobility from the samples described here are shown in Fig. 24. Over the whole temperature range from 50-300 K the electron density is essentially the same in the S ~ O . ~ ~ ~and C Othe . Oreference O~ sample. No electron capture by C or by any C-related defects is observed. In undoped Si0.996C0.004layers we find

415 1o4

z

g 103 I-

0

i!u

I-

0

FIG.24. Hall mobility and electron density (corrected for surface depletion) measured as a function of temperature in a Van der Pauw geometry from an n-type (phosphorus) 3 x 1017cm-3 doped 0.5 Krn thick S i 0 . 9 9 6 C o . ~layer and a reference layer without C. The doped layers were grown at 550 "C on (n-) 5000 R cm Si substrates with a 200-nm thick undoped Si buffer layer.

a high resistivity with no ohmic contacts to the layer. The electron mobility of the Si0.996C0.004sample and the reference sample are also closely matched down to about 180 K. For lower temperatures the mobility in the Si0.996Co.004sample is getting significantly higher as compared to the Si sample with still almost the same electron density. This is in contrast to measurements on 200-nm thick 1 x 10'7cm-3 n-type doped Sil-,C, layers already reported (Osten and Gaworzewski, 1997). The observation of increased mobility in thick homogeneous layers shown in Fig. 24 can be explained by the tensile strain in the Sio.996Co.004layer, which induces a splitting of the 6-fold A valleys, The A(2) valleys become the CB minima with the small in-plane effective mass for the electron. The splitting of the A(4) and A(2) levels is only about 20 meV for the small C concentration used in this sample; therefore, a mobility enhancement is expected only for low temperatures. The results on the thick homogeneously doped Sil-,C, alloy layers demonstrate that the samples show reasonable doping behavior and that the mobilities do not degrade. The mobility seems to be limited by charged dopant impurity scattering although the concentration of carbon atoms exceeds that of the phosphorus dopants by three orders of magnitude. Pseudomorphic Sil-,C, alloy layers on Si provide a significant band offset in the conduction band and have a small in-plane mass mA2 = 0.2 mo. The smaller effective mass with the A(2) levels mainly occupied should also reduce intervalley scattering. Consequently, Si/Sil -yCy heterostructures are very interesting for n-type modulationdoped field effect transistors (FET) (Nayak et al., 1994; Nay& and Chun, 1994; Doll-

416

KARLEBERL,KARLBRUNNERA N D OLIVER G. SCHMIDT

a) n-Si MOS-FET:

b) n-Sit.$, MOS-FET

FIG. 25. Comparison of a Si (a) and a SiI-,C, (b) n-channel MOSFET. The confinement induced splitting in pure Si MOS structures is only of the order of 10 meV. Thus, both A(2) and A(4) levels are occupied at room temperature. In (b) a Sil-yCy alloy layer is used at the Si02 interface or close to the interface as an inversion layer. The idea is to take advantage of the built-in tensile strain to increase the A(2)A(4) energy splitting and to achieve close to zero occupancy in the upper A(4) levels at room temperature.

fus and Meyer, private communication). A suggestion for an n-channel MOSFET is schematically shown in Fig. 25b. In this case a thin Sil-,Cy alloy layer is used at the Si02 interface or close to the interface as an inversion layer. The idea is to take advantage of the tensile strain in order to increase the A(2)-A(4) energy splitting just enough to achieve close to zero occupancy in the upper A(4) levels at room temperature (Brunner and Eberl, U.S. Patent). The confinement-induced splitting in pure Si MOS structures is only on the order of 10 meV, thus, both A(2) and A(4) levels are occupied at room temperature as schematically illustrated in Fig. 25a. The same structure would be interesting for p-channel devices because of the reduced effective mass for holes in tensile-strained Si (Nayak et al., 1994; Nayak and Chun, 1994). In a different approach, substitutional carbon is used for strain reduction in Si/Sil -x-yGe,Cy heterostructures. This increases the critical thickness and thus allows an increase in the Ge concentration. Ideally a Gel-,C, layer would be used as a p-channel in an FET with the C content just enough to reduce part of the compressive strain such that a thin (> 2 nm) planar layer can be grown. The idea is to take advantage of the high hole mobility in strained Ge (Manku and Nathan, 1991). However, it turned out to be extremely difficult to prepare planar Gel-,Cy layers on Si (100) because carbon causes Ge island formation as shown in Fig. 21. Extremely low substrate temperatures of only about 300°C are necessary to avoid the island formation, which, on the other hand, leads to low crystal quality due to incorporation of point defects (Brunner et al., 1996e). Osten and Klatt (1994) measured an increased critical thickness for Geo.99Co.ol layers of about 20 monolayers using an antimony-mediated growth technique. For a discussion of the bandgap of Ge-rich Sil-,-,Ge.,C, alloys see Orner et al. (1996).

417

z

n

hl

E

0

W

Oo0

I

1I

n--Si substrate

I

!!

0

I

100 10

20

30

40

50

60

Ge CONTENT x (%) FIG. 26. Hall mobilities measured at room temperature and 77 K in a Van der Pauw geometry from p-channel Sil -x-yGexCy modulation doped quantum well structures. The layer sequence is schematically shown in the inset. The growth temperature was 550 "C.

Figure 26 shows Hall mobilities measured at room temperature and 77 K in a Vander Pauw geometry from several p-channel Sil-,Ge, and one Si0.49Ge0.49C0.02 modulation doped quantum well structure represented by open and full symbols, respectively. The layer sequence is 400-nm undoped Si, 8 nm Sil-,-,Ge,C,, 10 nm Si spacer, a boron-doped Si layer and a 20-nm Si cap layer (see also the inset of Fig. 26). Looking at the hole mobilities in the Sil-,Ge, QWs we observe a maximum of about 220 cm2N s at 300 K and about 2000 cm2N s at 77 K for x = 30%. For higher Ge concentrations the mobilities degrade, which is attributed to strain-induced interface roughness and misfit dislocation nucleation. The 8-nm quantum well thickness is above the equilibrium critical thickness for pseudomorphic Si0.5Ge0.5 on Si. In the Si0.49Ge0.49Co.02 sample the compressive strain is reduced by about 30%. In other words, the strain is similar to a virtual Ge concentration of about 35%. The mobilities for the Si0.49Ge0.49C0.02 QW are 185 c m 2 N s at 300 K and 2750 c m 2 N s at 77 K, the latter being significantly improved against the corresponding sample without C. The higher hole mobility for the Si0.49Ge0.49Co.02QW is a consequence of the reduced strain in the layer due to substitutional C . For the Si0.5Geo.ssample we measure a hole density of 5 x 1011cm-2at 300 K and 1.5 x 1011cm-2 at 77 K. The hole density in the C alloyed QW is also 5 x 1011cm-2 at 300 K, but only about 0.5 x 1011cm-2at 77 K. So far, the samples are not optimized for maximum carrier transfer from the doping layer to the QW. The reduction of carrier density at low temperature may be a con-

418

KARLEBERL,KARLBRUNNERA N D O L I V E R G. SCHMIDT

sequence of reduced valence band offset, alloy inhomogeneities and local strain fields around the C atoms in the Sio.sGe0.5matrix. A first p-channel MODFET with 45% Ge and 1.2% C was demonstrated by Cluck et al. (1998). The device with 0.75 p m gate length provided a transconductance of 62 mS/mm at room temperature.

VII. SummaryDevices In pseudomorphic Sil-,C, layers on Si the bandgap is reduced by about 65 meV/%C. Considering the deformation potentials we find the bandgap of unstrained Sil-,C, alloys with small carbon concentration to be smaller than in Si by about 1020 meV/%C. The bandgap in pseudomorphic SiGeC is increased by substitutional C incorporation by about 24 meV percent of C. The band alignment in Si/Sil-, C, is type I with the offset mainly in the conduction band. A strong electron and hole confinement is achieved directly on Si in coupled Sil-xGex/Sil-yC, quantum wells, which results in a strong no-phonon PL intensity. Carbon-induced Ge quantum dots with dimensions in the 1Gnm range have been prepared; they provide very intensive PL intensity. Enhanced electron mobilities are observed in thick pseudomorphic n-type doped Sil-,C, layers at low temperatures, which are attributable to the splitting of the A valleys with the A(2) valleys being the conduction band minima. In a modulationdoped p-type Si0.49Ge0.49C0.02QW an improved hole mobility is observed at room temperature and 77 K compared to a corresponding sample without carbon, which is a consequence of the reduced strain in the layer due to substitutional carbon. The first device-relevant work applying substitutional carbon has been published (Huang and Wang et al., 1996; Soref et al., 1996; Soref, 1996; Lanzerotti et al., 1996; Chen et al., 1996; Bair et al., 1996; Mamor et al., 1996; Meyer et al., 1996; Osten and Bugiel, 1997; Osten et al., 1997a; Osten et al., 1997b). A first p-channel MODFET with 45% Ge and 1.2% C was demonstrated as mentioned in the previous section (Cluck et al., 1998). Most promising for device applications is the effect of significantly reduced boron outdiffusion in SiGe layers with carbon incorporated in the 1020cm-3 range (Osten et al., 1997a). Osten et al. (1997b) demonstrated SiGe:C heterojunction bipolar transistors (HBT) with fT/fm,, of 64 / 50 GHz and typical ring oscillator ECL gate delay times of 22.5 ps using 0.8pm design rules. Outdiffusion of boron from the SiGe base layer especially on the collector side leads to drastic degradation of the device during processing. Incorporation of a small amount of carbon into the base layer increases the process margins and thus allows more cost-effective device HBT with carbon concenfabrication (Osten et al., 1997a). The first Sil-,-,Ge,C, trations in the percent range, high enough to reduce strain significantly and change the bandgap in the base layer, was reported by Lanzerotti et al. (1996). Particularly interesting are Si1-,Cy, Sil-x-yGexCy layers and strain-symmetrized Sil-,-yGexC,/Si~-,C, coupled multiquantum wells or carbon-induced Ge quantum dot structures for the field of optoelectronic devices as already pointed out (Soref et al.,

8

S1l-,Cy

AND

SI1-x-yGExCy ALLOY LAYERS

419

1996; Soref, 1996; Eberl and Brunner, Patent). A first normal-incidence epitaxial SiGeC photodetector near 1.3pm wavelength grown on Si was reported by Huang and Wang (1996). The PL investigations and the Hall measurements presented provide a picture of the influence of substitutional C on both the bandgap and band alignment. The results demonstrate that Sil-,C, and Sil -x-yCe,C, alloys are useful semiconductor materials that offer more flexibility in the design of device structures on Si substrate.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge the excellent collaboration with M. Cluck and U. Konig from the Daimler Benz Research Center in Ulm and the skillful assistance of W. Winter, H. Seeberger, S. Schieker, and C. Lange. This work has been supported financially by the “Bundesministerium fiir Bildung und Forschung” within the “Si Nanoelektronik” project. The authors gratefully acknowledge the continuous support of H. Grimmeiss, E. Kasper, and K. von Klitzing.

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Index A Acoustical phonons, Raman scattering by, 260-265 Activation energy, and diffusion, 67-70 Adatoms absorption of, 62-64 diffusion of, 64 interaction with surface steps, 71-74 AlGaAs growth, 2 , 4 Antimony, as impurity in SiGe, 203,209 APCVD, 21-24 Arsenic, as impurity in SiGe, 205-209 Atmospheric pressure chemical vapor deposition (APCVD), 21-24 Atomic bonds, elastic distortion of, 103, 104 Atomic ordering, 3 1-32 Auger processes, 214-216 Avalanche photodiodes, 348-35 I

B Blocking, of dislocations, 150, 151, 152 Buffers against dislocations, 156-157 graded, 158-159 strained layer superlattices as, 159 Burgers vector, 109, 110 C

Cammarata-Sieradzki model, of critical thickness, 125 Carbon boron diffusion adjustment using, 397 as impurity, 4 induction ofdot structures by, 410-413 properties of, 388 strain adjustment using, 389-390 substitution for Si in S i c alloy, 397-400 Carriers generation and recombination of, 322-326 in GeSi/Si heterostructures, 334-339

minority, 339-341 mobility of, 3 2 6 3 3 4 Chemical vapor deposition (CVD) conditions for, 3-4 contamination risk in, 4 kinetic processes during, 52 Chidambarro model, of critical thickness, 125 Chlorides, use in RTCVD, 13 Cleaning procedures, 4-5 Climb, defined, 113 Conduction states, defect perturbations to, 207-210 Critical thickness models of, 120-126 in multilayer structures, 128-131 in partial misfit dislocations, 126-128

D Deep level transient spectroscopy (DLTS), 295 Deep levels, in GeSi, 295, 31 1 Density functional theory, 172 Diborane, 22 Dichlorosilane, 23 Differential spectroscopy, 2 2 6 2 3 I Diffusion, anisotropy of, 67 Diffusion coefficient, 65-67 and activation energy, 67-70 Directional couplers, 375-376 Dislocation theory, 109-120 Dislocations. See Misfit dislocations; Threading dislocations. Dopants, 28 in APCVD, 23 in MBE, 6 in RTCVD, 15 in UHVCVD, 2 1 Doping compensation, 316,319-322 E Edge dislocations, 111, 113, 114 Elastic strain, 102

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424

INDEX

Electromodulated reflectivity, 228-230 Electron transport, in bulk GeSi, 332-333 Electron traps, in GeSi, 303-309 Ellipsometry, spectroscopic, 230 Empirical pseudopotential (EPP) method, 171-172 Epitaxial films adatom-step interaction, 70-74 coarsening of, 75 equilibrium growth modes for, 50-52 kinetic growth modes of, 53-55 kinetic processes during deposition of, 52-53 Erbium, as dopant, 367-368

F Filtering, of dislocations, 157-161 Fox-Jesser model, of critical thickness, 125-126 Frank-Read mechanism, 138, 140 Frank-van der Merwe growth mode, 50,51 Frank-van der Merwe model of critical thickness, 124-125 Free-carrier injection devices, 377-379 G Gas source MBE, 23-24 Germanium bandstructures of, 174, I75 collection in GeSi alloy, 90 electroreflectivity spectrum of, 228 growth of submonolayer, 79-8 1 properties of, 387-388 GeSi atomic ordering in, 31-32 bandstructures of, 174-178, 182-188 boron diffusion ion, 396 carrier generation-recombination in, 322-325 carrier transport properties of, 326-341 deep levels in, 295-3 19 defects in, 317-326 doping compensation in, 3 19-322 electric field applied to, 215 electron transport in, 333 electron traps in, 303-309 extended defect states in, 295-301 growth of dimer vacancy lines, 82-84 growth of Ge wetting layer, 79-86 growth methods of, 2 9 4 2 9 5 hole mobility in, 326-332 hole traps in, 309-319,320 morphology of, 85-86 optical spectra of, 195-196

photoluminescence in, 29,277-279 strain in systems, 170-171 substrates of, 4 0 4 2 GeSi alloy films, 90-94 multilayer growth in, 93-94 Raman scattering in, 256-258 roughening and islanding in, 92-93 thermodynamic characteristics of, 91 GeSi crystal growth, 2-3 APCVD, 22-24 development of, 1-2 doping in, 28 layer thickness in, 25-27 majority carrier transport in, 28-29 MBE, 6-13 methods of, 4-5 minority carrier lifetime and, 30 RTCVD, 13-16 UHVCVD, 16-22 GeSi interfaces impurities at, 197-199,203-207 intermixing of atoms at, 84-85 microscopic signature of, 199-21 2 GeSi microstructures, 179-182 experiments on, 173 GeSiC, 388 annealing behavior of, 396 coupling with S i c alloy layers, 4 0 7 4 1 0 devices made from, 4 1 8 4 1 9 electrical transport properties of. 4 1 3 4 1 8 lattice constant of, 390-391 MBE preparation of, 392-394 optical properties of, 4 0 4 4 0 8 optoelectronic use of, 418 thermal stability of, 394-397 GeSilSi, carrier transport in, 334-341 Glide planes, 112-1 15 Guided-wave devices integrated and active components, 375-379 waveguides, 37 1-374

H Hagen-Strnnk mechanism, 138-1 39 Harmonic generation, 216-217 Henderson method, 5 Heterojunction bipolar transistors (HBTS), 8 SiGeC, 4 1 7 4 1 8 Heterojunction internal photoemission (HEP) photodetectors, 359-360

INDEX Hole mobility, 326-33 1 Hole traps, in GeSi, 308-317, 318 Hut islands, 86-89 Hydrides use in RTCVD, 14 use in UHVCVD, 17-18 Hydrogen, reactivity of, 4

I Image dislocation, 112 Infrared photodetectors, 359-361 SdSiGe superlattices in, 212 Integrated optical receivers, 362-363 Interdiffusion, 105-107 Interface islands, impurities at, 197-199 Islanding, 11, 32-38 carbon-induced, 410-413 dependence on diffusion coefficient, 65-67 in GeSi alloy films, 92-93 hut, 8 6 9 0 stable nuclei and, 74 Islands equilibrium shape of, 76 formation of, 92-93 multilayer organization of, 93-94 and step energies, 76 3-D, 86-90 K Kinetically rough growth, 53 Kinks, 113, 116-117 L Layer-by-layer growth, 54-55 Limited area epitaxy, 159-161 Linear-chain model, of Raman scattering, 261-262

Local density approximation, 172 Localization at Ge impurities in Si layers, 21 1-212 interface-induced, 203-207

M Matthews-Blakeslee model of critical thickness, 12g-123 accuracy of, 124 Metal-semiconductor-metal (MSM) photodiodes, 356-359 Metastability, 131

Minority carriers diffusion coefficient of, 339-341 lifetimes of, 339-341 Misfit dislocation arrays, 107 geometry of, 113-1 15 Misfit dislocations annihilation of, 157 density of, 132-133 dissociation of, 117-1 19 energy of, 111-1 12 forces on, 112 geometry of, 109-1 11 interactions among, 149-152, 157-158 motionof, 112-113, 115-117 multiplication of, 138-141 nucleation of, 133-144 p a h l vs. total, 119-120 propagation of, 144-149, 156 strain relaxation by, 152-155 techniques for reducing, 155-161 Mixed dislocations, I l l , 112, 113 MODFET structures, 334 SiCeC, 418 Modulation spectroscopy, 228 Molecular beam epitaxy (MBE), 2, 18 conditions for, 3-4,9-13 contamination risk in, 4, 8-9 disadvantages of, 9 dopants in, 6-7 gas source, 24 impurity introduction in, 4-5 machinery for, 7-9 Multilayer structures critical thickness in, 128-131 step bunching in, 93-94

N Nonlinearities, in optical response, 216-219 Nonplanar growth atomic ordering, 31-32 islands, 32-37 selective area epitaxy (SAG), 38-40 substrates for, 40-42 wires, 32-37 Nucleation heterogeneous, 133-1 35 homogeneous, 135-138 mechanisms of, 133, 142-144 quasi-homogeneous, 137 rates of, 141-142

425

426

INDEX

0 Optical modulators and switches, 375-379 Optical spectra, 195-196 microscopic electronic structure effects in, 2 12-21 9 nonlinearities in, 216-219 Optical transitions in GeSi quantum wells and superlattices, 243-252 pseudo-direct, 23 1-236 in Si/GeSi and Ge/GeSi microstructures, 236-243 P p-i-n photodiodes, 348-349 Partial dislocations, 117-120 critical thickness and, 126-128 People-Bean model, of critical thickness, 125 Photodetectors avalanche photodiodes, 350-35 1 heterojunction internal photoemission (HEP), 359-361 infrared, 359-360 integrated optical receivers, 362-363 metal-semiconductor-metal (MSM) photodiodes, 356-359 p-i-n photodiodes, 348-349 quantum well infrared (QWIP), 361-362 resonant-cavity photodiodes, 352-355 SiGeC, 4 18 waveguide photodiodes, 349-35 1,379-380 Photodiodes avalanche, 350-351 metal-semiconductor-metal (MSM), 356-359 p-i-n, 348-349 resonant-cavity, 352-355 waveguide, 349-351,379-380 Photoluminescence, 277-278 from bulk GeSi alloys, 278-279 by Er-doped silicon, 367-369 by porous silicon, 363-367 by SVGe quantum wells and superlattices, 369-37 1 from Si/GeSi microstructures, 280-286 from ultrathin quantum wells and superlattices, 286-288 Photomodulated reflectivity, 228-230 Pinning, 150, 151 Plastic relaxation, 104, 107-108 Porous Si, photoemission by, 363-367

Q Quantum dots, carbon-induced, 4 1 M 1 3 Quantum well infrared photodetectors (QWIP), 361-362 Quantum wells optical transitions in, 243-252 photoluminescence from, 286-288.369-37 1 Raman scattering in, 258-260 resonant Raman scattering in, 269-273

R Raman scattering, 253-256 by acoustical phonons, 260-265 in bulk GeSi random alloys, 256-258 resonant, 265-276 Rapid thermal chemical vapor deposition (RTCVD) dopants in. 15 machinery for, 13- 16 raw materials for, 13 temperature of, 14 RCA method, 5 Relaxation kinetic modeling of, 152-155 plastic, 104, 107-108 via 3-D cluster formation, 88-90 Resonant Raman scattering, 265-269 detecting interface roughness by, 273-276 in quantum wells and superlattices, 269-273 Resonant-cavity photodiodes, 352-355 Roughening detecting with resonant Raman scattering, 273-276 in GeSi alloy films, 92-93 of epitaxial layer, 105 reducing activation barriers, 137-1 38 Ryotov model, 260-261

s Sb, as impurity in SiGe, 203,207-208 Screw dislocations, 112, 113 Selective area epitaxy (SAG), 3 8 4 0 Shintani-Fujita model, of critical thickness, 126 Shiraki method, 5 Si (001],56-59 step configurations on, 76-78 Si{lll),61 Si islands equilibrium shape of, 75-76 and step energies, 76 P-SiC, properties o f , 388

INDEX S i c alloy, 388-390 coupling with SiGeC layers, 407-410 electrical transport properties of, 413-418 lattice constant of, 390-391 MBE preparation of, 392-394 optical properties of, 4 0 1 4 0 3 optoelectronic use of, 418 thermal stability of, 394-397 Silicon bandstructures of, 174, 175,348 characteristics of, 347-348 crystal structure of, 57-61 electroreflectivity spectrum of, 228 erbium-doped, 367-369 growth on Si (OOl], 62-75 MBE of, 6-1 photoemission by, 363-367 photoluminescence of, 29 porous, 363-367 properties of, 387-388 self-diffusion of, 64-70 Spectroscopic ellipsometry, 230 Step bunching, 93-94 of 3-D islands, 94 Step configurations bunching in multilayers, 93-94 on nominal surface, 76-77 on vicinal surface, 78 Step-flow growth, 54,55,70-74 Strain accommodation of, 103-109, 120 competition among relief mechanisms, 108-109 metastability and, 131 origins of, 102-103 relaxation of, 152-155 Strain-relaxed GeSi, 40-45 Strained layer superlattice filtering, 159 Stranski-Krastanov growth mode, 50 Superlattices bandstructures of, 174-182, 189-192 charge densities of, 194

critical point energies of, 246-248 first-principles calculations of, 200-203 imperfections in structure of, 189-192 optical transitions in, 193,243-252 photoluminescence from, 286-288,369-371 Raman scattering in, 258-260 resonant Raman scattering in, 269-273 strained layer, 159 Surface diffusion, 64 Surface vacancies, 82-84

T Temperature, measurement of, 16 Thermal mismatch, 103 Thermo-optic devices, 376 Threading dislocations, 110 filtering of, 157-161 3-D islands, 86-90 formation of, 92-93 self-organization of, 94

U Ultra-high vacuum chemical vapor deposition (UHVCVD) advantages and disadvantages of, 19-21 conditions for, 1 6 1 8 dopants in, 20-21 raw materials for, 17-19 V Vacancies, dimer, 82-84 Volmer-Weber growth mode, 50,51

w Wafer cleaning, 5 Wall deposition, 16 Waveguide photodiodes, 349-35 1 Waveguides, 371-374 integrated with photodetectors, 379-380 Willis model, of critical thickness, 125 Wires, quantum, 32-37

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Contents of Volumes in This Series

Volume 1 Physics of 111-V Compounds C. Hilsum, Some Key Features of 111-V Compounds Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds E. 0. Kane, The k - p Method V L. Bonch-Bruevich,Effect of Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of 111-V Compounds Laura M. Rorh and Petros N. Argyres, Magnetic Quantum Effects S. M. Puri and I: H. Geballe, Tnermomagnetic Effects in the Quantum Region W M. Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H. Purley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H. Weiss, Magnetoresistance Betsy Ancker-Johnson, Plasma in Semiconductors and Semimetals

Volume 2 Physics of 111-V Compounds M. G. Holland, Thermal Conductivity S. I. Novkova, Thermal Expansion (1. Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants J. R. Drabble, Elastic Properties A. U. Mac Rae and G. W. Gobeli, LOWEnergy Electron Diffraction Studies Robert Lee Mieher, Nuclear Magnetic Resonance Bernard Goldsrein, Electron Paramagnetic Resonance I: S. Moss, Photoconduction in 111-V Compounds E. Anfoncik and J. Tauc, Quantum Efficiency of the Internal Photoelectric Effect in InSb G. W Gobeli and I. G. Allen, Photoelectric Threshold and Work Function f! S. Pershan, Nonlinear Optics in 111-V Compounds M.Gershenzon, Radiative Recombination in the 111-V Compounds Frank Stern, Stimulated Emission in Semiconductors

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CONTENTS OF VOLUMES I N THISSERIES

Volume 3 Optical of Properties 111-V Compounds Marvin Hass, Lattice Reflection William G. Spifzer,Multiphonon Lattice Absorption D. L. Stienvalt and R. E Potter, Emittance Studies H. R. Philipp and H. Ehrenveich, Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Eamesr J. Johnson, Absorption near the Fundamental Edge John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors B. Lar and J. G. Mavroides, Interband Magnetooptical Effects H. K Fan, Effects of Free Caniers on Optical Properties Edward D.Palik and George B. Wright, Free-Canier Magnetooptical Effects Richard H. Bube, Photoelectronic Analysis B. 0. Seraphin and H. E. Bennett, Optical Constants

Volume 4 Physics of 111-V Compounds N. A. Goryunova, A. S.Borschevskii, and D. N. Tretiakov, Hardness N. N. Sirota, Heats of Formation and Temperatures and Heats of Fusion of Compounds A"'BV Don L. Kendall, Diffusion A. G. Chynoweth, Charge Multiplication Phenomena Robert N! Keyes, The Effects of Hydrostatic Pressure on the Properties of 111-V Semiconductors L. W Aukerman, Radiation Effects N. A. Goryunova, F: II Kesamanly, and D. N . Nasledov, Phenomena in Solid Solutions R. I: Bare, Electrical Properties of Nonuniform Crystals

Volume 5

Infrared Detectors

Henry Levinstein, Characterization of Infrared Detectors Paul W Kruse, Indium Antinionide Photoconductive and Photoelectromagnetic Detectors M. B. Prince, Narrowband Self-Filtering Detectors Ivars Melngalis and Z C. Harman, SingleCrystal Lead-Tin Chalcogenides Donald Long and Joseph L. Schmidt, Mercury-Cadmium Telluride and Closely Related Alloys E. H. Putley, The Pyroelectric Detector Norman B. Srevens, Radiation Thermopiles R. J. Keyes and I: M. Quist, Low Level Coherent and Incohei-entDetection in the Infrared M. C. Teich, Coherent Detection in the Infrared F: R. Arums, E. W Surd, B. J. Peyton, and F: P. Pace, Infrared Heterodyne Detection with Gigahertz IF Response H. S. Sommers, J K , Macrowave-Based Photoconductive Detector Robert Sehr and Ruiner Zuleeg, Imaging and Display

Volume 6 Injection Phenomena Murray A. Lampert and Ronald B. Schilling, Current Injection in Solids: The Regional Approximation Method Richard Williams, Injection by Internal Photoemission Allen M. Bametf, Current Filament Formation R. Baron and J. W Mayer, Double Injection in Semiconductors N! Ruppel, The Photoconductor-Metal Contact

CONTENTSOF VOLUMESIN THISSERIES

Volume 7 Application and Devices

Part A John A. Copeiand and Stephen Knight, Applications Utilizing Bulk Negative Resistance E A. Padovani, The Voltage-Current Characteristics of Metal-Semiconductor Contacts €? L. Hower; W W Hoopec B. R. Cairns, R. D. Fairman, and D. A. Tremere, The GaAs Field-Effect Transistor Marvin H. White, MOS Transistors G. R. Antell, Gallium Arsenide Transistors T L. Tansley, Heterojunction Properties

Part B I: Misawa, IMPA'lT Diodes H . C. Okean, Tunnel Diodes Robert B. Campbell and Hung-Chi Chang, Silicon Junction Carbide Devices R. E. Enstrom, H. Kressel, and L. Krassner, High-Temperature Power Rectifiers of GaAsl_,P,

Volume 8 Transport and Optical Phenomena Richard J. Srirn, Band Structure and Galvanomagnetic Effects in 111-V Compounds with Indirect Band Gaps Roland W Ure, J s , Thermoelectric Effects in 111-V Compounds Herbert Piller, Faraday Rotation H. Barry Bebb and E. W Williams, Photoluminescence I: Theory E. W Williams and H. Barry Bebb, Photoluminescence 11: Gallium Arsenide

Volume 9 Modulation Techniques B. 0. Seraphin, Electroreflectance R. L. Aggaiwal, Modulated Interband Magnetooptics Daniel E B l o s s q and Paul Handler, Electroabsorption Bruno Bafz, Thermal and Wavelength Modulation Spectroscopy Ivar Balslev, Piezopptical Effects D. E. Aspnes and N . Bottka, Electric-Field Effects on the Dielectric Function of Semiconductors and Insulators

Volume 10 Transport Phenomena R. L. Rhode, Low-Field Electron Transport J , D. Wiley, Mobility of Holes in 111-V Compounds C. M. Wolfe and G. E. Stillman, Apparent Mobility Enhancement in Inhomogeneous Crystals Robert L. Petersen, The Magnetophonon Effect

Volume 11 Solar Cells Harold J. Hovel, Introduction: Carrier Collection, Spectral Response, and Photocurrent; Solar Cell Electrical Characteristics; Efficiency: Thickness; Other Solar Cell Devices; Radiation Effects; Temperature and Intensity; Solar Cell Technology

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CONTENTS OF VOLUMES IN

THISSERIES

Volume 12 Infrared Detectors (11) W L. Eiseman, J. D. Merriam, and R. F: Potter, Operational Characteristics of Infrared Photodetectors Peter R. Bratt, Impurity Germanium and Silicon Infrared Detectors E. H. Putley, InSb Submillimeter Photoconductive Detectors G. E. Stillman, C. M. Wove, and J. 0.Dimmock, Far-Infrared Photoconductivity in High Purity GaAs G. E. Srillman and C. M.Wove, Avalanche Photodiodes I? L. Richards, The Josephson Junction as a Detector of Microwave and Far-Infrared Radiation E. H. Putley, The F'yroelectric Detector-An Update

Volume 13 Cadmium Telluride Kenneth Zanio, Materials Preparations; Physics; Defects; Applications

Volume 14 Lasers, Junctions, Transport N . Holonyak, Jr and M. H. Lee, Photopumped 111-V Semiconductor Lasers Henry Kressel and Jerome K. Butler, Heterojunction Laser Diodes A Van der Ziel, Space-Charge-Limited Solid-state Diodes Peter J. Price, Monte Carlo Calculation of Electron Transport in Solids

Volume 15 Contacts, Junctions, Emitters B. L. Sharma, Ohmic Contacts to 111-V Compounds Semiconductors Allen Nussbaum, The Theory of Semiconducting Junctions John S. Esclzer, N E A Semiconductor Photoemitters

Volume 16 Defects, (HgCd)Se, (HgCd)Te Henry Kressel, The Effect of Crystal Defects on Optoelectronic Devices C. R. Whitsett, J. G. Broerman, and C. J. Summers, Crystal Growth and Properties of Hgl-,Cd,Se alloys M. H. Weiler, Magnetooptical Properties of Hgl _*Cd, Te Alloys Paul W Kruse and John G. Ready, Nonlinear Optical Effects in Hgl -,Cd,Te

Volume 17 CW Processing of Silicon and Other Semiconductors James E Gibbons, Beam Processing o f Silicon Arto Lietoila, Richard B. Gold, James F: Gibbons,and Lee A. Christel, Temperature Distributions and Solid Phase Reaction Rates Produced by Scanning CW Beams Arlo Leiroila and Jumes E Gibbons, Applications of CW Beam Processing to Ion Implanted Crystalline Silicon N . M. Johnson, Electronic Defects in CW Transient Thermal Processed Silicon K. E Lee, I: J. Stultz, and James R Gibbons, Beam Recrystallized Polycrystalline Silicon: Properties, Applications, and Techniques Z Shibara, A. Wakira, Z W Sigrnon, and James E Gibbons, Metal-Silicon Reactions and Silicide Yves I. Nissim and James E Gibbons, CW Beam Processing of Gallium Arsenide

CONTENTS OF VOLUMES IN THIS SERIES

433

Volume 18 Mercury Cadmium Telluride Paul W Kruse, The Emergence of (Hgl -,Cd,)Te as a Modem Infrared Sensitive Material H. E. Hirsch, S. C. Liang, and A. G. White, Preparation o f High-Purity Cadmium, Mercury, and Tellurium W E H. Micklerhwaite, The Crystal Growth of Cadmium Mercury Telluride Paul E. Petersen, Auger Recombination in Mercury Cadmium Telluride R. M. Broudy and B J. Mazuxzyck, (HgCd)Te Photoconductive Detectors M . B. Reine, A. K. Soad, and 7: J. Tredwell, Photovoltaic Infrared Detectors M. A. Kinch. Metal-Insulator-Semiconductor Infrared Detectors

Volume 19 Deep Levels, GaAs, Alloys, Photochemistry G. E Neumark and K. Kosai, Deep Levels in Wide Band-Gap 111-V Semiconductors David C. Look, The Electrical and Photoelectronic Properties of Semi-Insulating GaAs R. E Brebrick, Ching-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te Yu. Ya. Gurevich and Yu. V Pleskon, Photoelectrochemistry of Semiconductors

Volume 20 Semi-InsulatingGaAs R. N. Thomas, H. M. Hobgood, G. W Eldridge, D. L. Barrett, Z 7: Braggins, L. B. Ta, and S. K. Wang, High-Purity LEC Growth and Direct Implantation of GaAs for Monolithic Microwave Circuits C. A. Sfolfe,Ion Implantation and Materials for GaAs Integrated Circuits C. G. Kirkpatrick. R. Z Chen, D. E. Holmes, P. M. Asbeck, K. R. Elliott, R. D. Fairman, and J. R. Oliver, LEC GaAs for Integrated Circuit Applications J. S. Blakemore and S. Rahimi, Models for Mid-Gap Centers in Gallium Arsenide

Volume 2 1 Hydrogenated Amorphous Silicon Part A Jacques I. Pankove, Introduction Masataka Hirose, Glow Discharge; Chemical Vapor Deposition Yoshiyuki Uchidu,di Glow Discharge Z D. Moustakas, Sputtering Isao Yamaah, Ionized-Cluster Beam Deposition Bruce A. Scott, Homogeneous Chemical Vapor Deposition Frank J. Kampus, Chemical Reactions in Plasma Deposition Paul A. Longeway, Plasma Kinetics Herbert A. Weakliem, Diagnostics of Silane Glow Discharges Using Probes and Mass Spectroscopy Lester Gluttman, Relation between the Atomic and the Electronic Structures A. Chenevas-Paule, Experiment Determination of Structure S. Minomura, Pressure Effects on the Local Atomic Structure David Adler, Defects and Density of Localized States

Part B Jacques I. Pankove, Introduction G. D. Cody, The Optical Absorption Edge of a-Si: H Nabil M. Amer and Warren B. Jackson, Optical Properties of Defect States in a-Si: H I! J. Zanzucchi, The Vibrational Spectra of a-Si: H YoshihiroHamakawa, Electroreflectance and Electroabsorption

434

CONTENTS OF VOLUMES IN

THISSERIES

Jefrey S.Lannin, Raman Scattering of Amorphous Si, Ge, and Their Alloys R. A. Street, Luminescence in a-Si: H Richard S. Crandall, Photoconductivity J. Tuuc, Time-Resolved Spectroscopy of Electronic Relaxation Processes R E. Vanier, IR-Induced Quenching and Enhancement of Photoconductivity and Photoluminescence H . Schade, Irradiation-Induced Metastable Effects L. Ley, Photoelectron Emission Studies

Part C Jacques I. Pankove, Introduction J. David Cohen, Density of States from lunction Measurements in Hydrogenated Amorphous Silicon II C. Taylor, Magnetic Resonance Measurements in a-Si: H K . Morigaki, Optically Detected Magnetic Resonance J. Dresner, Carrier Mobility in a-Si: H 1: Tiedje, Information about band-Tail States from Time-of-Flight Experiments Arnold R. Moore, Diffusion Length in Undoped a-Si: H W Be-yerand J. Overhof, Doping Effects in a-Si: H H. Frifzche, Electronic Properties of Surfaces in a-Si: H C. R. Wronski, The Staebler-Wronski Effect R. J. Nernanich, Schottky Barriers on a-Si: H B. Abeles and 7: Tiedje, Amorphous Semiconductor Superlattices

Part D Jacques 1. Pankove, Introduction D. E. Curlson, Solar Cells G. A. Swartz, Closed-Form Solution of I-V Characteristic for a a-Si: H Solar Cells fsamu Shimizu, Electrophotography Sachio Ishioka, Image Pickup Tubes F! G. LeComber and W E. Spear, The Development of the a-Si: H Field-Effect Transistor and Its Possible Applications D. G. Ast, a-Si: H FET-Addressed LCD Panel S. Kaneko, Solid-state Image Sensor Masakiyo Matsumura, Charge-Coupled Devices M. A. Bosch, Optical Recording A. D’Amico and G. Fortunato, Ambient Sensors Hiroshi Kukirnoto, Amorphous Light-Emitting Devices Roberr J. Phelan, JK,Fast Detectors and Modulators Jacques I. Pankove, Hybrid Structures F! G. LeCornber, A. E. Owen, W E. Spew J. Hajto, and W K. Choi, Electronic Switching in Amorphous Silicon Junction Devices

Volume 22 Lightwave CommunicationsTechnology

Part A Kazuo Nukajima, The Liquid-Phase Epitaxial Growth of InGaAsP W 7: Tsang, Molecular Beam Epitaxy for 111-V Compound Semiconductors G. B. Sfringfellow, Organometallic Vapor-Phase Epitaxial Growth of 111-V Semiconductors G. Beuchet, Halide and Chloride Transport Vapor-Phase Deposition of InGaAsP and GaAs

CONTENTS OF VOLUMES IN

435

THISSERIES

Manijeh Ruzeghi, Low-Pressure Metallo-Organic Chemical Vapor Deposition of Ga,Inl-,AsP1_, F! M. Pefrofl, Defects in 111-V Compound Semiconductors

Alloys

Part B J. F! van der Ziel, Mode Locking of Semiconductor Lasers Kum I.:Lau and Arnmon Yuriv, High-Frequency Current Modulation of Semiconductor Injection Lasers Charles H. Henry, Special Properties of Semiconductor Lasers Yasuharu Suemalsu, Katsumi Kishino, Shigehisu Arai, and Fumio Koyama. Dynamic Single-Mode Semiconductor Lasers with a Distributed Reflector W I: Tsang, The Cleaved-Coupled-Cavity (C3) Laser

Part C R. J. Nelson and N. K. Duttu, Review of InGaAsP InP Laser Structures and Comparison of Their Performance N . Chinone and M. Nakarnura, Mode-Stabilized Semiconductor Lasers for 0.74.8- and 1.1-1.6-pm Regions Yoshiji Horikoshi, Semiconductor Lasers with Wavelengths Exceeding 2 p m B. A. Dean and M. Dixon, The Functional Reliability of Semiconductor Lasers as Optical Transmitters R. H. Saul,Z k? Lee, and C. A. Burus, Light-Emitting Device Design C. L. Zipfel, Light-Emitting Diode-Reliability Tien Pei Lee and Tingye Li, LED-Based Multimode Lightwave Systems Kinichiro Ogawa, Semiconductor Noise-Mode Partition Noise

Part D Federico Capusso, The Physics of Avalanche Photodiodes 7: P. Peursull and M. A. Pollack, Compound Semiconductor Photodiodes Takuo Kunedu, Silicon and Germanium Avalanche Photodiodes S. R. Forrest, Sensitivity of Avalanche Photodetector Receivers for High-Bit-Rate Long-Wavelength Optical Communication Systems J. C. Campbell, Phototransistors for Lightwave Communications

Part E Shyh Wang, Principles and Characteristics of Integrable Active and Passive Optical Devices

Shiorno Margalit and Amnon Yariv, Integrated Electronic and Photonic Devices Tukuoki Mukui, Yoshihisa Yamarnoto, and Tufsuya Kimura, Optical Amplification by Semiconductor Lasers

Volume 23 Pulsed Laser Processing of Semiconductors R. E Wood, C. W White, and R. Z Young, Laser Processing of Semiconductors: An Overview C. W White, Segregation, Solute Trapping, and Supersaturated Alloys G. E. Jellison, J K ,Optical and Electrical Properties of Pulsed Laser-Annealed Silicon R. E Wood and G. E. Jellison, JK,Melting Model of Pulsed Laser Processing R. F: Wood and F: W Young, J K ,Nonequilibrium Solidification Following Pulsed Laser Melting D. H. Lowndes and G. E. Jellison, JK,Time-Resolved Measurement During Pulsed Laser Irradiation of Silicon D.M . Zebner. Surface Studies of Pulsed Laser Irradiated Semiconductors

436

CONTENTS OF VOLUMES IN THIS SERIES

D.H. Lowndes, Pulsed Beam Processing of Gallium Arsenide R. B. James, Pulsed COz Laser Annealing of Semiconductors R. I: Young and R. F: Wood, Applications of Pulsed Laser Processing

Volume 24 Applications of Multiquantum Wells, Selective Doping, and Superlattices C. Weisbuch, Fundamental Properties of 111-V Semiconductor Two-Dimensional Quantized Structures: The Basis for Optical and Electronic Device Applications H. Morkoc and H. Unlu, Factors Affecting the Performance of (Al, Ga)As/GaAs and (Al, Ga)AsflnCaAs Modulation-Doped Field-Effect Transistors: Microwave and Digital Applications N. L Linh, Two-Dimensional Electron Gas FETs: Microwave Applications M. Abe el al., Ultra-High-speed HEMT Integrated Circuits D.S. Chemla, D.A. B. Miller, and fl W Smith, Nonlinear Optical Properties of Multiple Quantum Well Structures for Optical Signal Processing E Capasso, Graded-Gap and Superlattice Devices by Band-Gap Engineering W L Tsang, Quantum Confinement Heterostructure Semiconductor Lasers G. C. Osbourn et al., Principles and Applications of Semiconductor Strained-Layer Superlattices

Volume 25 Diluted Magnetic Semiconductors W Giriat and J. K . Furdyna, Crystal Structure, Composition, and Materials Preparation of Diluted Magnetic Semiconductors W M . Becker, Band Structure and Optical Properties of Wide-Gap A:l-xMnxBlv Alloys at Zero Magnetic Field Saul Oseroff and Piefer H. Keesom, Magnetic Properties: Macroscopic Studies Giebulrowicz and L M. Holden, Neutron Scattering Studies of the Magnetic Structure and Dynamics of Diluted Magnetic Semiconductors J. Kossut, Band Structure and Quantum Transport Phenomena in Narrow-Gap Diluted Magnetic Semiconductors C. Riquaux, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J. A. Gaj, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J. Mycielski, Shallow Acceptors in Diluted Magnetic Semiconductors: Splitting, Boil-off, Giant Negative Magnetoresistance A. K. Ramadas and R. Rodriquez, Raman Scattering in Diluted Magnetic Semiconductors l? A. Wolff, Theory of Bound Magnetic Polarons in Semimagnetic Semiconductors

Volume 26

111-V Compound Semiconductors and Semiconductor Properties of Superionic Materials

Zou Yuami, 111-V Compounds H. K Winston, A. L Huntec H. Kimuru, and R. E. Lee, InAs-Alloyed GaAs Substrates for Direct Implantation l? K. Bhattacharya and S. Dhar, Deep Levels in 111-V Compound Semiconductors Grown by MBE Yu. Ya. Gurevich and A. K. Iuanou-Shits, Semiconductor Properties of Supersonic Materials

Volume 27 High Conducting Quasi-One-DimensionalOrganic Crystals E. M. Conwell, Introduction to Highly Conducting Quasi-One-Dimensiona1 Organic Crystals I. A. Howard, A Reference Guide to the Conducting Quasi-One-Dimensional Organic Molecular Crystals J. l? Pouquet, Structural Instabilities

CONTENTS OF VOLUMES IN THIS SERIES

437

E. M. Conwell, Transport Properties C. S. Jacobsen, Optical Properties J. C. Scoff,Magnetic Properties L. Zuppimli, Irradiation Effects: Perfect Crystals and Real Crystals

Volume 28 Measurement of High-speed Signals in Solid State Devices J. Frey and D.Ioannou, Materials and Devices for High-speed and Optoelectronic Applications H. Schumucher and E. Strid, Electronic Wafer Probing Techniques D. H. Ausron, Picosecond Photoconductivity: High-speed Measurements of Devices and Materials J. A. Valdmanis, Electro-Optic Measurement Techniques for Picosecond Materials, Devices, and Integrated Circuits J. M. Wiesenfeld and R. K. Jain, Direct Optical Probing of Integrated Circuits and High-speed Devices G. Plows, Electron-Beam Probing A. M. Weiner and R. B. Marcus, Photoemissive Probing

Volume 29 Very High Speed Integrated Circuits: Gallium Arsenide LSI M.Kuzuharu and 7: Nazuki, Active Layer Formation by Ion Implantation H. Husimoto, Focused Ion Beam Implantation Technology L Nozuki and A. Higashisuku. Device Fabrication Process Technology M. In0 and L Tukada, GaAs LSI Circuit Design M. Hirayumu, M. Ohmori, and K. Yamusuki, GaAs LSI Fabrication and Performance

Volume 30 Very High Speed Integrated Circuits: Heterostructure H. Wafanabe, L Mizutuni, and A. Usui, Fundamentals of Epitaxial Growth and Atomic Layer Epitaxy S. Hiyumizu, Characteristics of Two-Dimensional Electron Gas in 111-V Compound Heterostructures Grown by MBE L Nakanisi, Metalorganic Vapor Phase Epitaxy for High-Quality Active Layers I: Nimuru, High Electron Mobility Transistor and LSI Applications Z Sugefu and I: Ishibashi, Hetero-Bipolar Transistor and LSI Application H. Matsuedu, L Tanaka, and M. Nukamuru, Optoelectronic Integrated Circuits

Volume 3 1 Indium Phosphide: Crystal Growth and Characterization J. P. Farges, Growth of Discoloration-free InP M. J. McCollum and G. E. Stillman, High Purity InP Grown by Hydride Vapor Phase Epitaxy I: Inadu and 7: Fukuda, Direct Synthesis and Growth of Indium Phosphide by the Liquid Phosphorous Encapsulated Czochralski Method 0. Oda, K. Kutugiri, K. Shinohara, S. Katsuru, Y Tukahashi, K. Kainosho, K. Kohiro, and R. Hirano, InP Crystal Growth, Substrate Preparation and Evaluation K. Tuda, M. Tatsurni, M. Morioku, I: Araki, and L Kawase, InP Substrates: Production and Quality Control M. Razeghi, LP-MOCVD Growth, Characterization, and Application of InP Material 7: A. Kennedy and P. J. Lin-Chung, Stoichiometric Defects in InP

Volume 32 Strained-Layer Superlattices: Physics T. P. Pearsall, Strained-Layer Superlattices Fred H. Pollack, Effects of Homogeneous Strain on the Electronic and Vibrational Levels in Semiconductors

438

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J. Y. Marzin, J. M. Gerrird, I? Voisin,and J.A. Brum, Optical Studies of Strained 111-V Heterolayers R. People and S. A. Jackson, Structurally Induced States from Strain and Confinement M. Jarus, Microscopic Phenomena in Ordered Superlattices

Volume 33 Strained-Layer Superlattices: Materials Science and Technology R. Hull and J. C. Bean, Principles and Concepts of Strained-Layer Epitaxy William J. Schafi Paul J. Tuskel; Marc C. Fuisy, and Lester E Eastmun, Device Applications of Strained-Layer Epitaxy S. T. Picraux, B. L. Doyle, and J. Y. Tsao, Structure and Characterization of Strained-Layer Superlattices E. Kasper and I? Schaffer, Group IV Compounds Dale L. Martin, Molecular Beam Epitaxy of IV-VI Compounds Heterojunction Robert L. Gunshoc Leslie A. Kolodziejski, Arto V Nurmikko, and Nobuo Otsuka, Molecular Beam Epitaxy of 11-VI Semiconductor Microstructures

Volume 34 Hydrogen in Semiconductors J. I. Pankove and N. M. Johnson, Introduction to Hydrogen in Semiconductors C. H . Seager, Hydrogenation Methods J. I. Pankove, Hydrogenation of Defects in Crystalline Silicon J. W Corbett, I? Dea'k, U. V Desnica, and S. J. Pearton, Hydrogen Passivation of Damage Centers in Semiconductors S.J. Pearfon, Neutralization of Deep Levels in Silicon J. I. Pankove, Neutralization of Shallow Acceptors in Silicon N. M . Johnson, Neutralization of Donor Dopants and Formation of Hydrogen-Induced Defects in n-Type Silicon M. Stavola and S. J. Peartun, Vibrational Spectroscopy of Hydrogen-Related Defects in Silicon A. D. Marwick, Hydrogen in Semiconductors: Ion Beam Techniques C. Herring and N. M. Johnson, Hydrogen Migration and Solubility in Silicon E. E. Haller, Hydrogen-Related Phenomena in Crystalline Germanium J. Kakalios, Hydrogen Diffusion in Amorphous Silicon J. Chevaliel; 8.Clerjaud, and B. Pajot, Neutralization of Defects and Dopants in Ill-V Semiconductors G. G. DeLeo and W B. Fowler, Computational Studies of Hydrogen-Containing Complexes in Semiconductors R. F Kiefl and T. L. Estle, Muonium in Semiconductors C. C. Van de Walle, Theory of Isolated Interstitial Hydrogen and Muonium in Crystalline Semiconductors

Volume 35

Nanostructured Systems

Mark Reed, Introduction H. van Huuten, C. W J. Beenakkel; and B. J. van Wees, Quantum Point Contacts G. Timp, When Does a Wire Become an Electron Waveguide? M. Buttiker, The Quantum Hall Effects in Open Conductors W Hansen, J. I? Kotthaus, and U. Merkt, Electrons in Laterally Periodic Nanostructures

Volume 36 The Spectroscopy of Semiconductors D. Heiman, Spectroscopy of Semiconductors at Low Temperatures and High Magnetic Fields Arto V Nurmikko, Transient Spectroscopy by Ultrashort Laser Pulse Techniques

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439

A. K. Ramdas and S. Rodriguez, Piezospectroscopy of Semiconductors Orest J. Glembocki and Benjamin K Shanabrook, Photoreflectance Spectroscopy of Microstructures David G. Seiler; Christopher L. Littler, and Margaret H. Wiler, One- and Two-Photon Magneto-Optical Spectroscopy of InSb and Hgl-,Cd,Te

Volume 37 The Mechanical Properties of Semiconductors A.-B. Chen, Arden Sher and W 1: Yost, Elastic Constants and Related Properties of Semiconductor Compounds and Their Alloys David R. Clarke, Fracture of Silicon and Other Semiconductors Hans Siefhoff, The Plasticity of Elemental and Compound Semiconductors Sivaraman Guruswamy, Katherine T Faber and John P: Hirth, Mechanical Behavior of Compound Semiconductors Subhanh Mahajan, Deformation Behavior of Compound Semiconductors John P. Hirrh, Injection of Dislocations into Strained Multilayer Structures Don KendaJJ, Charles B. Fleddermann, and Kevin J. Malloy, Critical Technologies for the Micromachining of Silicon Ikuo Matsuba and Kinji Mokuya, Processing and Semiconductor Thermoelastic Behavior

Volume 38 Imperfections in I I W Materials Lido Scherz and Matthias Schefler, Density-Functional Theory of sp-Bonded Defects in IIW Semiconductors Maria Kaminska and Eicke R. Weber, El2 Defect in GaAs David C. Look, Defects Relevant for Compensation in Semi-Insulating GaAs R. C. Newman, Local Vibrational Mode Spectroscopy of Defects in IIW Compounds Andrzej M. Hennel, Transition Metals in I I W Compounds Kevin J. Malloy and Ken Khachaturyan, DX and Related Defects in Semiconductors R Swaminuthan and Andrew S. Jordan, Dislocations in IIW Compounds Krzysztof W Nauka, Deep Level Defects in the Epitaxial IIW Materials

Volume 39 Minority Carriers in Ill-V Semiconductors: Physics and Applications Niloy K . Dutra, Radiative Transitions in GaAs and Other 111-V Compounds Richard K . Ahrenkiel, Minority-Carrier Lifetime in 111-V Semiconductors Tomofumi Furura, High Field Minority Electron Transport in p-GaAs Mark S. Lundstrom, Minority-Carrier Transport in 111-V Semiconductors Richard A. Abram, Effects of Heavy Doping and High Excitation on the Band Structure of GaAs David Yevick and Witold Bardyszewski, An Introduction to Non-Equilibrium Many-Body Analyses of Optical Processes in 111-V Semiconductors

Volume 40 Epitaxial Microstructures E. F: Schubert, Delta-Doping of Semiconductors: Electronic, Optical, and Structural Properties of Materials and Devices A. Gossard, M. Sundaram, and f? Hupkins, Wide Graded Potential Wells P: Petroff, Direct Growth of Nanometer-Size Quantum Wire Superlattices E. Kapon, Lateral Patterning of Quantum Well Heterostructures by Growth of Nonplanar Substrates H. Temkin, D.Gershoni, and M. Panish, Optical Properties of Gal-,In,As/InP Quantum Wells

440

CONTENTS OF VOLUMES I N THSS SERIES

Volume 41

High Speed HeterostructureDevices

E Capasso, E Beltram, S. Sen, A. Pahlevi, and A. K Cho, Quantum Electron Devices: Physics and Applications k? Solomon, D.J. Frank, S. L. Wright, and E Canora, GaAs-Gate Semiconductor-Insulator-Semiconductor FET M. H. Hashemi and U. K. Mishra, Unipolar InP-Based Transistors R. Kiehl, Complementary Heterostmcture FET Integrated Circuits I: Ishibashi, GaAs-Based and InP-Based Heterostructure Bipolar Transistors H. C. Liu and T. C. L. G. Sollner, High-Frequency-Tunneling Devices H . Ohnishi, I: More, M. Takatsu, K. Imamura, and N. Yokoyama, Resonant-Tunneling Hot-Electron Transistors and Circuits

Volume 42 Oxygen in Silicon F: Shimura, Introduction to Oxygen in Silicon W Lin, The Incorporation of Oxygen into Silicon Crystals 7: J. Schafier and D.K . Schroder, Characterization Techniques for Oxygen in Silicon W M. Bullis, Oxygen Concentration Measurement S. M. Hu, Intrinsic Point Defects in Silicon B. Pajot, Some Atomic Configurations of Oxygen J. Michel and L. C. Kimerling, Electical Properties o f Oxygen in Silicon R. C. Newman and R. Jones, Diffusion of Oxygen in Silicon ?: E Tan and W J. Taylor, Mechanisms of Oxygen Precipitation: Some Quantitative Aspects M. Schrems, Simulation o f Oxygen Precipitation K. Simino and I. Yonenaga, Oxygen Effect on Mechanical Properties W Bergholz, Grown-in and Process-Induced Effects F: Shimura, Intrinsic/lntemal Gettering H. Tsuyu, Oxygen Effect on Electronic Device Performance

Volume 43 Semiconductors for Room Temperature Nuclear Detector Applications R. B. James and 7: E. Schlesinger, Introduction and Overview L. S. Darken and C. E. Cox, High-Purity Germanium Detectors A. Burger: D. Nason, L. Van den Berg, and M . Schieber, Growth of Mercuric Iodide X . J. Bao, I: E. Schlesinger, and R. B. James, Electrical Properties o f Mercuric Iodide X . J. Bao, R. B. James, and T. E. Schlesinger, Optical Properties of Red Mercuric Iodide M. Huge-Ali and F? Siffert, Growth Methods of CdTe Nuclear Detector Materials M. Hage-Ali and P Sigert, Characterization of CdTe Nuclear Detector Materials M. Huge-Ali and k? Sifert, CdTe Nuclear Detectors and Applications R. B. James, I: E. Schlesingeq J. Lund, and M. Schieber, C ~ I _ ~ Z spectrometers ~ , T ~ for Gamma and X-Ray Applications D. S. McGregor, J. E. Kammeraad, Gallium Arsenide Radiation Detectors and Spectrometers J. C. Lund, E Olschner, and A. Burger, Lead Iodide M . R. Squillante, and K. S. Shah, Other Materials: Status and Prospects I.: M. Gerrish, Characterization and Quantification of Detector Performance J. S. Iwanczyk and B. E. Patt, Electronics for X-ray and Gamma Ray Spectrometers M. Schieber: R. B. James, and I: E. Schlesinger, Summary and Remaining Issues for Room Temperature Radiation Spectrometers

CONTENTS OF VOLUMES IN

Volume 44

THISSERIES

441

11-IV Blue/Green Light Emitters: Device Physics and Epitaxial Growth

J. Han and R. L. Gunshor, MBE Growth and Electrical Properties of Wide Bandgap ZnSe-based 11-VI Semiconductors Shizuo Fujita and Shigeo Fujita, Growth and Characterization of ZnSe-based 11-VI Semiconductors by MOVPE Easen Ho and Leslie A. Kolodziejski, Gaseous Source UHV Epitaxy Technologies for Wide Bandgap 11-VI Semiconductors Chris G. Van de Walk, Doping of Wide-Band-Gap 11-VI Compounds-Theory Roberto Cingolani, Optical Properties of Excitons in ZnSe-Based Quantum Well Heterostructures A. Ishibashi and A. K Nurmikko, 11-VI Diode Lasers: A Current View of Device Performance and Issues Supratik Guha and John Petruzello, Defects and Degradation in Wide-Gap 11-VI-based Structures and Light Emitting Devices

Volume 45

Effect of Disorder and Defects in Ion-Implanted Semiconductors: Electrical and Physiochemical Characterization

Heiner Ryssel, Ion Implantation into Semiconductors: Historical Perspectives You-Nian Wang and Teng-Cai Ma, Electronic Stopping Power for Energetic Ions in Solids Sachiko 7: Nakagawa, Solid Effect on the Electronic Stopping of Crystalline Target and Application to Range Estimation G. Miiller; S. Kalbitzer and G. N. Greaves, Ion Beams in Amorphous Semiconductor Research Jumuna Boussey-Said, Sheet and Spreading Resistance Analysis of Ion Implanted and Annealed Semiconductors M. L. Polignano and G. Queirolo, Studies of the Stripping Hall Effect in Ion-Implanted Silicon J. Stoernenos, Transmission Electron Microscopy Analyses Roberta Nipoti and Marc0 Servidori, Rutherford Backscattering Studies of Ion Implanted Semi-conductors P Zuurnseil, X-ray Diffraction Techniques

Volume 46 Effect of Disorder and Defects in Ion-Implanted Semiconductors: Optical and Photothermal Characterization M. Fried, 7: Lohner and J. Gyulai, Ellipsometric Analysis Antonio3 Seas and Constantinos Christojdes, Transmission and Reflection Spectroscopy on Ion Implanted Semiconductors Andreas Othonos and Constantinos Christojides, Photoluminescence and Raman Scattering of Ion Implanted Semiconductors. Influence of Annealing Constantinos Christojdes, Photomodulated Thermoreflectance Investigation of Implanted Wafers. Annealing Kinetics of Defects U.Zarnrnit, Photothermal Deflection Spectroscopy Characterization of Ion-Implanted and Annealed Silicon Films Andreas Mandelis, Arief Budiman and Miguel Vargas, Photothermal Deep-Level Transient Spectroscopy of Impurities and Defects in Semiconductors R. Kalish and S. Charbonneau,Ion Implantation into Quantum-Well Structures Alexandre M. Myasnikov and Nikolay N. Gerasimenko, Ion Implantation and Thermal Annealing of 111-V Compound Semiconducting Systems: Some Problems of 111-V Narrow Gap Semiconductors

442

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Volume 47 Uncooled Infrared Imaging Arrays and Systems R. G. Buser and M. l? Tompsett, Historical Overview f? W. Kruse, Principles of Uncooled Infrared Focal Plane Arrays R. A. Wood, Monolithic Silicon Microbolometer Arrays C. M. Hanson, Hybrid Pyroelectric-FerroelectricBolometer Arrays D. L. Polla and J. R. Choi, Monolithic Pyroelectric Bolometer Arrays N. Teranishi, Thermoelectric Uncooled Infrared Focal Plane Arrays M. E Tompsetf, Pyroelectric Vidicon ?: W. Kenny, Tunneling Infrared Sensors J. R. Vig, R. L. Filler and E: Kim, Application of Quartz Microresonators to Uncooled Infrared Imaging Arrays l? W. Kruse, Application of Uncooled Monolithic Thermoelectric Linear Arrays to Imaging Radiometers

Volume 48

High Brightness Light Emitting Diodes

G. B. Stringfellow, Materials Issues in High-Brightness Light-Emitting Diodes M. G. Craford, Overview of Device Issues in High-Brightness Light-Emitting Diodes E M. Steranka, AlGaAs Red Light-Emitting Diodes C. H. Chen, S. A. Stockman, M. J. Peanasb, and C. l? Kuo, OMVPE Growth of AlGaInP for High Efficiency Visible Light-Emitting Diodes E A. Kish and R. M. Fletcher, AlGaInP Light-Emitting Diodes M. W. Hodapp, Applications for High Brightness Light-Emitting Diodes I. Akasaki and H. Amano, Organometallic Vapor Epitaxy of GaN for High Brightness Blue Light-Emitting Diodes S. Nakamura, Group 111-V Nitride Based Ultraviolet-Blue-Green-Yellow Light-Emitting Diodes and Laser Diodes

Volume 49

Light Emission in Silicon: from Physics to Devices

David J. Lockwood, Light Emission in Silicon Gerhard Absfreifer,Band Gaps and Light Emission in Si/SiGe Atomic Layer Structures Thomas G. Brown and Dennis G. Hall, Radiative Isoelectronic Impurities in Silicon and Silicon-Germanium Alloys and Superlattices 1. Michel, L. V C. Assali, M. 7: Morse, and L. C. Kimerling, Erbium in Silicon Yoshihiko Kanemifsu, Silicon and Germanium Nanoparticles Philippe M. Fauchet, Porous Silicon: Photoluminescence and Electroluminescent Devices C. Delerue, G. Allan, and M. Lannoo, Theory of Radiative and Nonradiative Processes in Silicon Nanocrystallites Louis Brus, Silicon Polymers and Nanocrystals

Volume 50 Gallium Nitride (GaN) J. I. Pankove and 7: D. Moustakas, Introduction S. I? DenBaars and S. Keller, Metalorganic Chemical Vapor Deposition (MOCVD) of Group 111Nitrides W. A. Bryden and 7: J. Kistenmacher, Growth of Group 111-A Nitrides by Reactive Sputtering N. Newman, Thermochemistry of 111-N Semiconductors S.J. Pearton and R. J. Shul, Etching of 111Nitrides S. M. Bedair, Indium-based Nitride Compounds A. Trampert, 0.Brandt, and K. H. Ploog, Crystal Structure of Group 111Nitrides

CONTENTS OF VOLUMES IN

THISSERIES

443

H. Morkoc, E Hamdani, and A. Salvador, Electronic and Optical Properties of 111-V Nitride based Quantum Wells and Superlattices K. Doverspike and J. I. Pankove, Doping in the 111-Nitrides I: Suski and P. Perlin, High Pressure Studies of Defects and Impurities in Gallium Nitride B. Monemar, Optical Properties of GaN W R. L.Lambrecht, Band Structure of the Group 111 Nitrides N. E. Christensen and P. Perlin, Phonons and Phase Transitions in GaN S. Nakamura, Applications of LEDs and LDs I. Akasaki and H. A m n o , Lasers J. A. Cooper;JK,Nonvolatile Random Access Memories in Wide Bandgap Semiconductors

Volume 5 1A Identification of Defects in Semiconductors George D.Warkins, EPR and ENDOR Studies of Defects in Semiconductors J.-M. Spaeth, Magneto-Optical and Electrical Detection of Paramagnetic Resonance in Semiconductors I: A. Kennedy and E. R. Glaser, Magnetic Resonance of Epitaxial Layers Detected by Photoluminescence K. H. Chow, B. Hitri, and R. E Kiefi, fiSR on Muonium in Semiconductors and Its Relation to Hydrogen Kimmo Saarinen, Pekka Hautojarvi, and Catherine Corbel, Positron Annihilation Spectroscopy of Defects in Semiconductors R. Jones and P. R. Briddon, The A b Initio Cluster Method and the Dynamics of Defects in Semiconductors

Volume 5 1B Identification of Defects in Semiconductors Gordon Davies, Optical Measurements of Point Defects P. M. Mooney, Defect Identification Using Capacitance Spectroscopy Michael Stavola, Vibrational Spectroscopy of Light Element Impurities in Semiconductors P. Schwande,: W D. Rau, C. Kisielowski, M. Gribelyuk, and A. Ourmazd, Defect Processes in Semiconductors Studied at the Atomic Level by Transmission Electron Microscopy Nikos D. Jager and Eicke R. Weber, Scanning Tunneling Microscopy of Defects in Semiconductors

Volume 52 S i c Materials and Devices K. Jarrendahl and R. E Davis, Materials Properties and Characterization of SIC V A. Dmitriev and M . G. Spencer, S i c Fabrication Technology: Growth and Doping 1.: Saxena and A. J. Steckl, Building Blocks for SIC Devices: Ohmic Contacts, Schottky Contacts, and p n Junctions M. S. Shur, S i c Transistors C. D. Brandt, R. C. Clarke, R. R. Siergiej, J. B. Casady, A. W Morse, S. Sriram, and A. K. Aganval, S i c for Applications in High-Power Electronics R. J. Trew, Sic Microwave Devices J. Edmond, H. Kong, G. Negley, M. Leonard, K. Doverspike, W Weeks, A. Suvorov, D. Waltz, and C. Carte6 Jr., Sic-Based UV Photodiodes and Light-Emitting Diodes H. Morkoc, Beyond Silicon Carbide! 111-V Nitride-Based Heterostructures and Devices

Volume 53 Cumulative Index

444

CONTENTS OF VOLUMES I N

THISSERIES

Volume 54 High Pressure in Semiconductor Physics I William Paul, High Pressure in Semiconductor Physics: A Historical Overview N. E. Christensen, Electronic Structure Calculations for Semiconductors under Pressure R. J. Nelmes and M. I. McMahon, Structural Transitions in the 111-V and 11-VI and Group-IV Semiconductors under Pressure A. R. Goni and K. Syassen, Optical Properties of Semiconductors under Pressure R Trautman, M. Baj, and J. M. Earanowski, Hydrostatic Pressure and Uniaxial Stress in Investigations of the EL2 Defect in GaAs M. Li and R !I Yu, High Pressure Study of DX Centers Using Capacitance Techniques 7: Suski, Spatial Correlations of Impurity Charges in Doped Semiconductors N. Kuroda, Pressure Effects on the Electronic Properties of Diluted Magnetic Semiconductors

Volume 55

High Pressure in Semiconductor Physics I1

D.K. Maude and J. C. Portal, Parallel Transport in Low-Dimensional Semiconductor Structures R C. Klipstein, Tunneling Under Pressure: High-pressure Studies of Vertical Transport in Semiconductor Heterostructures Evangelos Anastassakis and Manuel Cardona, Phonons, Strains, and Pressure in Semiconductors Fred H. Pollak, Effects of External Uniaxial Stress on the Optical Properties of Semiconductors and Semiconductor Microstructures A. R. Adams, M. Silvec and J. Allam, Semiconductor Optoelectronic Devices S.Porowski and I. Grzegory, The Application o f High Nitrogen Pressure in the Physics and Technology of 111-N Compounds Mohammad Yousuf,Diamond Anvil Cells in High Pressure Studies of Semiconductors

Volume 56 Germanium Silicon: Physics and Materials John C. Bean, Growth Techniques and Procedures Donald E. Savage, Feng Liu, Volkmar Zielasek, and Max G. Lagally, Fundamental Mechanisms of Film Growth R. Hull, Misfit Strain and Accommodation in SiGe Heterostructures M. J. Shaw and M. Jaros, Fundamental Physics of Strained Layer GeSi: Quo Vadis? Fernando Cerdeirn, Optical Properties Steven A. Ringel and Patrick N. Grillot, Electronic Properties and Deep Levels in Germanium-Silicon Joe C. Campbell, Optoelectronics in Silicon and Germanium Silicon Karl Eberl, Karl Brunner and Oliver G. Schmidt, Sil-,C, and Sil-,_,Ge,C, Alloy Layers

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