Developments in Surface Contamination and Cleaning

DEVELOPMENTS IN SURFACE CONTAMINATION AND CLEANING

Developments in Surface Contamination and Cleaning Fundamentals and Applied Aspects

Edited by Rajiv Kohli Houston, Texas and K. L. Mittal Consultant, Adhesion and Surface Cleaning Hopewell Junction, New York

Norwich, NY, USA

Copyright # 2008 by William Andrew, Inc. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the Publisher. Library of Congress Cataloging-in-Publication Data Developments in surface contamination and cleaning : fundamentals and applied aspects / edited by Rajiv Kohli and K.L. Mittal. p. cm. Includes bibliographical references and index. ISBN 978-0-8155-1555-5 (978-0-8155) 1. Surfaces (Technology)–Inspection. 2. Surface contamination–Prevention. 3. Particles–Measurement. 4. Cleaning. 5. Coatings. 6. Dust control. I. Kohli, Rajiv, 1947- II. Mittal, K. L., 1945TA418.7.D876 620'.44–dc22

2008 2007034322

Printed in the United States of America This book is printed on acid-free paper. 10 9 8 7 6 5 4 3 2 1 Published by: William Andrew Inc. 13 Eaton Avenue Norwich, NY 13815 1-800-932-7045 www.williamandrew.com NOTICE To the best of our knowledge the information in this publication is accurate; however the Publisher does not assume any responsibility or liability for the accuracy or completeness of, or consequences arising from, such information. This book is intended for informational purposes only. Mention of trade names or commercial products does not constitute endorsement or recommendation for their use by the Publisher. Final determination of the suitability of any information or product for any use, and the manner of that use, is the sole responsibility of the user. Anyone intending to rely upon any recommendation of materials or procedures mentioned in this publication should be independently satisfied as to such suitability, and must meet all applicable safety and health standards.

Contents

Introduction ............................................................................... Rajiv Kohli and Kash Mittal PART I

xxxiii

FUNDAMENTALS. . . . . . . . . . . . . . . . . . . . . . . . . .

1

1 The Physical Nature of Very, Very Small Particles and its Impact on Their Behavior . . . . . . . . . . . . . . . . . . . . . . . . . Othmar Preining

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1.1 1.2 1.3

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Spectrum of Aerosol Particle Sizes . . . . . . . . . . Atoms and Molecules—Concepts and Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 The Model of a Gas . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Particles and Gas Molecules . . . . . . . . . . . . . . . . . . 1.6 Particle Interactions . . . . . . . . . . . . . . . . . . . . . . . . 1.6.1 Coagulation . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.2 Homogeneous nucleation . . . . . . . . . . . . . . . 1.6.3 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Nanoparticles as Molecular Clusters . . . . . . . . . . . . 1.8 An Interaction Model for Nanometer–Sized Particles 1.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 8 10 15 15 15 17 18 19 21 23 23

2 Elucidating the Fundamental Interactions of Very Small Particles: Ultrafast Science . . . . . . . . . . . . . . . . . . . . . . . . . . Carlo Altucci and Domenico Paparo

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Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Techniques for the Generation of Ultrashort Pulses. 2.2.1 Basic concepts: mode locking and early generations of ultrashort laser sources . . . . . 2.2.2 Sub-100-fs pulses and chirped pulse amplification . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 The few-optical-cycle regime . . . . . . . . . . . . v

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CONTENTS 2.2.4 The carrier-envelope-phase (CEP) . . . . . . . 2.2.5 Techniques for ultrashort pulse measurements . . . . . . . . . . . . . . . . . . . . . 2.3 Dynamics of Atoms and Molecules in Strong Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.1 Perturbative regime . . . . . . . . . . . 2.3.1.2 The strong field regime . . . . . . . . 2.3.1.3 High-order harmonic generation . . 2.3.2 Attosecond pulse generation and characterization: the present border line of ultrafast science . . . . . . . . . . . . . . . . . . . . 2.3.3 Molecules . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.1 The birth of femtochemistry: probing the transition states . . . . . 2.3.3.2 Some basic theoretical concepts on wave-packet formation and dynamics. . . . . . . . . . . . . . . . . . . 2.3.3.3 Diatomic molecule and lasermolecule interaction . . . . . . . . . . . 2.3.4 Simple properties of a wave-packet . . . . . . 2.3.4.1 Wavepacket generation and influence of chirping . . . . . . . . . . 2.4 Bond-breaking in Single Molecules . . . . . . . . . . . 2.5 Controlling Molecular Populations and Chemical Reactions by Ultrafast Pulses . . . . . . . . . . . . . . . 2.6 Polyatomic Molecules and Nonadiabatic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Recent Results in Ultrafast Crystallography: UED and Time-resolved X-rays . . . . . . . . . . . . . . . . . . 2.8 New Nonlinear Optical Techniques for Probing Surfaces: Surface Second-harmonic and Sum-frequency Generation . . . . . . . . . . . . . . . . . 2.8.1 Theoretical considerations . . . . . . . . . . . . . 2.8.2 Local-field-induced enhancement of SSHG on metal surfaces . . . . . . . . . . . . . . . . . . . 2.8.3 Metal nanoparticles . . . . . . . . . . . . . . . . . 2.8.4 Femtochemistry of surfaces probed by pump-probe SSFG and SSHG. . . . . . . . . . 2.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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vii

CONTENTS 3 Transport and Deposition of Aerosol Particles . . . . . . . . . . . . Daniel J. Rader and Anthony S. Geller 3.1 3.2 3.3

3.4 3.5

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Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . Noncontinuum Considerations . . . . . . . . . . . . . Lagrangian Particle Equation of Motion . . . . . . 3.3.1 Fluid–particle drag force . . . . . . . . . . . . . 3.3.1.1 Fluid-drag force: assumptions and practical considerations . . . . 3.3.2 Gravitational force . . . . . . . . . . . . . . . . . 3.3.3 Thermophoretic force . . . . . . . . . . . . . . . 3.3.3.1 Continuum regime limit . . . . . . . 3.3.3.2 Free molecule regime limit . . . . . 3.3.4 Electrostatic force. . . . . . . . . . . . . . . . . . Inertial Effects . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Nondimensionalization . . . . . . . . . . . . . . Drift Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Gravitational drift velocity . . . . . . . . . . . 3.5.2 Thermophoretic drift velocity . . . . . . . . . 3.5.3 Electric drift velocity . . . . . . . . . . . . . . . Eulerian Formulation . . . . . . . . . . . . . . . . . . . . 3.6.1 Particle diffusion coefficient . . . . . . . . . . 3.6.2 Nondimensional formulation . . . . . . . . . . Particle Transport and Deposition in a Parallel Plate Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Fluid transport equations . . . . . . . . . . . . 3.7.1.1 Flow field in the showerhead holes. . . . . . . . . . . . . . . . . . . . . 3.7.1.2 Fluid transport between parallel plates . . . . . . . . . . . . . . 3.7.1.3 Summary: fluid flow analysis for the parallel plate geometry . . . . . 3.7.2 Particle collection efficiency. . . . . . . . . . . 3.7.3 Particles entering through the showerhead 3.7.3.1 External force limit . . . . . . . . . . 3.7.4 Particle traps/in situ nucleation . . . . . . . . 3.7.4.1 Efficiency for the Lagrangian formulation . . . . . . . . . . . . . . . . 3.7.4.2 Efficiency for the Eulerian formulation . . . . . . . . . . . . . . . . 3.7.4.3 External force limit . . . . . . . . . .

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viii

CONTENTS

3.7.5 Diffusion-enhanced deposition from traps or in situ nucleation . . . . . . . . . . . . . . . . . 3.7.5.1 Problem definition . . . . . . . . . . . . 3.7.5.2 Solution of the Eulerian particle transport equation . . . . . . . . . . . . 3.7.5.3 Particle collection efficiency . . . . . 3.7.5.4 Particle flux. . . . . . . . . . . . . . . . . 3.7.6 Nondimensional results. . . . . . . . . . . . . . . 3.7.6.1 Efficiency at intermediate Peclet numbers . . . . . . . . . . . . . . . . . . . 3.7.7 Dimensional results . . . . . . . . . . . . . . . . . 3.7.7.1 Trap height effects . . . . . . . . . . . . 3.7.7.2 Pressure effects . . . . . . . . . . . . . . 3.7.7.3 Mass flow rate effects . . . . . . . . . 3.7.7.4 Effect of thermophoresis . . . . . . . 3.7.8 Summary: diffusion-enhanced deposition . . 3.8 Inertia-Enhanced Deposition . . . . . . . . . . . . . . . . 3.8.1 Particle transport in the showerhead holes . 3.8.2 Particle transport between parallel plates . . 3.8.2.1 Asymptotic limit of critical Stokes number . . . . . . . . . . . . . . . . . . . . 3.8.3 Coupled transport—nondimensional results 3.8.3.1 Critical Stokes numbers . . . . . . . . 3.8.3.2 Grand design curves . . . . . . . . . . 3.8.3.3 External forces . . . . . . . . . . . . . . 3.8.3.4 Parabolic profile . . . . . . . . . . . . . 3.8.4 Coupled transport—dimensional results . . . 3.9 Chapter Summary and Practical Guidelines . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Relevance of Particle Transport in Surface Deposition and Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . Chao-Hsin Lin and Chao Zhu

267

4.1 4.2 4.3 4.4 4.5 4.6

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Particle–solid Surface Interactions . . . . . . . . . . . . . . . . Dry Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermophoresis and Its Relevance in Surface Cleaning . Electrostatic Force and Its Relevance in Surface Cleaning Dielectrophoresis and Its Relevance in Surface Cleaning

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ix

CONTENTS 4.7 Abrasive Erosion and Its Relevance in Surface Cleaning 4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

288 292 294

5 Tribological Implication of Particles . . . . . . . . . . . . . . . . . . . Koji Kato

299

5.1 5.2 5.3

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Micro-Site for Generation of Wear Particles. . . . Wear Modes and Particles. . . . . . . . . . . . . . . . . . . . 5.3.1 Adhesive transfer of atoms in contact and separation . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Adhesive transfer of flake-like particles in sliding contact . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Micro-cutting and generation of fine feather-like particles in abrasive sliding. . . . . . 5.3.4 Surface plastic flow and a thin filmy wear particle generation by repeated contacts . . . . . 5.3.5 Crack initiation and propagation in the subsurface of contact and generation of a flake-like particle by repeated contact . . . . . . 5.3.6 Tribo-oxidation and generation of particles of oxides by repeated contacts in air and water . . . . . . . . . . . . . . . . . . . . . . . . 5.3.7 Wear particles generated in sliding of steels in oil with additives . . . . . . . . . . . . . . . . . . . 5.4 Wear Rate and Number of Generated Wear Particles 5.5 The Size Distribution of Wear Particles . . . . . . . . . . 5.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Solid wear particles . . . . . . . . . . . . . . . . . . . 5.6.2 Gas molecules by wear . . . . . . . . . . . . . . . . . 5.6.3 Triboemission of electrons, ions, photons, and particles . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Airborne Molecular Contamination: Contamination on Substrates and the Environment in Semiconductors and Other Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taketoshi Fujimoto, Kikuo Takeda and Tatsuo Nonaka

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CONTENTS 6.1

6.2

6.3

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Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Changes in semiconductor integration . . . . 6.1.3 Changes in target contaminant . . . . . . . . . Definitions, Types and Sources of AMCs . . . . . . . 6.2.1 Definition of ‘‘Airborne Molecular Contamination’’ . . . . . . . . . . . . . . . . . . . . 6.2.2 Examples of AMC-induced problems in the manufacturing process . . . . . . . . . . . . . . . 6.2.3 Nature of AMC-induced effects . . . . . . . . . 6.2.4 Classification of airborne molecular contaminants . . . . . . . . . . . . . . . . . . . . . . 6.2.4.1 SEMATECH technology transfer report No. 95052812A-TR . . . . . . 6.2.4.2 International technology roadmap for semiconductor (ITRS) 1999 . . . . . . . . . . . . . . . . Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Substrate surface analysis . . . . . . . . . . . . . 6.3.1.1 Quantitative analysis . . . . . . . . . . 6.3.1.2 Surface (instrumental) analysis . . . 6.3.2 Air analysis . . . . . . . . . . . . . . . . . . . . . . . 6.3.2.1 Acids . . . . . . . . . . . . . . . . . . . . . 6.3.2.2 Bases: ammonia (NH3) and amines. . . . . . . . . . . . . . . . . . . . . 6.3.2.3 Condensables: organic compounds 6.3.2.4 Dopants: boron, phosphorus, and metals . . . . . . . . . . . . . . . . . 6.3.3 Outgassing evaluation method for construction materials. . . . . . . . . . . . . . . . 6.3.3.1 IEST WG 031 . . . . . . . . . . . . . . . 6.3.3.2 JACA No. 34-1999 . . . . . . . . . . . Nature of Airborne Molecular Contamination and Its Effects . . . . . . . . . . . . . . . 6.4.1 Investigation of the properties of AMCs. . . 6.4.1.1 Effects of rinsing the outdoor air . 6.4.1.2 Acids . . . . . . . . . . . . . . . . . . . . . 6.4.1.3 Bases . . . . . . . . . . . . . . . . . . . . . 6.4.1.4 Condensables: siloxanes, phthalates, phosphates and other organic compounds . . . . . . . . . . .

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xi

CONTENTS

6.5

6.4.2 Examples of problems caused by AMC contamination . . . . . . . . . . . . . . . . . . . . . 6.4.2.1 General. . . . . . . . . . . . . . . . . . . . 6.4.2.2 Effects of ammonia . . . . . . . . . . . 6.4.2.3 Effects of siloxanes . . . . . . . . . . . 6.4.2.4 Effects of HMDS . . . . . . . . . . . . 6.4.3 Chemistry of AMCs . . . . . . . . . . . . . . . . . 6.4.3.1 Monolayer and sub-monolayer contamination . . . . . . . . . . . . . . . 6.4.3.2 Clausius–Clapeyron relation . . . . . 6.4.3.3 Outgassing phenomenon: two-phase exponential model of vaporization and diffusion of contaminants . . . . . . . 6.4.3.4 Sticking probability, sticking coefficient, and staying tendency . . 6.4.3.5 Investigation of contamination based on the ‘‘Organic Conceptual Diagram’’ . . . . . . . . . . . . . . . . . . Examples of Application of Knowledge and Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Excursion of AMCs . . . . . . . . . . . . . . . . . 6.5.1.1 Data analysis . . . . . . . . . . . . . . . 6.5.1.2 Investigation of contaminant sources in cleanroom . . . . . . . . . . 6.5.2 Selection of construction materials with fewer AMC contaminant sources . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Chemical filter for air cleaning . . . . . . . . . 6.5.3.1 Change of total organic concentration with time . . . . . . . . 6.5.3.2 Change of siloxanes concentration in cleanroom air . . . . . . . . . . . . . 6.5.3.3 Effect of chemical filter . . . . . . . . 6.5.3.4 Published reports on removal mechanisms. . . . . . . . . . . . . . . . . 6.5.3.5 Other issues. . . . . . . . . . . . . . . . . 6.5.4 Removal from the substrate surface (carbon chemistry) . . . . . . . . . . . . . . . . . . 6.5.4.1 Cleaning technology using UV photoelectron with catalyst . . . . . .

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xii

CONTENTS 6.5.4.2 Other cleaning technology . . . . . . 6.5.5 Monitoring systems . . . . . . . . . . . . . . . . . 6.5.6 Recent developments . . . . . . . . . . . . . . . . 6.5.6.1 Cleanliness requirements for Si wafer . . . . . . . . . . . . . . . . . . . 6.5.6.2 Trends in standardization . . . . . . . 6.5.6.3 New analytical techniques . . . . . . 6.5.6.4 Achieving cleanroom cleanliness at low AMCs level (DOP 0.1 ng/m3) . . . . . . . . . . . . . 6.6 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Technology for cleanliness of AMCs . . . . . 6.6.2 Advances in analytical methods . . . . . . . . . 6.6.3 Application of air cleanliness technology to various fields . . . . . . . . . . . . . . . . . . . . . . 6.6.3.1 Sick house syndrome . . . . . . . . . . 6.6.3.2 Endocrine disrupters . . . . . . . . . . 6.6.3.3 Cleanliness of experiment and analysis environments . . . . . . . . . 6.6.3.4 Other applications . . . . . . . . . . . . 6.6.4 Contribution of the analyst/chemist to troubleshooting . . . . . . . . . . . . . . . . . . . . 6.7 Summary of the Chapter. . . . . . . . . . . . . . . . . . . Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Aspects of Particle Adhesion and Removal. . . . . . . . . . . . . . . David J. Quesnel, Donald S. Rimai and David M. Schaefer

475

7.1 7.2 7.3 7.4 7.5

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . Interactions Giving Rise to Particle Adhesion . . . Mechanics of Particle Adhesion . . . . . . . . . . . . . Factors Affecting Particle Adhesion . . . . . . . . . . Methods of Measuring the Adhesion of Particles to Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8 Relevance of Electrostatic Discharge Controls to Particle Contamination in Cleanroom Environments . . . . . . . . . . . . . . Larry Levit and Arnold Steinman

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xiii

CONTENTS 8.1 8.2 8.3 8.4 8.5 8.6

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . Electrostatic Charge Problems in Cleanrooms . Static Charge Generation . . . . . . . . . . . . . . . Insulators Versus Conductors . . . . . . . . . . . . Cleanroom Electrostatic Management . . . . . . Air Ionization for Static Charge Control . . . . 8.6.1 Corona ionization . . . . . . . . . . . . . . . 8.6.1.1 AC ionizer . . . . . . . . . . . . . . 8.6.1.2 DC ionizer . . . . . . . . . . . . . . 8.6.2 Photoelectric ionization. . . . . . . . . . . . 8.6.3 Radioisotope ionization . . . . . . . . . . . 8.6.4 Measuring ionizer performance . . . . . . 8.7 Air Ionizer Applications . . . . . . . . . . . . . . . . 8.7.1 Discharge in process tools . . . . . . . . . . 8.7.2 Flow benches and work surfaces . . . . . 8.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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503 504 508 510 511 514 515 515 517 519 520 521 521 524 525 526 527

CHARACTERIZATION OF SURFACE CONTAMINANTS . . . . . . . . . . . . . . . . . . . . . . . .

529

9 Electron Microscopy Techniques for Imaging and Analysis of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . .

531

PART II

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Zhong Lin Wang and Jean L. Lee 9.1

9.2

Scanning Electron Microscopy. . . . . . . . . . . . . . . . . . .

531

9.1.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1.1 Environmental scanning electron microscope . . . . . . . . . . . . . . . . . . . . . 9.1.2 Signals produced by the SEM . . . . . . . . . . . . . . 9.1.2.1 Imaging . . . . . . . . . . . . . . . . . . . . . . . 9.1.2.2 Composition analysis . . . . . . . . . . . . . . High-resolution Transmission Electron Microscopy . . . . 9.2.1 Main components of a transmission electron microscope . . . . . . . . . . . . . . . . . . . . . 9.2.2 The physics for atomic resolution lattice imaging 9.2.2.1 Phase contrast imaging. . . . . . . . . . . . . 9.2.2.2 Image formation . . . . . . . . . . . . . . . . . 9.2.2.3 Image interpretation of very thin samples. . . . . . . . . . . . . . . . . . . . . . . .

531 535 536 536 541 545 546 548 548 550 551

xiv

CONTENTS 9.2.2.4 Dynamic theory and image simulation. Shapes of Nanocrystals . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Polyhedral shapes. . . . . . . . . . . . . . . . . . . . . . 9.3.2 Twining structure and stacking faults . . . . . . . 9.3.3 Multiply twinned particles—decahedron and icosahedron . . . . . . . . . . . . . . . . . . . . . . 9.4 Nanodiffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Optics for nanodiffraction . . . . . . . . . . . . . . . 9.4.2 Experimental procedure to obtain a nanodiffraction pattern . . . . . . . . . . . . . . . . . 9.5 Scanning Transmission Electron Microscopy . . . . . . . 9.5.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Imaging modes . . . . . . . . . . . . . . . . . . . . . . . 9.5.3 Composition-sensitive imaging . . . . . . . . . . . . 9.5.4 Nanoscale microanalysis . . . . . . . . . . . . . . . . 9.6 In-situ TEM and Nanomeasurements . . . . . . . . . . . . 9.6.1 Thermodynamic properties of nanocrystals . . . . . . . . . . . . . . . . . . . . . . . . . 9.7 Electron Energy-loss Spectroscopy of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7.1 Quantitative nanoanalysis . . . . . . . . . . . . . . . 9.7.2 Near edge fine structure and bonding in transition metal oxides . . . . . . . . . . . . . . . . . 9.8 Energy Dispersive X-ray Microanalysis (EDS). . . . . . 9.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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552 555 555 558

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559 562 562

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563 564 564 566 568 569 570

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570

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576 577

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578 581 582 583

10 Surface Analysis Methods for Contaminant Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David A. Cole and Lei Zhang

585

9.3

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Auger Electron Spectroscopy (AES) . . . . . . . . 10.2.1 Background of AES. . . . . . . . . . . . . . 10.2.2 Basic principles of AES . . . . . . . . . . . 10.2.3 AES instrumentation . . . . . . . . . . . . . 10.2.4 Applications of AES for characterizing surface contaminants . . . . . . . . . . . . . 10.2.5 Recent developments and future directions of AES . . . . . . . . . . . . . . . 10.3 X-ray Photoelectron Spectroscopy (XPS). . . . .

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585 586 586 586 593

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594

..... .....

600 601

xv

CONTENTS 10.3.1 10.3.2 10.3.3 10.3.4

Background of XPS. . . . . . . . . . . . . . . Basic principles of XPS . . . . . . . . . . . . XPS instrumentation . . . . . . . . . . . . . . Applications of XPS for characterizing surface contaminants . . . . . . . . . . . . . . 10.3.5 Recent developments and future directions of XPS . . . . . . . . . . . . . . . . 10.4 Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) . . . . . . . . . . . . . . . . 10.4.1 Background of TOF-SIMS . . . . . . . . . . 10.4.2 Basic principles of TOF-SIMS . . . . . . . 10.4.3 TOF-SIMS instrumentation . . . . . . . . . 10.4.4 Applications of TOF-SIMS for characterizing surface contaminants . . . 10.4.5 Recent developments and future directions of TOF-SIMS . . . . . . . . . . . 10.5 Low-energy Ion Scattering (LEIS) . . . . . . . . . . 10.5.1 Background of LEIS . . . . . . . . . . . . . . 10.5.2 Basic principles of LEIS. . . . . . . . . . . . 10.5.3 LEIS instrumentation . . . . . . . . . . . . . 10.5.4 Applications of LEIS for characterizing surface contaminants . . . . . . . . . . . . . . 10.5.5 Recent developments and future directions of LEIS . . . . . . . . . . . . . . . . 10.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

601 602 611

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613

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620

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622 622 622 628

....

630

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. . . . .

634 635 635 635 640

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641

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

645 646 647

11 Ionic Contamination and Analytical Techniques for Ionic Contaminants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beverly Newton

653

11.1 What is an Ion? . . . . . . . . . . . . . . . . . . . . . . . 11.2 Sources and Effects of Ionic Contamination in Electronics Manufacturing . . . . . . . . . . . . . . . . 11.3 How Does Corrosion Begin? . . . . . . . . . . . . . . 11.4 Sources and Effects of Ionic Contamination for Semiconductor and MEMS Manufacturing . . . . 11.5 Ionic Contamination of Data Storage Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Ionic Contamination of Cleanroom and Packaging Materials . . . . . . . . . . . . . . . . . . . .

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. . . .

. . . . .

....

653

.... ....

654 656

....

656

....

658

....

658

xvi

CONTENTS 11.7 Analytical Techniques . . . . . . . . . . . . . . . . . . 11.8 Selection Criteria. . . . . . . . . . . . . . . . . . . . . . 11.9 Instrumentation Selection. . . . . . . . . . . . . . . . 11.9.1 Ultraviolet photoelectric emission . . . . 11.9.2 Phase imaging . . . . . . . . . . . . . . . . . . 11.9.3 Energy dispersive X-ray spectroscopy (EDS/EDX) . . . . . . . . . . . . . . . . . . . 11.9.4 Graphite furnace atomic absorption (GFAA) . . . . . . . . . . . . . . . . . . . . . . 11.9.5 Inductively coupled plasma/mass spectrometry (ICP/MS) . . . . . . . . . . . 11.9.6 Optically stimulated electron emission (OSEE). . . . . . . . . . . . . . . . . . . . . . . 11.9.7 Secondary ion mass spectroscopy (SIMS) . . . . . . . . . . . . . . . . . . . . . . . 11.9.8 Auger electron spectroscopy (AES) . . . 11.9.9 X-ray photoelectron spectroscopy/ electron spectroscopy for chemical analysis (XPS/ESCA). . . . . . . . . . . . . 11.9.10 Total reflection X-ray fluorescence (TXRF) . . . . . . . . . . . . . . . . . . . . . 11.9.11 Ion chromatography (IC) . . . . . . . . . . 11.9.12 Capillary ion electrophoresis (CIE) . . . 11.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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660 660 661 661 661

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662

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663

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664

.....

665

..... .....

665 666

.....

666

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667 667 671 671 672

12 Relevance of Colorimetric Interferometry for Thin Surface Film Contaminants . . . . . . . . . . . . . . . . . . . . . . . . Michel Querry, Philippe Vergne and Je´r^ ome Molimard

675

12.1 Introduction . . . . . . . . . . . . . . . . . . 12.2 Interferometry. . . . . . . . . . . . . . . . . 12.2.1 Elementary phenomena . . . . 12.2.2 White light interferometry . . 12.3 Colorimetry . . . . . . . . . . . . . . . . . . 12.3.1 Definition of the problem. . . 12.3.2 Colorimetric encoding . . . . . 12.3.3 Detectors . . . . . . . . . . . . . . 12.4 Colorimetric Interferometry . . . . . . . 12.4.1 Methods using colorimetric interferometry in lubrication.

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675 676 676 679 680 680 681 683 684

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684

xvii

CONTENTS 12.4.2 New developed method . . . . . . . . . . . . . . . . 12.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

684 689 690

13 Wettability Techniques to Monitor the Cleanliness of Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . William Birch, Alain Carre´ and Kashmiri L. Mittal

693

13.1 Background and Introduction. . . . . . . . . . . 13.2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . 13.3 Theoretical and Experimental Investigations 13.4 Instrumentation. . . . . . . . . . . . . . . . . . . . . 13.5 Examples of Applications. . . . . . . . . . . . . . 13.6 Recent Developments . . . . . . . . . . . . . . . . 13.7 Future Directions . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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693 694 696 700 705 716 718 721

PART III METHODS FOR REMOVAL OF SURFACE CONTAMINATION . . . . . . . . . . . . . . . . . . . . . . .

725

14 The Use of Surfactants to Enhance Particle Removal from Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Michael L. Free 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 14.1.1 Industrial perspective . . . . . . . . . . . . 14.1.2 Historical perspective . . . . . . . . . . . . 14.2 Surfactant Behavior in Solution . . . . . . . . . . 14.3 Interfacial Forces and Particle Removal . . . . 14.3.1 Introduction to interfacial forces. . . . 14.3.2 Measurement of surface forces . . . . . 14.3.3 Adhesion. . . . . . . . . . . . . . . . . . . . 14.3.4 Particle removal forces . . . . . . . . . . 14.3.5 Modification of surface forces using surfactants . . . . . . . . . . . . . . . . . . 14.3.6 Measurement of particle removal . . 14.3.7 Enhanced-particle removal results associated with surfactant use . . . . . 14.3.8 Post-cleaning surfactant removal . . . 14.3.9 Selection of surfactants for cleaning purposes . . . . . . . . . . . . . . . . . . . .

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727

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727 727 728 728 734 734 736 738 739

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739 744

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

745 749

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750

xviii

CONTENTS

14.3.10 Mathematical modeling of enhanced-particle removal using surfactants . . . . . . . . . . . . . . . . . . . . . . . . 14.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Cleaning with Solvents. . . . . . . . . . . . . . . . . . . . . . . . . . . . John B. Durkee 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Environmental and Regulatory Issues . . . . . . . 15.2.1 Ozone-depleting solvents (chemicals) . . . . . . . . . . . . . . . . . . . . 15.2.1.1 Regulation of ozonedepleting chemicals . . . . . . . 15.2.2 Reactions of ozone depletion in the stratosphere . . . . . . . . . . . . . . . . . . . 15.2.3 VOC solvents . . . . . . . . . . . . . . . . . . 15.2.3.1 Definition of a VOC . . . . . . 15.2.3.2 Definition of VOC exempt. . 15.2.3.3 Reactions leading to smog formation . . . . . . . . . . . . . . 15.2.3.4 Smog formed from VOCs . . 15.2.4 Global warming . . . . . . . . . . . . . . . . 15.2.4.1 Regulation of solvent cleaning because of global warming. . . . . . . . . . . . . . . 15.2.4.2 Specific regulations affecting solvent cleaning . . . . . . . . . 15.2.5 Relationship of solvent characteristics ODP, VOC, and GWP. . . . . . . . . . . . 15.3 Potential Health Consequences of Solvent Use in Cleaning. . . . . . . . . . . . . . . . . . . . . . . 15.3.1 Flammability issues . . . . . . . . . . . . . . 15.3.1.1 Flash point . . . . . . . . . . . . 15.3.1.2 Combustion . . . . . . . . . . . 15.3.1.3 Static discharge . . . . . . . . . 15.3.1.4 Procedures recommended to avoid fires . . . . . . . . . . 15.3.1.5 Body contact . . . . . . . . . . 15.3.1.6 Skin contact . . . . . . . . . . .

750 753 753 759

..... .....

759 760

.....

761

.....

762

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. . . .

772 776 776 780

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

782 785 789

.....

789

.....

792

.....

795

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796 797 797 802 807

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

809 810 812

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xix

CONTENTS 15.3.1.7 Carcinogenicity . . . . . . . . . . 15.3.1.8 Protection from hazards. . . . 15.3.1.9 Taking action . . . . . . . . . . . 15.3.1.10 Legal or regulatory hazards . 15.3.1.11 Economic hazards . . . . . . . . 15.4 Solvent Selection via Solubility Parameters . . . . 15.4.1 Background . . . . . . . . . . . . . . . . . . . . 15.4.2 The Kauri Butanol test . . . . . . . . . . . . 15.4.3 The Hildebrand Solubility Parameter . . 15.4.3.1 A one-dimensional solubility parameter. . . . . . . . . . . . . . . 15.4.3.2 Molecular forces . . . . . . . . . . 15.4.4 Hansen Solubility Parameters (HSP) . . . 15.4.4.1 Solvent substitution with HSP 15.4.5 Solvent substitution . . . . . . . . . . . . . . . 15.4.5.1 Multiple components. . . . . . . 15.4.5.2 HSP data and calculations . . . 15.5 Choosing Cleaning Solvents and Cleaning Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.5.1 Choices of solvents . . . . . . . . . . . . . . . 15.5.1.1 Chemical structure and atomic composition . . . . . . . . 15.5.1.2 Technical data . . . . . . . . . . . 15.5.2 Cleaning/rinsing/drying processes . . . . . 15.5.2.1 Solvent cleaning processes . . . 15.5.2.2 Rinsing processes . . . . . . . . . 15.5.2.3 Drying processes . . . . . . . . . . 15.5.2.4 Design features for environmental control . . . . . . 15.5.2.5 Multiple-stage processes . . . . 15.5.2.6 Selection of design features . . 15.6 Control of Quality in Solvent Cleaning . . . . . . . 15.7 Avoiding Common Mistakes . . . . . . . . . . . . . . 15.8 The Future of Solvents and Cleaning . . . . . . . . 15.8.1 Customer preferences . . . . . . . . . . . . . . 15.8.2 Environmental regulations . . . . . . . . . . 15.8.3 Innovation . . . . . . . . . . . . . . . . . . . . . 15.8.3.1 Business innovation. . . . . . . . 15.8.3.2 Technical innovation . . . . . . . 15.8.3.3 Regulatory innovation. . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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814 815 820 821 821 822 823 823 825

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826 827 829 830 831 831 833

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839 840

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840 851 851 852 853 853

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854 855 856 858 862 863 864 865 866 866 866 867 868

xx

CONTENTS

16 Removal of Particles by Chemical Cleaning . . . . . . . . . . . . . Philip G. Clark and Thomas J. Wagener 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 16.2 Particle/Surface Interactions . . . . . . . . . . . . 16.2.1 van der Waals Force . . . . . . . . . . . 16.2.2 Electrostatic force . . . . . . . . . . . . . 16.2.3 Hydrodynamic force . . . . . . . . . . . 16.3 Process Applications and Chemistries . . . . . 16.3.1 Particle challenge wafer preparation 16.3.2 dHF clean. . . . . . . . . . . . . . . . . . . 16.3.3 SC-1 Clean . . . . . . . . . . . . . . . . . . 16.3.4 Single-step clean . . . . . . . . . . . . . . 16.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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873 876 876 878 880 881 881 882 883 886 886 887

17 Cleaning Using a High-speed Impinging Jet . . . . . . . . . . . . . Kuniaki Gotoh

889

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 17.2 Fundamentals of Air Jet Removal . . . . . . . . 17.2.1 Apparatus and parameters . . . . . . . . 17.2.2 Definition of removal efficiency . . . . 17.2.3 Effect of operating conditions on the removal efficiency  . . . . . . . . . . . . . 17.2.3.1 Pressure drop
Pn and distance d . . . . . . . . . . . . . 17.2.3.2 Impinging angle  . . . . . . . 17.2.4 Condition of the environment. . . . . . 17.3 New Removal Methods Using the Air Jet Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3.1 Pre-charging method . . . . . . . . . . . . 17.3.2 Vibrating air jet method. . . . . . . . . . 17.3.3 Other removal methods . . . . . . . . . . 17.4 Remaining Problems . . . . . . . . . . . . . . . . . . 17.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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889 890 890 894

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896

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896 897 903

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906 906 909 913 914 916 916

18 Microabrasive Precision Cleaning and Processing Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rajiv Kohli

919

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873

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. . . . . . .

xxi

CONTENTS 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Microabrasive Technology . . . . . . . . . . . . . . . . . . 18.3 Fundamental Considerations . . . . . . . . . . . . . . . . 18.3.1 Removal of films . . . . . . . . . . . . . . . . . . . 18.3.1.1 Removal by delamination . . . . . 18.3.1.2 Removal by mechanical erosion . 18.3.2 Removal of particles . . . . . . . . . . . . . . . . 18.4 System Description . . . . . . . . . . . . . . . . . . . . . . . 18.4.1 Nozzle materials and design . . . . . . . . . . . 18.4.2 Type of abrasives . . . . . . . . . . . . . . . . . . 18.4.2.1 Selection of the abrasive . . . . . . 18.4.2.2 Abrasive quality . . . . . . . . . . . . 18.4.3 Air treatment . . . . . . . . . . . . . . . . . . . . . 18.4.3.1 Air drying . . . . . . . . . . . . . . . . 18.4.3.2 Oil contamination . . . . . . . . . . . 18.4.4 Dust collection . . . . . . . . . . . . . . . . . . . . 18.4.5 Recycling and secondary waste . . . . . . . . . 18.4.6 Static charging . . . . . . . . . . . . . . . . . . . . 18.4.7 Scalability . . . . . . . . . . . . . . . . . . . . . . . . 18.4.8 Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.5.1 Removal of conformal coatings . . . . . . . . 18.5.2 Thin film removal . . . . . . . . . . . . . . . . . . 18.5.3 Removal of coatings on dental components. . . . . . . . . . . . . . . . . . . . . . . 18.5.4 Cutting brittle materials . . . . . . . . . . . . . . 18.5.5 Precision deburring of metal components. . 18.5.6 Demarking . . . . . . . . . . . . . . . . . . . . . . . 18.5.7 Micromachining of three-dimensional structures . . . . . . . . . . . . . . . . . . . . . . . . 18.5.8 Decorative engraving, etching, and frosting . . . . . . . . . . . . . . . . . . . . . . 18.5.9 Miscellaneous applications . . . . . . . . . . . . 18.6 Advantages and Disadvantages. . . . . . . . . . . . . . . 18.6.1 Advantages . . . . . . . . . . . . . . . . . . . . . . . 18.6.2 Disadvantages . . . . . . . . . . . . . . . . . . . . . 18.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

919 920 921 922 922 923 924 925 926 927 931 932 933 933 935 935 935 936 937 938 938 938 939

. . . .

. . . .

940 940 941 942

..

944

. . . . . . . .

945 946 946 946 947 947 947 947

. . . . . . . .

xxii

CONTENTS

19 Cleaning Using Argon/Nitrogen Cryogenic Aerosols . . . . . . . Wayne T. McDermott and Jeffery W. Butterbaugh 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 19.2 Aerosol Jet Cleaning Mechanisms . . . . . . . . 19.2.1 Adhesion and hydrodynamic forces. 19.2.2 Particle collision . . . . . . . . . . . . . . 19.3 Production of Argon/Nitrogen Cryogenic Aerosol Jets . . . . . . . . . . . . . . . . . . . . . . . 19.3.1 Equipment requirements . . . . . . . . 19.3.2 Operating conditions . . . . . . . . . . . 19.3.3 Cleaning systems . . . . . . . . . . . . . . 19.4 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.5 Effectiveness and Applications . . . . . . . . . . 19.5.1 Kinetics of cleaning . . . . . . . . . . . . 19.5.2 Cleaning performance . . . . . . . . . . 19.5.3 Applications . . . . . . . . . . . . . . . . . 19.6 Future Directions . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

951

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

951 953 955 956

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

958 961 964 965 969 970 970 974 981 984 984

20 Carbon Dioxide Snow Cleaning . . . . . . . . . . . . . . . . . . . . . Robert Sherman

987

20.1 Introduction . . . . . . . . . . . . . . . . . . . . . 20.2 Thermodynamic Properties. . . . . . . . . . . 20.3 Cleaning Mechanisms . . . . . . . . . . . . . . 20.3.1 Particle removal . . . . . . . . . . . . 20.3.2 Organic removal . . . . . . . . . . . . 20.3.3 Other mechanisms . . . . . . . . . . . 20.4 Proof of Process . . . . . . . . . . . . . . . . . . 20.5 Equipment . . . . . . . . . . . . . . . . . . . . . . 20.5.1 Nozzles. . . . . . . . . . . . . . . . . . . 20.5.2 Other equipment items . . . . . . . . 20.5.2.1 Moisture control . . . . . 20.5.2.2 Static control . . . . . . . 20.5.3 Input pressure control . . . . . . . . 20.6 Process Parameters . . . . . . . . . . . . . . . . 20.6.1 Redeposition . . . . . . . . . . . . . . . 20.6.2 Recontamination sources . . . . . . 20.6.2.1 CO2 impurities . . . . . . 20.6.2.2 Moisture condensation

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

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

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

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

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

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

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

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

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

987 988 989 990 990 991 992 994 995 997 997 998 999 1000 1000 1001 1001 1002

xxiii

CONTENTS 20.6.2.3 Static charge. . . . . . . . . . . . . . . . 20.6.2.4 Cleaning technique . . . . . . . . . . . 20.6.3 Surface damage . . . . . . . . . . . . . . . . . . . . . 20.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.7.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . 20.7.2 Vacuum technologies . . . . . . . . . . . . . . . . . 20.7.3 Optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.7.4 Hard drive disks assemblies and components 20.7.5 Cleanrooms, process equipment, and tooling 20.7.6 Other applications . . . . . . . . . . . . . . . . . . . 20.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1002 1002 1003 1003 1004 1007 1007 1008 1009 1009 1010 1011

21 Coatings for Prevention or Deactivation of Biological Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joerg C. Tiller

1013

21.1 21.2 21.3 21.4 21.5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . Biological Contaminations . . . . . . . . . . . . . . . . . Means of Contamination . . . . . . . . . . . . . . . . . . General Requirements for Self-cleaning Coatings . Laboratory Tests for Antimicrobial Activity of Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.6 Agents Against Biological Contaminations . . . . . 21.7 Coating Methods . . . . . . . . . . . . . . . . . . . . . . . 21.7.1 Brush, pad, and roll coating . . . . . . . . . . 21.7.2 Dip and flow coatings . . . . . . . . . . . . . . 21.7.3 Spin coating . . . . . . . . . . . . . . . . . . . . . 21.7.4 Spray application . . . . . . . . . . . . . . . . . 21.7.5 Electroplating . . . . . . . . . . . . . . . . . . . . 21.7.6 Electroless plating . . . . . . . . . . . . . . . . . 21.7.7 Sputtering . . . . . . . . . . . . . . . . . . . . . . . 21.7.8 Physical vapor deposition. . . . . . . . . . . . 21.7.9 Chemical vapor deposition . . . . . . . . . . . 21.7.10 Surface modification . . . . . . . . . . . . . . . 21.8 Non-adhesive Coatings . . . . . . . . . . . . . . . . . . . 21.8.1 Coatings with hydrophilic polymers and hydrogels . . . . . . . . . . . . . . . . . . . . . . . 21.8.2 Ultrahydrophobic coatings . . . . . . . . . . .

. . . .

. . . .

1013 1015 1016 1016

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

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

1017 1019 1020 1020 1020 1020 1020 1021 1021 1021 1022 1022 1022 1022

.. ..

1023 1026

xxiv

CONTENTS

21.8.3 Influence of surface net charge on microbial adhesion. . . . . . . . . . . . . . . . 21.8.4 Proteins . . . . . . . . . . . . . . . . . . . . . . . 21.9 Microbe Killing or Growth Inhibiting Coatings . 21.9.1 Release systems . . . . . . . . . . . . . . . . . . 21.9.1.1 Diffusion systems . . . . . . . . . 21.9.2 Contact active antimicrobial surfaces. . . 21.9.2.1 Chemical action . . . . . . . . . . 21.9.2.2 Physicochemical action . . . . . 21.10 Metal Coatings . . . . . . . . . . . . . . . . . . . . . . . 21.11 Antifouling Paints . . . . . . . . . . . . . . . . . . . . . 21.12 Antimicrobial Surfaces with Multiple Action . . 21.13 Antiviral Coatings . . . . . . . . . . . . . . . . . . . . . 21.14 Surface Cleaning by Coating. . . . . . . . . . . . . . 21.15 Application Examples . . . . . . . . . . . . . . . . . . 21.15.1 Biomedical applications . . . . . . . . . . 21.15.2 Food protection . . . . . . . . . . . . . . . . 21.15.3 Textiles . . . . . . . . . . . . . . . . . . . . . . 21.15.4 Daily life products . . . . . . . . . . . . . . 21.15.5 Construction and ships . . . . . . . . . . . 21.16 Future Developments . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

1026 1027 1027 1028 1029 1038 1039 1042 1044 1045 1047 1047 1048 1049 1049 1052 1052 1052 1053 1053 1053

22 A Detailed Study of Semiconductor Wafer Drying . . . . . . . Wim Fyen, Frank Holsteyns, Twan Bearda, Sophia Arnauts, Jan Van Steenbergen, Geert Doumen, Karine Kenis, and Paul W. Mertens

1067

22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 22.1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . 22.1.2 Approach followed in this work . . . . 22.1.3 Drying techniques commonly used in semiconductor manufacturing . . . . . . 22.1.3.1 Spin drying . . . . . . . . . . . 22.1.3.2 Surface tension gradient (Marangoni) based drying . 22.2 Theoretical Background . . . . . . . . . . . . . . . . 22.2.1 Stability of wetting films on silica . . . 22.2.1.1 Surface forces . . . . . . . . . . 22.2.1.2 Disjoining pressure . . . . . .

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

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

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

1067 1067 1068

..... .....

1070 1070

. . . . .

1071 1074 1074 1074 1074

. . . . .

. . . . .

. . . . .

. . . . .

xxv

CONTENTS 22.2.1.3 Importance of short range repulsive interactions . . . . . . . . . 22.2.2 Adsorption of ions on silica surfaces . . . . . 22.2.2.1 Structure of the silica–water interface . . . . . . . . . . . . . . . . . . 22.2.2.2 Interaction between metal cations and a silica surface. . . . . 22.2.3 Literature models describing wafer drying . 22.2.3.1 Spin drying . . . . . . . . . . . . . . . 22.2.3.2 Vertical Marangoni-based wafer drying . . . . . . . . . . . . . . . 22.2.3.3 Applicability of the model for vertical drying to a rotating wafer system. . . . . . . . . . . . . . . 22.2.3.4 Limitations of the model for Marangoni-based drying . . . . . . 22.2.4 Salt tracer tests . . . . . . . . . . . . . . . . . . . . 22.2.4.1 Interpretation of salt tracer tests. 22.2.4.2 Available literature data . . . . . . 22.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . 22.3.1 Setups for wafer drying . . . . . . . . . . . . . . 22.3.1.1 Spin drying . . . . . . . . . . . . . . . 22.3.1.2 Vertical Marangoni-based drying 22.3.1.3 Marangoni-based drying of horizontally rotating wafer. . . . . 22.3.2 Analytical techniques . . . . . . . . . . . . . . . . 22.3.2.1 Metal surface concentration by TXRF . . . . . . . . . . . . . . . . . 22.3.2.2 Surface tension by Wilhelmy plate method . . . . . . . . . . . . . . 22.3.3 Characterization of materials and products 22.3.3.1 Wafers . . . . . . . . . . . . . . . . . . . 22.3.3.2 Liquid chemicals . . . . . . . . . . . . 22.3.3.3 Metal salts . . . . . . . . . . . . . . . . 22.3.4 Procedure for the salt tracer tests . . . . . . . 22.3.4.1 Spin drying . . . . . . . . . . . . . . . 22.3.4.2 Vertical Marangoni-based drying 22.3.4.3 Marangoni-based drying on a rotating wafer. . . . . . . . . . . . . . 22.4 Results of Salt Tracer Tests . . . . . . . . . . . . . . . . . 22.4.1 Spin drying . . . . . . . . . . . . . . . . . . . . . . .

. .

1075 1077

.

1078

. . .

1079 1081 1081

.

1086

.

1089

. . . . . . . .

1090 1091 1091 1093 1094 1094 1094 1095

. .

1097 1098

.

1098

. . . . . . . .

1100 1101 1101 1101 1102 1102 1102 1102

. . .

1103 1103 1103

xxvi 22.4.1.1 Spin-off vs. evaporation. . . . . . 22.4.1.2 Uniformity of the evaporated film . . . . . . . . . . . . . . . . . . . . 22.4.1.3 Effect of the rotation speed on evaporation . . . . . . . . . . . . 22.4.1.4 Investigation of adsorption . . . 22.4.2 Vertical Marangoni-based drying . . . . . . 22.4.2.1 Histogram of salt test results . . 22.4.2.2 Effect of IPA flow rate . . . . . . 22.4.2.3 Effect of withdrawal speed. . . . 22.4.3 Marangoni-based drying on a rotating wafer . . . . . . . . . . . . . . . . . . . . 22.4.3.1 Effect of liquid dispensation during drying . . . . . . . . . . . . . 22.4.3.2 Effect of nozzle speed . . . . . . . 22.4.3.3 Effect of liquid surface tension . 22.4.3.4 Investigation of adsorption . . . 22.5 Discussion of Experimental Data . . . . . . . . . . . . 22.5.1 Spin drying . . . . . . . . . . . . . . . . . . . . . . 22.5.1.1 Spin-off vs. evaporation. . . . . . 22.5.1.2 Effect of high rotation speeds. . 22.5.1.3 Wafer topography and surface heterogeneity . . . . . . . . 22.5.2 Marangoni-based drying . . . . . . . . . . . . 22.5.2.1 Limits to the use of salt tests . . 22.5.2.2 Mean surface tension gradient for Marangonibased drying. . . . . . . . . . . . . . 22.5.2.3 Drying speed . . . . . . . . . . . . . 22.5.2.4 Wafer topography and surface heterogeneity . . . . . . . . 22.5.2.5 Alternatives to IPA as a suitable tensioactive component 22.5.2.6 Residues of organic species after Marangoni-based drying . 22.6 Summary and Conclusions . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CONTENTS ..

1103

..

1105

. . . . . .

. . . . . .

1106 1108 1110 1110 1111 1113

..

1114

. . . . . . . .

. . . . . . . .

1114 1115 1117 1118 1120 1120 1120 1121

.. .. ..

1122 1123 1123

.. ..

1124 1126

..

1126

..

1127

.. .. ..

1128 1128 1130

Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1137

Contributors

Carlo Altucci Dipartimento di Scienze Fisiche Complesso Universitario di Monte S. Angelo Napoli Italy Sophia Arnauts IMEC Leuven Belgium Twan Bearda IMEC Leuven Belgium William Birch Institute for Materials Research and Engineering (IMRE) Singapore Jeffery W Butterbaugh FSI International Inc. Chaska, MN USA Alain Carre´ Corning S.A. Corning European Technology Center Avon France Philip G Clark 3M, Electronics Markets Materials Division 3M Center St. Paul, MN USA xxvii

xxviii David A Cole Evans Analytical Group LLC East Windsor, NJ USA Geert Doumen IMEC Leuven Belgium John B Durkee Hunt, TX USA Michael L Free Department of Metallurgical Engineering University of Utah Salt Lake City, UT USA Taketoshi Fujimoto Sumika Chemical Analysis Service Ltd. Osaka Japan Wim Fyen K. U. Leuven Research & Development (LRD) Katholieke Universiteit Leuven Leuven Belgium Anthony S Geller Sandia National Laboratories New Mexico Albuquerque, NM USA Kuniaki Gotoh Department of Applied Chemistry Okayama University Okayama Japan

CONTRIBUTORS

CONTRIBUTORS Frank Holsteyns IMEC Leuven Belgium Koji Kato Department of Mechanical Engineering College of Engineering Nihon University Koriyama City Japan Karine Kenis IMEC Leuven Belgium Rajiv Kohli Houston, TX USA Jean L Lee Nano-SciTech Norcross, GA USA Larry Levit MKS, Ion Systems Alameda, CA USA Chao-Hsin Lin Environmental Control Systems Boeing Commercial Airplanes Group Seattle, WA USA Wayne T McDermott Air Products and Chemicals Inc. Allentown, PA USA

xxix

xxx Paul W Mertens IMEC Leuven Belgium Kashmiri L Mittal Hopewell Junction, NY USA Je´r^ ome Molimard Centre SMS Ecole Nationale Supe´rieure des Mines de Saint Etienne Saint Etienne France Beverly Newton Rohnert Park, CA USA Tatsuo Nonaka Sumika Chemical Analysis Service Ltd. Osaka Japan Domenico Paparo Dipartimento di Scienze Fisiche Complesso Universitario di Monte S. Angelo Napoli Italy Othmar Preining Austrian Academy of Sciences Clean Air Commission Vienna Austria Michel Querry LaMCoS UMR CNRS/INSA INSA de Lyon Villeurbanne France

CONTRIBUTORS

CONTRIBUTORS David J Quesnel Department of Mechanical Engineering University of Rochester Rochester, NY USA Daniel J Rader Sandia National Laboratories New Mexico Albuquerque, NM USA Donald S Rimai Eastman Kodak Company Rochester, NY USA David M Schaefer Department of Physics Towson University Towson, MD USA Robert Sherman Applied Surface Technologies New Providence, NJ USA Jan Van Steenbergen IMEC Leuven Belgium Arnold Steinman MKS, Ion Systems Alameda, CA USA Kikuo Takeda Sumika Chemical Analysis Service Ltd. Osaka Japan

xxxi

xxxii Joerg C Tiller Freiburg Materials Research Center University of Freiburg Freiburg Germany Philippe Vergne LaMCoS UMR CNRS/INSA INSA de Lyon Villeurbanne France Thomas J Wagener FSI International Inc. Chaska, MN USA Zhong Lin Wang School of Materials Science and Engineering Georgia Institute of Technology Atlanta, GA USA Lei Zhang DuPont Central Research and Development Wilmington, DE USA Chao Zhu Departmental of Mechanical Engineering New Jersey Institute of Technology Newark, NJ USA

CONTRIBUTORS

I Introduction Rajiv Kohli and Kash L. Mittal

Contaminants on surfaces are of fundamental interest in a wide variety of industries due to their proclivity for causing the failure of critical components. These contaminants can be small particles, thin films, molecular species, ionic species, or microbiological species. Particulate contamination most often is present in the form of dust, for example, lint from clothing and lens tissue, or fine airborne particles. Tiny particles of abrasive or other machining debris also can become embedded in a surface during polishing or other processing operations. On the other hand, film contamination can originate from a variety of sources, including airborne pollutants (water vapor, organic materials, and cleanroom construction materials), outgassing of plastic containers holding finished components, residues from protective strip coatings, dried liquid residue following an improper cleaning operation, and fingerprints left during handling.

I.1

The Impact of Contaminants

In the form of contaminants, small particles can have a major impact on the performance of precision and other products. For example, the presence of impurities such as boron and phosphorous in the parts per billion range can result in the irrecoverable loss of an entire production lot of semiconductor wafers. In a hard disk drive, a particle of dimensions similar to the nominal flying height trapped between the head and the disk can lead to catastrophic failure of the drive. Similarly, the presence of low levels of hydrocarbon contaminants in the components for oxygen service can cause catastrophic damage to spacecraft due to autoignition. Film contaminant layers on the surface of high-quality metallic mirrors or other optical components can increase scattering. Particles on a surface can act as nucleation sites and produce larger cone-shaped defects in the film with increased scattering. Furthermore, contaminant layers on

R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, xxxiii–xliii ª 2008 William Andrew Inc.

xxxiii

xxxiv

I: INTRODUCTION

optical surfaces intended to be further coated with thin films, will affect the adhesion of the films. Similarly, airborne molecular contaminants (AMCs) on a silicon wafer can affect the performance of the device incorporating chips fabricated from such a contaminated wafer. Even on mechanical parts, such as precision gears or other precision metal components, that must be coated with a protective or performance coating, the presence of contaminant films or particles can lead to poor coating adhesion and subsequent failure of the critical component.

I.2

Size Range of Particles

For a detailed characterization, it is first necessary to resolve the particles by their sizes. Discrete particles can be generally classified by size according to Table I.1. Most precision technology applications require characterization of microsize and smaller particles. For example, civilian and defense space agencies in the United States (NASA, National Aeronautics and Space Administration) and Europe (ESA, European Space Agency) specify surface cleanliness levels for space hardware in the micro-particle size range. The cleanliness levels commonly used to specify particulates and nonvolatile residue (NVR) for hardware used for oxygen service are given in Table I.2. Table I.1 Range of Particle Sizes and Selected Techniques for Resolution of Particles for Characterization

Particle Class

Particle Size (nm)

Resolution Techniques

Macro Micro Submicrometer

>50,000 100–50,000 10–100

Nano Atomic

1–10 0.01–1

Subatomic

kSAM, solitary pulse shaping in the presence of a net negative intracavity GDD determines the steady-state pulse duration in KLM Ti:Sa lasers. In this condition and by relying on the weak pulse-shaping approximation j DA(t)/A(t) j 1 MHz repetition rate [101–103], and recently sub-ps (850 fs), high energy (100 mJ), nearly diffraction-limited pulses at a repetition rate of 32 kHz, and a 1060-nm central wavelength [104]. In this last case, a 150-fs, 25-pJ seed pulse, emitted by a Nd:glass based on a semiconductor saturable absorber (SESAM [105]), was coupled into a dispersive, 2-km-long, step-index, single-mode fiber delay line, which stretched the pulse to a width of about 800 ps and broadened the spectrum (Dl = 9.9 nm compared with 6.9 nm of the oscillator pulse), thanks to considerable self-phase-modulation. Such a pulse is then amplified by means of two fused-silica, double-clad, Nd2O3-doped fiber preamplifiers, followed by two power amplifiers consisting of two ytterbium-doped, double-clad fibers, which can raise the pulse energy up to 130 mJ at a repetition rate of 128 kHz, i.e. an average power of 16.5 W. The pulse is finally temporally compressed by means of a diffraction grating to give an 850-fs FWHM pulse width, with a very good optical quality resulting in a nearly diffraction-limited spatial mode. The limiting factor for pulse compression was represented by the third-order dispersion effect of the fiber stretcher, which could not be compensated by a grating compressor since the third-order dispersion of a grating pair has the same sign (positive) as the third-order dispersion of the fiber.

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Another interesting and novel pulse compression effect has been observed by focusing an ultrashort laser pulse onto a photonic crystal (PC) [106]. In this experiment, a small part of an amplified Ti:Sa laser pulse (270 fs of pulse duration, 8 nm of spectral width centered at l0 = 815 nm) with 3.5 mW of average power at 200 kHz repetition rate was focused onto a few micrometers 1D PC. This crystal consisted of eight layers of high refractive index (ZnS, n1 = 2.29) alternated with seven layers of low refractive index (SrF2, n2 = 1.46) deposited on a glass substrate, the whole structure strongly reflecting light in the range 745–830 nm at normal incidence, [107]. The incoming laser pulse duration could be varied by translating one of the mirrors of the gratingbased compressor. A different amount of either positive or negative chirp to the laser pulse could be given in such a way. An average pulse duration of t inc = 550 fs was used throughout the experiment. Depending on the incidence angle of the incoming laser pulse on the PC, the transmitted pulse duration was modulated between 1.1 tinc (positive chirp) and 0.85 t inc (negative chirp). The effect was ascribed to purely dispersive properties of the thin PC. In particular, due to the wide bandwidth of the femtosecond incoming laser pulse, higher-order dispersion effects also had to be taken into account for a full explanation of the observed experimental results. Pulse compression in PC appears to be even more interesting because it depends not only on the dispersion properties of the PC near the photonic band gap (PBG) [108], where linear propagation of light is forbidden [109], but also on the intensity of the laser electric field inside the structure [110]. This dynamical pulse compression originates by a perturbation of the refractive index due to the nonlinear interaction of the ultrashort laser pulse with the PC periodic media. The compression effect occurs where and when the laser field is localized inside the layers with high refractive index [111], and assumes noticeable importance for understanding pulse nonlinear compression in photonic structures with a large modulation of the refractive index [112].

2.2.3 The few-optical-cycle regime In this section the principal physical mechanisms and techniques that underlie the generation of few-optical-cycle laser pulses will be reviewed. As it has been mentioned in the previous section, pulse compression is essentially based on the interplay of two phenomena: Kerr-induced SPM of an ultrashort, ultraintense laser pulse which propagates through a

40

FUNDAMENTALS

nonlinear medium and negative GDD. The former effect acts as a new frequency generator: the time-dependent nonlinear phase shift accumulated by the pulse propagating through the Kerr medium is, in fact, DFnl ðtÞ = 2p l0 n2 IðtÞL, I(t) being the laser pulse intensity vs. the retarded time t defined above, and L is the propagation length. Therefore, SPM broadens the pulse spectrum: the higher the laser intensity or the nonlinear medium refractive index or the longer the propagation length, the larger time-dependent phase shift and, hence, pulse broadening (see among the others [113, 114]). SPM also implies relevant drawbacks such as phase aberrations introduced by the radial dependence of the nonlinear induced phase shift through the laser intensity I, which can lead to substantial spoiling of the spatial mode quality of the laser beam. But under proper experimental conditions spatial aberrations can be minimized and the induced DFnl can be used for generating ultrashort pulses. The new red-shifted and blue-shifted spectral components emerge at different positions of the pulse temporal envelope. Consequently, a proper delay line must introduce shorter group delay for the new components born in correspondence of the trailing edge of the laser pulse as compared to the delays given to the new components emerging in the leading edge of the pulse. This is, in effect, the role of a negative GDD delay line; naturally such an effect implies pulse compression, as shown in Figure 2.8. The frequency time variation d Fnl/dt, namely the laser pulse chirp, is linear with good approximation near the top of the pulse envelope (t = 0), where most of the energy content of the pulse is concentrated. As a consequence, optimizing temporal compression requires a group delay Tg(v) nearly linear with frequency in the delay line. Furthermore, since the nonlinear refractive index n2 is usually positive (unless some medium resonance falls rather close to the laser central wavelength l0), a negative GDD is needed for temporal compression (dTg/dv < 0). While the negative GDD delay line, although relying on several different but equivalent methods, essentially acts in the same manner, either when low-energy laser pulse compression is regarded (pulses generated by ultrashort laser oscillators have typically energies in the 1–50 nJ range) or when dealing with high energy (‡1 mJ) pulse compression, such as compression of amplified pulses, SPM is obtained in substantially different physical parameter regimes, depending on whether low energy or high energy laser pulses are concerned. First, let us briefly summarize the main properties of SPM in air or, more generally in a uniform medium. The general requirements in order to optimize pulse compression efficiency and to preserve the good optical quality of the laser beam are: (i) highest possible phase shift induced by

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Frequency domain

Time domain

∆ω(τ)

SPM

GDD

n2>0

D 0, imposes spectral broadening in frequency, pulse positive chirping in time, and an instantaneous frequency decreasing in time along the pulse envelope, with vinst = v0 just at the top of the pulse (t = 0). The action of the subsequent dispersive delay line with negative GDD consists in leaving unchanged the spectrum, but temporally compressing the pulse by compensating for the chirp, i.e. restoring vinst = v0 at any time during the pulse envelope.

SPM in order to maximize the spectrum bandwidth, and (ii) small depletion of the fundamental TEM00 mode when part of the incident pulse energy is transferred to higher order modes in the nonlinear interaction with the Kerr medium. This latter point implies keeping the peak power of the pulse, p0, well below the critical power in the uniform medium, pc,unif, at which self-focusing tends to heavily distort the laser beam. It has been shown that, in the perturbative approach where just a small fraction of the energy content carried by the fundamental beam is converted into higher order modes, the coupled-mode propagation equations can be analytically solved both in free space, i.e. in a uniform medium [115] and in a hollow waveguide [116]. Within this approximation the maximum energy transferred to the first excited TEM01 mode at the beam waist, G(0), and the peak nonlinear phase shift carried by the pulse exiting the Kerr

42

FUNDAMENTALS

medium, Dfnl,out (t = 0), is [116]:   k2 p0 2 ; Dfnl;out ðt = 0Þ = pk Gð0Þ = = 4 pc;unif

Eq. (2-10)

where k=

z0 l2 ; pc;unif = 0 Lnl pn2

Eq. (2-11)

z0 = pw20 =l0 being the Rayleigh length, w0 the 1/e2-radius at the beam waist, and Lnl = (gSPMp0)
1 the so-called nonlinear length, which turns out to be a useful scale parameter for the nonlinear interaction. Thus, if Lnl >> z0, just a small fraction of the energy carried by the incoming light is coupled into the nonlinear medium to higher order modes, and, for a sufficiently long medium (L >> z0) the perturbative approach can be followed. From Eq. (2-10) it is directly seen that the small depletion of the fundamental mode implies (p0/pc,unif)2 1

Eq. (2-90)

where t is the pulse duration. From a physical point of view this relation says that the laser pulse should contain a sufficient large number of optical cycles. In general, Eq. (2-89) must be solved numerically. However, when the electric field frequency is not resonant with that of plasmons, an approximate solution is provided by the steady-state solution given in Eq. (2-88). The deviation from the exact solution is of the order of [405] 1 t maxfG; j O
vjg

Eq. (2-91)

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For describing second harmonic generation it is necessary to introduce in Eq. (2-89) an anharmonic term of the form ax2. If a is not too big, the equation may be solved with a perturbative method. If we limit only to the second order, we can write x = x1 + x2, where x1 >> x2.x1 and x2 satisfy the following two coupled equations x1 ðtÞ + ði O + GÞx1 ðtÞ = fðtÞexpð
ivtÞ x2 ðtÞ + ði O + GÞx2 ðtÞ =
ax21 ðtÞ

Eq. (2-92)

Two cases must be considered. In the first case, the fundamental is resonant with O whereas the second harmonic is not. In the second case the opposite occurs. This is important in order to simplify the solution. In fact, as already stated, for the nonresonant case the steady-state solution can be used. In the case of resonant second harmonic, the solution of the first of Eq. (2-92) is straightforward. x1 is simply proportional to f(t). As a consequence the second of Eq. (2-92) becomes x2 ðtÞ + ðiO + GÞx2 ðtÞ = bf 2 ðtÞ

Eq. (2-93)

where b =
a/(iO+G ). The general solution of Eq. (2-93) is given by Z

¥

x2 ðtÞ = b expð
i2vtÞ 2

expf
½G + iðO
2vÞt0 g½fðt
t0 Þ dt0 2

0

Eq. (2-94) The second harmonic optical field is then proportional to this solution, i.e. Z

¥

Eðt; OÞ
expð
i2vtÞ

expf
½G + iðO
2vÞt0 g½ fðt
t0 Þ dt0 2

0

Eq. (2-95) In the autocorrelation experiment, if g(t) is the amplitude of the first pulse, then fðtÞ = gðtÞ + expðivtÞgðt
TÞ

Eq. (2-96)

where T is the temporal difference between the two optical arms of the Michelson interferometer. The autocorrelation signal is given by Z SðTÞ =

+ ¥



¥


2


EðtÞ
dt

Eq. (2-97)

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FUNDAMENTALS

In Figure 2.70, the result of a numerical simulation is shown by using a Gaussian function for the optical field amplitude. In this simulation a plasmon lifetime of 10 fs and a laser pulse duration of 50 fs are used. By knowing the autocorrelation response of the optical pulse it is possible to measure the plasmon lifetime. This was measured for the first time by Steinm€ uller et al. [406] in islands of Ag on indium tin oxide. The result of this experiment is shown in Figure 2.71. In this experiment, the first direct measurement of the plasma-oscillation relaxation in a solid was obtained. This result has recently been confirmed by other measurements concerning an array of nanolithographically designed silver posts that have given a more accurate value of the plasmon lifetime, which results to be of 10 fs [396]. Very recently the same technique has been used for studying the influence of nanoparticle size on the plasmon lifetime in clusters of alkali metals leading to very interesting results [402, 407].

1

autocorrelation signal (arb. un.)

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -60

-40

-20

0 Time (fs)

20

40

60

Figure 2.70 The result of a numerical simulation for the autocorrelation of a SSHG signal. Here a Gaussian function is used for modelizing the laser pulse. In this simulation a plasmon lifetime of 10 fs and a laser pulse duration of 50 fs is used.

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Figure 2.71 Solid line shows the envelope of a SSHG autocorrelation signal on Ag island film (from Ref. [406] with permission). For comparison the pulse autocorrelation signal from a KDP crystal is also reported (dotted line). The response of KDP is almost instantaneous since in this case the SHG is not resonant.

2.8.4 Femtochemistry of surfaces probed by pump-probe SSFG and SSHG Over the last few decades surface science has made large progress thanks also to the advent of new sophisticated techniques with surface sensitivity. The chemical composition, the electronic and geometric structure of many interfaces have been extensively studied and a significant progress in the knowledge of their features has been achieved. However, most of this information refers to the static equilibrium properties of the surface. Problems related to the dynamics of chemical bond rearrangement on surfaces, as well as solvation and molecular reorientation dynamics at interfaces, have not yet been addressed extensively. Studies on bond dynamics at interfaces might answer important questions, as for example, from where the energy for the rearrangement of bonds comes, or how fast is this energy flow. For these reasons, in the last years both theoretical and experimental studies on the mechanisms and rates of energy transfer at surfaces between the adsorbates and the substrate have been boosted up. In these processes both the electronic and phonon degrees of freedom of substrate and adsorbates are involved. The substrate may transfer energy from these degrees of freedom to the adsorbate and vice versa. A detailed knowledge of the time scale of these processes and their resulting rates is essential for a fully

158

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understanding of reactions at surfaces, and possibly for their control. The progress in this field over the last few years has been possible thanks to the advent of ultrafast laser technology. The first experiment that probed ultrafast dynamics at surfaces was performed by Budde and co-workers who studied desorption of NO from Pd(111) by means of a two-pulse correlation measurement [408]. Shortly after this work, the desorption of CO from a Cu surface was the first chemical reaction to be monitored in real time [409]. In this work, for the first time in such types of experiments, the authors used time-resolved SSHG. Recently, interesting results about this reaction, which can be considered a model for catalysis, have been obtained by means of time-resolved pump-probe IR spectroscopy [410] and photo-electron spectroscopy [411]. Interesting perspectives have been opened recently by the use of timeresolved nonlinear optical techniques for the study of orientational dynamics at interfaces on a ps timescale. Eisenthal and co-workers have been the first to apply time-resolved SSHG for monitoring the reorientation of molecules at air–water interface [355, 412]. In this work the first pump-pulse is used for aligning molecules at interface, while the SSHG induced by a second probe-pulse is monitored at adjustable temporal delay for obtaining information in real time on the molecular orientational dynamics. Other interesting examples in this field are given by Refs. [413, 414]. On a femtosecond temporal scale, very recently time-resolved SSHG proved to be a powerful tool for investigating solvation dynamics at interfaces where usual experimental tools like time-resolved fluorescence fail [415]. While these studies regard the orientational properties of a molecule as a whole, SSFG could raise the possibility of studying the orientational dynamics of single moieties within the whole molecule because of its capability of performing vibrational spectroscopy. The latter property is of great importance for investigating reaction intermediates and the coupling between different vibrational modes during the course of a surface reaction. In fact, molecular vibrations of adsorbates provide direct insights into the formation and breaking of chemical bonds at interface. Even if only few examples exist to date, femtosecond pulse technology has opened up new perspectives in this field, and it is expected that femtosecond pump–probe SSFG may give significant contributions in tracing short lived intermediates in interfacial chemical reactions and in probing their dynamics [347]. Several experimental schemes can be proposed for time-resolved SSFG [416]. However, the only suitable technique for having both tem-

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poral and frequency resolution is the one shown in Figure 2.72. In this clever scheme a first ultrafast pulse induces a surface reaction and the resulting transient changes of an adsorbate vibrational mode are probed by broadband-IR SSFG (bIR-SSFG) spectroscopy by varying the temporal delay between the pump-pulse and the pair of SSFG probe pulses. The time delay between the two beams of this pair is kept fixed. bIRSSFG is used for obtaining a high frequency resolution. This is because as wide is the temporal pulse is as narrow is its spectrum. The broadband IR probe-pulse induces an IR-polarization. This polarization decays typically in few ps due to dephasing. The second visible probe pulse, temporally wider, up converts the vibrational excitation to a virtual electronic level. The width of the resulting spectrum of the emitted SSFG signal is determined by the vibrational resonance because the

Temporally narrow IR pump pulse Temporal delay Temporally narrow IR probe pulse

SSFG signal

Temporally narrowspectrally broadband VIS probe pulse

Figure 2.72 Scheme of setup for time- and frequency-resolved SSFG spectroscopy. A first ultrafast pulse induces a surface reaction. The resulting transient changes of an adsorbate vibrational mode are probed by bIR-SSFG spectroscopy by varying the temporal delay between the pump-pulse and the pair of SSFG probe pulses. The time delay between the two beams of this pair is kept fixed. bIRSSFG is used for obtaining a high frequency resolution. This is because temporally wider pulses are spectrally narrow. In this probing technique the broadband IR pulse (temporally short) induces an IR-polarization. This polarization decays typically in few ps due to dephasing. The second visible probe pulse, temporally wider (spectrally narrower), upconverts the vibrational excitation to a virtual electronic level. The width of the resulting spectrum of the emitted SSFG signal is determined by the vibrational resonance because the SSFG is enhanced only in correspondence of the frequency components of the spectrally narrow visible pulse. The temporal resolution is achieved by varying the temporal delay between the pump pulse and the bIR-SSFG pair. The delay between the beams of the pair is kept fixed.

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SSFG is enhanced only in correspondence to that frequency component that matches with the wavelength of the spectrally narrow visible pulse. Then the temporal resolution is achieved by varying the temporal delay between the pump pulse and the bIR-SSFG pair. The resolution of this technique amounts to 500 fs in time and of 8 cm
1 in frequency. Another recent study concerns the CO stretch vibration of carbon monoxide adsorbed on a single-crystal Ru(001) surface [417, 418]. In Figure 2.73, the SSFG spectra obtained at different temporal delays with respect to an IR pumping pulse initiating CO desorption are shown. The main features are the initial red-shifting, a successive blue-shifting, a broadening and a lowering of the resonance peak in time. The set of these findings permit of singling out the fundamental role in the initial desorption process of the coupling between the internal CO stretching and the CO rotational mode which is frustrated by the substrate.

Figure 2.73 Transient SSFG spectra of the C–O stretch mode on a Ru(001) surface at pump energy inducing CO desorption (from Ref. [416] with permission). The main features are the initial red-shifting, a successive blue-shifting, a broadening and a lowering of the resonance peak in time. These findings together permit of singling out the fundamental role in the initial desorption process of the coupling between the internal CO stretching of the CO rotational mode which is frustrated by the substrate.

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It is worthwhile to mention, even if it is not a time-resolved SSFG experiment, that very recently SSFG spectroscopy has been used for studying the transition to delocalization of elementary excitation of CO on Ru surfaces [417]. As we have explained in Section 2.5, localization of vibrational energy in a specific bond is of fundamental importance in achieving mode-selective chemistry. The results of this important study are summarized in Figure 2.74 for different values of CO coverage over the Ru surface. For low values of CO coverage two resonant peaks are clearly seen. The principal one corresponds to SSFG signal coming from IR excitation from the ground state (v = 0) to the first excited vibrational level (v = 1). However, at high enough pump energy, absorption from the first to the second (v = 2) vibrational level can occur leading to the appearance of a new peak in the SSFG spectrum. This peak probes directly the n = 1 ! 2 stretching mode. However, by increasing the surface coverage dipole–dipole interactions between the neighbor molecules leads to delocalization of this elementary excitation all over the

Figure 2.74 On the left, SSFG spectra of the C–O stretch mode as a function of CO coverage (from Ref. [417] with permission). For low values of the CO coverage two resonant peaks are clearly seen. The principal one corresponds to SSFG signal coming from IR excitation from the ground state (v = 0) to the first excited vibrational level (v = 1). However, at high enough pump energy, absorption from the first vibrational level to the second (v = 2) can occur leading to the appearance of a new peak in the SSFG spectrum. This peak probes directly the v = 1 ! 2 stretching mode. By increasing the surface coverage dipole–dipole interactions between the neighbor molecules bring to a delocalization of this elementary excitation all over the molecular monolayer. On the right side, theoretical predictions are compared with experimental results (for details see Ref. [417]).

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molecular monolayer. This result has been recently confirmed by using a novel technique, the so-called ‘Infrared-Infrared-Visible’ SSFG [419]. Other interesting experimental examples of applications of timeresolved SSFG are provided in refs. [420–422]. This field is in its infancy and we believe that all the potential of time-resolved SSFG has not yet been completely exploited.

2.9

Summary

The investigation of nanoparticle properties and surface science, specifically the investigation of the chemical and physical behavior of these systems, has greatly benefited over this last decade from the use of many ultrafast optical techniques. Latest technological advances have pushed nanoscience to study smaller and smaller objects, whose linear size typically ranges nowadays from 1 to 20 nm. Just to cite an example taken from the day-to-day life, let us consider the very recent progresses of the car industry that have made possible the construction of cleaner and cleaner diesel engines, characterized by very high performances and low fuel consumption with apparently almost zero particulate matter emission. Recent studies are demonstrating that a noticeable part of the final products emitted during the combustion occurring in the last generation diesel engines contains organic carbon in the form of hydrocarbon nanoparticles or nanoparticle aggregates which, due to their very small size (1–20 nm), often escape common analytical techniques. Thus, both the amount of such nano-particulate matter present in the atmosphere and its impact on the environment and human health are, at the moment, relatively unknown. Consequently, a growing demand is arising for the implementation of new experimental techniques sensitive to the features of these new nano-materials. Many of these new methods, which mostly characterize the optical response of the system under investigation, are borrowed from ultrafast science. The detailed knowledge of the optical properties of the system often allows one to reconstruct its microscopic structure and its basic interactions with the rest of the world. Fortunately, ultrafast science has also rapidly developed over the past decade, now accessing the unprecedented temporal resolution of sub-femtosecond time-scale. This chapter, far from being a complete review of both ultrafast and nano-sciences, intends to bridge the gap between these two topics. To this purpose, we have illustrated the most widely used and most promising experimental techniques borrowed from ultrafast science and applied

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to the study of nanoparticles and thin films. The initial sections are dedicated to the basis of ultrafast science, namely ultrashort laser sources and their basic interactions with matter, i.e. with atoms and molecules. Special attention is devoted to the very hot topics, such as attosecond and few-optical-cycle pulse generation and characterization, which are presently at the border of science and may open the way for new intriguing techniques of time-resolved investigation. Some applications of ultrafast optical techniques to the study of interfacial properties are discussed. In particular, we describe two nonlinear optical techniques that recently have proven very promising for the study of interfaces: SSHG and SSFG. We briefly compare these two techniques with other classical optical techniques. However, given the limits of space of this chapter, we refer to the bibliography for a more complete review on the applications of optics to the study of interfaces. We provide the reader with some theoretical considerations about SSHG and SSFG. Special attention is devoted to describe those aspects of theory that are of interest for the chemistry and physics of nanoparticles. However, once again, these considerations cannot represent an exhaustive review of the subject and the reader is referred to a series of excellent articles existing in the literature. Finally, we have dealt with one of the hottest topics in ultrafast science, i.e. femtochemistry of surfaces. The latter is of fundamental importance, for example, in the study of nanoparticle contaminants and molecular films, catalysis, and other chemical reactions occurring at interfaces. Also in this case, given the vastness of the scientific literature on this topic, we focus on the very recent applications of SSHG and SSFG in surface femtochemistry. We stress that the application of these techniques in this particular field is still in its initial stage and a lot of work has to be done in order to fully exploit its potential.

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FUNDAMENTALS

n (particles/cm3) remains ([13], p. 190; [20]): qn þ UHn ¼ HD Hn
HðV tp nÞ þ L qt

Eq. (3-33)

where D (cm2/second) is the Stokes–Einstein particle diffusion coefficient (discussed below) and L (#/cm3/second) is a particle source/sink term to account for particle generation/consumption. The net drift velocity, Vti , appearing in Eq. (3-33) is the same one discussed previously. Although we will not make further use of the fact, it is interesting to note that Eq. (3-33) is applicable to either the Brownian motion of an individual particle or to the diffusion of a particle cloud taken from the continuum point of view ([13], p. 191). For a single particle, n is interpreted as the probability of finding a particle at position (x, y, z) at time t given that the particle was initially located at position (x0, y0, z0) at time t0. Thus, although semiconductor applications are likely characterized by very low particle concentration levels, the continuum approach can still be applied if we continue to associate the particle concentration with a probability distribution (for example, we may find particle concentrations less than 1 cm
3, which is acceptable from a probabilistic point of view). For boundary conditions, it is assumed that particles which contact the wall stick and are thus instantly removed from the gas, so that the concentration n equals zero at all walls. Only one-way coupling between the fluid flow and particle concentration fields is used in this work; i.e., the flow field is coupled to particle transport through the velocity field U which appears in Eq. (3-33), while the influence of the particle phase upon the flow is neglected. In practice, the flow field is calculated first (in the absence of a particle phase) and the resulting velocity field is supplied to Eq. (3-33) as a known solution.

3.6.1 Particle diffusion coefficient A more complete discussion of the Stokes–Einstein particle diffusion and its derivation is available in any aerosol text (e.g., [13], Chapter 5). The diffusion coefficient for a spherical particle is: D¼

kTCðKnÞ 3pmdp

Eq. (3-34)

where C(Kn) is defined by Eq. (3-8). The validity of Eq. (3-34) rests on several assumptions: (1) the particles move independently of one another

3: TRANSPORT

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DEPOSITION, RADER

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GELLER

207

and (2) the movements of a particle in consecutive time intervals are independent [16]. The latter assumption is met only if the condition t >> t holds true; in other words, the expression for the diffusion coefficient given in Eq. (3-34) is only valid for observation times much longer than the particle response time. Continuum regime limit The continuum regime limit for the diffusion coefficient is Dcontinuum ¼

kT 3pmdp

Eq. (3-35)

which is inversely proportional to particle diameter and independent of pressure. Free molecule regime limit In the free molecular limit, the diffusion coefficient reduces to Dmolecular

 1 ða þ bÞ RT 2 kT ¼ 3f 2pM Pd2p

Eq. (3-36)

which is inversely proportional to particle diameter squared and pressure. Example. The particle diffusion coefficient for a spherical particle as a function of particle size and pressure is shown in Figure 3.5 for a temperature of 293 K. For pressures below 100 torr and particle diameters below 1 mm, note that the lines are parallel and straight with a slope of negative two, as

Figure 3.5 Diffusion coefficient. Dependence of the particle diffusion coefficient on particle diameter for six process pressures in argon at 293 K.

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predicted for the free molecule regime limit. Thus, for most of the pressures and particle sizes of interest in semiconductor processing, the free molecule regime limit—Eq. (3-36)—can be used to calculate the particle diffusion coefficient.

3.6.2 Nondimensional formulation For generality, Eq. (3-33) can be nondimensionalized by choosing a characteristic length (taken here as S, the distance between the showerhead and wafer, Figure 3.2), velocity (taken here as U0, the mean inlet velocity of the flow at the showerhead, Figure 3.2), and concentration (n0¼Lh/U0, the trap source strength divided by inlet velocity). For steady state, and assuming a constant diffusion coefficient, Eq. (3-33) can be written as [20] ~ n ¼ 1 H2 n~
HðV~ t n~Þ þ 1 UH~ p Pe

Eq. (3-37)

where the Peclet number (the ratio of convective to diffusive transport) is defined as Pe ¼

SU0 : D

Eq. (3-38)

The continuum regime limit for the Peclet number is Pecontinuum ¼

3pmdp SU0 kT

Eq. (3-39)

which is proportional to particle diameter. Thus, in the continuum limit, the Peclet number can be used as a dimensionless particle diameter. In the free molecular limit: Pemolecular

 1 3f 2pM 2 Pd 2p SU0 ¼ kT ða þ bÞ RT

Eq. (3-40)

which is proportional to particle diameter squared and to pressure. In the free molecular limit, the square root of the Peclet number can be used as a dimensionless particle diameter. In standard problems of species mass transfer, the Peclet number would be sufficient to completely characterize the problem for a given

3: TRANSPORT

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geometry and flow field. For particles, however, the presence of a drift velocity term (the second term on the right-hand side) means that the Peclet number no longer uniquely specifies the solution and a dimensionless drift velocity ratio must also be considered: V~ tp ¼

Vtp Uo

Eq. (3-41)

3.7 Particle Transport and Deposition in a Parallel Plate Reactor To illustrate an application of the particle transport models, this section analyzes particle transport in an enclosed, parallel-plate reactor geometry characteristic of a wide range of single-wafer process tools. The axisymmetric geometry we consider consists of uniform flow exiting a showerhead separated by a small gap from a parallel susceptor, as shown in Figure 3.2. The wafer would rest on the susceptor, but for the present analysis the wafer is assumed to be thin enough to be ignored. The showerhead consists of a material (usually a metal or ceramic) through which a large number of holes are drilled (see Figure 3.2a). As one major function of the showerhead is to evenly distribute the flow across its face, the holes are usually made very small in diameter and are very numerous (hundreds to thousands for an 8 inch wafer process tool). Ideally, a showerhead would produce a flow characterized by a mean axial (or face) velocity that does not vary in the radial direction; such flow uniformity is needed to accomplish uniform deposition or etching of the wafer surface. In practice, however, commercial showerheads are typically designed empirically to improve process parameters (such as uniformity); the resulting showerhead designs often create nonuniform flow fields which compensate for other system deficiencies - such as radial temperature or reactive species gradients. Various flow fields can be obtained by manipulation of showerhead hole sizes, numbers, and positions. One common feature of showerhead design is that the area available to the flow is constricted inside the showerhead; consequently, the velocity of the gas inside the holes of the showerhead is much larger than the face velocity in the gap below. Particles originating upstream of the showerhead and suspended in the flow can be dramatically accelerated while passing through the showerhead, so that at the exit of the showerhead particle velocities much larger than the fluid face velocity are possible.

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Depending on conditions, particle acceleration by the showerhead can lead to inertia-enhanced particle deposition on the wafer below [21]. Thus, a complete description of particle deposition on a wafer in a parallel-plate reactor must include a description of particle transport through the showerhead as well as an analysis of particle transport in the inter-plate region. No attempt is made here to analyze particle generation mechanisms; for the present discussion, particles are assumed to originate either: (1) upstream of the showerhead with a known concentration or (2) from a specified position between the plates with a fixed number or at a known generation rate. The determination of particle transport in a reactor must always begin with a determination of the fluid flow and temperature fields. Particle concentrations are assumed to be low enough to allow a dilute approximation, for which the coupling between the fluid and particle phases is one-way. The fluid/thermal transport equations can be solved either analytically or numerically neglecting the particle phase. The resulting velocity and temperature fields are then used as input for the particle transport calculations.8 In all of the present work isothermal flow is assumed, although small temperature differences are allowed to drive particle thermophoresis. Both analytical and numerical solutions of the flow field are presented. To provide a single parameter that can be used to compare particle deposition among many cases, a particle collection efficiency is defined as the fraction of particles that deposit on the wafer. Particles are presumed to either enter the reactor through the showerhead (uniformly spread between r ¼ 0 and RW), or to originate in a plane parallel to the wafer. The latter case would correspond to particles being released from a plasma trap upon plasma extinction; in this case the particles are initially assumed to be uniformly spread radially between r ¼ 0 and RW at some distance h from the wafer. Analytical expressions for collection efficiency are presented for the limiting case where external forces control deposition (i.e., neglecting particle diffusion and inertia). Particle transport is predicted using both a Lagrangian approach (where individual particle trajectories are calculated) and an Eulerian approach (where the particles are modeled as a continuum phase). The strength of the Eulerian formulation is in predicting particle transport 8

The dilute mixture approximation is certainly valid for simulations of commercial semiconductor process tools, as the particle concentrations are typically controlled to very low levels.

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resulting from the combination of applied external forces (including the fluid drag force) and the chaotic effect of particle Brownian motion (i.e., particle diffusion), although the current implementation cannot account for particle inertia. In particular, the Eulerian formulation cannot accommodate particle acceleration effects within the showerhead, and is therefore restricted to particle transport in the inter-plate region. The Eulerian formulation yields an analytical description of particle deposition for the case where the flow field between the plates can be approximated analytically with a creeping-flow assumption and where the particles are assumed to originate from a planar trap located between the plates. The Lagrangian formulation can account for inertia-enhanced deposition resulting from particles which originate upstream of the showerhead and which are accelerated while passing through it. The problem is treated in two steps: (1) within a showerhead-hole and (2) between the showerhead and susceptor.

3.7.1 Fluid transport equations In both of the domains considered (flow within the showerhead and between two parallel plates), the geometry will be axisymmetric. With constant fluid properties, and incompressible, laminar, steady flow, the governing equations for axisymmetric flow are the conservation of mass: qu 1 q þ ðrvÞ ¼ 0 qz r qr

Eq. (3-42)

and conservation of momentum:  2    qv qv qv qP q v 1 qv q2 v v þ
þv þu ¼
þm þ qt qr qz qr qr2 r qr qz2 r2  2    qu qu qu qP q u 1 qu q2 u þ r þv þu ¼
þm þ qt qr qz qz qr2 r qr qz2 r

Eq. (3-43)

where u and v are the axial and radial components of the fluid velocity, P is the pressure, r is the fluid density, and m is the fluid viscosity ([22], p. 85). Boundary conditions are needed to complete the problem specification. In all of the following, no-slip (zero velocity) conditions are taken at all solid walls (i.e., on the showerhead, susceptor, and walls of the

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showerhead holes), zero radial velocity is assumed along the centerline, and zero traction is assumed at all outflows. For the two flow domains, specific boundary conditions and methods for solving the governing equations are discussed in greater detail below. Note that for convenience, a different coordinate system is used for describing the flow through a showerhead hole than in the region between the parallel plates (see Figure 3.2b). The generality of the present results are improved if the fluid equations are solved in nondimensional form. Because there are two domains of interest, there are two choices for a characteristic length and velocity. For flow in the showerhead holes, the hole diameter djet and the magnitude of the mean velocity Ujet are used as the characteristic length and velocity, for which the tube Reynolds number is defined as Rejet ¼ rUjetdjet/m. For the flow between two plates, the inter-plate separation S and the magnitude of the mean face velocity U0 are the appropriate choices, and the inter-plate flow is then characterized by a separate Reynolds number: Re ¼ rU0S/m

3.7.1.1 Flow field in the showerhead holes The idealized geometry and the coordinate system for fluid and particle transport in the showerhead holes is shown in the inset in Figure 3.2b. As seen, z is taken as increasing in the direction of flow (toward the wafer), so that all fluid and particle axial velocities considered in this part of the solution are positive. The flow in the showerhead holes is assumed laminar with parallel streamlines, thereby neglecting any axial variations in velocity. For laminar flow in a tube with a uniform inlet velocity, however, it is well known that a fully developed parabolic velocity profile develops over an entrance length given approximately by 0.04 djet Rejet ([5], p. 72). For many showerheads this entrance length is much less than the hole length (showerhead thickness) and so may be safely neglected; for thin showerheads, however, this may not be the case. In the present analysis, we consider two limiting velocity profiles that meet the above assumptions: (1) plug flow (constant velocity profile) and (2) fully developed laminar flow (parabolic velocity profile). For laminar flow, the velocity profile anywhere along the hole will fall somewhere between these two limiting cases. In case one, the velocity is constant throughout the tube and, for incompressible flow, is equal to the mean velocity in the hole, U jet ¼ 4Q=ðNjet pd 2jet Þ where Q is the total gas volumetric flow rate through the

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showerhead and Njet is the number of individual holes in the showerhead. By mass conservation it can be shown that the ratio of the mean axial velocity in a hole and the face velocity is the ratio of the showerhead area to the total hole area: U jet Ashowerhead D 2W ¼ ¼ Uo SAjet Njet d2jet

Eq. (3-44)

For case two, fully developed laminar flow in a tube is given by Ujet ðrÞ ¼ 2U jet

 2 ! r 1
ajet

Eq. (3-45)

where r is the radial distance from the tube centerline and ajet is the radius of the hole. The maximum velocity for parabolic flow is twice the mean velocity and occurs on the centerline.

3.7.1.2 Fluid transport between parallel plates Both analytical and numerical techniques have been used to calculate the fluid flow between the showerhead and susceptor. For both methods we assume axisymmetric, incompressible, constant property, laminar, steady flow between two parallel plates (Figure 3.2b). The flow enters through the showerhead (z ¼ S) and is assumed to spread immediately, so that the inlet boundary condition is assumed to be a uniform axial velocity,
U0, with zero radial velocity. Both the radial and axial components of velocity vanish at the lower plate (z ¼ 0). The analytical approach assumes that the plates are infinite in the radial direction and that the Reynolds number is small; the numerical technique is used for finite plates and is valid for higher Reynolds numbers. The numerical technique is relied on here to define the conditions over which the simpler analytical solution is valid. The assumption of constant-property flow requires further comment. Although the numerical methods used here can solve for coupled fluidthermal transport, we have not used this capability in the present analysis. For cases where temperature differences are large or where more accurate solutions are needed for a specific application, the reader is advised to solve the coupled fluid–temperature problem. As mentioned above, a modest temperature gradient is allowed to drive particle

214

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thermophoresis (the magnitude of all particle drift velocities will be calculated using fluid properties evaluated at the susceptor temperature). Under the above assumptions, the flow between the plates is entirely determined by the geometry and the Reynolds number Re ¼ rU0S/m. For the range of conditions encountered in semiconductor reactor processes, the associated Reynolds numbers are typically less than one, and seldom greater than 10. For small Reynolds numbers, viscous effects dominate fluid inertial effects and the ‘‘creeping flow’’ or Stokes flow regime is encountered; it is this regime that allows an analytical solution. The numerical method used for calculating the fluid velocity field was the commercial fluid dynamics analysis code FIDAP (Version 7, Fluid Dynamics International, Evanston, IL, USA). The numerical technique was used to calculate flow fields for Reynolds numbers up to eight. With fixed values for plate separation (S ¼ 1), mean inlet velocity (U0 ¼ 1), and fluid viscosity (m ¼ 1), the fluid density r was varied to obtain flow field solutions for Reynolds numbers between one and eight. The FIDAP option of solving the Stokes flow equations (Re ¼ 0) was also used. The results of these calculations are given in Figure 3.6, which shows axial and radial velocity profiles at r ¼ 1 for Re ¼ 0, 1, 2, 4, and 8 as a function of the dimensionless axial coordinate z/S. Note that all velocities have been normalized by the magnitude of the inlet velocity U0, and that the radial velocity is also normalized by radius. For Re ¼ 0, the radial velocity profile is found to be parabolic and symmetric around z/S ¼ 0.5. As Reynolds number increases, the symmetry vanishes and the maximum in the radial velocity moves closer to the plate (z/S ¼ 0). Variations in the axial and radial velocity profiles are seen to be quite small for Reynolds numbers less than two. As in previous work in a similar geometry [26], it was found that the flow was quasi-1-D: the axial velocity is independent of radius, while the radial velocity is found to scale with radius such that v/r is independent of radius. An analytical simplification is gained if the flow between the plates can be approximated as a quasi-1-D stagnation point flow. Terrill and Cornish [23] give an asymptotic solution to the problem of axisymmetric, laminar, incompressible, constant property and steady flow between two co-axial infinite parallel disks with constant injection across the disks (a uniform gas inlet velocity across the showerhead). Under these assumptions, a similarity solution reduces the 3-D Navier–Stokes equations to a system of ordinary differential equations; for low Reynolds numbers, these equations can be solved with a power series in Reynolds number [23]. The first two terms of their asymptotic expansion (translated into

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the present problem definition) are: uð~ zÞ Re ¼ 2~ z 3
3~ z2 þ z 6 þ 18~ z 3
13~ z2Þ ð2~ z 7
7~ Uo 70   Eq. (3-46) vð~r ; z~Þ 2 Re 6 5 2 v~ð~ r ; z~Þ ¼ ¼ r~ 3~ z
3~ z
z þ 27~ z
13~ zÞ ð7~ z
21~ Uo 70 u~ð~ zÞ ¼

Figure 3.6 Flow field results for various Reynolds numbers. Axial (a) and radial (b) velocity profiles for Re ¼ 0, 1, 2, 4, and 8 calculated on a refined (30 elements) mesh. (r/S ¼ 1 for all curves).

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where z~ ¼ z=S and r~ ¼ r=S. These two equations exactly satisfy all boundary conditions. The quasi-1-D nature of the result is clearly seen as the axial velocity is independent of radius, while the radial velocity scales linearly with radius. In the limit of vanishingly small Reynolds number, Eq. (3-46) reduces to a symmetric, parabolic profile for radial velocity, in excellent agreement with the Stokes flow solution (Re ¼ 0) obtained by FIDAP (this limit has also been previously reported by Houtman et al. [24]). Equation (3-46) does a very good job of approximating the axial velocity profile—agreeing with FIDAP solutions to better than 1% for Reynolds numbers less than 4, and to better than about 4% for Reynolds numbers up to 8. The success of Eq. (3-46) in predicting radial velocity is not nearly so good. Although the error is better than 1% for Re < 1, the maximum observed error quickly grows, reaching 15% for Re ¼ 4 and 70% at Re ¼ 8. As can be seen, the largest errors are found near the showerhead (z/S ¼ 1), where the magnitude of the radial velocity is quite small. Thus, although the relative error is quite large, the absolute error is small. In any case, our treatment of the region near the showerhead is only approximate because we have neglected the effect of the discrete jets issuing from the showerhead. Strictly from a fluid velocity point of view, Eq. (3-46) provides a very good approximation of the flow for Reynolds numbers less than two, and a reasonable approximation up to a Reynolds number of four.

3.7.1.3 Summary: fluid flow analysis for the parallel plate geometry This section has defined the parallel-plate geometry which will be used to approximate the flow inside a showerhead-type etch or CVD reactor. The acceleration of the gas flow as it passes through the showerhead will later be found to play a key role in enhancing particle deposition by particle inertia; for this reason, solutions for flow within the showerhead holes have been presented. The two limiting cases which were considered, plug and fully developed parabolic flow, should bracket the range of flows likely to be encountered in semiconductor applications. Laminar, incompressible, constant-property flow between two infinite, parallel plates was used to approximate the inter-plate flow in real reactors which are certainly more complicated. Reynolds number and edge effects were discussed, and an analytical solution was found that should provide

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a fairly accurate description of the flow for Reynolds numbers less than about four when the plate separation is much smaller than the overall system radial dimension. Variable temperature effects have not been considered.

3.7.2 Particle collection efficiency Particle collection efficiency is defined as the fraction of particles present in the inter-plate region that deposit on the wafer. The collection efficiency is introduced to provide a single parameter that can be used to compare particle transport and deposition results among many cases. Note that the use of collection efficiency side-steps the important issue of the particle source term. Thus, while the present transport analysis addresses the question of the fraction of gas-borne particles that deposit on the wafer, a prediction of the number of particles that deposit on the wafer additionally requires a clear understanding of the controlling particle generation mechanisms. In practical terms, the present analysis helps identify strategies for reducing the probability that particles are transported to and deposit on a wafer; a complete strategy for reduction of total particle-on-wafer counts also requires that particle source terms be understood and controlled. Three particle-source scenarios are considered: (1) a continuous source of particles entering the inter-plate region through the showerhead with known concentration (such as for contaminated process gases), (2) a discrete number of particles that are originally trapped between the plates (such as by a plasma) but are subsequently released (such as at plasma extinction), and (3) a continuous source of particles which are created between the plates at a known generation rate (such as by particle nucleation). General collection efficiency expressions for these cases are defined below. In addition, analytical expressions are provided for the limiting case where external forces control particle deposition—i.e., both particle inertia and Brownian motion are neglected. In the absence of particle inertia and Brownian motion, Robinson [25] has shown that particle concentration is constant along particle trajectories if: (1) the flow is incompressible and (2) the external forces acting on the particle are all divergence free. For the infinite parallel-plate geometry with constant-property flow, the flow is clearly incompressible and the second condition is met for the gravitational and Coulombic electric particle forces (which are each constant between the plates).

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3.7.3 Particles entering through the showerhead For this case, collection efficiency is defined as the fraction of particles entering the inter-plate region through the showerhead (between r ¼ 0 and RW) that deposit on the wafer. These particles are presumed to originate upstream of the showerhead and are assumed to be evenly distributed across the showerhead. Particle acceleration through the showerhead will be considered in Section 3.8.1. The present Lagrangian formulation accounts for the coupling between particle inertia and external forces in determining particle transport in the inter-plate region. The calculation of a collection efficiency with a Lagrangian technique requires the determination of the critical radius, Rcrit, which is the starting radial position (at the showerhead) of a particle that follows a trajectory that leads it to deposit at the edge of the wafer, RW (see Figure 3.7). All particles starting closer to the centerline will deposit on the wafer, while those starting farther out will exit the reactor. For a uniform concentration across the showerhead, the collection efficiency, h, can be written as  h¼

Rcrit RW

2 ¼

 2 Ri Rf

Eq. (3-47)

In general, the critical trajectory must be found by a trial-and-error method. The second equality of Eq. (3-47) is a simplification that only applies under our quasi-1-D approximation. In this case, all the factors that influence particle deposition (e.g., axial fluid velocity profile, the particle initial velocity, and particle axial drift velocity) are independent of radial position; thus, the question of whether a particle will hit CL R crit

rp•• RW

Figure 3.7 Critical trajectory. Diagram of a critical trajectory for a particle which starts at the showerhead at radial position Rcrit and deposits at the wafer edge RW.

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the wafer must not depend on its initial radial position, Ri (although the radial position at which the particle hits the wafer, Rf, will depend on Ri). It can be shown for our quasi-1-D case that the ratio Ri/Rf is independent of initial radial position. Thus, efficiency in the Lagrangian framework is calculated by starting the particle at a particular radial position (Ri ¼ 1) and calculating its trajectory to determine the radial position of contact with the wafer;9 the efficiency is then (Ri/Rf)2 ¼ (1/Rf)2 as given in Eq. (3-47). The total number of particles depositing on the wafer is the product of efficiency times the total flux of particles entering through the showerhead.

3.7.3.1 External force limit For the case where external forces control particle deposition (neglecting inertia, interception, and diffusion), Rader et al. [26, 27] used a Lagrangian analysis to obtain the following expression for deposition efficiency in isothermal, quasi-1-D parallel-plate flows:    2 jV tp j Rcrit 2 Ri ¼ ¼ t h¼ jV p j þ U0 RW Rf

V tp £ 0

Eq. (3-48)

where Vpt is the z-component of the net particle drift velocity (the resultant of all external forces in the axial direction).10 For net drift velocities greater than zero (net external force pushing particles away from the wafer), no particle deposition on the wafer is predicted (although it will be shown later that particle inertia or diffusion can cause deposition even in this case). Equation (3-48) provides a lower bound for particle deposition, as inertial and diffusional effects can only increase deposition from what is predicted. Interestingly, as the particle net drift velocity is typically much smaller than the fluid entrance velocity, Eq. (3-48) predicts that (in the absence of inertia and diffusion) the particles which land on the wafer originate from near the reactor centerline.

9

In the event that the particle axial velocity becomes zero, or begins to move away from the wafer, then the trajectory calculation is terminated and the efficiency is set to zero. 10 When inertia is neglected, the particles enter the reactor with the mean gas velocity so that Vpo ¼
U0. Also, note that U0 is the magnitude of the face velocity, and so is positive.

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Equation (3-48) is independent of the flow field (consider that the flow Reynolds number does not appear) that can be more easily understood by applying Robinson’s [25] result (as discussed above). Neglecting diffusion and inertia, the concentration over the lower plate must equal the inlet concentration, n0. The rate at which particles deposit on the lower plate becomes jV tp jno pR 2W , while the rate at which particles enter through the showerhead is ðjV tp j þ Uo Þno pR 2W . Taking the ratio of these expressions gives the same efficiency as Eq. (3-48) (see also [28]). Similar results, including Eq. (3-48), were found by Ramarao and Tien [29] for plane-stagnation flow. Interception effects were neglected in Eq. (3-48), which implies that a particle is collected only when its center of mass reaches the wafer surface. A better assumption is that particle collection occurs when the particle comes within one particle radius (rp ¼ dp/2) of the wafer surface.11 The derivation of Eq. (3-48) can be easily modified to include interception, with the following result:  h¼

Rcrit RW

2 ¼

 2 jV tp j þ juðz ¼ rp Þj Ri ¼ jV tp j þ Uo Rf

V tp £ juðz ¼ rp Þj Eq. (3-49)

Note that particle collection is now expected in the absence of external forces (or even for weak repulsive forces); the physical interpretation is that collection occurs when the flow brings the particle within one particle radius of the wall. The inclusion of interception also has the effect that Eq. (3-49) [unlike Eq. (3-48)] depends on the flow field through the term u(z ¼ rp). Because the gas velocity one particle radius away from the wafer is typically vanishingly small, interception effects are generally neglected in the following discussion, and Eq. (3-48) is used.

3.7.4 Particle traps/in situ nucleation Another source of wafer contamination is from particles that start somewhere between the plates, and are subsequently transported to the wafer. One example is particles generated in situ by nucleation. A second example is particles that are originally trapped between the plates during 11

The inclusion of particle interception effects is somewhat overkill, as we have neglected wafer surface roughness/structure which is likely characterized by dimensions similar to particle sizes.

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a plasma process, which are subsequently released at plasma extinction. While the plasma is on, contaminant particles generally accumulate in specific regions of the radio frequency (RF) discharge. Roth et al. [30] first used laser light scattering to observe that particles accumulate near the bulk plasma-sheath boundary in these discharges. Sommerer et al. [31] and Barnes et al. [32] first proposed that particle transport in the discharge is dominated by two forces: electrostatic and viscous ion drag. The electrostatic force accelerates negatively charged particles toward the center of electropositive plasmas, while viscous ion drag accelerates particles in the direction of net ion flux (generally toward plasma boundaries). Particle ‘‘traps’’ occur in regions where the sum of forces acting on the particle vanishes. In many cases these traps are approximately planar and parallel to the plates [33]; a schematic of a planar trap is shown in Figure 3.8, where the particles are uniformly distributed at a distance h above the lower plate. Only planar traps are considered in this work, although a variety of other trap structures (rings, domes, etc.) are well known in the literature. For any trap structure more complicated than an infinite plane the problem becomes inherently 2-D, which is beyond the scope of the present analysis. At the end of the process step, the discharge is extinguished and the plasma-induced forces responsible for particle trapping are assumed to dissipate rapidly (compared to particle transport times) in the afterglow. In this work, we assume that the charged particles are rapidly neutralized after the plasma extinction and can therefore be treated as neutral particles as experimentally observed by Jellum et al. [34], CL

Particle Trap R crit h

rp•• RW

Figure 3.8 Trap schematic. Diagram of particles in a planar trap located at a distance h from the lower plate; a critical trajectory is also shown for a particle which starts at radial position Rcrit and deposits at the wafer edge RW.

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Shiratani et al. [35], and Yeon et al. [36].12 Under the assumption of rapid neutralization, the particles are released from the traps and can deposit on the wafer as a result of external forces, inertia, or Brownian motion (diffusion). To analyze the extent of deposition both the Lagrangian and Eulerian formulations have been used. Although the physical interpretation of efficiency (fraction of particles starting in the trap that end up on the wafer) is the same for both approaches, the methods of calculating the efficiency are quite different.

3.7.4.1 Efficiency for the Lagrangian formulation In the Lagrangian formulation, Brownian motion is neglected and calculation of particle trajectories is determined from the coupling between particle inertia and external forces. Consequently, the determination of a collection efficiency reduces to the determination of a critical trajectory just as defined in Eq. (3-47) of the previous section, except that the particle starting position is now at axial position h and the particle initial velocity is assumed to be zero. As before, it can be shown for our quasi-1-D case that the ratio Ri/Rf is independent of initial radial position within the trap. Thus, efficiency in the Lagrangian framework is calculated by starting the particle at a particular radial position (Ri ¼ 1) in the trap (z ¼ h) and calculating its trajectory to determine the radial position of contact with the wafer; the efficiency is then calculated by Eq. (3-47).

3.7.4.2 Efficiency for the Eulerian formulation For small particles and/or at low pressure, the effects of Brownian motion on particle transport must be considered. Brownian motion results from random variations in the force exerted on the particle by background-gas molecular bombardment, and gives rise to particle diffusion along concentration gradients. Also, Brownian motion implies that particle trajectories are no longer deterministic; that is, identical particles started at the same initial location with the same initial conditions will not follow the same path through the reactor. In this case, an Eulerian formulation of particle transport is used, in which the particles 12

However, a study by Collins et al. [37] suggests that some particles might retain a few residual charges (positive or negative) in the afterglow.

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are treated as a continuum or cloud and the particle concentration field is calculated (inertia is neglected). Particle deposition is determined in terms of a particle flux at the wafer’s surface, J0 (#/cm2/s), which is calculated from the surface concentration gradient (where particle interception is neglected):  dn  Eq. (3-50) Jo ¼ D  dz z¼0 where n is the particle concentration and D is the particle diffusion coefficient. Note that a general expression for particle flux would include both a diffusional term, given by Eq. (3-50), and a drift-velocity term, given by nV~tp . In Eq. (3-50) only the diffusional term is shown because, under our assumption that particle concentration vanishes at surfaces, the drift-velocity contribution must also vanish at the susceptor. Thus, even when external forces are controlling deposition, a thin boundary layer must exist near the susceptor wherein the concentration drops from the free-stream value to zero at the susceptor’s surface. The particle collection efficiency is then calculated as the ratio of particle flux to the wafer divided by the particle source term (number of particles being released from the trap). Equation (3-50) can be extended to account for particle interception by evaluating the concentration derivative at rp (instead of zero):  dn  Eq. (3-51) Jo ¼ D  dz z¼rp

3.7.4.3 External force limit As in the previous section, an analytical result can be derived for deposition efficiency in the limiting case where external forces control particle deposition (particle inertia, interception, and diffusion are all neglected):    2 jV tp j Rcrit 2 Ri ¼ ¼ t h¼ RW Rf jV p j þ juðz ¼ hÞj

V tp £ 0

Eq. (3-52)

which is the same as Eq. (3-48) except that the gas axial velocity at the trap location replaces the mean gas velocity in the denominator. For net drift velocities greater than zero (net external force pushing particles away from the wafer), no particle deposition on the wafer is predicted.

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Equation (3-52) provides a lower bound for particle deposition, as inertial and diffusional effects can only increase deposition from what is predicted. As expected, the collection efficiency tends toward unity as the particle trap moves closer to the lower plate (h0) because the axial gas velocity must approach zero at the plate surface. For particles which ultimately deposit on the wafer, Equation (3-52) also can be used to determine the radial position on the wafer at which particles are collected, Rf, based on starting position r ¼ Ri and z ¼ h. As discussed in the previous section, particles which deposit on the wafer are those which start nearest to the reactor centerline. It should be noted that both the Eulerian and Lagrangian collection efficiencies defined above must tend to Eq. (3-52) in the limit when particle diffusion, inertia, and interception effects are all negligible. Equation (3-52) can be extended to include particle interception as in the previous section: h¼

   2 jV tp j þ juðz ¼ rp Þj t Rcrit 2 Ri ¼ ¼ V £0 jV tp j þ juðz ¼ hÞj p RW Rf

Eq. (3-53)

As before, particle collection is now predicted in the absence of (or for weak) external forces, and is seen to depend on the flow field through flow velocity terms in both the numerator and denominator. Both the Eulerian and Lagrangian collection efficiencies defined above must tend to Eq. (3-53) in the limit where particle diffusion and inertial effects are negligible.

3.7.5 Diffusion-enhanced deposition from traps or in situ nucleation One difference between these two particle–source scenarios is that the source term resulting from nucleation is continuous, while the source term for a plasma-trap release is a transient event characterized by the number of particles in the trap at the time of release. In either case, the particles of interest are likely to be quite small and chamber pressures may be low, so that the effect of particle Brownian motion must be considered. Although these very small particles are not currently considered to reduce yield, the trend towards smaller feature sizes on integrated circuits is continually reducing the size of a killer defect. Thus, the industry will inevitably be faced with the need to understand the role of diffusion in particle transport and deposition.

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The analysis of this section closely follows the previous work of Peters et al. [20] who investigated the diffusive deposition of particles onto disks in an infinite stagnation point flow (such as for a wafer exposed to the downward flow in a clean room). In their work, Peters and coworkers assume axisymmetric viscous stagnation point flow, while in this work an analytical asymptotic result for flow between two axisymmetric infinite parallel plates is used. Peters et al. also used different particle concentration boundary conditions than in this work: particle concentration was assumed to be zero at the disk and to approach a constant infinitely far away from it. Here, the two plates are considered perfectly absorbing (vanishing particle concentration), and a planar particle source is assumed to be located somewhere between them.

3.7.5.1 Problem definition We assume the geometry shown in Figure 3.9: axisymmetric flow between two infinite, parallel plates (a showerhead and a susceptor) separated by a distance S. The effect of jetting out of the showerhead holes is neglected, so that the flow is assumed to be uniformly distributed across the bottom of the showerhead with velocity, U0. The flow is assumed to be isothermal (constant gas properties), steady, laminar, incompressible, and viscous such that the quasi-1-D analytical result [Eq. (3-46)] can be used. As discussed, Eq. (3-46) is reasonably accurate for flow Reynolds numbers less than about four based on comparison to more accurate numerical finite-element simulations. The particles are assumed to enter the domain at a steady volumetric rate L (#/cm3/second) from a planar source located a distance h from CL SHOWERHEAD −Uo Particle Trap Λ

S z

h r

SUSCEPTOR

Figure 3.9 Geometry. Diagram of parallel, infinite-plate geometry with particles in a planar trap located at a distance h from the lower plate.

226

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the susceptor. Although this description adequately applies to a continuous source such as particle nucleation, it is not immediately obvious that a steady-state analysis is applicable to the transient case where a finite number of particles are simultaneously released from a trap at time t ¼ 0. Analysis of the governing equations reveals that the particle collection efficiencies from the steady-state and transient problems are in fact the same under the following conditions: (1) steady flow field, (2) infinite parallel-plate (1-D) domain, (3) radially uniform distribution of initial particle positions for the transient problem, and (4) radially uniform particle source for the steady-state problem. To confirm this contention, particle transport calculations using the present steady-state Eulerian approach have been compared with the Brownian dynamics simulations (BDS) of Choi et al. [38]. Choi and coworkers solved the Langevin equation directly using a massively parallel numerical Lagrangian particle tracking model which included a fluctuating Brownian force; transport calculations were presented for particles that were initially distributed in planar traps in a parallel-plate geometry similar to that assumed here. The BDS method is inherently transient in nature, in that a large number of particles were initially distributed uniformly throughout the trap, and their trajectories followed in time until the particles either deposited on a plate or left the calculation domain. For comparison with the present approach, Brownian dynamics simulations were performed with the analytical velocity field given by Eq. (3-46). As expected, BDS results for particle collection efficiency were in excellent agreement with the steadystate Eulerian formulation presented here. Thus, the analytical result for particle collection efficiency given below applies equally well for a steadystate particle planar source as for the case of a cloud of particles released from a planar trap.

3.7.5.2 Solution of the Eulerian particle transport equation Neglecting particle inertia, the Eulerian expression for particle concentration, n (#/cm3), is Eq. (3-33) which is reproduced here: qn þ UHn ¼ HDHn
HðV tp nÞ þ L qt

Eq. (3-54)

where D (cm2/second) is the Stokes–Einstein particle diffusion coefficient, L (#/cm3/second) is the particle source term, and is the net drift velocity vector. Consistent with our flow assumptions, the concentration field is assumed to be steady and one-dimensional (depending only axial

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position). Also, for isothermal flow, the diffusion coefficient and particle drift velocity are constant. With these assumptions and simplifications, Eq. (3-33) may be rewritten as u

dn d 2n dn ¼ D 2
V tp þ L dz dz dz

Eq. (3-55)

In Eq. (3-55), V tp is the z-component of the net drift velocity vector and u is the axial velocity field given by Eq. (3-46). For boundary conditions, the assumption of perfectly absorbing walls is made which implies that the particle concentration is zero at both the upper and lower plates, i.e. n(z ¼ 0) ¼ n(z ¼ S) ¼ 0.13 Note that by assuming an absorbing surface at the showerhead we are neglecting the showerhead holes, but this is reasonable as the holes typically account for only a few per cent of the total showerhead surface. For this analysis, the particle source is assumed to be infinitely thin so that L ¼ Lh dðz
hÞ

Eq. (3-56)

where Lh (#/cm2/second) is a constant area source term and d (cm
1) is the Dirac delta function. Although the following derivation also could be followed for a finite-thickness source term, the resulting analytical expression for particle collection efficiency would be much more complicated than that given below. To nondimensionalize Eq. (3-55), the appropriate characteristic length and velocity scales are S and U0, respectively. A characteristic particle concentration, n0, can be defined based on the particle source strength and gas inlet velocity: n0 ¼

Lh U0

Eq. (3-57)

Using these definitions, Eq. (3-55) becomes: u~

d~ n 1 d2 n~ ~ t d~ n ~
V p þ dð~ ¼ z
hÞ d~ z Pe d~ d~ z z2

Eq. (3-58)

where n~ ¼ n=n0 , u~ ¼ u=Uo , z~ ¼ z=S, V~ tp ¼ V tp =U0 , Pe¼SU0/D, and h~ ¼ h=S. As discussed above, the solution for the dimensionless 13

Deposition by interception, due to the finite size of the particle, is neglected. To account for interception requires that the boundary conditions be given as n(z ¼ rp) ¼ n(S
rp) ¼ 0 where rp is the particle radius.

228

FUNDAMENTALS

~ concentration is completely determined by the dimensionless groups Pe, h, t ~ V p , and Re (which enters implicitly as u~ depends on Reynolds number). After defining a dimensionless concentration gradient d~ n G~ ¼ d~ z

Eq. (3-59)

equation (3-58) can be rewritten as dG~ ~ z
hÞ
Peð~ u þ V~ tp ÞG~ ¼
Pe dð~ d~ z

Eq. (3-60)

The solution to Eq. (3-60) is G~ ¼ G~ 0 expðAÞ
expðAÞ

Zz~

~ Pedð~ z
hÞexpð
AÞd~ z

Eq. (3-61)

0

where 

   1 4 3 Re 1 8 7 9 4 13 3 t ~ Að~ z Þ ¼ Pe z~
~ z þ z þ z~
z~ þ V p z~ z~
~ 2 70 4 2 3

Eq. (3-62)

and G~ o is the dimensionless concentration gradient at the lower plate, z~ ¼ 0. Note that G~ o is frequently referred to as the Sherwood number, Sh z ¼ 0Þ ¼ (e.g., [20]). To determine G~ o , apply the boundary conditions ð~ n~ð~ z ¼ 1Þ ¼ 0 after integrating Eq. (3-59): Z1

d~ n d~ z¼ d~ z

0

Z1

Z1 d~ n¼0¼ 0

~ z Gd~

Eq. (3-63)

0

Solving Eq. (3-63) for G~ o gives

Eq. (3-64)

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3.7.5.3 Particle collection efficiency The particle collection efficiency is found as the ratio of particle flux to the lower plate divided by the total number of particles entering the reactor:  dn  DLh d~ n Aw D  j dz z¼0 SU0 d~ z z~¼0 G~ 0 Eq. (3-65) ¼ ¼ h¼ RS Lh Pe Aw Lh dðz
hÞdz 0

where Aw is the area in the r–u plane. Thus, an analytical result for the particle collection efficiency is given by Eqs. (3-64) and (3-65)—although the solution requires numerical quadrature. The dependence of the col~ V~ t , and Pe, is lection efficiency on the four dimensionless groups, Re, h, p clearly shown in Eqs. (3-64) and (3-65). For comparison to previous work in the literature, the particle collection efficiency defined by Eq. (3-65) can also be expressed as the ratio of the Sherwood to Peclet numbers, h ¼ Sh/Pe. The use of collection efficiency as the dimensionless number characterizing the deposition process is preferred to the Sherwood number for this application for two reasons: (1) determination of the collection efficiency is also straightforward for Lagrangian formulations to be applied to showerhead-enhanced inertial deposition in which critical trajectories can be calculated and (2) efficiency is a commonly accepted concept within the semiconductor industry (e.g., yield). In practical terms, an efficiency of unity indicates that all particles in the chamber are depositing on the wafer, while an efficiency of zero indicates that no particles are depositing on the wafer.

3.7.5.4 Particle flux The particle deposition rate on the wafer is found as the product of collection efficiency times the number of particles released from the trap (or generated by nucleation): J0 ¼ D

dn DLh d~ n G~ 0 ¼ Lh h ¼ jz~¼0 ¼ Lh Pe dz SU0 d~ z

Eq. (3-66).

When the nature of the source term Lh is not known, the best strategy for reducing the number of defects on a wafer is to choose conditions that inhibit particle transport to the wafer, i.e., minimize the collection

230

FUNDAMENTALS

efficiency. One potential weakness of this strategy is if process conditions selected to reduce the collection efficiency result in a corresponding increase in the particle generation rate; this possibility is certainly of concern for particle nucleation.

3.7.6 Nondimensional results This section presents calculations of particle collection efficiency using numerical quadrature of Eqs. (3-64) and (3-65) based on a fourth-order Runge–Kutta technique with automatic error control. Both local and global error control parameters can be set, and convergence tests showed that the resulting integrals were unchanged in the fifth place when these parameters were set to 10
10. Efficiency is found to be a function of four ~ V~ t , and Pe (a fifth—the interception dimensionless parameters: Re, h, p parameter dp/S—is neglected in this work). Calculations of particle collection efficiency versus Peclet number are shown in Figure 3.10 for creeping flow (Re ¼ 0) for three attractive forces (characterized by V~ tp ¼
0:1;
0:5; and
1:0), for no external force (V~ tp ¼ 0), and for three repulsive forces (V~ tp ¼ 0:1; 0:5; and1:0). Plots are shown for three different trap heights, where the particles are trapped: (a) near the wafer (h/S ¼ 0.1), (b) midway between the wafer and showerhead (h/S ¼ 0.5), and (c) near the showerhead (h/S ¼ 0.9).

3.7.6.1 Efficiency at intermediate Peclet numbers Although the small- and large-Pe asymptotic limits for the collection efficiency are well described by analytical expressions, the shape of the collection efficiency curves for intermediate Peclet numbers can be quite complex and requires the full numerical integration of Eqs. (3-64) and (3-65). For example, while the efficiency-curve transition between the small- and large-Pe asymptotic limits is generally monotonic (e.g., Figure 3.10a for V~ tp > 0 or Figure 3.10c for V~ tp <
0:5), in some cases there may be a local minimum (e.g., Figure 3.10a for V~ tp ¼
0:1) or maximum (e.g., Figure 3.10c for V~ tp ¼
0:1). The exact shape of the efficiency ~ V~ t , and curve depends on the magnitudes of the three parameters, h, p Pe, and although the interaction among them can be complex, a few simple observations can be made. First, moving the particle trap away ~ always tends to lower the collection from the wafer (i.e., increasing h) efficiency. Although this effect is most notable for low or intermediate

3: TRANSPORT (a)

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–1 –0.5

EFFICIENCY

0.8 –0.1

h˜ = 0.1 0.6

Re = 0

0.4

V˜ pt = 1.0

0.5

0.1

0

0.2 0

(b)

.01

.1

1

10

100

104

103

104

103

104

1.0

h˜ = 0.5

0.8

V˜ pt = –1.0

Re = 0 EFFICIENCY

103

0.6 –0.5

0.4 1.

0 .5

0

0.2

–0.1

0. 1

0

0

(c)

.01

1

10

100

1.0 0.8

EFFICIENCY

0.1

h˜ = 0.9 Re = 0

0.6

V˜ pt = –1.0

0.4

–0.5

0.2 0

–0.1 1

.01

0.1

1

0.5

0

0.1

10 Pe

100

Figure 3.10 Efficiency vs. Pe for various deposition velocities. Figures show calculated efficiencies for particles starting in traps at: (a) h/S ¼ 0.1, (b) h/S ¼ 0.5, and (c) h/S ¼ 0.9.

Pe values where diffusional effects are strong, it is also true for large Pe values where deposition is controlled by external forces. The latter ~ claim is supported by noting that gas velocity at the trap location, u~ðhÞ, increases with increasing distance from the wafer so that collection

232

FUNDAMENTALS

efficiency decreases. Trap manipulation can be accomplished in practice under some conditions. For example, in plasma processing, the trap location is determined by process parameters such as pressure, rf (radio frequency) power, and flow rate; while these parameters may be fixed during etching by process requirements, they could be adjusted to manipulate the particle trap location just prior to plasma extinction. Similarly, trap position when particle nucleation is present could be controlled by pressure, wall temperature, flow rates, or chemistry selections. Second, reducing the dimensionless attractive external force or increasing the dimensionless repulsive force always lowers the collection efficiency. This trend is clearly evident in Figure 3.10 for intermediate and large Peclet numbers, although the benefit becomes less significant at low Pe where diffusion dominates deposition. It is interesting to note that for attractive forces such as gravity (wafer facing up) or thermophoresis (wafer cooler than the surrounding gas), the dimensionless drift velocity increases as pressure is decreased (for constant U0). In this case, the tendency toward processing at lower pressures ultimately must lead to an increase in the fraction of particles which end up on the wafer. If a process recipe is selected that maintains the wafer warmer than its surroundings, however, the drift velocity resulting from this repulsive external force will increase with decreasing operating pressure (for constant U0) and thereby reduce the fraction of particles depositing on the wafer. To explore the effect of Reynolds number on collection efficiency, calculations were made for Reynolds numbers of 0 and 8 using the analytical approximation for the flow field given in Eq. (3-46);14 the results are shown in Figure 3.11. As shown, even this relatively large variation in Re (spanning the Re range of the majority of low pressure commercial tools) produces only modest variations in the collection efficiency. Reynolds number effects are most apparent in the large-Pe limit for attractive forces. This effect can be quantified by noting that: (1) the large-Pe effi~ ciency limit of Eq. (3-52) depends on gas velocity at the trap location, u~ðhÞ, ~ and (2) the value of u~ðhÞ changes from
0.5 at Re ¼ 0 to a value of
0.625 ~ associated with Re being increased at Re ¼ 8. This 25% increase in u~ðhÞ from 0 to 8 leads to an approximately 25% decrease in collection efficiency ~ As V~ t is increased to a u ðhÞj. for a weak attractive force, i.e. jV~ tp j 1 (which includes the case where the particle initial velocity is zero). In this limiting case, the ratio of the showerhead-exit velocity of the particle to Ujet depends only on the jet Stokes number. This result suggests plotting the results of Eqs. (3-67) and (3-68) as Vpo/Ujet against Stjet—such as shown in Figure 3.16. As can be seen, the dimensionless particle velocity at the exit of the showerhead, Vpo/Ujet, is reasonably insensitive to the velocity ratio when Ujet/U0 > 10.

Vpo / Ujet = (Vpo /Uo)(Uo /Ujet )

1.0

0.8 0.6

Ujet /Uo = 2

0.4 5 10

0.2

50,100 0.0

0

20

40 60 Stjet = St (Ujet /Uo)(S/L)

80

100

Figure 3.16 Acceleration of particles through the showerhead. Dimensionless velocity of particles exiting showerhead tubes, Vpo/Ujet, as a function of jet Stokes number, Stjet, for a range of velocity ratios (Ujet/U0 ¼ 2, 5, 10, 50, and 100).

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Thus, the analysis of particle transport in the showerhead domain is complete: given the three inputs U jet =U0 , L/S, and St (and particle initial radial position to determine Ujet(r) for parabolic flow), we can calculate the dimensionless velocity Vpo/U0 at which the particle exits the showerhead. Interestingly, both the mean velocity ratio and the length ratio depend only on reactor geometry; process conditions such as temperature, pressure, or flow rate enter only through the Stokes number. Thus, for a given Stokes number, the extent of particle acceleration in the showerhead is entirely determined by hardware and is thus a characteristic of a specific tool design. Finally, in moving to the calculation of particle trajectories between the plates, the sign of the particle velocity Vpo/ Ujet must be switched to account for the different coordinate systems used in the two domains (see Figure 3.5b and the inset).

3.8.2 Particle transport between parallel plates In this section, a Lagrangian formulation is used to calculate particle trajectories in the inter-plate region using both numerical FIDAP and analytical solutions of the flow field. Under the present assumptions, four dimensionless parameters uniquely determine particle transport in the inter-plate region: Re, St, Vpt/U0, and Vpo/U0 (a fifth—the interception parameter dp/S— is neglected in this section). The first parameter, the Reynolds number, completely specifies the flow field for the infinite parallel-plate geometry—as demonstrated in the analytical low-Re approximation to the flow field given in Eq (3-46). For a finite-plate geometry, the aspect ratio is also needed to specify the flow. The second parameter, the particle Stokes number, is used in this work as a dimensionless particle diameter—as suggested by the free molecule limit Eq. (3-23). The influence of external forces enters through the third parameter, the dimensionless particle drift velocity, which parameterizes the forces via the z-component of the net drift velocity, Vpt. The fourth parameter, the dimensionless particle velocity at the showerhead exit, is determined by the strength of the showerhead acceleration effect as described in Section 3.8.1. Initially, however, Vpo/U0 will be taken as an independent variable; later, we discuss the coupling of the showerhead and parallel-plate domains. The effect of the these dimensionless parameters is shown in Figure 3.17, where particle collection efficiency is plotted against Stokes number for Re ¼ 8. For Figure 3.17a, an initial dimensionless particle velocity Vpo/U0 ¼
1 is assumed (no particle showerhead acceleration), while in

246

FUNDAMENTALS 1.0

a)

Re = 8 Vpo /Uo = -1

EFFICIENCY

0.8

0.6 Vpt /Uo = -0.5

0.4

0.2

0

-0.1 0 0.1

-0.01 .01

.1

St

1.0

1

10

1.0

b)

EFFICIENCY

0.8

Re = 8 Vpo /Uo = -100

0.6

0.4

Vpt /Uo = -0.5

0.2 -0.1 0 .001

-0.01

0 .01

1.0 .02

St

Figure 3.17 Efficiency vs. Stokes number for various deposition velocities for Re ¼ 8. Solid lines are calculated using an analytical flow field and a Runga–Kutta integrator, while the symbols are calculated using numerical flow solutions and the FIDAP particle tracking post-processing routines. (a) Particle dimensionless initial velocity of
1 and (b) particle dimensionless initial velocity of
100.

Figure 3.17b the initial velocity is taken as -100 (substantial showerhead acceleration characteristic of commercial reactors). In each plot the influence of external forces is explored by varying the drift velocity: curves for Vpt/U0 ¼
0.5,
0.1,
0.01, 0, 0.1, and 1.0 are shown. Negative values of the drift velocity correspond to an external force

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directed toward the wafer (attractive, enhancing deposition), while positive values correspond to an external force directed away from the wafer (repulsive, inhibiting deposition). Several important features of these plots will now be explored. First, inertial effects lead to particle deposition even in the absence of external forces as shown by the curves for Vpt/U0 ¼ 0 in Figure 3.17. In this case there is a critical Stokes number, Stcrit, below which no deposition occurs. At Stcrit there is a sharp jump in efficiency, which then increases toward unity with increasing St. The jump is steeper, higher (approaching unit collection efficiency) and occurs for a much smaller Stcrit in the case with substantial showerhead acceleration than when the particles enter with the fluid face velocity. This effect is discussed in greater detail below. As seen in Figure 3.17, particle inertia can also lead to deposition even when an external force is pushing particles away (Vpt/U0 > 0). The extent of external force ‘‘protection’’ is significantly reduced for large initial velocities: compare the Vpo/U0 ¼ 0 and 1 curves in Figure 3.17a and b. Second, when an external force is directed toward the wafer (Vpt/U0 < 0), particle deposition occurs at all values of the Stokes number. In the small-St limit (negligible particle inertia), the collection efficiency should tend to Eq. (3-48) for external forces that can be described by a potential; this trend is clearly evident in Figure 3.17. For example, for Vpt/U0 ¼
0.5, Eq. (3.48) predicts an efficiency of 1/3 which is the observed asymptote of the appropriate curves in Figure 3.17a and b. The presence of an attractive external force smooths the shape of the efficiency curves for large attractive forces; however, when the magnitude of the attractive force is small (e.g., Vpt/U0 ¼
0.1), the efficiency still exhibits a sharp increase in the neighborhood of Stcrit (from the no-force case). The rise in efficiency near Stcrit is much steeper for high initial particle velocities. Finally, in the large-St limit, the collection efficiency must approach unity for all cases. That is, for large enough Stokes numbers, particle inertia leads to straight trajectories and complete deposition independent of the details of the flow field, the external forces, or particle initial velocity (assuming it is not zero). This limit is approached in all of the calculations shown in Figure 3.17.

3.8.2.1 Asymptotic limit of critical Stokes number An interesting result is suggested by Figure 3.17b for the case of no external force: as the particle initial velocity becomes large, the collection

248

FUNDAMENTALS

efficiency tends toward a step function which jumps from zero to unity at a critical Stokes value equal to the inverse of the dimensionless initial particle velocity. To confirm this result, a series of calculations were made to explore the dependence of the critical Stokes number on initial particle velocity in the absence of an external force. These results are shown in Figure 3.18, where Stcrit is plotted as a function of Vpo/U0 for fluid Reynolds numbers of 0, 4, and 8. For a given value of Vpo/U0, particles with St < Stcrit (below the line) will exit the reactor, while particles with St > Stcrit (above the line) will impact the reactor. The effect of Reynolds number is negligible for large values of Vpo/U0; in fact, for Vpo/U0 > 10 the three Re curves approach the same asymptotic limit. For large values of Vpo/U0 particle inertia dominates deposition and the details of the flow field become unimportant. Inspection of the large initial-velocity asymptotic limit reveals the following relationship: Stcrit !

Uo Vpo

Eq. (3-70)

A simple explanation of this limit is readily illustrated by rearranging Eq. (3-70) to give StcritVpo/U0 ¼ t Vpo/S ¼ 1, which states that impaction

10 Re 0 4 8

t

Vp /Uo = 1 1 Stcrit

COLLECTED t Vp /Uo =

0

0.1 NOT COLLECTED

0.01 .1

1

10

100

Vpo /Uo Figure 3.18 Crtical Stokes number vs. particle dimensionless inlet velocity. Values of the critical Stokes number were calculated using the analytical approximation to the flow field for Reynolds numbers of 0, 4, and 8. One set of curves applies for no external force (Vpt/U0 ¼ 0), the other set applies for a strong force resisting deposition (Vpt/U0 ¼ 1).

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occurs when the particle stopping distance based on its initial velocity Vpo equals the showerhead-to-wafer gap.16 Figure 3.18 also shows the variation of the critical Stokes number when a large external force opposing deposition is applied (Vpt/U0 ¼ 1). Although the value of Stcrit is greatly increased for small Vpo/U0 (compared to the case with no external force acting), all curves approach the same asymptote —Eq. (3-70)—in the limit of very large initial particle velocity. The Stcrit value for a large external force was found to be 4% higher than without an external force for Vpo/U0 ¼ 100. As noted above, the influence of Reynolds number on Stcrit is greatly reduced when a repulsive force is acting. Thus, for no or repulsive external forces, a great simplification results for large values of the initial particle velocity (say for Vpo/U0 > 100): the collection efficiency can be closely approximated by a step function (from zero to unity) at a critical Stokes number calculated by Eq. (370). When an attractive force is present, the concept of a critical Stokes number breaks down, as there is some deposition at all Stokes numbers. Even in this case, however, a sharp increase in efficiency near Stcrit is still seen (such as shown in Figure 3.17b).

3.8.3 Coupled transport—nondimensional results In this section, showerhead-enhanced inertial deposition is explored by coupling the transport of particles through the showerhead and in the inter-plate region. The procedure is as follows: (1) for given values of Ujet/ U0, L/S, and St, calculate the dimensionless velocity of the particle exiting the showerhead, Vpo/U0, using Eqs. (3-67) and (3-68); and then (2) using Vpo/U0 as the initial particle velocity, and the parameters Re, St, and Vpt/ U0, integrate the particle trajectory between the plates to determine the particle collection efficiency. Thus, the coupled particle transport problem (for an infinite parallel-plate geometry and under the present assumptions) is completely specified by five independent dimensionless parameters (note that Vpo/U0 is dependent). Efficiency results from these coupled calculations should look qualitatively like those shown in Figure 3.17, although some variations are expected as the initial particle velocity

16

A further implication of Eq. (3.70) is that for large values of Vpo/U0 a more appropriate choice for the characteristic velocity in defining particle Stokes number would have been Vpo.

250

FUNDAMENTALS

is no longer fixed but depends on the degree of particle acceleration through the showerhead. It is valuable at this point to clarify the use of the jet to face-velocity parameter Ujet/U0, which is the local fluid velocity that a particle experiences while passing through a showerhead hole. For the assumption of plug flow through the showerhead, Ujet =U0 ¼ U jet =Uo ¼ Ashowerhead =SAjet where U jet is the mean velocity in the tube. In the plug-flow case, Ujet/U0 must always be larger than unity and is constant across each showerhead tube cross-section. In commercial reactors, values of U jet =U0 are seldom less than twenty, and can range up to several hundred. The other limit considered in this work is parabolic flow through the showerhead holes. In this case, Ujet/U0 is function of both the area ratio and the radial starting position of the particle in the showerhead tube. For example, a particle starting on the tube centerline would experience a fluid velocity twice the mean, so that Ujet ðr ¼ 0Þ=U0 ¼ 2U jet =Uo . Because the fluid velocity must vanish at the tube wall, jet to face-velocity ratios less than one are possible for the parabolic case for particles starting near the wall. In the following, results are parameterized with the most general form Ujet/U0.

3.8.3.1 Critical Stokes numbers One set of coupled efficiency calculations is shown in Figure 3.19, which plots efficiency versus Stokes number for jet to face-velocity ratios of 0.1, 1, 10, 100, and 1000. For these calculations, the showerhead thickness was assumed equal to the plate gap (L/S ¼ 1) for the case of Re ¼ 0 and no external forces acting (Vpt/U0 ¼ 0). The critical Stokes number (the smallest St for which collection occurs) is found to decrease with increasing values of Ujet/U0. This result is not surprising: as Ujet/U0 increases the particle velocity at the showerhead exit (Vpo/ U0) must also increase, and we have shown in Section 3.8.2 that increasing values of Vpo/U0 lead to smaller values for Stcrit (see Figure 3.18). In particular, we have shown in the limit of large Vpo/U0 that Stcrit U0/!Vpo. It is interesting to note that, for coupled transport, the large Ujet/U0 limit of Stcrit is not U0 /Ujet, but a slightly higher value (e.g., for Ujet/U0 ¼ 100, Stcrit ¼ 0.01237). This difference is explained by the fact that, because of inertia, the particle cannot accelerate to the jet velocity before exiting the showerhead (i.e., Vpo/U0 Ujet/U0); consequently, a larger Stokes number is required to initiate deposition.

3: TRANSPORT

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251

1.0

EFFICIENCY

0.8

0.6

Ujet /Uo= 1000

100

10

1

0.1

0.4

Re = 0 L/S = 1 Vpt /Uo = 0

0.2

0

10-4

10-3

10-2

St

10-1

100

101

Figure 3.19 Effect of jet to face–velocity ratio. Efficiency vs. Stokes number for Ujet/U0 ¼ 1, 10, 100, and 1000 including coupling between showerhead and inter-plate transport (for this calculation L/S ¼ 1, Re ¼ 0, Vpt/U0 ¼ 0, and rp/S ¼ 1 · 10
7).

In the slow-jet limit, say Ujet/U0 < 1, the critical Stokes number becomes less sensitive to the particle inlet velocity, although the shapes of the efficiency curves can be quite different (e.g., compare the curves for Ujet/U0 ¼ 0.1 and 1). Here, the details of the efficiency curve result from a complicated interplay among the parameters. Overall, reducing the value of Ujet /U0 (more and/or larger showerhead holes) increases Stcrit—with the favorable result of increasing the minimum size for which inertial effects lead to particle deposition on the wafer. The showerhead thickness also plays a role in determining the magnitude of the critical Stokes number. The effect of showerhead thickness is presented in Figure 3.20, in which collection efficiency is plotted against St for L/S ¼0.1, 0.5, 1 and 2 (for Ujet/U0 ¼ 100, Re ¼ 0, and Vpt/U0 ¼ 0). For large L/S values, there is sufficient time in the showerhead for the particle to accelerate to the jet velocity (Vpo/U0 Ujet/ U0), which by Eq. (3-70) gives the asymptotic limit StcritU0/Ujet. As seen in Figure 3.20, this limit is approached for L/S > 2. For very thin showerheads, the particles spend only a short time in the showerhead, and will exit the showerhead with a velocity much less than the jet velocity. In this case, larger Stokes numbers are needed to initiate deposition—as seen in Figure 3.20 for the curves with L/S ¼ 0.1 and 0.5. Based on these results, Stcrit can be increased (and inertial deposition reduced) by reducing the dimensionless showerhead thickness L/S.

252

FUNDAMENTALS 1.0

EFFICIENCY

0.8

0.6 L/S =2 1

0.5

0.1

0.4 Ujet /Uo = 100 Re = 0 Vp t /Uo = 0

0.2

0

0.01

0.1 St

Figure 3.20 Effect of showerhead thickness. Efficiency vs. Stokes number for L/S ¼ 0.1, 0.5, 1, and 2 including coupling between showerhead and interplate transport (for this calculation Ujet/U0 ¼ 100, Re ¼ 0, Vpt/U0 ¼ 0, and rp/S ¼ 1 · 10
7).

3.8.3.2 Grand design curves If the effect of a repulsive force is neglected, then the value of Stcrit (for a given flow field) is determined solely by the values of Ujet/U0 and L/S. Interestingly, both of these parameters are geometrical in nature. The geometric interpretation of L/S is obvious (the ratio of showerhead thickness to inter-plate gap), while that for Ujet/U0 requires some explanation. Under the assumption of plug flow within the showerhead holes, it has already been shown that Ujet =U0 ¼ U jet =Uo ¼ Ashowerhead =SAjet where U jet is the mean velocity in the tube. Thus, in the plug-flow limit the velocity ratio is completely specified by the number and size of the showerhead holes and by the diameter of the showerhead—purely geometric properties of the showerhead. Under the assumption of parabolic flow, the radial starting position of the particle within the showerhead hole must also be considered, but this is another geometrical parameter. Thus, for a specific flow field and neglecting external forces, the critical Stokes number is uniquely specified by chamber and showerhead geometry (and possibly an assumed particle starting position), and is independent of process parameters (e.g., gas temperature, pressure, or flow rate). This simplification leads to the idea of the grand design curves, which give critical Stokes number as a function of the velocity ratio Ujet/U0 for

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various dimensionless showerhead thicknesses L/S. An example of a grand design curve over a wide range of these two parameters is shown in Figure 3.21 for Re ¼ 0 and Vpt/U0 ¼ 0. The qualitative trends are consistent with earlier discussion: the critical Stokes number decreases with increasing values of Ujet/U0 and L/S. The curves for all values of L/S intersect at Ujet/U0 ¼ 1, which corresponds to the case for which the particle enters (and exits) the showerhead at the same velocity. Variations in Stcrit with L/S become small for dimensionless showerhead thicknesses larger than about two; in this case, the particle has had sufficient time to accelerate to near the gas velocity, so that making the showerhead longer has little effect. For velocity ratios less than one, the critical Stokes number is essentially independent of velocity ratio and the dimensionless showerhead thickness. For large velocity ratios, the curves in Figure 3.21 for different L/S values become parallel with a slope of unity— suggesting that in this limit Stcrit becomes proportional to U0/Ujet. As shown, the value of Ujet/U0 at which this asymptotic limit is reached depends on L/S: for thick showerheads the linear limit is achieved at much smaller velocity ratios than for thin showerheads. For design applications, the grand design curves are used with the parameters Ujet/U0 and L/S to find the critical Stokes number for the proposed reactor geometry. To minimize particle deposition on the wafer, it is desirable to choose parameters that give as large a critical 1

Stcrit

Re = 0 Vp t / Uo = 0

0.1

0.01

L/S 0.05 0.1 0.2 0.5 1.0 2.0 5.0

1

10 Ujet / Uo

100

Figure 3.21 Grand design curve for estimating the critical Stokes number based on showerhead parameters (for this calculation Re ¼ 0, Vpt/U0 ¼ 0, and rp/S ¼ 1 · 10
7).

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Stokes number as possible, as increasing Stcrit increases the minimum size at which inertial deposition begins. Based on Figure 3.21, larger values of Stcrit are obtained by decreasing Ujet/U0 (use more and/or larger showerhead holes) or by decreasing L/S (use a thin showerhead or a large inter-plate gap). Introducing a force that opposes deposition (such as by heating the wafer relative to the showerhead) will always help, but as discussed above, the effect is fairly small under realistic conditions. Once Stcrit has been determined, the corresponding particle critical size, dp,crit, can be found from Eq. (3-21). Note that although the critical Stokes number depends only on geometric parameters, the critical particle diameter depends on geometric, process, and particle parameters. Thus, particle density and gas pressure, temperature, type, and flow rate all play a role in determining dp,crit. The effects of process parameters on showerhead-enhanced inertial deposition are discussed in a later section.

3.8.3.3 External forces Although particle deposition only occurs for St > Stcrit for repulsive or zero external forces, inertial deposition will always take place when the net external forces are attractive. To demonstrate this behavior, particle collection efficiencies calculated using fully coupled particle transport (i.e., including showerhead acceleration) are shown for various values of the external force in Figure 3.22 (for Re ¼ 0, Ujet/U0 ¼ 100, L/S ¼ 1). The results are very similar to those in Figure 3.17b, which gives efficiency for a fixed particle inlet velocity (Vpo/U0 ¼ 100) instead of the present case where the showerhead exit velocity is calculated based on showerhead parameters.17 The large and small Stokes limits are the same: for small St inertial effects vanish and the efficiency must tend to Eq. (3-48), while for large St inertia dominates and efficiency must tend to unity. At intermediate values of St there are some differences. For example, it is seen that the critical Stokes number for the coupled analysis is slightly larger than for the case where Vpo/U0 is held constant; as discussed above, for a finite-length showerhead the particle velocity at the showerhead exit must be slightly less that Ujet/U0, so that a larger Stokes number is needed to initiate inertial deposition. Note that the case of constant Vpt/U0 (i.e., Vpt/U0 is independent of particle size or Note that although Re ¼ 8 in Figure 3.10b and Re ¼ 0 in Figure 3.22, Reynolds number effects are small. 17

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1.0

EFFICIENCY

0.8

Re=0 L / S=1 Ujet / Uo =100

0.6

0.4

Vpt / Uo = -0.5

0.2 -0.1 0

-0.01 0

.001

0.01

1.0 0.02

St

Figure 3.22 Efficiency vs. Stokes number for various deposition velocities. Collection efficiencies for fully coupled particle transport for Vpt/U0 values of
0.5.
0.1, 0, and 1 (for this calculation L/S ¼ 1, Re ¼ 0, Ujet/U0 ¼ 100, and rp/S ¼ 1 · 10
7).

Stokes number) corresponds to the physically meaningful situation in which a thermophoretic force is acting (as the thermophoretic drift velocity is independent of particle diameter). For other external forces—such as gravity—the net drift velocity will not be a constant but will vary with particle diameter (and hence with St).

3.8.3.4 Parabolic profile For fully developed parabolic flow in the showerhead hole, the gas velocity varies with radial position within the hole as given by Eq. (3-45); in this case the local velocity experienced by a particle in a showerhead hole depends on its radial starting position and the mean velocityU jet [as given by Eq. (3-44)]. For example, a particle starting on the hole centerline will experience the highest local gas velocity (2U jet ), while ones starting near the hole wall will experience much lower velocities. As the amount of acceleration the particle experiences within the showerhead depends on the local gas velocity, the particle collection efficiency must vary with particle radial position within the showerhead hole. Thus, the calculation of the net collection efficiency for the parabolic flow case requires integrating the local efficiency radially across the showerhead hole. Assuming that the particles are uniformly distributed

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across the showerhead hole (i.e., that the flux of particles across the tube cross-section is constant), the net efficiency is: 2 hnet ðStÞ ¼ 2 Rjet

R Zjet

h½Ujet ðrÞ; Strdr

Eq (3-71)

0

The numerical integration of Eq. (3-71) is computationally expensive, as each evaluation of the integrand h[ Ujet(r), St] requires a coupled calculation of the particle acceleration through the showerhead [with local gas velocity Ujet(r)] along with the corresponding numerical integration of the particle trajectory between the two plates. The integration of Eq. (3-71) is further complicated by the fact that, in some cases, efficiency can change significantly with small changes in St or Ujet(r). In the present work, an adaptive Gauss integration scheme with automatic error control has been used to evaluate Eq. (3-71). An example of a net efficiency curve for a parabolic velocity profile is shown in Figure 3.23 for the case where there is no external force (Re ¼ 0, U jet =Uo ¼ 100, L/S ¼ 1, and Vpt/U0 ¼ 0). For comparison, efficiency curves are also shown for plug flow (where all the particles experience the mean velocity) and for the hypothetical case where all of the particles 1.0

EFFIC IENCY

0.8

Re=0 L / S=1 Ujet / Uo =100 Vp t / Uo =0 Parabolic Profile

0.6

0.4

Centerline Velocity Mean Velocity

0.2

0

.001

0.01 St

0.1

Figure 3.23 Efficiency vs. Stokes number for parabolic showerhead profile (no external force). Collection efficiencies for fully coupled particle transport for particles experiencing the showerhead hole centerline and mean velocities (plug flow assumption), and integrated over the parabolic velocity profile in the showerhead holes in the absence of external forces (L/S ¼ 1, Re ¼ 0, U jet/U0 ¼ 100, and rp/S ¼ 1 · 10
7).

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experience the centerline velocity (essentially a plug flow moving at twice the mean velocity). These three curves show three interesting effects. First, the critical Stokes number for the centerline case is approximately one half that for the plug flow case; this result is explained by the fact that the critical Stokes number is inversely proportional to jet velocity in the limit of large values of Ujet/U0 (i.e., doubling the local showerhead gas velocity halves Stcrit).18 Second, the efficiency curve for the parabolic case approaches unity much slower than either of the plug flow curves. This is expected, as particles located near the tube wall experience very low local velocities; for some region very close to the wall, particles actually deaccelerate while passing through the showerhead. Note that although this slow approach to complete collection is favorable from a defect reduction point of view, it is not of practical significance because in this large Stokes regime the majority of particles entrained in the flow would still be deposited. Third, the critical Stokes number for the parabolic case is the same as for the centerline case. The smallest particles deposited are those experiencing the highest velocity in the showerhead hole; thus, for parabolic flow inertia-enhanced deposition begins with those particles moving along the showerhead-hole centerline. The slope of the parabolic case is not as steep as for the centerline case because few particles are contained in the small-area region near the centerline, whereas in the centerline case we have assumed all of the particles are moving at the centerline velocity. The centerline case therefore serves as a limit of the smallest Stokes value for which inertial-enhancement to deposition becomes important in parabolic flow. In fact, the centerline case serves as a lower limit for all laminar flow conditions in the tubes, since even for developing flow the maximum velocity in the tube will always be less than 2U jet . Thus, the most conservative practice for predicting the effects of inertia-enhanced deposition in real reactors is to use Ujet =Uo ¼ 2U jet =Uo as the characteristic velocity ratio in the grand design curves. The present results show that, for parabolic flow in the showerhead, the best practice for determining net efficiency is to perform the full integration of Equation (6.71). However, since this calculation can be computationally expensive, the following approximations are suggested: for attractive external forces (say Vpt/U0 <
0.01) use the mean velocity approximation, otherwise (say Vpt/U0 > 0) use the more conservative centerline approximation. 18

The critical Stokes number becomes less dependent on the velocity ratio for small Ujet/U0.

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3.8.4 Coupled transport—dimensional results The two approaches to reduce inertia-enhanced particle deposition are:19 (1) design equipment with as large a value of Stcrit as possible and (2) select process conditions that give as high a value of dp,crit as possible. Based on our previous analysis, the only three ways to increase Stcrit is to design for minimum U jet =U0 and/or L/S, and to apply an external force that opposes deposition. To minimizeU jet =U0 , very porous showerhead designs are needed to reduce the constriction of the flow (decrease the area ratio given by Eq. (3-44) by either increasing the number or the size of holes). The ratio L/S can be reduced by reducing the showerhead thickness or by increasing the showerhead-to-wafer gap. Intuitively, a short showerhead thickness reduces the time available to accelerate the particle, and a large showerhead-to-wafer gap provides the particle more opportunity to slow down. Finally, an opposing external force could be used to inhibit inertial deposition such as by keeping the wafer warmer than the showerhead to take advantage of thermophoresis but remembering that the opposing force typically had a fairly weak effect on reducing inertia-enhanced deposition. Once a hardware design is fixed, Stcrit is fixed, but it is still possible to minimize inertial deposition by selecting process conditions that give as high a value of dp,crit as possible. Based on the free molecule definition of Stokes number in Eq. (3-23), we can see that low face velocities U0 and large showerhead-to-wafer gaps S are preferred. Mean gas velocities can be reduced by reducing mass flow rates (at constant pressure) or by operating at higher pressures (for a fixed mass flow rate). As seen in Eq. (3-23), operating at higher pressures also directly increases dp,crit. Thus, for a constant mass flow rate, a twofold increase in pressure produces a fourfold increase in dp,crit (one factor of two directly from the pressure reduction, and an additional factor of two from lowering the face velocity).20 Recall that Eq. (3-23) strictly applies to particles in the free molecular limit (small sizes and/or low pressures) which is a reasonable 19

It is impossible to eliminate inertial effects, as one can always imagine a particle large enough so that it will impact. 20 For higher pressures and/or larger particle diameters the quadratic relationship between pressure and critical diameter fails as the free-molecule expression for Stokes number given by Eq. (3.23) becomes inaccurate. In the continuum limit the particle relaxation time becomes independent of pressure and proportional to diameter squared, so that a fourfold pressure increase would result in a twofold increase in dp,crit. Thus, the influence of pressure on dp,crit is most pronounced in the free-molecule regime.

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assumption for the pressure and particle size regimes in typical semiconductor manufacturing reactors. An example of particle collection efficiency as a function of particle size is shown in Figure 3.24 for a hypothetical 200 mm (diameter) reactor characterized by: an argon flow rate of 1000 sccm (standard cubic centimeters per minute) through a showerhead 2.54 cm thick with 1000 holes of diameter 0.0635 cm with a showerhead-to-wafer gap of 2.54 cm. The flow is assumed isothermal and a particle density of 1 g/cm3 is used. These reasonable physical parameters give the dimensionless quantities L/S ¼ 1, U jet =U0 ¼ 99:2 and Re ¼ 0.984; the dimensionless drift velocity varies with size according to the expression for gravitational settling velocity—Eq. (3-26). Efficiency curves are shown for reactor pressures (i.e., pressure between the two plates) of 0.5, 1.0, 2.0, and 10. torr. For pressures less than 2 torr, inertial-enhancement to deposition is clearly evident by the abrupt jump in efficiency from nearly zero to unity in the vicinity of a critical size. As seen, this critical size is a strong function of pressure, with an approximately fourfold decrease in the critical size for a twofold decrease in chamber pressure. For chamber pressures above about 10 torr inertial effects no longer contribute to deposition; the increase in efficiency for increasing particle size seen in 1.0

EFFICIENCY

0.8

ρp = 1. g/cc 1000 sccm Argon L / S =1 T=300K

0.6 0.5 torr

1.0

2.0

0.4

10.

0.2

0

0.1

1 dp (µm)

10

Figure 3.24 Efficiency vs. particle diameter and pressure (isothermal case). Collection efficiencies for fully coupled particle transport assuming plug flow through the showerhead hole for reactor pressures of 0.5, 1.0, 2.0, and 1 torr (L/S ¼ 2.54 cm, Ujet/U0 ¼ 99.2, Q ¼ 1000 sccm argon, T ¼ 300 K, Re ¼ 0.98, and particle density ¼ 1 g/cm3).

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Figure 3.24 for the P ¼ 10 torr case results because the gravitational drift velocity increases with size. The same reactor geometry and process conditions have been used to calculate the effect of thermophoresis on collection efficiency as shown in Figure 3.25. The showerhead temperature has been held constant at 300 K while the wafer (lower plate) temperature is made colder (280 K), isothermal (300 K), or hotter (320 K). Fairly modest temperature differences have been used in accordance with our isothermal (constant gas properties) assumption for flow calculations, but that small temperature differences are allowed to drive particle thermophoresis. The isothermal case shows that, for small particle sizes, deposition decreases with decreasing size because the gravitational drift velocity is decreasing. When the wafer temperature is less than the showerhead temperature, thermophoresis acts to increase deposition compared to the isothermal case. Although the differences become small for sizes larger than dp,crit (about 1.5 mm), the thermophoretic contribution is clear in the smallparticle limit where the efficiency approaches a constant.21 Heating the 1.0 ρp = 1. g/cc

EFFICI ENCY

0.8

0.6

1000 sccm argon P = 1 torr L/S = 1 Tshowerhead = 300K

0.4

Twafer 280K 300K 320K

0.2

0 0.1

1 dp (µm)

10

Figure 3.25 Efficiency vs. particle diameter and wafer temperature (with thermophoresis). Collection efficiencies for fully coupled particle transport assuming plug flow through the showerhead hole for wafer temperatures of 280, 300, and 320 K (L/S ¼ 2.54 cm, Ujet/U0 ¼ 99.2, Q ¼ 1000 sccm argon, P ¼ 1 torr, Tshowerhead ¼ 300 K, Re ¼ 0.98, and particle density ¼ 1 g/cm3). 21

Since the thermophoretic drift velocity is independent of particle diameter (Eq. (331)) while the settling velocity is proportional to diameter, for small particles thermophoretic deposition dominates and the efficiency becomes constant.

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wafer relative to the showerhead eliminates all small-particle deposition as the thermophoretic resistive force overwhelms the attractive gravitational force. The critical diameter at which inertial effects dominate is shifted to a slightly larger size than for the isothermal case, although the shift is fairly small since the effect of an external force on Stcrit is fairly weak. By using thermophoretic protection and by designing a reactor with a sufficiently large dp,crit particle deposition can be mitigated over the particle size range of interest. The two previous examples highlight two important points: (1) that inertia-enhanced deposition becomes dramatically more important at low pressure and (2) that thermophoretic protection coupled with careful control of inertial effects can significantly reduce particle deposition. Dimensional calculations could also be used to demonstrate all of the effects reported in Section 3.8.3, however, because of the wide variability in reactor geometry and particle and process parameters, only these two examples are presented.

3.9

Chapter Summary and Practical Guidelines

This chapter reviewed the basic phenomena controlling particle transport and the underlying general equations with an emphasis on conditions encountered in semiconductor process tools (i.e., subatmospheric pressures and submicron particles). The discussion included expressions for the following particle forces: fluid drag, gravity, thermophoresis, and electrophoresis. The concepts of particle drift velocity and stopping distance were introduced, and issues of continuum vs. free molecular particle transport were outlined. Particle concentrations were assumed to be low enough to allow a dilute approximation, for which the coupling between the fluid and particle phases is one-way. In this case, the fluid/ thermal transport equations can be solved either analytically or numerically neglecting the particle phase; the resulting velocity and temperature fields were then used as input for the particle transport calculations. Isothermal flow was assumed, although small temperature differences were allowed to drive particle thermophoresis; both analytical and numerical solutions of the flow field representative of a parallel plate geometry were presented. Particle collection efficiency was defined as the fraction of particles present in the inter-plate region of the reactor that deposit on the wafer. Particles were presumed to either enter the reactor through the showerhead (uniformly spread between r ¼ 0 and RW), or to originate in a plane parallel to the wafer. The latter case corresponds to

262

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particles being released from a plasma trap upon plasma extinction or being formed in a nucleation process; in this case, the particles are initially assumed to be uniformly spread radially between r ¼ 0 and RW at some distance h from the wafer. Analytical expressions for collection efficiency were presented for the limiting case where external forces control deposition (i.e., neglecting particle diffusion and inertia). Particle transport in the parallel-plate geometry was predicted using both the Lagrangian approach (where individual particle trajectories are calculated) and the Eulerian approach (where the particles are modeled as a cloud). The Eulerian formulation yielded an analytical, integral description of particle deposition for the case where the flow field between the plates can be approximated analytically. The strength of the Eulerian formulation is in predicting particle transport resulting from the combination of applied external forces (including the fluid drag force) and the chaotic effect of particle Brownian motion (i.e., particle diffusion), although the current implementation cannot account for particle inertia. In particular, the Eulerian formulation cannot accommodate particle acceleration effects within the showerhead, and is therefore restricted to particle transport in the inter-plate region. The need to properly account for diffusion-enhanced particle deposition becomes increasingly important as the semiconductor industry moves toward smaller feature sizes and becomes concerned with smaller-sized particles. Based on the Eulerian analysis, the following guidelines are intended to help tool operators and designers reduce particle deposition when diffusional effects are important:  Keep traps as far from the wafer as possible.  Take advantage of repulsive forces, such as thermophoretic protection gained by keeping the wafer warmer than the showerhead.  Reduce attractive forces.  For a specific pressure, use as high a mass flow rate as possible. The strength of the Lagrangian formulation is in predicting particle transport resulting from the combination of applied external forces and particle inertia, although the current implementation cannot account for particle diffusion. It is the Lagrangian formulation, that can properly account for inertia-enhanced deposition resulting from particle acceleration in the showerhead. The problem was treated in two steps, in which both particle and fluid transport were determined: (1) within a

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showerhead- hole and (2) between the showerhead and the susceptor. For fluid and particle transport in the showerhead, approximate analytical expressions were derived based on a few assumptions. The output of this first step was the particle velocity at the exit of the showerhead, as a function of showerhead geometry, flow rate, and gas and particle properties. The particle showerhead-exit velocity was next used as an initial condition required for particle transport between the plates. The output of the second step was a prediction of particle collection efficiency by the susceptor (wafer), as a function of showerhead-exit particle velocity, the plate separation, flow rate, and gas and particle properties. Based on the Lagrangian analysis, two approaches were identified to help tool operators and designers reduce particle deposition when inertial effects are important: (1) design equipment with as large a value of Stcrit as possible and (2) select process conditions that give as high a value of dp,crit as possible. Based on this analysis, Stcrit is determined primarily by reactor and showerhead geometry. Only three methods were identified for increasing Stcrit:  Decrease the showerhead velocity ratio U jet =U0 by increasing the number of holes and/or enlarging the size of the showerhead holes.  Decrease the showerhead thickness ratio L/S by making the showerhead very thin or the inter-plate gap large.  Apply an external force that opposes particle deposition (such as keeping the wafer warmer than the adjacent gas). Given a specific hardware design (and corresponding Stcrit), inertial deposition can be reduced by selecting process conditions that give as high a value of dp,crit as possible. Based on the free molecule limit of Stokes number, the following general guidelines are offered to increase the critical diameter (for a given Stcrit):    

Increase the gap between the showerhead and wafer Use low mass flowrates Raise chamber pressure Use a high molecular weight gas

The previous recommendations specifically pertain to reducing particle deposition given an assumed dominant deposition mechanism; note that one set of guidelines (e.g., for inertia) may conflict with those intended to reduce deposition by other mechanisms (e.g., gravity or diffusion).

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In order to reduce particle deposition in real tools, it is up to equipment designers/operators to first identify the dominant deposition mechanism so that an effective improvement strategy can be identified. Note that the guidelines given above are not intended to replace detailed calculations (using the proper analysis with the actual process conditions), but to provide the user with a general feel for inherently-clean practices. In addition, equipment designers should be aware that while these recommendations should improve particle performance, the effect of any changes on process performance must also be investigated.

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17. L. Talbot, R. K. Cheng, R. W. Schefer and D. R. Willis, ‘‘Thermophoresis of Particles in a Heated Boundary Layer,’’ J. Fluid Mech. 101, 737 (1980). 18. G. K. Batchelor and C. Shen, ‘‘Thermophoretic Deposition of Particles in Gas Flowing over Cold Surfaces,’’ J. Colloid Interface Sci. 107, 21 (1985). 19. L. Waldmann and K. H. Schmitt, ‘‘Thermophoresis and Diffusiophoresis of Aerosols,’’ Chapter VI in Aerosol Science, C. N. Davies (Ed.), Academic Press, New York (1966). 20. M. H. Peters, D. W. Cooper and R. J. Miller, ‘‘The Effects of Electrostatic And Inertial Forces on the Diffusive Deposition of Small Particles onto Large Disks: Viscous Axisymmetric Stagnation Point Flow Approximations,’’ J. Aerosol Sci. 20, 123 (1989). 21. D. J. Rader and A. S. Geller, ‘‘Showerhead-Enhanced Inertial Particle Deposition in Parallel-Plate Reactors,’’ Aerosol Sci. Technol. 28, 105 (1998). 22. R. B. Bird, W. E. Stewart and E. N. Lightfoot, ‘‘Transport Phenomena,’’ John Wiley, New York (1960). 23. R. M. Terril and J. P. Cornish, ‘‘Radial Flow of a Viscous, Incompressible Fluid Between Two Stationary, Uniformly Porous Discs,’’ J. Appl. Math. Phys. (ZAMP) 24, 676 (1973). 24. C. Houtman, D. B. Graves and K. F. Jensen, ‘‘CVD in Stagnation Point Flow: An Evaluation of the Classical 1D Treatment,’’ J. Electrochem. Soc. 133, 961 (1986). 25. A. Robinson, ‘‘On the Motion of Small Particles in a Potential Field of Flow,’’ Comm. Pure Appl. Math. 9, 69 (1956). 26. D. J. Rader, A. S. Geller, S. J. Choi and M. J. Kushner, ‘‘Application of Numerical Models to Predict Particle Contamination in Semiconductor Process Environments,’’ in Proc. IES 40th Tech. Mtg., pp. 308–315, Institute of Environmental Sciences and Technology, Rolling Meadows, IL (1994). 27. D. J. Rader, A. S. Geller, S. J. Choi and M. J. Kushner, ‘‘Particle Transport in Plasma Reactors,’’ in Proc. Microcontamination 94 Conference, pp. 39–48, Sematech, San Jose, CA (1994). 28. D. W. Cooper, R. J. Miller, J. J. Wu and M. H. Peters, ‘‘Deposition of Submicron Aerosol Particles During Integrated Circuit Manufacturing: Theory,’’ Part. Sci. Technol. 8, 209 (1990). 29. B. V. Ramarao and C. Tien, ‘‘Aerosol Deposition in Two-Dimensional Laminar Stagnation Flow,’’ J. Aerosol Sci. 20, 775 (1989). 30. R. M. Roth, K. G. Sears, G. D. Stein and G. Wong, ‘‘Spatial Dependence of Particle Light Scattering in an RF Silane Discharge,’’ Appl. Phys. Lett. 46, 253 (1985). 31. T. J. Sommerer, M. S. Barnes, J. H. Keller, M. J. McCaughey and M. J. Kushner, ‘‘Monte Carlo-Fluid Hybrid Model of the Accumulation of Dust Particles at Sheath Edges in Radio-Frequency Discharges,’’ Appl. Phys. Lett. 59, 638 (1991). 32. M. S. Barnes, J. H. Keller, J. C. Forster, J. A. O’Neill and D. K. Coultas, ‘‘Transport of Dust Particles in Glow-Discharge Plasmas,’’ Phys. Rev. Lett. 68, 313 (1992). 33. S. J. Choi, P. L. G. Ventzek, R. J. Hoekstra and M. J. Kushner, ‘‘Spatial Distributions of Dust Particles in Plasmas Generated by Capacitively Coupled Radio Frequency Discharges,’’ Plasma Sources Sci. Technol. 3, 418 (1994).

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34. G. M. Jellum, J. E. Daugherty and D. B. Graves, ‘‘Particle Thermophoresis in Low Pressure Glow Discharges,’’ J. Appl. Phys. 69, 6923 (1991). 35. M. Shiratani, S. Matsuo and Y. Watanabe, ‘‘In Situ Observation of Particle Behavior in RF Silane Plasmas,’’ Jpn. J. Appl. Phys. 30, 1887 (1991). 36. C.-K. Yeon, J.-H. Kim and K.-W. Whang, ‘‘Dynamics of Particulates in the Afterglow of a Radio Frequency Excited Plasma,’’ J. Vac. Sci. Technol. A 13, 927 1995). 37. J. Kang, R. N. Carlile, J. F. O’Hanlon and S. M. Collins, ‘‘Mapping of Radio Frequency Plasma Potential Throughout a Particle Trapping Region using an Emissive Probe,’’ J. Vac. Sci. Technol. A 14, 639 (1996). 38. S. J. Choi, D. J. Rader and A. S. Geller, ‘‘Massively Parallel Simulations of Brownian Dynamics Particle Transport in Low Pressure Parallel-Plate Reactors,’’ J. Vac. Sci. Technol. A 14, 660 (1996). 39. D. W. Cooper, M. H. Peters and R. J. Miller, ‘‘Predicted Deposition of Submicrometer Particles due to Diffusion and Electrostatics in Viscous Axisymmetric Stagnation-Point Flow,’’ Aerosol Sci. Technol. 11, 133 (1989).

4 Relevance of Particle Transport in Surface Deposition and Cleaning Chao-Hsin Lin Environmental Control Systems, Boeing Commercial Airplanes Group, Seattle, WA, USA Chao Zhu Departmental of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ, USA

4.1

Introduction

Through numerous natural phenomena as well as human activities, we have ample experience about foreign objects in various fluid media and their interactions. To name a few that occur naturally are sandstorms, precipitation, cloud formation, and botanical reproduction. In our daily economic life activities, such as pest control through spraying, dust collection, mining and manufacturing processes, and transportation and pollution control are just a tiny fraction of examples that involve interaction of droplets, vapors, particles, and bubbles with various fluid media. Physically speaking, we live in a world of tremendous systems of fluid–particle interactions, as first delineated by Soo in 1965 [1]. Researches on this subject and its related phenomena have progressed significantly since the second half of the last century [2–4]. In this chapter, we are focusing primarily on the recent progress in gas-particle flows, in general, and their relevance to fine particle surface deposition/cleaning, in particular. The characteristics of gas-particle flows vary widely with respect to the geometric and material properties of the particle [4]. In solid fuel combustion, pneumatic conveying, fluidization, gas-particle separation, particle deposition on semiconductor wafers [5], and other processes, gas-particle flows are commonly witnessed. Likewise, gas-particle flows play important roles in various natural phenomena such as dry

R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 267–297 ª 2008 William Andrew, Inc.

267

268

FUNDAMENTALS

deposition of particulate matters on natural surfaces [6], dispersion of natural allergens, volcanic ashes, cosmic dusts, etc. Surface contamination due to the presence of fine particles has caused enormous yield loss and degradation of reliability in microelectronics manufacturing [7] and material processing [8], damages in agricultural and forestry products [9] and art works [10]. In general, deposition of atmospheric contaminants onto solid surfaces is a dynamic process. This process is carried out in three steps as follows: (1) particles are transported aerodynamically to the proximity of the boundary layer surrounding the solid surfaces, (2) particles are transported within the boundary layer and toward the gas– solid interfaces, and (3) particles come physically in contact with the solid surfaces [11]. In this chapter, descriptions of the important mechanisms that are involved in this process are provided. In Section 4.2, particle transport in gas-particle flows related to surface deposition is described. At the particle–solid interfaces, the primary adhesion mechanisms are also detailed and discussed in Section 4.2. Subsequently, Section 4.3 presents the various mechanisms of the aerodynamic and boundary layer transport of particles. The relevance of the particle transport theories is given. In Sections 4.4–4.6, three mechanisms, namely thermophoresis, electrostatics and dielectrophoresis, and their implications in particle deposition are delineated. Section 4.7 is devoted to a unique particle deposition problem, namely abrasive erosion and its relevance in surface cleaning. The recent progress in numerical and experimental studies on particle transport phenomena described in the aforementioned sections is summarized.

4.2

Particle–solid Surface Interactions

For understanding the various phenomena involved in surface contamination by particles to developing means for monitoring and removing the contaminants, it is necessary to learn and apply the mechanics of gasparticle flows. Fuchs [12] and Friedlander [13], in their widely cited books, have compiled and provided the most up-to-date knowledge on the motion of aerosols (i.e. solid or liquid particles) in natural or manmade environments in the 1960s and 1970s, respectively. Hinds summarized further progress in aerosol technology in his well-received textbook [14]. Most recently, Fan and Zhu have given a thorough description of the basic principles and fundamental phenomena associated with gas–solid flows [4]. In this chapter, from the application perspectives of surface

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deposition and cleaning, we focus our discussion on the important mechanisms involved in the context of gas-particle flows. For more rigorous theoretical derivations, the readers are encouraged to refer to the references cited in this chapter. When a solid particle physically contacts either another solid particle or a solid surface, the forces between these solid objects are primarily attractive in nature and result in adhesion of particles to each other or to the solid surface. The finer the size of the particles, the adhesion forces involved become more significant and particles become more difficult to remove [15]. Particle agglomeration due to adhesion could change the particle size distribution and other physical properties in the gas–solid system. Consequently, this effect would alter the effectiveness of particle removal. From the perspectives of surface deposition of particles, the most affected industry is the manufacturing of microelectronics [16]. Therefore, the entire clean room technology was mostly built with the aim of controlling the deposition of fine particles to reduce yield losses during the manufacturing of integrated circuits. After a physical contact between particles and a solid surface is established, it is considered that van der Waals and electrostatic forces are the predominant attractive forces between the adhering particles. Other interfacial forces such as liquid bridges, double-layer repulsion and chemical bonds may play important roles under specific circumstances [15, 16]. Penney and Klingler [17] have reported that, by measuring the contact potential differences of adjoining dust particles, the combination of van der Waals and electrostatic forces is normally an order of magnitude greater than the adhesion force by mechanical means. Figure 4.1 shows a schematic of adhesion by the van der Waals forces. For a spherical particle depositing on a planar surface, the resulting van der Waals forces

3

1 dp

Z0

2

Figure 4.1 van der Waals interaction: sphere-planar surface [15].

270

FUNDAMENTALS

are expressed as FvdW ¼ A

dp z 20

Eq. (4-1)

where FvdW is the van der Waals forces, A is the Hamaker constant, dp is the particle diameter, and z0 is the clearance between the particle and the surface [14, 16]. For the same configuration, as shown in Figure 4.1, the difference in the work functions of the two materials results in a contact potential, fc, between the particle and the surface. The force due to the electrostatic double-layer is given [15] as Fe ¼ pe0

dp f2c 2 z0

Eq. (4-2)

where Fe is the force due to the electrostatic double-layer and e0 is the dielectric constant of vacuum. With the common presence of humidity in the environment, it is not unusual to have some moisture adsorbed on the surface of most materials. At the interface where two different materials contact, a liquid bridge (or film) forms and results in an attractive force due to the surface tension of the liquid, as shown in Figure 4.2. For an ambient relative humidity above 90%, this attractive force is given as Fs ¼ 2pgdp

Eq. (4-3)

where Fs is the adhesion force due to the surface tension, g, of the liquid bridge. The major adhesion forces mentioned above are all proportional to the particle diameter, dp. In contrast, to remove the particle by mechanical means, we need to employ either a centrifugal force that is proportional to dp3 or an air current force that is proportional to dp2. Therefore, much greater force is needed to remove deposited micrometer and sub-micrometer particles. Based on measurements of hard materials

Particle

Flat surface Figure 4.2 Adhesion force due to a liquid film.

Liquid

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and clean surfaces at 298 K, an empirical formula for the overall adhesion force, Fad, is given as [14]: Fad ffi150dp ½0:5 þ 0:0045ð%RHÞ

Eq. (4-4)

For spherical particles of unit density, a comparison among the adhesion force, calculated using Eq. (4-4), and the corresponding gravitational and aerodynamic drag forces is made in Table 4.1. This example illustrates the significance of adhesion force and the difficulty in dislodging the deposited particles from the surface, especially for fine particles. Even though we can calculate the primary mechanisms of particle–solid surface adhesion based on the equations above, in reality, however, the distance of separation, z0, is not measurable and an assumed range from 0.4 to 1.0 nm is used. Therefore, this introduces a certain degree of uncertainty into both the measured and predicted data. In addition, approximations are made to define the roughness and asperities of the adhering bodies, as illustrated in Figure 4.3. Further research to improve the accuracy of adhesion forces, experimentally and computationally, is rightly justified. Numerous ways, dry and wet, have been proposed and investigated to remove particles from surfaces. To reduce contamination, researchers and practitioners, though not always in agreement, prefer dry approaches, as reported by Cooper et al. [7] and Ranade [16]. It is known that blowing dry air or nitrogen jet is not effective to remove particles smaller than 10 mm in diameter. Cooper et al. [7] applied an electric field between an electrostatic film cleaner and the particle-deposited product to remove particles by electrostatic force, as shown in Figure 4.4. Their success was not universal with respect to all the particles they had tested, as Table 4.1 Comparison of Adhesion, Gravity, and Air Current Forces on Spherical Unit-density Particles [14]

Diameter (mm) 0.1 1.0 10 100 a

Adhesiona 108 107 106 105

Calculated by Eq. (4-4) for 50% RH.

Force (N) Gravity Air Current (at 1 m/s) 5 5 5 5

· · · ·

1018 1015 1012 109

2 · 1010 2 · 109 3 · 108 6 · 107

272

FUNDAMENTALS

dp

(a)

dp

(b)

Figure 4.3 Effect of surface roughness on particle deposition [15]. (a) Asperities smaller than particle size. (b) Asperities larger than particle size.

Take-up roller DC Power Supply

Film, particles

Conductive roller

Product Ground Plate

Figure 4.4 Schematic diagram of the electrostatic film cleaner [7].

summarized in Table 4.2 [7]. Ranade [16] reviewed many removal schemes and processes, both dry and wet, and no preferred technique was recommended due to the complexity involved in the phenomena of surface deposition of particles.

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Table 4.2 Summary of Measured Removal Efficiencies, Using an Electrostatic Film Cleaner [7]

Particle Diameter (mm)

Particle Type

Film Used

Removal Field Voltage Efficiency (%) (MV/cm) (kV)

Conductive surfaces—smooth (specular) Metal film 1.1 Latex Polyimide >46–98 0.5 Latex Polyimide >95 Polyimide >95 0.3 SiO2 Silicon wafer 6 Ni Laminate 80–100 Laminate >95 2 SiO2 Laminate >80 0.5 SiO2 Conductive surfaces—patterned or rough Semiconductor chips post-metallization 2–5 Ni Laminate 60–90 Laminate >50 2 SiO2 Insulator surfaces—smooth (specular) SiO2 (0.5 mm) silicon wafer 2–5 Ni Laminate 98 Laminate 97 2 SiO2 1 Latex Laminate  60 Ceramic substrate Laminate 96–100 12 SiO2 6 Ni Laminate 96–100 Glass plate. 1.5 mm thick 6 Ni Laminate 93 Laminate 2 SiO2 Laminate 0.5 SiO2 Insulator surfaces—patterned or rough Multilayer ceramic with metal pads Laminate 97 12 SiO2 6 Ni Laminate 95–99

4.3

2.8 7.0 8.4

– – –

– – –

4 6 6

– –

14 14

– – –

4 3 3

– –

10 10

– – –

8 8 8

– –

3–4 3–4

Dry Deposition

Dry deposition of particulate matter on natural systems such as vegetated canopies and natural water bodies has been studies for several decades [6, 9, 11]. For a wide variety of biotic and natural surfaces, Sehmel gave a detailed review of published dry particle and gas deposition

274

FUNDAMENTALS

velocities that ranged over three and four orders of magnitude, respectively [6]. The factors that may affect dry deposition of particles and gas species are summarized in Table 4.3 [6]. The mechanisms for dry deposition could be inertial impaction [18–22], interception [23, 24], diffusion [5, 25–27], sedimentation [5, 25, 26], and electrostatic precipitation and thermophoresis [28]. For surface deposition of particles in many industrial processes, inertial impaction and interception are the dominant forces encountered in particle deposition on filters, work benches and in particle sampling of high purity gases for semiconductor manufacture. On the other hand, for finer particles (such as micrometer and sub-micrometer particles), Brownian diffusion emerges as one of the primary mechanisms for deposition of particles on surfaces. Conventionally, to study particle deposition on a surface, many researchers favor a rotating disk in a stagnation flow setting [8, 23]. Ramarao and Tien [23] proposed a procedure to study the combined effect of inertial impaction, sedimentation and interception on particle deposition in a two-dimensional stagnation flow field. For particle size ranges from 1 to 100 mm in diameter, they found that the deposition flux, J, was greater by taking the boundary layer effect (denoted as JBL) into account than by excluding it (denoted as JID). A correction factor, F = JID/ JBL, for the effect of the boundary layer on particle deposition under a range of the flow field constant, a, is obtained, as shown in Figure 4.5. Thus, a laminar flow is usually maintained in microelectronics manufacturing in cleanrooms. Usually finer particles whose diameter ranges between 0.01 and 10 mm are deposited on semiconductor wafers and diffusion is known to be the predominant deposition mechanism. By using the analogy with heat and mass transfer, Liu and Ahn [5] deduced the particle deposition velocity for three laminar flow settings typically used in the manufacturing environment for semiconductor wafers, as shown in Figure 4.6. For a horizontal wafer in a vertical airflow configuration, as shown in Figure 4.6(a), the mass transfer is given as Sh=1:08Sc1=3 Re1=2

Eq. (4-5)

Sh0 ¼ 0:834Sc1=3 Re1=2

Eq. (4-6)

and

where Sh = KDw/D is the mean Sherwood number, K is the mass transfer coefficient, Dw is the wafer diameter, D = kTC/(3pmdp) is the diffusion coefficient, k is the Boltzmann constant, T is the absolute

ZHU

(Continued)

AND

Inversion layer

Electrostatic effects —Attraction —Repulsion Gravitational settling Hygroscopicity

Canopy structure —Area density —Bark —Bole —Leaves —Porosity —Reproductive structure —Soils —Stem —Type

Senescence

Biotic surfaces Canopy growth —Dormant —Expanding

Adhesion

Surface Variables

SURFACE DEPOSITION, LIN

Friction velocity

Flow separation —Above canopy —Below canopy

Diffusion, effect of —Canopy —Diurnal variation —Fetch

Diffusion —Brownian —Eddy equal to (a) Particle (b) Momentum (c) Heat —Effect of canopy on diffusiophoresis Partial pressure in equilibrium with surface solubility

Diffusion —Brownian —Eddy

Diameter Density

Chemical activity

Gases

Agglomeration

Particles

Deposition Material

IN

Atmospheric stability

Aerodynamic roughness —Mass transfer (a) Particles (b) Gases —Heat transfer —Momentum transfer

Micrometeorology Variables

Table 4.3 Some Factors that Influence Dry Deposition of Particles [6]

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Momentum Physical properties Re-suspension Shape Size

Seasonal variation

Solar radiation

Surface heating

Temperature

Terrain —Uniform —Non-uniform

Zero-plane displacements —Mass transfer (a) Particles (b) Gases —Heat transfer —Momentum transfer

Turbulence

Interception

Relative humidity

Thermophoresis

Solubility

Impaction

Particles

Gases

Deposition Material

Pollutant concentration

Micrometeorology Variables

Table 4.3 Some Factors that Influence Dry Deposition of Particles [6] (cont’d)

Water

Prior deposition loading

Pollutant penetration and distribution in canopy

Non-biotic surfaces pH effects on —Reaction —Solubility

Leaf-vegetation —Boundary layer —Change at high winds —Flutter —Stomatal resistant

Electrostatic properties

Surface Variables

276 FUNDAMENTALS

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1 α=0.1 α=1 α=5 α=10

F = JID/JBL

0.9

0.8

0.7 1

10 Particle diameter (mm),dp

100

Figure 4.5 Flux correction factor, F, as a function of particle diameter for various values of a, flow field constant [23].

temperature, C is the Cunningham slip correction factor, m is the molecular viscosity of the fluid, Sc = n/D is the Schmidt number, Re = UDw/ n is the Reynolds number, U is the airflow velocity, and n is the kinematic viscosity. In Eqs. (4-5) and (4-6), the symbol Sh denotes the mean Sherwood number based on the mean mass transfer coefficient, K, for the entire wafer; and Sh0 denotes the Sherwood number at the stagnation point. Note the definition of K = j/N, where j is the particle deposition flux in number of particles per unit surface area of the wafer per unit time and N is the number concentration of particles in the free stream. Therefore, K is also the deposition velocity of the particles. For the airflow configuration depicted in Figure 4.6(a), the overall deposition velocity, V, becomes V ¼ K þ rp gCd 2p =18m

Eq. (4-7)

where the second term on the right-hand side of the equation is the sedimentation velocity, rp is the material density of the particles, and g is the gravitational acceleration.

278

FUNDAMENTALS

(a)

(b)

(c)

Figure 4.6 Schematic diagram showing three types of airflow in semiconductor manufacturing [5]. (a) A horizontal wafer in a vertical laminar flow cleanroom. (b) A horizontal wafer in a horizontal-flow clean hood. (c) Vertical wafers in a wafer carrier.

For a horizontal wafer in a horizontal airflow configuration, as illustrated in Figure 4.6(b), the mean and the local mass transfers are given in Eqs. (4-8) and (4-9) and expressed as Shx ¼ 0:664Sc1=3 Re1=2 x

Eq. (4-8)

Shx ¼ 0:332Sc1=3 Rex1=2

Eq. (4-9)

and

where Shx ¼ Kx=D, Shx = Kx/D and Rex = Ux/n are all based on the distance, x, measured from the leading edge of the wafer and the air

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velocity, U. By performing an integration of K over the entire surface area of the wafer, we have 1=2

ShD ¼ 0:739Sc1=3 ReD

Eq. (4-10)

where ShD ¼ KDw =D, ShD = KDw/D and ReD = UDw/n are all based on the wafer diameter, Dw. As shown in Figure 4.6(c), the third configuration is an array of vertical wafers in a wafer carrier. The mean mass transfer coefficient, K, is given by K ¼ ð2h=pRw ÞUfd

Eq. (4-11)

where h is the half width of the channel formed by two neighboring wafers, Rw is the radius of the wafers, U is the mean air velocity in the channel, and fd is the fractional particle deposition and is expressed as fd ¼ 97:27V0:6654

Eq. (4-12)

where V = DDw/h2U is a dimensionless parameter. For the first configuration, as shown in Figure 4.6(a), Liu and Ahn’s prediction on particle deposition velocity was in good agreement with the measured data reported by Pui, Ye and Liu using ammonium fluorescein aerosols [26], as depicted in Figure 4.7.

Deposition Velocity, cm/s

1.0000

Theoretical [5] Experimental

0.1000

0.0100

0.0010

0.0001 0.01

0.1 1 Particle Diameter, mm

10

Figure 4.7 Comparison of the final deposition data from the theory of Liu and Ahn [5] with experimental data of [26] for 3.8-cm diameter wafer and for a free stream velocity of 20 cm/s.

280

FUNDAMENTALS

By taking convection, diffusion, sedimentation, electrical forces, and thermophoresis into account, a numerical simulation of particle deposition on a typical semiconductor wafer in a cleanroom using two different modeling approaches was reported by Peterson et al. [28]. The predicted particle deposition velocity and flux showed a good agreement between the two approaches (i.e. a boundary layer approach and a full numerical simulation) they had adopted. For particle sizes between 0.02 and 0.7 mm at a surface temperature of 330 K, they found that the effect of thermophoresis could be effectively utilized to prevent such particles from depositing on a surface [28].

4.4 Thermophoresis and Its Relevance in Surface Cleaning The phenomenon of particle repulsion from hot surfaces was first observed in the 1880s. However, the theoretical interpretation of the mechanism is still far from complete due to the complexity of the physical processes involved and the new findings obtained recently [12, 29–34]. The radiometric forces acting on particles due either to a temperature gradient in the gas medium or to non-uniform radiation cause this phenomenon. The radiometric motion of particles by temperature gradient is called thermophoresis while the motion of particles by non-uniform radiation is called photophoresis [2, 12, 35, 36]. If, instead a concentration exists and causes particle movement, this phenomenon is then called diffusophoresis [37, 38]. Thermophoresis has been studied by numerous researchers to understand its effect on particle deposition on a cold surface [10, 39, 40], or on particle removal from a heated surface, or in a thermal precipitator [14, 41, 42]. In the air, for spherical particles ranging between 0.05 and 1 mm in diameter, the corresponding Schmidt numbers, Sc = n/D, are from 6 · 103 to 5 · 105. Therefore, Brownian diffusion is negligible and the predominant mechanisms for the movement of the aforementioned particles are convection and thermophoresis [39]. For an airborne particle much smaller than the mean free path of air molecule, l (l = 0.065 mm at 298 K and 1 atm), the particle motion is in the so-called freemolecular regime where the Knudsen number Kn = l/dp  1. The calculation of the thermophoretic force in this regime has long been acknowledged to be in good agreement with experimental data [30]. However, due to the boundary layer effect and other complexities, the theoretical development of the thermophoresis in the transition regime

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(Kn  1) and the slip-flow regime (Kn < 1) is still evolving. The available formulas for these two regimes should be considered as tentative. Talbot et al. [29] have proposed an expression to calculate the thermophoretic velocity applicable to all Knudsen numbers. This formula has been received quite favorably by other researchers [10, 39] and is given as n vt ¼ K
T T

Eq. (4-13)

and K ¼ 2Cs

ðkg =kp þ Ct l=Rp Þ½1 þ ðl=Rp Þð1:2 þ 0:41e0:88Rp =l Þ ð1 þ 3Cm l=Rp Þð1 þ 2kg =kp þ 2Ct l=Rp Þ Eq. (4-14)

where K is the thermophoretic coefficient, T is the ambient absolute temperature of the gas and
T is the temperature gradient, Cs = 1.147, Cm = 1.146, Ct = 2.2, kg is the thermal conductivity of the surrounding gas, and kp is the thermal conductivity of the particle. For various kg/kp ratios, K in Eq. (4-14) is plotted against l/Rp as shown in Figure 4.8 [39]. Adjacent to a heated planar surface, within the laminar boundary layer, 0.7 0.6

Kg/Kp=0.5

0.5 0.4 0.2

K 0.3

0.1

0.2

0.05 0.1 0.01 0 0.001

0.01

0.1

1

10

λ/Rp

Figure 4.8 Values of the thermophoretic coefficient K for a spherical particle of radius a according to the expression in Eq. (4-14). l is the mean free path of gas molecules and kg/kp is the ratio of the thermal conductivity of the gas to that of the particle [39].

282

FUNDAMENTALS

a particle-free zone about one half of the boundary-layer thickness was reported by Talbot et al. [29]. However, as particles may rotate in the boundary layer under certain conditions, Chomiak and Gupta [43] and Batchelor [44] argued that the effect of thermophoresis on particle removal might not be as conspicuous as predicted from Eqs. (4-13) and (4-14). As reported in Chomiak and Gupta [43], in a laminar boundary layer, thermophoretic force would not affect the particle if its radius, Rp, is 0

11=2 18nD k =k Re x1=4 Tp g p A Rp >@  2l 1 U¥ þ  aRp 1þl =Rp

Eq. (4-15)

where DTp is the thermal diffusivity of the particle material, a is the accommodation coefficient, l* = {(2lCp/Cv)/[Pr(Cp/Cv+1)]} is the heat conduction mean free path, Cp and Cv are the specific heats of the gas at constant pressure and volume, respectively, Pr is the Prandtl number, Rex is the Reynolds number of the flow depending on the distance from the leading edge, and U¥ is the gas velocity outside of the boundary layer. Likewise, in a turbulent boundary layer, the critical particle size is given as 0 11=2 202:7nD k =k Re0:1 Tp g pA x R p >@  2l 1 U ¥ þ  aRp 1þl =Rp

Eq. (4-16)

While applying thermophoresis as a cleaning mechanism to remove deposited particles in a naturally convective airflow, as observed in most Table 4.4 Temperature Gradient and Thermophoretic Velocity [33]

Particle

MgO SiO2

Temperature Gradient
T (K/mm)

Thermophoretic Velocity Predicted Using the Theory in [29] vt (mm/s)

16 45 22 80

0.042 0.13 0.20 0.86

Thermophoretic velocity measured in [33] vt (mm/s) 0.22 0.67 0.58 3.00

– – – –

0.021 0.097 0.017 0.094

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Table 4.5 The Measured Temperature Gradient and Thermophoretic Effect

Particles Material Diameter (mm) SiO2 SiO2

1.0 2.7

SiO2 SiO2 PMMA

10 30 5.0

PMMA

12

PMMA

30

Temperature Gradient
T (K/mm)

Particle Velocity Measured in [34] vt (mm/s)

40.0 22.0 80 40.0a 40.0 40.0 31.4 49.5 40.0a 31.4 42.0 40.0a 31.4 49.5 40.0a

1.68 0.58 3.00 1.03 0.69 0.53 0.55 1.14 0.80 0.40 0.73 0.66 0.35 0.78 0.53

a

These values are obtained by interpolation using two preceding data values.

cleanroom operations, the conditions indicated in Eqs. (4-15) and (4-16) are rarely encountered, as reported by Nazaroff et al. [10, 45]. Experimental investigations on thermophoresis have been reported by a number of researchers. Like the corresponding theoretical development in the transition and slip-flow regimes mentioned above, the complexity of the phenomenon has limited the quantity and quality of the experimental data available for model validation. The greatest hindrance to obtain reliable measured data in thermophoresis studies is the interference of natural convection generated also by a temperature gradient in normal gravity [33, 34]. By conducting thermophoresis experiments in a microgravity environment, Toda et al. produced some interesting data as listed in Tables 4.4 and 4.5 [33, 34]. The comparison between the thermophoretic velocity measured by Toda et al. [33, 34] and the predictions using Eq. (4-17), derived by Talbot et al. [29], for Kn < 1, vt ¼ 2Cs n

ðkg =kp þ Ct l=Rp Þ
T ð1 þ 2Cm l=Rp Þð1 þ 2kg =kp þ 2Ct l=Rp Þ T

Eq. (4-17)

284

FUNDAMENTALS

Figure 4.9 The relation between the diameter and velocity of the SiO2 particles (
T = 40 K/mm). Solid line: measured in [34]. Dotted line: predicted values based on the Brock equation in [29, 30].

Figure 4.10 The relation between the diameter and velocity of the PMMA particles (
T = 40 K/mm). Solid line: measured in [34]. Dotted line: predicted values based on the Brock equation in [29, 30].

is shown in Figures 4.9 and 4.10 [29, 30, 33, 34]. As shown in Figure 4.9, Eq. (4-17) has substantially under-predicted the thermophoretic velocity for the SiO2 particles (size ranging from 1 to 30 mm). For the polymethyl methacrylate (PMMA) particles (size ranging from 5 to 30 mm), under-predictions of thermophoretic velocity exist for dp < 25 mm particles and a slight over-prediction for dp = 30 mm particles, as shown in Figure 4.10. The above discrepancies indicated the importance of

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gravity effect. Hence the existing theories on thermophoresis could be biased due to the fact that they were deduced from experimental data in the presence of gravity.

4.5 Electrostatic Force and Its Relevance in Surface Cleaning As shown in Figure 4.4, an artificial electrostatic field was created to remove particles deposited on microelectronics products [7, 46, 47]. On the other hand, similar to the thermophoretic effect, the electrostatic force is another mechanism that would affect particle deposition on surfaces [48–50]. Electrostatic phenomena have been observed since the early period of human civilization, but electrostatic force had not been quantified until the discovery of the Coulomb’s law that laid the foundation for the science of electrostatics two centuries ago. Even though a primitive electrostatic device for cleaning polluted air was built in 1885, it was never developed to the stage suitable for commercialization [51]. Electrostatic precipitators have been widely used to collect fine particles such as fly ashes from coal-fired furnaces or reactors. Another example of the application of the effect of electrostatic precipitation is the electrostatic air cleaners for household use. Particles may acquire charges through surface contact, collection of atmospheric electricity, ionization, and similar phenomena [52]. For a conductive particle, the acquisition of charge on its surface is almost instantaneous. The total charge on the surface of a particle, q, is given as q ¼ e0 p3 d 2p E=6

Eq. (4-18)

where e0 is the dielectric constant of vacuum and E is the electric field strength. For particles with different electrical charges, it was theoretically shown that for dissimilar particles their agglomeration rates were enhanced with increasing surface charge and particle size polydispersity [53]. To remove conductive spherical particles adhered to a conductive surface, the force required to overcome the adhesion force, Fe, is expressed as [46, 47]: Fe ¼ 1:37pe0 E 2 d 2p

Eq. (4-19)

For several simple configurations such as parallel plate, tubular, and wire–plate geometry, the electric field distribution could be obtained

286

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Figure 4.11 Particle sizes for which the electrostatic force just equals that of adhesion or of gravitation (lines). The legends shown on the lower left corner on this plot indicate the type of the particle used. ‘‘’’ are the Ni particles. ‘‘^’’ are the SiO2 glass particles. ‘‘&’’ are the polystyrene latex particles [46].

either by measurement or by solving the governing equation of electrical potential distribution numerically. Figure 4.11 illustrates the relative strength of adhesion, gravitational and electrostatic forces with respect to various particle sizes. To remove particles of various sizes and chemical compositions, the required electric fields are listed in Table 4.6 [46].

4.6 Dielectrophoresis and Its Relevance in Surface Cleaning When a neutral particle of dielectric material is placed in an electric field, the particle becomes polarized and behaves like an electric dipole. If the electric field is not uniform, the force exerted on the particle is not balanced and results in the movement of the particle. This phenomenon is called dielectrophoresis [54–56]. In the natural environment, most of the particles are not spherical in shape. Therefore, the effect of particle shape plays an important role in the deposition

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Table 4.6 Electric Fields Needed to Remove Particles of the Indicated Size and Composition [46]

Particle Material

Diameter (mm)

Glass

34–35a 9–15

SiO2 Nickel

0.52 60–75 8–10 5–8 3–5 1–3

Polystyrene

10

d

1.1

Field (kV/cm) Needed to Remove the Percentage of Particles Indicated 5% 50% 95% 27 20 29 22 20 >525 10 18 550e

72 55 69 72 88

116 91 109 123 156

21 87 77 100 78 159 137

32 155 163 174 144 289 227

600c 243 367

446 644

The symbol > means a higher field is needed to remove 5%. a Data from 11 runs, taken after 60 minutes on fully charged particles. b Two of 35 removed. c 23 of 43 removed. d Only 25 particles total, both runs; not likely fully charged. e One of 109 removed; not likely fully charged.

of non-spherical particles. For instance, much effort has been invested to study the deposition of fibers along the human respiratory tract [56]. It is imperative to sort out particles by their specific aspect ratio or by length for the applications mentioned above. For a conductive fiber with an aspect ratio, b = L/dp, its dielectrophoretic velocity is given by Lipowicz and Yeh [56] as v = limb!¥

Km e0 2 ln 2b  0:5 L
E2 24m ln 2b  1

Eq. (4-20)

288

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where v is the dielectrophoretic velocity, Km is the dielectric constant of the electrically insulating medium, L is the length of the fiber, and E is the strength of the electric field. As indicated in Eq. (4-20), v is proportional to the square of the length of the fiber. Therefore, dielectrophoresis is a more effective fiber classifier than electrophoresis, as recommended by Lipowicz and Yeh [56]. In the presence of a strong electric field, to avoid the interference by electrophoresis, it is necessary to use either uncharged particles or use an alternating (AC) electric field to fully utilize the effect of dielectrophoresis [55, 56].

4.7 Abrasive Erosion and Its Relevance in Surface Cleaning Solid particle erosion or abrasive blasting erosion refers to the general mechanical degradation or wear of a solid material subjected to a jet stream of abrasive particles impinging on its surface. Examples of the application of abrasive erosion can be found in abrasive cleaning of metal surfaces for coating [58] and for stress corrosion cracking investigation [59], in chemical mechanical polishing [60], and in abrasive drilling and cutting by water jet [61, 62]. However, in many other applications, abrasive erosion causes sever surface damage, which is, of course, not desired. Abrasive erosion damage has been extensively reported, such as in rocket motor tail nozzle [63], on helicopter rotors and gas turbine blades [64], and in pipeline systems for pneumatic or hydraulic transportation of solids [4, 65]. In this section, some recent developments on fundamental mechanisms of solid particle erosion, including abrasive erosion by a single particle impact and erosion by multiple impacts of a solid particle stream, as well as parametric effects on the abrasive erosion rate are discussed. When a solid particle impinges on a material surface, it may skid and/ or rotate on the surface and at the same time create an indentation (ductile materials) or crater (brittle materials). With successive impacts of particles on the same location, this indentation causes material removal due to the repeated plastic deformation and the skidding of sharp-edged hard particles over a surface of relatively low hardness. When the impact velocity is lower than the critical impact velocity, the particle does not skid but rotate, resulting in no cutting damage but only plastic fatigue damage. When the impact velocity is higher than

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n

Ω′ Vt V′n θ Vn

V′ V′t

V G r

t

β C

Figure 4.12 Schematic diagram of surface impact of an abrasive particle.

the critical velocity, the solid particle will skid on the surface, creating a crater, and then rotate on the surface, as shown in Figure 4.12. The critical impact velocity, Vc, can be estimated based on a rolling/sliding contact mechanism [66], as: Vc ¼

K þ cos bðcos b  f sin bÞ f ðK þ sin bÞ  cos b

kl d sy  qffiffiffiffiffiffiffiffi  ffi 10E sin u 1=5 m  ke V n ð1 þ eÞ p 2ppr s Eq. (4-21)

where u is the impact angle, b is the contact angle, Vn is the normal component of impact velocity, p is the yield pressure, rs is the equivalent radius of a solid particle, d is the maximum crater diameter, m is the particle mass, ke and kl are material property related constants, f is the friction coefficient, E is elasticity or Young’s modulus, sy is the yield stress, e is the rebounding coefficient, and K is the shape factor of particle. The friction coefficient was further estimated by Yabuki and Matsumura [66] and given as: p 2 1 d3 0   rffiffiffiffiffiffiffiffiffiffiffiffi p d sþ p m ke 1=5 8 12 rs · þ V f¼ 2 2pprs 2 n mð1 þ eÞVn

Eq. (4-22)

where p0 is the average pressure required to displace the soft material from the front of the particle and s is the shear strength of the soft material.

290

FUNDAMENTALS

The rebounding coefficient was calculated by Tabor [67] using a normal impact model and is given by 104 e¼

m

!1=8

p5 43 35 2r3s

1  n2p 1  n2s þ Ep Es

!2 p5=8 

Vn

3 V 2n  Vn02 8

3=8

Eq. (4-23) where e is the restitution coefficient (or rebounding coefficient), n is the Poisson’s ratio, V n0 is the normal component of rebounding velocity. The most important issue in abrasive erosion is the erosion rate. The volume of material, Q, removed by a single abrasive impact was given by Finnie [68] and is expressed as:   8 mV2 6 > > sin2u sinu < rck  k Q¼ 2 > mV k > : ðcosuÞ2 rck 6

k 6 k tan u > 6

tan u £

Eq. (4-24)

where c and k are the ratio of length to depth of the scratch formed and the ratio of vertical to horizontal force components, respectively, r is the energy required to remove a unit volume of material from the body. Winter and Hutchings [69] further identified two mechanisms for volume removal, namely, ploughing and cutting. Ploughing occurs when a particle rolls over, instead of sliding along the surface, which causes the cutting edge of the particle to penetrate deeply into the material surface instead of performing a scooping action. The total volume removed by an abrasive impact comes from two contributions: the ploughing loss [65], QP ¼

0:5m ðVsin u  kÞ2 O

Eq. (4-25)

m 2 2 ðV cos u  V2r Þ 2f

Eq. (4-26)

and the cutting loss [70], QC ¼

where O and f are the energies required to remove a unit volume of material from the body by ploughing and cutting, respectively, k is a material property related constant, and Vr is the particle rebounding velocity.

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Despite a relatively clear understanding of abrasive erosion by a single particle impingement, the current knowledge on abrasive erosion by a jet stream of abrasive particles is still inadequate to provide predictive and reliable information on the erosion rate for a given engineering design or application. This lack of knowledge has resulted from insufficient information in three interrelated areas: (1) definition of erosion resistance as an objective material property; (2) establishment of the quantitative relationship among erosion rate, erosion resistance, and environmental parameters; and (3) the determination of these environmental parameters for a given application. So far most studies on erosion rate are reported in terms of the material loss curves or loss rates for particular types of materials of interest. The erosion rate is defined as the ratio of mass loss to mass of erodent particle, which is a dimensionless quantity. There have been many attempts to correlate the erosion rates measured for different materials with one or more established mechanical properties of these materials [71–73]. A theoretical dynamic analysis of a new laboratory technique was recently proposed by Talia et al. [74] for investigating the abrasive erosion mechanisms of brittle, ductile and semi-ductile materials. As shown in Figure 4.13, the solid material samples are mounted on a rotating disk, which are air-blasted by abrasive particles. This measurement system is easy to individually investigate the effects of abrasive impact angle, impact velocity components (normal and tangential), and abrasive material properties. Typical effect of the impact angle on erosion rate is shown in Figure 4.14, in which a nonlinear relationship between erosion rate and impact angle is seen. In addition, the erosion loss appears to be undetectable at small impact angles, which indicates that a minimum angle is required for material removal. Typical effect of impact velocity on erosion rate is illustrated in

Figure 4.13 Experimental system for study of particle erosion mechanism [74].

292

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Figure 4.14 Example of effect of impact angle on erosion rate [74].

Figure 4.15, in which the erosion rate of different materials representing ductile, brittle and semi-ductile at various impact velocities but with the same impact angle are presented. The apparent linear relationships between the erosion rate and normal impact velocity in a semi-logarithm scale indicate certain similarities of the materials tested.

4.8

Summary

Particle deposition problems are vital challenges to the practitioners in the industries dealing with contaminant removal and surface cleaning. In many manufacturing and processing environments, such as that for producing semiconductors and integrated circuits, substantial amounts of time and efforts are devoted to tackle the ubiquitous problems of particle deposition. Multiple mechanisms are involved in the deposition of particles on various surfaces encountered in industrial processes. In this chapter, the most common and influencing mechanisms of particle deposition are described. The physical aspects of the effect due to dry deposition, thermophoresis, electrostatic force and dielectrophoresis on particle deposition on surfaces are delineated and emphasized to

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Figure 4.15 Example of effect of normal impact particle velocity on erosion rate [74].

strengthen their relevance in contaminant removal and surface cleaning. The applicable range of a specific theory and related caveats when applied to an industrial setting are also provided throughout this chapter. For an in-depth understanding of each of the mechanisms involved in particle deposition, the references cited in this chapter should serve as further reading material and guide to the specific knowledge as well. Surface cleaning by mechanical means can be achieved by abrasive erosion from impingement of fine and hard particles on the surface to be cleaned. The effectiveness of abrasive erosion depends on impact velocity, impact angle, and materials involved. The available empirical correlations are typically application oriented, namely, they are valid for specific applications and within a narrow range of parametric conditions. One particular difficulty in model generalization of abrasive erosion for practical applications is the low predictability of particle behaviors in turbulent jets and boundary layer flows over rugged (eroded) surfaces. Theories with a much wider applicability and a deeper scientific basis are yet to be developed.

294

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References 1. S. L. Soo, Fluid Dynamics of Multiphase Systems, Blaisdell-Ginn, Waltham, MA (1967). 2. S. L. Soo, Multiphase Fluid Dynamics, Science Press, Beijing (1990). 3. V. G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ (1962). 4. L.-S. Fan and C. Zhu, Principles of Gas-Solid Flows, Cambridge University Press, London (1998). 5. B. Y. H. Liu and K. Ahn, ‘‘Particle Deposition on Semiconductor Wafers,’’ Aerosol Sci. Technol. 6, 215 (1987). 6. G. A. Sehmel, ‘‘Particle and Gas Dry Deposition: A Review,’’ Atmos. Environ. 14, 983 (1980). 7. D. W. Cooper, H. L. Wolfe, J. T. C. Yeh and R. J. Miller, ‘‘Surface Cleaning by Electrostatic Removal of Particles,’’ Aerosol Sci. Technol. 13, 116 (1990). 8. T. Debros and T. G. M. van de Ven, ‘‘A Direct Method for Studying Particle Deposition onto Solid Surfaces,’’ Colloid Polym. Sci. 261, 694 (1983). 9. B. L. B. Wiman, M. H. Unsworth, S. E. Lindberg, B. Bergkvist, R. Jaenicke and H.-C. Hansson, ‘‘Perspectives on Aerosol Deposition to Natural Surfaces: Interactions between Aerosol Residence Times, Removal Processes, the Biosphere and Global Environmental Change,’’ J. Aerosol Sci. 21, 313 (1990). 10. W. W. Nazaroff and G. R. Cass, ‘‘Particle Deposition from a Natural Convection Flow onto a Vertical Isothermal Flat Plate,’’ J. Aerosol Sci. 18, 445 (1987). 11. Y.-L. Wu, C. I. Davison, D. A. Dolske and S. I. Sherwood, ‘‘Dry Deposition of Atmospheric Contaminants: The Relative Importance of Aerodynamic, Boundary Layer, and Surface Resistances,’’ Aerosol Sci. Technol. 16, 65 (1992). 12. N. A. Fuchs, The Mechanics of Aerosols, Pergamon Press, Oxford (1962). 13. S. K. Friedlander, Smoke, Dust and Haze, John Wiley, New York (2000). 14. W. C. Hinds, Aerosol Technology, John Wiley, New York (1999). 15. H. Krupp, ‘‘Particle Adhesion: Theory and Experiment,’’ Adv. Colloid Interface Sci. 1, 111 (1967). 16. M. B. Ranade, ‘‘Adhesion and Removal of Fine Particles on Surfaces,’’ Aerosol Sci. Technol. 7, 161 (1987). 17. G. W. Penney and E. H. Klingler, ‘‘Contact Potentials and the Adhesion of Dusts,’’ AIEE Paper 61–184, American Institute of Electrical Engineers Winter General Meeting, New York (1961). 18. S. Wall, W. John, H.-C. Wang and S. L. Goren, ‘‘Measurements of Kinetic Energy for Particles Impacting Surfaces,’’ Aerosol Sci. Technol. 12, 926 (1990). 19. Y.-L. Wu, D. I. Davidson and A. G. Russell, ‘‘A Stochastic Model for Particle Deposition and Bounceoff,’’ Aerosol Sci. Technol. 17, 231 (1992). 20. C. Zhu, C. H. Lin and C. S. Cheung, ‘‘Inertial Impaction-dominated Fibrous Filtration with Rectangular or Cylindrical Fibers,’’ Powder Technol. 112, 149 (2000). 21. S. Chen, C. S. Cheung, C. K. Chan and C. Zhu, ‘‘Numerical Simulation of Aerosol Collection in Filters with Staggered Parallel Rectangular Fibers,’’ Comput. Mech. 28, 152 (2002).

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22. H.-C. Wang and G. Kasper, ‘‘Note on Inertial Deposition of Particles on an Orifice Disc,’’ J. Aerosol Sci. 21, 213 (1990). 23. B. V. Ramarao and C. Tien, ‘‘Aerosol Deposition in Two-Dimensional Laminar Stagnation Flow,’’ J. Aerosol Sci. 20, 775 (1990). 24. Y. Ye and D. Y. H. Pui, ‘‘Particle Deposition in a Tube with an Abrupt Contraction,’’ J. Aerosol Sci. 21, 29 (1990). 25. Y. Otani, H. Emi, C. Kanaoka and K. Kato, ‘‘Determination of Deposition Velocity onto a Wafer for Particles in the Size Range between 0.03 and 0.8 mm,’’ J. Aerosol Sci. 20, 787 (1989). 26. D. Y. H. Pui, Y. Ye and B. Y. H. Liu, ‘‘Experimental Study of Particle Deposition on Semiconductor Wafers,’’ Aerosol Sci. Technol. 12, 795 (1990). 27. H. Ounis and G. Ahmadi, ‘‘A Comparison of Brownian and Turbulent Diffusion,’’ Aerosol Sci. Technol. 13, 47 (1990). 28. T. W. Peterson, F. Stratmann and H. Fissan, ‘‘Particle Deposition on Wafers: A Comparison between Two Modeling Approaches,’’ J. Aerosol Sci. 20, 683 (1989). 29. L. Talbot, R. K. Cheng, R. W. Schefer and D. R. Willis, ‘‘Thermophoresis of Particles in a Heated Boundary Layer,’’ J. Fluid Mech. 101, 737 (1980). 30. J. R. Brock, ‘‘On the Theory of Thermal Forces Acting on Aerosol Particles,’’ J. Colloid Sci. 17, 768 (1962). 31. B. V. Derjaguin and Y. Yalamov, ‘‘Theory of Thermophoresis of Large Aerosol Particles,’’ J. Colloid Sci. 20, 555 (1965). 32. H. A. Dwyer, ‘‘Thirteen-Moment Theory of the Thermal Force on a Spherical Particle,’’ Phys. Fluids 10, 976 (1967). 33. A. Toda, Y. Ohi, R. Dobashi and T. Hirano, ‘‘Accurate Measurement of Thermophoretic Effect in Microgravity,’’ J. Chem. Phys. 105, 7083 (1996). 34. A. Toda, H. Ohnishi, R. Dobashi and T. Hirano, ‘‘Experimental Study on the Relation between Thermophoresis and Size of Aerosol Particles,’’ Int. J. Heat Mass Transf. 41, 2710 (1998). 35. J. W. Cipolla, Jr. and T. F. Moore, ‘‘Thermophoresis in an Absorbing Aerosol,’’ J. Aerosol Sci. 18, 245 (1987). 36. X. Chen and D.-Y. Xu, ‘‘Thermophoresis of a Near-wall Particle at Great Knudsen Numbers,’’ Aerosol Sci. Technol. 36, 39 (2002). 37. S. P. Bakanov and V. I. Roldughin, ‘‘Diffusophoresis in Gases,’’ Aerosol Sci. Technol. 7, 249 (1987). 38. E. R. Shchukin and A. N. Kabanov, ‘‘Characteristic Features of the Thermodiffusophoretic Motion of Aerosol Particles in the Vicinity of a Catalytically Active Surface,’’ J. Aerosol Sci. 21, 409 (1990). 39. G. K. Batchelor and C. Shen, ‘‘Thermophoretic Deposition of Particles in Gas Flowing over Cold Surfaces,’’ J. Colloid Interface Sci. 107, 21 (1985). 40. E. R. Shchukin, A. N. Kabanov, E. Yankovska and V. S. Beskov, ‘‘Thermodiffusophoretic Deposition of Aerosol Particles on Cylindrical Surfaces,’’ J. Aerosol Sci. 21, 397 (1990). 41. C.-J. Tsai and H.-C. Lu, ‘‘Design and Evaluation of a Particle-to-Plate Thermophoretic Precipitator,’’ Aerosol Sci. Technol. 22, 172 (1995). 42. C. He and G. Ahmadi, ‘‘Particle Deposition with Thermophoresis in Laminar and Turbulent Duct Flows,’’ Aerosol Sci. Technol. 29, 525 (1998).

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43. J. Chomiak and A. K. Gupta, ‘‘Thermophoresis in Boundary Layer Flows,’’ J. Aerosol Sci. 20, 1 (1989). 44. G. K. Batchelor, ‘‘Mass Transfer from a Particle Suspended in Fluid with a Steady Linear Ambient Velocity Distribution,’’ J. Fluid Mech. 95, 369 (1979). 45. W. W. Nazaroff, J. Chomiak and A. K. Gupta, ‘‘Discussion: Thermophoresis in Boundary Layer Flows,’’ J. Aerosol Sci. 21, 827 (1990). 46. D. W. Cooper and H. L. Wolfe, ‘‘Electrostatic Removal of Particle Singlets and Doublets from Conductive Surfaces,’’ Aerosol Sci. Technol. 12, 508 (1990). 47. V. J. Novick, C. R. Hummer and P. F. Dunn, ‘‘Minimum DC Electric Field Requirements for Removing Powder Layers from a Conductive Surface,’’ J. Appl. Phys. 65, 3242 (1989). 48. D. W. Cooper, M. H. Peters and R. J. Miller, ‘‘Predicted Deposition of Submicrometer Particles due to Diffusion and Electrostatics in Viscous Axisymmetric Stagnation-Point Flow,’’ Aerosol Sci. Technol. 11, 133 (1989). 49. A. M. Johnston, J. H. Vicent and A. D. Jones, ‘‘Measurements of Electric Charge for Workplace Aerosols,’’ Am. Occup. Hyg. 29, 271 (1985). 50. A. V. Filippov, ‘‘Electrostatic Deposition of a Moving Charged Aerosol Cloud onto a Conducting Sphere,’’ J. Aerosol Sci. 23, 203 (1992). 51. S. Oglesby, Jr. and G. B. Nichols, Electrostatic Precipitation, Marcel Dekker, New York (1978). 52. S. L. Soo, ‘‘Dynamics of Charged Suspension,’’ in: International Reviews in Aerosol Physics and Chemistry, Vol. 2, G. M. Hidy and J. Brock (Eds.), pp.61–149, Pergamon Press, Oxford (1971). 53. A. V. Khachatourian and A. O. Wistrom, ‘‘Size Effects in Aerosol Electrostatic Interactions,’’ J. Colloid Interface Sci. 242, 52 (2001). 54. H. A. Pohl, Dielectrophoresis: The Behavior of Neutral Matter in Nonuniform Electric Fields, Cambridge University Press, London (1978). 55. L. Benguigui and I. J. Lin, ‘‘The Dielectrophoresis Force,’’ Am. J. Phys. 54, 447 (1986). 56. P. L. Lipowicz and H. C. Yeh, ‘‘Fiber Dielectrophoresis,’’ Aerosol Sci. Technol. 11, 206 (1989). 57. A. Acrivos, D. J. Jeffrey and D. A. Saville, ‘‘Particle Migration in Suspensions by Thermocapillary or Electrophoretic Motion,’’ J. Fluid Mech. 212, 95 (1990). 58. R. R. Embly, ‘‘Surface preparation and the porcelain enameling industry,’’ Ceramic Engineering and Science Proceedings 21(5), 43, 62nd Porcelain Enamel Institute Technical Forum, Nashville, TN, USA, May 16–19 (2000). 59. P. Crevolin and W. Kresic, ‘‘Study of Pipe Cleaning and Magnetic Particle Techniques for Stress Corrosion Cracking Investigation,’’ Mater. Perform. 37(2), 84 (1998). 60. F. Zhang and A. Busnaina, ‘‘Role of Particle Adhesion and Surface Deformation in Chemical Mechanical Polishing Processes,’’ Electrochemical Solid State Lett. 1, 184 (1998). 61. Z. Yong and R. Kovacevic, ‘‘Modeling of Jet Flow Drilling with Consideration of the Chaotic Erosion Histories of Particles,’’ Wear 209, 284 (1997). 62. J. Chao, G. Zhou, M. C. Leu and E. Geskin, ‘‘Characteristics of Abrasive Waterjet Generated Surfaces and Effects of Cutting Parameters and Structure Vibration,’’ J. Engineering for Industry, Trans. ASME 117, 516 (1995).

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63. J. H. Neilson and A. Gilchrist, ‘‘Erosion by a Stream of Solid Particles,’’ Wear 11, 111 (1968). 64. W. A. Hibbert, ‘‘Helicopter Trials over Sand and Sea: Helicopter Rotor Blade and Engine Erosion by Sand and Seawater,’’ J. R. Aeronaut. Soc. 69, 769 (1965). 65. J. G. A. Bitter, ‘‘A Study of Erosion Phenomena,’’ Wear 6,169 (1963). 66. A. Yabuki and M. Matsumura, ‘‘Theoretical Equation of the Critical Impact Velocity in Solid Particles Impact Erosion,’’ Wear 233–235, 476 (1999). 67. D. Tabor, The Hardness of Metals, p.129, Clarendon Press (1951). 68. I. Finnie, ‘‘Erosion of Surfaces by Solid Particles,’’ Wear 3, 87 (1960). 69. R. E. Winter and I. M. Hutchings, ‘‘Solid Particle Erosion Studies Using Single Angular Particles,’’ Wear 29, 181 (1974). 70. A. Magnee, ‘‘Generalised Law of Erosion: Application to Various Alloys and Intermetalics,’’ Wear 181–183, 550 (1995). 71. Y. Ballout, J. A. Mathis and J. E. Talia, ‘‘Solid Particle Erosion Mechanism in Glass,’’ Wear 196, 263 (1996). 72. Y. Iwai, T. Honda, H. Yamada, T. Matsubara, M. Larsson and S. Hogmark, ‘‘Evaluation of Wear Resistance of Thin Hard Coatings by a New Solid Particle Impact Test,’’ Wear 251, 861 (2001). 73. K. L. Rutherford, R. I. Trezona, A. C. Ramamurthy and I. M. Hutchings, ‘‘The Abrasive and Erosive Wear of Polymeric Paint Films,’’ Wear 203–204, 325 (1997). 74. M. Talia, H. Lankarani and J. E. Talia, ‘‘New Experimental Technique for the Study and Analysis of Solid Particle Erosion Mechanisms,’’ Wear 225–229, 1070 (1999).

5

Tribological Implication of Particles Koji Kato

Department of Mechanical Engineering, College of Engineering, Nihon University, Koriyama City, Japan

5.1

Introduction

When two solid surfaces are brought into contact and are followed by separation or sliding, wear particles are generated at the contact interface and they behave as contaminants for the contact surfaces and surroundings. These particles are generated by the mechanisms of adhesive, abrasive, plastic flow, fatigue, corrosive, diffusive, and melting wear, some of which take place at the same time in the contact region [1, 2]. The size of a wear particle ranges from the scale of nm to that of mm, and the microstructure of the particle material is very different from that of the original surface material in general. Both dry and wet contact systems generate wear particles of this character. Wear particles and the mechanisms of their generation are described in this chapter from this view point.

5.2 The Micro-Site for Generation of Wear Particles Any solid surface is not ideally smooth from a microscopic view point. The cleaved surface of mica sheet is rough at the scale of a silicon atom. The well polished silicon wafer surface of single crystalline structure is still rough at the scale of nanometer. The surfaces of standard glass mirrors, optical lenses, and fine diamond tips of manipulators have surface asperities whose height ranges from about 10 to about 100 nm. The surfaces of machine elements and devices made of metals, ceramics or

R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 299–327 ª 2008 William Andrew, Inc.

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300

FUNDAMENTALS

plastics have surface asperities whose height ranges from about 0.1 to about 100 mm. Figure 5.1 shows an example of surface asperities observed with the AFM (atomic force microscope) on the mirror surface of a silicon wafer. A cross section of a flat surface as shown in Figure 5.1 is schematically shown in Figure 5.2, where asperities distribute along the center line of z = 0 at various heights in the direction of z-axis and the probability density of the asperity height at the level z is given by the function f(z). By introducing this function f(z) for describing the height distribution of asperities, the number n(d) of asperities in contact against an ideally flat surface at the height of z = d in Figure 5.2 is given by the following equation: Z¥ fðzÞdz

nðdÞ ¼ hA0

Eq. (5-1)

d

Figure 5.1 An AFM image of surface asperities on a polished silicon wafer.

Figure 5.2 A schematic model of height distribution of asperities along the center line and a function f(z) showing the distribution of probability density of contact of asperities at the level z.

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where h is the density of asperities on the nominally flat surface, A0 is the nominal surface area, and f(z) is generally given by the Gaussian. The value of h varies depending on the level of surface finish and a certain finishing method does not always give its specific value. Briefly speaking, the value of h may be supposed to vary in the range from 102 per mm2 to 104 per mm2. Therefore, when a flat surface has the nominal or apparent surface area of 10 · 10 mm2 for contact, the total number of asperities for the consideration of real contact between asperities is supposed to vary from 104 to 106. Among these asperities, the relatively higher asperities contact first and the contact level of z = d shown in Figure 5.2 is determined so as to give the necessary size of the real contact area to support the applied load. If two asperities are assumed to have the semi-spherical tip shape with the radii of R1 and R2, a model of initiation of sliding between them is schematically shown in Figure 5.3, where W is the normal load, F is the friction force for initiating sliding, and A is the real contact area. The mean contact pressure p and the shear strength si at the contact interface are given by p = W=A

Eq. (5-2)

si = F=A

Eq. (5-3)

When two asperities are in contact with perfectly elastic deformation only, the contact area A is theoretically given by Hertz [3] as follows:
 3 WR 2=3 A=p
4 E

Eq. (5-4)

Figure 5.3 A schematic model of contact of two spherical asperities. R1, R2: radius of asperity; E1, E2: Young’s modulus; n1, n2: Poisson’s ratio; W: normal load; F: friction force; A: real contact area; p: mean contact pressure; si : shear strength of the contact interface.

302

FUNDAMENTALS

where 1/R = 1/R1 + 1/R2; 1/E = (1  n12 )/E1 + (1  n22 )/E2; E1, E2 are Young’s modulus; n1, n2: Poisson’s ratio. When a single asperity is in contact with perfectly plastic deformation only, the contact area A is experimentally given by McFarlane and Tabor [4] as follows: pffiffiffi W= ak A = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eq. (5-5) 1ðsi =kÞ2 where a is the experimental constant of 3.3–25, k is the shear strength of the material of the asperity in plastic deformation, and si is the shear strength of the contact interface. By comparing Eqs. (5-4) and (5-5), it is clear that the contact area A is independent of the shear strength si in elastic contact, but it strongly depends on the value of si in plastic contact, where si is close to zero in ideally lubricated condition and is close to k in high vacuum with uncontaminated surfaces of ductile material. It is obvious that the smallest pffiffiffi value of A is given by W= ak. The value of a changes with the ductility of the asperity material and the shape of contact [5]. Friction between two asperities given in Figure 5.3 is generated at the contact interface of the area A given by Eqs. (5-4) or (5-5), and the friction coefficient m defined as the ratio of the friction force F against the load W is given by Eqs. (5-2) and (5-3) as follows: m = F=W = si =p

Eq. (5-6)

From these analyses of micro-mechanisms of contact and friction, it is confirmed that the wear particles are generated at the contact interface of surface asperities whose size is determined by Eq. (5-4) or (5-5), and it depends on the shear strength si of the contact interface in plastic contact. Micro-contacts of this mechanism distribute at the apparent large contact interface as shown in Figure 5.2 and generate a large number of wear particles from them in contact and separation or sliding.

5.3

Wear Modes and Particles

5.3.1 Adhesive transfer of atoms in contact and separation When two uncontaminated solid surfaces are in contact, surface atoms on both surfaces form atomic bonds as they are in the bulk, and the

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substrates on both sides of the contact interface are deformed elastically or plastically. In many practical cases, the microstructure of the solid has micro-defects such as vacancies, voids, inclusions, dislocations, and grain boundaries. Therefore, the strain in the contact region is not perfectly removed microscopically by unloading even when the apparent strain is within the elastic limit. When two uncontaminated solid surfaces are in contact, surface atoms on both surfaces form atomic bonds by their original nature. In the process of unloading, there is no reason for separation to occur only at the contact interface. The contact region around the contact interface also has a strain distribution. As a result, fracture in separation of two surfaces can take place at a new site different from the initial contact interface. This means that some atoms are transferred to the mating contact surface. In the contact and separation between a clean spherical pin tip of tungsten and a clean flat surface of gold in high vacuum, the transfer of atoms of gold to the surface of tungsten was experimentally observed by field ion micrographs [6]. In the contact and separation between a tip of nickel and a flat surface of gold, the mutual adhesive transfer of atoms of gold and nickel was shown theoretically by molecular dynamics simulation [7].

5.3.2 Adhesive transfer of flake-like particles in sliding contact Macroscopic sliding occurs at the contact interface without fracture in its vicinity when the contact surfaces are well contaminated or lubricated and the shear strength si of the contact interface is relatively much smaller than the shear strength k of the contact material. The generation of wear particles from the contact surfaces does not happen in such a situation. Relative displacement at the contact interfaces is expected to take place between atoms or molecules of contaminants or lubricating materials. However, contaminants or lubricants at the contact interface are partially removed from there by sliding in practice because of the nonuniformity of the atomic structure in the surface layer and that of the surface roughness. As a result, atomic bonds are partially formed in such parts in the contact interface where contaminants or lubricants are removed. The distributions of contact stresses of shear and tension or compression become complex at the nanometer scale, which introduces cracking in

304

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the subsurface and generates adhesive transfer of particles of bulk material to the mating surface. Figure 5.4 shows three modes of crack initiation and propagation caused by the strong adhesion at the contact interface [8]. In Figure 5.4(a), a fragment is generated as an adhesive wear particle in sliding by having a crack in the lower body at the exit side of the contact and another crack in the upper body at the entry side of the contact. When each crack reaches the front free surface, a fragment is formed as a mixture of materials of the upper and the lower bodies. It is generally rolled up in the following sliding [9]. In Figure 5.4(b), a crack is introduced in the lower body at the entry side of the contact and it propagates to the contact interface by generating the adhesive transfer of a thin fragment from the lower body to the upper surface. In Figure 5.4 (c), a crack is introduced in the lower body at the exit side of the contact and it propagates to the free surface on the other side by generating the adhesive transfer of a thick fragment from the lower body to the upper surface. These three modes of generation of adhesive transfer of a fragment can take place at any scale from nanometer to micrometer. Figure 5.5 shows the cluster of thin flake-like fragments which are transferred by the mode of Figure 5.4(b) from the mating surface by adhesion. The thickness of each fragment ranges from about 0.1 to about 1.0 mm [8].

Figure 5.4 The modes of crack initiation and propagation for the adhesive transfer of a particle. (a) Curving of the adhesive contact interface and crack initiation and propagation on entry and exit sides of contact. (b) Strong adhesion at the contact interface and crack initiation and propagation at the exit side of contact. (c) Strong adhesion at the contact interface and crack initiation and propagation at the entry side of contact.

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Figure 5.5 Adhesive wear particles of SUS 304 stainless steel transferred from the mating surface by one pass of sliding [8].

5.3.3 Micro-cutting and generation of fine feather-like particles in abrasive sliding When the upper asperity is relatively harder and has a certain amount of indentation on the relatively softer and flatter surface, a fine featherlike particle is generated by the mechanism of micro-cutting. The shear strength si of the contact interface must be low enough to have continuous relative movement at the contact interface without adhesion between two surfaces. The fine feather-like particle detaches from the surface when a crack is introduced at its neck. The mechanism of this micro-cutting is the continuous plastic flow of the material in the subsurface of the lower body along the surface of the harder upper body. This mechanism can take place even at the nanometer scale on the surfaces of metals and ceramics. Figure 5.7 shows a cluster of fine feather-like particles of silicon formed by this mechanism at the tip of diamond by one pass of sliding on a silicon wafer [10]. When the shear strength si at the contact interface is relatively large because of partial adhesion and when the amount of indentation of the upper spherical asperity is relatively small, a fine feather-like particle described in Figure 5.6(a) is not formed, but a wedge-like particle is formed as described in Figure 5.6(b). The wedge is detached from the surface when it is hit by surface irregularities during the following sliding motion.

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Figure 5.6 The modes of plastic deformation and particle generation in abrasive sliding. (a) Fine feather-like particle generation. Sliding takes place between the spherical asperity and the particle. (b) Wedge generation. Sliding takes place at the bottom of the wedge as a result of adhesion between the wedge and the spherical asperity. (c) Ploughing with a small amount of plastic deformation on the flat surface without generating a free particle. An accumulated plastic deformation by repeated sliding contact generates a filmy wear particle by the mechanism of plastic flow wear or low cycle fatigue wear.

When the indentation of the upper spherical asperity is relatively small and the shear strength si is also small, the surface layer of the lower flat is slightly deformed plastically, but a free particle is not generated by a single pass of sliding as shown in Figure 5.6(c). The accumulation of plastic deformation by the repeated contact of sliding is necessary to generate a free particle from the flat surface by the mechanism of plastic flow or low cycle fatigue. The regimes of these three modes of wear are theoretically described in Figure 5.8 by the degree of penetration Dp and the normalized shear strength f as follows:
1=2
 hðdepth of indentationÞ pHv 1=2 pHv 2 Dp =  R 1 =R 2W 2W aðradius of contact areaÞ Eq. (5-7)

f=

si ðshear strength of the contact interfaceÞ kðshear strength of the grooved materialÞ

Eq. (5-8)

where R is the radius of asperity tip, W is the normal load, and Hv is the hardness of the grooved material. It is experimentally well confirmed that Figure 5.8 predicts each wear mode very well [11].

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(a)

(b)

Figure 5.7 A cluster of fine feather-like particles of silicon formed by the abrasive cutting of a diamond pin. Small abrasive asperities on the surface of the tip are invisible [10]. (a) 2 mm sliding and (b) 20 mm sliding.

5.3.4 Surface plastic flow and thin filmy wear particle generation by repeated contacts When a ductile asperity is repeatedly rubbed by a relatively harder flat surface in plastic contact with low shear strength si at the contact interface, the surface layer of the asperity flows plastically and generates a thin filmy particle which is smeared out of the interface as shown in Figure 5.9 (a). Figure 5.10 shows one thin filmy particle generated from steel in oil by this mechanism after 8 · 103 cycles [12].

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Figure 5.8 Abrasive wear mode diagram [11].

Figure 5.9 The modes of plastic flow and generation of thin filmy wear particles in the repeated sliding contact with the relatively low shear strength si at the interface. (a) A thin filmy wear particle is squeezed out from the surface layer to the sliding direction by the repeated unidirectional shear under compression (upper figure). (b) Thin filmy wear particles are squeezed out from the surface layer to the vertical direction against the sliding direction by the repeated compression (lower figure). ˜ Denotes the sliding direction of the upper surface which is perpendicular to the paper surface.

A similar mechanism operates, as shown in Figure 5.9(b), on a flat surface of a ductile material when a relatively harder spherical asperity slides repeatedly on the same groove formed by the plastic deformation of the flat surface. Thin filmy particles are formed on both sides of the groove as a result of accumulated plastic strain in the repeated contact.

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Figure 5.10 A thin filmy wear particle of steel generated at a ridge after 8 · 103 cycles of sliding contact against a steel flat pin in oil [12].The arrow indicates the sliding direction of the counter surface.

5.3.5 Crack initiation and propagation in the subsurface of contact and generation of a flake-like particle by repeated contact When an asperity repeatedly slides over the same interface in elastic– plastic contact, a crack is generated at the local region of plastic yield and it propagates within the subsurface until it reaches the surface and generates a thin flake-like particle by the mechanism of fatigue as shown in Figure 5.11. In Figure 5.12, a very thin flake-like particle is delaminated by the low cycle fatigue mechanism from the surface of CNx coating, which has hardness around 25 GPa, after repeated sliding contact of a diamond pin under the light load in the mN range [13].

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Figure 5.11 The mode of crack initiation and propagation for the generation of a flake-like particle by the mechanism of fatigue fracture. (a)

(b)

(c)

Figure 5.12 AFM images of delamination of thin flake-like particles from the CNx coating by the repeated sliding contact of a diamond pin of 15 nm radius under the load of 14 mN [13]. (a) A wavy pattern of wear scar after 18 cycles of sliding, (b) sudden surface delamination after 19 cycles, and (c) whole image of the wear scar after 19 cycles.

Wear particles of similar type can be generated from metals, ceramics, and plastics. Depending on the amount of the contact load and the contact geometry, the thickness of the flake-like particle ranges from the order of nanometer to that of micrometer.

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5.3.6 Tribo-oxidation and generation of particles of oxides by repeated contacts in air and water In the case of sliding contact of steel elements in air without lubrication, contact surfaces are quickly oxidized by friction and the oxide film of iron grows on the rubbed surface. The iron oxide delaminates from the surface by itself at a certain thickness and forms free particles. The growth of oxide film is not simply a function of temperature at the interface, which is raised by frictional heat, but a function of tribological activation of oxidation through the deformation and fracture of surface materials and the successive mechanical removal of oxides by friction. A wear model based on this understanding of oxidative wear gives an expression of wear coefficient K as follows [14]: K=

wear volume=sliding distance = dA expðQ=Rq T Þ=j2 r2 v Eq. (5-9) load=hardness

where j is the critical thickness of oxide for self delamination, d is the contact length, v is the sliding speed, A is the Arrhenius constant, Q is the activation energy, Rq is the gas constant, T is the temperature, and r is the density of the oxide. Tribological activation of oxidation is well observed in rolling contact of silicon nitride Si3N4 which is known as an inert ceramic. Figure 5.13(a) shows fine and transparent fragments of SiO2 on the surface of a Si3N4

(a)

(b)

Figure 5.13 Optical images of fine and transparent wear particles of Si3N4 generated in pure rolling contact in air. Particles are SiO2 [15]. (a) Particles on the roller surface of Si3N4 after 106 rolling cycles. (b) One transparent wear particle of SiO2.

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roller generated after 106 rolling cycles in air, and Figure 5.13(b) shows the collection of these fragments as oxidative wear particles [15]. In the pure rolling contact for the observation of Figure 5.13, frictional heat generation is negligibly small at the contact interface and the microscopic contact pressure at asperities is close to the hardness value of Si3N4 which is around 20 GPa. In this contact condition, the oxidation of Si3N4 was enhanced at the contact interface in air at room temperature. When a Si3N4 pin slides against a Si3N4 disk in water, Si3N4 reacts with oxygen and water as follows, Si3 N4 þ 6H2 O ! 3SiO2 þ 4NH3 SiO2 þ 2H2 O ! SiðOHÞ4

Eq. (5-10) Eq. (5-11)

where SiO2 dissolves into water by forming the structure of Si(OH)4 [16, 17]. When the content of Si(OH)4 in water is over the saturation point, SiO2 precipitates as fine particles from the solution. Figure 5.14(a) shows the thin films of SiO2 growth by friction in water at 40 C. Figure 5.14(b) shows fine needles of SiO2 formed by friction of Si3N4 against itself in water at 20 C, and Figure 5.14(c) shows fine particles of SiO2 precipitated from the solution of Si(OH)4 formed by wear of Si3N4 in water.

5.3.7 Wear particles generated in sliding of steels in oil with additives When steel surfaces slide against each other under the condition of boundary lubrication with a base oil (hexadecane), which contains antiwear additives such as zinc dialkyl-dithiophosphate (ZDDP) or metatricresyl phosphate (TCP), wear particles of various sizes are generated as shown in Table 5.1 [19] and Tables 5.2 and 5.3 [20]. Table 5.1 shows that many wear particles have a thickness of about 100 nm and size in the range of 1000–5000 nm. Small particles of thickness of about 5–10 nm are also included. Table 5.2 shows that the typical size of small particles (debris) ranges from 10 to 300 nm and the typical size of large particles ranges from 500 to 2000 nm depending on the type of the additive. The thickness of the particles has a range smaller than 500 nm.

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Figure 5.14 Wear particles formed on the surface of Si3N4 by the self-mated sliding in water [18]. (a) Thin films of SiO2 on the surface of Si3N4 grown by friction against itself at 40 C. (b) Fine needle-like particles rolled up from SiO2 film on the surface of Si3N4 by friction against itself at 20 C. (c) Fine particles precipitated from the water containing Si(OH)4 generated by wear of Si3N4.

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Table 5.1 Mean Sizes of Particles [19]

Nature of Interfacial Material

h/h*

d/d*

1000–5000 ffi 5000 100

1 1 ffi 101

102 102 103

3000 500 >5000

1 1 1

105 2 · 103 2 · 102 2 · 103

Mean Size (nm) h

Without additives Delaminated plates 100 Chips 500–1000 Particles 100 With antiwear additives Particles 5–10 Rolls ffi 100 Lumps ffi 100 Films ffi 100

d

h: height; d: lateral mean size; h*: interfacial thickness; d*: Hertzian diameter (approximately 1.5 · 105 nm).

Table 5.2 Shape and Size of Wear Particles Generated in Boundary Lubrication [20]

Film on Scar

Second ZDDP TCP Amine phosphate Amine monothiophosphate S/P Thiocarbamate Base oil

Typical Large Debris (mm)

Thick 0.5 mm 3 · 2 (composite) Thick 0.2 mm 0.5 (few, composite) Thin* 0.5 (composite) Thin 0.5 (flakes) Thin Thin Thin

0.5 (composite) gel 2 (composite)

Typical Small Debris (nm) 50 120 300 200 80 30 10

Table 5.3 shows that carbon, oxygen, and phosphorous are highly contained in the wear particles although they are generated by friction between steels. It means wear particles are formed from the chemical reaction products of steel, oil, additives and oxygen.

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Table 5.3 Chemical Composition of Wear Particles and Wear Surfaces [20]

Sample On ball (5 minutes)

Analyses

Location

C

O

P

Fe

Scar 11 42 Film on scar 6 52 Auger Debris ahead 31 44 of scar SEM/EDX 63 24

10 15 8

34 24 17

2

1.3

Auger

Gold extraction replica (6.5 minutes) Carbon adhesive replica (6.5 minutes) Centrifuge (30 minutes) SEM/EDX Filter (60 minutes) SEM/EDX

86 12 0.7 0.5 75 22 1 0.1

5.4 Wear Rate and Number of Generated Wear Particles The wear rate ws is generally defined as the wear volume V divided by the load W and the sliding distance L as follows: ws = V=WL

Eq. (5-12)

It is called specific wear volume or specific wear amount, and has the dimension of mm3/Nm for the convenience of engineering usage. When a non-dimensional coefficient is preferred to describe the wear rate, the wear coefficient K is introduced by the following definition: K=

V=L W=Hv

Eq. (5-13)

where Hv is the hardness of wearing material and W/Hv is an estimation of the real contact area in plastic contact. Hv has the dimension of N/m2, so K is non-dimensional. The value of Hv is of the order of 1 GPa for metallic materials and 10 GPa for ceramics. Therefore, the value of ws expressed by the unit of nm3/Nm ranges within a value that is about ten times smaller than the value for K. The value of wear coefficient K of metals in self-mated sliding in air varies of the order from 103 to 102 as shown in Table 5.4 [21]. The value of K of AISI 52100 steel in self-mated sliding is of the order of 102 in dry argon and it is reduced down to the order of 1010 by the condition of lubrication as shown in Table 5.5 [22].

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Table 5.4 Wear Coefficient K in Self-mated Sliding of AISI 52100 Steel [21]

Environment Dry argon Dry air Cyclohexane Paraffinic oil Paraffinic oil + TCP Engine oil

Wear Coefficient (K) 1.0 · 102 1.0 · 103 8.4 · 106 3.2 · 107 3.3 · 109 2.0 · 1010

TCP: Meta-tricresylphosphate.

Table 5.5 Wear coefficient K in self-mated sliding of pure metals in air [22]

Materials Combination Silver/silver Cadmium/cadmium Copper/copper Platinum/platinum Zinc/zinc

Wear Coefficient (K) 4.0 5.7 1.1 1.3 5.3

· · · · ·

103 103 102 102 102

Figure 5.15 shows the distribution of the specific wear volume ws and the friction coefficient m observed with Al2O3, ZrO2 and SiC in self-mated sliding in air where ws varies from 109 to 102 mm3/Nm depending on the load and velocity. The similar distribution of ws is confirmed with Si3N4/ Si3N4, SiC/SiC, PSZ/PSZ (partially stabilized zirconia) and Al2O3/Al2O3 [24]. If the self-mated sliding of Si3N4 and SiC is carried out in water, the specific wear amount ws changes from 106 to 108 mm3/Nm by the repetition of friction cycle [25]. Figure 5.16 shows a comparison of the specific wear amount of three kinds of materials: cermets, ceramics, and metals. Here ws of ceramics and cermets varies in the range from 107 to 105 mm3/Nm and that of the metals varies in the range from 104 to 103 mm3/Nm [26]. By considering all these observations shown in Tables 5.4 and 5.5 and in Figures 5.15 and 5.16, the value of ws can be supposed to vary in a wide range from 1010 to 102 mm3/Nm depending on the contact material, load, velocity, environment, and lubricant. Only when lubrication is very

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Figure 5.15 Specific wear amount ws and friction coefficient m observed with self-mated sliding of Al2O3, ZnO2, and SiC in air without lubrication [23].

Figure 5.16 The specific wear amount ws of ceramics, cermets and metals, where the ceramics are original ones and metals are binders for cermets. Observations are made under the same load and velocity in air with self-mated materials [23].

well applied and the contact surfaces are well separated by a lubricant film, a specific wear volume smaller than 1010 mm3/Nm can be expected. If we suppose that all wear particles have the same size and shape of a thin rectangular plate, which has the thickness t, the width l, and the

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length l, the volume DV of one wear particle is described by DV = tl2

Eq. (5-14)

By introducing the total number N of the wear particles for the wear volume V, V is described by V = Ntl2

Eq. (5-15)

It is generally observed by experiments that t/l  1/10. By introducing this experimental relationship into Eq. (5-15), V=

N 3 l 10

Eq. (5-16)

By introducing Eq. (5-16) into Eq. (5-12), the total number N of wear particles under the load W and after the sliding distance L is described by N 10 = 3 ws WL l

Eq. (5-17)

If we assume the value of l = 104 mm and ws = 106 mm3/Nm, Eq. (5-17) gives the following value: N = 107 ð1=NmÞ WL

Eq. (5-18)

This value given by the brief calculation shows that very large number of wear particles are generated even when the wear rate is acceptably small for practice. For more exact prediction of the number of wear particles generated at a certain wear rate, the distribution of particle size must be more precisely understood. It is easy to understand that the total number of wear particles generated under the unit load and unit sliding distance must be much larger than the value of Eq. (5-18) when wear particles in the size range of nm are counted for the calculation.

5.5

The Size Distribution of Wear Particles

In sliding of a spherical pin against a flat surface, wear particles are generated by different wear mechanisms working at the same time,

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although one or two dominant wear mechanisms can be expected. Therefore, the size of a wear particle is obtained on all particles by measuring its largest aspect length with a particle counter as a characteristic parameter without regard to the mode of wear for the generation of each particle. Figure 5.17 shows the inversely set friction apparatus for producing wear particles by sliding of a pin against a rotary disk from which wear particles drop on the surface of silicon wafer by gravity in the SEM with the vacuum of 9 · 103 Pa [27]. Figure 5.18 shows the number n of wear particles generated from a disk of stainless steel for each cycle of disk rotation and sliding against a pin of WC or diamond. Wear particles of the size in the range from 0.25 to 10 mm are observed in the figure [28]. In the case of sliding against a diamond pin, the particle number n reaches a maximum value in the fourth friction cycle and it becomes smaller as the friction cycle is increased up to ten cycles. But in the case of sliding against a WC pin, the particle number n varies rather randomly for each friction cycle from the first to the tenth cycle. The total number of wear particles generated in ten friction cycles is larger for the WC pin than for the diamond pin. Some experimental relationships between the number of

Figure 5.17 Friction apparatus of pin on disk which is inversely set in the SEM and has a silicon wafer of 500 diameter for receiving wear particles dropped from the contact by gravity in the vacuum of 9 · 103 Pa [27].

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Figure 5.18 The number n of wear particles generated from a stainless steel disk in its each cycle of rotation for 10 cycles sliding against a pin of WC or diamond [28].

wear particles n and the friction conditions in the abrasive sliding tests by the apparatus shown in Figure 5.17 are obtained as follows:  For diamond pin/SUS 304 stainless steel disk n = 6:0 · 102 D2:3 p

Eq. (5-19)

 For sapphire pin/SUS 304 stainless steel disk n = 9:8 · 104 D2:3 p

Eq. (5-20)

 For WC pin/SUS 304 stainless steel disk n = 1:1 · 104 D1:2 p

Eq. (5-21)

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where n is the total number of wear particles of stainless steel generated in the sliding of 1 m and Dp is the parameter defined by Eq. (5-7). The differences among these three equations are caused by the different shear strength of si at the contact interface. Diamond has the smallest value of si and WC has the largest value of si among the three materials of the pin [28]. Figure 5.19 shows the effects of pin material, pin tip radius and normal load on the mean size d of wear particles. The load does not seem to have strong effect on the mean size d, but the material and tip radius of the pin show much stronger effect on d. Diamond is the material that generates smaller wear particles and WC generates larger wear particles [29]. For more exact analysis of the distribution of the size of wear particles, the description of the style of Figure 5.20 is useful, where f(d) is a function to give the probability density of the size d. Figure 5.20 is observed with WC pin/SUS304 stainless steel disk for the different pin tip radius and normal load. The number of wear particles for sliding of 1 m is given for n in the figure. As is observed in the figure, the value of f(d) increases in the range below 1.0 mm. The particles smaller than 0.25 mm are not observed in the figure because of the limit of resolution of the particle counter used for counting. If the particles smaller than 0.25 mm could be counted down to the size in nm scale, an enormously

Figure 5.19 The mean size
d of wear particles generated from the SUS 304 stainless steel disk sliding against a pin made of sapphire or SiC. The value of
d is obtained for the different combinations of pin material, pin tip radius and load [29].

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Figure 5.20 The probability density f(d) of the size d of wear particles observed on particles generated from the SUS 304 stainless steel disk sliding against a WC pin in vacuum of 9 · 103 Pa. The number of wear particles is shown by n in the figure [29].

large number of wear particles would be counted and a value of f(d) much higher than 100 might be observed in the range below 0.25 mm. Equations (5-19)–(5-21) must be changed for such high-resolution particle counting.

5.6

Concluding Remarks

5.6.1 Solid wear particles The representative wear mechanisms of solids (metals, ceramics, and hard coatings) and characteristics of wear particles were explained in this chapter by introducing wear models and experimental observations in vacuum, air, water, and oil. In order to give better understanding about the microscopic contact points between surface asperities where wear particles are generated, the mechanisms of contact and friction were briefly introduced before

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explaining the wear mechanisms and the size and distribution of wear particles. The mechanisms of generation of wear particles introduced in this chapter are applicable to particles in the size range from nm to mm. Experimental observations of wear particles in the range of 1–10 nm are not yet well made. However, the wear models confirmed in the range of mm may be applied to wear at the nm scale, because the usefulness of the traditional contact mechanics based on the continuum theory is very well confirmed in the theoretical analysis with the molecular dynamics simulations [30, 31].

5.6.2 Gas molecules by wear In the unlubricated sliding of diamond against hard materials in air, a high temperature is generated at the contact region as the result of frictional heating and diamond is worn by oxidation generating carbon dioxide CO2 [32]. If silicon nitride Si3N4 is rubbed in air, it is oxidized and NH3 gas is generated together with silicon oxide (SiO2) as shown in Eq. (5-10) [17, 18]. These gases CO2 and NH3 are contaminants on a molecular scale for various clean surfaces. These kinds of gas molecules generated by wear were not explained in this chapter, because there are very few published reports and these are insufficient to provide useful information from the viewpoint of contamination sources.

5.6.3 Triboemission of electrons, ions, photons, and particles Electrons, ions, photons, and particles, which are charged negatively or positively, are emitted from the contact region during friction [33]. The amount of their emission increases with load and sliding velocity. Tribo-microplasma is generated near the contact region and it introduces unique tribo-chemical reactions [33, 34]. Figure 5.21 shows the total image, UV image and IR image observed from the side of the contact through the sapphire disk [35]. Figure 5.22 shows the images observed from the bottom of contact through the sapphire disk [35]. The plasma observed in these figures enhances the chemical reaction at the contact region. The resultant chemical reaction products work as contaminants in some cases. However, practically useful explanations from the viewpoint of contamination are not considered in this chapter at the present time,

324

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Figure 5.21 The images of tribo-microplasma observed from the side of sliding contact between a spherical diamond pin and a sapphire disk [35]. (a) Total side image. The arrow for V denotes the sliding direction of lower disk. The arrow for F denotes the loading direction at the center of contact. (b) UV image. (c) IR image.

Figure 5.22 The images of tribo-microplasma observed from the bottom of sliding contact between a spherical diamond pin and a sapphire disk. The rings O in the image denote observed contact area [35]. (a) Total image. The arrow for V denotes the sliding direction of lower disk. (b) UV image. (c) IR image.

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because this tribo-plasma was found very recently [35, 36]. Further research from the viewpoint of contamination and cleaning is planned in the future.

Acknowledgment This author would like to express his appreciation to Mr. Boyko Stoimenov and Mr. Kosuke Ito in the Laboratory of Tribology at Tohoku University for their considerable help in preparing materials for this chapter.

References 1. K. Kato, ‘‘Classification of Wear Mechanisms/Models,’’ Proc. Inst. Mech. Engrs., J. Eng. Tribol. 216, 349 (2002). 2. K. Kato, ‘‘Wear Mechanisms,’’ in New Directions in Tribology, I. Hutchings (Ed.), pp. 39–56, Mechanical Engineering Publications, London (1997). € 3. H. Hertz, ‘‘Uber die Ber€ uhrung fester elastischer Ko¨rper (On the contact of elastic solids),’’ J. reine und angewandte Mathematik 92, 156–171 (1882) [For English translation see ‘‘Miscellaneous Papers by H. Hertz,’’ D. E. Jones and G. A. Schott (Eds.), Macmillan, London (1896)]. 4. J. S. McFarlane and D. Tabor, ‘‘Relation between Friction and Adhesion,’’ Proc. Roy. Soc. London, Series A 202, 244 (1950). 5. T. Kayaba and K. Kato, ‘‘Experimental Analysis of Junction Growth with a Junction Model,’’ Wear 51, 105 (1978). 6. D. Buckley, ‘‘Surface Effects in Adhesion, Friction, Wear and Lubrication,’’ in Tribology Series, Volume 5, pp. 253–254, Elsevier, London (1981). 7. U. Landman, W. Luedtke, N. Burnham and R. Colton, ‘‘Atomistic Mechanisms and Dynamics of Adhesion, Nanoindentation and Fracture,’’ Science 248, 454 (1990). 8. T. Kayaba and K. Kato, ‘‘The Adhesive Transfer of the Slip-Tongue and the Wedge,’’ ASLE Trans. 24, 164 (1981). 9. J. A. Greenwood and D. Tabor, ‘‘The Properties of Model Friction Junctions,’’ Proc. Conf. on Lubrication and Wear, Inst. Mech. Engs. 314 (1957). 10. J. G. Xu and K. Kato, ‘‘Microwear Mechanisms of Silicon Sliding Against Diamond in Water Vapor,’’ STLE Tribology Transactions 39, 621 (1996). 11. K. Hokkirigawa and K. Kato, ‘‘An Experimental and Theoretical Investigation of Ploughing, Cutting, and Wedge Formation during Abrasive Wear,’’ Tribology International 21, 151 (1988). 12. T. Akagaki and K. Kato, ‘‘Plastic Flow Process of Surface Layer in Flow Wear Under Boundary Lubricated Conditions’’, Wear 117, 179 (1987). 13. K. Kato, H. Koide and N. Umehara, ‘‘Micro-Wear Mechanisms of Thin Hard Coatings Sliding Against Diamond Tip of AFM,’’ Advances in Information Storage Systems 8, 289 (1998).

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14. T. F. J. Quinn, in Proc. Int. Conf. on Tribology-Friction, Lubrication and Wear Fifty Years On, Inst. Mech. Engrs. Conf. Series 1987-5, 253 (1987). 15. M. Akazawa, K. Kato and K. Umeya, ‘‘Wear Properties of Silicon Nitride in Rolling Contact,’’ Wear 110, 285 (1986). 16. T. E. Fischer and H. Tomizawa, ‘‘Interaction of Tribochemistry and Microfracture in the Friction and Wear of Silicon Nitride,’’ Wear 105, 29 (1985). 17. T. Saito, Y. Imada and F. Honda, ‘‘An Analytical Observation of the Tribochemical Reaction of Silicon Nitride Sliding with Low Friction in Aqueous Solutions,’’ Wear 205, 153 (1997). 18. J. Xu, K. Kato and T. Hirayama, ‘‘The Transition of Wear Mode during the Running-in Process of Silicon Nitride Sliding in Water,’’ Wear 205, 55 (1997). 19. J. M. Georges, ‘‘Colloidal Behavior of Films in Boundary Lubrication,’’ in Microscopic Aspects of Adhesion and Lubrication, J. M. Georges (Ed.), pp. 729–761, Elsevier, New York (1982). 20. J. Sheasby, T. Canghlim, S. Terranova and A.Cohen, ‘‘An Examination ofAdditive Debris to Give Insight into Boundary Lubrication,’’ in The Third Body Concept, D. Dowson , C. M. Taylor, T. H. C. Childs, G. Dalmaz, Y. Berthier, L. Flamand, J.-M. Georges and A. A. Lubrecht (Eds.), pp. 685–693, Elsevier, New York (1996). 21. R. S. Fein, ‘‘AWN-A Proposed Qualitative Measure of Wear Protects,’’ Lub. Engr. 31, 581 (1975). 22. J. F. Archard, ‘‘Contact and Rubbing of Flat Surfaces,’’ J. Appl. Phys. 24, 981 (1953). 23. K. Adachi, K. Kato and N. Chen, ‘‘Wear Map of Ceramics,’’ Wear 103–204, 291 (1997). 24. P. Gautier and K. Kato, ‘‘Wear Mechanism of Silicon Nitride, Partially Stabilized Zirconia and Alumina in Unlubricated Sliding Against Steel,’’ Wear 162–164, 305 (1993). 25. M. Chen, K. Kato and K. Adachi, ‘‘Friction and Wear of Self-Mated SiC And Si3N4 Sliding in Water,’’ Wear 250, 246 (2001). 26. Y. Tsuya and S. Ishii, ‘‘Wear Characteristics of Ceramics and Cermets,’’ J. Jap. Soc. Tribol. 35, 384 (1989). 27. M. Mizumoto and K. Kato, ‘‘The Principal Characteristics of Wear Particles Generation Observed By SEM-Tribosystem,’’ in Proc. Japan Int. Tribol. Conf., Nagoya, pp. 899–904 (1990). 28. M. Mizumoto and K. Kato, ‘‘Mechanism of Abrasive Particle Generation (Part 2): The Number of Wear Particles,’’ J. Jap. Soc. Tribol. 38, 87 (1993). 29. M. Mizumoto and K. Kato, ‘‘Size Distribution and Number of Wear Particles Generated by the Abrasive Sliding of a Model Asperity in the SEM-Tribosystem,’’ in Proceedings of the 18th Leeds–Lyon Symposium on Tribology ‘‘Wear Particles: From the Cradle to the Grave,’’ M. Godet, D. Dowson, C. M. Taylor, T. H. C. Childs and G. Dalmaz (Eds.), Elsevier, London (1992). 30. U. Landman, W. D. Luedtke and E. Ringer, ‘‘Molecular Dynamics Simulations of Adhesive Contact Formation and Friction,’’ in Fundamentals of Friction: Macroscopic and Microscopic Processes, L. Singer and H. M. Pollock (Eds.), pp. 463–510, Springer, Berlin (1991). 31. K. Kato, ‘‘Nanoscale Analyses of Wear Mechanisms,’’ in Nanotribology: Critical Assessment and Research Needs, S. M. Hsu and Z. C. Ying (Eds.), pp. 45–54, Kluwer Academic Publishers, Boston (2003).

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32. D. Tabor and J. E. Field, ‘‘Friction of Diamond,’’ in The Properties of Natural and Synthetic Diamond, J. E. Field (Ed.), pp. 549–571, Academic Press, London (1992). 33. K. Nakayama and H. Hashimoto, ‘‘Triboemission of Charged Particles and Photons from Wearing Ceramic Surfaces in Various Gases,’’ Tribol. Trans. 35, 643 (1992). 34. K. Nakayama and H. Hashimoto, ‘‘Effect of Surrounding Gas Pressure on Triboemission of Charged Particles and Photons from Wearing Ceramic Surfaces,’’ Tribol. Trans. 38, 35 (1995). 35. K. Nakayama and R. A. Nevshupa, ‘‘Plasma Generation in a Gap of Sliding Contact,’’ J. Phys. D. Appl. Phys. 35, L53 (2002). 36. K. Nakayama and R. A. Nevshupa, ‘‘Characteristics and Pattern of Plasma Generated at Sliding Contact,’’ J. Tribol. 125, 780 (2003).

6 Airborne Molecular Contamination: Contamination on Substrates and the Environment in Semiconductors and Other Industries Taketoshi Fujimoto, Kikuo Takeda, and Tatsuo Nonaka Sumika Chemical Analysis Service Ltd., Osaka, Japan

6.1

Introduction

A Japanese book to systematically describe airborne molecular contaminants (AMCs) from various viewpoints, such as primary sources, analytical methods to determine their concentrations on surfaces, in the air, and at the source, monitoring methods, chemical properties, detrimental mechanisms, and removal methods, was published 10 years ago [1]. This is one of the few books that systematically describe AMCs and their effects. In the present chapter, the authors intend to focus on the activities that have occurred since the book was published 10 years ago. At that time, there were only a very small number of people in Japan who understood what AMCs were. In the past 10 years, the number of reports on AMCs has increased considerably and outstanding progress has been made in various fields. Studies to establish principles to systematically describe relevant phenomena, as well as to formulate equations by means of modeling, are also increasing. The authors believe that the study of AMCs is entering a new paradigm. In 2001, a cleanroom was planned to be installed at the National Institute for Environmental Studies for the study of endocrine disruptors (Environmental Hormones). It had been previously doubted that many AMCs, including ester phthalates, exhibited the effects of an endocrine disruptor. In order to evaluate an endocrine disruptor, it is necessary to conduct the evaluation of the AMCs in an ultra cleanroom. All the knowledge and technology described in this chapter were used and considered to construct a cleanroom to evaluate potential endocrine actions. R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 329
474 ª 2008 William Andrew, Inc.

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After construction of the cleanroom was completed, the quantification of AMCs that have a dramatic effect on endocrine actions, including ester phthalates, resulted in concentrations below ng/m3 levels. This result is evidence to support the usefulness and validity of our research into clean technology as a countermeasure to mitigate AMCs in cleanroom environments. The technology to reduce AMCs in cleanrooms was demonstrated to be possible. From this point onwards, the subject of clean technology has shifted to cost-effective and efficient countermeasures to mitigate AMCs.

6.1.1 Background Scientific personnel and research and development activities to study airborne molecular contaminants (AMCs) are increasing these days. Ten years ago reports on particle removal filters such as HEPA (high efficiency particulate air) and ULPA (ultra low penetration air) constituted the majority of the activities in the air cleanliness field. This trend has drastically changed over the past 10 years. AMCs have become a major topic in the study of cleanliness in cleanroom air and on Si wafer surface. The trends in the study of AMCs in Japan over the past 5
10 years are summarized below by quoting the proportion of papers reported at the Annual Technical Meeting on Air Cleaning and Contamination Control held by the Japan Air Cleaning Association (JACA). 1. Total presentation papers: about 100. 2. The papers on AMCs account for 65%. 3. Adding the papers on dwellings (sick house syndrome, indoor facilities, including hospitals, and bio-cleanrooms) of 15%, the papers on AMCs account for over 80%. 4. The papers on analytical methods for AMCs in the air, AMCs on Si wafer surface and outgassing account for 30%. 5. The papers on removal methods for AMCs account for 20%. Recently, reports on other removal methods than chemical filtration, such as use of UV (ultraviolet)/ photoelectron radiation, UV radiation/catalyst, and TiO2 catalysts, have been increasing. 6. The papers that report new contaminant sources are not exhausted, but the number of papers reporting on new contaminants (even including those in indoor air environment) is decreasing. For example, dioctylphthalate

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(DOP; synonym: bis (2-ethylhexyl) phthalate) is often detected, and it is very frequently reported as a cause of deleterious effects. The DOP concentration calculated based on the currently available data from all DOP sources is still only half of the DOP concentration actually measured in the air. This means the material balance has not yet been correctly calculated. 7. Air cleanliness in a wider range of places, such as art and other museums and large computer rooms in banks, as well as bio-cleanrooms and indoor dwellings, is now being studied. 8. Studies to establish generic models and equations by interpreting various phenomena and data are increasing to 20%. Some of these quantitative equations feature outstanding compatibility with actual data, universality and usefulness. They help analyze and interpret large amounts of data appropriately. It has been reported recently that a cleanroom with high cleanliness has been developed in which phthalate and phosphate concentrations are as low as 10 ng/m3 or lower. These reports indicate that actual cleanliness is getting closer to a target cleanliness level. It is not impossible to improve cleanliness by one or two orders of magnitude to achieve the ultimate target in the future. These trends indicate that the study of AMCs has been regarded as a target theme in Japan, and that the study of AMCs is moving through the following evolutionary stages, namely from frontier technology and know-how to science (a new paradigm). 1. Know-how for countermeasures against deleterious effects 2. Developments in analytical chemistry methods for qualification and quantification. 3. Establishment of database and reports on phenomenological mechanisms and findings. 4. Models and equations that have a wide-range versatility and applicability. 5. Science. The present authors feel that the study of AMCs is in the transition period from Stage 3 to 4. Therefore, this chapter needs to not only generally introduce frontier technology reports, but also to describe the laws and

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chemistry to summarize the behavior of AMCs which will then be applied to a wide range of industrial and environmental chemistry. To comprehensively describe here new technologies and to systematically explain them are intrinsically contradictory to each other. It was difficult to avoid some issues. There are a number of literature references and there is some overlap when systematically introducing theories, interpretations and data. It is very much expected that a more systematic book on science and technology of AMCs will be published in the near future. In the meanwhile, the authors expect the readers to keep in mind that this chapter describes a situation which is premature as science and that therefore it describes a precursor of the science of AMCs. Guides and primers on AMCs include SEMATECH Technology Transfer Report [2], as well as published papers [3
5] and proceedings of recent SEMICON Europe conferences [6]. Guides and primers published in Japan regarding AMCs include the 1997 AMC book [1], plenary lectures at the Japan Aerosol Society [7
9], the special issue of JACA [10], Realize Inc. Seminar [11] and review papers [12, 14]. For basic information on the analytical methods for AMCs, the papers of Fabry [13
15], Kaiser [16] and Miki [17] are informative. Trends in standardization of the analytical methods will be discussed in Section 6.5.6.2.

6.1.2 Changes in semiconductor integration The semiconductor industry has been growing by increasing the density of semiconductor devices [2]. Currently, the industry is exploring technologies to fabricate 256M bit DRAM (dynamic random access memory) with 0.15 mm geometry on 300 mm wafers. As the density of semiconductor devices increases, higher cleanliness levels must be achieved on the Si wafer surface [18]. Accordingly, the air in the manufacturing environment is also required to achieve higher cleanliness levels. Also, in cleanrooms used by other advanced industries, such as magnetic disk drives [19
22] and liquid crystal display [23], as well as the brewery and biotechnology industries, contamination caused by AMCs and by particles becomes an issue that must be overcome [24].

6.1.3 Changes in target contaminant One of the biggest contributors to advancing semiconductor manufacturing technology was cleanliness improvement in the manufacturing

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environment. In the 1980s, particles were regarded as a major contaminant. Particle contamination was successfully controlled by development of cleanrooms equipped with HEPA and ULPA filters and even SULPA (super ultra low penetration air) filters. To manufacture 1M bit DRAM, the cleanliness of the manufacturing environment must be controlled at ISO (International Standards Organization) Class 3 for particles of 0.5 mm or larger. Currently, the highest cleanliness of a cleanroom in ISO Class 3 is 0.1 mm, i.e. no more than 1000 particles of 0.1 mm size in one cubic meter. Particle contamination has the following features.  Particle contamination can be detected by means of electron microscopic examination.  Particle contamination physically affects devices, e.g. defective interconnect and particle adhesion.  Particle contamination can be overcome (cleanliness in terms of particle can be increased) by improving the filter performance. In the 1990s, the detrimental effects caused by contaminants other than particles started to be reported, characterized by the following features.  These contaminants were too small to be detected by means of electron microscopic examination.  Some chemical reactions contribute to these effects.  The behavior and detrimental effects of each contaminant are different and, therefore, a unique mitigation solution must be developed for each contaminant. It was gradually realized that these new contamination effects were attributable to AMCs.

6.2

Definitions, Types and Sources of AMCs

6.2.1 Definition of ‘‘Airborne Molecular Contamination’’ For the purpose of this chapter, the following definition will be used in order to make it easier to describe the complex issues related to AMCs.

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‘‘Contamination mainly comes from airborne molecular contaminants which are unable to be removed with particle filters such as HEPA and ULPA.’’ In order to explore the mechanisms of AMC contamination and their potential solutions, it is necessary to investigate not only AMCs in a narrow classification, but also metal vapor and mist which may not exist in the air in a gaseous phase. At present, measures are being taken against not only AMCs, but also other contamination caused by chemical reaction of metals and contaminants. The International Technology Roadmap for Semiconductors (ITRS) Roadmap (1999, 2001, and 2004) [18] sets a requirement on the cleanliness of a Si wafer surface and the air in the manufacturing environment by specifying not only classical contaminants which are in a gaseous phase at room temperature, but also metals which are referred to as AMCs. In other words, the ITRS Roadmap uses the term AMCs to refer to all contaminants that degrade air cleanliness and that cannot be removed with particle filters such as HEPA and ULPA filters. Airborne Molecular Contamination, the title of this chapter, is comparable to particle contamination. The most common film contamination occurs when organic impurities which are in a gaseous phase in the air adhere to the Si wafer surface to form a contaminant film on the surface. In order to come up with comprehensive understanding and practical solutions, however, it is necessary to interpret the airborne molecular contamination more extensively including the following cases. 1. Airborne Molecular Contamination includes inorganic compounds and metal organic compounds as well as organic compounds, such as hydrogen fluoride, boron trifluoride, ammonia, cyclosiloxane, and tributyl phosphate. Recently it has also included metal contaminants. 2. Airborne Molecular Contamination is much more limited in concentration than molecular layer contamination. What typically causes problems is not contamination that covers the entire surface of a Si wafer, glass or a hard disk, but a local contaminant island with thickness of less than 1/100 or 1/1000 of a molecular layer. In other words, it is usually not a ‘‘film’’ of contaminants. 3. Airborne Molecular Contamination is detected as particle on Si substrate (Si wafer), while it does not exist as a

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particle in the air. Rather, it is generated from gaseous contaminant sources. For example:  Hydrochloric acid in the air corrodes Al interconnect, eventually generating corrosion products such as aluminum oxide.  Ammonia in the air gets adsorbed onto a Si wafer surface. It then reacts with sulfur dioxide gas in the air to generate ammonia sulfate which is eventually detected as an impurity.  Cyclosiloxanes adhering to a glass surface react with UV radiation used in subsequent lithography process, and consequently through photochemical reaction (decomposition), SiO2 particles are generated on the glass surface.  Phosphorus oxide solidified on SiO2 layer absorbs NH3 and moisture in the air. By repeating the fusionprecipitation process, compounds are generated whose moisture and NH3 concentrations are in equilibrium with these concentrations in the air. During this process, isolated spots and/or continuous lines are formed, which may be incorrectly identified as particle contamination. 4. Airborne Molecular Contamination may degrade the underlying surface. For example:  When the perfluoro oil lubricant layer of ten plus angstroms thick on the disk surface in a HDD (hard disk drive) gets contaminated with siloxane or alcohol, the head crash phenomenon occurs in too many localized areas to determine which areas are precisely contaminated [19, 20, 25]. It is hypothesized that the impurities change the conformation of the perfluoro oil lubricant which is present not as a film but as multiple molecular layers on the surface. Three dimensionally, fluorine and oxygen are no longer randomly distributed, exhibiting self-insoluble tendency which is often observed in paint technology. In this case, AMCs affect film conformation on HDD substrate surface.  Since ammonia and amines react with protons on the surface of photoresist used in the lithography process, protons on the surface decrease in number. As a result, the lithography process does not proceed satisfactorily,

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FUNDAMENTALS and photoresist residues remain like T-shaped bridges on the surface. This is referred to as the T-top phenomenon.  Hexamethyldisilazane (HMDS) which is used to change intrinsically hydrophilic Si wafer surface to lipophilic surface so as to enhance photoresist adhesion, as well as trimethylsilanol which is a derivative generated when HMDS reacts with moisture in the air, adhere to the glass surface to generate lipophilic spots. Discoloration takes place when pigments selectively adhere to these lipophilic spots.  Boron compounds and ester phosphate adhere to the Si wafer surface and diffuse into the Si wafer during subsequent manufacturing processes to change the dopant doses.

What is common to the above degradation mechanisms is that these effects are caused not by film-type contamination, but by contaminants in cleanroom air which cannot be removed with particle removal filters. Therefore, this chapter uses the term airborne molecular contamination when comparing it to contamination by a particle. As a generic term that refers to all contaminants that cannot be removed with particle removal filters, however, this chapter uses AMCs similarly to its usage in SEMATECH Technology Transfer No. 95052812A-TR [2]. Contamination generated on Si wafer due to these AMCs will be referred to as film contamination. This chapter uses the term AMC contamination when the contamination is attributed to AMCs even if the contaminants are of particulate shape.

6.2.2 Examples of AMC-induced problems in the manufacturing process Below is a list of AMCs and the problems caused by them in the device manufacturing process [1, 26
42].  Boron compounds: shift of threshold voltage and drop of driving voltage.  SOX: interconnect corrosion.  NH3 and amines: lithography pattern defect and T-top phenomenon.

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 HMDS (hexamethyldisilizane): fogged glass and lens.  LMCS (low molecular weight polycyclodimethylsiloxane): fogged glass and lens.  DOP (dioctylphthalate): dielectric breakdown voltage failure of gate oxide.  TCEP (trichloroethyl phosphate): shift of threshold voltage. Sources of these contaminants are mainly non-natural compounds, including construction materials of the cleanroom and chemicals used in the manufacturing process. Usually AMC concentrations are lower in outdoor air than in cleanroom air. In a sense, AMC contamination can be regarded as a contamination side effect which is induced by using the cleanroom to suppress particle contamination.

6.2.3 Nature of AMC-induced effects The deleterious effects induced by AMCs are quite different from those induced by particles.  AMC concentration in a cleanroom does not show a visible day-to-day fluctuation. It is a gradual drift from a month to another.  By setting manufacturing conditions at current AMC contamination levels, therefore, it is possible to maintain the manufacturing yield to some extent. In these cases, AMC contamination may not be recognized.  In observing that the appropriate manufacturing conditions are different between cleanrooms, engineers often recognize for the first time that the differences are attributed to the difference in chemical contamination level in cleanrooms.  In order to work out solutions to eliminate the deleterious effects of different contaminants, it is necessary to study each individual chemical contaminant in terms of source, generation mechanism, state in the air, mechanism to adhere to a clean surface, mechanism to cause these effects, and physical and chemical characteristics.  One of the major sources of AMCs contamination is construction material of the cleanroom. Therefore, it is important to select appropriate materials prior to start of

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FUNDAMENTALS cleanroom construction. Even if cleanliness of the cleanroom is found to be inadequate, it is not easy to replace construction materials after cleanroom construction is completed as cleanroom operation needs to be suspended for a long time. AMC contamination can be significantly decreased by replacing common construction materials with low outgassing cleanroom construction materials.  The required AMC concentration is extremely low of the order of ng/m3 order. This concentration is far lower than the chemical concentration that affects the human body. It is only very hazardous toxic gases (sarin, soman, nickel carbonyl, etc.) that are found to be dangerous at ppt (parts per trillion) or ng/m3 level. There are few formal (and practical) analytical methods reported for these concentration levels. The environmental regulations in Japan [43] use the unit of microgram/m3 for all contaminants except dioxin. AMC contamination in semiconductor wafer fabs having no odor is hardly sensed by people working there. When a water droplet of 10 ml is deposited on a substrate such as clean glass or a Si wafer that was exposed to cleanroom air, the surface of the substrate gradually changes from hydrophilic to hydrophobic due to AMCs in the air deposited on the surface. The change in the contact angle of the water droplet as a function of exposure time is one of the few phenomena, other than analytical results, that provide evidence of AMC contamination.  A practical chemical filter capable of removing AMCs to maintain cleanliness of less than the order of mg/m3 for a long time is still under development. A chemical filter to selectively remove certain target low-concentration molecules is harder to develop than a particle removal filter, and it also requires chemical consideration. The removal efficiency of a particle filter is 99.9999%, while that of an AMC chemical filter is around 99%. Chemical filters for AMC contamination feature low efficiency and short lifetime and they are costly. When the manufacturing process is affected by particle contamination, such a solution as filter replacement (upgrade to more advanced particle removal filter) is effective. In the case of AMC contamination, however, installing a chemical filter is not

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necessarily the best solution as AMCs vary a lot in type. Although the performance of chemical filters has increased remarkably, it is necessary to improve it further technically and economically. Improvement of chemical filters requires research and development of trace-amount analysis. Some chemical filters feature removal efficiency of 99.99% in removing high-concentration AMCs. This level of chemical filter performance, however, is not sufficient to solve the problems of low-concentration AMCs. What is critical in maintaining cleanliness of the cleanroom air in the semiconductor industry is the ultimate AMC concentration at the downstream location of the chemical filter. Section 6.5.3 describes a case where the removal efficiency of a chemical filter is different between highconcentration AMC environment and an extremely low-concentration AMC environment due to the difference in adsorption mechanism of the chemical filter for NH3 removal in which oxides of phosphorus have been impregnated in the filter as an adsorbing center. When multiple types of AMCs coexist, it is necessary to consider the fruit-basket phenomenon described in Section 6.4.3.4.4. AMC contamination must be fully understood in terms of source, behavior in the air, contamination mechanism on substrates such as Si wafer, and the mechanisms that can cause problems. Based on this understanding, it is then necessary to develop appropriate mitigation solutions. The objectives of this chapter are (1) to describe the development of qualitative and quantitative analyses for various AMCs for different sources such as air, substrates and cleanroom construction materials, (2) to study the behavior of AMCs by using established analytical methods, and (3) to describe solutions that have been worked out based on personal investigation.

6.2.4 Classification of airborne molecular contaminants The International Technology Roadmap for Semiconductors (ITRS) 1999 classifies AMCs into five groups of acids, bases, condensables, dopants and metals, and specifies the required AMC concentration in the air for each group as shown in Table 6.1 [18]. The required AMC concentration on a Si wafer is defined in Tables 6.2 and 6.3.

Wafer environmental control Particles Critical particle size (nm) Particles of critical size (/m
3) AMCs (ppt M) Lithography—Bases (as amine, amide, or NH3) Gate—metals (as Cu, E = 2 · 10
5) Gate—organics (as MW > 250, E = 1 · 10
3) Organics (as CH2) (*: Cn = 18) Salicidation contact—acids Salicidation contact—bases Dopants P or B

Year Technology Node

90 10 1000 0.3 170 3000 10 32