III-Nitride Semiconductors: Electrical, Structural and Defects Properties

V

Preface

Research advances in Ill-nitride semiconductor materials and device have led to an exponential increase in activity directed towards electronic and optoelectronic applications. There is also great scientific interest in this class of materials because they appear to form the first semiconductor system in which extended defects do not severely affect the optical properties of devices. This volume consists of chapters written by a number of leading researchers in nitride materials and device technology with the emphasis on the dopants incorporation, impurities identifications, defects engineering, defects characterization, ion implantation, irradiation-induced defects, residual stress, structural defects, and phonon confinement. This unique volume provides a comprehensive review and introduction of defects and structural properties of GaN and related compounds for newcomers to the field and stimulus to further advances for experienced researchers. Given the current level of interest and research activity directed towards nitride materials and devices, the publication of this volume is particularly timely. Early pioneering work by Pankove and co-workers in the 1970s yielded a metal-insulator-semiconductor GaN light-emitting diode (LED), but the difficulty of producing p-type GaN precluded much further effort. The current level of activity in nitride semiconductors was inspired largely by the results of Akasaki and co-workers and of Nakamura and co-workers in the late 1980s and early 1990s in the development of p-type doping in GaN and the demonstration of nitride-based LEDs at visible wavelengths. These advances were followed by the successful fabrication and commercialization of nitride blue laser diodes by Nakamura et al at Nichia. The chapters contained in this volume constitutes a mere sampling of the broad range of research on nitride semiconductor materials and defect issues currently being pursued in academic, government, and industrial laboratories worldwide. I would like to thank all authors of the chapters, whose excellent efforts have made this volume possible. M.O.

MANASREH

University of New Mexico August 2000

VII

List of Contributors

ED. Auret

Physics Department, University^ of Pretoria, Pretoria 0002, South Africa. E-mail: [email protected]

M. Babiker

Department of Physics, University of Essex, Colchester C04 3SQ, Engeland

C.R. Bennett

Department of Physics, University of Essex, Colchester C04 3SQ, Engeland

J.C. Culbertson

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA

Nora V. Edwards

Department of Physics and Measurement Technology, Materials Science, Linkopings Universitet, S-58183 Linkoping, Sweden. E-mail: [email protected]

M. Eatemi

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA

S.A. Goodman

Physics Department, University of Pretoria, Pretoria 0002, South Africa

R.L. Henry

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA

H.X. Jiang

Department of Physics, Kansas State University, Manhattan, KS 66506, USA. E-mail: [email protected]

M. Kamiriska

Institute of Experimental Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland

D.D. Koleske

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA

J.Y. Lin

Department of Physics, Kansas State University, Manhattan, KS 66506, USA. E-mail: [email protected]

VIII

List of Contributors

M. Omar Manasreh

Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131-1356, USA. E-mail: [email protected]

M. Palczewska

Institute of Electronic Materials Technology, Wolczynska 133, 01-919 Warsaw, Poland, E-mail: [email protected]

Bemd Rauschenbach Universitdt Augsburg, Institut fUr Physik Universitdtsstrasse 1, D-86135 Augsburg, Germany. E-mail: [email protected] B.K. Ridley

Department of Electronic Systems Engineering, University of Essex, Colchester C04 3SQ, Engeland

S. Ruvimov

Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. E-mail: [email protected]

K. Saarinen

Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 Hut, Finland. E-mail: [email protected]

John T. Torvik

Astralux, Inc., 2500 Central Ave., Boulder, CO 80301, USA. E-mail: [email protected]

M.E. Twigg

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA. E-mail: [email protected]

A.E. Wickenden

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA

N.A. Zakhleniuk

Department of Electronic Systems Engineering, University of Essex, Colchester C04 3SQ, Engeland. E-mail: [email protected]

III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 1

Introduction to defects and structural properties of Ill-nitride semiconductors M.O. Manasreh 1. Introduction GaN and related compounds attracted tremendous interest for their applications to blue/green diode lasers and LEDs, high-temperature electronics, high-density optical data storage, and electronics for aerospace and automobiles. There is also great scientific interest in this class of materials because they appear to form the first semiconductor system in which extended defects do not severely affect the optical properties of devices. This volume is focused on the defects and structural properties of Ill-nitrides featuring chapters written by experts in the field. This unique volume provides a comprehensive review and introduction of defects and structural properties of GaN and related compounds for newcomers to the field and stimulus to further advances for experienced researchers. This introductory chapter is constructed based on the input and information reported by the authors of the technical chapters. Hence it provides some ideas about each chapter and the topics discussed by the authors. When Maruska and Titjen succeeded in growing GaN on sapphire substrates in the late 1960s using chemical vapor deposition [1], it quickly became obvious that doping and defects would play a vital role in the future development of GaN. The early unintentionally doped GaN was invariably n-type, which at the time was believed due to nitrogen vacancies. The high n-type background carrier concentration on the order of 10^^ cm~^ proved difficult to minimize and the absence of a shallow acceptor dinmied the prospects of a production-scale GaN-based device effort. Nevertheless, the early work using zinc-compensation led to the first demonstrations of blue, green, yellow and red metal-insulating-n-type GaN light emitting diodes (LEDs) [2], but further device development was still stifled by the seemingly insurmountable problem of making conducting p-type GaN. The search for p-type GaN was not successful until Akasaki and Amano demonstrated this feat in 1989 [3]. This remarkable achievement was actually a result of two significant milestones. First, the crystalline quality and the background n-type carrier density in unintentionally doped GaN films was significantly reduced by the use of a low temperature AIN buffer layer [4,5]. Second, p-type GaN was demonstrated with Mg-doping followed by an ex situ low energy electron beam irradiation (LEEBI) treatment. Conducting p-type GaN had previously remained elusive despite other Mg-doping efforts because it was found that hydrogen passivates the Mg-acceptors [6], similar to the effect of hydrogen on acceptors in Si [7]. Thus, it was theorized that the LEEBI treatment, which was accidentally discovered while studying

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the cathodoluminescence of a Mg-doped sample, disassociated the H-Mg complex allowing the Mg to form a quasi-shallow acceptor level. This theory was later confirmed by producing p-GaN by annealing GaNiMg in a hydrogen-free ambient such as N2 [8]. The process was also reversible rendering GaN:Mg insulating by annealing in a hydrogen-rich environment such as ammonia (NH3). These remarkable discoveries eventually led to the demonstration of a variety of bipolar devices, such as blue and green p-n junction LEDs and violet laser diodes (for examples see ref. [9]), solar-blind and ultraviolet sensitive p-i-n photodiodes [10-13] and high-power, high-temperature bipolar transistors [14,15]. Even though much progress has been made in doping GaN, there still exists significant challenges; especially with p-type doping. The low hole mobility and low achievable free hole concentration result in large sheet resistance preventing the fabrication of reliable Ohmic contacts with low contact resistivities. These material challenges have prevented the use of the AlGaN/GaN system to its full potential in electronic applications such as microwave heterojunction bipolar transistors (HBTs). Furthermore, the immature p-type doping technology has led to degradation (lifetime) problems and required that InGaN laser diodes operate at a higher than expected bias voltage. The ten technical chapters in this volume are focused on various aspects of dopants, impurities, defects, electrical and structural properties. The chapters are treating different aspects of Ill-nitrides as described in the following sections. 2. Dopants and defect engineering The aim of chapter two is to describe the state-of-the-art undoped and doped GaN by comparing select optical and electronic properties. The results reported in this chapter show that N-type doping of GaN using Si is well-understood, as Si readily incorporates on a Ga-site forming a single shallow donor with an activation energy of 12-15 meV leading to near complete donor ionization at room temperature. The growth is largely controlled over a wide range of densities from low-10^^ to mid-10^^ cm~^, although some structural problems occur in thick and heavily doped films. On the other hand, P-type doping remains a major challenge, as Mg forms a 'quasi-shallow' acceptor level located more than 170 meV above the valence band edge. The deep nature of the acceptor level leads to poor acceptor ionization of several percent at room temperature. Excessively high Mg concentrations are therefore needed to produce p-type films above mid-10^^ cm~^, which often results in resistive films. The near-band edge optical transitions are well understood in GaN, and thus, low temperature photoluminescence spectroscopy is a valuable tool in characterizing nominally undoped GaN. On the other hand, the origins of various defect-related transitions such as the ever-present yellow PL are still hotly debated and will require further investigations to unambiguously identify. The broad defect-related PL signatures observed well below the intrinsic optical band edge tends to dominate the spectra and often limit the useful information that can be extracted from PL measurements on heavily doped material. PL can generally be used to identify the presence of and to extract the binding energies for common dopants such as Mg and Si in low and medium doped GaN.

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The Hall-effect measurement is a useful tool to determine the carrier concentration, mobility and resistively in conducting GaN and temperature-dependent measurements yield info regarding the thermal activation energies. However, caution should be placed on equating the thermal activation energy to the actual location of the donor/acceptor levels responsible for electron/hole conduction with respect to the band edges. The electrical measurements can substantially underestimate the location of the donor/acceptor levels as heavily doped material is most often used, which causes potential fluctuations in the lattice leading to significant band-tailing. A comparison with PL measurements on modestly doped material can often clarify the situation. This is particularly true for Mg-doped GaN as shown in chapter two. Diffusion as a doping technique is impractical for GaN due to the vanishing small diffusivities at temperatures below 1 lOO^'C. Ion implantation is more promising for both conductivity modulation and optical purposes, but further work is required to optimize activation and minimize residual implantation damage. The process compatibility of implantation is limited due to the high annealing temperatures needed above 1500°C to repair implantation-induced damage. Nevertheless, implantation can possibly be used in areas of the device that is removed from critical (minority) carrier flow such for creating heavily doped contact layers facilitating tunneling contacts with low resistivities. In situ doping is therefore the doping technique of choice due to the above-mentioned challenges. Tricks such as piezoelectric enhanced superlattice doping can create p-layers with low resistivities, but is not practical for vertical carrier conduction. Molecular doping of paired donors and acceptors is another alternative that deserves further exploration. How does the current status of dopants in GaN impact the future device efforts? It is clear that devices will continue to exhibit large series resistances and contact problems until the above-mentioned fundamental p-type doping problem is solved. The most glaring examples are the high operating voltages and lifetime problems associated with GaN-based lasers and the absence of microwave operation in HBTs. The fundamental problems can be circumvented on an individual basis by clever device design using techniques such as re-growth, selective growth, implantation, superlattice doping, deep-sub-micron lithography and wafer bonding with a penalty in increased processing costs. However, a general and fundamental solution to the p-type doping problem GaN and the related alloy system (Al-In-Ga-N) has tremendous potential for both optoelectronic and electronic devices due to superior materials parameters such as a wide and direct bandgap energy, high breakdown fields, high saturated electron velocity and adequate electron mobility and thermal conductivity. Chapter three reviews the common crystallographic defects observed in the GaN and related Ill-nitride systems based on the electron microscopy results. All foreign substrates available for the GaN epitaxy have a high mismatch in lattice parameters, thermal expansion and chemical composition with the GaN layer. Among a large number of different foreign substrates tested for the GaN deposition [16], sapphire and 6H silicon carbide have demonstrated the best results in terms of the layer quality. The mismatch in lattice parameters and thermal expansion coefficients between the GaN and these substrates is high. It leads to a generation of the high density of defects at the epi-layer-substrate interface. The lattice mismatch between the GaN and SiC is about

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2%, but it is even higher in case of the GaN layers grown on sapphire being about 16 and 30% for c- or a-facet of sapphire, respectively. However, the defect densities in the GaN layers grown by metal-organic vapor phase epitaxy (MOVPE) on SiC and sapphire substrates were found to be comparable [17]. This could be explained taking into account that defect density in the GaN layer is controlled by structure of the buffer layer and its roughness, in particular. Defect generation and annihilation discussed in chapter three were shown to be mainly growth-related processes. Because of the very low dislocation mobility in the GaN, the high misfit stress relaxes mainly at earlier growth stages resulting in the high defect density at the interface with the substrate. On the other hand, the low dislocation mobility is favorable for long lifetime of the GaN-based optoelectronic devices. The majority of defects are generated at the interfaces with the substrate and the buffer layer. The dislocation annihilation also occurs mainly in the buffer layer and in the area close to it by the lateral overgrowth of some grains over the others. The proper preparation of substrate surface and optimization of the buffer layer enhancing the lateral overgrowth is essential for the reduction of the defects in the GaN layer. The structural quality of the GaN layer can be controlled by the growth conditions, especially during the first growth stages. 3. Identification and characterization of defects Several characterization tools were employed in this volume to identify and characterize defects in Ill-nitride semiconductors. For example, magnetic resonance, which is the subject of chapter four, is a very useful technique in solid state physics. The term 'magnetic resonance' means: resonance absorption of electromagnetic radiation at microwave (radiofrequency) range, by paramagnetic defect center present in investigated crystal, with magnetic field of values characteristic for the center applied as well. Basic advantage of wide family of methods based on the magnetic resonance is that they provide information about microscopic nature of paramagnetic defects. Simultaneously, the sensitivity of magnetic resonance methods is much higher than that of most other techniques leading to understand a microscopic picture of investigated centers. The classical magnetic resonance method is electron spin resonance (ESR), which has been developing very rapidly since 1945 [18]. Electron spin resonance means resonant absorption of microwave power by electronic levels of magnetic ion or defect, in applied magnetic field. These electronic levels originate from the ground state of magnetic center, splitted by Zeeman effect. Electron spin resonance experiments are performed in order to determine the nature, symmetry and environment of paramagnetic defects in crystals. They have been successfully used for many years to study defects in different semiconductors [19-22], providing considerable information about the ground states of paramagnetic centers introduced intentionally, as well as present as unintentional contamination. In ESR, sensitivities even of the order of 10^^ spins (ions) can be achieved in some cases. The other magnetic resonance technique, called optically detected magnetic resonance (ODMR), allows studying excited states of defects. It can essentially provide similar information about investigated defects as ESR technique, i.e. determine their

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nature and symmetry. The idea of ODMR experiment consists in detection of emission changes due to microwave absorption at the excited states in applied magnetic field. Samples are irradiated with light that causes emission, and are subject to microwave radiation. In such an arrangement, magnetic resonance of defects in excited state can lead to changes in emission intensity. Increase or decrease of sample irradiation intensity is viewed either in polarized light or as changes of total emission. ODMR technique has been successfully used to study defects in different semiconductors, like II-VI, III-V, amorphous Si [23]. In general, the analysis of ESR or ODMR spectra is the same and can provide similar information about defect center. However, in the case of ODMR the line widths are typically substantially broader than in ESR spectra. Therefore, the determination of resonance parameters is more difficult and less accurate from ODMR spectra. On the other hand, the great advantage of optical method is its sensitivity, which increases to about three orders of magnitude over conventional ESR. Another advantage of ODMR is the possibility of directly linking a resonance with a particular emission process. Another magnetic resonance technique is electrically detected magnetic resonance (EDMR). In analogy to ODMR, in EDMR method the magnetic resonance is observed through spin-dependent electrical properties (optical in ODMR) of sample. Such measurements give great enhancement in sensitivity in comparison with ESR as well as they allow to observe centers participating in electrical processes, not necessary paramagnetic under thermal equilibrium conditions [24]. EDMR studies have been mainly performed on devices, especially in case of GaN-based materials. The results of EDMR experiments on GaN-based devices are not a subject of this book, but and can be found elsewhere [25]. In chapter four, a review of magnetic resonance studies of defects in nitrides is given. Results of research performed by different scientific groups are sunmiarized. The investigated crystals were grown by different techniques: bulk material by high pressure method [26], epitaxial layers by molecular organic chemical vapor deposition (MOCVD) [27] and microcrystalline powder by ammonothermal method [28]. An attempt was made in this chapter to present the main achievements of magnetic resonance studies on defects in nitride compounds. In spite of huge amount of work performed on nitrides, especially in the last 5 years, not too much has been clarified in the area of defect identification. One of the main reasons is the difficulty to obtain bulk nitride crystals, the best materials for ESR studies. The ESR signal due to shallow donor characteristic for MOCVD grown GaN is well established in chapter four. Its parameters are the same for undoped n-type as well as Si-doped layers. However, it has not been definitively proven that Si is the main shallow donor defect in MOCVD-grown GaN. Signal coming from shallow donor in bulk GaN of slightly different parameters has also been identified. In this case, oxygen nature should be strongly considered as possible origin, since bulk GaN suffers from oxygen contamination. On the other hand, quite clear situation is in the area of two main acceptors of GaN, namely Mg and Zn. Their magnetic resonance spectra have been positively identified and found to follow the well know process of hydrogen passivation and its diffusion out of acceptor centers. Transition metal impurities, common trace impurities of many semiconductors, are far from being known in GaN when it comes to their magnetic resonance properties. Up

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to now, ESR spectra of only manganese Mn^^ (3d^), iron Fe^+ (3d^), nickel Ni^+ (3d^) and recently erbium Er^+ (4f^^) have been published. The studies of electron-irradiated GaN have not come up to expectations and have not led to positive identification of any of hoped-for simple native defects. For mixed AUGai_;cN (0 < JC < 0.26) layers ESR signal of shallow donor has also been reported in chapter four, but the origin of this donor remains still unknown. ESR spectrum observed for polycrystalline AIN ceramics, containing intentional Cr impurities, has been attributed to Cr^"^ (3d^). Finally, in some studies, nitrogen vacancy related ESR defects have been suggested in AIN and BN materials. Since it seems that intentional doping of nitrides and studies of such materials have just started, one can expect much more yet to come in the area of defect identification in nitride compounds in the coming years. Traditionally the experimental information on point defects has been obtained by electrical and optical characterization techniques, such as Hall measurements and infrared absorption. Although the defects can be detected in these experiments, their atomic structures remain very often unresolved. The methods based on ESR (as discussed in chapter four) are more sensitive to the structure of defects, but so far these techniques have given only limited information in GaN materials. An experimental technique is thus needed for the unambiguous defect identification. This goal is reached for vacancy-type defects by utilizing the positron annihilation spectroscopy as discussed thoroughly in chapter five. Thermalized positrons in solids get trapped by the vacant lattice sites. The reduced electron density at the vacancies increases positron lifetime and narrows the positron-electron momentum distribution. The detection of these quantities yields direct information on the vacancy defects in solids. Positron lifetime measurements can be used to probe homogeneous defect distributions in semiconductor substrates. This technique is relatively simple to implement, but yet very powerful in identifying the atomic structure of the defect, its charge state and concentration. Defects in the near-surface region 0-3 ixm can be studied by a monoenergetic positron beam. This technique is well suited for the defect studies of epitaxial semiconductor materials. The information provided by positron experiments is especially useful when combined with those of other spectroscopies. The correlation of positron measurements with electrical and optical methods enables quantitative studies of technologically important phenomena, such as electrical compensation, light absorption and photoluminescence. In chapter five, the author presented positron annihilation spectroscopy technique, which was used to identify vacancy defects in GaN epitaxial layers. It yields quantitative information on vacancy concentrations in the range 10^^-10^° cm"^. Positron experiments detect Ga vacancies as native defects in GaN bulk crystals. It is reported in this chapter that the concentration of Voa decreases with increasing Mg doping, as expected from the behavior of their formation energy as a function of the Fermi level. The trapping of positrons at the hydrogenic state around negative ions gives evidence that most of the Mg atoms are negatively charged. This suggests that Mg doping converts n-type GaN to semi-insulating mainly due to the electrical compensation of O^ donors by MgQ^ acceptors. Ga vacancies are observed as native defects in various n-type GaN overlayers grown by MOCVD on sapphire. Their concentration is >10^^ cm~^ in nominally undoped

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material, which show n-type conductivity due to residual oxygen. When similar doping is done with Si impurities and less oxygen is present, the concentration of Ga vacancies is lower by at least an order of magnitude. No Ga vacancies are observed in p-type or semi-insulating layers doped with Mg. These trends agree well with the theoretical calculations, which predict that the formation energy of Ga vacancy is high in p-type and semi-insulating material, but greatly reduced in n-type GaN, and even further reduced due to the formation of Voa-ON complexes. In addition to doping, the presence of open-volume defects in GaN layers depends on the growth conditions. The concentrations of Ga vacancies increases strongly when more N-rich stoichiometry is applied in the MOCVD growth. On the other hand, the lattice mismatch and associated dislocation density seem to have less influence on the formation of point defects than doping and stoichiometry — at least at distances >0.5 |xm from the layer/substrate interface. This suggests that the formation of point defect in both epitaxial layers and bulk crystals follows mainly the trends expected for defects in thermal equilibrium. Due to their wide band gaps, effects of deep level centers on the Ill-nitride materials and devices are expected to be more pronounced than in narrower band gap materials. Indeed, deep level centers and the associated persistent photoconductivity (PPC) effect described in chapter six have been observed in a wide variety of Ill-nitride materials and structures. Their presence indicates possible charge trapping (or charge freeze out) effects in Ill-nitride devices, which could cause instabilities in such devices and hence have significant influences on the device performance. For example, there is evidence that the presence of deep level impurities are responsible for the current-voltage characteristic collapse seen in Ill-nitride field effect transistors (FETs) [29-31]. The prolonged carrier capture time in the PPC state was also shown to affect the photocurrent transient behaviors in AlGaN/GaN heterojunction UV detectors [32]. The research to determine the origin of PPC in Ill-nitrides has been driven not only by its peculiar and interesting physical properties, but more importantly by its relevance for device applications, i.e. an understanding of the physics as well as the control of PPC and the associated deep level centers is necessary in order to further optimize Ill-nitride devices. PPC is the light-enhanced conductivity that persists for a long period of time after the removal of photoexcitation and has been observed in many semiconductor materials and structures. At low temperatures, the PPC decay times become extremely long (of the order of minutes to years) and incompatible with normal lifetime-limiting recombination processes in semiconductor materials. Earlier work on conventional IIIV and II-VI semiconductors has shown that understanding of the PPC phenomena can provide mechanisms for carrier generation and relaxation. It is also known that the PPC has a profound effect on device operations, e.g. it is detrimental to the operation of AlGaAs/GaAs modulation doped heterojunction field effect transistors (MOD-FETs) [33-37]. On the other hand, PPC is useful for adjusting the density of the two-dimensional electron gas (2DEG) at a semiconductor interface[38] and for possible device applications such as memory device and optical gratings [39,40]. It can also be utilized to probe the profile of the impurities [41], properties of metal-insulator transition [42], and transport properties of the tail states in the density of states in semiconductor alloys [43,44].

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The aim of chapter six is to review the PPC in Ill-nitrides and to provide an overview on such an effect in these materials. The PPC characteristics including its buildup and decay behaviors, evidence of DX-like centers as well as the nature of defects, and implications on PPC mechanisms, effects of PPC on Ill-nitride devices including FETs and photodetectors, and possible uses of PPC are discussed in this chapter. As shown in this chapter, our understandings of the properties of PPC and associated deep level centers in Ill-nitrides have built on the early studies on AlGaAs alloys. Studies of PPC in Ill-nitrides, just as any other topics in this field, are driven primarily by technological developments and needs. This trend will be continued. Current devices in the Ill-nitrides all take advantages of heterostructures and quantum wells. In this sense, understanding and control of PPC as well as the associated deep level centers and their effects on devices based heterostructures and quantum wells will become more and more important. As the nitride materials quality further improves, the nature of deep level center as well as their characteristics can be identified. With the insights from theoretical calculations, the detailed information regarding the energy levels as well as their atomic configurations in Ill-nitride lattices will be understood. 4. Ion implantation and radiation effects Ion implantation has become a highly developed tool for modifying the structure and properties of semiconductors. The energetic implants are applied in the doping of semiconductor material, the formation of insulator regions to isolate the active regions of circuits, in the fabrication of optical active regions and also in the device application. According to chapter seven, the advantages of the ion implantation are: • An accurate dose control is possible by measurement of the ion current. • The depth distribution of the injected dopants and the introduced lattice disorder are directly related to the ion energy and the masses of the target material and ion. By variation of the ion energy and dose the concentration profile of the impurities and also the structural changes can be tailored. • In contrast to high temperature processing, the ion implantation is an intrinsic low temperature process, although subsequent annealing is generally necessary. In this respect, it differs greatly from the diffusion approach, where high temperatures during doping may lead to decomposition of the near surface region. • Ion implantation is insensitive to the lattice structure, lattice defects and the presence of impurities. • The implantation process is not constrained by thermodynamic considerations. This means, that any species of ion may be implanted into any host. A wide concentration range can be achieved with the upper limit generally set by the sputtering yield rather than by equilibrium solubility. • Ion implantation can be included in the semiconductor process technology and implantation machines can be designed for specific applications. To understand and to control the electrical and optical properties of group Ill-nitride is one of the great challenges associated with the development of semiconductors. It is well-known that wide band gap semiconductors are difficult to dope by ion implantation due to the native defects and the high resistance against the damage recovery. As the

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quality of epitaxial GaN layers continues to improve, ion implantation is considered to be a promising doping technology. Recent progress has been made in this field such as the controlled p-type doping, damage annealing, implant isolation, implantation induced optical activation as well as device fabrication. The main disadvantage of the ion implantation in semiconductors is related to the lattice disorder caused by implanted ions. Because of the high background electron concentration of the as-growth GaN, ion implantation with high concentrations of acceptors is generally needed to compensate the native electron background and to realize the transition to p-type. However, the crystalline structure is diminished by implantation induced damage after implantation with high dopant concentrations. Consequently, a precise control of implantation conditions such as ion energy, temperature during implantation, ion dose, etc., and an optimal annealing process are essential to successful doping by ion implantation. The purpose of chapter seven is to present an introduction into and a review of the state of ion implantation in GaN and related III-V materials. Although significant progress has been reported for doping and isolation of wide band gap semiconductors, there are still many problems to be solved before an extensive application of ion implantation in device fabrication can be realized. In recent years several excellent review papers have appeared addressing various aspects of the implantation technology of group Ill-nitrides [45-47]. This chapter is devoted to the implantation induced damage and the defect annealing. The realization of the controlled n-type and p-type doping by ion implantation is discussed with the main emphasis on the results of GaN. Then, the impurity luminescence and isolation by ion implantation are discussed. During several semiconductor-processing steps, for example particle irradiation for lifetime tailoring [48,49] dry etching [50,51], metallization [52,53] and device isolation [54,55] the semiconductor is intentionally or unintentionally exposed to a variety of particles with energies ranging from a few eV to several MeV. When these particles impinge on the semiconductor, they enter into it, transfer energy to the semiconductor lattice and introduce defects. These defects can have a profound influence on the semiconductor properties and on the characteristics of devices fabricated on it, which may be either beneficial or deleterious, depending on the application. Chapter eight is presenting the latest research efforts on radiation-induced defects in GaN. In order to avoid the deleterious effects of some of these particle-induced defects and utilize the beneficial effects of others, depending on the application, it is imperative to understand the effect of radiation on electronic materials and devices fabricated on them as discussed in chapter eight. To achieve this, it is essential that the electronic properties and concentration of radiation induced defects should be known, allowing calculation of their effect on the properties of electronic materials and devices. In addition, the structure, introduction rate, introduction mechanism and thermal stability of the defects should be determined, so that they can be reproducibly introduced, avoided or eliminated, depending on the application. Regarding electrical techniques for defect characterization, deep level transient spectroscopy (DLTS), which allows independent studies of different defect species in the same semiconductor, has played a key role in providing most of this information. Hall effect measurements have also contributed a fair deal to our understanding of radiation-induced defects and its effect on carrier mobility and donor and acceptor concentration. As far as the electrical

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characterization of simple devices are concerned, current-voltage (/-V) and capacitance (C-V) measurements have traditionally been used to evaluate the effect of defects on diode performance and the free carrier density of semiconductors, respectively. Since growth-induced defects have an inhibiting effect on the detection of process induced defects, chapter eight describes which defects are present in GaN grown by different epitaxial techniques. This should not be seen as a complete review of growth induced defects, but rather as a guideline as to which defects can be expected in epitaxially grown GaN when attempting to characterize process induced defects in it. High energy particle irradiation introduces several electron traps in n-GaN, as shown in this chapter, with energy levels between 0.06 and 0.95 eV below the conduction band. Some controversy surrounds the nature of the most frequently observed level at 0.20 eV. It has recently been shown that the DLTS signal of this level can be deconvoluted into at least two levels. One of these is a shallow donor at EQ —0.06 eV which has previously been assigned to the VN- The origin of the deeper lying defects is not clear yet. All the observed high energy irradiation induced defects anneal out at 700 K. Resistive (joule) evaporation and electrodeposition of metals do not introduce defects in semiconductors according to chapter eight. However, two other metallization processes, E-beam and sputter deposition, were shown to introduce electrically active defects in GaN. Both of these processes introduce a defect with a level similar to that of ER3, believed to be related to the nitrogen vacancy. In addition, each of these processes introduces defects characteristic to the process. The concentration of these process induced defects can be minimized by optimizing the deposition conditions as discussed in chapter eight. For sputter deposition, this can be achieved by minimizing the deposition power and maximizing the plasma pressure. In the case of E-beam evaporation, the geometry of the e-gun with respect to the sample position should also be taken into account. Finally, the thermal stability of these metallization induced defects has not yet been reported. This, in conjunction with the thermal stability of the Schottky contacts, is required to assess whether or not post-deposition annealing can remove the defects responsible for diode degradation. 5. Stress, structural and phonon properties One of the preliminary goals of chapter nine is to show that residual stresses have a profound effect on nitride optical data. And since these materials are being heavily developed for optoelectronic applications, the presumption is that anything affecting nitride optical properties to such a large extent should be investigated, at the very least so that such perturbations can be eventually eliminated or exploited to improve nitride-based LED and laser diode performance. Such an investigation will naturally center around the fundamental ways that stress affects the optical properties of a material, but we will also be concemed with the materials and growth parameters that produce such stresses in the first place. Chapter nine will also examine the extent to which it has been possible to manipulate residual stresses in these materials, with the goal of improving optical properties. The focus in this chapter is on GaN films and will largely ignore the non-negligible role that defects and impurities (readers interested in this topic should see, for example [56]) play in this study. This is justified for the simple

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reason that the strain states of even the most rudimentary GaN heterostructures are not at all well-understood and that we must master the simplest case before proceeding to more complex combinations of materials. Chapter nine demonstrates with a collection of selected GaN low temperature reflectance lineshapes [57] obtained from films grown under a variety of conditions. Prior to proceeding with the optical data, this chapter examines the physical structure of the samples that are being measured. Because much has been learned lately about nitride physical properties and growth mechanisms since the first reflectance data were taken by R. Dingle and coworkers in 1971 [58]. Indeed, during the course of this chapter, we shall see that a lack of information about the physical properties of the material has been the source of considerable misunderstanding about strain behavior in the GaN literature. There are several examples of phenomenological strategies to manage strain in nitride heterostructures; one of the most successful is the Lateral Epitaxial Overgrowth technique [59]. Here, briefly, GaN is deposited on an underlying GaN layer through the windows of an Si02 mask. The deposited material first grows vertically on top of the mask then proceeds to grow laterally over the mask (and vertically as well) until the growth fronts from all of the windows coalesce into a continuous layer. What is remarkable about GaN films grown by this technique is the dramatic reduction in threading dislocation density observed in the films: the usual 10^-10^^ cm"-^ in the area beside the mask and less than 10"^ cm~^ in the area above it. Since dislocations have their origins in lattice mismatch and are detrimental to device operation, the technique is an excellent example of engineering stress in order to enhance device performance. Indeed, the threshold current of Ill-nitride lasers is substantially reduced using LEO 'substrates' and these lasers experience a corresponding and dramatic increase in lifetime [60]. Unfortunately a simple look at the thermal and lattice mismatch behavior of nitride materials still cannot neatly explain the wide range of stress-related phenomena observed, even for simple heterostructures. Not surprisingly the majority of unexplained issues are related to the failure of classical Matthews-Blakeslee thin film relaxation models. Some examples involve stresses formed by the coalescence of two dimensional islands, stresses that cause growth mode changes and then in turn exert stresses, and the observation of what appears to be multiple slip systems in simple structures. These appear to play an important but as of yet unclarified role in the relief of residual stress in GaN films in a way that transcend simple lattice mismatch. Again, this tells us that though impressive optoelectronic devices have been demonstrated and commercialized in recent years, it has been done with only a rudimentary and indeed merely phenomenological understanding of stress. The big implication is that the work is not yet finished with regard to relaxation phenomena in this materials system. Though much has been achieved with this phenomenological 'understanding', far more could be achieved if relaxation phenomena were thoroughly understood (and controlled) even in simple nitride heterostructures. Chapter ten is focused on the structural defects in nitride heterojunctions. Because of the difficulty in growing sufficiently large GaN substrates, GaN films must be grown heteroepitaxially on a variety of alternative substrates. Despite large differences in lattice parameters and thermal expansion coefficients, technologically ^omising GaN thin films have been grown on c-plane (i.e. {0001}) sapphire, a-plane {1120} sapphire.

12

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M.O. Manasreh

and {0001} SiC. As a consequence of heteroepitaxy, however, the resulting film suffers from a large density of extended defects. Differences in lattice parameter and coefficient of thermal expansion necessarily lead to large dislocation densities, whereas differences in surface and interfacial energies often lead to the formation of islands and planar defects. Heteroepitaxial c-axis growth of a polar material like GaN also introduces the problem of inversion domain boundaries (IDBs), as well as the possibility that the deposited film may have one of two polarities: Ga-terminated or N-terminated. Properly optimized MOVPE growth of GaN has succeeded in producing GaN films with dislocation densities between 10^ and 10^/cm^. Advances in the understanding of the effects of substrate nitridation and vicinality, reactor pressure, and dislocation filtering have led to strategies for reducing dislocation density and increasing grain size. These strategies, in turn, have contributed to the growth of uniform GaN films with properties suitable for electronic and electro-optic devices. Extended defects, which are thoroughly discussed in chapter ten, in heteroepitaxial GaN films grown by MOVPE scatter carriers, resulting in lower mobility, and appear to surround themselves with point defects and impurities which act to compensate dopants. It also appears that point defects may be able to compensate dopants without associating with extended defects; the SIMS and TEM study of carbon in GaN films deposited by variable pressure growth supports this contention. In particular, it is interesting to consider carbon as a point defect involved in compensation, since it is an inevitable by-product of the MOVPE process which can be controlled, to some degree, by altering the reactor pressure. According to chapter ten, reactor pressure influences grain size as well as carbon concentration and there appears to be a reactor-dependent optimal pressure for growing grains that are large without the onset of faceting, or the onset of associated lattice tilting and twist boundaries. These reactor parameters for growing a film with the minimum extended defect density on a nucleation layer is similar to growth via LEO in that the lateral growth rate must be as large as possible without the onset of faceting. There is also reason to believe that both LEO and conventional growth can be optimized by the use of vicinal c-plane SiC or a-plane sapphire substrates, in order to improve grain alignment and thereby reduce the edge dislocation density occurring at grain boundaries. The role of the nucleation layer in heteroepitaxial GaN growth and the procedures for optimizing this layer are still not well understood. For some reactors, at least, it appears that the optimal nucleation layer goes down with a significant fraction of the film consisting of the zinc blende polymorph, which then transforms into the wurtzite phase upon annealing. Although there has been a preliminary effort to explain these structural constraints; there is not yet a sufficiently general understanding to guide a grower in achieving a good nucleation layer. There is some indication that optimizing the nucleation layer results in defining a specific film polarity (i.e. Ga-terminated) and that this desirable result may be achieved by reducing the oxygen composition and thereby eliminate oxygen-rich inversion domain boundaries in the nucleation layer. It also appears that achieving a film with no inversion boundaries is frustrated by a rough substrate morphology. In chapter eleven, the authors systematize the theory underlying the dispersive continuum model and apply it to describe the lattice vibrations in layered heterostructures.

Properties of lll-nitride semiconductors

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13

with particular emphasis on heterostructures based on III-V nitride materials. The nitride-based heterostructures have, in general, very special dynamical properties which distinguish them from the more traditional GaAs/AlAs heterostructures. The differences in properties between the two types of heterostructure are so significant that a more in-depth analysis of macroscopic lattice dynamics is required to deal correctly with the situation in nitride-based heterostructures. Another important question that chapter eleven has addressed concerns the mechanical boundary conditions. It turns out that the only rigorous self-consistent route to arrive at physically acceptable boundary conditions is to start from the microscopic mechanical equations, which describe the vibrations of the separate ions and then carefully proceed to obtain the continuum limit. This is done in this chapter using the Keating model approach [61]. Chapter eleven presents a brief description of the essential features of bulk nitride materials, particularly in relation to lattice vibrations and dielectric properties and a treatment of the quantum field theory of dispersive polar optical (PO) continuum modes in bulk nitrides, emphasizing the additional features introduced by the incorporation of spatial dispersion. This rigorous theory is presented in this chapter for the first time and applied in the context of electron-phonon interactions in the bulk. This chapter also presents the application of the dispersive continuum theory to the situation in a heterostructure. Once more the inclusion of dispersion in the theory makes this section an original account presented here for the first time. The microscopic origin of the continuum theory of PO phonons in heterostructures is also presented in this chapter. In particular, the authors seek to shed some light on how the boundary conditions to be satisfied by PO modes at interfaces between different media emerge from a microscopic treatment when the continuum limit is carefully applied. Descriptions of results emerging from the hybrid models, the double hybrid and extended hybrid models, in the context of electron-PO phonon interactions in double heterostructures and superlattices based on GaN systems are also shown in chapter eleven. The existence of a sum-rule which holds whenever one is concerned with total contributions from the entire spectrum of allowed modes is discussed for the first time. The relationship between the dispersive continuum theory (in its hybrid model form) and the DC model is clarified. Section 8 of chapter eleven contains a brief summary of optical phonons and their interaction in nitride-based heterostructures. However, the authors found that the task would have been incomplete without a presentation of a quantum field theory of the dispersive continuum model of optical phonons in the bulk and in heterostructures. The treatment is presented in this chapter for the first time and it completes the picture of the continuum description of dispersive polar optical modes and their interaction with electrons in heterostructures. The issues of boundary conditions have also been explored in depth in this chapter from a microscopic point of view and the application of the theory to double heterostructures and superlattices has been presented. One important conclusion that has been reached is the existence of a sum-rule, which applies whenever the interaction of electrons with phonons involves the full set of optical phonons irrespective of the model that has been used to describe the PO modes in the heterosystem.

14

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6. Conclusion This introductory chapter summarized the subjects and issues discussed thoroughly in the ten technical chapters. The focus of this volume is directed toward dopants incorporation, impurities identifications, defects engineering, defects characterization, ion implantation, irradiation-induced defects, residual stress, structural defects, and phonon confinement in Ill-nitride semiconductors. There is also great scientific interest in this class of materials because they appear to form the first semiconductor system in which extended defects do not severely affect the optical properties of devices. This unique volume provides a comprehensive review and introduction of defects and structural properties of GaN and related compounds for newcomers to the field and stimulus to further advances for experienced researchers. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

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H.P. Maruska and J.J. Teitjen, Appl. Phys. Lett. 15, 367 (1969). J.I. Pankove, J. Lumin. 7, 114 (1973). H. Amano, M. Kito, K. Hiramatsu and I. Akasaki, Jpn. J. Appl. Phys. 28, L2112 (1989). H. Amano, N. Sawaki, I. Akasaki and Y. Toyoda, Appl. Phys. Lett. 48, 353 (1986). I. Akasaki, H. Amano, Y. Koide, K. Hiramnatsu and N. Sawaki, J. Crystal Growth 98, 209 (1989). J.A. van Vechten, J.D. Zook and R.D. Homing, Jpn. J. Appl. Phys. 31, 3662 (1992). J.L Pankove, PJ. Zanzucchi and C.W. Magee, Appl. Phys. Lett. 46, 421 (1985). S. Nakamura, T. Mukai, M. Senoh and N. Iwasa, Jpn. J. Appl. Phys. 31, L139 (1992). See for example: S. Nakamura and G. Fasol, The Blue Laser Diode, Springer, Berlin, 1997. G.Y. Xu, A. Salvador, W. Kim, Z. Fan, C. Lu, H. Tang, H. Morkoc, G. Smith, M. Estes, B. Goldenberg, W. Yang and S. Krishnankutty, Appl. Phys. Lett. 71, 2154 (1997). J.M. Van Hove, R. Hickman, J.J. Klaassen, P.P Chow and P P Ruden, Appl. Phys. Lett. 70, 2282 (1997). A. Osinsky, S. Gangopadhyay, R. Gaska, B. Williams, M.A. Khan, D. Kuksenkov and H. Temkin, Appl. Phys. Lett. 71, 2334 (1997). J.T. Torvik, J.L Pankove and B. Van Zeghbroeck, IEEE Trans. Electron Devices 46, 1326 (1999). L. McCarthy, P. Kozodoy, M. Rodwell, S. DenBaars and U. Mishra, Compound Semiconductor 4, 19 (1998). F. Ren, C.R. Abemathy, J.M. Van Hove, P P Chow, R. Hickman, J.J. Klaassen, R.R Kopf, H. Cho, K.B. Jung, J.R. La Roche, R.G. Wilson, J. Han, R.J. Shul, A.G. Baca and S.J. Pearton, MRS Internet J. Nitride Semicond. Res. 3, 41 (1998). H. Hellmann, MRS Internet J. Nitride Semicond. Res. 1, 33 (1996). S. Ruvimov, Z. Liliental-Weber, J. Washburn, H. Amano, I. Akasaki and H. Koike, Mat. Res. Soc. Symp. Proc. 423, 487 (1996). E. Zavoiski, J. Phys. USSR 9, 211, 245, 447 (1945). H.H. Woodbury and G.W. Ludwig, Phys. Rev. 117, 102 (1960). W. Low, Paramagnetic resonance in solids. In: F. Seitz, D. Turnbull (Eds.), Solid Satate Phys., Suppl. 2, 1960. G.W. Ludwig and H.H. Woodbury, Solid State Phys. 13, 223 (1962). J.W Allen, Semicond. Sci. Technol. 10, 1049 (1995). B.C. Cavenett, Adv. Phys. 30, 475 (1981). I. Solomon, Proc. 11th Intern. Conf. Phys. Semicond., Polish Science, Warsaw, 1972, p. 27; D.J. Lepine, Phys. Rev. B6, 436 (1972); B. Stich, S. Greulich-Weber, J.-M. Spaeth, J. Appl. Phys. 77, 1546 (1995). WE. Carlos, E.R. Glaser, T.A. Kennedy, S. Nakamura, Appl. Phys. Lett. 67, 2376 (1995); WE.

Properties of lU-nitride semiconductors

[26]

[27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56]

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Carlos, S. Nakamura, Appl. Phys. Lett. 70, 2019 (1997); W.E. Carlos, S. Nakamura, J. Cryst. Growth 189/190, 794 (1998). I. Grzegory, M. Bockowski, B. Lucznik, M. Wr6blewski, S. Krukowski, J. Weyher, G. Nowak, T. Suski, M. Leszczynski, S. Litwin-Staszewska and S. Porowski, Mat. Res. Soc. Symp. Proc. 482, 15 (1998). O. Ambacher, J. Phys. D: Appl. Phys. 31, 2653 (1998). R. Dwilinski, R. Doradzinski, J. Garczynski, L. Sierzputowski, J.M. Baranowski and M. Kamiriska, Diamond Related Mater. 7, 1348 (1998). N. Nakamura and G. Fasol, The Blue Laser Diode, Springer-Verlag, Berlin, 1997. S.C. Binari, W. Kruppa, H.B. Dietrich, G. Kelner, A.E. Wickenden and J.A. Freitas Jr., Solid State Electron. 41, 1549 (1997). RB. Klein, J.A. Freitas Jr., S.C. Binari and A.E. Wickenden, Appl. Phys. Lett. 75, 4016 (1999). J.Z. Li, J.Y. Lin, H.X. Jiang and M. Asif Khan, Appl. Phys. Lett. 72, 2868 (1998). RM. Solomon and H. Morkoc, IEEE Trans. Electron Devices ED-31, 1051 (1984). J.F. Rochette, P. Delescluse, M. Lavin, D. Delagebeaudeuf, J. Chevrier and N.T. Linh, Inst. Phys. Conf. Ser. 65, 385 (1982). R. Fisher, T.J. Drummond, J. Klem, W. Kopp, T.S. Henderson, D. Perrachione and H. Morkoc, IEEE Trans. Electron Devices ED-31, 1028 (1984). A. Kastalsky and R.A. Kiehl, IEEE Trans. Electron Devices ED-33, 414 (1986). RM. Mooney, J. Appl. Phys. 67, Rl (1990). H.J. Stormer, R. Dingle, A.C. Gossard, W.W. Wiegmann and M.D. Sturge, Solid State Commun. 29, 705 (1974). R.A. Linke, T. Thio, J.D. Chadi and G.E. Devlin, Appl. Phys. Lett. 65, 16 (1994). R.L. MacDonald, R.A. Linke, J.D. Chadi, T. Thio, G.E. Devlin and P Becla, Optics Lett. 19, 2131 (1994). D.E. Theodorou, H.J. Queisser and E. Bauser, Appl. Phys. Lett. 41, 628 (1982). H.X. Jiang, A. Dissanayake and J.Y. Lin, Phys. Rev. B45, 4520 (1992). M. Smith, J.Y. Lin and H.X. Jiang, Phys. Rev. B51, 4132 (1995). M. Smith, J.Y. Lin and H.X. Jiang, Phys. Rev. B54, 1471 (1996). R.G. Wilson, Proc. Electrochem. Soc. 95 (21), 152 (1995). J.C. Zolper, In: S.J. Pearton (Ed.), GaN and Related Materials, Gordon and Breach, New York, 1997, p. 371. S.J. Pearton, J.C. Zolper, R.J. Shul and E Ren, J. Appl. Phys. 86, 1 (1999). A. Mogro-Campero, R.P Love, M.F. Chang and R.F. Dyer, IEEE Trans. Electron Devices 33, 1667 (1986). D.C. Sawko and J. Bartko, IEEE Nucl. Sci. 30, 1756 (1983). S.J. Pearton, W.S. Hobson, U.K. Chakrabarti, G.E. Derkits Jr. and A.R Kinsella, J. Electrochem. Soc. 137, 3892 (1990). F.D. Auret, S.A. Goodman, G. Myburg and W.E. Meyer, J. Vac. Sci. Technol. B 10, 2366 (1992). F.H. Mullins and A. Brunnschweiler, Solid State Electron. 19, 47 (1976). E. Grussell, S. Berg and L.R Andersson, J. Electrochem. Soc. 127, 1573 (1980). A.G. Foyt, W.T. Lindley, CM. Wolfe and J.P Donnelly, Solid State Electron. 12, 209 (1969). J.C. Dyment, J.C. North and L.A. D'Asaro, J. Appl. Phys. 44, 207 (1973). C. Kisielowski, J. Krueger, M. Leung, R. Klockenbrink, H. Fujii, T. Suski, G.S. Sudhir, M. Rubin and E.R. Weber. In: M. Scheffler and R. Zimmerman (Eds.), Proc. 23rd Internal. Conf. on the Physics of Semiconductors (ICPS-23), World Scientific, Berlin, 1996, p. 513; I. Gorczyca, A. Svane and N.E. Christensen, MRS Internet J. Nitride Semicond. Res., 2, 18 (1997). N.V. Edwards, S.D. Yoo, M.D. Bremser, T.W. Weeks Jr., O.H. Nam, H. Liu, R.A. Stall, M.N. Horton, N.R. Perkins, T.F. Kuech and D.E. Aspnes, Appl. Phys. Lett. 70, 2001 (1996). R. Dingle, D.D. Sell, S.E. Stokowski and M. Ilegems, Phys. Rev. B 4, 1211 (1971). O.-H. Nam, M.D. Bremser, T.S. Zheleva and R.R Davis, Appl. Phys. Lett. 71, 2638 (1997). B. Monemar, Summary of the Lateral Epitaxial Overgrowth Workshop, Junea, Alaska, Jun 2-5, 1999, In: MRS Internet J. Nitride Semicond. Res. RN. Keating, Phys. Rev. 145, 637 (1966).

III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 2

Dopants in GaN John T. Torvik

1. Introduction GaN and the related alloy system (Al-In-Ga-N) has tremendous potential for both optoelectronic and electronic devices due to superior materials parameters such as a wide and direct bandgap energy, high breakdown fields, high saturated electron velocity and adequate electron mobility and thermal conductivity. However, when Maruska and Titjen succeeded in growing GaN on sapphire substrates in the late 1960s using chemical vapor deposition [1], it quickly became obvious that doping and defects would play a vital role in the future development of GaN. The early unintentionally doped GaN was invariably n-type, which at the time was believed due to nitrogen vacancies. The high n-type background carrier concentration on the order of 10^^ cm~^ proved difficult to minimize and the absence of a shallow acceptor dimmed the prospects of a production-scale GaN-based device effort. Nevertheless, the early work using zinc-compensation led to the first demonstrations of blue, green, yellow and red metal-insulating-n-type GaN light-emitting diodes (LEDs) [2] but, further device development was still stifled by the seemingly insurmountable problem of making conducting p-type GaN. The search for p-type GaN was not successful until Akasaki and Amano demonstrated this feat in 1989 [3]. This remarkable achievement was actually a result of two significant milestones. First, the crystalline quality and the background n-type carrier density in unintentionally doped GaN films was significantly reduced by the use of a low temperature AIN buffer layer [4,5]. Second, p-type GaN was demonstrated with Mg-doping followed by an ex situ low energy electron beam irradiation (LEEBI) treatment. Conducting p-type GaN had previously remained elusive despite other Mg-doping efforts because it was found that hydrogen passivates the Mg-acceptors [6], similar to the effect of hydrogen on acceptors in Si [7]. Thus, it was theorized that the LEEBI treatment, which was accidentally discovered while studying the cathodoluminescence of a Mg-doped sample, disassociated the H-Mg complex allowing the Mg to form a quasi-shallow acceptor level. This theory was later confirmed by producing p-GaN by annealing GaN:Mg in a hydrogen-free ambient such as N2 [8]. The process was also reversible rendering GaNiMg insulating by annealing in a hydrogen-rich environment such as ammonia (NH3). These remarkable discoveries eventually led to the demonstration of a variety of bipolar devices such as blue and green pn junction LEDs and violet laser diodes (for example, see [9]), solar-blind and ultraviolet sensitive p-i~n photodiodes [10-13] and high-power, high-temperature bipolar transistors [14,15].

18

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J.T. Torvik

Even though much progress has been made in doping GaN there still exists significant challenges; especially with p-type doping. The low hole mobility and low achievable free hole concentration result in large sheet resistance preventing the fabrication of reliable Ohmic contacts with low contact resistivities. These material challenges have prevented the use of the AlGaN/GaN system to its full potential in electronic applications such as microwave heterojunction bipolar transistors (HBTs). Furthermore, the immature p-type doping technology has led to degradation (lifetime) problems and required that InGaN laser diodes operate at a higher than expected bias voltage. The aim of this chapter is to describe the state-of-the-art undoped and doped GaN by comparing select optical and electronic properties. This is not an attempt to exhaustively cover all material properties or varieties, but rather to compare fundamental phenomena, such as luminescence, absorption, and conduction. Furthermore, we explore the electrical and optical characteristics using relatively simple and inexpensive measurement techniques, which are readily available in most semiconductor laboratories. 2. Background Doping control is a prerequisite for the fabrication of most optical and electrical devices. For example, n- and p-type layers are the basic building blocks for bipolar devices, such as light-emitting diodes, laser diodes, photodiodes, and bipolar transistors, while undoped (or high resistivity) layers are needed for field effect transistors and photodiodes. Ideally, one should be able to grow intrinsic GaN prior to intentionally introducing dopants into GaN for conductivity modulation. However, as previously mentioned, unintentionally doped GaN tends to be n-type, which has been attributed to nitrogen vacancies [1,16] and residual oxygen [17] impurities. Recent electron irradiation experiments suggests that the background electron concentration cannot be due to nitrogen vacancies as this defect forms a level at 65 meV below the conduction band edge [18]. For comparison, the thermal activation energy(s) of electrons from the donor level(s) to the conduction band edge in unintentionally doped GaN is typically less than 37 meV [19]. Another challenge with GaN growth is the lack of a cheap and lattice matched substrate. C-plane (0001) sapphire and a-SiC are the most conmmon substrates with a lattice mismatch of 16 and 3%, respectively [20]. The resulting strain necessitates the use of GaN or AIN nucleation (buffer) layers prior to growth of high quality GaN epitaxial layers with high electron mobility, specular surface morphology and low background electron concentration. Conductivity modulation can be achieved in GaN by doping with donors such as Si, O and Ge or with acceptors such as Mg, Zn and Be. Si and Mg are primarily the n-type and p-type dopants of choice, respectively. Si-doping has been successfully used to produce films with free electron concentrations from the low 10^^ to the mid 10^^ cm~^ with almost complete room temperature donor activation. Furthermore, Si-doped GaN can routinely be grown with a bulk electron mobility above 300 cm^/V-s at modest doping densities. However, cracking of thicker films (>1 |xm) has been observed in heavily Si-doped films when the doping density exceeds 10^^ cm~^. The cracking has been attributed to the smaller ionic radius of Si"^ (0.41 A) compared to Ga^ (0.62 A) [19]. Unfortunately, the story is less encouraging for p-type GaN. The

Dopants in GaN

Ch.2

19

maximum reproducible hole concentration achieved in p-GaN with conventional doping techniques barely exceeds 10^^ cm~^ without compromising the surface morphology. Furthermore, the deep nature of the Mg acceptor (Ey > 170 meV) leads to a poor room temperature hole activation of several percent. This leads to the use of excessively high Mg-concentrations above the mid 10^^ cm~^ for heavy p-doping. The high Mg concentration degrades the hole mobility; often to below 10 cm^/V-s. This results in quite resistive (typically >2 ^-cm) p-GaN epilayers and devices exhibiting large series resistances and poor contacts. 3. Experiment It is important to understand both the electrical and optical properties of GaN, due to the tremendous potential for GaN in both the electronic and optoelectronic arena. The optical and electronic properties of undoped, n-type and p-type GaN are therefore discussed in detail in this chapter. The discussion relies heavily on Hall-effect measurements and photoluminescence and photoconductivity spectroscopy, which are relatively simple and powerful measurements techniques and as shown in this chapter can yield a wealth of information regarding GaN. 3.1, Characterization Photoluminescence (PL) spectroscopy has been the workhorse of the optical characterization techniques due to its non-destructive nature and ability to yield valuable information about both intrinsic and extrinsic transitions. The latter is important since both defect-related and near bandgap transitions are frequently observed in GaN. The photoluminescence measurements presented in this chapter are performed using singlepass 0.5 m prism monochromator or a 0.32 m grating monochromator. The detectors used were a photomultiplier tube for the visible and UV, while a thermoelectrically cooled InGaAs detector was used for the IR part of the spectrum. The temperature-dependent measurements were performed using a closed-cycle He-cooled cryostat equipped with quartz windows. The UV excitation sources used include a HeCd laser operating at 325 nm, a UV line from an Ar-ion laser at 351.1 nm, and a pulsed (sub ns) N2 laser operating at 337 nm. The IR excitation source (for the Er-doped section) was an InGaAs laser diode operating at 983 nm or a tunable Ti: sapphire laser. The laser spot size diameters were < 1 mm. The PL signals were detected using the lock-in technique and recorded using a computer. Photoconductivity (PC) spectroscopy is another sensitive and non-destructive optical characterization tool. In PC spectroscopy, one measures the change in conductivity between two Ohmic contacts in response to optical illumination. PC measurements can therefore be sensitive to defect-related absorption allowing the investigation of the defect distribution in the 'forbidden' energy gap as well as the absorption near and above the bandgap energy [21]. The PC measurement was performed using co-planar indium contacts spaced about 1 mm apart or interdigitated finger contacts (Ni/Au for p-GaN and Ti/Al for n-GaN) with finger spacing of 3 |xm. Up to 50 V was applied across the samples and the photocurrent was measured across a variable load using a

20

Ch. 2

J.T. Torvik

lock-in amplifier and recorded by a computer. The light source was a tungsten-lamp (GE 1493) or a deuterium light source dispersed by a the prism monochromater and focused onto the samples using quartz optics. The Hall measurement can give useful information about the electrical properties of GaN films such as sheet resistance, carrier concentration and mobility (for example, see [22]). Furthermore, the ionization energy of shallow dopants can be extracted from temperature dependent measurements. The only materials quantity needed is the film thickness assuming uniform transport within the film. However, it is worth pointing out that the experimental setup and contact geometry is important [23,24]. The GaN samples used for the Hall-effect measurement were ~ 5 x 5 mm^ squares with indium contacts at the comers. The Ohmic contacts were checked using current-voltage measurements assuring linearity to avoid depletion effects associated with Schottky contacts. The temperature-dependent Hall data presented in this chapter are obtained using a computer-controlled Hall system equipped with a magnet typically operated at 3500 Gauss. This system is capable of scanning from 80 to 400 K. 3.2. Samples The GaN samples described in this chapter can broadly placed into four categories; unintentionally doped. Si-doped, Mg-doped, and Er-doped. The unintentionally doped GaN includes samples grown by MOCVD and HVPE. Details on the growth and substrate pre-treatments of the 57-74 |xm-thick GaN samples produced by a chloride-transport HVPE are given elsewhere [25]. One of the samples grown by MOCVD is a free-standing unintentionally doped ~100-|xm-thick GaN sample grown using epitaxial lateral overgrowth [26,27]. The sample was semi-insulating and we were therefore unable to determine the carrier concentration and mobility by Hall measurements. The GaN was made free-standing by polishing off the sapphire substrate. These samples typically have a threading dislocation density between 10^ and 10^ cm~^. 'Conventional' 2-|xm-thick GaN films grown by atmospheric pressure MOCVD using GaN buffer layers on sapphire substrates were used for comparison [28]. These films have a typical threading dislocation density of > 10^ cm~^. The Mg- and Si-doped GaN samples used were grown by MOCVD (Mg), MBE (Mg and Si) and bulk platelets (Mg) grown at high temperatures and pressures. The bulk Mg-doped GaN samples used in this study were grown under N2 pressures of 10-20 kbar at temperatures ranging from 1400 to 1700°C from a Ga solution containing 0.1-0.5 at.% Mg [29,30]. The Mg concentration is ^ 10^^ cm"^ and the thickness is ^ 1 0 0 |JLm. SIMS measurements show a typical background oxygen concentration of 10^^-10^^ cm"^. The bulk-GaN typically exhibits a threading dislocation density of

o E To

o

cc

X o o

0.1

• r ^

10

100 1000 Temperature (K)

-I

1

T"

3 4 5 6 1000/T(1000/K)

7

Fig. 15. Left: mobility vs. temperature for a 0.45-(xm-thick 'as-grown' Mg-doped GaN sample grown by ECR-assisted MBE. Right: resistivity (open triangles) and carrier concentration (solid circles) vs. reciprocal temperature for the same sample.

data. A fit to the linear region of the p vs. 1/T region yields a single acceptor level with an activation energy of ~ 110 meV. Although, other authors have reported values of approximately 170 meV [118], this value is consistent with the activation energy reported at high Mg-concentrations discussed above [117]. After discussing both the electrical and optical properties of p-GaN, it is instructive to compare the results. The most obvious feature is the discrepancy between the activation energy measured for the Mg-level responsible for hole conduction (110-200 meV) and the optically determined binding energies ( 1 and for 8 > 2 the first and second axial terms in Eq. 3 differ from zero, respectively. When the symmetry of the magnetic ion site is axial, the symmetry of g tensor should also be axial. For z-axis parallel to c-axis of crystal field the gz = g , gx = gy = g± and generally g 7^ gj_. Therefore, the spin Hamiltonian describing the Zeeman interaction with magnetic field for axial symmetry may be written as [15,16]: p . H . g . S = p • (g Hz8z + gxHx8, + g^Hy8y),

(4)

Similarly, the spin Hamiltonian describing hyperfine interaction for axial symmetry may be written as [15,16]: S • A • I = A 8zlz + Aj.8xlx + Aj.8yly.

(5)

From the above it is evident that in case of axial crystal field and 8 = 1/2 the spin Hamiltonian may be written as a sum of Eqs. 4 and 5. All elements forming group III nitrides have non-zero nuclear spins and quite large magnetic moments (see Table 1). Therefore, the hyperfine interactions in these compounds results in splitting or broadening of resonance lines (Fig. 1). So far, the superhyperfine interaction of unpaired electrons in GaN has not been visible in E8R spectra. The crystal field approach to resonance problems, described above, may be successfully used for many impurity atoms or native defects, for which the unpaired electrons are localized in the inmiediate vicinity of the lattice site occupied by them. In contrast to

82

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Table 1. Nucleus

M. Palczewska and M. Kaminska

Nuclear properties of elements creating group III nitrides Natural abundance

Nuclear spin

Magnetic moment PN

Electric quadrupole moment (|e|-10-24 cm^)

3 3/2 5/2 3/2 3/2 9/2 9/2 1

1.8006 2.6880 3.6385 2.0108 2.5549 5.4960 5.5072 0.40357

0.086 0.040 0.150 0.168 0.106 0.846 0.861 0.0193

(%) lOg iiB 27 Al

^^Ga 7^Ga

''Hn ''Hn 14N

19.8 80.2 100 60.1 39.9 4.3 95.7 99.63

these deep centers, there is another group of defects — so-called shallow impurities, for which electron density is strongly delocalized, and energy levels are very close to the band gap edges. Shallow impurities generally contribute to extra carriers, electrons or holes, in semiconducting crystals. The resonance properties of the unlocalized carriers are determined largely by the energy band structure of the host lattice [4]. Non-localized electrons may exist either in the conduction band or in an impurity band. The latter is formed by overlapping of donor wave functions at high defect concentration. The detailed calculation of the band structure in semiconductors is not simple, therefore semiempirical approximation, namely the k p perturbation theory, have been developed [18,19]. It allows to obtain the expressions for energies and wave functions of conduction electrons in the vicinity of a semiconductor band extremum. According to theoretical predictions based on the k p calculation in frame of five-band model for a cubic direct-gap semiconductors, the g value of conduction band is given by the expression (3) in [20], which after some simple transformations may be written in the following form: A _ 1= _ ^ ( ^0 . go 3 VE^iEo + Ao)

A\ ( £ ; - Eo){E'^ - Eo - A'^) J '

^^

where go is the free electron g value equal to 2.0023. The meaning of the rest of the symbols used in Eq. 6 can be easily read from Fig. 2, in which the band structure at F point for a cubic direct-gap semiconductor, limited to energy bands involved in the five band k p calculations, is schematically shown. In agreement with notation in Fig. 2, Eo is the r^ - r^ gap, Ao is the valence-band spin-orbit splitting (AQ = F^ - Vj), AQ is the conduction-band spin-orbit splitting (AQ = F^ - F^), EQ is the F^ - F^ gap. The energies origin is taken at the top of F^ band. The energies P^ and ?'^ = X^P^ describe couplings of the conduction band with the valence band or the upper conduction bands, respectively. For wide band-gap crystals, the spin-orbit splittings AQ and AQ are much smaller than the energy gap EQ. Therefore, they may be neglected in the denominators of Eq. 6, which becomes simplified to:

Magnetic resonance studies of defects in GaN and related compounds

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83

Fig. 2. Schematics of the energy bands structure near F point in a cubic direct-band semiconductor. Only energy bands involved in the five band k-p calculations of the conduction electrons g value are shown.

For wurtzite type crystals, like GaN, the procedure described above, leading to Eq. 7, allows to compare theoretically predicted g value of unpaired electrons only with average g value derived from ESR measurements. Moreover, merely few parameters (Eo, EQ and AQ) present in Eqs. 6 and 7 have been determined experimentally for GaN crystals. Values of the remaining parameters ( AQ, P^ and X) may be only estimated from comparison with the respective parameters of other semiconducting compounds. In a case of shallow acceptors, their resonance properties are determined mainly by the valence band structure. In cubic A^B^ compounds the spin-orbit interaction leads to the splitting of the valence band into three bands. Two of them, the light-hole band Eg and heavy-hole band T\, are degenerated at k = 0, and marked as T\ in Fig. 2. The third one, Fy band lies AQ below the Fg bands (see Fig. 2). Therefore, a hole ground state at k = 0 is fourfold degenerated (including spin) and it may be described by total angular momentum J = 3/2. The degeneration of the valence band at k = 0 is related to the symmetry of the lattice structure, and it may be lifted (except for spin) by applying uniaxial stress. The resonance transitions between Zeeman splitted levels of two doublets are then possible. Real crystals are commonly strained, what leads to spontaneous lifting of the valence band degeneration. However, randomness of the intemal stress directions causes broadening of the ESR lines [4,5], and magnetic resonance signals are difficult to be detected. An axial component of the wurtzite crystal structure splits the valence band, lifting its degeneracy at k = 0. This splitting, generally much higher than induced by random strain, makes the observation of a hole state resonance transitions possible. The uppermost valence band has F9 symmetry and two lower bands transform as F7 [21]. For a hole being lighdy bound to a shallow acceptor, the predicted values of g factor are highly anisotropic: g (F9) = 4.0 and gi. = 0 [22]. Reduction of g (F9) value.

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experimentally observed in some cases [22], was assigned to partial hole localization. The gj. = 0 value is recognized as a fingerprint of an effective mass-like acceptor [22]. 2.2. Experimental technique In this part, only brief description of magnetic resonance techniques is given, especially with intention of helping readers not familiar with such experimental methods. For deeper understanding, and in order to get more details it is recommended to look into monographs on ESR [4,14-17,23] or ODMR [8,24] methods and results of studies on defects performed by use of them [2-8,25]. As mentioned above (Section 2.1), in ESR experiment the resonance absorption of electromagnetic radiation causes electron transitions between energy levels to split in magnetic field. From simple resonance condition (Section 2.1) it follows, that higher radiation frequency requires higher magnetic fields. Generally, it is possible to use any frequency in ESR experiment. However, at lower frequencies sensitivity of ESR method decreases, and also the corresponding resonance magnetic field may become comparable with the field at electron place caused by surrounding nuclei with nonzero magnetic moments. Therefore, typically used microwave frequencies are of about 10 GHz (X-band), 23 GHz (K-band), 35 GHz (Q-band) and recently also of about 100 GHz (D-band). Usually microwave sources can only be tuned within a very narrow range of frequencies, so the resonance conditions in ESR experiment are conmionly met by varying the magnetic field. Investigated samples are placed in a microwave cavity, where standing microwaves may be created in order to enhance the magnetic field amplitude Hi of the microwave radiation. The magnification factor of the unloaded cavity is defined as [15]: (mean stored energy) power dissipated in cavity

ITTVQX

Typical values of Qo-factor are of the order of about 5 x 10^. Introduction of any sample to a cavity causes increase of power loss, even out of resonance. This power loss clearly results in a loss of sensitivity due to a decrease of cavity Q-factor. Frequently, using small size samples (in comparison with the cavity dimensions) may minimize this problem. Sometimes the specific loss of the sample itself is large (e.g. metallic samples) and in such case the substantial loss of sensitivity is difficult to avoid. During ESR experiment, microwave source is tuned to resonant frequency (VQ) of the applied cavity, and this frequency is kept constant while the magnetic field is varied. For the magnetic field meeting resonance condition, microwave power is absorbed by unpaired spins, which leads to a decrease of the cavity Q-factor. This can be described by the imaginary (absorptive) part x" of the sample magnetic susceptibility. On the other hand, the resonant frequency of the cavity changes when the magnetic field is tuned through the sample resonance condition, allowing an evaluation of the real (dispersive) part x' of the magnetic susceptibility. Both methods of resonance observation: changes in cavity Q-factor {x''W\) or changes in cavity frequency ix'^i) may be used, depending on the way of the microwave circuit is adjusted. The first approach is usually preferred.

Magnetic resonance studies of defects in GaN and related compounds

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85

In most cases in ESR experiments, high sensitivity and good resolution are achieved by means of so-called phase-sensitive detection, associated with appropriate magnetic field modulation. In such a method, high frequency modulation is applied (typically 100 kHz) to magnetic field slowly changing across the absorption line, causing the magnetic field to oscillate around the mean instantaneous value. The receiver is only sensitive to signals of the same frequency and phase as the high frequency magnetic field modulation, and any signals that do not meet these requirements are suppressed, leading to improve sensitivity. Such detection method permits the recording of the derivative of the microwave power absorption with respect to the magnetic field, and thereby improves the resonance line resolution. It is especially useful when the separation between absorption lines is of the order of the line widths. At resonance, transitions between the two electron levels occur in both directions: upwards caused by energy absorption and downwards accompanied by energy emission. Thus, under thermal equilibrium conditions, for much lower electron population at higher energy level, upward transitions prevail, and it results ii;i microwave energy absorption. However, when electrons remain sufficiiehtly long time at the excited level, such situation leads to saturation of microwave absorption and therefore magnetic spins can absorb no more power. / It is obvious, that for ESR method it is useful when the resonance lines are narrow, because it helps to detect ESR active centers as well as increases sensitivity of the method. In ESR experiments a line broadening may be caused by many different processes such as: dipolar spin-spin and exchange interactions, unresolved hyperfine and superhyperfine structures, inhomogenity in the crystal structure and poor uniformity of the applied magnetic field. Only the last contribution to the line broadening is controllable, and may be decreased through high uniformity of the magnet gap field. The remaining contributions are caused by nature of crystal and defects under examination themselves and cannot be avoided. In real crystals, electron spins may also interact with lattice vibrations (phonons) what allows them to lose energy by non-radiative processes, characterized by spin-lattice relaxation time Ti. From Heisenberg's uncertainty principle it follows that shorter lifetime leads to larger energy uncertainty and as a consequence wider resonance lines. Therefore, many ESR experiments, especially for semiconductors, are performed at low temperatures in order to diminish interactions with lattice as well as to reduce the undesired electrical conductivity of some semiconductors. This results in longer relaxation time Ti and narrower resonance lines. On the other hand, however, electrons remaining longer at excited level may cause saturation, which leads to reductions of the observable signal and distorts the absorption shape. In some cases decrease of microwave power level allows to avoid problems with the signal saturation. In ODMR experiment, resonance transitions are observed through their influence on luminescence processes in crystals. Similarly to a conventional ESR technique, in ODMR experiment sample is placed in a cavity resonator, in uniform magnetic field. The resonator walls must provide possibility to excite the sample with a laser beam, and to get the emission light back with minimal degradation of the microwave performance. The incident microwave power is switched on and off with audio frequency (100 Hz to 5 kHz), and a lock-in amplifier is used to detect any changes in the emission properties

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that are induced when the magnetic field is adjusted for resonance during its slow sweep through the appropriate range. Similarly as in ESR experiment, ODMR measurements are usually performed at low temperatures. 3. Nitride crystals The group III nitride crystals can exist in two basic structures: wurtzite and zincblende. The nearest neighbors of each atom, group III metal as well as nitrogen, create exactly the same surroundings in both structures. Each metal atom is enclosed in tetrahedron of four N atoms, and each N atom is enclosed in tetrahedron of four metal atoms. The difference between wurtzite and zincblende structures consists only in different stacking sequence of tetrahedral bounded group III metal-nitrogen bilayers. As a result, the local atomic environments are nearly identical, while the overall synunetry of the hole crystal is determined by the stacking periodicity. This difference can best be visible when one looks at the nitride crystal along a chemical bond direction: [111] in the case of zincblende structure or equivalently [0001] (c-axis) in the case of wurtzite one. As it is shown in Fig. 3, for wurtzite structure (Fig. 3b) the three nearest neighbors of metal atom, located at one end of this bond, are aligned with the three nearest neighbors of nitrogen atom placed at the opposite end of the bond. Differently, in the zincblende structure (Fig. 3a) the three nearest neighbors of metal atom are rotated by 60° in relation to the three nearest neighbors of nitrogen atom. Let us now compare two possible adjacent positions of an impurity atom substituting for one of components of nitride compound (in Fig. 4 one can trace it for an impurity atom substituting for Ga atom). In the zincblende structure, such two lattice positions are equivalent. In the wurtzite structure, rotation by 60° around [0001] direction for an impurity atom, placed at one of the sites together with its four nearest neighbors, is necessary in order to make it crystalographically equivalent to an impurity atom placed at the second site. These two sites are magnetically distinguishable for ions with electron spin above 3/2. In the mathematical formalism of spin Hamiltonian, distinction between

{111}

{0001} Fig. 3. Bonding between metal III and nitrogen atoms in adjacent planes for zincblende (a) and wurtzite (b) structures. The three tetrahedral bonds are 60° rotated in zincblende structure and they are aligned with each other in wurtzite structure.

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87

O Ga •

(a) Fig. 4.

N

(b)

The zincblende (a) and wurtzite (b) structures.

these two types of sites in the wurtzite structure is described by connection of each site with its own set of cubic axes (see Section 2.1, Eqs. 2 and 3). So far, all existing experimental results indicate that transition metal impurities substitute for the Ga ion in GaN structure and the angular dependencies of their resonance lines display the synmietry of the substitutional site. Gallium nitride and aluminum nitride crystals, grown by different techniques, are mostly of the wurtzite structure, although zincblende crystals can be obtained by epitaxial growth on silicon or gallium arsenic substrates under special conditions. For boron nitride a stable phase has the zincblende structure. 4. Resonance studies 4.1. Shallow donors As-grown undoped GaN epitaxial thin films, as well as single bulk crystals, are conmionly n-type conductive with the concentration of electrons ranging typically from 10^^ to a few times 10^^ cm~^ The residual donor has not been positively identified up to now, and defects of either intrinsic or extrinsic origin have been proposed as the source of high free carrier concentrations. For many years, the n-type conductivity of GaN has been commonly associated with presence of nitrogen vacancy [26,27], because of typical gallium-rich growth conditions of GaN. However, residual oxygen [28] and silicon [29] have also been proposed as prime candidates. Both silicon and oxygen contamination are difficult to avoid. Moreover, silicon has been commonly used as the intentional donor dopant and free electron concentration up to the 10^^ cm~^ range has been achieved [30]. One of technique, which could shine some light at the origin of dominant shallow donor defect in GaN, is ESR. First results of GaN studies by means of ESR measurement were published in 1993 for wurtzite [31] and zincblende [32] type structures.

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M. Palczewska and M. Kaminska

In [31] authors measured unintentionally doped thin GaN films of wurtzite structure, with carrier concentrations 0) indicated electron configuration d^ [62]. Therefore, this ESR spectrum was attributed to the trace impurity of nickel in the charge state 3+, substituting for Ga ion in GaN structure [62]. In an electric field of cubic symmetry, the ground state of a free Ni^+ ion C^F) splits into two orbital triplets, ^^2 and "^Ti, and a ground-state orbital singlet, ^Ai [14]. Trigonal component of the crystalline field, present in GaN structure, together with the spin-orbit interaction caused splitting of the '^A2 ground state into two Kramers doublets. In such case the ESR spectrum can be described by the spin Hamiltonian shown in Eq. 3 and Eq. 4 (see Section 2.1), which for S = 3/2 will take a shorter form [62]: H = g pHzS, + gxP(HxSx + HySy) + D [S,^ - 1/3S(S + 1)]

(8)

The z denotes c-axis of the crystal. The parameter D characterizes the axial crystal field (wurtzite structure). For strong zero-field case, it means that the magnitude of zero field splitting 2D is much larger than the microwave energy at X-band frequency, and only transitions within the lowest Kramers doublet can be observed in ESR experiment. Therefore, the spin Hamiltonian described in Eq. 8 can be transformed as [62]:

// = g'pH,s; + gip(Hxs; + Hys;) where g' is the effective g value, and S' is an effective spin S' = 1/2. The spin Hamiltonian above has no hyperfine term, because nickel has only one stable isotope ^^Ni of natural abundance 1.13% having non zero nuclear spin, I = 3/2. The angular dependencies of Ni^"^ ESR lines, calculated using spin Hamiltonian described in Eq. 8 with parameters S = 3/2, g = gx = 2.10 and D = 2 cm~^ are in good agreement with experimental data [62]. An analogy was revealed between the spin Hamiltonian parameters of Ni^+ ions in GaN and ZnO crystals [62]. Similarly, such analogy was pointed out for Fe^"^ and Mn^"*", also in GaN and ZnO. Such comparison is plausible, because both crystals have the same hexagonal (wurtzite) structure and close physical parameters [60-62]. Authors of [62] could not completely exclude that the anisotropic ESR line, described above and attributed to Ni-^"^ ions in GaN layers, might in fact be connected with the presence of another impurity, isoelectronic to Ni^"*", e.g. Fe^ or other ions of 4d^ or 5d^ configuration. These doubts were justifiable since no hyperfine interaction was observed in the ESR spectrum [62]. Also, Ni in the measured samples was not an intentional impurity. Very recently, the ESR spectra of Er^"*" ions in bulk wurtzite GaN crystals were obtained [63]. Erbium is a metal of rare earth (RE) group with unfilled 4f shell. These unpaired 4f electrons of Er^"*" are screened by closed outer shells of 5s and 5p electrons, what reduces the crystal field interaction on 4f electrons. In such case, so-called weak crystal field approximation can be used, since the interaction of 4f electrons with surrounding ligand ions is weaker than the spin-orbit coupling, and the ground state can be described in terms of the total angular momentum quantum number J. In general, crystal field can partially remove the degeneracy of (2J -f- 1) states. For ions with an

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M. Palczewska and M. Kaminska

odd number of electrons, the crystal field lifts such degeneracy completely, except for the twofold degeneracy imposed by Kramers theorem, so that the levels consist of (J -f 1/2) doublets. However, magnetic field raises Kramers degeneracy completely and ESR may be observed. This is not always the case for ions with an even number of electrons, for which the ground state may be an orbital singlet with energy distance to first excited level too large for ESR [14,15]. The ESR method can be very useful to determine the local-site symmetry of RE impurity in a crystal structure. The main reason of it arises from large spin-orbit coupling of the RE ion, compared to the crystal field effect. It leads to large difference between the g factor of free electron (equal to 2.0023) and the g values obtained for unpaired electrons of RE ion incorporated into crystal lattice [64]. These values are characteristic of the nature of the crystal field and differentiate between various possible sites of RE impurity in crystal structure. For RE ions with 4f electrons shielded by 5s and 5p shells, splitting of the free electron ground state by the crystal field is determined approximately by the electrostatic crystal field point charge model, and depends on its strength and symmetry [65]. Therefore, a comparison of g value obtained in experiment with the g values expected for different possible sites in crystal structure allows determining the way of RE incorporation. In some cases, a small correction in g value of RE ion due to covalency effects should be taken into consideration [66]. The electronic configuration of Er^^ ion is 4f^^ with a ground state "^115/2. In a cubic field, the sixteenfold degeneracy splits into three Eg quartets and two doublets r6 and r7 from which either r6 or FT state corresponds to the lowest level of Er^"^ in tetrahedral coordination [65]. Theoretically predicted g value for F^ state is 6.8, while it is 6.0 for F7 doublet state. A ground state of substitutional Er^"^ ion on a metallic site surrounded by four anions is of F7 nature [67]. A hexagonal structure can be treated as a cubic one, modified by an extra axial electric field. If this field is small in comparison with the cubic interactions, an average g factor gav = l/3(g 4- 2gj_), obtained from experiment, can be compared with theoretical predictions made for the cubic type of local symmetry [68]. The ESR spectrum of wurtzite bulk GaN crystals revealed a single anisotropic line, with visible much smaller eight lines of hyperfine structure (see Fig. 11). Therefore, the observed resonance signals were assigned to Er^"^ ions, which consisted of ^^^Er isotope of nuclear spin I = 7/2 and natural abundance of 22.9%. The observed lines were the only ESR fines seen in the whole range of applied magnetic field (up to IT). The ESR spectrum could be described by an effective axial spin Hamiltonian (see Eqs. 4 and 5 in Section 2.1), which contained terms due to electron Zeeman splitting and hyperfine interaction of effective spin S = 1/2 with ^^'^Er of I = 7/2: H = pH(g Sz cos © + g^Sx sin 0 ) + A Szlz + Aj.(SxIx + Syly) where z is parallel to the c-axis of the crystal. The obtained angular dependence of g value is shown in Fig. 12, where solid line was calculated for the best fitted parameters, listed in Table 2. For Er-^"^ ions in GaN crystals, the ratio (A_L g /A gx) is equal to 0.99, what indicated that the first excited state of Er^+ was sufficiently distant from the ground level, and first order theory approximation including only matrix elements within a J = 15/2 manifold gave quite good agreement with the ESR experiment.

Magnetic resonance studies of defects in GaN and related compounds I

I t I

I

I

I I I ; I

I I I

I

I I I t I I I I

*

210

•

'

*

220

'

I » I

I I

I

-3* wurtzite bulk GaN : Er

200

I I

*

Ch. 4

101

I I

(a)

•

•

230

•

•

*

'

•

•

240

•

'

'

250

260

magnetic field [mT] I •! I I I I

' I [

I

' ' '

' I ' ' • ' I

' • '

'

I

wurtzite bulk GaN : Er

H I c, X-band. T = 6 K 60

70

80

90

100

110

120

magneticfield[mT] Fig. 11. The ESR spectra of Er^+ ions in GaN bulk crystals measured at 6 K for magnetic field parallel (a) and perpendicular (b) to c-axis.

Knowing values of the g factor for Er^+ ions, gav value was determined for GaN crystals, assuming that the crystal field is mainly of cubic type with a small hexagonal contribution. The gav value was equal to 6.05, and it was close to the predicted value for a ground state of T-j symmetry, what indicated Er substituting for Ga in GaN

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M. Palczewska and M. Kaminska

60

70

80

90

e [degrees] Fig. 12. Angular dependence of Er^"^ g factor in GaN bulk crystals. The solid line was calculated using the relation g^ = g^cos^0 + g^^sin^© with g = 2.861 and gx = 7.645, where 0 is the angle between the magnetic field and the c-axis.

Structure. Therefore, ESR experiment determined that Er impurity in bulk GaN crystals was mostly isolated one, and it occupied the Ga site. It seemed puzzling, however, that no traces of ESR lines coming from Er~0 complexes were observed, although there was a strong evidence of oxygen presence in the investigated crystals. Such complexes have been observed with ESR technique in other semiconductors like Si and GaAs [63]. 4.5. Electron-irradiated GaN As it clearly comes out from the previous parts of this chapter, our knowledge about defects in GaN is still insufficient, despite of great efforts undertaken for defect studies in the last years. The hope is that electron irradiation of GaN crystals may help to understand the role and properties of intrinsic defects present in this material. Recently, ODMR studies of as-grown and electron-irradiated MOVPE wurtzite undoped GaN layers on sapphire substrates have been performed [69,70]. Before irradiation, three distinct PL bands at 3.47, 3.27 and 2.2 eV energy and two ODMR signals originating from EM shallow and DD deep donor defects in 2.2 eV PL band were observed, what is typical of high quality n-type GaN layers (see Sections 4.1 and 4.2). After irradiation with 2.5 MeV electrons, the two higher energy PL bands vanished completely, and the 2.2 eV band decreased about 15 times. Nevertheless, the same two ODMR lines could still be weakly detected via the 2.2 eV PL band [69]. Simultaneously, at least two overlapping PL bands appeared with maxima at about 0.85 and 0.93 eV. ODMR studies in the higher energy range (above 0.88 eV) revealed three new anisotropic spectra labeled LEI (g = 2.004 ± 0.001, gx = 2.008 d= 0.001), LE2 (g = 1.960 ± 0.002,

Magnetic resonance studies of defects in GaN and related compounds

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103

g_L --2.03) and LE3 (gj. = 2.002 ± 0.005, ^^A_L = (1580 ± 50) MHz). For lower light energy (below 0.83 eV), apart from LEI and LE2, an additional new ODMR signal LE4 (g = 2.050 ± 0.002, gx -1.97) was observed [69]. All four ODMR signals had electron spin S = 1/2. An additional structure of ODMR signal was observed only for LE3 defect. Its angular dependence has been successfully simulated in [69] as arising from hyperfine interaction of electron spin S = 1/2 with the two naturally abundant Ga isotope atoms of nuclear spin I = 5/2 (see Table 1). Therefore, LE3 defect was at first tentatively assigned to a displaced Ga atom, either in interstitial or antisite position, isolated or complexed with another defect [69]. Unfortunately, subsequent annealing studies of electron irradiated GaN layers performed in [70] have not confirmed such defect model and authors of [70] are not certain about origin of the LE3 defect at present. 5. Resonance studies of AIN and BN Much less of magnetic resonance studies have been undertaken for other nitrides than GaN. Therefore, the knowledge of ESR or ODMR active defects in these compounds is rather poor up to now. The results of performed investigations of different nitride compounds are presented in short below. The data obtained for mixed AlGaN crystals are followed by discussion of results for AIN, and in the end-magnetic resonance studies of BN are sunmiarized. A similar single anisotropic resonance line to the one originating from EM donors in GaN was observed in a series of mixed wurtzite AlxGa(i_x)N crystals grown on 6H-SiC substrates by MOCVD method, where the Al mole fraction x changed from 0 to 0.26 [33]. The ESR linewidth did not vary appreciably with x, indicating good homogeneity of thin films studied. For all AlxGa(i_x)N samples, the same degree of anisotropy (g — gjL4) ~0.002-0.003 was found. The measured average g values changed linearly from 1.95 to about 1.963 for Al mole fraction x varying from 0 to 0.26 [33]. Calculations of the donor average g value for mixed AlxGa(i_x)N crystals were also done, on the base of a simple five-band k p approximation [33] (Eq. 7, Section 2.1). For such crystals, the value of energy gap EQ was taken from respective spectra of optical absorption measurements. The difference (EQ—EQ), which according to theoretical calculations weakly depends on x, was assumed equal to 5.5 eV, the value for GaN [33]. On the other hand, (since Ga spin-orbit splitting is much larger than Al) the spin-orbit splitting of the r^ conduction band, AQ, primarily due to cations, was taken to be equal to 0.25 (1 — x) eV, where 0.25 eV is AQ value for GaN [33]. For the spin-orbit splitting of the valence band, AQ, most of all due to anions, a constant value was used, equal to 11 meV as determined from optical studies for GaN [21]. The parameters P^ and \^ were assumed equal to 17 eV and 0.4, respectively, consistently with their values obtained for other III-V and II-VI semiconductors. The authors of [33] assumed that both of these parameters were constant for the whole range of measured Al composition in mixed AlxGa(i_x)N crystals. The calculated average g factors for different values of Al mole fraction in the thin films under study were in a good agreement with the experimental data discussed above [33]. Polycrystalline wurtzite AIN ceramics containing 10 ppm of Cr impurities were

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studied using ESR and photoluminescence methods in [71]. Their ESR spectra revealed a sharp isotropic signal of g = 1.9970, associated with a distinctive resolved hyperfine structure containing 4 much weaker lines with a hyperfine coupling constant A = 1.907 mT. The number of hyperfine components and their intensity in relation to the central line (equal to about 10%) were consistent with the isotope ^^Cr (I = 3/2, 9.5%). The authors of [71] assigned the chromium impurity of d^ electron configuration, i.e. Cr^"^, as most likely explanation for the observed ESR signal. The isotropy of the central resonance signal (g = 1.9970) ascribed to ^E (D) ground state of Cr^"^ ion indicated that the ^E trigonal field splitting due to AIN wurtzite axial field was small and comparable to the splittings induced by random strains in crystal. After fast neutron irradiation the Cr^"^ ESR signal nearly vanished, what was explained as a result of creation of nitrogen vacancies in AIN structure [72] leading to a change of Fermi level, and as a consequence to a change of Cr charge state (from Cr^+ (3d^) to Cr'^^ (3d^)) [71]. ESR signal assigned to electron trapped at N^~ vacancy was observed for neutronirradiated polycrystalline AIN samples [73]. A broad line of g value equal to 2.007 ± 0.001 and a width of about 7.7 mT was observed already at room temperature. Its shape was similar to the Gaussian one with an exception of the tails, as usually seen for F-type centers [73]. The line shape and its broadening were explained in [73] by the unresolved hyperfine interaction of electron trapped in the nitrogen vacancy (S = 1/2) and nuclear spin of its closest neighbors, i.e. four nearest aluminum nuclei (I = 5/2, see Table 1). A hyperfine constant, equal to A = (10.9 ± 0.5) x 10""^ cm~\ was determined [73]. Very recently, single AIN crystals coming from different suppliers were studied using ODMR method [70,74]. The crystals were not intentionally doped, but most of them contained oxygen and carbon as unintentional impurity, and a few samples might also have been contaminated with bismuth, titanium, vanadium or chromium at different concentrations in particular crystals. The authors of [74] observed many strong, well-resolved anisotropic ODMR signals in visible luminescence for this set of as-grown AIN crystals, and could distinguish twelve different defect centers. For all observed ODMR lines the spin Hamiltonian parameters were determined [74]. Unfortunately, the absence of any resolved hyperfine structure for most centers except one, (named D5) did not allow for chemical identification of the impurity involved. The ODMR line of D5 center with electron spin S = 1/2 displayed an anisotropic flat-topped shape that was simulated quite well by including an anisotropic hyperfine interaction with impurity atom of 100% abundance and nuclear spin I of 7/2 > I > 3/2. This D5 center was tentatively assigned to a displaced aluminum ^^Al host atom of some kind [74]. However, the D5 spectrum indicated some similarity to ESR signal observed for neutron-irradiated polycrystalline AIN samples and attributed to a nitrogen vacancy [70,73]. BN films studied by ESR in [75,76] were grown by RF diode sputtering from a hexagonal BN-target in nitrogen atmosphere and it was found that layers produced by lower N2 partial pressure had a zincblende structure. The ESR spectra consisted of a single line with unresolved hyperfine structure and Gaussian shape. Its isotropic g-value changed a little, depending on N2 partial pressure, between 2.0024 and 2.0029 and was equal to 2.0025 ± 0.0004 for cubic BN films. The linewidth also changed with N2

Magnetic resonance studies of defects in GaN and related compounds

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105

partial pressure and was equal from 3.1 to 1.7 mT. The concentration of paramagnetic defects were found to depend on partial pressure of N2 and therefore ESR signal was assigned to nitrogen vacancy, expected in such films in a variable concentration [76]. Similar isotropic single ESR line was also observed in undoped zincblende BN crystals by other authors [77]. Its peak-to-peak width was 2.7 mT and the g value was 2.00248, very close to the parameters of ESR Hne reported in [75,76]. Interesting studies of highly defective metastable wurtzite phase of BN were performed in [78]. Heat treatment of such BN led to phase stabilization process: wurtzite BN-zincblende BN. By means of ESR it was found that this thermal treatment is accompanied by at least one order of magnitude decrease in concentration of paramagnetic defects. Unfortunately, the authors of [78] did not give any parameters of the observed ESR signal. 6. Summary In this chapter an attempt was made to present the main achievements of magnetic resonance studies on defects in nitride compounds. In spite of huge amount of work performed on nitrides, especially in the last 5 years, not too much has been clarified in the area of defect identification. One of the main reasons is difficulty to obtain bulk nitride crystals, the best materials for ESR studies, because of technological problems in growing them. The best knowledge has been achieved for GaN. The ESR signal due to shallow donor characteristic for MOCVD grown GaN is well established. Its parameters are the same for undoped n-type as well as Si-doped layers. However, it has not been definitively proved that Si is the main shallow donor defect in MOCVD-grown GaN. Signal coming from shallow donor in bulk GaN of slightly different parameters has also been identified. In this case oxygen nature should be strongly considered as possible origin, since bulk GaN suffers from oxygen contamination. Two different deep donors have been found by ODMR in GaN layers but no suggestion about their nature has come yet. On the other hand, quite clear situation is in the area of two main acceptors of GaN, namely Mg and Zn. Their magnetic resonance spectra have been positively identified and found to follow the well known process of hydrogen passivation and its diffusion out of acceptor centers. Transition metal impurities, common trace impurities of many semiconductors, are far from being known in GaN when it comes to their magnetic resonance properties. Up to now ESR spectra of only manganese Mn^"^ (3d^), iron Fe^"^ (3d^), nickel Ni^"^ (3d^) and recently erbium Er^"^ (4f^^) have been published. The studies of electron-irradiated GaN have not come up to expectations and have not led to positive identification of any of hoped-for simple native defects. Even much less is known about magnetic resonance-active defects in AIN and BN. For mixed AlxGai_xN (0 < x < 0.26) layers ESR signal of shallow donor has been found, but the origin of this donor remains still unknown. Also, ESR spectrum observed for polycrystalline AIN ceramics, containing intentional Cr impurities, has been attributed to Cr^+ (3d^). Finally, in some studies nitrogen vacancy related ESR defects have been suggested in AIN and BN materials. Since it seems that intentional doping of nitrides and studies of such materials have

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just started, one can expect much more yet to come in the area of defect identification in nitride compounds in the coming years. Acknowledgements The authors would like to acknowledge special assistance of the Institute of Electronic Materials Technology for MP during preparation of this work. The paper was also partially supported by the Committee for Scientific Research (Poland) under Grant 7T 08A 031 15 and ITME project No 02-1-1018-9. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

[10]

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Magnetic resonance studies of defects in GaN and related compounds [30] [31]

[32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47]

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III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B. V. All rights reserved

CHAPTER 5

Characterization of native point defects in GaN by positron annihilation spectroscopy K. Saarinen 1. Introduction Gallium nitride exhibits electronic, optical, and thermal properties, which make it a promising material for optoelectronic and high-power devices. Especially, its large direct band gap (3.4 eV) and strong interatomic bonds enable the construction of very efficient blue light-emitting diodes and promise the development of long-lifetime blue lasers. Unfortunately, GaN and related materials are difficult to fabricate. Since lattice-matched substrates for GaN epitaxy are generally not available, dislocation densities as high as 10^^ cm~^ are conmion in overlayers grown by metal-organic chemical vapor deposition (MOCVD) on sapphire. These and other extended defects have been studied extensively (for example, see [1-7] and citations therein). Much less is known about simple point defects such as vacancies and interstitial atoms, although it is likely that they are formed at high concentrations in the crystal growth of GaN. Point defects induce localized electron levels into the band gap of the semiconductor. These states can trap charge carriers, thus inducing compensation, scattering of free carriers, and subsequent change of electrical properties. Moreover, the states interact with light, inducing increase in the absorption or emission photons in radiative recombination processes. For example, the parasitic optical transition leading to yellow luminescence is observed in both GaN bulk crystals and epitaxial layers. The atomic structure of the defect responsible for the yellow emission has been much debated, although even the positions of the electronic levels participating in this optical process have been under discussion [8-11]. The understanding and control of these effects requires both the identification of the defects as well as the characterization of their physical properties. Traditionally the experimental information on point defects has been obtained by electrical and optical characterization techniques, such as Hall measurements and infrared absorption. Although the defects can be detected in these experiments, their atomic structures remain very often unresolved. The methods based on electron paramagnetic resonance (EPR) are more sensitive to the structure of defects, but so far these techniques have given only limited information in GaN materials. An experimental technique is thus needed for the unambiguous defect identification. This goal is reached for vacancy-type defects by utilizing the positron annihilation spectroscopy. Thermalized positrons in solids get trapped by the vacant lattice sites. The reduced electron density at the vacancies increases positron lifetime and narrows the positron-

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K. Saarinen

electron momentum distribution. The detection of these quantities yields direct information on the vacancy defects in solids. Positron lifetime measurements can be used to probe homogeneous defect distributions in semiconductor substrates. This technique is relatively simple to implement, but yet very powerful in identifying the atomic structure of the defect, its charge state and concentration. Defects in the near-surface region 0-3 ^xm can be studied by a monoenergetic positron beam. This technique is well suited for the defect studies of epitaxial semiconductor materials. The information provided by positron experiments is especially useful when combined with those of other spectroscopies. The correlation of positron measurements with electrical and optical methods enables quantitative studies of technologically important phenomena such as electrical compensation, light absorption and photoluminescence. In this chapter we present a brief overview of positron annihilation spectroscopy in Section 2. The goal is to introduce the reader with this technique at the level which is needed for understanding the results in GaN materials. More extensive reviews of the experimental methods can be found in the literature (see [12-16]). The positron results concerning the native defects in GaN bulk crystals are presented in Section 3. The vacancies in GaN layers on sapphire are discussed in Section 4 by summarizing the existing data in samples doped n-type with O or Si or p-type with Mg. The formation of point defects at various growth conditions of GaN layers are reviewed in Section 5. These include studies of stoichiometry, dislocation density and substrate material. Section 6 is a brief sununary. 2. Positron annihilation spectroscopy In this section we review the principles of positron annihilation spectroscopy and describe the experimental techniques. The thermalized positrons in lattices behave like free electrons and holes. Analogously, positrons have shallow hydrogenic states at negative ions such as acceptor impurities. Furthermore, vacancies and other centers with open-volume act as deep traps for positrons. These defects can be experimentally detected by measuring either the positron lifetime or the momentum density of the annihilating positron-electron pairs. 2.1. Positron implantation and diffusion in solids The basic positron experiment is schematically shown in Fig. 1. Positrons are obtained from P+ active isotopes like ^^Na, ^^Co, ^Cu and ^^Ge. The most commonly used isotope is ^^Na, where the positron emission is accompanied by a 1.28 MeV photon. This photon is used as the time signal of the positron birth in positron lifetime experiments. The stopping profile of positrons from p+ emission is exponential. For the ^^Na source (Emax = 0.54 MeV), the positron mean stopping depth is 110 |xm in Si and 40 |xm in GaN. The positrons emitted directly from a radioactive source thus probe the bulk ofa solid [12-16]. Low-energy positrons are needed for studies of thin layers and near-surface regions. Positrons from P^ emission are first slowed down and thermalized in a moderator. This is usually a thin film placed in front of the positron source and made of a material (e.g.

Characterization of native point defects in GaN

Ch. 5

1.28 MeV

111 511±AEkeV

Lifetime t /y\

Angular ^ correlation 180° ± 0

^^Na source Sample Doppler broadening 511keV±AE Fig. I. Schematic figure of positron experiment, where positron is implanted into a sample from ^^Na source. The positron lifetime is determined as a time difference between 511 keV annihilation photons and a 1.28 MeV photon emitted together with a positron from ^^Na. The Doppler shift AE and the angular deviation 0 result from the momentum of the annihilating electron-positron pairs.

Cu or W) which has a negative affinity for positrons. Thermalized positrons close to the moderator surface are emitted into vacuum with an energy of the order of 1 eV and a beam is formed using electric and magnetic fields. The positron beam is accelerated to a variable energy of 0-40 keV and in this way the positron stopping depth in the sample is controlled. The typical positron beam intensity is lO'^-lO^ e"*" s~^ [12-17]. For monoenergetic positrons, the stopping profile can be described by a derivative of a Gaussian function with the mean stopping depth [16,18] x = AE"[kcWl

(1)

where E is the positron energy, A = (4/p) jxg/cm^; n ^ 1.6, and p is the density of the material. The mean stopping depth varies with energy from 1 nm up to a few |xm. A 20 keV energy corresponds to 2 |xm in Si and 0.8 |xm in GaN. The width of the stopping profile is rather broad and the positron energy must be carefully chosen so that e.g. the signal from an overlayer is not contaminated by that from the substrate or surface. In a solid, the fast positron rapidly looses its energy via ionization and core electron excitations. Finally, the positron momentum distribution relaxes to a MaxwellBoltzmann one via electron-hole excitations and phonon emissions. The thermalization time at 300 K is 1-3 ps, i.e. much less than a typical positron lifetime of 200 ps [19,20]. Positron behaves thus as a fully thermalized particle in semiconductors. The transport of thermalized positrons in solids is described by diffusion theory. The positron diffusion coefficient has been measured in several semiconductors by implanting low-energy positrons at various depths and observing the fraction which diffuses back to the entrance surface [21-23]. The diffusion coefficient at 300 K is in the range of 1.5-3 cm^ s~K The total diffusion length during the finite positron lifetime

112

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K. Saarinen

T is L+ = (6D+T)^/^ ^ 5000 A.

(2)

If defects are present, the positron may get trapped before annihilation and this naturally reduces the effective diffusion length. 2.2. Experimental techniques 2.2.1. Positron lifetime spectroscopy Lifetime spectroscopy is a powerful technique in defect studies, because the various positron states appear as different exponential decay components. The number of positron states, their annihilation rates and relative intensities can be determined. In a positron lifetime measurement, one needs to detect the start and stop signals corresponding to the positron entrance and annihilation times in the sample, respectively (Fig. 1). A suitable start signal is the 1.28 MeV photon accompanying the positron emission from the ^^^^Na isotope. The 511 keV annihilation photon serves as the stop signal. The positron source is prepared by sealing about 10 ixCi of radioactive isotope between two thin foils. The source is then sandwiched between two identical pieces (e.g. 5 X 5 X 0.5 mm^) of the sample material. This technique is standard for bulk crystal studies. Pulsed positron beams have been constructed for lifetime spectroscopy of thin layers [24,25], but so far they have not been used much in defect studies. The standard lifetime spectrometer consists of start and stop detectors, each of them made by coupling a fast scintillator to a photomultiplier. The timing pulses are obtained by differential constant-fraction discrimination. The time delays between the start and stop signals are converted into amplitude pulses, the heights of which are stored in a multichannel analyzer. About 10^ lifetime events are recorded in 1 h. The experimental spectrum represents the probability of positron annihilation at time t and it consists of exponential decay components

^

= X^/A,exp[-A,r],

(3)

where n{t) is the probability of positron to be alive at time t. The decay constants Xi — \/Xi are called annihilation rates and they are the inverses on the positron lifetimes x/. Each positron lifetime has the intensity of /,. In practise the ideal spectrum of Eq. 3 is convoluted by a Gaussian resolution function which has a width of 200-250 ps (full width at half maximum, FWHM). About 5-10% of positrons annihilate in the source material and proper 'source corrections' must be made. Due to the finite time resolution, annihilations in the source materials, and random background, typically only 1-3 lifetime components can be resolved in the analysis of the experimental spectra. The separation of two lifetimes is successful only, if the ratio A1/A.2 is > 1.5. Fig. 2 shows positron lifetime spectra recorded in undoped and Mg-doped GaN bulk crystals [26]. Positrons enter the sample and thermalize at the time t = 0. The vertical axis of Fig. 2 gives the number of annihilations at a time interval of 25 ps. In the heavily Mg-doped sample the positron lifetime spectrum has a single component of 165 ± 1 ps at 300 K corresponding to positron annihilations in the defect-free lattice. The

Characterization of native point defects in GaN

Ch. 5

113

GaN • O

Undoped n-type Highly Mg-doped

Fig. 2. Examples of positron lifetime spectra in undoped and highly Mg-doped GaN bulk crystals. A constant background and annihilations in the source materials have been subtracted from the spectra, which consist of 2 X 10^ recorded annihilation events. The solid lines are fits to the sum of exponential decay components convoluted with the resolution function of the spectrometer. The data in the highly Mg-doped sample was recorded at 300 K and it has only a single component of 165 di 1 ps. The spectrum in the undoped crystal was recorded at 490 K and it can be decomposed into two components of xi = 150 ± 10 ps, 12 = 235 ± 5 ps, and h = 48 db 6% [26].

undoped sample has two lifetime components, the longer of which (t2 = 235 ps) is due to positrons annihilating as trapped at native Ga vacancies. For more discussion see Section 3. The experimental results are often presented in terms of the average positron lifetime lav defined as

f ^'(-57)=r *"«=!:'"'•

(4)

The average lifetime is a statistically accurate parameter, because it is equal to the center-of-mass of the experimental lifetime spectrum. Hence it can be correctly calculated from the intensity and lifetime values even if the decomposition represented only a good fit to the experimental data without any physical meaning. For example, the positron average lifetimes in the two spectra of Fig. 2 are 191 ps (undoped GaN) and 165 ps (Mg-doped GaN). The difference is very significant because changes below 1 ps can be reliably observed in the experiments. 2.2.2. Doppler broadening spectroscopy The Doppler broadening spectroscopy is often applied especially in the low-energy positron beam experiments, where the lifetime spectroscopy is usually very difficult due to the missing start signal. The motion of the annihilating electron-positron pair causes

Ch. 5

114 !

•

Positron annihilation in GaN lattice

o

Energy resolution (Sr-85 source)

5

10

T"

\

o O

r

10'

r

°

o

_

O

JJ j ~H H J

-\ H ]

J

\

o o

^

—f-a ~j

\

/ \ /° °\ ••/ oo o \ • •• o oo ••• • o •• o •• •• o •• o • • i ° : o •• o ••\•

\ \

"CB, which is also evident in Fig. 2. Positron annihilation at a vacancy-type defect leads to changes in the momentum distribution p(p) probed by the Doppler broadening experiment. The momentum distribution arising from valence electron annihilation becomes narrower due to a lower electron density. In addition, the localized positron at a vacancy has a reduced overlap with ion cores leading to a considerable decrease in annihilation with high momentum core electrons. Experimentally, the increase of S parameter and decrease of W parameter are thus clear signs of vacancy defects in the samples. As an example, the experimental momentum distribution in the Ga vacancy is indeed much narrower than that recorded in the defect-free GaN lattice (Fig. 4). 2.3.3. Shallow positron states at negative ions A negatively charged impurity atom or an intrinsic point defect can bind positrons at shallow states even if these defects do not contain open volume [31,32]. Being a positive particle, the positron can be localized at the hydrogenic (Rydberg) state of the Coulomb field around a negatively charged center. The situation is analogous to the binding of an electron to a shallow donor atom. The positron binding energy at the negative ion can be estimated from the simple effective-mass theory Eion,n =

13.6eV / m * \ Z^ r— — - T ^ 10 - lOOmeV,

(11)

where s is the dielectric constant, m* is the effective mass of the positron, Z is the charge of the negative ion, and n is the quantum number. With Z = 1-3 and n = 1-4, Eq. 11 yields typically ^ion = 10-100 meV, indicating that positrons are thermally emitted from the Rydberg states at 100-200 K. The hydrogenic positron state around negative ions has a typical extension of 10 A and thus positrons probe the same electron density as in the defect-free lattice. Consequently, the annihilation characteristics (positron lifetime, positron-electron momentum distribution) are not different from those in the lattice. In the experiments we thus get T^ion = "CB, 5'ion = SB and Wion = WB for the lifetime, 5 and W parameters at the negative ions. Although the negative ions cannot be identified with these parameters, information on their concentration can be obtained in the positron lifetime and Doppler broadening experiments [31,32]. 2.4. Positron trapping at point defects 2.4.1. Positron trapping rate and trapping coefficient The positron transition from a free Bloch state to a localized state at a defect is called positron trapping. The trapping is analogous to carrier capture. However, it must be fast enough to compete with annihilation. The positron trapping rate K onto defect D is proportional to its concentration co KD = I^DCD'

(12)

The trapping coefficient fio depends on the defect and the host lattice. Since the

Characterization of native point defects in GaN

Ch. 5

119

positron binding energy at vacancies is >1 eV, the thermal emission (detrapping) of positrons from the vacancies can be usually neglected. Due to the Coulombic repulsion, the trapping coefficient at positively charged vacancies is so small that the trapping does not occur during the short positron lifetime [33]. Therefore, the positron technique does not detect vacancies in their positive charge states. The trapping coefficient at neutral vacancies is typically fjio ^ lO^'^-lO^^ at. s~^ independently of temperature [33-35]. This value means that neutral vacancies are observed at the concentrations > 10^^ cm~^. The positron trapping coefficient at negative vacancies is typically /JLD ^ 10^^-10^^ at. s~^ at 300 K temperature [33-35]. The sensitivity to detect negative vacancies is thus >10^^ cm~-^. The experimental fingerprint of a negative vacancy is the increase of /XD with decreasing temperature [34,35]. The T"^/^ dependence of /JLO is simply due to the increase of the amplitude of the free positron Coulombic wave as the thermal velocity of the positron decreases [33]. The temperature dependence of fio allows to distinguish experimentally negative vacancy defects from neutral ones. The positron trapping coefficient /Xion at the hydrogenic states around negative ions is of the same order of magnitude as that at negative vacancies [32,36]. Furthermore, the trapping coefficient exhibits a similar T"^/^ temperature dependence. Unlike in the case of vacancy defects, the thermal emission of positrons from the negative ions plays a crucial role at usual experimental temperatures. The principle of detailed balance yields the following equation for the detrapping rate 300 K), where the detrapping rate (Eq. 13) is large. 2.4.2. Kinetic trapping model In practise the positron annihilation data is analyzed in terms of kinetic rate equations describing the positron transitions between the free Bloch states and localized states at defects [12,13]. Very often the experimental data show the presence of two defects, one of which is a vacancy and the other is a negative ion. The probability of positron to be in the free state is «fi(0» trapped at vacancies ny{t) and ions wionCO- We can write the rate equations as driB - T - = - ( ^ f i -^KV + KiordriB + ^ion^ion, At

Any

"dT

= KyriB — ^V^y,

(14)

(15)

dnw = KmnnB " (^ion + 5ion)«ion,

(1^)

at where A., K and 8 refer to the corresponding annihilation, trapping and detrapping rates.

120

^^- ^

K. Saarinen

Assuming that the positron at r = 0 in the free Bloch state, Eqs. 14-16 can be solved and the probability of positron to be alive at time t is obtained as 3

n{t) = Wfi(0 H-«v(0 + «ion(0 = X ] ^i exp[-X,r], indicating that the lifetime spectrum -dn{t)/dt positron annihilations at various states are

(17)

has three components. The fractions of

/•OO

r]B =

dtXsnBit)

= 1 - Y}ion - rjv,

dtkynvit)

=

(18)

Jo r)v= f Jo

"^^^^ )^B-\-K:V

-^

,

1 + ^ion/^ic ^.^^

poo

rjion = /

(19)

dr, Xionnionit) =

Jo

7

'^

(1 + ^ion/-^ion) ( Afi + /Cy +

^. .'''"

(20)

)

These equations are useful because they can be related with the experimental average lifetime Xav, positron-electron momentum distribution P(PL) and Doppler lineshape parameters S and W as tav = ^ B T B + ??ion'Cion + rjvTy, piPl)

= r)BpB{PL)

(21)

+ rjionPioniPl)

+ TlvPviPl),

(22)

S = TJBSB + y?ion*5ion + rjvSy,

(23)

W = r?B W5 + r^ionWion + y/vWv.

(24)

Eqs. 18-24 allow the experimental determination of the trapping rates Ky and fCjon and consequently the defect concentrations can be obtained from Eq. 12. Furthermore, these equations enable the combination of positron lifetime and Doppler broadening results and various correlations between Xav, P(PL)^ S and W can be studied. At high temperatures, all positrons escape from the hydrogenic state of the negative ions and no annihilations take place at them. In this case the lifetime spectrum has two components h'

=^~B'-^f^v.

(25)

^2 = '^v,

(26)

h = l-h=

"' Ky -\-

AB

, —

.

(27)

AD

The first lifetime xi represents the effective lifetime in the lattice in the presence of positron trapping at vacancies. Since Ky > 0 and /2 > 0, xi is less than x^. The second lifetime component xi characterizes positrons trapped at vacancies, and it can

Characterization of native point defects in GaN

Ch. 5

121

be directly used to identify the open volume of the vacancy defect. When y/jon = 0 and ^ion/^ion > 1 the determination of the positron trapping rate and vacancy concentration is straightforward using Eqs. 18-24 Kv = IXyCy = A5

= Afi "^V — "tflu

= A^ — Ov ~ O

Wy

--.

(28)

— W

Notice that in this case tav, S and W depend linearly on each others. The linearity of experimental points in the (Xav, S), (Xav, W) and (5, W) plots provides thus evidence that only a single type of vacancy defect is trapping positrons in the samples. 3. Native vacancies and negative ions in GaN bulk crystals Bulk GaN crystals are ideal substrates for the epitaxy of GaN overlayers for optoelectronic components at the blue wavelength. Such material can be synthesized of liquid Ga in high N overpressure at elevated temperatures [37,38]. Nominally undoped GaN crystals show usually high n-type conductivity with the concentration of electrons exceeding 10^^ cm~^. This is most likely due to the residual oxygen atoms acting as shallow donors [39,40]. When GaN is doped with Mg the electron concentration decreases and for sufficiently high amount of Mg dopants the samples become semi-insulating. It is interesting to study how the movement of the Fermi level toward the midgap changes the formation of charged native defects such as the Ga vacancy. Another basic question concerns the mechanism of the electrical deactivation. One can consider either (i) the gettering role of Mg leading to the formation of MgO molecules [41] or (ii) electrical compensation of O j donors by Mg^^ acceptors. In this section we review our recent works [26,29,42,43] and show that Ga vacancy acts as a native defect in GaN crystals. We pay special attention to the identification of Voa by correlating the results of positron experiments with those of theoretical calculations. Our data indicate that the formation of Ga vacancies is suppressed by Mg doping. We show further that most of Mg is in a negative charge state, suggesting that the loss of n-type conductivity is due to compensation of OjJ donors by MgQ^ acceptors. 3.1. Samples and their impurity concentrations The bulk GaN crystals were grown at the nitrogen pressure of 1.5 GPa and temperature of 1500°C [38]. We studied three samples, where the Mg doping level was intentionally varied during the crystal growth (Table 1). The Mg and O concentrations of the samples were determined experimentally by secondary ion-mass spectrometry (SIMS). The absolute concentrations were calibrated by implanting known amounts of O and Mg to undoped epitaxial GaN layers, where the residual Mg and O concentrations were well below 10^^ cm~^ The secondary ion-mass spectrometry indicates that the oxygen concentration is about 4 X 10^^ cm"^ in undoped GaN (Table 1). The concentration of conduction electrons (n = 5 x 10^^ cm~^ at 300 K) in this sample is thus almost the same as oxygen concentration. This is in good agreement with the previous evidence [39,40] that the n-type conductivity of GaN is due to unintentional oxygen doping. In the lightly Mg

122 Table L

Ch, 5

K. Saarinen

The concentrations of impurities and defects in the studied GaN bulk crystals

Sample

Undoped Lightly Mg doped Heavily Mg-doped

Oxygen concentration (cm-3)

Magnesium concentration (cm-3)

Ga vacancy concentration (cm-3)

Negative ion concentration (cm-3)

4 X 10^^ 12 X 10^9 9 X 10'^

1 X 10'^ 6 X 10'9 10 X 10'^

2 x 10*^ 7 X 10^^ 10^^ cm~^ in the undoped samples studied by positron spectroscopy. In fact, the 'undoped' GaN layers are thus heavily doped with oxygen.

Characterization of native point defects in GaN

129

Ch. 5

Mean implantation depth (p,m) 0.09

0.26

0.50

T

0.79

1.13

T

0.47

• GaN(Mg) reference O Und.n=3.7xl0''cm^450K • Und.n=3.7xl0'^cm'\300K 0.46

a

0.45 A A A,

»^

0.44

A A A ^

A

4

••^•^ J

I 5

A A

^°o L 10

15

J 20

L

25

Positron energy (keV) Fig. 10. The low electron momentum parameter S as a function of the positron implantation energy in three nominally undoped GaN layers, which show n-type conductivity. The Mg-doped GaN reference sample indicates the level corresponding to positron annihilations in defect-free GaN. The top axis shows the mean stopping depth corresponding to the positron implantation energy [50].

4.2.7. Observation of native vacancies Fig. 10 shows the 5 parameter as a function of the incident positron energy E in the defect-free Mg-doped GaN reference sample and in two undoped GaN layers. The surface induces a large S parameter of Ss = 0.47 at £" = 0. When E increases S parameter decreases until it levels off at E = 5-15 keV to a plateau value S^, which characterizes the GaN layer. At larger incident energies S parameter decreases as annihilations start to take place at the sapphire substrate. The difference between the undoped and Mg-doped layers is clear. In the undoped n-type samples S parameter at the GaN layer SL is clearly larger than in the Mg-doped reference sample, i.e. SL > SB- AS explained in Section 2, the reduced electron density at open-volume defects narrows the positron-electron momentum distribution and increases the S parameter. Hence, the experiment of Fig. 10 shows that nominally undoped n-type GaN layers contain vacancy defects. The vacancies in the undoped layers were further studied by recording the lowmomentum parameter 5 as a function of temperature (Fig. 11). This experiment was performed at a fixed positron energy of 10 keV, because at this energy the contributions of the annihilation events at the surface and in the substrate are negligible and all annihilations take place at the GaN layer (rji = 1). The low-momentum annihilation

Ch. 5

130

0.450 Y-

K. Saarinen

GaN

0.445

o o n=2.0xl0»8 cm-3

0.435

J100

300

500

TEMPERATURE (K) Fig. 11. The low electron momentum parameter S vs. measurement temperature in various undoped GaN samples. The carrier concentrations of the GaN layers are indicated in the figure [42]. The solid lines are fits to the temperature dependent positron trapping model [32,36].

parameter S in the GaN(n = 2.0 x 10^^ cm~^) layer increases only slightly as a function of temperature (Fig. 11). This increase is similar as observed in defect-free GaN(Mg) sample, and it can be attributed to the thermal expansion of the lattice. The S parameter in all other GaN layers is clearly larger (Fig. 11), indicating again that vacancies are present. The temperature dependence of the S parameter in GaN(n = 3.7 x 10^^ cm"^) and GaN(n = 1.2 x 10^^ cm~^) samples is similar to that of the average positron lifetime or S parameter in the GaN bulk crystal. The low-momentum parameter S decreases at low temperatures because less positrons annihilate at vacancies. As explained in Section 3, this behavior can be attributed to shallow positron traps such as negative ions. 4.2.2. Identification of vacancies The positron lifetime spectrum in bulk samples can be analyzed with two components thus enabling the distinction between free and trapped positron annihilation events. However, the Doppler broadened annihilation line cannot be decomposed directly into momentum density spectra originating from the lattice and the vacancies. The identification of the vacancies is thus less direct. On the other hand, the combined lifetime and Doppler experiments in GaN bulk crystals allow the detailed analysis of the data recorded also in the GaN layers. The number of different vacancy-type positron traps in the material can be studied by investigating the linearity between the annihilation parameters Xav, S and W. If only

Characterization of native point defects in GaN

Ch. 5

131

0.070 F

0.068

13 0.066 < OH

0.064 n Bulk crystal O Layer n=2.0x]0'«cm-3 O Layer n= 1.2x10'^cm-^

0.062

0.060

•

Layer n=7.()xlO'''cm-3

•

Layer n=3.7xl0''cni-3

I

0.435

.

I

0.440 0.445 S PARAMETER

J =j 0.450

Fig. 12. The electron-momentum parameters S and W in the GaN samples at various temperatures. The straight line indicates that the same defect (Ga vacancy) is found in all samples.

a single type of a vacancy is present, these parameters depend linearly on each other (Section 2), when the fraction riy of positron annihilations at vacancies varies: A — {\ — riy)AB + r]yAy, where A is lav, 5 or W. The data in all GaN samples at various temperatures form a straight line in the (5, W) plane (Fig. 12). The same type of vacancy is thus present in the bulk crystal as well as in all GaN layers. In the GaN bulk crystal the positron lifetime experiments show that the native vacancies are in the Ga sublattice (Section 3). On the other hand, the results of Fig. 12 indicate that the vacancy in the layers is the same as that in the bulk crystals. We can thus assign the native vacancies in the nominally undoped GaN layers with the Ga vacancy. The (5, Xav) and {W, tav) plots can be used to determine the S and W parameters corresponding to the lifetimes XB = 165 ps in the lattice and xy = 235 ps at the vacancy. The relative changes of S and W due to positron trapping at the vacancy with Tv = 235 ps are 5^/5^ = 1.038(2) and WV/WB = 0.86(2). To confirm the identification of the Ga vacancy the high-momentum part of the Doppler broadening spectrum can be recorded using the coincidence of two y ray detectors for background reduction [29,42,49]. This experiment yields the superimposed electron momentum distribution p(p) = (1 — r]v) PB(P) + IvPv(p)^ where Psip) and Pv(p) are the momentum distributions in the lattice and at the vacancy, respectively. For a sample with the measured (5, W) values rjy, S/SB-1

W/WB-1

SV/SB-I

WV/WB-I'

(31)

can be determined using the positron trapping model and the parameters SV/SB = 1.038(2) and WV/WB = 0.86(2) deduced above (see Eqs. 18-24). Since the momentum distribution in the lattice psip) can be measured in the defect-free reference sample

Ch. 5

132

K. Saarinen

Theoretical Lattice V N vac. Ga vac.

Electron momentum (10 mQc) Fig. 13. The lower panel presents experimental core electron momentum densities at the perfect GaN lattice and at the Ga vacancy. The upper panel shows the result of the theoretical calculation at perfect GaN and at N and Ga vacancies. The momentum distributions are normalized to unity [29,42].

such as heavily Mg-doped GaN crystal, the distributions pvip) at vacancies can be decomposed from the measured spectrum p{p). Fig. 13 shows the core electron momentum distributions psip) and pv{p) in the perfect GaN lattice and at the vacancy defect present in the undoped GaN layers, respectively. The intensity of the core electron momentum distribution is clearly smaller in the vacancy than in the GaN lattice. However, the momentum distributions at vacancies and in the bulk have clearly similar shapes over a wide momentum range. The core electron momentum distributions (Eq. 9) can be theoretically calculated in a straightforward way, since the wave functions of free atoms can be applied (Section 2). The curves in Fig. 13 were calculated using the atomic superposition method [27], the generalized gradient approximation and the state-dependent enhancement scheme [45,53]. The theoretical results show that the annihilations with Ga 3d electrons give the clearly dominant contribution to the measured core electron momentum distribution at

Characterization of native point defects in GaN

Ch. 5

133

GaN lattice as well as at Ga and N vacancies. The shape of the momentum distributions is thus similar in all these three systems. The calculated momentum distribution at the Ga vacancy has a cleariy lower intensity than that in the GaN lattice (Fig. 13), because the contribution of Ga 3d is reduced due to the surrounding N atoms. At the N vacancy the neighboring Ga atoms yield a core annihilation component, which is as strong as in the bulk lattice (Fig. 13). The experimental curve is compatible with the Ga vacancy, but not with the N vacancy. The Doppler broadening experiments thus support the identification of the Ga vacancy in nominally undoped n-type GaN bulk crystals. However, the present results cannot be used to specify further if the Ga vacancy is isolated or part of a larger complex. 4.3. Si'doped n-type GaN layers and correlation with oxygen Ga vacancies are experimentally observed in n-type GaN layers and bulk crystals, when the n-type conductivity is due to residual oxygen. It is interesting to study whether the formation of Ga vacancies is promoted by other impurities acting as shallow donors, such as Si. For this purpose a set of 3-5 ixm GaN(Si) layers grown by MOCVD on sapphire was studied. These samples contain an order of magnitude less oxygen than Si as determined by magneto-optical measurements [54]. The S parameter in GaN(Si) samples is shown in Fig. 14 as a function of the positron implantation energy E. A high Ss parameter is recorded at the surface of the sample at £• = 0, but with increasing energy S(E) curve decreases and saturates to a value Si characterizing the layer at £" > 15 keV. It is remarkable that the layer-characteristic value SL is equal to the bulk value SB recorded in the Mg-doped reference sample. No vacancies are thus observed in GaN(Si) samples, indicating that their concentration is 10^^ cm~^ in nominally undoped GaN layers, which show n-type conductivity due to residual oxygen, (iii) Much lower Ga vacancy concentrations are observed in samples, where the n-type doping is done with Si impurities and the amount of residual oxygen is reduced. According to the positron experiments the presence of Ga vacancies in GaN layers depends both on the Fermi level and impurity atoms in the samples. The same general trend is found in the epitaxial layers as in the bulk crystals: Ga vacancies are formed only in n-type doping concentrations when oxygen is present. However, if a similar doping is done with Si donors, no Ga vacancies are formed. A natural way to explain this behavior is to associate the observed Ga vacancies with complexes involving oxygen, such as Vca-ON. Although the direct observation of oxygen surrounding Voa has not

Ch. 5

134

K. Saarinen

Mean implantation depth (|j,m) 0 0.48

0.26

"1 —

\ •

•

s

T O

^°V

1.5

2.4

f"

^

n

GaN(Mg) reference Si-doped, n= 1.3x10 cm' _J Si-doped, n = 5.3 x 10 cm" Si-doped,n=1.2xl0^^cm"^

•

0.47

0.79

0.46

CO CO

CO

0.45

-.

• AO AO%

0.44 - . J

" ^ ^•

w

i»?fi»^8ll^...

1 10

1

1

1

L

20

30

40

Positron energy (keV) Fig. 14. The low electron-momentum parameter S as a function of the positron implantation energy in three Si-doped GaN layers. The Mg-doped GaN reference sample and the dashed line indicate the level corresponding to positron annihilations in defect-free GaN. The top axis shows the mean stopping depth corresponding to the positron implantation energy [50].

been conclusive in the positron experiments so far, this is in principle possible using the Doppler broadening technique to probe the electron momentum density (Section 2). Theoretically the formation energies of charged defects in thermal equilibrium depend on the position of the Fermi level in the energy gap, as shown in the calculated results of Fig. 15 [9,10,46]. The negatively charged defects such as the Ga vacancy have their lowest formation energy when the Fermi level is close to the conduction band, i.e. in n-type material (Fig. 15). On the other hand, the formation energy of Vca is high in semi-insulating and p-type material. These trends correlate well with the experimental observations with the positron spectroscopy, where Ga vacancies are observed only in n-type material. In fact, the theoretical results of Fig. 15 predict that the formation energy of Voa-ON pair is even lower than that of isolated Voa- This is consistent with the experimental arguments to associate the observed Ga vacancies with the Voa-ON complex. In general, the creation of Ga vacancies (or Vca complexes) in the growth of both GaN crystals (Section 3) and epitaxial layers seems to follow the trends expected for acceptor defects in thermal equilibrium. The Voa-ON complexes may form at the growth temperature, when mobile Ga vacancies are trapped by oxygen impurities. Similarly, one could expect the formation of Vca-Sica complexes in Si-doped GaN, as suggested by Kaufmann et al. [55]. In the

Characterization of native point defects in GaN

1.0

Ch. 5

135

2.0

Fig. 15. The formation energies of various defects in GaN as a function of the Fermi level |Xe according to theoretical calculations [10].

positron experiments of Fig. 14, however, these complexes are not observed. According to theory [9], the binding energy of Vca-ON pair (about 1.8 eV) is much larger than that of Voa-Sioa complexes (0.23 eV). The difference in stability is due to the electrostatic attraction: Voa and ON are nearest neighbors whereas Vca and Sica are only second nearest neighbors. The Voa-ON pairs are thus more likely to survive the cooldown from the growth temperature than Voa-SiGa- Hence, Ga vacancy complexes are detected by positrons only in materials containing substantial concentrations of oxygen, but their concentration in Si-doped material is much lower. However, the Vca-Sioa may be present in other type of GaN samples [55], particularly since the formation of Ga vacancies depends also on the stoichiometry of growth conditions as shown in Section 5.1. 4.5. Yellow luminescence The parasitic yellow luminescence band at about 2.2-2.3 eV is commonly observed in n-type GaN. There is an increasing amount of evidence that this transition takes place between a shallow donor and a deep acceptor [8-10,56], and the Ga vacancy has been suggested as the defect responsible for the acceptor level [9,10,57]. Since Ga vacancies can be both identified and quantified by positron annihilation spectroscopy, it is interesting to compare their concentration with the intensity of the yellow luminescence. The Ga vacancies were studied by positron measurements in a set of undoped n-type GaN epilayers grown on sapphire by MOCVD. The results of the Doppler broadening experiments have been given in Figs. 10 and 11 in Section 4.2. The concentration of the Ga vacancies can be estimated using the simple formula (Eq. 28) [Voa] = ^ ^ ^ | ^

(32)

/XyXfi {Sy - S)

at the high temperature plateau of Fig. 11, where the influence of negative ions and

Ch. 5

136

K. Saarinen

Ga VACANCY CONCENTRATION (10^^ cm'^) Fig. 16. The intensity of the yellow luminescence vs. the Ga vacancy concentration in GaN epitaxial layers. The inset shows the luminescence spectrum in the four studied layers, indexed according to the increasing Ga vacancy concentration [42].

Other type of shallow positron traps can be neglected (A^at is the atomic density). Taking the positron trapping coefficient iiy ^ 10^^ s~^ and Sy/Ss = 1.038 we obtain the concentrations in the 10^*^-10^^ cm~^ range. They are shown by the horizontal axis of Fig. 16. The luminescence experiments were performed by exciting with the 325 nm line of a He-Cd laser. In order to probe approximately the same region below the surface of the epilayer as in the positron experiments, the luminescence was excited from the substrate side of the sample. The emitted radiation was analyzed by a 0.5-m monochromator equipped with a photomultiplier. In order to compare the yellow luminescence of different samples its intensity was averaged over the surface of a particular sample and the same optical alignment was used to collect the light emitted by each sample. No special normalization to the band-edge luminescence was done, but it was rather assumed that the dominant recombination channels are non-radiative in each sample. In such a case the intensity of the yellow luminescence can be expected to be proportional to the concentration of defects participating in this optical transition. Fig. 16 shows the intensity of the yellow luminescence in MOCVD layers as a function of the Voa concentration obtained from positron experiments. In this set of samples the yellow luminescence correlates perfectly with the concentration of the Ga vacancies. This correlation provides evidence that native Ga vacancies participate the luminescense transition by acting as the deep acceptors. The experimental results in GaN bulk crystals support further that Ga vacancies are responsible for the yellow luminescence. The Ga vacancies are present at concentrations 10^^-10^^ cm~^ in undoped heavily n-type material (Section 3), which always shows

Characterization of native point defects in GaN

Ch. 5

137

strong emission of yellow light [40]. Furthermore, no signs of Vca nor yellow luminescence is observed in semi-insulating Mg-doped crystals (Section 3). Very interestingly, recent results provide evidence that yellow luminescence is due to defects acting as compensating acceptors in n-type GaN [58]. Together with the present positron data this suggests that the Ga vacancy is the dominating intrinsic acceptor (see also Section 5.1) as well as responsible for the yellow luminescence. However, correlations such as that in Fig. 16 are inherently complicated, mainly because the quantification of photoluminescence data is difficult. For example, the yellow luminescence has been observed to disappear after electron irradiation [59-61], most likely because other photoelectron recombination channels become possible due to the introduction of irradiation-induced defects. 5. Point defects and growth conditions of epitaxial GaN Epitaxial GaN layers can be grown using several methods, the most common of which are the metal-organic chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE). The lattice mismatch at the layer/substrate interface induces dislocations in the layers at concentrations up to 10^^ cm"-^. The quality and the properties of the layers depend further on various parameters such as the stoichiometry of the growth conditions, growth temperature and the intermixing of the atoms between the layer and the substrate. In this section we review the positron results concerning the point defects formed in GaN layers under various Idnds of growth conditions. 5.1. Stoichiometry of the MOCVD growth The formation of Ga vacancies was studied in samples where the stoichiometry of growth conditions was varied in the MOCDV reactor [62]. The undoped GaN layers of thicknesses 1-5 jxm were grown on sapphire substrates by MOCVD technique at 950-1100°C, as described earlier [63]. The precursors employed were triethylgallium (TEGa) and ammonia (NH3). The same TEGa flow was used for all samples and the NH3 flow was adjusted to change the stoichiometry of the growth conditions. The V/III molar ratio varied from 1000 to 10,000. As reported earlier [63], the growth rate as well as the electrical and optical properties of the samples change strongly with the V/III molar ratio. At lower ratios the photoluminescence shows broadened band edge structures and enhanced donor-acceptor pair recombination. The carrier concentrations at room temperature decrease from 10^^ to 10^^ cm~^ when the V/III molar ratio increases from 1000 to 10,000 [63]. All samples were investigated at room temperature as a function of the positron beam energy E (Fig. 17). When positrons are implanted close to the sample surface with £• = 0-1 keV, the same S parameter of 5 = 0.49 is recorded in all samples. This value characterizes the defects and chemical nature of the near-surface region of the sample at the depth 0-5 nm. At 5-15 keV the S parameter is constant indicating that all positrons annihilate in the GaN layer. The data recorded at these energies can thus be taken as characteristic of the layer. The lowest S parameter is obtained in the Mg-doped reference layer, where we get S = 0.434 at £ = 5-15 keV. This value corresponds to positrons annihilating as delocalized particles in the defect-free GaN lattice.

Ch. 5

138

K. Saarinen

Mean implantation depth (jim) 0 0.09 0.47 - 1 ^ • 1 '

0.26 0.50 0.79 1.13 \ ' \ ' 1 ' r=|

\ 0.46

GaN

" o

o

0.45

"

j

• Mg-dopedref. J O V/m ratio 5000 1 A V/m ratio 8000 "^

J

\

1

cP

\

-^

cP 0.44

0.43 =J

^

1

1

\ 10

^

1 15

1

1 20

1

L= 25

Positron energy (keV) Fig. 17. The low electron-momentum parameter S as a function of the positron implantation energy in three GaN samples. The top axis shows the mean stopping depth corresponding to the positron implantation energy [62].

The 5 parameter in all n-type layers is larger than in the Mg-doped reference sample (Fig. 17). The increased S parameter indicates that the positron-electron momentum distribution is narrower than in the defect-free reference sample. The narrowing is due to positrons annihilating as trapped at vacancy defects, where the electron density is lower and the probability of annihilation with high-momentum core electrons is reduced compared to that of delocalized positrons in the lattice (Section 2). The increased S parameter is thus a clear sign of vacancy defects present in the n-type GaN layers. The number of different vacancy defects trapping positrons can be investigated through the linearity between the low and high electron-momentum parameters S and W. If only a single type of vacancy is present, the W parameter depends linearly on the 5* parameter when the fraction of positron annihilations at vacancies rjy varies. The plot of the W parameter vs. S parameter thus forms a line between the endpoints (5^, WB) and (5v, Wy) corresponding to the defect-free lattice and the total positron trapping at vacancies, respectively. The S and W parameters of all samples are plotted in Fig. 18. All data points fall on the same line, which goes through the endpoint (5^, WB) = (0.434, 0.069) obtained in the Mg-doped reference sample. The same type of vacancy is thus found in all samples. The positron trapping fraction r)y and the S parameter vary from one sample to another due to the different vacancy concentrations. The slope of the line in Fig. 18 characterizes the vacancy defect present in all layers. The value A5'/AW = 2 is the same as determined for the native Ga vacancy in

Characterization of native point defects in GaN

Ch. 5

139

0.070

T^

0.068 h

8000-i 0.435

0.440

0.445

0.450

0.455

S parameter Fig. 18. The low and high electron-momentum parameters S and W in various samples. The V/III molar ratio of each sample is indicated in the figure. The straight line indicates that the same vacancy defect (Ga vacancy) is observed in all samples [62].

Section 4. To confirm the identification, we recorded the positron-electron momentum distribution in the Mg-doped sample and the layer with V/III ratio of 8000 using the two-detector coincidence technique [27]. The high-momentum part of the momentum distribution was similar as observed for the Ga vacancy (Fig. 13 in Section 4). We can thus identify the native vacancy in the GaN layers as the Ga vacancy. As explained in Section 4, the presence of Ga vacancies can be expected in n-type undoped GaN due to their low formation energy. The different levels of the S parameter in Fig. 17 indicate that the concentration of the Ga vacancies seems to depend on the stoichiometry of growth. In the samples with the V/III molar ratios 8000 and 5000 the Doppler broadening experiments were performed as a function of temperature at 20-500 K. The curves were qualitatively similar as shown in Fig. 11 in Section 4. At low temperatures T < 150 K the S parameter decreases indicating that positrons are trapped at shallow traps such as the Rydberg states of negative ions in addition to Ga vacancies. At high temperatures T > 250 K positrons are able to escape from these traps. This effect increases the S parameter as a function of temperature, because more positrons are able to get trapped at vacancy defects. At 300-500 K the S parameter is constant indicating that the detrapping from the negative ions is complete. At these temperatures only Ga vacancies act as positron traps. In order to quantify the concentration of Voa the S parameter data at 300 K was analyzed with the positron trapping model (Section 2.4.2). When Ga vacancies are the

Ch. 5

140

K. Saarinen

10

10"

10'

a

10^^ L i . 3000

6000

9000

V/III Molar ratio Fig. 19. The concentration of Ga vacancies vs. the V/III molar ratio in undoped GaN samples. The straight line is drawn to emphasize the correlation [62].

only defects trapping positrons, their concentration can be determined with the simple formula (Eq. 28) [Vca]

fJiXB Sv -

S'

(33)

where XB = 165 ps is the positron lifetime at the GaN lattice,[42] /x = 10^^ s~^ is the positron trapping coefficient [12] and A^at = 8.775 x 10^^ cm~^ is the atomic density of GaN. For the S parameter at the Ga vacancy we take SV/SB = 1.046. This value is slightly larger than presented eariier in Section 4, because the energy resolution of the ganmia spectroscopy system used in this study (1.2 at 511 keV) is better than in our earlier study [42] (1.5 at 511 keV). The results in Fig. 19 indicate that the concentration of Ga vacancies is proportional to the stoichiometry of the growth conditions. Rather low [Vca] ^ 10^^ cm~^ is observed for the sample with the V/III molar ratio of 1000. When the V/III molar ratio becomes 10,000, the Voa concentration increases by almost three orders of magnitude to [Voa] ^ 10^^ cm~^. This behavior shows that empty Ga lattice sites are likely formed in strongly N rich environment. It has been shown in previous works that the V/III molar ratio has an influence on the growth rate as well as on the electrical and optical properties of the GaN layers [63]. The present results indicate that the formation of intrinsic point defects such as the Ga vacancy depend also heavily on the stoichiometry of the growth conditions. The Ga vacancy is negatively charged and thus acts as a compensating center in n-type material.

Characterization of native point defects in GaN

Ch. 5

141

Table 2. The concentrations of free electrons, oxygen and Ga vacancies in the GaN layers grown with different V/III molar ratios V/III molar ratio 1000 5000 8000

Carrier concentration (cm~^)

Oxygen concentration (cm~^)

Ga vacancy concentration (cm~^)

10^0

>1020 4 X 10^^ 1 X 10*9

3x10^^ 4 X 10'^ 1 X 10*9

10^6

The oxygen concentrations were determined by secondary ion mass spectrometry and the concentrations of Ga vacancies were obtained from the positron annihilation data.

Indeed, the Hall experiments show that the free electron concentration decreases from 10^^ to 10^^ cm"^ when the V/III molar ratio increases from 1000 to 10,000 [63]. Simultaneously, [Vca] increases from 10*^ to 10^^ cm"^ (Fig. 19). The charge state of Vca in n-type material is 3— [9,10]. The compensation via the formation of Ga vacancies explains thus most of the decrease of the carrier concentration, when the V/III molar ratio increases from 1000 to 10,000. In order to obtain a more quantitative picture of the electrical compensation of GaN the oxygen concentrations were determined in some of the samples using secondary ion-mass spectrometry. As seen in Table 2, the oxygen concentrations vary non-monotonously in the 10^^-10^^ cm~^ range when the V/III ratio increases from 1000 to 8000. Interestingly, the carrier concentration seems to follow approximately the relation n ^ [0]-[VGa] in the data of Table 2. The SIMS, positron and electrical data are thus consistent with the simple picture that free electrons are supplied by shallow O^ donors, which are partially compensated by negative Ga vacancies (or Voa complexes) acting as dominant deep acceptors. To summarize, we have applied positron annihilation spectroscopy to study the vacancy defects in undoped GaN layers, where the stoichiometry was changed by adjusting the V/III molar ratio. Gallium vacancies are observed in all samples. Their concentration increases from 10^^ to 10^^ cm~^ when the V/III ratio changes from 1000 to 10,000. Hence, the Ga vacancies are formed very abundantly when the growth conditions become more nitrogen rich. The decrease of free electron concentration with increasing V/III molar ratio correlates with the creation of Ga vacancies. This effect can be attributed to the compensation of impurities induced by the negatively charged Ga vacancies. 5.2. Dislocations and the formation ofGa vacancies in GaN layers The results of Sections 3 and 4 indicate that Ga vacancies (or complexes involving Voa) exist in GaN when the material is n-type and contains oxygen. The same trend is observed for both GaN bulk crystals and GaN grown by MOCVD on sapphire. However, the dislocation densities in these materials are very different. The lattice mismatch between GaN layer and sapphire substrate generates a highly dislocated region within a few hundred nanometers from the interface. The threading dislocations pass through the whole layer and have typically a high concentration of 10^° cm"^ [1].

Ch. 5

142

K. Saarinen

Mean implantation depth (^m) 0.26

0.79

1.5

2.4

0.46 h O GaN(Mg) sample #1 • GaN(Mg) sample #2 0.45

§

0.44

-• '''^"Se*o55^88S^®c 'oOo

••

H

0.43 c^

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20

30

40

Positron energy (keV) Fig. 20. The low electron-momentum parameter S as a function of the positron implantation energy in two Mg-doped GaN layers grown on sapphire. The top axis shows the mean stopping depth corresponding to the positron implantation energy. The maximum of the S(E) curve at E = 30 keV indicate the presence of open-volume defects at the highly dislocated GaN/AhOs interface [50].

On the other hand, the dislocation density in GaN bulk crystals is only V

\

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\

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0.50

0.48

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A* ^

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°°s»4i>»64»««;J...«

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o 0=°

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0.44

o

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1

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Positron energy (keV) Fig. 22. The low electron-momentum parameter S vs. positron implantation energy in undoped GaN/Si(lll) grown by MBE at various temperatures. The dashed lines indicate the specific S values for free positrons in the GaN lattice and trapped positrons in Ga vacancies [64].

Characterization of native point defects in GaN "T

Ch. 5

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A

0.07 rh 0.5 |xm from the layer/substrate interface. This suggests that the formation of point defect in both epitaxial layers and bulk crystals follows mainly the trends expected for defects in thermal equilibrium. Acknowledgements I would like to acknowledge the essential contributions of my collaborators P. Hautojarvi, T. Laine, J. Nissila and J. Oila in the positron spectroscopy group of Laboratory of Physics at Helsinki University of Technology, Finland. I am grateful for the theoretical support and discussions with M.J. Puska, M. Hakala, T. Mattila and R.M. Nieminen. I would like to thank T. Suski, I. Grzegory and S. Porowski (UNIPRESS, Warsaw, Poland) for providing bulk GaN crystals for positron experiments and for many discussions. GaN epitaxial layers for positron studies have been supplied by J.M. Baranowski's group (University of Warsaw, Poland), O. Briot's group (Universite Montpellier II, France) and E. Calleja's group (Universidad Politecnica, Madrid, Spain). I would like to acknowledge their effort, collaboration and comments. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

J.S. Speck and SJ. Rossner, Physica B 273-274, 24 (1999). X.H. Wu, L.M. Brown, D. Kapolnek, S. Keller, B. Keller, S.R DenBaars and J.S. Speck, J. Appl. Phys. 80, 3228 (1996). F.A. Ponce, D. Chems, W.T. Young and J.W. Steeds, Appl. Phys. Lett. 69, 770 (1996). J. Eisner, R. Jones, PK. Sitch, D.V. Porezag, M. Elstner, T. Frauenheim, M.I. Heggie, S. Oberg and PR. Briddon, Phys. Rev. Lett. 79, 3672 (1997). A.F. Wright and U. Grossner, Appl. Phys. Lett. 73, 2751 (1998). D.C. Look and J.R. Sizelove, Phys. Rev. Lett. 82, 1237 (1999). Z. Liliental-Weber, Y. Chen, S. Ruvimov and J. Washburn, Phys. Rev. Lett. 79, 2835 (1997). P Perlin, T. Suski, H. Teisseyre, M. Leszczynski, L Grzegory, J. Jun, S. Porowski, P. Boguslawski, J. Bemholc, J.C. Chervin, A. Polian and T.D. Moustakas, Phys. Rev. Lett. 75, 296 (1995). J. Neugebauer and C. van de Walle, Appl. Phys. Lett. 69, 503 (1996). T. Mattila and R.M. Nieminen, Phys. Rev. B 55, 9571 (1997). E.R. Glaser, T.A. Kennedy, K. Doverspike, L.B. Rowland, D.K. Gaskill, J.J.A. Freitas, M.A. Khan, D.T. Olson, J.N. Kuznia and D.K. Wickenden, Phys. Rev. B 51, 13326 (1995). K. Saarinen, P Hautojarvi, C. Corbel. In: M. Stavola (Ed.), Identification of Defects in Semiconductors, Academic Press, New York, 1998, p. 209.

148 [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

[43]

[44] [45] [46] [47] [48]

Ch. 5

K. Saarinen

R. Krause-Rehberg, H.S. Leipner, Positron Annihilation in Semiconductors, Springer, Heidelberg, 1999. R Asoka-Kumar, K.G. Lynn and D.O. Welch, J. Appl. Phys. 76, 4935 (1994). M.J. Puska and R.M. Nieminen, Rev. Mod. Phys. 66, 841 (1994). RJ. Schultz and K.G. Lynn, Rev. Mod. Phys. 60, 701 (1988). J. Lahtinen, A. Vehanen, H. Huomo, J. Makinen, P. Huttunen, K. Rytsola, M. Bentzon and R Hautojarvi, Nucl. Instnim. Methods Phys. Res. B 17, 73 (1986). S. Valkealahti and R.M. Nieminen, Appl. Phys. A 35, 51 (1984). R.M. Nieminen and J. Oliva, Phys. Rev. B 22, 2226 (1980). K.O. Jensen and A.B. Walker, J. Phys.: Condens. Matter 2, 9757 (1990). J. Makinen, C. Corbel and R Hautojarvi, Phys. Rev. B 43, 12114 (1991). E. Soininen, J. Makinen, D. Beyer and R Hautojarvi, Phys. Rev. B 46, 13104 (1992). Y.Y. Shan, R Asoka-Kumar, K.G. Lynn, S. Fung and C.B. Beling, Phys. Rev. B 54, 1982 (1996). D. Schodlbauer, R Sperr, G. Kogel and W. Trifthauser, Nucl. Instrum. Methods B 34, 258 (1988). R. Suzuki, Y. Kobayashi, T. Mikado, H. Ohgald, M. Chiwaki, T. Yamazaki and T. Tomimatsu, Jpn. J. Appl. Phys. B 30, L532 (1991). K. Saarinen, J. Nissila, P. Hautojarvi, J. Likonen, T. Suski, I. Grzegory, B. Lucznik and S. Porowski, Appl. Phys. Lett. 75, 2441 (1999). M. Alatalo, H. Kauppinen, K. Saarinen, M.J. Puska, J. Makinen, P. Hautojarvi and R.M. Nieminen, Phys. Rev. B 51, 4176 (1995). P. Asoka-Kumar, M. Alatalo, V.J. Ghosh, A.C. Kruseman, B. Nielsen and K.G. Lynn, Phys. Rev. Lett. 77, 2097 (1996). K. Saarinen, J. Nissila, J. Oila, V. Ranki, M. Hakala, M.J. Puska, R Hautojarvi, J. Likonen, T. Suski, I. Grzegory, B. Lucznik and S. Porowski, Physica B 273-274, 33 (1999). O.V. Boev, M.J. Puska and R.M. Nieminen, Phys. Rev. B 36, 7786 (1987). K. Saarinen, R Hautojarvi, A. Vehanen, R. Krause and G. Dlubek, Phys. Rev. B 39, 5287 (1989). C. Corbel, R Pierre, K. Saarinen, R Hautojarvi and R Moser, Phys. Rev. B 45, 3386 (1992). M.J. Puska, C. Corbel and R.M. Nieminen, Phys. Rev. B 41, 9980 (1990). J. Makinen, C. Corbel, R Hautojarvi, R Moser and F. Pierre, Phys. Rev. B 39, 10162 (1989). J. Makinen, R Hautojarvi and C. Corbel, J. Phys.: Condens. Matter 4, 5137 (1992). K. Saarinen, S. Kuisma, J. Makinen, P. Hautojarvi, M. Tomqvist and C. Corbel, Phys. Rev. B 51, 14152 (1995). G.R. Grzegory and S. Krukowski, Phys. Scr. T39, 242 (1991). S. Porowski, L Grzegory. In: S.J. Pearton (Eds.), GaN and Related Materials; Vol. 2, Gordon and Breach. Amsterdam, 1997, p. 295. C. Wetzel, T. Suski, J.W Ager III, E.R. Weber, E.E. Haller, S. Fischer, B.K. Meyer, R.J. Molnar and R Periin, Phys. Rev. Lett. 78, 3923 (1997). T. Suski, R Periin. In: J.I. Pankove, T.D. Moustakas (Eds.), Gallium Nitride (GaN) I; Vol. 50, Academic Press, San Diego, 1998, p. 279. J.I. Pankove, J.T. Torvik, C.-H. Qiu, I. Grzegory, S. Porowski, R Quigley and B. Martin, Appl. Phys. Lett. 74, 416 (1999). K. Saarinen, T. Laine, S. Kuisma, J. Nissila, P. Hautojarvi, L. Dobrzynski, J.M. Baranowski, K. Pakula, R. Stepniewski, M. Wojdak, A. Wysmolek, T. Suski, M. Leszczynski, I. Grzegory and S. Porowski, Phys. Rev. Lett, 79, 3030 (1997). K. Saarinen, T. Laine, S. Kuisma, J. Nissila, P. Hautojarvi, L. Dobrzynski, J.M. Baranowski, K. Pakula, R. Stepniewski, M. Wojdak, A. Wysmolek, T. Suski, M. Leszczynski, I. Grzegory and S. Porowski, Mat. Res. Soc. Symp. Proc. 482, 757 (1998). S. Dannefaer, W. Puff and D. Kerr, Phys. Rev. B 55, 9571 (1997). M. Alatalo, B. Barbiellini, M. Hakala, H. Kauppinen, T. Korhonen, M.J. Puska, K. Saarinen, P. Hautojarvi and R.M. Nieminen, Phys. Rev. B 54, 2397 (1996). R Boguslawski, E.L. Briggs and J. Bernholc, Phys. Rev. B 51, 17255 (1995). D.C. Look, D.C. Reynolds, J.W. Hemsky, J.R. Sizelove, R.L. Jones and R.J. Molnar, Phys. Rev. Lett. 79, 2273 (1997). J. Gebauer, R. Krause-Rehberg, C. Domke, R Ebert and K. Urban, Phys. Rev. Lett. 78, 3334 (1997).

Characterization of native point defects in GaN [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64]

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L.V. Jorgensen, A.C. Kruseman, H. Schut, A. van Veen, M. Fanciulli and T.D. Moustakas, Mat. Res. Soc. Symp. Proc. Vol. 449, 853 (1997). J. Oila, V. Ranki, K. Saarinen, R Hautojarvi, J. Likonen, J.M. Baranowski, K. Pakula, M. Leszczynski, I. Grzegory, Phys. Rev. B, in press. T.L. Tansley and R.J. Egan, Phys. Rev. B 45, 10942 (1992). W. Gotz, N.M. Johnson, C. Chen, H. Liu, C. Kuo and W. Imler, Appl. Phys. Lett. 68, 3144 (1996). B. Barbiellini, M.J. Puska, T. Torsti and R.M. Nieminen, Phys. Rev. B 51, 7341 (1995). A.M. Witowski, M.L. Sadowski, K. Pakula, B. Suchanek, R. Stepniewski, J.M. Baranowski, M. Potemski, G. Martinez and R Wyder, MRS Internet J. Nitride Semicond Res. 3, 33 (1998). U. Kaufmann, M. Kunzer, H. Oblog, M. Maier, C. Manz, A. Ramakrishnan and B. Santic, Phys. Rev. B 59, 5561 (1999). E. Calleja, F.J. Sanchez, D. Basak, M.A. Sanchez-Garcia, E. Munoz, L Izpura, F. Calle, J.M.G. Tijero, J.L. Sanchez-Rojas, B. Beaumont, P. Lorenzini and P Gibart, Phys. Rev. B 55, 4689 (1997). X. Zhang, P Kung, D. Walker, A. Saxler and M. Razeghi, Mater. Res. Soc. Symp. Proc. 395, 625 (1996). E.F. Schubert, LD. Goepfert and J.M. Redwing, Appl. Phys. Lett. 71, 3224 (1997). M. Linde, S.J. Uftring, G.D. Watkins, V. Harle and F. Scholz, Phys. Rev. B 55, 10177 (1997). LA. Buyanova, M. Wagner, W.M. Chen, B. Monemar, J.L. Lindstrom, H. Amano and L Akasaki, Appl. Phys. Lett. 73, 2968 (1998). C. Bozdog, H. Przybylinska, G.D. Watkins, V. Harle, E Scholz, M. Mayer, M. Kamp, R.J. Molnar, A.E. Wickenden, D.D. Koleske and R.L. Henry, Phys. Rev. B 59, 12479 (1999). K. Saarinen, P. Seppala, J. Oila, P. Hautojarvi, C. Corbel, O. Briot and R.L. Aulombard, Appl. Phys. Lett. 73, 3253 (1998). O. Briot, J.P Alexis, S. Sanchez, B. Gil and R.L. Aulombard, Solid State Electronics 41, 315 (1997). E. Calleja, M.A. Sanchez-Garcia, D. Basak, F.J. Sanchez, F. Calle, P. Youinou, E. Munoz, J.J. Serrano, J.M. Blanco, C. Villar, T. Laine, J. Oila, K. Saarinen, R Hautojarvi, CH. Molloy, D.J. Somerford and L Harrison, Phys. Rev. B 58, 1550 (1998).

III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 6

Persistent photoconductivity in Ill-nitrides H.X. Jiang and J. Y. Lin

1. Introduction Ill-nitride based devices offer great potential for applications such as high power and high temperature electronics, UV-blue light emitting diodes (LEDs) and lasers, and solar-blind UV detectors. Researchers in this field have made extremely rapid progress toward materials growth as well as device fabrication [1,2]. Despite the many efforts on these materials, understanding and control of impurity properties and p-type doping in these materials remain one of the most important aspects to be further improved. Needless to say, the future development of GaN devices depends critically on improving n- and p-type doping, which would rely heavily on the full understanding of physical properties of doped impurities, native defects, as well as impurity-defect complexes in these materials. Due to their wide band gaps, effects of deep level centers on the Ill-nitride materials and devices are expected to be more pronounced than in narrower band gap materials. In deed, deep level centers and the associated persistent photoconductivity (PPC) effect, have been observed in a wide variety of Ill-nitride materials and structures. Their presence indicates possible charge trapping (or charge freeze out) effects in Ill-nitride devices, which could cause instabilities in such devices and hence have significant influences on the device performance. For example, there is evidence that the presence of deep level impurities are responsible for the current-voltage characteristic collapse seen in Ill-nitride field effect transistors (FETs) [3-5]. The prolonged carrier capture time in the PPC state was also shown to affect the photocurrent transient behaviors in AlGaN/GaN heterojunction UV detectors [6]. The research to determine the origin of PPC in Ill-nitrides has been driven not only by its peculiar and interesting physical properties, but more importantly by its relevance for device applications, i.e., an understanding of the physics as well as the control of PPC and the associated deep level centers is necessary in order to further optimize Ill-nitride devices. PPC is the light-enhanced conductivity that persists for a long period of time after the removal of photoexcitation and has been observed in many semiconductor materials and structures configurations. At low temperatures the PPC decay times become extremely long (of the order of minutes to years) and incompatible with normal lifetime-limiting recombination processes in semiconductor materials. Earlier work on conventional IIIV and II-VI semiconductors has shown that understanding of the PPC phenomena can provide mechanisms for carrier generation and relaxation. It is also known that

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H.X. Jiang and J. Y. Lin

the PPC has a profound effect on device operations, e.g., it is detrimental to the operation of AlGaAs/GaAs modulation doped heterojunction field effect transistors (MOD-FETs) [7-12]. On the other hand, PPC is useful for adjusting the density of the two-dimensional electron gas (2DEG) at a semiconductor interface [13] and for possible device applications such as memory device and optical gratings [14,15]. It can also be utilized to probe the profile of the impurities [16], properties of metal-insulator transition [17], and transport properties of the tail states in the density of states in semiconductor alloys [18,19]. PPC in many cases is related with deep level centers associated with defects such as vacancies, antisites, self-interstitials, and impurity-defect complexes. These deep level centers are considerably more localized compared with shallow impurities and often have energy levels located deep inside the bandgap. Moreover, in the vicinity of these deep centers, lattice relaxation is quite conmion [20]. For example, it is now known in AlGaAs alloys and other III-V semiconductors that the PPC effect is natural properties of what has been termed as the DX centers that under go a large lattice relaxation (LLR) [21] with a negative U character [22]. According to this model, which is illustrated schematically in Fig. 1, at low temperatures, PPC decay is prevented by a large carrier capture barrier. The large difference between the optical and thermal ionization energies (the Stokes shift) can be explained by LLR. Extensive work in this area has led to the conviction that the effect of PPC is strongly correlated with deep level centers that exhibit the property of metastability, which may occur when the lowest total energy of a particular atomic configuration varies with the charge states of the defects. This implies that there is a physical property that inhibits the relaxation of the center to its

. CB

D

/

gB \

G

m

'Hop

V i- V

o U

Eth

/

T VB

S «

1

1

Qo

QT

•

Defect Configuration Coordinate, Q Fig. 1. Configurational coordinate diagram showing the four energies which characterize the DX center. The parabolas represent the total energy when the electrons are in the conduction band (Qo) or bound to the DX level (QT). The shift in the value of Q represents a change in the atomic configuration around the defect (after [21]).

Persistent photoconductivity in ni-nitrides

Ch. 6

153

ground state. In such a context, the PPC relaxation is related to a change in energy and configuration of the center that is associated with a return to its electronic ground state. Examples of such deep centers include EL2 centers in GaAs and DX centers in AlGaAs. The present knowledge on these types of deep level centers is based on nearly forty years of research efforts, which has been summarized very well in several review articles and books [11,23-25]. As for other III-V and II~VI semiconductors, the DX center in AlGaAs alloys can serve as a model that can be invoked in the study of deep level defects or impurities (or DX-like centers) in Ill-nitrides. For Ill-nitrides, however, the epitaxial films are grown on foreign substrates and contain high density of extended defects, such as dislocations, grain boundaries, and stacking faults. These make the understanding of PPC and the nature of deep level centers in Ill-nitrides more difficult. Other mechanisms have also been proposed to account for PPC effect in a variety of semiconductors. In doped layered structures, the macroscopic barrier due to band offset at the interface between epitaxial layers or between epitaxial layer and substrate could also cause a spatial separation between photoexcited electrons and holes and hence PPC [26,27]. In undoped semiconductor alloys, the alloy-induced compositional fluctuations can also be a cause of the PPC effect, especially in tumary alloys with a large energy bandgap difference between the two compound semiconductors [28,29]. In such systems, photoexcited electrons and hole are localized at the low-potential sites in the conduction and valence bands at low temperatures. Since the low-potential sites in the conduction and valence bands are spatially separated, recombination rate of photoexcited carriers is reduced and PPC may result. The aim of this chapter is to review PPC in Ill-nitrides and to provide an overview on such an effect in these materials. It is our intention to cover articles written prior to January 2000, but we are sure that there were related articles left out unintentionally. The PPC characteristics including its buildup and decay behaviors, evidence of DX-like centers as well as the nature of defects, and implications on PPC mechanisms are presented and discussed in Section 2. Effects of PPC on Ill-nitride devices including FETs and photodetectors are discussed in Section 3. In Section 4, possible uses of PPC are discussed. Concluding remarks are made in Section 5. 2. Characteristics and possible mechanisms of PPC in Ill-nitrides The techniques which have been employed most often to characterize the PPC effect as well as to determine important parameters associated with deep level centers are temperature-dependent photoconductivity transient measurements which probe the capture and emission kinetics of carriers to and from the deep level centers (or localized states) as well as the carrier capture barrier. Spectral-dependent photoconductivity measurements are often employed to provide the optical ionization energy and optical cross section of the deep level center involved. Other techniques such as temperature-dependent Halleffect, deep level transient spectroscopy (DLTS), photoluminescence (PL), and optical detection of magnetic resonance (ODMR) measurements can provide information on the energetic levels of deep level centers as well as carrier-defect scattering mechanisms. PPC in Ill-nitride epitaxial layers was first observed in p-type (Mg doped) epilayers grown both by metalorganic chemical vapor deposition (MOCVD) and reactive

Ch. 6

154

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photon energy (eV) Fig. 24. (a) Photocurrent spectra measured at various bias voltages for a 500 A Alo.15Gao.85N/GaN Schottky diode for illumination provided from the top of the sample, (b) Photocurrent spectra from the same structure, obtained at 2.0 V bias with illumination from the top (dashed line) and bottom (solid line) of the sample (after [39]).

tration under non-equilibrium growth conditions [65-71]. The 1.0 eV GaxIni_xNyAsi_y alloy system appears to be an ideal candidate material for the third junction in the multijunction solar cells. Very recently, a GaxIni_xNyAsi_y solar cell with an internal quantum efficiency (IQE) greater than 70% has been achieved [65]. However, the device performance is still rigidly limited partly due to the presence of defects in GalnNAs, which may result in low IQE and small minority carrier diffusion lengths. PPC effect has been observed in unintentionally doped p-type GalnNAs epilayers [72]. The PPC decay behavior in the temperature region (50 ^ 320 K) is very well described by a stretched-exponential function of Eq. 2 and the PPC relaxation time

Persistent photoconductivity in Ill-nitrides

Ch. 6

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becomes very long below 175 K. The PPC level is still about 75% of its initial value after 1000 s of decay at 175 K. However, as the sample temperature was increased to above 320 K, no PPC effect was observed. The Arrhenius plot of the PPC decay time constant {In x versus 1 /T) showed two distinct temperature regions, similar to the feature seen in p-GaN epilayers shown in Fig. 5a. At temperatures T > 220 K, i decreased rapidly with temperature following an activated behavior, from which the capture barrier Ec was obtained to be around 0.57 eV. However, t was only weakly dependent on temperature at T < 220 K. The decay exponent p increased linearly with T at T > 200 K and was also nearly temperature independent at T < 200 K. Detailed studies showed that the PPC decay kinetics observed in InGaNAs quaternary alloys were very similar to those of DX centers in AlxGai_xAs alloys and GaN. The relative optical cross-section, aopt, as a function of excitation photon energy hv was also measured, from which an optical ionization energy of 0.70 eV was obtained. The free hole concentration /? as a function of reciprocal temperature was measured in darkness in the temperature range from 10 to 450 K. From the appearance of the Hall data, different slopes were present in the ln(p) versus 1/T plot, which indicates that more than one acceptor state may be involved in the conduction process. Furthermore, alloy scattering is probably very important in this quaternary material, which can lead to a hopping conduction in the low temperature region. However, the average impurity binding energy (Eb) estimated from the slope of the ln(p) versus 1/T plot in the high temperature region was about 67 meV. This gave a Stokes shift of about 0.64 eV (Estokes = Eopt — Eo). Such a large Stokes shift, which is one of the common features of lattice relaxation associated with impurities, provided an additional evidence that AX-like centers were the primary cause of PPC in GalnNAs. However, these results could not provide insight regarding the origin of the AX-centers in this material system. 3. PPC effects on heterojunction devices As a consequence of PPC in AlGaN/GaN HFET structures, the device characteristics are sensitive to light and the sensitivity is associated with persistent photoinduced increase in the 2DEG carrier mobility and density. As for the AlGaAs/GaAs modulation doped field-effect transistors, PPC by itself is not a problem for device operation, but its presence indicates the possibility of other device instabilities associated with cases such as charge trapping. Effects of PPC are expected to be strong, in particular for the minority carrier devices based on Ill-nitrides. In majority-carrier devices or semiconductor LEDs and lasers, these effects are less prominent. However, to be shown in Section 4, the effects of PPC in AlGaN/GaN HFET structures can be minimized by varying the structural parameters. 3.1. Effects on heterojunction field effect transistors The deep level centers located in the regions outside of the conducting channel could trap carriers and result a current collapse (CC) in the transistors, which have been observed in AlxGai_xN/GaN HFETs [3] and GaN metal-semiconductor field effect transistors

Ch. 6

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H.X. Jiang and J. Y. Lin

normal l-V illuminated 470nm fully collapsed (dark)

10 20 DRAIN VOLTAGE (V)

Fig. 25.

I-V characteristics of a GaN MESFETs measured under different conditions (after [5]).

(MESFETs) [4,5]. The effect of current collapse observed in GaN MESFETs, like PPC, can be reversed by liberating trapped carriers by thermal emission or light excitation. The effect of light on the current collapse of GaN FETs has been studied by measuring the transistor characteristics under light excitation. An increase in the drain current was observed in an AlGaN/GaN HFET under light excitation with photon wavelengths near 360 nm, corresponding to the AlGaN band edge, and near 650 nm, which was associated with an unidentified trap located in the AlGaN barrier layers in the AlGaN/GaN HFETs [3]. An optically induced restoration of the drain current was also observed in GaN MESFETs [4]. Fig. 25 shows the I-V characteristics of a GaN MESFET obtained under different conditions including I-V curves under normal, illuminated under light with photon wavelength 470 nm, and fully collapsed (dark) conditions. The increase of drain current AI between the dark and under the illumination after the application of a high source-drain bias reflects the numbers of carriers that have been optically excited from the traps. The results suggested that traps responsible for the CC effect were located in the high resistive GaN insulting layer in the GaN MESFETs [4]. Photoionization spectra of GaN MESFETs revealed two electron traps, which are strongly coupled to the lattice [5]. Photoionization thresholds for these two traps were determined at 1.8 and 2.85 eV and both appeared to be the same traps associated with PPC in GaN epilayers. The drain current under a high source-drain voltage in the dark and light excitation with different wavelength X was measured, from which the current collapse function S(>v.) was obtained [5],

where (t)(X) is the incident photon flux, t is the duration of light illumination time, AI(X) and Idark are the light-induced drain current increase and the fully collapsed (dark) drain current, respectively. The measured S(hv) as a function of incident photon energy hv is plotted as the open circles in Fig. 27, showing clearly two broad absorption associated with photoionization from two deep traps with optical ionization energies of 1.8 and 2.85 eV, respectively. The results of PPC spectral studies in GaN epilayers by Reddy

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3.2. Effects on AlGaN/GaN heterostructure UVphotoconductors PPC effect can influence the photocurrent (PC) transient characteristics of GaN photoconductors [6]. PC transient characteristics of an AlGaN/GaN heterostructure photoconductor have been measured at different conditions. The PC transient characteristics of the AlGaN/GaN heterostructure was found to depend strongly on its history (or initial conditions). Fig. 27 illustrates the typical room temperature photoresponses of an AlGaN/GaN heterostructure to a successive N2 pulsed laser excitation at 338 nm starting from a dark equilibrium condition, measured at an excitation laser frequency of 1 Hz. As we can see from Fig. 27, the PC transient characteristics are different for the initial and the later pulses. The changes are progressive and can be summarized below: (i) the PC responsivity of the earlier pulses are smaller than those of the later pulses; (ii) the quasi-dark level of the previous transient is always lower than that of the subsequent transients; and (iii) the eariier PC transients decay faster than the later transients. The results shown in Fig. 29 imply that the detectivity (or sensitivity), dark level, and response speed of UV detectors fabricated from AlGaN/GaN heterostructures will all depend on the device history. The PC decay transients can be described very well by an exponential function and

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the decay time constant, x, increases gradually with the number of successive excitation pulses. Fig. 28 plots (a) the photovoltage (or the photo-responsivity), (b) the quasi-dark level, and (c) the PC decay time constant t as functions of the pulsed laser illumination time. An interesting feature exhibited in Fig. 30 is that all of these three physical parameters, y(t), have a systematic dependence on the pulsed laser illumination time and the exact dependence is identical to the PPC buildup kinetics of Eq. 1 by replacing Ippc with y(t),

y(t) = yd + (ymax - yd)(i - e""^).

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Here y(t) describes the time dependence of the three physical quantities (photo-responsivity, dark level, and PC decay time constant), yd (ymax) denotes their values near the initial dark (saturation) state, and a~^ is a characteristic time that is required for the device to reach the saturation (or steady) state. The solid curves in Fig. 30 are the least

182

Ch, 6

H.X. Jiang and J. Y. Lin

squares fit of data with Eq. 13. The fitted values of a"^ obtained from Fig. 30a-c are all identical, i.e., a"^ = 33.1 ±0.1 s. This clearly demonstrates that the observed characteristics are directly correlated with the effect of PPC in the AlGaN/GaN heterostructure and can have a significant effect on the characteristics of the UV photodetectors based on AlGaN/GaN heterostructures, including sensitivity, noise property, dark level, and response speed. 4. The uses of PPC The principal feature of PPC, namely the prolonged carrier capture and recombination times, has been utilized to probe the transport properties of II-VI semiconductor alloys [17-19]. In the PPC state, the electron concentration in the conduction band can be conveniently varied in a single sample with excitation photon dose, so direct comparisons between different electron concentrations can be made more easily. The distribution of the tail states in the density of states (DOS) caused by alloy disorder, for example in AlGaN alloys, can be determined through the use of PPC. Contrary to the AlGaAs alloys, the effect of alloy disorder in AlGaN system is very strong due to the large energy gap difference between AIN and GaN. Important parameters such as the total DOS below the mobility edge in the conduction band of AlGaN alloys can be determine through the use of PPC, regardless what is the origin of PPC itself. Moreover, the magnitude of PPC can also be used to monitor the electronic qualities of AlGaN alloys and AlGaN/GaN heterostructures. 4,1. Effects of alloy fluctuation in Al^Gai^x^ alloys probed by PPC PPC has been used to study the effects of alloy fluctuations on the electron transport properties of AlxGai_xN alloys [76]. By utilizing the unique features of PPC, namely the very long lifetimes of the photoexcited carriers and the continues variation of the electron concentration in the conduction band, the electron mobility (/x^) as a function of electron concentration in) in a single sample can be measured. Fig. 29 shows a typical PPC behavior for one of the MOCVD grown and undoped Alo.35Gao.65N epilayers. The time-dependent PPC decay Ippc(t) can be very well described by a stretched-exponential function of Eq. 2. The fitted values of x and f> for the data shown in Fig. 31 are 1350 s and 0.35, respectively. However, as illustrated in Fig. 31, the PPC buildup kinetics in Alo.35Gao.65N epilayers can no longer be described by Eq. 1 and in fact the use of Eq. 1 results in a poor fit, particularly near the PPC saturation region (bold part). If the PPC buildup can be described by Eq. 1, then a linear time-dependent behavior at the initial PPC buildup stage, /ppc(0 oc {at < 1), is expected. Initial PPC buildup kinetics in Alo.35Gao.65N epilayers has been monitored by systematically varying excitation intensity, lexc- Fig- 30 shows the time-dependent PPC buildup behaviors during the first 50 seconds measured for varying Iexc» which clearly illustrates that for the samples studied here, a linear time-dependent PPC buildup at the initial stage was absent. On the other hand, previous work has shown that the electron transport properties in II-VI semiconductor alloys are strongly influenced by the tail states caused by the alloy

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disorder [17-19]. In semiconductors (n-type) with alloy fluctuations, the conductivity results mainly from the electron hopping between localized states when the electron quasi-Fermi-level, Ef, is below the mobility edge, Em [77]. Assuming that the Fermi distribution is a step function (at low temperatures) and that the alloy disorder induced an exponential tail states in the conduction band edge, a quadratic time-dependent initial PPC buildup was derived from the Kubo-Greenwood formula [17-19], /," PPC {t) — Id + const. [1 - exp(-QfO] oc t^{at < 1),

(14)

which agreed well with experimental observations in ZnxCdi_xSe alloys. The quadratic time-dependent initial PPC buildup behavior implies that the electron mobility (/x^) in the tail states of ZnxCdi_xSe alloys is proportional to the electron concentration (n), {jie) a {n), since the conductivity cr(t) is effectively proportional to the product of (/>6en), where () stands for an assemble average and {n) is proportional to [1 — exp(—Of/)]However, for Alo.35Gao.65N epilayers, the initial PPC buildup behavior is neither linear nor quadratic with time. Instead, the observed PPC buildup behavior follows

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Time (s) Fig. 30. The kinetics of the initial PPC buildup for an Alo.35Gao.65N alloy measured at four different excitation light intensities, i.e., lexc = lo, 0.4Io, 0.16I0, 0.064Io. The dark currents have been subtracted out. The solid curves are the least squares fit of data with Eq. 15, with the fitted value of y being approximately 2.9 ± 0.2 for different lexc (after [76]).

/ppc(r) = Id + const, [l - exp(-QfO]'' oct^(at < 1),

(15)

where a and y are constants. The least squares fits of the initial PPC buildup data with Eq. 15 are plotted in Fig. 30 as solid lines with thefittedvalue of y being approximately 2.9 ± 0.2 for different lexc- The initial PPC buildup behavior in Alo.35Gao.65N epilayers is also caused by the tail states in the conduction band due to alloyfluctuations,similar to the case in ZnCdSe alloys. The novel feature exhibited by the initial PPC buildup kinetics observed in Al xGai_xN alloys, (/ppc(0 c< r^^"^^^), can be attributed to a unique functional dependence of (/x^> on {n) to be described below. The experimentally measured functional form of (/z^) vs (n) in Al xGai_xN alloys is shown in Fig. 31, which shows that /x^ is a constant when n is below a critical value He and it increases with « at « > AZ^. This behavior is caused by the electron filling effects in the localized tail states in AlGaN alloys. When n < ric, electrons are localized in the tail states and contribute to the Hall-mobility only through hopping or tunneling. As « increases and reaches a certain critical value itc, the electron quasi-Fermi-level, Ef, reaches above the mobility edge E^, at which a transition from localized electron transport to a free electron transport takes place. Thus the electron mobility is expected to increase with n above ric. The experimentally measured dependence of (/x^) on {n) in

Persistent photoconductivity in IlJ-nitrides

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Al xGai_xN alloys can be well described by M^ = A^o + A{n - ncYO{n - ric).

(16)

where |Xo is the electron mobility 3i n < ric and 9(n — ric) is a step function, with A, He, and p being fitting parameters. The second term in Eq. 16 describes the conduction contributed by electrons with energies above E^. The least squares fit of data with Eq. 16 is plotted as the solid line in Fig. 31 and the fitted values are /XQ = 86.4 cm^/Vs, He = 1.46 X 10^^ cm~^, and p = 1.6, respectively. Since the measured electron concentration in darkness is about 1.43 x 10^^ cm~^ ^ He, SO (n — He) corresponds approximately to the photoexcited electron concentration, HQ. From the fitted value of HQ (^ 1.46 x 10^^ cm~^), we can also conclude that the total density of the band tail states below the mobility edge in AlxGai_xN alloys is about 1.46 X 10^^ cm"^, which is direcdy correlated with the degree of alloy fluctuations in these materials. From Eq. 16 and Fig. 33, one obtains /z^ a [n^(0]^'^ (for n > ric). One therefore obtains /ppc(0 oc a(t) a (/Xen^) a [rieit)]^^ oc r^-^, since rieit) ex t at Q?/ < 1 from Eq. 1. On the other hand, when one fits the initial PPC buildup kinetics shown in Fig. 30 directly to Eq. 15, /^pc(0 a r^, y = 2.9 ± 0.2 (at < 1), which is very close to the value obtained from the mobility measurements. Thus one can conclude that the initial PPC buildup kinetics in AlGaN alloys shown in Fig. 30 is a nature consequence of the unique relationship between /Xg and n described by Eq. 16. These results have demonstrated that alloy fluctuation strongly influences the transport properties of AlGaN alloys and that the PPC effects can be utilized to probe

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H.X. Jiang and J. Y. Lin

the properties induced by alloy fluctuations, such as the density of the tail states and the mobility behavior near the mobility edge. Moreover, these results also indicate that for Ill-nitride device applications using AlxGai_xN, effects of alloy fluctuations are important even at room temperature due to the large band gap difference between GaN and AIN. Different relationships between jie and n as well as the initial PPC buildup kinetics observed in AlxGai_xN and ZnxCdi_xSe alloys may be due to the fact that the band gap difference between AIN and GaN (AEg = 2.8 eV) is much larger than the difference between ZnSe and CdSe (AEg = 1.1 eV), which may result in a stronger effect of alloy fluctuations as well as a different distribution of the tail states in AlxGai_xN alloys. 4,2, Electronic quality ofAlGaN/GaN HFET structures probed by PPC The correlation between the PPC effect and the electronic quality of MOCVD grown AlGaN/GaN HFET structures was investigated [78]. The generic structure of samples used in for this particular study consisted of a 1.3 |Jim highly insulating GaN epilayer followed by a Alo.iGao.gN spacer layer (between 4 and 25 nm) and finally a Si-doped Alo.2Gao.8N epilayer of 25 nm. A total of seven samples with varying growth or structural parameters were studied, all of which exhibited PPC effect. Fig. 32 presents the PPC results obtained for three representative samples measured at two different

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Persistent photoconductivity in lll-nitrides

Ch. 6

187

Table 1. Hall-effect and PPC results measured at 20 and 300 K of the seven Alo.2Gao.8N/GaN HFET structures, together with the structural parameters (spacer and Si-doped AlGaN layer thicknesses), the relative Si-doping levels (SiJij flow rate), and the growth pressure Sample no.

Mobility Sheet density PPC ratio i-AIFaN/ SiH4 Pressure HsM (lO^Vcm^) (cmVVs) (torr) (lO^VVs) [(Ippc - Id)/Id] X 100% n-AlGaN (seem) 20 K/300 K 20 K/300 K 20 K/300 K 20 K/300 K thickness (nm)

1 2 3 4 5 6 7

4950/1230 3760/870 2920/884 2150/573 1620/703 600/280 2800/485

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4.95/1.42 2.86/1.19 2.28/1.00 1.81/0.53 1.13/0.52 0.59/0.33 0.31/0.05

3.31/3.42 5.84/5.32 7.10/6.75 8.34/11.2 37.4/14.3 39.2/18.3 200/300

6/25 8/25 4/25 6/25 6/25 6/25 25/25

3 1 1 1 1 0 0

100 150 150 150 100 100 77

All structures were grown at 1050°C in a variable pressure MOCVD. Here Ippc denotes the buildup levels of the persistent currents for a fixed excitation intensity and buildup time span and U the initial dark current levels.

temperatures. We can see that the decay time constants of the low temperature PPC are very long. Interestingly, the magnitude of PPC in AlGaN/GaN HFET structures and hence the device instabilities can be minimized by varying the growth conditions as well as structural parameters. Table 1 summarizes the Hall and PPC measurement results for all seven structures with different structural and growth parameters. As shown in Table 1, the magnitude of PPC or the photoinduced conductivity enhancement (^ppc — h) over its dark level {Id) is about 200% in sample #7, but is negligibly small (only about 3%) in sample #1. The general trends shown in Table 1 are that samples possess higher mobilities as well as higher sheet carrier densities exhibit reduced PPC. By carefully inspecting the results summarized in Table 1, we can clearly see that the magnitude of PPC, or the photoinduced conductivity enhancement, has a systematic dependence only on the product of the 2DEG sheet carrier density and mobility, i.e., n^/x, the most important intrinsic material parameter for the HFET device design. In Fig. 33, the magnitude of PPC versus n^/x measured at 20 K (a) and 300 K (b) are replotted. At both temperatures, the magnitude of PPC decreases monotonously with an increase of n^/x, follows the relationship of Rppc = A(/2,/x)-^

(17)

Here the magnitude of PPC (Rppc) is defined as [(/ppc — Id)/ld\ and A and a are two constants. As illustrated in Table 1, the better structures (i.e., larger values of W5/X) were achieved by varying the AlGaN space layer thickness, the Si-doped AlGaN layer thickness, the doping levels in the Si-doped AlGaN layer, and the growth pressure. The electronic qualities (or n^/x values) of these HFET structures can be further improved by adjusting the four parameters described above until the magnitude of PPC further reduces to zero. In desired structures with minimal PPC effects, enhanced mobilities can be accomplished by barrier or channel doping. However, at much greater sheet carrier densities.

Ch. 6

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the population of the higher-lying subbands could limit the overall mobility of the structure due to intersubband scattering as well as the loss of the true two-dimensional character due to a virtual continuum of bands being populated [79,80]. Thus a trade-off between these effects must be considered in the design and optimization of AlGaN/GaN HFETs. 5. Concluding remarks Our understandings of the properties of PPC and associated deep level centers in Ill-nitrides have built on the early studies on AlGaAs alloys. Studies of PPC in Ill-nitrides, just as any other topics in this field, are driven primarily by technological developments and needs. This trend will be continued. Current devices in the Ill-nitrides all take advantages of heterostructures and quantum wells. In this sense, understanding and control of PPC as well as the associated deep level centers and their effects

Persistent photoconductivity in Ill-nitrides Ch. 6

189

on devices based heterostructures and quantum wells will become more and more important. As the nitride materials quality further improves, the nature of deep level center as well as their characteristics can be identified. With the insights from theoretical calculations, the detailed information regarding the energy levels as well as their atomic configurations in IE-nitride lattices will be understood. Acknowledgements We are indebted to many of the pioneers as well as our respected friends in the field. Professor H.J. Queisser, Dr. J.D. Chadi, Professor J. Furdyna, Professor D. Redfield, Professor G. Neumark, and Professor D.C. Look, whose earlier work on PPC and DX like centers in conventional III-V and II-VI semiconductors have inspired us greatly. We are grateful to Professor Hadis Morkoc and Professor M. Asif Khan for their long term collaboration and support. We would like to acknowledge assistance from the following members in our group, J.Z. Li, J. Li„ K.C. Zeng, C. Johnson, M. Smith, R. Mair, C. Ellis, and S.X. Jin. We would like to take this opportunity to thank Dr. John Zavada, Dr. Kepi Wu, Dr. Yoon Soo Park, Dr. Vem Hess, and Dr. Jerry Smith, for their insights and constant support. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

S.N. Mohammad and H. Morkoc, Prog. Quantum Electron. 208, 361 (1996). N. Nakamura, G. Fasol, The Blue Laser Diode, Springer Veriag, Beriin, 1997. M.A. Khan, M.S. Shur, Q.C. Chen and J.N. Kuznia, Electron. Lett. 30, 2175 (1994). S.C. Binari, W. Kruppa, H.B. Dietrich, G. Kelner, A.E. Wickenden and A.J. Freitas Jr., Solid State Electron. 41, 1549 (1997). RB. Klein, J.A. Freitas Jr., S.C. Binari and A.E. Wickenden, Appl. Phys. Lett. 75, 4016 (1999). J.Z. Li, J.Y. Lin, H.X. Jiang and M. Asif Khan, Appl. Phys. Lett. 72, 2868 (1998). RM. Solomon and H. Morkoc, IEEE Trans. Electron Devices ED-31, 1051 (1984). J.F. Rochette, P. Delescluse, M. Lavin, D. Delagebeaudeuf, J. Chevrier and N.T. Linh, Inst. Phys. Conf. Ser. 65, 385 (1982). R. Fisher, T.J. Drummond, J. Klem, W. Kopp, T.S. Henderson, D. Perrachione and H. Morkoc, IEEE Trans. Electron Devices ED-31, 1028 (1984). A. Kastalsky and R.A. Kiehl, IEEE Trans. Electron Devices ED-33, 414 (1986). RM. Mooney, J. Appl. Phys. 67, Rl (1990). M.I. Nathan, Solid State Electron. 29, 167 (1986). H.J. Stormer, R. Dingle, A.C. Gossard, W.W. Wiegmann and M.D. Sttirge, Solid State Commun. 29, 705 (1974). R.A. Linke, T. Thio, J.D. Chadi and G.E. Devlin, Appl. Phys. Lett. 65, 16 (1994). R.L. MacDonald, R.A. Linke, J.D. Chadi, T. Thio, G.E. Devlin and R Becla, Optics Lett. 19, 2131 (1994). D.E. Theodorou, H.J. Queisser and E. Bauser, Appl. Phys. Lett. 41, 628 (1982). H.X. Jiang, A. Dissanayake and J.Y. Lin, Phys. Rev. B 45, 4520 (1992). M. Smith, J.Y. Lin and H.X. Jiang, Phys. Rev. B 51, 4132 (1995). M. Smith, J.Y. Lin and H.X. Jiang, Phys. Rev. B 54, 1471 (1996). CH. Henry and D.V. Lang, Phys. Rev. B 15, 989 (1977). D.V. Lang and R.A. Logan, Phys. Rev. Lett. 39, 635 (1977). D.J. Chadi and K.J. Chang, Phys. Rev. Lett. 61, 873 (1988).

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D.V. Lang. In: S. Pantelides (Ed.), Deep Centers in Semiconductors, 2nd ed., Gordon and Breach, New York, 1992, p. 591. J.M. Langer. In: F. Beleznay, G. Ferenczi, J. Giber (Eds.), New Developments in Semiconductor Physics, Springer Verlag, Berlin, 1980, p. 123. D. Redfield, R.H. Bube, Photoinduced Defects in Semiconductors, Cambridge University Press, Cambridge, 1996. H.J. Queisser and D.E. Theodorou, Phys. Rev. Lett. 43, 401 (1979). H.J. Queisser and D.E. Theodorou, Phys. Rev. B 33, 4027 (1986). H.X. Jiang and J.Y. Lin, Phys. Rev. B 40, 10025 (1989). H.X. Jiang and J.Y. Lin, Phys. Rev. Lett. 64, 2547 (1990). C. Johnson, J.Y. Lin, H.X. Jiang, M. Asif Khan and C.J. Sun, Appl. Phys. Lett. 68, 1808 (1996). J.Z. Li, J.Y. Lin, H.X. Jiang, A. Salvador, A. Botchkarev and H. Morkoc, Appl. Phys. Lett. 69, 1474 (1996). G. Beadie, W.S. Rabinovich, A.E. Wickenden, D.D. Koleske, S.C. Binari and J.A. Freitsa Jr., Appl. Phys. Lett. 71, 1092(1997). C H . Qiu and J.I. Pankove, Appl. Phys. Lett. 70, 1983 (1997). M.T. Hirsch, A. Wolk, W. Walukiewicz and E.E. Haller, Appl. Phys. Lett. 71, 1098 (1997). H.IVI. Chen, YR Chen, IVI.C. Lee and M.S. Feng, J. Appl. Phys. 82, 899 (1997). H.M. Chen, YE Chen, M.C. Lee and M.S. Feng, Phys. Rev. B 56, 6942 (1997). J.Z. Li, J.Y. Lin, H.X. Jiang, M. Asif Khan and Q. Chen, J. Appl. Phys. 82, 1227 (1997). J.Z. Li, J.Y Lin, H.X. Jiang, M. Asif Khan and Q. Chen, J. Vac. Sci. Technol. B 15, 1117 (1997). X.Z. Dang, CD. Wang, E.T. Yu, K.S. Boutros and J.M. Redwing, Appl. Lett. Phys. 72, 2745 (1998). R.J. Nelson, Appl. Phys. Lett. 31, 351 (1977). W. Rieger, R. Dimitrov, D. Brunner, E. Rohrer, O. Ambacher and M. Stutzmann, Phys. Rev. B 54 (17), 596 (1996). D.E. Lacklison, J.J. Harris, CT. Foxon, J. Hewett, D. Hihon and C Robert, Semicond. Sci. Technol. 3, 633 (1988). A. Dissanayake, M. Elahi, H.X. Jiang and J.Y. Lin, Phys. Rev. B 45, 13996 (1992). J.Y. Lin, A. Dissanayake, G. Brown and H.X. Jiang, Phys. Rev. B 42, 5855 (1990). V.C Aguilera-Navarro, G.A. Estevez and A. Kostecki, J. Appl. Phys. 63, 2848 (1988). T. Tanaka, A. Watanabe, A. Amana, Y Lobayashi, I. Akasaki, S. Yamazaki and Koike, Appl. Phys. Lett. 65, 593 (1994). W. Gotz, N.M. Johnson, J. Walker and D.P Bour, Appl. Phys. Lett. 67, 2666 (1995). I.K. Shmagin, J.R Muth, J.H. Lee, R.M. Kolbas, C M . Balkas, Z. Sitar and R.E Davis, Appl. Phys. Lett. 71, 455 (1997). S.J. Xu, G. Li, S.J. Chua, X.C Wang and W. Wang, Appl. Phys. Lett. 72, 2451 (1998). B. Kim, I. Kuskovsky, I.R Herman, D. Li and G.R Neumark, J. Appl. Phys. 86, 2034 (1999). V.A. Joshkin, J.C Koberts, E.G. Mcintosh, S.M. Bedair, E.L. Finer and M.K. Behbehani, Appl. Phys. Lett. 71, 234 (1997). I.K. Shmagin, J.E Muth, R.M. Kolbas, M.R Mack, A.C Abare, S. Keller, L.A. Coldren, U.K. Mishra and S.P DenBaars, Appl. Phys. Lett. 71, 1455 (1997). V.G. Sidorov, M.D. Shagalov, Yu.K. Shalabutov and I.G. Pichugin, Sov. Phys. Semicond. 11, 94 (1977). G. Lucovsky, Solid State Commun. 3, 299 (1965). D.J. Chadi and K.J. Chang, Phys. Rev. Lett 60, 2187 (1988). J. Dabrowski and Scheffler, Phys. Rev. Lett. 60, 2183 (1988). CV. Reddy, K. Balakrishnan, H. Okumura and S. Yoshida, Appl. Phys. Lett. 73, 244 (1998). M.D. McCluskey, N.M. Johnson, CG. Van de Walle, D.P Bour, M. Kneissl and W. Walukiewicz, Phys. Rev. Lett. 80, 4008 (1998). C Skierbiszewki, T. Suski, M. Leszczynski, M. Shin, M. Skoweonski, M.D. Bremser and R.E Davis, Appl. Phys. Lett. 74, 3833 (1999). M. Stutzmann, O. Ambacher, A. Cros, M.S. Brandt, H. Angerer, R. Dimirov, N. Reinacher and T. Metzger, Mater. Sci. Eng. B 50, 212 (1997).

Persistent photoconductivity in Ill-nitrides [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80]

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III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 7

Ion implantation, isolation and thermal processing of GaN and related materials Bemd Rauschenbach 1. Introduction GaN has attracted a widespread attention for the fabrication of blue light-emitting diodes, blue laser diodes and high-power or high-temperature devices (see e.g. [1,2]). These applications are related to very distinct properties of GaN such as the large direct bandgap or the high thermal conductivity. Ion implantation has become a highly developed tool for modifying the structure and properties of semiconductors. The energetic implants are applied in the doping of semiconductor material, the formation of insulator regions to isolate the active regions of circuits, in the fabrication of optical active regions and also in the device application. The advantages of the ion implantation are: • An accurate dose control is possible by measurement of the ion current. • The depth distribution of the injected dopants and the introduced lattice disorder are directly related to the ion energy and the masses of the target material and ion. By variation of the ion energy and dose the concentration profile of the impurities and also the structural changes can be tailored. • In contrast to high temperature processing the ion implantation is an intrinsic low temperature process, although subsequent annealing is generally necessary. In this respect it differs greatly from the diffusion approach, where high temperatures during doping may lead to decomposition of the near surface region. • Ion implantation is insensitive to the lattice structure, lattice defects and the presence of impurities. • The implantation process is not constrained by thermodynamic considerations. This means, that any species of ion may be implanted into any host. A wide concentration range can be achieved with the upper limit generally set by the sputtering yield rather than by equilibrium solubility. • Ion implantation can be included in the semiconductor process technology and implantation machines can be designed for specific applications. To understand and to control the electrical and optical properties of group Ill-nitride is one of the great challenges associated with the development of semiconductors. It is well-known that wide band gap semiconductors are difficult to dope by ion implantation due to the native defects and the high resistance against the damage recovery. As the quality of epitaxial GaN layers continues to improve, ion implantation is considered to be a promising doping technology. Recent progress has been made in this field

194

Ch. 7

B. Rauschenbach

such as the controlled p-type doping, damage annealing, implant isolation, implantation induced optical activation as well as device fabrication. The main disadvantage of the ion implantation in semiconductors is related to the lattice disorder caused by implanted ions. Because of the high background electron concentration of the as-growth GaN, ion implantation with high concentrations of acceptors is generally needed to compensate the native electron background and to realize the transition to p-type. However, the crystalline structure is diminished by implantation induced damage after implantation with high dopant concentrations. Consequently, a precise control of implantation conditions such as ion energy, temperature during implantation, ion dose, etc., and an optimal annealing process are essential to successful doping by ion implantation. The purpose of this review is to present an introduction into and a review of the state of ion implantation in GaN and related III-V materials. Although significant progress has been reported for doping and isolation of wide band gap semiconductors, there are still many problems to be solved before an extensive application of ion implantation in device fabrication can be realized. In recent years several excellent review papers have appeared addressing various aspects of the implantation technology of group Ill-nitrides [3-5]. This review is devoted to the implantation induced damage and the defect annealing. The realization of the controlled n-type and p-type doping by ion implantation is discussed with the main emphasis on the results of GaN. Then, the impurity luminescence and isolation by ion implantation are discussed. 2. Ion implantation process 2.1. Range and range distribution When an energetic ion strikes a solid surface the ion will in general lose energy through scattering events involving the Coulomb interaction with the target atoms. This collision process is a complicated many-body event described by an extremely difficult Hamiltonian. The problem can be simplified when it is recognized that the interaction range is very short (forces between the ion and target atom decrease rapidly with the distance). This circumstance allows to consider the interaction of the incident ion or the recoiling target atom with the target atom individually and to ignore the contributions due to more remote lattice atoms. In this so-called binary collision approximation the slowing down process of an incoming ion in a solid can be roughly divided into two energy loss mechanisms: the elastic or nuclear energy loss (Coulomb interaction between two screened positive charges) and the inelastic or electronic energy loss (direct electron-electron energy transfer, excitation of band and conduction electrons, excitation or ionization of strongly bounded target and projectile electrons). Energy loss of an ion through an amorphous material is given by dE

, _ _

/dE\

/dE\

- = -NS(E) = ( - ) _ + (_)^

,„

where N is the atomic density, dE is the energy loss by an ion traversing a distance dx and S(E) the stopping cross-section. The so-called stopping power dE/dx, depending on the mass and velocity of the ion and the target, can be separated into the nuclear

Ion implantation^ isolation and thermal processing ofGaN 105

1 '

'r^ o k— o E

10^

103

195

1

'

E3

Ch. 7

E,

(dE/dx), ~ E'^ (dE/dx),-E' 1

• """^x^"^""^^

X H

\

HI "D 102

X

10^ 10^

102

103

lO'^

(dE/dxG (dE/dx)„|

^

;

105

106

Ion energy (keV) Fig. 1. Dependence of the nuclear (dE/dx)n and the electronic (dE/dx)e stopping power in GaN on the energy of incident Ca"^ ions. Also indicated are the characteristic energies Ea, Eb and Ec (after [6]).

and the electronic stopping cross-sections, Sn(E) and Se(E), corresponding to the two energy loss processes. The nuclear stopping dominates at low energies and the electronic stopping at high energies. This behavior is illustrated in Fig. 1 for the implantation of Ca"^-ions into GaN. Three characteristic energies are given: Ea ^ 30 keV, is the energy where the nuclear stopping power reaches its maximum, Eb ^ 270 keV is the energy where the electronic and nuclear stopping power are equal and Ec ^ 50 MeV is the energy where the electronic stopping power has its maximum [6]. It is important to notice that host atoms are severely displaced only in the energy regime in which nuclear stopping power dominates, while electronic stopping usually does not create extensive damages. Inverting the expression (Eq. 1), the total path length R(E) travelling by a particle of initial energy before coming to rest is '^

dE

(2) Jo NS(E) Clearly, for individual projectiles the number of collisions, the energy transferred and thus the total path length will vary. The ion range normal to the surface, termed the mean projected range Rp(E) is smaller than R(E). The range traveled along the axis perpendicular to that of incidence is called the lateral range Rx. The stochastic fluctuations in the energy loss mechanisms lead to a spreading ion range described by the projected range straggling ARp. The spreading (standard deviation) is a function of mass ratio (mass of the target material to the mass of the incident ions, M2/M1) and will increase with increasing depth into the target. The straggling effect results in an ion depth distribution C(x) which is approximately Gaussian in shape R(E)

C(x)

(X - Rp)^

O /TTT ARt

exp

2AR2

(3)

where 4> is the ion dose in [ions/cm^]. The maximum or peak concentration is Cmax = 0.4/ARp. Furthermore, as a result of multiple collisions the ions will be deviated from

196

^h. 7

B. Rauschenbach

their original direction and there will be lateral spreading (lateral straggling ARj.) of the incident ions. ARx = ARp for M2/M1 ^ 10, ARj. = 0.5 ARp for M2 = Mi, and AR_L ^ ARp for M2/M1 = 0.1. In practice, the lateral spreading is only of relevance when the implanted region is defined by a mask window. Two general methods for the calculation of the range and range distribution have been developed. Firstly, an analytical approach based on the Boltzmann transport equation was pioneered by Lindhard et al. [7], and is often referred to as LSS theory. A more exact calculation is available using the PRAL (Project Range ALgorithm) code [8]. Second, Monte Carlo binary collision computer simulations are carried out for range and damage analysis, where both a random target (e.g. TRIM, TRansport of Ions in Matter, or TRIDYN, dynamical TRIM) or a single-crystalline targets (e.g. MARLOWE) are used (details see [9]). As an example, the mean projected range Rp(E) and the projected range straggling ARp of several ion species for implantation with energies up to 500 keV into GaN calculated using TRIM are shown in Fig. 2a. On this basis, the concentration versus depth distribution can be calculated with Eq. 3. Fig. 2b shows the calculated calcium concentration distribution in GaN for implantation with a dose of 1 x 10^"^ Ca'^-ions/cm^ and three different energies. With increasing ion energy and depth of ion penetration the maximum concentration decreases because of the larger standard deviations. By comparison with experimental results, the Gaussian distribution is often not a satisfactory fit. The experimentally determined doping profiles tend to be asymmetrical, that means the concentration distributions are shifted or spread out. Often the Pearson distribution is used which based is on the first four moments (Rp, ARp, skewness, kurtosis). Additional physical effects can influence the concentration distribution. Mainly three effects have to be discussed in this context: 2.1.1. Influence of sputtering The sputtering yield Y is the number of ejected target atoms per incident ion and depends on E, Mi, M2, angle of incidence and temperature. For the implantation in GaN and related compounds the sputtering effect plays an important role for low energy implantation with heavy ions, because the nuclear stopping is large under these conditions (see Fig. 1). Eq. 3 can easily be extended to include the sputtering effect. Now, the concentration profile is described by .(X) =

^

^x — Rp + z X — Rp erf—-=r^ erf— V5ARp V2ARp

(4)

where Y is the sputtering coefficient and z = O Y / N is the thickness of the sputtered layer [10]. Sputtering yields between about 0.25 and 2.0 have been measured after Ar^-ion bombardment of GaN with energies between 150 and 600 eV [11]. Unfortunately, more detailed information about the sputtering yield of GaN cannot be found in the literature. 2.1.2. Influence of radiation enhanced diffusion In presence of ion irradiation, the thermally activated migration of implantation-induced vacancy and interstitial defects is known as radiation enhanced diffusion (RED). The

Ion implantation, isolation and thermal processing ofGaN

Ch. 7

197

200

E Q.

DC < 400

E c DC 2 0 0

200

100

300

400

500

Energy (keV)

1

(b)

A 50 keV E o

-

2

c g m C 1 0 O

J /

\

/

\

1/

/

lO^^CaVcm^GaN 100 keV

\

\

200 keV

c o O

50

100

150

200

250

Depth (nm) Fig. 2. (a) Calculated values of the mean projected range Rp(E) and the projected range straggling ARp for several ion species after implantation with energies up to 500 keV into GaN. (b) Calculated calcium concentration distribution in GaN for implantation with a dose of 1 x 10*"^ Ca"*"-ions/cm^ and three different energies.

diffusion can be significantly enhanced under irradiation by both increasing the concentration of implantation-induced defects and by creating other diffusion mechanisms via usually not active defect species [12]. The descriptions based on a set of coupled chemical rate equations. The radiation-enhanced diffusion coefficient DR is given by the sum DR = CyDv + QDi, where Cv,i are the concentrations of the interstitials or vacancies and Dv,i are the diffusivities of vacancies or interstitials induced by implantation. The diffusivity is calculated from the equation Dyj = Doexp(-AHv,i/kBT), where AHv,i is the migration enthalpy of the vacancy or interstitial atoms and ICB is the Boltzmann constant. The influence of the RED on the concentration distribution of the implanted atom species can be approximately calculated under the assumption that the diffusion of

198

Ch, 7

B. Rauschenbach

implantation induced vacancies determines the diffusion process (the migration enthalpy of interstitials is very small, AHi < 0.3 eV) [10]. The concentration profiles become increasingly asymmetrical and larger depths are reached in presence of the RED. 2.13. Influence of channeling In the preceding discussion the target is assumed to be amorphous and isotropic. However, the interactions between the incoming ions and the lattice atoms will be minimized if the ions are directed down a crystallographic axis or plane. A careful alignment between the ion beam direction and a planar or axial channel is to give an enhanced penetration into the solid which can be as much as 10 Rp. The key parameter is the critical acceptance angle which depends on the ion energy, the ion species and the lattice parameters. The implantation at angles between the main crystal axes and the ion beam smaller than the critical angle gives rise to tails of in the concentration profiles. Consequently, the shape of the concentration distribution is difficult to predict. Two standard approaches to overcome channeling are (i) the implantation into a tilted target (tilt angle e.g. T off main crystal axes) or (ii) low-energy self-ion implantation to amorphize the near surface region. Especially for doses higher than 10^^ ions/cm^ the precise reproducibility of the concentration profiles is difficult to realize because the radiation damage generation reinforces the dechanneling. 2.2. Damage and damage distribution An energetic ion which penetrates into a solid loses its energy via both electronic excitation/ionization and elastic collisions with the target atoms before coming to rest in the host lattice. The latter process, dominant at low ion velocities, leads to atomic displacements (radiation damage). The energy required to displace an atom from a lattice site and form a Frenkel pair is larger than the so-called displacement energy Ed. For example, the threshold displacement energy for GaN is 24.3 eV [13]. The primary knock-on target atom (PKA) will collide with other lattice atoms which in turn will displace further lattice atoms. Thus an avalanche-like process of moving atoms which distribute the energy in successive collisions until the energy is below Ed is obtained. Assuming that only those recoiled atoms become displaced which received an energy E > Ed, the total number of displaced atoms Nd is obtained from the modified Kinchin-Pease relationship [14] to Nd(x) = 0 . 8 ^ ^

(6)

zbd

where FD(X) is the deposited energy depth distribution function, i.e. the total energy deposited in elastic collision processes or nuclear recoil loss. The damage energy is smaller than the nuclear stopping power of the primary ion because the recoils partially lose their kinetic energy by electronic processes in subsequent collisions. A rough approximation is FD(X) = 0.7 . . . 0.8 Sn(E(x)). Commonly, the number of

Ion implantation, isolation and thermal processing ofGaN

150

200

Ch. 7

199

250

Depth [nm] Fig. 3. Defect concentration distribution in GaN measured by RBS/C (solid points) and calculated by TRIDYN (line) after implantation with 5 x 10^^ Ca^/cm^ and an energy of 180 keV (after [15]).

displacements per atom, dpa, is used to describe the damage and is given by the equation .FD(X)C|>

dpa(x) = 0.8-

(7)

FD(x)dx = NSn(E(x))dx

(8)

2Ed N The damage distribution is in a similar form as the distribution of the implanted ions,

however, the peak is closer to the surface. The Gaussian form of the damage distribution reflects the statistical nature of the scattering events. Conmionly used algorithms for defect formation are based on the previously mentioned TRIM or TRIDYN codes. As an example, in Fig. 3 the measured depth distribution of defects after Ca^-ion implantation in GaN is compared with results of a Monte-Carlo simulation. The agreement between the measured and simulated curves is good. A comparison of the mean projected range of 180 keV Ca-ions after implantation in GaN (see Fig. 2a) with the mean projected damage range (peak in Fig. 3) demonstrates that the damage profile is closer to the surface. The shape of the damage profile tends to be non-Gaussian. It is obvious that the calculation only refers to the initial damage situation during the passage of the ion. A complete or partial lattice recovery can occur after the implantation process. This results in an overestimation of the defect concentration by simulation especially for implantation at higher temperatures. Consequently, the temperature at which the target is bombarded is an important parameter since it governs the mobility of defects. As long as the collision density is sufficiently small, so that each collision can be described by a binary event, the energy deposition is given by the linear Boltzmann transport equation. For such a linear cascade, the number of defects varies linearly with the total deposited elastic energy. The concept of successive binary collisions with a fixed threshold energy does no longer hold if in a cascade volume each atom receives more than 1 eV/atom. A collective motion of all cascade atoms (thermal spike concept)

200

Ch. 7

B. Rauschenbach

is a better picture to describe this state (displacement cascade). Such highly disordered region is not in thermal equilibrium. The energy deposition within a cascade survives for times between 10"^^ and 10"^ s. The final state of such a cascade is critically dependent on relaxation process and it can vary from an amorphous region to a region in which there is perfect epitaxial regrowth. 2,3, Defect

evolution

In semiconductors, the implanted ions are incorporated interstitially, which causes small lattice deformations and generate defects. Especially, the latter accumulate during the implantation process. In the linear cascade regime, the damage build-up would result from the defect accumulation up to a critical defect density and in the displacement cascade regime, a disordered region including amorphization would arise due to direct ion impact mechanism. In semiconductor targets it can be observed that an amorphous region is built-up around the whole ion track, whereas in the case of metals only a small amorphized volume around an implanted ion can be kept. Consequently, a substantial difference in order of magnitude of amorphization doses has been measured in semiconductors (10^-^-10*^ ions/cm^) and metals (10^^-10^'^ ions/cm^). The evolution of the damage formation in dependence on the ion dose and temperature depends mainly on both the energy density deposited by the implanted ions and the impurities acting as disorder stabilizers. A large number of semiconductor implantation experiments exhibit that the crystalline-to-disorder (amorphization) transition results from the combination of these two effects (disorder production and chemical stabilization). For the process of damage generation and accumulation until amorphization a sigmoidally shaped curve of damage as a function of doses on a double-log scale has been found. This behavior has been observed for one-component semiconductors, such as Si, Ge and also III-V compound semiconductors. It is obviously that this transition occurs locally, since the fraction of disorder or amorphous volume changes continuously with the ion dose. Several models describe the dose dependence of the disorder or amorphized fraction. In general, the time (dose) evolution of phase transformation under isothermal conditions has been described by the Johnson-Mehl-Avrami equation [16]. This equation has become widely used to analyse transformations, in spite of the fact that the interpretation of its parameters is far from straightforward. Morehead and Crowder [17] proposed a model which hypothesized that each ion impinging on the target produces a cylindrical amorphous core. Amorphization occurs when such damage cores completely fill the area of the target. According to this semi-quantitative model, the critical dose for amorphization decreases with increasing ion mass and is constant at sufficiently low temperature. Gibbons [18] has modified this model by assuming that an amorphous layer can also be produced by the overlap of damaged, nonamorphous regions associated with individual damage clusters. In this model amorphization (most extreme possible disorder) is supposed to occur either by a direct ion impact mechanism (n = 1) i.e. immediate amorphization caused by the first ion penetrating an undamaged region, or by overlapping of damaged regions around the ion collision cascades (n > 2), as during amorphization by accumulation of defects. The transformed volume fraction Vtr/Vo can

Ion implantation, isolation and thermal processing ofGaN

Ch. 7

201

be expressed as Vtr(O)

.

;^(Vion^

—TT— = 1 - 2 ^

jl

, ,,

^,

exp(-VionO)

(9)

^^ /=o ^• where Vion is the damage volume around the track of the implanted ion and Vo the total volume being implanted. The integer n is the number of ions required in the same region to cause amorphization. Therefore, simultaneous thermal defect relaxation during ion implantation at high temperatures has been taken into account [17]. 2.4. Post-implantation annealing The aim of the post-annealing process is both to activate electrically the dopants and to eliminate the implantation induced defects. In general the situation after implantation is characterized by the presence of several kinds of damage: heavily disordered crystalline regions, locally amorphous zones and an amorphous layer. The residual damage after annealing results in stacking faults, twins, dislocation lines, dislocation loops and point defects. Especially, the residual disorder in III-V semiconductors will compensate the electrical activity of dopants. The diving force for the transition from the damage state (non-equilibrium state) to a nearly damage-free state (equilibrium state) is the minimization of the appropriate thermodynamic energy function. It is often the configuration for which the lowest strain is attained. The following mechanisms contribute to the recovery: • migration of defects to fixed sinks (e.g. surfaces, dislocations, grain boundaries), • annihilation of defects by recombination (e.g. vacancies with interstitials), • agglomeration into more complex defects (e.g. formation of dislocation loops or vacancy-impurity complexes), • trapping at impurities. These processes are thermally activated by annealing and require high temperatures for long times. In general, the annealing of extended defects requires very high temperatures (> 1000°C). The temporal change of the concentration Cj of defect type j during annealing is given through a rate equation to

? = -kc;

(10)

dt ^ where, a is the rank of reaction (e.g. a = 1 for vacancy-interstitial annihilation), k is the rate constant and can be obtained from thermodynamic consideration to k= koexp(-^) (11) where ko is a temperature-independent constant which contains an entropy term and the jump rate and AE is the activation energy of the defect reaction. The type of defects can be determined by measuring of the activation energy using isothermal or isochronal annealing experiments. For example, the isochronal annealing experiment is characterized by annealing at a defined temperature for the duration At and a subsequent measurement of the defect concentration at room temperature (RT). This procedure is repeated many times for higher annealing temperatures.

202

Ch. 7

B. Rauschenbach

Together with Eq. 11, the integration of Eq. 10 leads for a first-rank reaction (a =

""[IS]—(-a In

where Ci and Ce are the measured defect concentrations before and after the annealing step at the temperature T. By fitting the measured concentration with Eq. 12 the activation energy and also the rate constant ko can be determined. The recovery by the mentioned defect reactions has been extensively studied. But, no broadly accepted model exists for semiconductors. Nevertheless, through a large number of systematic electrical resistivity, channeling and electron paramagnetic resonance (EPR) measurements it was possible to develop a qualitative model of recovery at isochronal annealing. There different recovery stages with increase of temperature are distinguished: • recombination of close interstitial-vacancy pairs at the lowest temperature, • free migration of interstitials, • growth of interstitial clusters followed eventually by dislocation loop formation, • free migration of vacancies, • growth of vacancy clusters, • dissociation of defect clusters at the highest temperature. Usually, the total recovery of compound semiconductors will not be obtained. Especially, irradiated III-V semiconductor materials show a poor recovery characteristic and exhibit a high degree of residual disorder in form of point defects, twins and stacking faults. These residual defects dramatically influence the electrical and optical properties. In praxis, furnace annealing and rapid thermal annealing (RTA) are used to remove the implantation induced damages and to activate the dopants. The furnace annealing of GaN and related materials is restricted both regarding relatively low temperatures, because these materials begin to decompose when the temperature is above 750-800°C and long annealing times are used (several hours). Prolonged annealing at these temperatures broaden the implanted dopant profiles. The post annealing distribution is given by C(x,t) y27i(AR2 + 2Dt)

exp

"2(AR2+2Dt)

diexp

(x + Rp)^ "2(AR2+2Dt) (13)

where D is the diffusion coefficient and t is the annealing time. The sign before the last term in Eq. 13 reflecting all out diffusing atoms from the surface (+) or through the surface (—). The disadvantages of the furnace annealing can be overcame using RTA by lamps with processing times of few seconds (1-30 s). The sample is typically heated to higher temperatures (< 1200°C) through transparent windows coupled with highly reflective mirrors. The emissivity and absorption are strongly influenced by the bulk and surface properties of the implanted samples. Consequently, these optical properties can change drastically by the implantation conditions (impurity content, damages, etc.) and surface coatings.

Ion implantation, isolation and thermal processing ofGaN

Ch. 7

203

3. Implantation induced defects As the quality of epitaxial GaN films continues to improve, ion implantation is considered to be a promising doping technology in fabricating planar devices of GaN and related group Ill-nitrides, because it can introduce a well-defined impurity concentration in a designed region and, therefore, allows isolation of devices from each other. 3.1. As-grown defect state GaN and related nitride layers are grown in their wurtzite structure on hexagonal sapphire (a-Al203) and 6H-SiC substrates. Because of the large lattice mismatch (approximately 15% between sapphire and GaN and 3% between SiC and GaN) and the differences in thermal expansion between deposited layer and the substrate material, point defects (native and extrinsic) and as well as one- and two-dimensional structural defects (dislocations, planar faults, etc.) are generated. These defects can profoundly influence the electrical, optical and mechanical properties. The native defects with the lowest formation energy and very low transition levels are the nitrogen vacancies, V^f, and the gallium vacancies, Voa, [19]. In the thermodynamic equilibrium, the nitrogen vacancies can be excluded as the source for the n-type doping of as grown GaN, i.e. the nitrogen vacancy acts as a single donor. Donor impurities such as carbon, silicon and oxygen which are unintentionally incorporated during the growth may be also responsible for the n-type doping of the as-grown GaN. These elements occupy Ga and N substitutional lattice sites as well as interstitial sites. For example, silicon on a Ga site, Sioa, is a shallow donor, oxygen and also carbon sit on nitrogen sites, CN, or form a defect cluster with Ga vacancies, CN-Voa [20]. Epitaxial GaN layers usually contain a high density of dislocations, microtwins and stacking faults. In general, dislocations start at the interface between substrate and the GaN layer and extend through the entire layer thickness. The main slip system in hexagonal GaN is 1/3 {0001} with a Burgers vector b = l / 3 < l l 20> equal to the shortest lattice vector along a close-packed direction. Dislocation densities in the range of 10^-10^^ cm""^ have been measured. 3.2. Damage buildup and amorphization The technique of ion implantation is extremely attractive for the fabrication of GaN and related III-V compound devices because it can introduce a well defined impurity concentration in a designed zone. However, this technique is still far away from application in processing GaN based semiconductor devices, primarily owing to ion beam induced lattice disorder, which deteriorates the electrical and optical properties. Although the research on GaN is in the ascendant, there remains almost a blank of understanding about the implant damage buildup, removal and their effects on the transport properties of GaN devices. So far there are only a few papers, which demonstrate damage generation due to ion implantation. Therefore, more work in both theory and experiment is necessary to get a reasonable picture of this important area. The

Ch. 7

204

B. Rauschenbach

damage of GaN films before and after implantation can be characterized by Rutherford backscattering/channeling spectrometry (RBS/C), cross-sectional transmission electron microscopy (XTEM), high resolution X-ray diffraction (XRD) and Raman spectroscopy (RS). In Table 1 studies are summarized which investigate the damage in GaN by ion implantation. Tan et al. [21-23] have studied the amorphization of GaN by Si"^-ion implantation at liquid nitrogen temperature (LNT). For a dose smaller than 1 x 10*^ Si'^-ions/cm^ the residual disorder consists of a dense network of small loops, clusters and dislocations whereas for a dose greater than 2.4 x 10^^ Si'^-ions/cm^ an amorphous structure is formed. These results indicate that the amorphous threshold for GaN is very high in comparison to other compound semiconductors (e.g. AlxGai_x As). Consequently, GaN is extremely resistant to amorphization during LNT implantation. Recently, systematic investigation of damage generation and accumulation until amorphization induced by Ca"^-, Mg"^- and Ar"^-ion implantation in GaN films at different temperatures have been published [6,24-27]. Fig. 4 shows [0001]-aligned and random backscattering spectra of the GaN films implanted with different Ca"*"-ion doses at LNT. It demonstrates the whole process of damage generation and accumulation until amorphization as a function of the ion dose. With the increase of Ca"^-ion fiuence, a damage peak arises in the channeling spectra. When the dose exceeds 1 x 10^^ ions/cm^, this peak grows up more quicldy, accompanied by a broadening towards the surface and greater depth, and reaches the random level at the dose of 6 x 10^^ ions/cm^. This means that a closed amorphized layer is formed. Jiang et al. [28] have shown that the damage evolution after implantation of the lighter element oxygen into GaN at low temperature (210 K) ranges from dilute defects up to the formation of a disorder saturation state that was not fully amorphous. It was found that the defects are

100 200 300 400 500 600 700 800 Channel Fig. 4. [0001]-oriented RBS/C spectra (2.5 MeV, '^He2+) illustrating the damage buildup in GaN films for 180 keV Ca+ implantation with different doses at LNT (after [25]).

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Ion implantation, isolation and thermal processing ofGaN

a

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a.

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; io ^ ;s ;s u s pQu u < u u u u

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212

Ch. 7

B. Rauschenbach

For partly ionic III-V compounds, the influence of the charge of dopant atoms on the lattice expansion should be additionally taken into account. In contrast to Ar, Ca atoms can set up chemical bonds with N atoms and reduce their volume when they occupy Ga vacancies. Thus the lattice expansion was somewhat restricted. Consequently, Ar doping leads to greater lattice expansion than Ca doping. The results suggest that ion implantation for p-type doping has to be carried out below this dose, in order to avoid unrecoverable structural damage and to achieve better transport properties. On the other hand, implantation with higher doses is generally needed to compensate the native electron background of GaN and to realize p-type reverse. This conflict uncovers the essential difficulty for p-type doping of GaN by ion implantation. 3.3. Damage recovery The main drawback of ion implantation in wide-bandgap semiconductors is related to the lattice disorder caused by energetic ions. Although GaN is extremely resistive against amorphization, it is not easily removed by thermal annealing even in the high temperature range of 1100°C [24,39] at which the electrical activation of dopants can be achieved. Additionally, GaN is known to degrade during post-annealing at temperatures over 800°C [40,41]. It is well laiown that the density of ion damage is a critical parameter for the subsequent defects removal and for the electrical activation of the implanted dopants [42]. The residual damage makes the electrical and optical properties of the doped GaN films undesirable and limits the application of ion implantation doping in GaN. Therefore, it is imperative to determine the relationship between damage buildup, recovery and the implanted dose. So far only a few contributions (see Table 1) concern with this important topic [26-28,31,38,43-49], but detailed information, such as the quantitative dependence of the implant damage on the dose, the critical dose, below which implantation-induced damage can be well removed by rapid thermal annealing (RTA), the impact of the residual damage on impurity activation and on electrical transport properties, has not been reported. Two different procedures are known for annealing after ion implantation. On the one hand, conventional tube furnace (CTF) and on the other hand the so-called rapid thermal annealing (RTA) are used. For the choice of the annealing approach, the best possible optimization of the thermal process is crucial with regard to anneal defects, to limit diffusion, to activate the dopants and to suppress the decomposition of the near-surface region. The furnace annealing is used to realize temperatures up to 1000°C for some hours. To overcome the limited temperature range, RTA treatments by tungsten-halogen lamps as heat sources with processing times of a few seconds are suitable up to 1200°C. Recently, RTA equipment have been developed which are capable to achieve temperatures up to 1900°C [50]. These RTA systems possess a molybdenum intermetallic composite heater and allow heat fluxes up to 100 W/cm^ in the order of seconds. Annealing of implanted GaN at high temperatures is extraordinarily difficult, because GaN begins to degrade at temperatures higher than 800°C. Several ways are used to anneal implanted GaN [5,43,51-53] by furnace or RTA, namely by four

Ion implantation, isolation and thermal processing ofGaN

Ch. 7

213

methods: (i) face-to-face arrangement so that the onset of the nitrogen loss can be suppressed, (ii) placing the implanted sample in a SiC-coated graphit susceptor in which powered AIN or InN are contained for production of a nitrogen vapor pressure over the sample, (iii) surface protection by Si3N4, SiC or AIN encupsulant layers, and (iv) annealing under a high nitrogen overpressure. The usual environment is NH3 or Ar for the furnace annealing and N2 or a mixture of N2 and NH3 for the RTA treatment. Virtually all experiments have shown that an annealing process up to temperatures of about 1200°C is insufficient to completely remove the implantation damage. Significant implantation induced damage remains after RTA or conventional furnace treatment at high temperatures when GaN has been implanted with Si"^-ions doses below 10^"^ ions/cm^ [45] or 10^^ ions/cm^ [43], with Si"^-ions and Mg"^-ions up to doses of 10^^ ions/cm^, with Er"^-ions up to doses of 5 x 10^^ ions/cm^ [46], with 0^-ions up to doses of 5 X 10^^ ions/cm^ [28] and with Ca"^-ions or Mg'*"-ions up to doses of 7.3 X 10^^ ions/cm^ [27,31]. An example is given in Fig. 10. RBS/C spectra of GaN after Ca"^-ion implantation with different doses at room temperature and after RTA treatment in flowing N2 are shown [25]. For doses below 1 x 10^^ ions/cm^, the channeling spectra exhibit the similar shape to that of the unimplanted sample. Especially, those implanted with doses lower than 8 x 10^"^ ions/cm^ coincide almost with the virgin's. This result indicates that the implant damage after room temperature implantation can be well removed by RTA, if the sample was implanted at low doses. Therefore, Ca'^-ion implantation for p-type doping should be carried out below the dose of 8 X 10^"* ions/cm^ at an ion energy of 180 keV, in order to avoid unrecoverable structural damage and to achieve better transport properties. For the Ca"^-ion dose of 3 X 10^^ ions/cm^, the damage peak can still be observed in the channeling spectrum. This means that significant damage remains after the RTA process. It seems reasonable

500

1000

1500

2000

Backscattering Energy (keV) Fig. 10. [0001]-oriented RBS/C spectra (2.5 MeV, '^He^+^ons) illustrating the damage residual after rapid thermal annealing at 1150°C for 15 s in flowing N2. GaN were implanted at room temperature. The data for two Ca+-ion implanted GaN samples are multiplied by a factor of 2 (after [26]).

Ch. 7

214

B. Rauschenbach

to increase the annealing temperature and to prolong the annealing time. However, the fact that GaN begins to decompose at temperatures over 800°C [41] limits the possibility of long-time annealing at higher temperatures. Similar results could be obtained after RTA treatment of GaN implanted at LNT [24,27]. It has been found that the implant damage can be well removed after the process of RTA, if the implantation dose is lower than 3 x 10^"^ Ca"^-ions/cm^ the dose at which the amorphous component arises. The amorphization of GaN develops very slowly up to the dose of 8 x 10*"^ Ca+-ion/cm^ (see Fig. 5) because of dynamic beam annealing [30]. However, when the dose exceeds 1 X 10^^ Ca"^-ions/cm^, the tendency of amorphization is increased more and more rapidly. Great residual damage remains in the doped GaN films and no significant reduction of damage can be observed even after 1150°C activation [31]. Therefore, Ca+-ion implantation at low temperature for p-type doping should be carried out at a dose below 3 x 10^"^ cm~^ in order to avoid unrecoverable structural damage and to achieve better transport properties. On the other hand, since unimplanted GaN films have generally a very high background electron concentration (about 1 x 10^^ cm~^ for a MBE as-grown GaN film), a high dose of acceptors (>1 x 10^^ ions/cm^) is needed to be implanted for the realization of p-type reversion. Unfortunately, this high dose implantation introduces unrecoverable damage, and the doped p-type carriers are easily trapped and compensated by the radiation defects, resulting in a less effective activation even after a high temperature annealing. Consequently, p-type doping in GaN is difficult to realize by ion implantation. The role of RTA is assessed by quantitatively comparing the area density of displaced atoms of the as-implanted and annealed samples. Fig. 11 shows the dose dependence of the density of the displaced atoms in GaN implanted with 180 keV Ca+- and 90 keV

101'

E o

as Ca'^-implanted

y

CO

c

CD

E o• -•— CO

W ]

critical level

•D

CD

Ca"*" implanted &/annealed

O _C0 GL

m io'6

^

10'^

n

Mg"^ implanted & annealed

10'5

w

Implanted ion dose (cm'^) Fig. 11. Dose dependence of the displaced atomic density induced by 180 keV Ca+-ion and 90 keV Mg+-ion implantation in GaN at room temperature before (filled dots and triangles) and after (open dots and triangles) rapid thermal annealing at 1150°C for 15 s inflowingN2 (after [31]).

Ion implantation, isolation and thermal processing of GaN

Ch. 7

215

Mg"^-ions at room temperature [31]. For Ca'*"-ion implantation, the density of the displaced atoms decreases after the process of RTA by an order of magnitude if the dose is lower than 8 x 10^"* ions/cm^. At this dose an initial amorphous component has been formed which is not easily removed by RTA [6]. Ronning et al. [54] found also that GaN after Be'^-ion implantation with a low dose up to 3 x 10^^ ions/cm^ is almost recovered after annealing at 1100°C for 1 h. When the dose is higher than 8 x 10^"* Ca~^-ions/cm^, the residual damage increases, and only a portion of the implantation induced damage can be annealed out. Moreover, for doses in excess of 3 x 10^^ ions/cm-^, great damage resides and no significant damage recovery can be achieved. This results indicates that the density of ion damage is a critical parameter for the subsequent defect removal and for the electrical activation of the implanted dopants. A similar relationship has been observed for Mg"^-ion implanted GaN (Fig. 11). Recovery of the implantation-induced damage can be achieved up to a dose of 2.5 x 10^"^ Mg"^-ions/cm^, a dose which is about three times higher than of Ca'^-ion implantation for the same amount of residual damage. In this sense, Mg"^-ion implantation has an advantage over Ca'^-ion implantation for p-type doping. For both Ca"^- and Mg"^- ion implantation, it can be concluded, quantitatively, that an integral defect density of 2 x 10^^ ions/cm^ is a critical level. Below this the implantation-induced damage can be well reduced by RTA. However, significant damage resides still after RTA if the integral damage density is higher than this critical level. This result reflects that the present annealing conditions are not suitable for highly doped GaN. Since the implanted p-type carriers are easily trapped and compensated by the radiation defects, it is necessary, especially for the highly doped GaN, to explore new annealing conditions and new methods to remove the damage and to activate the dopants. Exploring new ways and means to effectively remove the radiation damage by high dose implantation should also be placed on the agenda. Recently, Zolper [47] compared the melting point and activation temperature of the common compound semiconductors and deduced that the optimum implant activation temperature for GaN may be close to 1700°C. However, at this temperature GaN will decompose and a protective layer on GaN must be deposited before annealing and removed after annealing. Cao et al. [51] observe a strong reduction in lattice disorder of GaN implanted with several donor and acceptor species after annealing at 1500°C compared to samples annealed at 1100°C. Strite [48] and Suski [49] found that under considerable N2 overpressure GaN can be annealed at temperatures as high as 1550°C without significant N loss enabling efficient optical activation of implanted Zn in GaN. Annealing experiments of Si"^-ions implanted GaN up to 1500°C under high N-overpressure (up to 15.3 kbar) have also demonstrated that the RES channeling yield is equivalent to that of the unimplanted sample and no macroscopic surface decomposition could be observed [5,35]. Another way is to repress the damage buildup during the implantation. According to experiments by Liu et al. [26], it seems attractive to carry out ion implantation at high substrate temperature. Alternately, one can implant GaN in a smaller dose increment and anneal in between the implants to recover damage completely [34]. Anyway, the most important factor that affects p-type doping by ion implantation is the undoped background electron concentration which should be kept as low as possible.

216

Ch. 7

B. Rauschenbach

4. Doping The doping of semiconductors is very important for the control of its electrical properties. It is known that all intrinsic GaN layers are characterized by n-type conductivity. In general, the background electron concentration in unintentionally doped GaN is approximately between 10^^ and 10^^ cm~^ using van der Pauw geometry Hall measurements (HM). Different species have been discussed to be responsible for this high carrier background concentration (nitrogen and gallium vacancies, impurities such as Si, O or C acting as shallow donors, antisite defects, for details see Section 3.1). Bulk mobilities between 50 and 300 cm^/Vs at room temperature are typical for undoped GaN material. The doping of wide band gap semiconductors by ion implantation is difficult due to this high background concentration. A high implantation dose of acceptors is generally needed to compensate the native electron background. However, this means the crystallinity is degraded by the implantation-induced damage. Consequently, the doping by ion implantation is carried out in two steps: (i) implantation of the dopant species, and (ii) post-implantation annealing at higher temperatures at which the electrical activation of dopants can be achieved and the implantation induced damage can be removed. Studies to the lattice site location and redistribution after annealing are necessary to explain the electrical and optical results after doping by implantation. 4.1. Lattice site location Only few results have been published on the examination of lattice sites after ion implantation into GaN although the knowledge of the lattice occupation is an important prerequisite for the explanation of the optical and electronic qualities of doped materials. So, only a few works are known about the study of the location of potential dopants [56,57]. In [58] or rare earth doping in GaN [59,60]. The location of implanted foreign atoms relative to the GaN lattice were determined by Rutherford backscattering in combination with ion channeling (RBS/C), nuclear reaction analysis (NRA) and also emission channeling technique (EC). GaN is frequently doped with the acceptor Mg. Fig. 12 shows examples of the lattice site analysis by RBS/channeling measurements. The angular scans through the axis before implantation show a nearly complete Ga sublattice. Angular scans though the direction are also shown in Fig. 12 after Mg'^-ion implantation and subsequent annealing. The random fraction demonstrates that the GaN lattice is still partially damaged because the minimum yield for Ga is increased from about 5% up to about 20%. The incomplete overlap of the Ga scan and the Mg scan indicates that the Mg atoms have partially occupied the sites of the Ga sublattice. It can be assumed that only about 75% of the Mg atoms are in regular Ga sites of the lattice. Ca has been also suggested as a shallow acceptor in GaN [32]. Kobayashi and Gibson [57] have studied the Ca dopant site in the GaN lattice after Ca-ion implantation at LNT and subsequent annealing at 1100°C. More than 80% of the Ca-atoms are slightly displaced from the Ga site after implantation and move to the exact Ga site after annealing. It is assumed that the displaced Ca-atoms in the as-implanted state form

Ion implantation, isolation and thermal processing ofGaN

Ch. 7

217

Tilt angle from -1 0 1 1.0 1

•D

N

1 0.5E o Z

0.0- 1

,

V\H

Mg^

l \

^^/j^ ,

1

31 32 Tilt angle from Fig. 12. Angular scans through the and the axis for GaN before and after implantation with 1 X lO'^ Mg"*"-ions/cm^ and annealing at 1150°C for 15 s.

donor-like point defects and that Caca becomes electrically active when these defects are broken by subsequent annealing. The lattice location of the donor Si after implantation in GaN was examined by the same authors [56]. The results indicate that all Si atoms occupy substitutional sites in GaN after annealing at 1100°C. The electrical activation of this donor seems to be connected with the annealing process at this temperature. Dalmer et al. [60] expects that Li acts as a donor atom if located on interstitial sites and as an acceptor atom if located on substitutional sites. Interstitial sites in the center of the c-axis hexagons of GaN have been found after Li-ion implantation at temperatures up to 700 K. Above this temperature, Li atoms are able to diffuse, interact with vacancies and occupy substitutional Ga-sites. An oxygen co-implantation leads to a strongly changed intensity of the luminescence [59]. The local lattice environments after In"^-ion implantation and subsequent annealing up to 900°C have been studied by emission channeling technique (a-EC) and perturbed y-y-angular correlation [58]. The majority of the In atoms were substitutional as-implanted in a heavily defective lattice. Recovery of the damage between 600 and 900°C leads a to defect free surrounding with half of the In atoms occupying substitutional lattice sites. Finally, very few information is available about the location of dopants after implantation. Further studies are necessary in order to clarify the physical processes of GaN doping by ion implantation. 4.2. Impurity redistribution The production of group-III-nitride semiconductor devices places a challenge to the performance of ultra-microanalysis, including thin film, and the three-dimensional distribution analysis of the low-level dopant concentration required in semiconductor material for semiconductor device production. Identifying the major elements is most

Ch. 7

218

B. Rauschenbach

^20 -.

.

•

1

'

1

•

•

•

1

'

'

'

1

'

'

as-implanted 1125°C

n^

E

10^^

c •-•

c CD O

c o o O

10^^ 0

0.2

0.4

0.6

0.8

1

depth (^im) Fig. 13. SIMS depth distributions of oxygen (70 keV, 5 x 10'"^ ions/cm^) implanted in GaN before and after annealing at 1125°C for 15 s (after [4,62]).

Straightforward. Analyzing the minor or trace elements is dependant on the sensitivity of the used method. The concentration distribution in GaN after ion implantation and also subsequent annealing is preferentially studied using secondary ion mass spectrometry (SIMS). SIMS is a sensitive technique which can detect all elements in many cases with detection limits smaller than 10^^ cm"^. Measurements of the concentration profiles after implantation in GaN with doses greater than 10^^ ions/cm^ have been reported in literature. In general, Cs primary ion bombardment is used to measure negative secondary ions and a O ion primary ion beam is used to measure positive secondary ions. In some cases, other techniques, such as Rutherford backscattering spectrometry (RBS) [61] and elastic recoil detection analysis (ERDA) [15] are used to analyze the implantation depth profiles. Figs. 13 and 14 show typical oxygen [62] and calcium [15] concentration distributions after implantation in GaN and also after RTA annealing at high temperatures The profiles are characterized by the expected Gaussian-like shape of the distribution. The important feature in both figures is that no measurable redistribution is seen after annealing. Consequently, an upper limit can be determined for the diffusion of the implanted species in GaN at this annealing temperatures (2.7 x 10"^^ cmVs for O in GaN at 1125°C and 1 x 10"^^ cmVs for Ca in GaN at 1150°C). The lack of significant redistribution has been observed for potential acceptor species, donor species and also species for optical applications. A redistribution could not been detected after implantation with F+-, Be"^- and Zn^-ions [63], Mg+and Si+-ions [64], Ca+- and 0+-ions [39,62], Si+-, Be+- and Zn-^-ions [47], C+- and Ca'^-ions [15], Si+-ions [53] and Mg^-ions [65] in GaN and subsequent annealing at higher temperatures. This effect is also known for the implantation of AIN with Be"^or Ge"^-ions [63] and InN with Be+-ions [64] and annealing up to temperatures of 8(X) and 600°C, respectively. These experiments demonstrate the high thermal stability of the

Ion implantation, isolation and thermal processing ofGaN 60 O

50 i

Ck 7

219

after implantation after annealing simulation

660

640

620

600

Channel Fig. 14. ERDA depth distributions of Ca (180 keV, 5 x 10^^ ions/cm^) implanted in GaN before and after annealing at 1150°C for 15 s. For comparison, the calculated concentration distribution using TRIM is also given (after [15]).

implanted materials and indicate that the occupied lattice sites by the implanted species are very stable. In contrast, the thermally stimulated redistribution could be measured in GaN after implantation with Se"^- and S+-ions and annealing at 700 and 600°C [63,64], respectively, and also after implantation of Mg"^-, Se"^- and Zn"^-ions and annealing at temperatures greater than 1000°C [47,54,66]. There a slight diffusion of the implanted species towards the surface is detectable. 43. N-type doping Typical experimental conditions for the implantation of n-type dopants are summarized in Table 2. N-type doping of GaN by ion implantation is predominately done with Si"^-ions at room temperature and the temperature of liquid nitrogen (LNT). While the element Si is the most common, other elements such as O, Te, S, Se and also N may be used (see Table 2). Oxygen was also proposed as donor [41] because its 6 valence electrons on a N site would be a single donor (N has 5 valence electrons). The donor behavior of N-vacancies follows from a missing N atom surrounded by four Ga atoms that provide three valence electrons. Two of these electrons can be donated to the conduction band [67]. Se is of particular interest being a nitrogen site donor and shows an interesting compensation behavior at high doping levels. Oxygen is of interest as a possible alternative n-type dopant. The first experiments to the n-type doping by ion implantation have been carried out by Chung and Gershenzon [68]. The n-type doping of GaN by Si^-ion implantation has been studied by Zolper and coworkers (overview about their results see [4,69]) and as well by other groups [70-73]. Fig. 15 shows the sheet resistance of GaN after Si"^-ion implantation with a dose of 5 X 10^"^ ions/cm^ and subsequent annealing at temperatures between 700 and llOO^C for 20 s [4,74]. Fig. 15 demonstrates that for temperatures greater than 1050°C

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Besides Mg and Ca doping by ion implantation, Be"^-ions were implanted in the hope that it would lead to shallow acceptor levels and subsequently conducting p-type GaN layers. Ronning et al. [86] have demonstrated that isolated Be is an acceptor in GaN with an ionization energy of about 150 meV. Unfortunately, Be displays damage-enhanced diffusion at temperatures greater than 900°C and is immobile once the point defects concentration is removed [51]. Carbon is expected to be an acceptor if it substitutes for N in GaN [83]. Up to now, p-type conductivity in GaN after C"^-ion implantation and subsequent annealing at temperatures smaller than 1150°C [27] and smaller than 1300°C [51] could not be achieved. 5. Impurity luminescence The group-Ill nitrides GaN, AIN and InN are interesting due to their potential application for optoelectronic devices at short wavelengths. Optical spectra of III-V semiconductors provide a rich source of information on their electronic properties because the photons can interact with lattice vibrations and with electrons localized on defects (for details see e.g. [82]). Possible methods to excite the sample are the photoluminescence (PL), the cathodoluminescence (CL) and the electroluminescence (EL). Photoluminescence is the process, in which photons of energy higher than that of the bandgap are used to excite the sample to emit photons. The production of radiation by an external current is known as electroluminescence, while the light emission by electron bombardment is called cathodoluminescence. The PL spectrometry is preferentially used for the characterization of the electronic properties of GaN. With the availability of continuously tunable laser, a new emission spectroscopy has become possible, the photoluminescence excitation spectroscopy (PLE). It has become important for studying thin layers on opaque substrates.

228

^^- 7

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Optical emission spectra are characterized by different peaks which can be attributed to several excited states in the semiconductor material. High-quality semiconductors, such as GaN, are strong emitters of band gap radiation, if they have a direct-band gap and electronic dipole transitions are allowed. Then the electron-hole pairs will thermalize and accumulate at the conduction and valance band extrema, where they tend to recombine. These band-to-band transitions dominate at higher temperatures where all the shallow impurities are ionized. The emitted photon energy is given by Ec ~ Ey, where Ec is the energy of the conduction band edge and Ey is the energy of the valence band edge. At sufficiently low temperatures, the carrier are frozen on impurities. The photoexcitation process in a p-type semiconductor with NA acceptors per unit volume creates free electrons with a density of Ue in the conduction band, where Ue < NA- These free electrons can recombine radiatively with the holes trapped on the acceptors. Such a transition, known as free-to-bound transition is characterized by the emission of photons with an energy of Eg — EA, where EA is the shallow acceptor binding energy (this process is inverse for n-type semiconductors). Consequently, PL spectra of such transitions contain information about the impurity binding energies. A compensated semiconductor contains both ionized donors and acceptors. By optical excitation, electrons are created in the conduction band and holes in the valence band. Then, these carriers can be trapped at the ionized donor or acceptor sites and produce neutral donor and acceptor centers. A donor-acceptor pair transition (DAP transition) is given when electrons on the neutral donors recombine radiatively with holes on the neutral acceptors. In a first approximation, the photons emitted in a DAP process have the energy EA — ED, where EA and ED are the acceptor and donor binding energies, respectively. At low temperatures, the photoexcited holes and electrons can be attracted to each other by Coulomb interaction and generate excitons. As a result of the hole-electron annihilation the free-exciton emission peak can be detected in the PL spectra. Excitons can be also attracted to neutral donors or acceptors sites via van der Waals interaction. Such neutral impurities are very efficient at trapping excitons, known as bound excitons, because the attraction lowers the exciton energy. In PL spectra measured at low temperatures a sharp peak can be identified with the recombination of an exciton bound to a neutral donor atom, usually denoted by D^X or I2, or with an exciton bound to a neutral acceptor (A^X or Ii). The binding energy of an exciton is close to the band gap energy, where the ratio of the binding energy of a bound exciton to that of a free exciton will depend on the ratio of the hole effective mass to the electron effective mass. High-temperature free exciton luminescence can also be expected when the thermal lattice energy kT is of the order of the binding energy. In GaN typical values of the exciton energy are near 20 meV. As a consequence, free exciton peaks appear in the PL spectra at room temperature (kT % 25 meV). 5.7. Implantation-induced optical activation The purpose of the studies of the photoluminescence after non-rare earth ion implantation into GaN or related group Ill-nitrides are: (i) investigation of the implantation

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induced damages, (ii) increase of the PL efficiency of these materials at room or higher temperatures and (iii) fabrication of optoelectronic devices by selective area implantation. First experiments have been carried out in the 1970s by Pankove and Hutchby [78,88] and by Metcalfe et al. [89]. The annealing after ion implantation has been recognized as crucial for the optical activation of the implanted species. The efficiency of the photoluminescence in GaN has been investigated after noble gas ion implantation [78,90,91] and in dependence on the condition of the subsequent annealing [92]. Typical low temperature PL spectra of GaN before and after Ar'^-ion implantation and also post-implantation annealing are shown in Fig. 19. The intensity of the PL spectra is drastically decreased. The luminescence is dominated by a donor bound exciton (D^X) at 3.472 eV, known as I2 and the 3.41 eV band coinciding with the L2 line. In most of the implanted GaN samples the narrow peak at about 3.45 eV has been detected independent on the ion species [78]. The ion dose dependence of the L2 intensity indicates that the 3.41 eV luminescence is not related to a particular impurity but to structural defects. Joskin et al. [90] have studied the photoluminescence of GaN after low dose He'*"-ion implantation in detail. The fine structure of the near-band gap PL in dependence on the temperature and the ion dose is characterized by several sharp lines. The main feature is that oxygen can form a complex, which is characterized by a strong localization of free carriers and a large lattice distortion. Broad luminescence bands with different energetic locations have been observed after ion implantation of 35 dopants in GaN and damage annealing [78,88]. Especially, the ion species Zn, Mg, Cd, As, Hg, Ca, P, and Ag are producing a characteristic spectral photoluminescence. For example, the characteristic blue photoluminescence at about 2.9 eV of Zn acceptors was even the basis of the first light emitting diode generation [93]. Consequently, the PL of Zn"^-ion implanted GaN has been studied by Strite et al. [52,66,94] and Suski et al. [49,95]. In these studies high pressure annealing procedures (up to 16 kbar) have been used which enable the application of increased annealing temperatures up to 1550°C. The Zn-acceptor related blue PL intensity after Zn+-ion

Ch. 7

230

B. Rauschenhach

implantation in GaN could be maximized by annealing at an N2'Overpressure above 1350°C after which the PL intensity exceeds that of epitaxially doped GaN material /ith comparable Zn concentration by the factor 15. The implantation of other transition with( aetal ion species, e.g V+-ions with an energy of 250 keV and doses between 1 x 10^^ metal and 1 X 10^^ ions/cm^, gives rise to an intense near-infrared defect luminescence at 1.51 |xm[96]. 5.2. Luminescence by rare earth ion implantation Rare earth doped semiconductor materials have received attention because of possible application in the optoelectronics for low power, temperature insensitive, continuous wave sources of 1.54 |xm (0.806 eV) radiation. Especially, the rare earth element Er has shown luminescence at this wavelength corresponding to a transition between the energy levels "^In/a and \si2 in triply charged erbium, Er^+, under the influence of the crystal field. The lanthanide rare earth elements possess partially filled 4f shells. These are screened by the outer closed 5s^ and 5p^ shells. Consequently, intrashell transitions of 4f electrons give rise to sharp emission spectra, where this spectra is approximately independent of the host lattice and relatively insensitive to temperature. Fig. 20 shows schematically the energy level diagram for the free Er"^-ion and also the splitting of the levels in a solid due to the Stark effect, labeled with the standard Russel-Saunders (LS coupling) notation. The incorporation of the rare earth elements into GaN during growth by different methods is studied in detail. Room temperature infrared and visible emission by both photoluminescence and electroluminescence have been achieved by hydride vapor phase epitaxy (HVPE) and metalorganic molecular beam epitaxy (MOCVD). However, several problems still restrict the utilization of rare earth doped semiconductor materials 2IJ -"11/2

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Ch. 7

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including GaN in optoelectronic devices. First, the achieved quantum efficiencies are too low for practical applications (i.e. PL lifetime is too small), because presently the Er solubility in semiconductor materials is too low. Second, in Er-doped Si and GaAs it has been observed that the luminescence is quenched by several orders of magnitude when the temperature is increased from LNT to room temperature. Partially, thermal quenching effect on the luminescence efficiency can be reduced when a codoping with light elements such as O and F has been carried out [97]. Third, the understanding of both the incorporation in the host lattice and the excitation mechanism for the emission is not yet sufficient. Ion implantation of rare earth ions has attracted attention as improvements in the growth process has made high quality GaN more readily available. Several groups have implanted Er"^-ions, but also Pr+-, Yb"^-, Tm+- and Nd^-ions (see Table 5). The Er"^-ion implantation is often combined with an 0"*"-ion coimplantation. The implantation is followed by a subsequent annealing process at temperatures between 650 and 1050°C (see Table 5). A few studies on lattice site location of rare earth elements in GaN after implantation at room temperature have shown that these atoms immediately occupy relaxed substitutional sites [59]. RBS/C studies have shown that after subsequent annealing more than 70% of the implanted Er^-ions occupy Ga sites [46]. An annealing at temperatures greater than 800°C and the coimplantation of O'^-ions do not influence significantly the rare lattice sites. A typical PL spectra of GaN after implantation with 2 x 10*^ Er"*"-ions/cm^ and 1 X 10^^ O"^- ions/cm^ at room temperature and subsequent annealing at 900°C for 30 min in flowing NH3 is shown in Fig. 21 [98]. The excitation source was an InGaAs laser diode with 100 mW at 983 nm. Erbium atom induced luminescence was only observed after annealing. Polman et al. [99] suppose that the annealing process can promote the implanted Er^^-ions to Er^^-ions as well as the formation of erbium oxide (Er203). On the other hand, the annealing increases the annihilation of the implantation induced defects. Since the laser excitation energy was below the GaN band gap, the observed luminescence appears due to direct optical excitation of Er"^-ions. The insert schematically shows the three energy levels in Er^^ involved in this PL process (see also Fig. 20). The PL spectra, characterized by the 1.54 |xm luminescence line, have been measured at LNT and at room temperature. It is suggested that the peak at 1.54 |xm corresponds to the radiative transition from the first excited state ^Ii3/2 to the ^Ii5/2 ground state. This 1.54 jxm luminescence line has been observed in the PL or PLE spectra after Er'^-ion implantation [100-103], after coimplantation of Er"^- and 0"^-ions [61,98,104-108], after Pr+-ion implantation [109], Nd+-ion implantation [100] and also after coimplantation of Er"^- and 0"^-ions in the cathodoluminescence spectra [110] and electroluminescence spectra [104]. The erbium ions can be also excited to the third excited ^^19/2 state by pumping with 809 nm light [61]. Then, the erbium ions quickly relax nonradiatively to the excited "^113/2 state and radiatively to the ground state (see Fig. 20). Detailed studies with below band gap excitation have shown that well resolved crystal-field split intrashell emissions of rare earth ions implanted in GaN can be observed. For example, Silkowski et al. [100] have detected the three manifolds of the 4f lines '^F3/2 to "^19/2, '^F3/2 to "^111/2 and '^F3/2 to

Ch. 7

232

B. Rauschenbach

Table 5. Optical activation of GaN and related compounds by ion implantation: experimental conditions of implantation, annealing, layer deposition and analysis Substrate

Condition of implantation Target: ion

Energy (keV)

Dose (xlO*^ cm~2)

GaN 35 species P, As V Zn Zn Zn Zn Zn CO Si, Ar Be, Mg Be He Ar Er Er-hO^ Er + O^ Er + O Er + 0 ^ Er + O'' ErH-O^ Er + O" Er-hO" Er + O" Er, Er + O Er,Nd Tm,Yb O + Tm Pr

40,82 250 200 200 200 200 200 390 390 200, 300 100, 200 1800 180 280 300 + 40 400 + 80 300 350 + 80 350 + 80 350 + 80 350 + 80 300 + 40 300 + 40 160, 160 + 25 910, 1150 60 13 + 60 300

10-^ 10-2 0.08-50 0.1 0.1 0.1 0.1 0.1 0.5 0.05-0.82 0.01-0.25 7 0.05 410-3 0.2+1 0.1, 1 + 10 0.3 1 + 10 0.02-1+0.1-10 0.01-5 + 0.1-10 2+10 0.2 + 2 0.2 + 2 0.5,5 0.01,0.05 0.02 0.4 + 0.02 0.47, 1

300 + 40 300

2+10 3

AIN Er + O Er + O

Material

Deposition technique

sapphire sapphire sapphire sapphire sapphire sapphire sapphire sapphire

MOVPE MOVPE MOVPE MOVPE MOVPE MOVPE MOCVD MOCVD, MBE

6H-SiC 6H-SIC 6H-SiC sapphire sapphire sapphire GaAs, sapphire sapphire sapphire sapphire sapphire sapphire sapphire sapphire sapphire 6H-SiC

MOVPE MOCVD MOCVD MOCVD MOMBE CVD MOMBE MOCVD

sapphire

HVPE, MBE, MOCVD

GaAs GaAs

MOMBE MOMBE

MOCVD MOCVD lA-MBE HVPE MOCVD MOCVD MOVPE

%2>/2 after Nd"^-ion implantation at low temperature (see also Fig. 20). Fig. 22 shows a PLE spectra measured at room temperature after Er^- and 0"^-ion coimplantation [107]. The Er^+ PL was monitored at 1.54 |xm (inset). The PLE spectra is characterized by a broad band ranging from 425 to 680 nm and sharp bands. Thaik et al. [107] have found coincidences between the PLE peaks and the Er^"^-intra 4f transitions "^115/2 to "^^1/2, %y2 to 2Hn/2, "^115/2 to ^83/2, ^Ii5/2 to ^F9/2 and ^115/2 to ^111/2 after Er+- and 0+-ion implantation and subsequent annealing. The broad band is attributed to Er^"^ excitation processes involving defects in GaN. It is obvious, that the PL intensity is quenched by several orders of magnitude when going from the low temperature to the room temperature measurement (Fig. 21). The

Ion implantation, isolation and thermal processing ofGaN Table 5.

Target: ion

AIN Er + O Er + O

233

(continued)

Condition of annealing

GaN 35 species P, As V Zn Zn Zn Zn Zn CO Si, Ar Be, Mg Be He Ar Er Er + O^ Er + 0 ^ Er + O Er + 0 ^ Er + O'' Er + O^ Er + O*' Er + 0 ^ Er + O^ Er, Er + 0 Er, Nd Tm,Yb O + Tm Pr

Ch. 7

Temperature (°C)

Time

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1050 600-930

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Frequency (cm'^) Fig. 24. Vibrational spectra measured near 4.2 K for (a) deuterium implanted GaN and (b) hydrogen implanted GaN samples which were subsequently annealed at the temperatures indicated (after [131]).

the occupation of nitrogen lattice sites. The deep level transition spectroscopy (DLTS) has been used to characterize the formed defects by high energy He irradiation in GaN [129,133,134]. Different electron traps with energy levels between 0.13 and 0.95 eV below the conductivity band could be identified. These energies can be assigned to specific defects, where the proton and He+-ion irradiation partially creates different defect types. The ion implantation has been successful used for the isolation of AlGaN/GaN heterostructure field effect transistor structures [135,136]. 7. Devices In the semiconductor technology, the ion implantation allows to implant selected areas and to realize devices such as light emitting diodes (LEDs) or junction field effect transistors (JFET). Although only a few results are known for the ion implantation in GaN and related compounds, different experiments were undertaken to manufacture electronic devices. The studies were aimed at the fabrication of low-ohmic contacts, p-n junctions, light-emitting diodes and field effect transistors. Ohmic contacts are limiting factors in the GaN devices. Therefore, the realization of good reliable metal contacts is an important condition in achieving high performance GaN based devices. Recently, Lester et al. [140] have studied the formation and quality of ohmic contacts formed by nonalloyed Ti/Al metallization on Si-ion implanted GaN. A specific contact resistance as low as 10~^ ^ cm^ could be formed. Also Burm and coworkers [141] have fabricated Si+-ion implanted ohmic contacts on GaN, where the overlay metal was Ti/Au. The measured maximum contact resistance was 0.097 Q mm and the specific contact resistance was 3.6 x 10"^ ^ cm^.

Ion implantation, isolation and thermal processing ofGaN

Ch. 7

243

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Schematic of the implantation processing steps for a GaN JFET (after [144]).

As early as in the year 1969, Maruska and Tiefjen [142] have shown that GaN LEDs emit at 430 nm (violet) after implantation with Mg"^-ions and at 590 nm (yellow) after co-implantation with Mg+- and Zn^-ions. The implantation of Zn+-ions alone generates a green emission. Torvik et al. [104] have demonstrated the room temperature Er^"*"-related electroluminescence at 1.54 and 1 |xm from a Er"^-ion and O'^-ion coimplanted GaN metal-insulator n-type LED. A insulating GaN layer has been implanted with both ion species and then annealed at 800^*0 for 45 min in flowing NH3. The co-implantation leads to a 20 times increase in the Er-related PL. The LED was dc reversed biased, where the integrated emission around 1.54 |xm showed a linear dependence on the applied current between 100 and 318 (jiA. GaN p-n diodes have been formed by Mg'^-ion implantation in n-type GaN epitaxial layers and subsequent annealing. Kalinina et al. [65] have demonstrated that a rectification factor of not less than 10^ at a voltage of 3 V can be obtained for such p-n mesa structures. The first GaN junction field-effect transistor (JFET) has been realized with multiple ion implantation by Zolper and coworkers [39,143]. Fig. 25 shows schematically the implantation steps for a GaN JFET. The device processing contains the implantation steps besides the activation annealing at high temperatures: Si"^-ion implantation of the n-channel, Ca+-ion implantation of the p-gate and nonself-aligned Si'^-ion implantation of the source and drain regions. A gate turn-on voltage of 1.84 V at 1 mA/mm of the gate current was achieved. The hydrogen ion implantation has been also used to isolate the mesa at the fabrication

244

Ch. 7

B. Rauschenhach

of an AlGaN/GaN modulation-doped FET [135]. A very effective isolation of such a FET has been achieved after co-implantation of P^-ions with two different doses (5 x 10*^ and 2 x 10^^ ions/cm^) followed by He+-ion implantation (6 x 10^^ ions/cm^) [136]. The sheet resistance was about 10^^ ^ / D and the activation energy 0.71 eV. Notwithstanding the vast promise of the GaN material, there is still very limited work in the field of ion implantation in GaN electronics. As a consequence, a comparison of the state of ion implantation in GaN electronic and optoelectronic technology with those of silicon or gallium arsenide based technology is clearly not warranted. With increasing research and investments in technology, ion implantation is very likely to fulfill its enormous potential as the ultimate method in the GaN based technology. Acknowledgements The author would like to acknowledge Wolfgang Bruckner, Liu Chang, Jiirgen Gerlach, Stephan Mandl, Bemd Mensching, Wolfgang Reiber, Stephan Sienz, Axel Wenzel (Universiat Augsburg), H. Riechert (Siemens AG), A. Kritschil (Universitat Magdeburg), S. Fischer (Universitat GieBen), W. Assmann (Universitat Munchen), H. Riechert and R. Averbeck (Siemens AG Munchen), A. Lell (Osram Opto Semiconductors Regensburg), R. Sauer, W. Limmer and A. Komitzer (Universitat Ulm) for their collaboration on this work. Portions of this work were supported by the Schwerpunktprogramm 'Gruppe Ill-Nitride und ihre Heterostrukturen' of the Deutschen Forschungsgesellschaft (DFG). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

H. Morkoc, Wide Band Gap Nitrides and Devices, Springer-Veriag, Berlin, 1998. S. Nakamura, G. Fasol, The Blue Laser Diode, Springer-Veriag, Berlin, 1998. R.G. Wilson, Proc. Electrochem. Soc. 95-21, 152 (1995). J.C. Zolper. In: S.J. Pearton (Ed.), GaN and Related Materials, Gordon and Breach, New York, 1997, p. 371. S.J. Pearton, J.C. Zolper, R.J. Shul and F. Ren, J. Appl. Phys. 86, 1 (1999). C. Liu, A. Wenzel, H. Riechert, B. Rauschenhach, Proceed of the Intern. Conf. Ion Implantation Technology, Kyoto, 1998, Proc. IEEE, in press. J. Lindhard, M. Scharff, H.E. Schiott, Mat. Phys. Medd. Dan. Vid. Selsk. 33 (1963) no. 14. J.P Biersack, Nucl. Instr. Meth. 182/183, 199 (1981). W.D. Eckstein, Computer Simulation of Ion-Solid Interactions, Springer-Veriag, Berlin 1991. H. Ryssel, I. Ruge, lonenimplantation, Akademische Verlagsgesellschaft Geest, Portig K.-G., Leipzig, 1978. I.R Soshnikov, Yu.A. Kudravtsev, A.V. Lunev and N.A. Bert, Nucl. Instr. Meth. B 127/128, 115 (1997). R. Sizmann, J. Nucl. Mater. 69/70, 386 (1978). J.A. van Vechten. In: T.S. Moss, S.R Keller (Eds.), Handbook of Semiconductors, Vol. 3, Elsevier, Amsterdam, 1980. M.T. Robinson, Phil. Mag. 12, 741 (1995). B. Mensching, diploma thesis. University Augsburg 1997. J.W. Christian, The Theory of Transformation in Metals and Alloys, Pergamon Press, Oxford, 1975. P.P. Morehead, B.L. Crowder. In: F.H. Eisen, C.S. Chadderton (Eds.), Ion Implantation, London, 1971, p. 25. J.F. Gibbons, Proceed. IEEE 60, 1062 (1972). J. Neugebauer and C.G. Van de Walle, Phys. Rev. B 50, 8067 (1994).

Ion implantation, isolation and thermal processing ofGaN [20] [21]

[22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35]

[36]

[37] [38] [39]

[40] [41] [42] [43] [44] [45] [46] [47] [48] [49]

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III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 8

Radiation and processed induced defects inGaN ED. Auret and S.A. Goodman 1. Introduction During several semiconductor-processing steps, for example particle irradiation for lifetime tailoring [1,2], dry etching [3,4], metallization [5,6] and device isolation [7,8] the semiconductor is intentionally or unintentionally exposed to a variety of particles with energies ranging from a few eV to several MeV. When these particles impinge on the semiconductor, they enter into it, transfer energy to the semiconductor lattice and introduce defects. These defects can have a profound influence on the semiconductor properties and on the characteristics of devices fabricated on it [3-6], which may be either beneficial or deleterious, depending on the application. In order to avoid the deleterious effects of some of these particle-induced defects and utilize the beneficial effects of others, depending on the application, it is imperative to understand the effect of radiation on electronic materials and devices fabricated on them. To achieve this, it is essential that the electronic properties and concentration of radiation induced defects should be known, allowing calculation of their effect on the properties of electronic materials and devices. In addition, the structure, introduction rate, introduction mechanism and thermal stability of the defects should be determined, so that they can be reproducibly introduced, avoided or eliminated, depending on the application. Regarding electrical techniques for defect characterization, deep level transient spectroscopy (DLTS) [9], which allows independent studies of different defect species in the same semiconductor, has played a key role in providing most of this information. Hall effect measurements [10] have also contributed a fair deal to our understanding of radiation-induced defects and its effect on carrier mobility and donor and acceptor concentration. As far as the electrical characterization of simple devices are concerned, current-voltage (I-V) and capacitance (C-V) measurements have traditionally been used to evaluate the effect of defects on diode performance and the free carrier density of semiconductors, respectively. In order to successfully characterize process-induced defects by DLTS, it is ideally necessary to start with defect-free semiconductor materials. For most semiconductors this is, however, not possible. The closest to this ideal is high quality silicon that contains very low concentrations (usually below the DLTS detection limit) of hole and electron trap defects with deep levels in the band gap. Most compound semiconductors contain at least one deep electron or hole trap. For example, GaAs grown by all techniques except liquid phase epitaxy (LPE) contains significant concentrations of the infamous

Ch. 8

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EL2 defect [11] (an electron trap) whereas molecular beam epitaxy (MBE) [12] and LPE [13] grown GaAs contain their own characteristic set of electron and hole traps, respectively. It has been proposed that the EL2 is also introduced during high-energy particle irradiation [14], which is exactly why the starting material should contain as low as possible concentrations of defects in order that such findings be uniquely established. GaN, too, is no exception. Several studies have shown that n-type material contains at least two to three prominent electron traps with energy levels in the upper half of the band gap, depending on the growth method. This will be elucidated in Section 2. Since these growth-induced defects have an inhibiting effect on the detection of process induced defects, we shall devote a few paragraphs in Section 2 to describe which defects are present in GaN grown by different epitaxial techniques. This should not be seen as a complete review of growth induced defects, but rather as a guideline as to which defects can be expected in epitaxially grown GaN when attempting to characterize process induced defects in it. 2. Defects in epitaxially grown GaN In this section we briefly discuss and summarize the defects detected by DLTS in as-grown GaN. The properties of the defects, the substrates, buffer layers, epitaxial layers and some growth parameters are summarized in Table 1. In Fig. 1 we compare the DLTS 'signatures' of the defects in the form of conventional DLTS Arrhenius plots, using data from the literature. The first DLTS report of growth induced defects in GaN was by Hacke et al. [15] who used a SBD structure fabricated on n-GaN grown by hydride vapor-phase epitaxy (HVPE). The n-GaN was grown on two different types of buffer layers, either MOVPE grown GaN or sputtered ZnO. They detected three electron traps in both substrate types, labeled El, E2 and E3, with activation energies of 0.264, 0.580 and 0.665 eV,

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respectively. In addition, they demonstrated that the concentration of the deepest of these three levels depended on the type of buffer layer (GaN or ZnO) between the sapphire substrate and the HVPE epitaxial layer. In Si-doped GaN grown by metalorganic vapor-phase epitaxy (MOVPE), Gotz et al. [16] detected two electron traps (E2 and Ei) with activation energies (not T^ corrected) of 0.18 and 0.49 eV, respectively. These appear to be the same as the E1 and E2 in HVPE grown GaN. Subsequentiy, Hacke et al. [17] found, what appears to be the same two levels located at Ec —0.26 eV and Ec —0.62 eV, respectively, in undoped MOVPE GaN. An interesting observation on the part of Hacke et al. [17] was that the concentration of the level at Ec —0.62 eV increased significantly in weakly doped n-type GaN. Lee et al. [18] grew MOVPE layers using trimethylgallium (TMGa) and triethylgallium (TEGa) as the alkyl sources. Using DLTS they detected three distinct deep levels in films grown by TMGa (El, E2 and E3) with activation energies of 0.14, 0.49 and 1.44 eV, respectively. The shallowest two of these defects are presumably the same as the El and E2 mentioned above for MOVPE grown GaN. Interestingly, only a level at 1.63 eV, speculated to be the same as that at 1.44 eV, was detected in the layer prepared using TEGa. It must be noted that due to the high peak temperature the 'signature' of defect E3 was determined from a 2-point Arrhenius plot, and may consequently not be accurate. Lee et al. [18] proposed that the two shallower levels are either related to the carbon and/or hydrogen atoms from the methyl radicals, or alternatively, that they are due to the slight difference in growth temperatures of the two layers. Recently, Auret et al. [19] have also reported the presence of two prominent electron traps (E02 and EOS) with activation energies of 0.27 and 0.61 eV, respectively, in undoped MOVPE grown n-GaN. For these calculations the emission rate, Cn, was taken as 3.3 X lOl^^Gxpi—Et/kT). These traps seem to be the same as the El and E2 in HVPE and MOVPE grown GaN, and are seemingly characteristic of GaN grown by this method. By using special pulse conditions, Auret et al. [19] were also able to show the existence of two other less prominent traps (EOl and E03) in this material of which the DLTS peaks are obscured by the peaks of the major defects at normal pulse conditions. For p-type GaN grown by MOVPE, Gotz et al. [20] used a p'^-n structure and detected three hole traps with activation energies of 0.21, 0.39 and 0.41 eV in the lower half of the band gap. However, using ODLTS, they found a dominant deep level with an optical threshold energy for photo-ionization at about 1.80 eV This level is positioned near midgap and is the dominant defect. Although several deep levels were detected, their concentrations are small compared to the total acceptor concentration and would hence not influence the acceptor concentration through compensation. The properties of electron traps in reactive MBE (RMBE) grown GaN, with a free carrier concentration of 6 x 10^^ cm~^, were reported in considerable detail by Wang et al. [21]. They characterized five electron traps and found their activation energies to be 0.234, 0.578, 0.657, 0.961 and 0.240 eV. The first of these (0.234 eV) is thought to be the same as the 0.264 eV level reported by Hacke et al. [17] and the 0.18 eV level reported by Gotz et al. [16] The second level (0.578 eV) has a very similar signature as the 0.58 eV level of Hacke et al. [18], the 0.49 eV level of Gotz et al. [16] and the 0.598 eV level reported by Haase et al. [22]. The third level (0.657 eV) appears to be the same as the 0.665 eV level measured by Hacke et al. [17] and the 0.67 eV level measured

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in some or other degree of damage at and beneath the semiconductor surface. In the sections below, we describe the effect of this damage on the electronic properties of the semiconductor and on device performance. 4.2. Pre-metallization plasma treatments Mistele et al. [58] reported on the influence of different pre-etch methods on the specific contact parameters of n-GaN contacts. For these investigations they used ex-situ chemically assisted ion beam etching and in-situ sputter etching before metal deposition. The electrical contact parameters were determined using the extended circular transmission line model. For nitrogen as an etching gas they obtained rectifying character (Schottky) of metal-n-GaN contacts compared with mostly linear (Ohmic) behavior for conventional etching gases such as Ar or Ar + CI2. They speculate that a decrease of N vacancies caused by the N2 treatment is responsible for the Schottky behavior of these contacts. Pre-etch sputtering with Ar ions reduced on the one hand the specific contact resistance, but on the other hand it resulted in an increase in the sheet resistance in near-surface region. Cao et al. [59] exposed n-GaN Schottky diodes to N2 or H2 inductively coupled plasmas prior to deposition of the rectifying contacts. Subsequent annealing, wet photochemical etching, or (NH4)2S surface passivation treatments were examined for their effect on diode I-V characteristics. They found that, either annealing at 750°C under N2, or removal of about 500-600 A of the surface, essentially restored the initial I-V characteristics. There was no measurable improvement in the plasma-exposed diode behavior with (NH4)2S treatments. Cao et al. [60] examined the effects of H2 or N2 plasma exposure on the current-voltage characteristics of Ti/Au/n-GaN Schottky contacts as a function of source power and rf chuck power. Under all conditions they observed a severe degradation of the electrical characteristics of the GaN surfaces. This resulted in a strong reduction in diode reverse breakdown voltage and an increase in forward and reverse currents. These authors interpreted the results as being consistent

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with creation of a thin (< 600 A) conducting n-type surface layer resulting from energetic ion bombardment. Further, they observed that heavier ions (Nj) created more damage than the Ughter (H^) ions, where damage accumulates without any concurrent etching of the surface. Much of the degradation in diode quality could be recovered by annealing in N2 at 750°C. For p-type GaN, Cao et al. [61] used the reverse breakdown voltage of Schottky diodes to measure the electrical effects of high density Ar or H2 plasma exposure. They found that the near surface of the p-GaN became more compensated through introduction of shallow donor states whose concentration depended on ion flux, ion energy, and ion mass. At high fluxes or energies, the donor concentration exceeded 10^^ cm"^ and produced p-io-n surface conversion. Based on electrical and wet etch rate measurements, the damage depth was established as about 400 A. Rapid thermal annealing at 900°C under a N2 ambient restored the initial electrical properties of the p-GaN, similar to the thermal stability of implant isolated p-GaN [47]. In summary, from the studies discussed above it appears that plasma processing results in a conductive n-type surface layer on n- or p-type GaN. It has been proposed that donor-like defects are responsible for the observed effects. Mistele et al. [58] speculated that these defects are related to N vacancies. However, in none of the studies discussed above were any mention made of electrical characterization of the plasma processing induced defects, and consequently their electronic properties are not yet known. 4.3. Metallization The fabrication of electronic devices requires, among others, metallization for ohmic or Schottky contacts on the GaN. The metallization method chosen for this purpose should fulfil several requirements, including good adhesion of the metal to GaN, the ability to deposit compounds stoichiometrically and the ability to deposit high melting point metals at controllable rates. Most importantly, the metallization method should not introduce unwanted defects in the semiconductor. This latter requirement is particularly important for depletion layer based devices, such as metal field effect transistors. Defects that are introduced during metallization processes of semiconductors have, amongst others, been shown to give rise to modified rectification quality of Schottky barrier diodes (SBDs). In Sections 4.3.1, 4.3.2, 4.3.3 and 4.3.4 below, we discuss some results that have been recently reported for the metallization of GaN using different techniques. 4.3.1. Resistive (Joule) evaporation This method has been recognized for a long time to be a 'defect-free' metallization method. The material to be melted is simply evaporated by passing current through a crucible of some form. This method, however, has at least one serious disadvantage: it cannot easily evaporate high melting point metals. On the other hand, it is perfect for evaporating metals like Au, Pd, Al and Ni, which are all frequently used for the formation of ohmic and Schottky contacts. In the DLTS data thus far reported for GaN, no mention has been made to any defects that could possibly have been introduced during resistive evaporation of Schottky contacts.

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4.3.2. Sputter deposition Sputter deposition is a metallization method which is frequently employed because sputter-deposited layers exhibit better adhesion compared to layers deposited by other methods [62]. In addition, sputter deposition facilitates the stoichiometric deposition of compounds and controllable deposition of high melting point metals, and yields high deposition rates. However, due to the energetic particles involved, sputter deposition is damaging on an atomic scale and causes lattice disorder at and below the semiconductor surface [5]. Sputter deposition induced defects in semiconductors, and the influence of these defects on the rectification quality of SBDs, have been studied for many years. Generally, it has been found that these defects reduce the barrier height of SBDs on «-type semiconductors and increase it on p-type semiconductors. Using DLTS, it was shown that sputter deposition induces defects at and below the semiconductor surface, and it is thought that these defects are the cause of the barrier alteration [5]. The degree of barrier modification depends on the sputter conditions. Most of the pioneering studies regarding the electrical characterization of sputter induced defects and their influence on metal-semiconductor contacts have been performed using Si and GaAs, and little data is presently available for GaN. Auret et al. [63] reported the characteristics, determined by DLTS, of defects detected in epitaxially grown GaN before and after sputter deposition of Au Schottky contacts thereon. For this purpose, they used epitaxial GaN with a free carrier density of (2-3) X 10^^ cm"^, grown by metalorganic vapor phase epitaxy (MOVPE). Before contact fabrication, the samples were cleaned employing wet chemistry [64]. Following this, Ti/Al/Ni/Au (150 A/2200 A/400 A/500 A) ohmic contacts were fabricated [65]. Prior to Schottky barrier diode (SBD) fabrication, the samples were again degreased and dipped in an HCl rHaO (1:1) solution. Thereafter, circular Au Schottky contacts, 0.5 mm in diameter and 1 jxm thick, were sputter-deposited on the GaN through a metal contact mask, as close as possible to the ohmic contact to minimize the diode series resistance. Sputter deposition was performed in DC mode at a power of 0.141 kW in an Ar pressure of 4.8 x 10~^ mbar at a deposition rate of 4.5 nm s~^. For control purposes, Au SBDs were resistively deposited next to the sputter deposited SBDs. Current-voltage (I-V) measurements (Fig. 13) showed that for sputter deposited SBDs the current at a 1 V reverse bias was (1-2) x 10""^ A, compared to the

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that after sputter deposition, defects labeled ESI, ES2/E02, ES3 and ES4 are detected. Curves b-d show that the peak heights of the sputter induced defects increase with increasing filling pulse height, indicating an increase of the concentration of the sputter induced defects towards the Au/GaN interface. This trend was also previously observed for defects introduced by sputter deposition of Schottky contacts on Si [66] and GaAs [67,68]. Note that E05 is absent in the spectra of sputter deposited SBDs. The reason

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for this is that the energy level of E05 is 0.61 eV below the conduction band whereas the barrier height of the sputter deposited SBDs is only 0.47 eV. Therefore, during the quiescent DLTS bias the £ 0 5 level remains below the Fermi level [69] and does not emit carriers. For determining the defect signatures, the overlapping peaks in Fig. 14 were separated using different pulse conditions [63]. From Fig. 15 and Table 3, where the signatures of the sputter induced defects are compared to those of radiation-induced defects and defects in as-grown OMVPE GaN, it seems that two of the defects observed after sputter deposition may be the same as other defects previously reported in GaN. Firstly, ES2, with a level at Ec -0.30 ± 0.01 eV, appears to be similar to E02, with a level at EQ —0.27 ± 0.01 eV, which is present in as-grown GaN. However, it does seem as if sputter deposition resulted in an increase of the ES2 concentration towards the GaN surface. Secondly, the signature of ESI, with a level at Ec -0.22 ± 0.02 eV, is similar to that of the ER3 defect with a level at ^c -0.20 ± 0.01 eV, which was observed after 5.4 MeV He-ion irradiation (Section 3.3) and 2 MeV proton irradiation (Section 3.2) of the

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same epitaxial GaN, and the E defects observed by Fang et al. [24] in electron irradiated n-type GaN. The ESS and ES4 defects, with levels at Ec -0.40 ± 0.01 eV and Ec -0.45 ih 0.10 eV, do not correspond to defects observed in irradiated or in as-grov^n epitaxial n-GaN. Their signatures also do not correspond to those of defects introduced by nitrogen implantation of GaN, where it was suggested that one of the defects thus introduced may be a N interstitial [22]. These observations suggest that ESS and ES4 are not related to the simple radiation induced point defects. This can be explained by the fact that, during sputter deposition, energetic particles, like Ar ions, enter the GaN and lose energy at a high enough rate to create defects in close proximity of each other. These defects then combine or interact to form larger defect complexes. The peak shape and electronic properties of ES4 were found to be strongly dependent on the pulse height-increasing the pulse height resulted in a broadening of the peak and a shift to lower temperatures. The same behavior could not be seen when maintaining a fixed pulse level, and increasing the reverse bias, ruling out the possibility of this behavior being due to electric field assisted emission. This behavior of ES4 is similar to that of defects introduced during low energy Ar ion bombardment of GaAs where it was shown that those defects are located close to the surface and have a band-like energy distribution [68]. In a recent paper, DeLucca et al. [70] reported the properties of defects introduced in a 20 micron thick HVPE grown GaN layer with a carrier density of 1.5 x 10^^ cm~^ by DC magnetron sputter deposition. After ohmic contact formation, photoresist patterned samples were immersed in 1:1 HCl: DI for ten minutes, rinsed with DI water, blown dry with N2 gas, and immediately loaded in the deposition chamber for evacuation to 10"^ Torr. After a pumpdown of at least eight hours, 500 A thick Pt layers were deposited followed by lift-off in acetone. Three different sputter conditions were investigated, with decreasing power {P) and increasing Ar pressure (/?) conditions, intended to reduce the energy of incident species on the GaN surface [71]. These conditions are (1) high-power low-pressure (P = 100 W, /? = 5 mTorr), (2) 'normal' (F = 6 W, /? = 5 mTorr), and (S) low-power high pressure (P = 6 W, /? = 15 mTorr). Firstly, consider the DLTS results of contacts deposited under 'normal' sputter conditions. Curves a-e in Fig. 16 show the presence of at least four sputter induced electron traps, ES1-ES4. The peaks of ESI-ESS are not well separated and only ES4 could be accurately characterized. These spectra are very similar to those recently reported [6S] and discussed above for sputter deposited Au contacts on OMVPE grown n-GaN. In that case it was demonstrated that the ESI-ESS peaks could only be deconvolved by recording spectra using a wide range of pulse widths, extending from nano- to milliseconds. Defect depth profiling was performed considering only the maximum (combined) peak height, ESC, of the ES1-ESS defect group, without deconvoluting the defect peaks. Fig. 17 reveals that the concentration profile seems to be composed of two parts: one part that increases sharply towards the interface, and another that extends much deeper into the GaN. This is the result of ESC being the superposition of unresolved defect peaks-one close to the surface and the other deeper. Because ES4 displayed a band-like behavior, it was not possible to extract its depth profile in the conventional way. Next, consider the results for contacts deposited under high plasma pressure and low

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Fig. 16. DLTS spectra of a Pt contact on HVPE grown n-GaN, sputter deposited under 'normal' conditions. Curves a-e were recorded using filling pulse amplitudes of 1.0. 1.5, 2.0, 2.5 and 2.9 V, respectively. All spectra were recorded using afillingpulse width of tp = 0.2 ms, a reverse quiescent bias of Vr = 2 V and a pulse frequency of f = 46 Hz. i-T-r 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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power conditions. Curves c and d in Fig. 18 that show that sputter deposition under these conditions does not seem do introduce any discrete level defects, except for ES2 in very low concentrations. However, the spectra c and d in Fig. 18 are characterized by a skewed baseline of which the offset increases with increasing temperature. This phenomenon is consistent with the presence of defects, located close to the interface, with a continuous energy distribution of which the concentration increases with the

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depth of the level below the conduction band [68]. A further interesting phenomenon is observed when comparing curves c and d at temperatures above 350 K. It is clear that the increase in Vp (from 2.2 V for curve c to 2.4 V for curve d gave rise to a broad feature where the E06 is usually located. Its broadness indicates that this could be due to a band of defects close to the surface. Further low frequency or high temperature characterization is required to resolve this issue. The results discussed here for sputter deposited SBDs on GaN follow the same trends as for Si and GaAs: firstly, the barrier height of sputter deposited is lower than those of contacts deposited by resistive deposition or electro-deposition (Section 4.3.4) — processes which do not introduce defects. Secondly, the barrier height of contacts deposited using a higher plasma pressure (15 mTorr) is higher than that of contacts deposited under 'normal' pressure (5 mTorr) conditions. In confirmation, DLTS revealed that 'normal' sputter conditions introduce more defects than high-pressure sputter deposition. This, in turn, can be explained by considering the energy of particles that impinge on the GaN during sputter deposition. Under higher pressures the mean free path of these particles are shorter and consequently the maximum energy that they gain before reaching the sample is lower. Consequently, particles from high-pressure plasmas create fewer defects in the GaN than particles from low-pressure plasmas. In summary, sputter deposition of Schottky contacts on n-GaN generally results in SBDs with degraded rectification properties. The degree of degradation can be controlled by varying the sputter conditions, for example the gas pressure and sputter power. The SBD quality improves if they are deposited using low power and high-pressure conditions. Finally, remember that sputter deposition is frequently employed to provide better adhesion. The study of DeLucca et al. [70] showed that SBDs deposited at high

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powers and low pressures exhibited good adhesion but poorer I-V characteristics, while for the diodes deposited at lower powers the opposite was true. It therefore seems that, depending on the application, a trade-off has to be made between obtaining good adhesion or good I-V characteristics. 4.3.3. Electron beam deposition It has been shown that, although sputter deposition is the method that yields the best metal adhesion to semiconductors, and is also useful in depositing stoichiometric compounds, it introduces defects at and below the surface of semiconductors, including GaN [63,70], which result in SBDs with degraded rectification properties. Electron beam (EB) deposition, on the other hand, is also widely used in the semiconductor industry, in particular where high melting point metals have to be evaporated. However, unless proper care is taken, it too introduces defects in the semiconductor because stray particles originating in the region of the filament or molten metal can impinge on the semiconductor surface. In this respect, the important difference between sputter- and electron beam deposition is that in the latter case defect introduction can be virtually eliminated by introducing proper shielding [71,72]. To study the defects introduced in GaN during EB deposition, Auret et al. [73] have used n-type GaN with a free carrier density of (2-3) x 10^^ cm~^, grown by metalorganic vapor phase epitaxy (MOVPE) on sapphire substrates. After conventional wet chemical cleaning, Ti/Al/Ni/Au (150 A/2200 A/400 A/500 A) ohmic contacts were fabricated [65]. Prior to Schottky barrier diode (SBD) fabrication, the samples were again degreased and dipped in an HC1:H20 (1:1) solution. Following this, circular Ru Schottky contacts, 0.6 mm in diameter and 50 nm thick, were evaporated on two identical GaN samples by EB deposition through a metal contact mask at a pressure of 2 X 10"^ mbar [73]. On the first sample, Ru was deposited at rate of 0.01 nm s"^ without shielding the GaN, and on the second sample it was deposited at a rate of 0.05 nm s~^ whilst shielding the GaN from stray particles. For control purposes, Au SBDs were resistively deposited next to the EB deposited SBDs. I-V measurements (Fig. 19) revealed that for unshielded EB deposited SBDs (curves b, the current at a 1 V reverse bias is 2 x 10"^ A. These characteristics are poorer than those of the resistively deposited Au diodes (curves a), but much better than those of a sputter deposited contact (curves d) on the same sample. The forward log (/) vs V characteristics of the unshielded EB deposited diodes are linear only between 10"^ A and 10~^ A. In this region the ideality factor and barrier height, calculated assuming thermionic emission, are 1.07 ±0.02 and (1.00 ±0.02) eV, respectively. From the shapes of curves b it is evident that in the low-current region recombination-generation (RG) currents dominate, whereas in the high-current region the series resistance limits the current. These I-V measurements confirm that, as for GaAs [71,72], EB deposition of Schottky contacts on n-GaN, without shielding it from stray particles originating at the filament, yields diodes with non-ideal rectification characteristics. Curve c in Fig. 19 was recorded from a diode that was shielded from the filament when metallizing at a deposition rate of 0.05 nm s'\ Its ideality factor and barrier height are 1.08 ± 0.01 and (1.08 ± 0.02) eV, respectively. No significant evidence of RG currents can be seen. From a comparison of curves b and c in Fig. 19 it is clear that shielding the GaN from

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1.0

Fig. 19. I-V characteristics of resistively deposited Au contacts (curve a), EB deposited Ru contacts (curves b and c) and sputter deposited Au contacts SBDs (curve d) on n-GaN. 'F' and 'R' refer to the forward and reverse characteristics, respectively. Curve b and c are for contacts deposited at 0.01 nm s~^ without shielding, and at 0.05 nm s~^ with shielding, respectively.

the filament and depositing at higher rates, significantly improves the diode quality. This can be understood in that the GaN is exposed to energetic particles originating from, amongst others, a region close to the filament. These particles cause damage at and below the surface and this damage leads to the transport of charge by mechanisms in addition to thermionic emission, e.g. RG currents. When shielded from the filament and depositing at a high rate, the exposure of the surface to energetic particles originating at the filament is reduced and thus the concentration of defects that give rise to RG currents is reduced. On the other hand, when depositing without shielding the GaN from the filament and when depositing a low rate, the total particle dose on the GaN is higher and therefore more defects are introduced which, in tum, cause poorer I-V characteristics. Fig. 20 depicts the DLTS spectra of control (resistively deposited) and EB-deposited diodes. Curve a shows that the control sample contained two defects, labeled E02 and E05, with energy levels at 0.27 ± 0.01 eV and 0.61 ± 0.02 eV below the conduction band, respectively (Section 2). Curves b and c in Fig. 20 show that after EB deposition, defects labeled Eel and Ee2 are detected. Note that in curves b and c the peak height of Ee2 has been reduced by a factor of ten with respect to that of Eel. These defects are produced by the particles impinging on the substrate during EB deposition. The energy and apparent capture cross section of Eel, as determined from Fig. 15, are (0.19 ± 0.01) eV and (1.2 ± 0.2) x 10"^^ cm^, respectively, while for Ee2 these parameters are (0.92 ± 0.04) eV and (7.9 d= 2) x lO'^^ cm^ respectively. As can be seen from Fig. 15 and Table 4, the DLTS signature of Eel matches that of ER3 well. ER3 is introduced in n-GaN during high energy (>MeV) proton [19] and He-ion irradiation [36]. ER3,

Radiation and processed induced defects in GaN

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200

400

Temperature (K)

Fig. 20. Curve a: DLTS spectrum of resistively deposited SBD on epitaxial n-GaN. Curves b and c: DLTS spectra recorded from the EB deposited Schottky contact without and with shielding, respectively, using a filling pulse frequencies of 46 Hz and 0.1 Hz, as indicated. All spectra were recorded using a filling pulse width of 0.2 ms and amplitude of 1.6 V, superimposed on a quiescent reverse bias of 1 V.

Table 4. contacts

Electronic properties of defects introduced in n-GaN during electron beam deposition of Schottky

Defect label Eel Ee2

^peak

(eV)

(cm^)

(K)

0.19 ± 0 . 0 1 0.92 ± 0.04

1.2 ± 0.2 X 10-^5 7.9 ± 2.0 X 10-^^

% 120 (46 Hz) % 350 (0.1 Hz)

Similar defects ER3 [19], E [24]

^ Peak temperature at a lock-in amplifier frequency of 46 Hz, i.e. a decay time-constant of 9.23 ms.

in turn, is thought to be the same as a defect, labeled E, with a level at EQ —0.18 eV, observed by Fang et al. [24] after MeV electron irradiation of IVIBE-grown GaN. The energy level of the major EB deposition induced defect, Ee2, is similar to that of ER5 introduced during high-energy particle irradiation of GaN [36] which is as yet unidentified. The depth distributions of Eel and Ee2 for unshielded deposited SBDs were calculated using the constant bias variable pulse DLTS technique. By applying a reverse bias of 1 V and increasing the pulse in steps of 0.1 V, a region up to 0.17 |xm below the interface could be probed. Fig. 21 shows that within this region the concentration of the prominent defect, Ee2, decreases from an estimated 1 x 10^^ cm"-^ just below the interface to 1 x 10^^ cm~^ at 0.06 jxm into the GaN. Clearly, Ee2 will significantly reduce the free carrier concentration directly below the Ru/GaN junction at room temperature. Fig. 21 also shows that the concentration of Eel decreases from 2 x 10^^ cm~^ just below the interface to 5 x 10^^ cm"^ at 0.17 |jim into the GaN. The concentration of Eel is too low to significantly affect the GaN free carrier concentration. For shielded diodes deposited at 0.05 nm s~^ the concentration of Ee2 is estimated (from Fig. 21) as about

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1016 . Ee1:Ec-0.19eV . EO2:Ec-0.27eV . Ee2: E- - 0.92 eV

E c ro C 1013 t O

10^2

0.00

0.05

0.10

0.15

0.20

Depth below junction (microns)

Fig. 21. DLTS depth profiles of defects in as-grown n-GaN before EB deposition (E02), and after EB deposition without shielding (Eel and Ee2) of Ru SBDs.

4-5 times less than for unshielded diodes. The concentration of Eel (Fig. 21) is even more reduced than that of Ee2 with shielding and increased deposition rate. Subsequently, the effects of forming Pt Schottky contacts on HVPE grown n-GaN with EB deposition have been investigated [70]. In this investigation no intentional screening was placed to protect the sample from stray particles. It was found that the I-V and C-V characteristics were poorer than those of electrodeposited contacts fabricated on the same epitaxial layer. DLTS showed that the same two EB induced defects, Eel and Ee2, that were detected in OMVPE grown GaN were also detected in the HVPE GaN after depositing the contacts. Their properties are included in Table 4. In sununary, during EB deposition stray electrons impinge on the sample, introduce defects in it and result in degraded rectification properties of SBDs. The concentration of these defects, and thus the degree of device degradation, can be reduced by shielding the sample from these stray particles. When doing this, it should be borne in mind that the physical construction of EB deposition systems may be different and therefore each system has to be separately optimized. The governing principle here is that most of the particles originate in the region of the filament and molten metal. The effect of these stray particles can further be reduced by increasing the deposition rate. This reduces the particle dose onto the sample and hence the defect concentration, and consequently results in an increase in SBD quality. 4.3.4. Electrodeposition The motivation for employing this metallization method is two-fold [70]. First, it is thought that a cleaner, more intimate contact could be realized through the use of electrodeposition compared to physical vapor deposition methods, since electrodeposition could be performed in an acidic solution that could potentially remove the native oxide or other surface contaminants. Second, electrodeposition is a room-temperature process with extremely low processing energy (below 1 eV) [74]. DLTS results of

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Pt Schottky contacts to n-lnP [75] and w-GaAs [76] indicated that concentrations of electrically active defects induced by the electrodeposition process are negligible compared to, for example, those of defects introduced during electron beam evaporation. In addition, the electrodeposited Pt/n-lnP contacts exhibited a much higher barrier height [75] than what is typically reported for contacts prepared by physical vapor deposition methods. The suitability of electrodeposition for Schottky contact fabrication on GaN was recently demonstrated when Pt Schottky contacts, fabricated on the same HVPE grown n-type GaN by electrodeposition, electron beam evaporation, and DC magnetron sputtering, were studied [70]. The electrodeposited contacts were shown to produce significantly higher I-V and C-V barrier heights than most electron beam evaporated and sputter deposited contacts studied, with reverse currents reduced by three to four orders of magnitude. In Fig. 22 we compare the DLTS spectra of Pt Schottky contacts deposited on the same HVPE grown n-GaN using DC magnetron sputter deposition, electron beam deposition and electrodeposition. This figure reveals that, whereas several defects are introduced during DC magnetron sputtering and electron beam evaporation, no detectable defects are introduced during electrodeposition. The high barrier heights obtained using electrodeposition together with the fact that it 14

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0

50

100

150

200

250

300

350

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Fig. 22. DLTS spectra recorded using Pt Schottky contacts deposited on HVPE grown n-GaN by electro-deposition (curve a), electron beam deposition (curve b)), high-pressure low-power sputter deposition (curve c) and high-power low pressure sputter deposition (curve d). All spectra were recorded using a filling pulse width of tp = 0.2 ms, a reverse quiescent bias of Vr = 2 V, a filling pulse amplitude of Vp = 2.2 V and a pulse frequency of / = 46 Hz.

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does not introduce defects, renders this method very suitable for the fabrication of high quality rectifying contacts to n-GaN. 5. Summary and conclusions High energy particle irradiation introduces several electron traps in n-GaN with energy levels between 0.06 and 0.95 eV below the conduction band. Some controversy surrounds the nature of the most frequently level at 0.20 eV. It has recently been shown that the DLTS signal of this level can be deconvoluted into at least two levels. One of these is a shallow donor at EQ —0.06 eV which has previously been assigned to the VNThe origin of the deeper lying defects is not clear yet. All the observed high energy irradiation induced defects anneal out at 700 K. Resistive (Joule) evaporation and electrodeposition of metals do not introduce defects in semiconductors. However, two other metallization processes, E-beam and sputter deposition, were shown to introduce electrically active defects in GaN. Both these processes introduce a defect with a level similar to that of ER3, believed to be related to the nitrogen vacancy. In addition, each of these processes introduces defects characteristic to the process. The concentration of these process induced defects can be minimized by optimizing the deposition conditions. For sputter deposition this can be achieved by minimizing the deposition power and maximizing the plasma pressure. In the case of E-beam evaporation, the geometry of the e-gun with respect to the sample position should also be taken into account. Finally, the thermal stability of these metallization induced defects has not yet been reported. This, in conjunction with the thermal stability of the Schottky contacts, is required to assess whether or not post-deposition annealing can remove the defects responsible for diode degradation. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]

A. Mogro-Campero, R.P. Love, M.F. Chang and R.F. Dyer, IEEE Trans. Electron Devices 33, 1667 (1986). D.C. Sawko and J. Bartko, IEEE Nucl. Sci. 30, 1756 (1983). S.J. Pearton, W.S. Hobson, U.K. Chakrabarti, G.E. Derkits Jr. and A.P Kinsella, J. Electrochem. Soc. 137, 3892 (1990). F.D. Auret, S.A. Goodman, G. Myburg and W.E. Meyer, J. Vac. Sci. Technol. B 10, 2366 (1992). F.H. Mullins and A. Brunnschweiler, Solid State Electron. 19, 47 (1976). E. Grussell, S. Berg and L.R Andersson, J. Electrochem. Soc. 127, 1573 (1980). A.G. Foyt, V^.T. Lindley, C M . Wolfe and J.P Donnelly, Solid State Electronics 12, 209 (1969). J.C. Dyment, J.C. North and L.A. D'Asaro, J. Appl. Phys. 44, 207 (1973). D.V. Lang, J. Appl. Phys. 45, 3014 (1974). O. Lindberg, Proc. IRE 40, 1414 (1952). H.J. von Bardeleben, D. Stievenard and J.C. Bourgoin, Appl. Phys. Lett. 47, 970 (1985). D.V. Lang, A.Y. Cho, A.C. Gossard, M. Ilegems and W. Wiegmann, J. Appl. Phys. 47, 2558 (1976). A. Mitonneau, G.M. Martin and A. Mircea, Electron. Lett. 13, 666 (1976). PN. Brunkov, VS. Kalinovski, V.G. Nikitin and M.M. Sobolev, Semicond. Sci. Technol. 7, 1237 (1992). P. Hacke, T. Detchprohm, K. Hiramatsu, N. Sawaki, K. Tadatomo and K. Miyake, J. Appl. Phys. 76, 304 (1994). W. Gotz, N.M. Johnson, H. Amano and I. Aksaki, Appl. Phys. Lett. 65, 463 (1994).

Radiation and processed induced defects in GaN [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51]

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P. Hacke, H. Nakayama, T. Detchprohm, K. Hiramatsu and N. Sawaki, Appl. Phys. Lett 68, 1362 (1996). W.I. Lee, T.C. Huang, J.D. Guo and M.S. Feng, Appl. Phys. Lett. 67, 1721 (1995). F.D. Auret, S.A. Goodman, F.K. Koschnick, J.-M. Spaeth, B. Beaumont and P Gibart, Appl. Phys. Lett. 74, 407 (1999). W. Gotz, N.M. Johnson and D.P Bour, Appl. Phys. Lett. 68, 3470 (1996). C D . Wang, L.S. Yu, S.S. Lau, E.T. Yu, W. Kim, A.E. Botchkarev and H. Morkoc, Appl. Phys. Lett. 72, 1211 (1998). D. Haase, M. Schmid, W. Kumer, A. Domen, V. Harle, F. Scholz, M. Burkard and H. Schweizer, Appl. Phys. Lett. 69, 2525 (1996). Z.-Q. Fang, D.C. Look, W. Kim, Z. Fan, A. Botchkarev and H. Morkoc, Appl. Phys. Lett. 72, 2277 (1998). Z.-Q. Fang, J.W. Hemsky, D.C. Look and M.P Mack, Appl. Phys. Lett. 72, 448 (1998). O.H. Nam, M.D. Bremser, T.S. Zheleva and R.R Davis, Appl. Phys. Lett. 71, 2638 (1997). M. Lambsdorff, J. Kohl, J. Rosenzweig, A. Axmann and J. Schneider, Appl. Phys. Lett. 58, 1881 (1991). V.M. Rao, W.-P Hong, C. Caneau, G.-K. Chang, N. Papanicolaou and H.B. Dietrich, J. Appl. Phys. 70, 3943 (1991). T.P. Ma, P.V. Dressendorfer: Ionizing Radiation Effects in MOS devices and Circuits, John Wiley and Sons, New York, Vol. 47, 1989. M. Linde, S.J. Uftring, G.D. Watkins, V. Harle and F Scholz, Phys. Rev. B 55, R10177 (1997). V.V. Emstev, V.Yu. Davydov, I.N. Goncharuk, E.V. Kalinina, V.V. Kozlovskii, D.S. Poloskin, A.V. Sakharov, N.M. Schmidt, A.N. Smimov and A.S. Usikov, Mat. Sci. Forum Ft. 2, 1143 (1997). I.A. Buyanova, Mt. Wagner, W.M. Chen, B. Monemar, J.L. Lindstrom, H. Amano and I. Akasaki, Appl. Phys. Lett. 73, 2968 (1998). D.C. Look, D.C. Reynolds, J.W. Hemsky, J.R. Sizelove, R.L. Jones and R.J. Molnar, Phys. Rev. Lett. 79, 2273 (1997). L. Polenta, Z.-Q. Fang, D.C. Look, Appl. Phys. Lett., in press. S.A. Goodman, F.D. Auret, P Gibart, B. Beaumont, Appl. Phys. Lett. (2000). S.A. Goodman, F.D. Auret, F.K. Koschnick, J.-M. Spaeth, P Gibart, B. Beaumont, Mat. Res. Soc. Symp. Proc. 537, G6.13 (1999). F.D. Auret, S.A. Goodman, F.K. Koschnick, J.-M. Spaeth, P. Gibart and B. Beaumont, Appl. Phys. Lett. 73, 3745 (1998). O. Ambacher, H. Angerer, R. Dimitrov, W. Rieger, M. Stutzmann, G. Dollinger and A. Bergmaier, Phys. Stat. Sol. (a) 159, 105 (1997). M.J. Weinstein, C.Y. Song, M. Stavola, S.J. Pearton, R.G. Wilson, R.J. Shul, K.P Killeen and M.J. Ludowise, Appl. Phys. Lett. 72 (14), 1703 (1998). S.J. Pearton, C.R. Abemathy, R.G. Wilson, J.M. Zavada, C.Y. Song, M.G. Weinstein, M. Stavola, J. Han and R.J. Shul, Nucl. Instrum. Meth. B147, 171 (1999). J. Neugebauer and C.G. Van de Walle, Semiconductors Semimetals 61, 479 (1999). D.V. Lang, J. Appl. Phys. 45, 3023 (1974). J. Frenkel, Phys. Rev. 54, 647 (1938). Y. Zohta and M.O. Watanabe, J. Appl. Phys. 53, 1809 (1982). M. Asif Khan, J.N. Kuznia, A.R. Bhattarai and D.H. Olson, Appl. Phys. Lett. 62, 1786 (1993). S.C. Binari, L.B. Rowland, W. Kruppa, G. Kelner, K. Doverspike and D.K. Gaskill, Electron. Lett. 30, 1248 (1994). S.C. Binari, H.B. Dietrich, G. Kelner, L.B. Rowland, K. Doverspike and D.K. Wickenden, J. Appl. Phys. 78, 3008 (1995). S.J. Pearton, C.B. Vartuli, J.C. Zolper, C. Yuan and R.A. Stall, Appl. Phys. Lett. 67, 1435 (1995). FD. Auret, S.A. Goodman, G. Myburg and WE. Meyer, Appl. Phys. A 56, 547 (1993). J. Neugebauer and C.G. Van de Walle, Phys. Rev. B 50, 8067 (1994). T. Mattila, A.R Seitsonen and R.M. Nieminen, Phys. Rev. B 54, 1474 (1996). T. Wosinski, J. Appl. Phys. 65, 1566 (1988).

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III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 9

Residual stress in III-V nitrides Nora V. Edwards

1. Introduction A preliminary goal of this chapter is to convince the reader that residual stresses have a profound effect on nitride optical data. And since these materials are being heavily developed for opto-electronic applications, the presumption is that anything affecting nitride optical properties to such a large extent should be investigated, at the very least so that such perturbations can be eventually eliminated or exploited to improve nitride-based LED and laser diode performance. Such an investigation will naturally center around the fundamental ways that stress affects the optical properties of a material, but we will also be concerned with the materials and growth parameters that produce such stresses in the first place. That having been done, we will also examine the extent to which it has been possible to manipulate residual stresses in these materials, with the goal of improving optical properties. We will focus on GaN films and will largely ignore the non-negligible role that defects and impurities (readers interested in this topic should see, for example, Kisielowski et al. [1] and Gorczyca et al. [2]) play in this drama. This is justified for the simple reason that the strain states of even the most rudimentary GaN heterostructures are not at all well-understood and that we must master the simplest case before proceeding to more complex combinations of materials. In short, we must learn to walk before we can run. It is a simple matter to establish that residual stress readily perturbs GaN optical properties. We demonstrate with a collection of selected GaN low-temperature reflectance lineshapes [3] (Fig. 1) obtained from films grown under a variety of conditions. At the time of publication, researchers were interested in obtaining the 'proper' value of the critical point energies of the A, B, and C excitons — which are closely tied to the strain-sensitive valence band structure — from the extrema of the peaks shown. We immediately see that there is no simple recipe for extracting such information. The number and position of the peaks vary in almost each case, where each case again represents a GaN film grown under a different set of heterostructure design and growth conditions. The focus of this chapter will revolve around two seemingly simple questions: how is this selection of lineshapes possible for a single material? and more pointedly, why does this range of phenomena occur? We will, where possible, address these questions from both a phenomenological and fundamental perspective. Prior to proceeding with the optical data, we maintain that it is absolutely crucial to

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E(eV) Fig. 1. Selection of representative GaN reflectance lineshapes (10 K) designed to show that samples with different states of strain have different optical properties. Samples were grown under a variety of conditions representing different combinations of the following: substrates, buffer layers, growth temperatures, and growth techniques.

examine the physical structure of the samples that are being measured. Accordingly, the next section is a summary of the basic physical issues affecting the state of strain in the GaN films that were used to generate the seminal optical data. Because much has been learned lately about nitride physical properties and growth mechanisms — certainly since the first reflectance data were taken by Dingle et al. in 1971 [4] and even since the renewal of interest in such spectra in the mid-1990s — we in hindsight have the information necessary to decode these data that were largely unavailable to the workers initially investigating the problem. Indeed, during the course of this chapter we shall see that a lack of information about the physical properties of the material has been the source of considerable misunderstanding about strain behavior in the GaN literature. Indeed, we will use these structural and related materials issues to explain: • why the GaN optical data was an initial source of confusion; • why the trends in residual stress for GaN films were discovered to be contrary to conventional wisdom; and • why unusual growth strategies — beyond what has been necessary to manage residual stresses in traditional III-V strained layer systems — have been necessary to move the material forward technologically.

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2. Basic physical issues surrounding GaN heteroepitaxy 2.1. Introduction We will begin our discussion with a bit of history. To understand residual stress behavior in GaN films — and indeed to understand the evolution of the material from cracked, rough films to the foundation of viable commercial products — it is instructive to first tell the story of the humble AIN buffer layer that assisted this transformation. Though nitride stress-control methods have evolved beyond this relatively simple strategy, the story of the initial struggle to achieve specular GaN films highlights some crucial materials issues pertaining to residual stress behavior for a variety of nitride structures. Because GaN substrate material was not and still is not available commercially, it has been necessary to insert a thin layer of AIN between the GaN film and the two conmion substrate choices, Qf-Al203 or 6H-SiC. Other substrate materials have been tried but with less success. Among these are Si, GaAs, NaCl, GaP, InP, W, Ti02, ZnO, LiGa02, MgAl204, MgO, and ScAlMg04. See Hellman et al. [5] for more details. Not surprisingly, buffer layers are meant to minimize the considerable mismatch between film and substrate. But the physical structure of the constituents of nitride heterostructures often makes what should be simple mediation into a far more complex matter. In this section we will focus upon issues surrounding (a) lattice mismatch, (b) buffer layer morphology and initial film growth, and (c) thermal mismatch behavior for four materials: GaN, AIN, 6H-SiC and a-Al203. These are three interrelated issues that largely dictate the state of strain in GaN heteroepitaxial films. While the materials issues surrounding the achievement of specular GaN films are naturally more our concern than the historical picture of its development, we mention nonetheless that GaN films were actually achieved as early as 1969 [6] in order to illustrate the importance of the AIN buffer layer. This is because further developments — beyond the initial growth of HVPE material [6] and other key achievements [7-9] in the early 1970s — were stymied until quite recently by poor morphology and difficulty with the control of impurities [10]. To be balanced in our treatment we must observe that the solution of the problems conceming the control of n-type conductivity [11] and with the activation of holes in Mg-doped material [12,13], were watershed innovations that enabled the current frenzy of nitride development. But before these issues could even be addressed, specular films needed to be achieved. Key developments in this area are summarized in Table 1 [11,14-21]. The buffer layer mediates mismatch by different mechanisms, depending on the substrate material. These differences, not surprisingly, are the source of the further differences that we will encounter between the two heterostructure systems with respect to both optical and residual stress behavior. For growth on 6H-SiC, the buffer layer appears to be a true mediator of lattice mismatch, while for growth on sapphire it acts more like a 'platform' for epitaxy. The high-resolution transmission electron micrograph of the substrate-buffer layer interface [10] for both materials shown in Fig. 2 is clearly indicative of differences in each that must be occurring during buffer layer growth. The transition between the AIN buffer layer and the sapphire substrate is abrupt and yet incoherent, though the AIN layer is still generally considered epitaxial. Indeed, the film

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i^^^p'^«^^^^

,j

,^. , j , ,

:

^SSS !*>:.#• m -m WW-m

#

*

#• # #

f

f

f

#

§

S

f | . |: 0i 0- 0 §

^

•^' f

#•

#

^ , ^ , *: :::.*, %. %. ,- %, ^,1: .# ,.fcS# •*•« # # # # f # f f # f | f J | f | J f f # f f ^

AlaOa

W : f %

: i

- # :

i m i -i 4 i S €. • # # # # # § I f |: f # I |i fi J f # f :|i: # # i i # f f # # f^ # i

Fig. 2. High-resolution transmission electron micrograph of the respective interfaces of the AIN/AI2O3 (left) and AlN/6H-SiC buffer layer/substrate systems. Note that the interface on the left is abrupt and incoherent while the one on the right has a direct, one-to-one correspondence between the two lattices. In each case, the overlying GaN film quality is high. Reprinted with permission from Ponce and Bour [10].

quality manages to be quite high without a direct, one-to-one correspondence between the two lattices. In contrast the 6H-SiC/AlN interface is coherent and is indicative of the relative similarity in lattice structure between the two materials [10]. 2.2. Lattice mismatch The simplest way to view strain is from the perspective of lattice mismatch, where we are concerned with the quantity Aa/a or Ac/c, where a is the lattice parameter in the [1120] or the [1010] direction and c is its counterpart in the [0001] direction, given that the most common phase of GaN and AIN crystallizes in the wurtzite structure. The mismatch itself is defined as Aa/a = [^caN — ^AIN]/ ac, except AI2O3, where «« < occ, and for 6H-SiC, where «« > oic [24-28]. The result of this is a compounded degree of complexity in the GaN/AlN/6H-SiC system; as stated, the interplay between the ofs of the layers is even more complex in the c-direction, as seen in Fig. 7d. Here we see that there are two crossover points in this system instead of the one at '^547 K seen with AIN and GaN in the (^-direction (Fig. 7a,b). There is one with GaN and AIN, where at T < ~647 K^AiN < cifGaN ^ud the reverse is true above this temperature and another at r = ^^1201 K, where asic < otQaN below this temperature and is greater above it. Since films and buffer are grown at 1323 K (1100°C) and 1373 K (1050X), respectively, the SiC-based system passes through both crossover points upon cooling. This, again, can be contrasted to the case of sapphire-based growth (Fig. 7c), where the a of AI2O3 is so mismatched, i.e. so much greater than the others, that the interplay between GaN and AIN is in all likelihood obscured by it in the majority of cases. However, the implications of how the c-plane behavior complicates matters through the considerable anisotropics that we have seen (and its impact on issues such as variations in nitrogen vacancy concentrations via disturbances in c/a, for example) are not yet clear and have been investigated by several research groups [29,30,44,52,53]. For our purposes, the simple message is: thermal behavior in even these basic heterostructures is complex and the understanding of it is incomplete, and predicting stress behavior in GaN films is a far larger matter than merely comparing room temperature values of a. We will now turn our attention to the impact that this and the other two interrelated origins of strain — lattice mismatch and island coalescence behavior — have on GaN optical data. 3. Stress-related ambiguities in GaN optical data 3.1. Introduction: discussion of problems The optical behavior of GaN is quite similar to that of CdS, which was studied extensively by Thomas and Hopfield in the early 1960s [54,55]. For this material the triply degenerate (6-fold degenerate with spin) states at /: = 0 are split by a combination of the crystal-field potential and the spin-orbit interaction into three singlet levels (doublets with spin included) whose associated excitons are labeled A, B, and C in order of increasing transition energy. The appropriate group theory and the general procedure for determining these levels in terms of the crystal-field and spin-orbit interactions were also detailed by Hopfield [56]. For GaN, if the crystal-field potential were the only operative interaction the selection rules for light normally incident along the c-axis are such that only the A and B excitons would be observed. With the spin-orbit interaction included the B transition becomes weaker and the C transition becomes allowed, but only weakly. The strain caused by biaxial stress in the plane of the surface for films with the c-axis normal to the surface

Residual stress in III-V nitrides Table 3.

Ch. 9

303

Early excitonic splittings observed for GaN heterostructures

Ref.

Authors

Year

^A

EE

^c

[4] [57] [58] [41] [59] [60] [61]

Dingle et al. Monemar et al. Harris et al. Shan et al. Mohammed et al. Gil et al. Pakula et al.

1971 1974 1995 1995 1995 1995 1996

3.474 3.4751 3.488 3.485 3.4831 3.4775 3.4780

3.480 3.4815 3.495 3.492 3.4896 3.4845 3.4835

3.501 3.493 3.506 3.518 3.518 3.5062 3.502

^EBA

AEBC

6.0 6.4 7.0 7.0 6.5 7.0 5.5

21.0 12.0 11.0 26.0 28.0 21.7 18.5

has the same symmetry as the crystal-field potential and can be treated as an additive effect. Accordingly, researchers measuring this material generally expect to see three excitons in low-temperature optical data corresponding to these physical perturbations. The seminal low-temperature reflectance data obtained by Dingle and coworkers [4] in 1971 conformed to this expectation. It is shown in Fig. 8 to illustrate. The relevant polarization state is the a (E ± c,k c), used to obtain the energy position of the A exciton EA = 3.474 ± 0.002 eV and A-B and A-C excitonic splittings A£'BA = 6.0 and AEcA = 20.5 meV, respectively. These were obtained, it seems, by assigning the values at peak extrema. Such values were representative of data obtained on 100 [xm thick samples that had free electron concentrations of ^^10^^ cm~^ and mobilities >300 cm^/Vs. They were grown by 'vapor epitaxy' on (OOOl)-oriented sapphire substrates, with no buffer layer [4]. Later research groups confirmed the observation of three free excitons, with some variation in peak positions and splittings, as shown in Table 3 [4,57-61]. The only conspicuous deviation in A^BA values is the one from Ref. [61]. By way of explanation we note that except for the data on bulk GaN obtained by Pakula et al. [61] all of the data were obtained on GaN heterostructures with sapphire substrates. On the other hand, among this seemingly similar material we see that the A^BC values given by Monemar [57] and Harris [58] are in some cases half as large as the other values, obtained on material producing a very broad linewidth for the C transition. Gil [60] noted that perhaps there was a misinterpretation of the data in these cases, but without a definitive lineshape analysis for the material, it was difficult to say which interpretation was correct. New data for GaN growth with 6H-SiC substrates complicated matters further. We see that there was even a small amount of controversy surrounding the data taken from material on sapphire substrates, where interpretation of relatively similar lineshapes eased matters. For this new heterostructure, initially, only two excitonic features were seen. Some of the earliest data were taken with spectroscopic ellipsometry, where two broad, closely spaced excitonic features in the vicinity of the fundamental absorption edge were observed in narrowband (3.3-3.6 eV) room temperature spectra. Representative spectra are shown in Fig. 9a [62], with data taken on a sample with a sapphire substrate included for comparison. Here the imaginary part of the pseudodielectric function vs. energy of GaN layers grown on AI2O3 (upper curve) and 6H-SiC (lower curve) substrates is shown. Again, it is clear that GaN layers grown on different substrates have different optical properties: the excitonic features in the

Ch.9

304

N,V.Edwards

A CM

V

2 h GaN on 6H-SiC:

oh

18meV

3.35

3.40

3.45

3.50

E(eV)

3.44

3.46

3.48

3.50

3.52

3.54

3.56

PHOTON ENERGY (eV) Fig. 9. Imaginary part of the pseudodielectric function of GaN layers grown on AI2O3 (upper) and 6H-SiC (lower). The spectra were taken with a resolution of 2 meV. Reprinted with permission from Edwards et al. [62]. (b) One of the first low-temperature reflectance lineshapes obtained for GaN grown directly on 6H-SiC. The relevant curve is the top in the series; the other two curves are derivative reflectance (middle) and photoluminescence spectra (bottom). Reprinted with permission from Buyanova et al. [47].

Residual stress in III-V nitrides

Ch. 9

305

upper curve are separated by ^ 7 meV, consistent with other values reported in Table 3, while at '^IS meV the excitonic splitting observed for the material on 6H-SiC is much larger. Note the conspicuous lack of a third excitonic feature compared to the seminal lineshape shown in Fig. 8. Of course, the observed features were broad, as the data were taken at room temperature. But without a third excitonic feature, it was not possible to use emerging perturbation theory calculation [62] of the variation of the A, B, and C absorption thresholds as a function of crystal field and biaxial stress potential (the Hopfield Quasicubic Model [56]) to assist in spectral interpretation. This was the case because of the ambiguity associated with the fact that Vspin orbit is obtainable from the excitonic splittings only by solving a quadratic equation, by necessarily has two roots (See Ref. [62]). Further, it could be argued that there was simply not enough data — or rather, data with dissimilar enough strain states — to provide a solid basis for the fitting procedures in the calculations. (Interested readers can look ahead to the significant scatter in the values of fit parameters ACF and ASO prior to 1997 to confirm this; see Table 5.) In short, it was unclear whether the same optical transitions in both cases in Fig. 9a were being observed. Work at low temperatures, to try to resolve a third feature, was necessary to resolve this issue. Shortly thereafter, Buyanova and coworkers [47] obtained low-temperature reflectance data on a 3.9 |xm GaN film grown directly on 6H-SiC. Surprisingly, they also could not find any evidence of a third resonance. The spectra are shown in Fig. 9b, the top curve in the series. This did not resolve the controversy, as it was not possible to determine whether the B-A excitonic energy separation with an unresolved C exciton or an unresolved B-A splitting with a resolved C were being observed. A coherent lineshape analysis for GaN was sorely needed, as were a greater variety of strained samples to lift the ambiguity from the perturbation theory calculations. 3.2. Solution: Fourier analysis plus heterogeneous sample set Such a study was published a year later by Edwards et al. [3] that undertook this task. The problem was addressed first by studying GaN layers designed to represent the widest range of residual in-plane strain that were available at that point and second by analyzing lineshapes in reciprocal space, where critical point energies can be determined independent of baseline artifacts to ±0.5 meV. Fourier analysis is especially suited to the challenges presented by this particular problem, as the technique can be used to determine critical point (CP) energies even if real-space lineshapes are not known a priori. This follows because baseline effects, information, and noise are localized in the low, middle, and high Fourier coefficients, respectively, ensuring that spectral information can be extracted independent of baseline and noise artifacts. In reciprocal space, critical point parameters also divide into 2 groups: one associated with the amplitude and one with the phase, which reduces correlations during least-squares fitting. In particular, the parameter associated with the CP energy appears only in the phase. The Fourier coefficients, then, are typically described according to the complex representation C„ = C„ exp(—/$„), where C„ is the amplitude of the coefficients, and ^„ is the phase. Further advantages of fitting optical data with Fourier analysis and details of specific procedures are given elsewhere, by Yoo et al. [63] and by Aspnes [64].

Ch.9

306

N.V.Edwards

0.25

0.20

^ 0.15

0.10

3.48 Energy [eV]

3.44

3.52

-T

-2 I-

E^ + 0.3 meV E = 3.4764 eV 20

40

60

80

n Fig. 10. (a) Reflectance data (points) and real-space fit results (solid line) from Baranowski et al. [65], obtained from a homoepitaxial GaN sample. Location of excitonic CP energies obtained by Fourier analysis, done in this laboratory, are indicated by the arrows. Vertical lines denote division of the spectrum into sections isolating CPs for more accurate analysis, (b) Top half, solid line: ln(C„) of the selected data segment under analysis. Dashed line: variation of ln(C„) for a single CP representation. Bottom half, solid line: ^„ of the segment. Central dashed line: ^„ for a single CP representation for EQ = 3.468 eV. Dotted lines: variation of ^„ for EQ = 3.4764±0.0003 eV. Both reprinted with permission from Edwards et al. [75].

To demonstrate the efficacy of the technique, we show the comparison of Fourier analysis results to that which is still is regarded as one of the more sophisticated real-space fits for GaN reflectance spectra. Fig. 10a features such a comparison. The points represent data obtained from a homoepitaxial GaN layer, taken from Baranowski et al. [65] and the thin solid line corresponds to the results of their relatively elaborate real-space fit, including polariton effects. (A more current 'strain-free' value of the A exciton can be found in Komizer et al. [66]. Strain-free is in quotation marks because there has been considerable discussion over the degree to which homoepitaxial films are without stress. See Monemar [67].) Further details of the fit are given elsewhere [68]. The vertical lines denote the division of the spectrum into sections isolating the CPs for more accurate analysis in reciprocal space.

Residual stress in III-V nitrides

Ch.9

307

Excitonic CP energies from the real-space fit were EA = 3.4767, E^ = 3.4815, and Ec = 3.4987 eV, with no uncertainty specified. CP values determined by Fourier analysis are as indicated by the arrows in Fig. 10a: 3.4764, 3.4822, and 3.4983 eV, respectively, all determined to within ±0.5 meV. The degree of agreement with the real-space fit is excellent ( A £ A = 0.3 meV, AEB = 0.7 meV, and AEQ = 0.4 meV). Even so, to further demonstrate the capabilities of the technique, we show that Fourier analysis can be used to determine CPs to accuracies of the order of magnitude of these small differences, as illustrated in Fig. 10b. Shown is a plot of ln(C„) and §„ vs. n, the index of the Fourier coefficients. The linear behavior of both ln(C„) and ^„ implies for the former that the lineshape of the dominant exciton is Lorentzian and for the latter that this excitonic CP energy is the energy of the inversion origin, here 3.4764 eV. The dotted lines here demonstrate the degree of accuracy associated with this determination, quite conservatively expressed as Ep, = (3.4764 ± 0.0003) eV. Even a 0.3 meV derivation from the fitted EA value yields a line with a finite slope, in contrast to the zero slope that occurs when the inversion origin equals the CP energy. Uncertainties are uniformly given as 0.5 meV in the following discussion to account for the variation of the individual uncertainties of the 45 excitonic CP energies determined here; some uncertainties may actually be less than this value, as shown. The same selection of reflectance spectra that was shown in Fig. 1 is shown again here (Fig. 11) with the excitonic critical point energies, as determined by Fourier Analysis, indicated by the points. The historical lineshape of Dingle et al. [4] is shown in (d) with the original assignments indicated by the arrows. Our lineshape analysis indicates that A^'BA and A^CA are closer to 5 and 23 meV, respectively, rather than the 6.0 and 20.5 meV they reported. The lineshapes are arranged in order of descending excitonic energy separation AEB A = EB — EA- They were obtained from GaN layers grown by (1) metallorganic chemical vapor deposition (MOCVD) on AI2O3 substrates with 250 A GaN buffer layers, (2) Hydride Vapor Phase Epitaxy (HVPE) on AI2O3 substrates without buffer layers, and (3) MOCVD on 6H-SiC substrates with 1000 A AIN buffer layers. They were referred to by the authors as Category I, II, and III samples, respectively, shown in Table 4. Details of crystal growth are given elsewhere [19,69,70]. Fig. 11a is typical of reflectance spectra of Category (I) films. The feature farthest to the left is an interference oscillation; the excitonic features of interest lie to the right. Here AEBA and AEQA are 9.2 and 27.8 meV, respectively; however, real-space assignments for the same sample yielded AEBA = 11 m^V and A ^ C A = 34 meV. The other Category (I) samples exhibit similar discrepancies as a result of baseline ambiguities. Reciprocal space AEBA values are as shown in Table 4, but the real-space values for Category (I) samples were all ~11 meV. Reliance on real-space analysis in this case would have lead (the authors maintain) to the incorrect corroboration of the work of Orton [71], who, performing a Hopfield Quasicubic model [56] calculation on a few samples grown only on AI2O3 (nearly all of the excitonic splitting values published at the time, however) concluded that AEBA was invariant. Reciprocal-space analysis was sufficiently sensitive to detect the non-negligible variation of AEBA for a sample set varying by only 0.5 |xm in thickness. We observe a similar pattern in a sample set within Category (III), a 1.32 ^^m

Ch.9

308 •

N.V.Edwards

Reciprocal Space Analysis Results I

AEg^ = 9.2 meV AE.. s 27.8 meV


, \xyz i)

\yz t>, \yz I) \zx t), \zx i) \xy t)' \xy i)

(2 states)

Ec

(6 states)

Ev

we will introduce the following perturbations: (1) the crystal-field, (2) the spin-orbit, and (3) the biaxial stress potentials. The first, the crystal field (C-F) term, is relevant because materials such as GaN, that are of hexagonal or wurtzitic structure, have a lower symmetry than cubic materials. Hexagonal and cubic materials differ most notably on the atomic scale by 4th nearest

Residual stress in III-V nitrides

Ch. 9

317 #

As, N Top, 4th n.n. Ga

^ ^ ^ S ; + z) + ^

(yz + zx + xy)

(14)

Note that this interaction has a symmetry identical to that of trigonal shear. The practical consequences are that for epitaxial GaN films with the c-axis perpendicular to the plane of the surface, the CF and biaxial strain terms cannot be distinguished without further information, such as the energy of the fundamental absorption edge in an unstrained (i.e. bulk) crystal. Note as well that the shortening of the c-axis relative to the zincblende case gives rise to a negative V25 for GaN, in this equation. The spin-orbit interaction concerns the interaction between the spin magnetic dipole moment of an electron and the internal magnetic field of an atom (in the one-electron picture). This internal magnetic field is related to an electron's orbital angular momentum. For multi-electron atoms, these internal magnetic fields are quite strong, so the spin-orbit effect is usually quite strong as well. The perturbation term due to the spin-orbit interaction is given by (15)

I \i operates on the basis set

\j I

z \u

-1 /

(16)

318

Ch.9

N,V Edwards

and L = r X p

The coefficient ^ = §(r) depends on the radial derivative of the core potential. It is largest for heavy atoms, thus the dependence of the spin-orbit interaction on size etc. A full basis set at A: = 0 for the S-O splitting is conduction band: \xyz t>» l^yz i) valence band: \yz t ) , 1^-^ t>. 1-^3^ t)» \yz I ) , \zx 4), \xy i) where, for example: Ly\yz t ) = -i^(^^

- ^ ^ ) i^^ t> = +i^\xy t>

(18)

i.e. x(d/dz) effectively replaces z with x, and the z(d/dx) operator yields zero. Likewise

LAyz t> = -ih (y^^ - z^^

yzt)=o

(19)

since \y'^) and \z^) are not part of the set. Using the general linear combination ^ = ai\x \) -\-a2\y \) H-aslz t ) +«4|-^ i) + aslx I) + ae\x 4), we can find the resultant eigenvalues and eigenvectors, shown in Table 6. These linear combinations are eigenfunctions of §L • S with the eigenvalues shown. Note (1) that ^ is usually negative, so the j = 1/2 (spin-orbit split) band lies below the j = 3/2 band, and (2) that the difference in eigenvalues is +3/2(fi§). Selection rules involving momentum matrix elements can now be calculated, allowing us to build the Hamiltonian matrix and calculated transition oscillator strengths. Note also that the non-degenerate bands (i.e. the lower conduction bands) are not affected by the spin-orbit interaction. The final perturbation is the biaxial stress interaction. The actual interaction with the electronic wavefunctions of a material is via strain, not stress. The change in lattice constants cause the change in electronic structure, not the applied or residual stress itself. Of course, strain results from stress; hence the confusion that often arises. Strain and stress are connected by the compliance tensor, as given in the previous section. Table 6. Resultant eigenvalues and eigenvectors for the spin-orbit perturbation J 3/2 3/2 3/2 3/2 1/2 1/2

rrij

Wavefunction

Eigenvalue

3/2 1/2 -1/2

(X t +iy t)/^/2 (x I +iy i -2z V/Ve

-^2'iH

-3/2 1/2 -1/2

ix t -iy t +2z ;)/V6 (X 4. -iy i)/V2

-^hH -{hH -is^i

(X 4. +iy i +z t)/V3

-ift^t

(X t -iy t -z

-^ft^l

i)/V3

Residual stress in III-V nitrides

Ch. 9

319

The perturbation term usually used to describe the effect of strain was originally derived by Pikus and Bir H' =

EijPikj

SijPiPj 4- SijVij

(20)

where P/ is the /th component of the momentum operator, eij is the //th element of the strain tensor, and

At the zone center ^ = 0 and the first term vanishes. As with other perturbations the most efficient approach is to divide s into combinations satisfying certain symmetries; thus sn = \Ti(e)

= I (EJCX + Syy + Szz) = hydrostatic component

(21)

^T = ^zz - jTr (?) = |f,, - I [e^jc + £yy) = tetragonal shear

(22)

£R = ^xy = ^yz — ^zx = trigoual (or rhombohedral) shear (23) Note that the relative volume change is just Ss^. Tetragonal shear represents a flattening along z with no volume change (so x and y expand), whereas trigonal shear represents compression along the body diagonal, with no change in volume as well. If we make the appropriate substitutions into the Pikus-Bir Hamiltonian [89], we can determine the strain contribution from these three terms (24) hydrostatic: H^^^^^^ = I^H {P^ + P^ + P^) = ^^HP^

(25)

which is the same as the kinetic energy term p^/2m and hence this strain only shifts energy levels around by a constant, in accordance with conventional wisdom about the effect of hydrostatic stress on optical spectra. The other components of strain are the ones that modify the spacing between valence bands and hence the excitonic splittings. In general terms, the *other components' are typically expressed, tetragonal shear: H^^^ = ^sj [ipl - p]-

p])

(26)

and trigonal/rhombohedral shear: H^ = 3£R {pyPz + PzPx + PxPy)

(27)

Thus for the case of GaN, we can simplify Eq. 20 to (Pikus-Bir [42], k = 0) Ve (r) = VH3Tr (,) 4- — 5 . ( ^

4- —

4- — )

K(.) = fa(5H4-25.)Tr(,) + - ^ 5 4 4 ( — + ^

(28)

+ ^

j

We further specify the conditions for biaxial stress perpendicular to the c-axis.

(29)

Ch.9

320

N.V Edwards

in the lab frame:

t

o 0 o\ 0 0

a 0

(30)

0 a/

in the crystal frame: (31)

a. = and apply the cubic approximation of the strain tensor: ' f a (5ii + ISn) £

=

-|a544 a (Sn +25i2) -|a544

— ^aS44 — ^aS44

-|cr544 — ^aS44

(32)

lcr(Su+Si2)

where the Sij are as defined in the previous section. As noted earlier, the C-F and biaxial strain perturbation will be treated as additive, since they have the same synmietry. Given the proper forms of the perturbation terms, the general strategy is to rotate the wavefunctions |z f), |z |> so that they are parallel to the (111) direction. \Z) = j ^ (\yz) + \zx) + \xy))

(33)

\x) = j ^ (\yz) - \zx))

(34)

\y) = j=,i\yz) +

(35)

\zx)-2\xy))

where \z} has three-fold rotational symmetry like the r25 valence band, and |x> and \y) are orthogonal to |z). We must diagonalize the Hamiltonian matrix (given in Table 7) defined according to the general relationship Ho^ = W^. Ho is simply [p^/lm) + V (r), where the crystal field, spin-orbit and biaxial strain interactions will be introduced through V(r). Since we chose a rotated basis, the matrix in Table 7 is already diagonal in the crystal-field and trigonal shear potentials. The diagonalization is typically approached in two pieces: first by diagonalizing the lower right 4 x 4 block involving \x \),\x \r),\y \),\y \) with respect to the S-0 orbit interaction, which generates a pair of states that are not mixed by the C-F and strain terms, and then by diagonalizing the remaining 4 x 4 block that involves strain and the C-F interactions. It is customary to use a wavefunction built up from linear combinations of the rotated wavefunctions: ^ = a\z t ) + b\z 1) + c\x f) -}- d\z i) + e\y t> + f\y i). The final result of the diagonalization is given below. Readers interested in further detail are advised to see similar published calculations in Refs. [56,77], for example. Here we have merely set up the problem and given the results so that the interested reader can have an informed starting point.

1

JUJS

Ch. 9

^

ttj

^ r^

C

^7

^

Residual stress in III-V nitrides

o

-8

o

a + + >

1^

I I

Mr (N

I

^

t^^

1

(N

1^7 ^ ^-^

Mr

I

CM

>

I

K

1 ""l

O

I I

CN

^

^

>

O

Mr

Mr r-i J^

+ ' • ^

+

+

^U

CD

(/3 1)

a.

:

321

Ch.9

322 \A+)

\B+)

\A')

\B~)

\A+) /W+ 0 \B+)\ 0 \A-)\ 0 \B-) 0 \^a)

0 w+ 0 0 0 0

0 0

0 0 0

\%)

V0

w-

\K) \%') 0 0 0 0 W^ 0

w-

0 0 0

N.V Edwards

0 0

0 \ 0 0 0 0 W^ )

(36)

where W^ = \ (Wi.fW2): t V w -W2f Wi = £v +

2VR

+

(37)

+ 2h*^^

(38)

* ^ 2 .

W2 = £ v - V R - ^ V 2 5 + in^^

(39)

w^ = £ v - V R - ^ y 2 5 - i ; i 2 ^

(40)

\A'

[^ (Wi - W2) ± [/] iz t> + — I [2/IJC t) + (1 - 0 |jc;) + V3 (1 + /) 13';)] 2x/6

[[\{Wi-W2)±uf

1/2

+ \tf^''\

(41)

|B±) [i (ivi - W2) ±U]\zi)-^

[2i\x 4.) + (1 + /) |jc t> + V3 (1 - /) \y t>]

j[^(W,-W2)±t/f+ i?iVJ

1/2

(42)

I*:„/-.;)=[V3|Art)+/|3't)-(l-Ol3';)]

(43)

I*-) = -L [V3|Ar ;) + (!+ 1) Ij t) - i\y 4>]

(44)

t/ = i (IV, - W2f + 2li^^^

(45)

Residual stress in III-V nitrides

323

Ch. 9 Tension

3.46

Compression

3.47

3.48

3.49

EA(eV)

—r-2 (kbar) Fig. 16. Excitonic energy splittings A £ B A and A£cA vs. energy position of the A exciton; data shown by points. Least-squares fit shown by soUd lines. Note the wider range of samples than in Fig. 13. Reprinted from Edwards et al. [90], with permission.

5. Stress trends for nitride heterostructures Once a trustworthy Hopfield Quasicubic Model calculation is achieved, workers taking optical data on GaN films had a template for interpreting data for films with non-standard strain states. We illustrate this with Fig. 16 [90]. Here the Hopfield plot from Fig. 13 [3] is shown with a much larger collection of samples than those initially investigated. Material grown on 6H-SiC substrates is shown by the circles; on sapphire by the triangles (we will postpone the discussion of the 'SMU until the next section). The zero stress reference point is given by the asterisk [65,75]. Applying the knowledge from Section 4 to calculate the associated in-plane residual stress values for these excitonic splittings, we find for the data of Fig. 16 that an ranges from about - 3 . 8 kbar compressive to 3.5 kbar tensile, suggesting, not surprisingly, that the epitaxial material can withstand roughly equal amounts of tensile and compressive stress. We also see that some material grown on 6H-SiC is compressive, contrary to the conventional behavior

324

Ch. 9

N.V Edwards

described in Section 2.4. This section will be primarily devoted to the explanation of this phenomenon, which will involve debunking some of the then-standard concepts about residual stress in GaN films. Accordingly, we will only discuss growth on 6H-SiC in this section, as films grown on this substrate have exhibited more 'non-standard' behavior thus far than their counterparts grown on sapphire. We will focus on 6H-SiC films in this section, partly due to space constraints. Although much has been published about stress for GaN grown on sapphire, only a few reports are systematic studies of the variation of stress with various growth parameters. However, these do exist, though the majority deal with variations in buffer layer parameters, after the seminal work by Detchprohm et al. [44] established the trends for the variation of stress in GaN layers with film thickness. Perhaps the most extensive work on buffer layer conditions is by Kisielowski [1,2,30] though a smaller but very interesting study by Lundin et al. [91] addresses buffer layer conditions as well, and actually finds a change in the sign of the residual stress in the c-direction for certain buffer layer thicknesses, unobserved until that time. Other references of interest in this area include the seminal work on cracking by Itoh et al. [92], a detailed study of relaxation and PL exciton energies by Gfrorer et al. [93], and stress measurements from wafer curvature by Skromme et al. [94]. And of course there is the novel in situ stress monitoring work of Heame et al. [38] that we have already mentioned in Section 2.4. Clearly, there are others, but it is beyond the scope of this work to do an inclusive review. As evident from the wide range of excitonic energy positions that we saw in Table 3 and in Section 3, we can see that residual stress in GaN clearly manifests itself in optical data. Samples grown under different conditions yield reflectance spectra with different lineshapes and excitonic splittings due to different states of residual stress in the layers. However, this wide range has typically resulted from the use of two very different substrate materials, 6H-SiC and AI2O3, rather than from achieving a wide variety of stresses on a single type of substrate. It should be noted that Krueger and coworkers had recently (at the time of publication for Ref. 51) achieved an impressive range of compressive stresses on AI2O3 substrates by varying various growth parameters. However, these are still within the realm of expected behavior for this substrate choice. See Krueger et al. [95]. Optical data in the literature historically gave the impression that compressive stress is the inevitable result of growth on AI2O3 substrates [4,41-46], while the relative scarcity of data for GaN on 6H-SiC reinforced the impression that only tensile material could be grown on this substrate [41,47-50]. We will show in this discussion that such observations are simply a result of growth in the regime where GaN on 6H-SiC is tensile. Empirical trends in residual stress for selected growth parameters in simple 6H-SiC substrate/AIN buffer/GaN film heterostructures (which still represent the widest range of stress reported thus far for this substrate material) [3] will be examined [51]. We show that compressive GaN layers are indeed achievable on this substrate, further supporting the earlier hypothesis [3] that there is no a priori correlation between substrate material and residual stress. We will illustrate with a set of thirty GaN layers grown by metal organic chemical vapor deposition (MOCVD) on 6H-SiC substrates. All of the samples we will show are undoped, were grown with the same III-V flux ratio, have 1000 A thick AIN buffer layers grown at 1000°C, and were subject to the same post-growth rate of cooling [20].

Residual stress in III-V nitrides

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325

As described in Section 3, reflectance lineshapes were analyzed in reciprocal space to yield the energies EA, E^ and EQ of the A, B and C excitons associated with the TQ, Fj and V^ valence bands, respectively, to within ±0.5 meV [3,63]. Residual in-plane stresses axx — cFyy = cfw were estimated to within an additive constant EAO from the measured critical point energy E^ as described previously [3]. Finally, film thicknesses were measured in cross-section to within 5% using a JEOL 6400FE field emission scanning electron microscope (FE-SEM) and verified by the reflectance data below the bandedge. As stated, by conventional wisdom simple structures grown on AI2O3 are in compression while those grown on 6H-SiC are in tension. It is usually assumed for growth on 6H-SiC that compressive lattice-mismatch stresses [45,46] are relieved after a few nanometers of growth [96] and tensile thermal mismatch stresses [45,46] persist thereafter. To investigate these issues we plot E^ and GXX values for the samples vs. film thickness in Fig. 17, vs. growth temperature in Fig. 18, and compare on-axis and vicinal samples in Fig. 19. From Fig. 17 it is apparent that we can classify these films as very thin (^0.7 jxm), moderately thick (~0.7 to -^1.9 |xm), or very thick (--1.9 |xm) according to their residual stress. Some global trends are evident in Fig. 17, independent of growth temperature or offcut angle. Contrary to conventional wisdom, very thin samples are generally in compression. Consistent with previously reported XRD and TEM measurements on these samples, though Perry et al. [97] found six compressive samples. Possible explanations are differing penetration depths of the probe beams and different measurement temperatures. Moderately thick samples are in tension with stress typically increasing with thickness up to a critical thickness somewhere near 2-3 |xm. Above this critical thickness samples are in tension at a reduced stress of ^ 1 kbar. It

3.49

Q.

E

3.48

> (D

3.47

3.46 0.0

0.5

1.0

1.5 2.0 2.5 Thickness (^m)

3.0

3.5

4.0

Fig. 17. EA and a^x vs. thickness d for GaN films on 6H-SiC. Lines are shown to guide the eye. Reprinted from Edwards et al. [51], with permission.

Ch.9

326 3.490

1—

-— 1 —

L • •

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^^2.5 |xm is consistent with the idea that for sufficiently thick films an underlying interface is no longer able to withstand the stress and an abrupt relaxation occurs. Other evidence supports this picture. While cross-sectional TEM micrographs show that the AlN/6H-SiC and GaN/AIN interfaces of these films are heavily dislocated (~10^^/cm^) [98,99], and calculated critical thicknesses of these layers are 46 A [100] and 12 A [98], respectively, high-resolution micrographs show that the films are not

Residual stress in III-V nitrides

327

Ch. 9

3.490 (0001)

vicinal

•

3.480 L

0.19nm

•

0.62 4 0.18 0.83 I

>

0.61

0.47 •

0

0 rt n

V 1 '^ 3.470

1.30.

• 0.95 4 0.76

^ 4 ' 0.59 0.64 4

Y 3

1.20

3.460 1000 1050 1100 Growth Temperature (°C) Fig. 19. EA and CTXX VS. growth temperature for growth on (0001) and vicinal (3-4° toward [1120]) 6H-SiC. The numbers indicate film thicknesses in ixm. Sample pairs linked by dotted lines were grown at the same time under identical growth conditions. Reprinted with permission from Edwards et al. [51].

fully relaxed [98]. In fact, Perry and coworkers found additional evidence of residual compressive lattice mismatch strain in the high resolution TEM micrographs taken on these samples. It was in the form of rounded peaks and grooves in the GaN film within 50-80 A of the AIN interface. They maintain that this sort of behavior is typical of films under compression [97]. This observation is also supported by the scatter of the data in Fig. 16 [90], and by reflection-difference (RD) data taken on the same samples [101], which shows evidence for anisotropic relaxation. Further, calculated coherency stresses at the GaN/AIN interface (a^cjc = 56.5 kbar and ayy = 54.8 kbar) [98], are sufficiently large to reasonably account for residual stresses of an order of magnitude less after initial relaxation processes occur. And a multiplicity of defects with different Burgers vectors have been observed within a selection of representative films [99], a possible indication that different slip mechanisms could be activated as forces accumulate within a heterostructure with increasing GaN layer thicknesses. The effect of growth temperature on these processes is shown for on-axis (0001) 6HSiC samples in Fig. 18, and the additional influence of substrate orientation is shown in Fig. 19. Three trends are apparent. First, from Fig. 18 the thickness at which compressive stress changes to tensile appears to vary with growth temperature. ~0.6 i^m films are slightly tensile at 1050°C and are sUghtly compressive at 1000°C. And at llOO'^C,

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328

N.V.Edwards

Lattice Parameter (a) vs. Temperature 4.8 K 4.6

(a)

4.4 4.2 4.0 CO

3.8

6H-SIC'

3.6 3.4 3.2 3.0

^ 500

-

-•-•-•-•-•-•-•-•-•-• ' - ' 1000

1500

2000

2500

T(K)

Coefficient of Thermal Expansion (a)

400

800

1200

1600

2000

T(K)

Fig. 20. Basal-plane lattice parameters vs. temperature, (a); coefficient of thermal expansion, (b), for: GaN (Reeber and Wang [26]), AIN (Wang and Reeber [24]), and 6H-SiC (Reeber [27]). Reprinted with permission.

a moderately thick sample is compressive, unlike those grown at lower temperatures. Second, at 1050°C the tension in moderately thick samples increases with increasing thickness while the reverse appears to be true at 975''C. Third, we see that the range of stress over which these processes occur appears to increase with increasing growth temperature. It seems plausible that at any given temperature any film will follow the same general trend of progressive relaxation shown in Fig. 17, although the specific values of thicknesses and range parameters will vary with growth temperature. Granted, we have not enough samples were examined to confirm this hypothesis (and further work needs to be done), but it would explain the apparently unusual progression of stress with increasing thickness at 1050°C as opposed to the behavior at lower temperatures. The effect of substrate off-cut angle on the relationship between residual stress and

Residual stress in III~V nitrides

Ch. 9

329

growth temperature is shown in Fig. 19. Data are given for 6 pairs, each of which consists of one sample grown on an on-axis substrate (squares) and the other on a substrate offcut 3-4° toward [1120] (diamonds). Members of each pair were grown simultaneously. In each case, the vicinal sample is more tensile (or less compressive) and thinner than its on-axis counterpart. Here, as in Fig. 18, higher growth temperatures yield greater stress differences for each pair. Vicinal substrates have more surface steps to act as sites for the generation of dislocations, and therefore for stress relief, yet a variety of stresses for the 6 vicinal samples are achieved. Initial relaxation mechanisms appear partial here as well. Indeed, for the same samples Perry and coworkers [97] found TEM evidence of the higher number of steps on the vicinal wafers — not surprising — but what is interesting is that these steps served as formation sites for inversion domain boundaries. Threading dislocation densities for this sample set were -^lO^^/cm^ and -lO^Vcm^ for GaN on AIN grown on vicinal and (0001) 6H-SiC wafers, respectively. They theorized that the on-axis substrates had less formation sites (i.e. less steps) for the formation of these lattice mismatch relief-generating defects at the growth temperature. This, then, is the source of the residual compressive stress in these films compared to their off-axis counterparts [96]. Additionally, growth rates are slower for vicinal samples, while the reverse is generally true for other materials. The difference between GaN on- and off-axis growth rates suggests that cation desorption is promoted by steps, whereas cation desorption is not generally a factor for non-nitride III-Vs where the growth temperatures are much lower. Another study, by Nikitina et al. [102], of stress trends in the 6H-SiC-based heterostructure system involved the variation of residual stress with varying buffer layer growth and material parameters (something not addressed by the previously described study of Edwards et al.) [51]. They also found that the relaxation of mismatch stresses were not complete. They studied 19 samples, both without buffer layers and with AIN and AlGaN buffers (of various thicknesses, and compositions in the case of the AlGaN) and concluded: (1) that largest residual strains were actually observed in the layers grown directly on SiC; (2) that a thick (500 A) AIN buffer layer reduced the absolute value of strains; and (3) that AlGaN buffer layers caused further reductions in strains values and could change the signs of them depending on the composition and thickness of the buffer layer. From what we know of the thermal behavior of the heterostructure materials (cf. Fig. 20b), conclusions two and three seem reasonable; number one is contrary to expectations, as one would typically expect fully relaxed films for such a large mismatch. Further, Waltereit et al. [103] have also reported that a significant amount of compressive lattice mismatch remains as well in their GaN layers grown with 'thin (5 nm) coherently strained AIN nucleation layers' on 6H-SiC. Indeed, they found that up to 0.3% can remain even after 1 |xm of growth. But their GaN layers grown directly on 6H-SiC were relaxed, the opposite of what Nikitina et al. observed [102]. Unfortunately, they did not report if dislocation densities were reduced relative to the relaxed layers, so we are unable to draw any conclusions concerning relief mechanisms in the films. However, they did observe that the strain state of the overlying GaN was determined by growth mode. This is in turn determined by the degree of wetting of the underlayer rather than by lattice mismatch, reminiscent of growth on sapphire. These seemingly contradictory results are mentioned to demonstrate the complex — and as of

330

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KV Edwards

yet, not fully understood — interplay between the interrelated physical mechanisms of lattice mismatch, thermal mismatch, and growth mode/islanding/coalescence behavior as origins of residual stress. But we can observe the following. The complexity of the results indicates that because of the closer match in substrate, buffer and film physical properties (as opposed to the single-handed dominance exerted in similar scenarios by the very much larger a and a of sapphire) we are able to observe this subtle interplay between what appears to be compressive lattice mismatch and tensile thermal mismatch stresses. And in some scenarios, yet to be fully determined, these factors may change the growth mode of the system as well. And for other sets of growth parameters, we may see more of an interplay between the anisotropic thermal properties of the heterostructure components discussed in Section 2.4, making it difficult to predict thermal behavior of the heterostructure a priori. Thus it appears that the 6H-SiC substrate/high-temperature AIN buffer layer combination enables a wide variety of options for tailoring stress states in GaN layers, to an extent thus far superior to its sapphire-based counterpart. 6. Conclusion: future directions, unanswered questions, and clever strategies for circumventing the status quo We have seen the extent to which open questions exist, even for the simplest GaN heterostructures, composed of only three layers. Yet optoelectronic devices fabricated from far more complex combinations of materials than these, such as the InGaN multiple quantum well diode laser structure shown in Fig. 21 [104], have not only been demonstrated but in many cases have been brought to market as well. In fact, it is common knowledge that this has typically been done when many fundamental physical parameters were yet unknown. As one colleague, K.P. O'Donnell, noted during his presentation at one of the many annual nitride professional meetings, "Usually one speaks of 'reverse engineering'. In the nitrides, we are usually having to do 'reverse physics'." Issues such as the role of strain in these heterostructures are indeed managed in some fashion without being fully understood. There are several examples of phenomenological strategies to manage strain in nitride heterostructures; one of the most successful is the Lateral Epitaxial Overgrowth technique [105]. Here, briefly, GaN is deposited on an underlying GaN layer through the windows of an Si02 mask. The deposited material first grows vertically on top of the mask then proceeds to grow laterally over the mask (and vertically as well) until the growth fronts from all of the windows coalesce into a continuous layer. What is remarkable about GaN films grown by this technique is the dramatic reduction in threading dislocation density observed in the films: the usual 10^ to 10^^ cm"^ in the area beside the mask and less than lO'* cm~^ in the area above it. This startling difference is shown in Fig. 22. Since dislocations have their origins in lattice mismatch and are detrimental to device operation, the technique is an excellent example of engineering stress in order to enhance device performance. Indeed, the threshold current of Ill-Nitride lasers is substantially reduced using LEO 'substrates' and these lasers experience a corresponding and dramatic increase in lifetime [106]. Another fascinating aspect of this material is that (1) the amount of lateral growth

Residual stress in III-V nitrides

331

Ch, 9

Multi-quantum-welt structure P-AI008 Gao92 N

p-GaN

n-GaN ^-^Kim G^dj)^ N

Energy

Fig. 21. An InGaN multiple quantum well structure shown to illustrate the complexity of device heterostructures. Reprinted with permission from Nakamura et al. [104].

has been found to be strongly dependent on the orientation of the SiOi stripe, and (2) that the morphologies of the GaN layers on the stripe openings, grown on , were a strong function of growth temperature [105]. The observed progression from a triangular to rectangular cross-section are reminiscent of the island behavior we saw for growth on sapphire (cf. Section 2). Indeed, it is attributed to an increase in the diffusion coefficient (and therefore in the flux of the Ga species) along the (0001) plane onto the {1101} planes with increasing growth temperature [105]. This information has been very helpful in understanding another stress control strategy, this involving a concept called a strain mediating layer (SML). The goal was to develop a strategy to control residual stress in nitride layers grown on 6H-SiC, not only to eliminate epilayer cracking but also to manipulate nitride valence bands to achieve optimally low laser threshold currents [107]. Recall that for GaN film/AlN buffer/6H-SiC substrate heterostructures, we observed a greater versatility in achievable residual stresses than predicted by conventional wisdom or observed thus far for films on AI2O3 substrates (cf. Section 5). There GaN films were shown to be mostly compressive for films less than about 0.7 |xm thick, were tensile up to about 2 |xm, then abruptly became less tensile with stress values near 1 kbar thereafter. Despite this increased flexibility, the thickness dependence meant that a given combination of growth and material parameters nonetheless dictated a unique value of stress in the overlying film. However, with the SML technique, researchers found that the inclusion of a negligibly

332

Ch.9

N.V.Edwards

Fig. 22. Cross-section transmission electron micrograph of a lateral epitaxial overgrown (LEO) structure. Note the dramatic reduction in threading dislocation density above the masked region relative to the region on the left beside the mask. From Nam et al. [105], reprinted with permission.

thin (--375-750 A) layer of GaN or AlGaN between the AIN buffer layer and overlying GaN film could potentially circumvent these trends for moderately thick (~2 |xm) GaN layers (normally >4 kbar, tensile), yielding a range of stresses between 0 and —2 kbar, compressive, without altering the optical and structural properties of the film. Thus the SML, when used in conjunction with current buffer layer technology, has the potential to provide even greater flexibility than the AlN/SiC combination alone. In fact, it enabled otherwise unachievable combinations of growth temperatures, film thicknesses and residual stresses [107]. The impact of the SML is shown in Fig. 23, which is the stress trends curve we for growth on 6H-SiC (Fig. 17) with the SML samples included. Note that without the SMLs, these samples would have been as tensile as sample 5, the most tensile on the graph (as they were all grown under the same conditions). This impact can be seen as well from our earlier Hopfield Model Calculation plot (Fig. 16). The SML samples there are represented by the triangles. We see that the inclusion of a very small layer

Residual stress in III—V nitrides o.*t»

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Ch. 9

333 I — — 1 ——

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F/^. 23. EA and a^jc vs. thickness d for GaN films on 6H-SiC. Points [•] represent samples without strain mediating layers (SML); X's represent samples with SMLs. Reprinted with permission from Edwards et al. [107].

grown at slightly different growth temperatures than the overlying layer has the capacity to reverse the sign of the expected strain state [107]. What was difficult to understand in this case was the relationship between SML sample growth properties and the associated GaN film properties. These are shown in Table 8. How could such a small change in growth temperature between SML and film reverse the sign of the strain? And strangely, samples with thin (400 A. To explain this behavior we must consider the anticipated morphology of the SML. Initial investigations of GaN growth on the high-temperature AIN buffer layer determined that growth was layer-by-layer only after an initial coalescence of two-dimensional, flat-topped islands that occurs after -^400 A of growth [21]. It is plausible that the samples with reduced

Table 8.

Properties of SMLs and associated GaN films SML properties

Material

1 2 3 4 5

GaN GaN GaN Alo.13Gao.87N

-

Time at TCO 2 min 6min 4 min 2 min

-

1000 1120 1000 1000

Properties of associated G a N film

^d

d

(^xx

(A)

(M^m)

(kbar)

PL linewidth (meV)

XRD FWHM (arcsec)

AFM Rms roughness

375 450 750 375

0.9 2.1 2.2 1.2 1.9

0.26 -1.02 -0.44 -1.98 4.63

3.56 3.27 4.26 4.35 8.13

53 56 59 59 52

3.95 4.49 6.85 2.72 2.61

-

Reprinted with permission from Edwards et al. [107].

(A)

334

Ck9

N.V.Edwards

growth rates had SMLs that were not fully planarized and that growth was in fact occurring on non-(OOOl) planes. Growth on such planes occurs at significantly reduced rates, due in theory to reduced Ga incorporation relative to that for the (0001) direction [108]. The degree of reduction of growth rate would then depend on the degree of coalescence of the thin SML. The finer details of how this occurs is still being investigated. However, after the progress made with LEO samples, the results seem more plausible. (As do similar results for growth on sapphire with low-temperature interlayers that reduce both etch pit density and dislocation densities [109,110].) In the LEO case, coalescence and lateral growth rate were also extremely temperature and orientation-dependent. But why the strain state is altered is an open question, as is much of the behavior we saw in the last section. Unfortunately, a simple look at the thermal and lattice mismatch behavior of nitride materials still cannot neatly explain the wide range of stress-related phenomena observed, even for simple heterostructures. Not surprisingly the majority of unexplained issues are related to the failure of classical Matthews-Blakeslee thin film relaxation models. Some examples involve stresses formed by the coalescence of two-dimensional islands, stresses that cause growth mode changes and then in turn exert stresses, and the observation of what appears to be multiple slip systems in simple structures. These appear to play an important but as of yet unclarified role in the relief of residual stress in GaN films in a way that transcend simple lattice mismatch. Again, this tells us that though impressive optoelectronic devices have been demonstrated and commercialized in recent years, it has been done with only a rudimentary and indeed merely phenomenological understanding of stress. The big implication is that work is not yet finished with regard to relaxation phenomena in this materials system. Though much has been achieved with this phenomenological 'understanding', far more could be achieved if relaxation phenomena were thoroughly understood (and controlled) even in simple nitride heterostructures. References [1]

[2] [3] [4] [5]

[6] [7] [8] [9] [10] [11] [12] [13]

C. Kisielowski, J. Krueger, M. Leung, R. Klockenbrink, H. Fujii, T. Suski, G.S. Sudhir, M. Rubin, E.R. Weber. In: M. Scheffler, R. Zimmerman (Eds.), Proc. 23rd Int. Conf. Physics of Semiconductors (ICPS-23), World Scientific, Berlin, 1996, p. 513. I. Gorczyca, A. Svane and N.E. Christensen, MRS Internet J. Nitride Semicond. Res. 2, 18 (1997). N.V. Edwards, S.D. Yoo, M.D. Bremser, T.W. Weeks Jr., O.H. Nam, H. Liu, R.A. Stall, M.N. Horton, N.R. Perkins, T.F. Kuech and D.E. Aspnes, Appl. Phys. Lett. 70, 2001 (1996). R. Dingle, D.D. Sell, S.E. Stokowski and M. Ilegems, Phys. Rev. B 4, 1211 (1971). E.S. Hellman, C D . Brandle, L.F. Schneemeyer, D. Wiesmann, I. Brener, T. Siegrist, G.W. Berkstresser, D.N.E. Buchanan and E.H. Hartford, MRS Internet J. Nitride Semicond. Res. 1, 1 (1996). H.P Maruska and J.J. Tietjen, Appl. Phys. Lett. 15, 327 (1969). J.I. Pankove, E.A. Miller and J.E. Berkeyheiser, RCA Rev. 32, 383 (1971). H.M. Manasevit, P.M. Erdmann and W.I. Simpson, J. Electrochem. Soc. 118, 1864 (1971). R. Dingle, K.L. Shaklee, R.F. Leheny and R.B. Zetterstrom, Appl. Phys. Lett. 19, 5 (1971). F.A. Ponce and D.R Bour, Nature 386, 351 (1997). H. Amano, N. Sawaki, I. Akasaki and Y. Toyoda, Appl. Phys. Lett. 48, 353 (1986). H. Amano, M. Kito, K. Hiramatsu and I. Akasaki, Jpn. J. Appl. Phys. 28, L2112 (1989). S. Nakamura, T. Mukai, M. Senoh and N. Iwasa, Jpn. J. Appl. Phys. 31, L139 (1992).

Residual stress in III-V nitrides [14 [15 [16: [IT [18 [19; [2o: [21 [22 [23: [24: [25: [26 [27: [28 [29:

[3o: [31 [32: [33 [34: [35: [36; [37; [38; [39 [40; [41 [42; [43; [44; [45; [46; [47; [48 [49; [5o; [51

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III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 10

Structural defects in nitride heteroepitaxy M.E. Twigg, D.D. Koleske, A.E. Wickenden, R.L. Henry, M. Fatemi and J.C. Culbertson

1. Introduction Gallium-nitride-based semiconductors have demonstrated the potential to serve as the basis of a new generation of optoelectronic, high-temperature, and high-power microelectronic devices [1-5]. Because of the difficulty in growing sufficiently large GaN substrates [6], GaN films must be grown heteroepitaxially on a variety of alternative substrates. Despite large differences in lattice parameters and thermal expansion coefficients, technologically promisingGaN thin films have been grown on c-plane (i.e. {0001}) sapphire [7-10], a-plane {1120} sapphire [11,12], and {0001} SiC [13,14]. As a consequence of heteroepitaxy, however, the resulting film suffers from a large density of extended defects. Differences in lattice parameter and coefficient of thermal expansion necessarily lead to large dislocation densities, whereas differences in surface and interfacial energies often lead to the formation of islands and planar defects. Heteroepitaxial c-axis growth of a polar material like GaN also introduces the problem of inversion domain boundaries (IDBs), as well as the possibility that the deposited film may have one of two polarities: Ga-terminated or N-terminated [15]. Properly optimized MOVPE (metalorganic vapor phase epitaxy) growth of GaN has succeeded in producing GaN films with dislocation densities between 10^ and 10^/cm^. Advances in the understanding of the effects of substrate nitridation and vicinality, reactor pressure, and dislocation filtering have led to strategies for reducing dislocation density and increasing grain size. These strategies, in turn, have contributed to the growth of uniform GaN films with properties suitable for electronic and electro-optic devices. 2. Growth and microstructure The group III nitrides have stronger chemical bonds than other III-V semiconductors. The Ga-N bond, for example, is estimated to be 4.2 eV [16], which is comparable to the C-C bond strength of 3.6 eV bond for diamond [17] and much larger than that of Ga-As or In-P, which is 2.0 eV for both semiconductors [16]. Because of these strong and largely ionic bonds, nitride lattice parameters are relatively small. The lattice parameter of zinc blende GaN is 0.451 nm [18], as compared with that of 0.565 for GaAs. This strong bonding results in the wide band gap characteristics, making nitrides useful in a wide range of electro-optical [1,2] and power semiconductor devices [3-5]. Such strong

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bonds also result in small cation surface diffusion lengths, so that step-flow growth in MOVPE can only be achieved at high growth temperatures (--lOOO^C) [19,20]. High growth temperatures are also mandated by the kinetic constraints of MOVPE growth, in that high temperatures are required for ammonia (NH3) cracking. Growing GaN directly on sapphire at elevated temperatures, however, results in a large-grained (~1 [xm grain size) film with a hexagonally faceted surface. This rough morphology can be traced, in turn, to nucleation of GaN islands with widely varying heights. This wide range in island height is due to the tendency for GaN islands to nucleate at different moments over the course of growth as well as to differences in island polarity (Ga or N termination). For GaN films grown on c-plane sapphire substrates, N-terminated films tend to be rough whereas Ga-terminated films have smoother surfaces [21]. MOVPE growth of GaN on sapphire at lower temperatures ('^SOO^C) results in a fine-grained (~10 nm grain size) film with a smoother surface morphology. Smaller grains are expected at lower growth temperatures, since the cation diffusion length is smaller. A fine-grained film, however, suffers from an extremely large density of extended defects, and is therefore unsuitable for electronic and electro-optical applications. Ultimately, it has become apparent that neither low-temperature nor high-temperature heteroepitaxial growth of GaN, directly on a sapphire or SiC, is suitable for depositing GaN films with good surface morphology. Thus Akasaki et al. and Nakamura et al. adopted a two-step growth process for GaN thin films [22,23]. The first step consists of AIN or GaN growth at lower temperatures (~600°C) in order to achieve a smooth, fine-grained film; the second step consists of GaN growth at higher temperatures (~1100°C). This initial low-temperature deposition, although extremely defective, establishes a growth template with a surface energy much closer to that of the desired large-grained GaN film; the resulting interfacial energy should be significantly less than that for heteroepitaxial growth of GaN on sapphire or SiC substrates. Because the initial low-temperature GaN or AIN layer has a surface energy similar to the subsequent high-temperature (HT) layer, the tendency for islanding associated with Volmer-Weber growth would be minimized [24,25]. Because the low-temperature layer provides an array of properly optimized nucleation sites for subsequent HT growth, it is often referred to as the nucleation layer (NL), although some authors refer to it as a buffer layer. 2.1. MOVPE growth conditions In order to address the problem of extended defects in heteroepitaxial MOVPE-grown GaN with sufficient generality, we need to make a few observations regarding the reactors used in growing the films discussed in this chapter. MOVPE growth of GaN films at the Naval Research Laboratory (NRL) has been conducted in two types of vertical reactors: a conventional vertical (CV) reactor consisting of a water-cooled, inductively heated, quartz tube with the gas inlet located 10 cm above the sample, and a resistively heated, close-spaced showerhead (CSS) reactor with the gas inlet 1 cm above the sample (Fig. 1). In both reactors, trimethylgallium (TMG) is the group III precursor for GaN growth. The group III precursors for AIN growth in the CSS and CV

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"showerhead" Injector group III water cooling group V

Advantages quartz rf-heated - Higher growth rates - Increased flexibility - Better nucleation layers - Higher temperatures TMG + NH3 + H2

graphite susceptor heater quartz liner water cooled steinless steel wall

pyrometer

I

/

quartz glass tube

quartz tube

Advantages close-spaced showerhead - Avoid pre-mixing of alkyls and NH3 - Fixed boundary layer - More uniform film growth - Large grain size - Better high temperature growth

rf coil

exhaust rotation

Fig. 1. Schematic diagrams of NRL's close-spaced showerhead (CSS) and conventional vertical (CV) MOVPE reactors.

reactors are trimethylaluminum (TMA) and triethylaluminum, respectively. Ammonia is the group V source, and hydrogen is the carrier gas. Silane or disilane serve as the dopant source for Si-doped films. Prior to growth of the high-temperature GaN layer, a --20-50 nm nucleation layer (NL) is deposited. For the CV reactor, only AIN NLs are used, whereas in the CSS reactor both AIN and GaN NLs have been investigated [26]. Typically, NRL's CV and CSS MOVPE reactors operate at a total pressure of 4 0 300 Torr. The sapphire substrate is annealed for 10 min in H2 at --UOO^C prior to growth. The substrate is then cooled to a temperature of 500-600°C for 4-5 min of nitridation using 1-2 SLM (standard liters per minute) of ammonia (NH3). At this same temperature the AIN NL is then deposited using 1.5 |imole/min TMA (or TEA), 1-2 SLM NH3, and 2.0 SLM H2. The growth of the NL is followed by a 2-min ramp to 1020°C, after which the NL is annealed in this same temperature range for 10 min. A GaN film is then grown at 1020°C using 26 |xmole/min of TMG, 1 SLM NH3, and 2 SLM H2. The GaN film is doped using 8 ppm Si2H6 in H2, at a flow rate of 0.2 seem (standard cubic centimeters per minute). The V/III ratio for GaN growth must lie in a range where the desorption rate of N does not greatly exceed that of Ga, thereby achieving the so-called nitrogen-rich growth condition. The V/III ratio at 1030°C, for example, must exceed 10^ in order to prevent GaN decomposition and the formation of Ga droplets. Because desorption rates exhibit Arrhenius exponential behavior with respect to temperature, the logarithm

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of the V/III threshold can be plotted as a linear function of inverse temperature. This threshold has been shown to be well defined for a wide range of reactors and growth conditions. Above this threshold, the GaN surface of an MOVPE-grown film is capable of maintaining a smooth morphology. Below this threshold the surface is invariably rough [20]. According to the atomic force microscopy (AFM) study of Keying et al., this change in morphology is traceable to dislocation-mediated growth (i.e. the effect of dislocation pinning on step flow) [27]. We should also note that other research efforts, notably those at Nichia [23] and University of CaUfomia at Santa Barbara (UCSB) [28], have been carried out using horizontal-flow MOVPE reactors. Although these reactors use the same reagents as those at NRL, some of the gas jets are directed horizontally across the substrate wafer. Nevertheless, there are a number of similarities between GaN films grown in vertical reactors and those grown using horizontal reactors. There are also common features among GaN films grown on different substrates. The concepts explored here are therefore sufficiently general to be useful to most growers of MOVPE GaN films. It is with these thoughts in mind that we seek to provide growers with a number of microstructural landmarks to guide them through the welter of parameters that describe MOVPE nitride growth and the constantly changing reactor environment. 2.2, The nucleation layer Because the nucleation layer plays a very important role in determining the morphology of the HT layer, the configuration of the nucleation layer is a topic of considerable interest. Much that is known about the NL comes from the study of its influence on the morphology of the HT layer. As shown in Fig. 2, we have used cross-sectional transmission electron microscopy (XTEM) to study the resulting thin (50 nm) HT film for two differently prepared NLs grown in the CSS reactor. The two growth sequences shown in Fig. 2 differ in the temperature at which the a-plane sapphire substrate [29] is initially exposed to ammonia (i.e. the nitridation temperature). In each case, the nitridation procedure lasts for 10 min and is followed by the growth of a GaN NL at 550°C [11]. A smoother and larger-grained HT morphology, indicative of successful lateral growth, was obtained by nitriding at the higher temperature of 1065°C. The rougher and smaller-grained HT morphology was obtained by nitriding at 625°C. From the corresponding diffraction patterns shown in Fig. 2, we determined that the two nitridation conditions result in two distinctly different orientations for nitride growth on (2-plane sapphire. The 1065°C nitridation resulted in the orientation relationship GaN[2ll0]/sap [ll20]; GaN(0001)/sap(ll20). The 625°C nitridation resulted in the configuration GaN[1100]/sap[1100]; GaN(0001)/sap(li20) [30]. (Please note that the effects of nitridation on orientation relationships, in GaN films grown on a-plane sapphire, are given correctly in [30], but not in [11].) In a second set of samples, the effects of different nitridation procedures were found to result in significant differences in the structure of the thicker coalesced films, as shown in Fig. 3. XTEM of the film using the higher-temperature nitridation process (800°C) reveals a dislocation density of less than 10^/cm^, as shown in Fig. 3a. The HT film grown following the lower-temperature nitridation condition (500°C), and subsequent

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NitrJdation Crystallography and Temperature GaN[2 T T0]/Sap[1 ToO]

GaN[1 T00]/Sap[1 ToO]

Fig. 2. DF XTEM images of GaN films after 10 min of HT deposition, (a) HT deposition after high-temperature nitridation. Diffraction pattern corresponding to GaN[2iiO]; sapphire[1100]. (b) HT deposition after low-temperature nitridation. Diffraction pattern corresponds to GaN[ll00] zone axis.

NL deposition and annealing, suffers from poor grain alignment, with large dislocation densities (> 10^^/cm^) at the grain boundaries, as shown in Fig. 3b. There are additional differences in growth conditions between these two films: the film with the higher nitridation temperature was also grown at a higher reactor pressure (150 Torr) than the film with the lower nitridation temperature (76 Torr). Nevertheless, it is only in films nitrided at low temperatures (shown in Fig. 2 and Fig. 3b) that the GaN[1100]/sap[ll00] orientation was observed. All of NRL's MOVPE GaN films that were grown on ^-plane sapphire using the high-temperature nitridation procedure were found to have the orientation relationship GaN[2i 10]/sap[l 100]; GaN(0001)/sap(l 120) [30]. Further evidence of the impact of nitridation on film structure has been observed by researchers at UCSB, who have traced the effect of nitridation time on c-plane sapphire (i.e. the ammonia dose prior to NL growth). Sample A, the film with the lower ammonia dose (3 SLM for 60 s), was found to form well oriented grains giving rise to a film with a dislocation density of less than 10^/cm^. Sample B, the film resulting from the larger dose (3 SLM for 400 s), suffered from a dislocation density greater than 10^^/cm^, which appeared to have resulted from both larger grain misorientation and

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0110

Fig. 3. XTEM of coalesced GaN films, (a) Following high-temperature nitridation: GaN[2ilO]/ sapphire[liOO]; dislocation density 10^^/cm^.

smaller grain size [28,31,32]. Both films exhibited the familiar GaN[2110]/sap[li00]; GaN(0001)/sap(0001) epitaxial relationship. Preliminary TEM observations of Wu et al. indicated that the as-grown GaN NL of sample A consisted of well oriented faceted islands predominantly of the cubic zinc blende crystal structure, which transformed into

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the hexagonal wurtzite phase upon annealing [33,34]. The as-grown NL for sample B, however, had a 2-5 nm thick wurtzite 'wetting layer' which covered the sapphire substrate; upon this layer a rough layer of faceted islands grew of mixed wurtzite and zinc blende polymorphs with significant stacking disorder [32]. A recent study of UCSB's A and B NLs using grazing incidence X-ray scattering, indicated that the NL of sample A is a mix of zinc blende and wurtzite phases, with a zinc blende to wurtzite ratio of 0.56 [35]. The large fraction of the zinc blende phase was ascribed, in part, to a high density of stacking faults, which are clearly observable in XTEM. The NL associated with sample B, however, was found to have a zinc blende to wurtzite ratio of only 0.17. According to both theory and experiment, GaN has a low stacking fault energy [36,37]: 20 mJ/m^, as compared with 45 mJ/m^ for GaAs and 55 mJ/m^ for Si. The stacking fault energy indicates the cost in energy that must be paid when an atom assumes a position on a close-packed plane (i.e. (0001) for wurtzite; {111} for zinc blende) that does not correspond to the equilibrium crystal structure. A low stacking fault energy would allow deposited atoms to more easily sustain such a metastable configuration. A large stacking fault density, and the significant presence of the metastable zinc blende polymorph in a NL that is wurtzite in structure at equilibrium, suggest that the NL was deposited at a relatively low temperature. Therefore, the presence of the zinc blende polymorph in a nitride NL may be regarded as evidence of a suitably low deposition temperature for a given set of growth conditions. It has been observed by Suda et al. that GaN deposited by metalorganic molecular beam epitaxy (MOMBE) on c-plane SiC favors the zinc blende phase when the surface is Ga-stabilized [38]. The Ga-stabilized surface is thought to result in a difference in the charge distribution at the film surface so that a very thin Ga-stabilized GaN layer is less ionic than in the bulk. Because it is the ionic nature of GaN that is thought to be responsible for the stability of the wurtzite polymorph [39], any tendency to reduce ionicity would contribute the formation of the zinc blende polymorph favored by less strongly ionic semiconductors (e.g. Si and GaAs). The presence of the zinc blende nitride polymorph in the NL may also result from its tendency to reduce the polarization field. Spontaneous polarization (i.e. pyroelectricity) is absent in zinc blende nitrides. A polarization field cannot be maintained in an unstrained cubic crystal, such as in the zinc blende nitride polymorph, since such a direction would have to be a unique direction of high symmetry [40]. In wurtzite nitrides, the [0001] is indeed a unique direction of high symmetry, whereas the analogous zinc blende directions are not. The presence of the zinc blende polymorph in a NL would reduce the polarization field because of its own lack of a spontaneous field, as well as the tendency for its piezoelectric field to counter the spontaneous field of adjacent wurtzite GaN for some cases of pseudomorphic strain [41]. The TEM study of Twigg et al. also linked the presence of the zinc blende phase in the as-grown NL to the quality of the subsequent HT layer [42]. In this study, an AIN NL was grown on a-plane sapphire by MOVPE in the CV reactor. Unlike the NLs described by Wu et al. [33], these NLs were flat from center to edge, rather than consisting of separate islands. The NL at the wafer edge was found to have a greater presence of the zinc blende phase than at the wafer center. Because the HT grain size

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M.E, Twigg et al

was larger at the wafer edge than at the wafer center, these observations support the conjecture that a successful NL should have a significant volume fraction of the zinc blende phase. It should be noted, however, that in these NLs, the wurtzite polymorph was always predominant over zinc blende, possibly because the AIN stacking fault energy of 200 mJ/cm^ is much larger than that of GaN at 20 mJ/cm^ [36,37]. 2.3. Film uniformity and grain size

Many important aspects of extended defect formation in heteroepitaxial GaN films can be understood by considering center-to-edge differences in films grown on a-plane sapphire in the CV reactor. The sources of these differences are thought to be the variations in temperature and deposition conditions (i.e. gas flow dynamics) from wafer center to wafer edge, and which may be attributable to the geometry of the CV reactor: namely that the reactants are delivered by a single inlet directed at the wafer center. Throughout the wafer the dislocation density was found to be approximately 10^/cm^. It is apparent from XTEM, however, that the GaN grain size at the wafer edge is approximately 1 |xm, whereas the GaN grain size at the wafer center ranges from 0.1 to 0.5 |xm, as shown in Fig. 4 [42].

Wafer Edge

Wafer Center

1 [Am

0110

Fig. 4. XTEM of edge-to-center coalesced film grown in CV MOVPE reactor. GaN grain size at the wafer edge is approximately 1 jxm, whereas the GaN grain size at the wafer center ranges from 0,1 to 0.5 |xm.

Structural defects in nitride heteroepitaxy

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Ch. 10

Using XTEM, we have studied the as-grown NL as well as the NL following the 2-min ramp to 1030°C. From transmission electron diffraction observations, we have determined that at the wafer center both as-grown and ramped NLs are polycrystalline with little tendency towards the preferred orientation. In the as-grown and ramped NLs at the wafer edge, however, we find evidence of properly oriented zinc blende and wurtzite AIN. At the wafer edge, the as-grown NL is a mixture of zinc blende and wurtzite polymorphs, and becomes more predominantly wurtzite upon annealing. The apparent necessity for some fraction of the zinc blende polymorph in the as-grown NL, for high-mobility GaN films grown on differently oriented substrates (c-plane and a-plane sapphire) in differently configured reactors, suggests the importance of NL crystallinity over that of the nitride/sapphire epitaxial relationship. In order to develop a better understanding of the influence of the NL on the subsequent GaN growth, we grew a nominally 20 nm HT GaN layer on a fully annealed 50 nm AIN NL. From XTEM observations, as shown in Fig. 5, we see that the HT GaN film nucleates in the form of 100-200 nm wide islands at the wafer center, while no HT GaN growth appears to occur at the wafer edge. This difference in island density, from center to edge, is also observed in AFM, as shown in Fig. 6. Although the NL layer in

Wafer Center

Wafer Edge

100 nm

0110

Fig. 5. XTEM of edge-to-center 10-min islands from CV reactor. A 20-nm HT GaN film nucleates in the form of 100-200 nm wide islands at the wafer center, while no HT GaN growth appears to occur at the wafer edge.

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10 mm

0.4 mm

1 7 mm

1 ^im Fig. 6. AFM of edge-to-center 10-min islands from CV reactor. It is clear that islands only nucleate near the wafer center.

this film is seen to consist of properly oriented wurtzite AIN, the extended defect density is extremely high. At the wafer edge the extended defect density is 10^°/cm^, which is still drastically lower than that found at the wafer center, where the extended defect density is over 10^ Vcm^As shown by XTEM in Fig. 7, the islands at the wafer center appear to form at clusters of extended defects in the underlying NL, suggesting that these defect clusters are responsible for GaN island nucleation. The absence of such nucleation sites at the

Fig. 7. Island at wafer center nucleating on defect cluster, (a) XTEM of islands formed at cluster of extended defects in the underlying NL. The absence of such nucleation sites at the wafer edge allows the formation of a large-grained GaN film, (b) HRTEM image showing the defect clusters responsible for the island nucleation.

Structural defects in nitride heteroepitaxy

Ch. 10

10 nm

10 nm

GaN Nucleation Site in AIN NL

349

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Twiggetal

wafer edge allows the formation of a large-grained GaN film, whereas the presence of these clusters at the wafer center results in the formation of a smaller-grained GaN film. These observations are also consistent with recent studies addressing the influence of reactor pressure on GaN grain size [11,43]. Growing at higher pressures effectively suppresses grain nucleation in the HT GaN to such an extent that the overall grain size increases to well over 1 |xm, with the result that center-to-edge variation of film structure and electrical properties are effectively eliminated. Another important observation relates to the nature of grain morphology. As shown in Fig. 8, the grain structure is well defined up to 1 [xm above the NL. In the region of the HT film greater than 1 |xm above the NL layer, however, the definition of the grains in the XTEM image begins to fade. In part, this loss of grain definition is due to dislocation annihilation with film thickness, since it is largely the threading dislocations

1 |im

0110

Fig. 8. Dark-field XTEM image of coalesced GaN film. Grain structure is well defined in the first 1 jjim from the NL. Farther from the NL layer the definition of the grains in the XTEM image begins to fade. This loss of grain definition is due to dislocation annihilation with film thickness.

Structural defects in nitride heteroepitaxy

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351

that define grain boundaries in GaN films [32,44]. For this reason, GaN device structures are best grown on thicker and therefore relatively dislocation-free GaN films, at least to the degree allowed by the constraints imposed by thermal mismatch and the associated hazards of crack formation. 2.4. Threading dislocations The line direction of threading dislocations in GaN films usually runs parallel to the c-axis. The Burgers vector for these dislocations may be 1/3 (edge type), (screw type), or mixed (e.g. l/3). Edge dislocations occur at tilt grain boundaries, whereas screw dislocations occur at twist grain boundaries. A tilt boundary is defined as the interface between two grains that are rotated in a plane perpendicular to the grain boundary [45]. For the case of GaN grains in a heteroepitaxial film, tilt boundaries are formed when grains rotate a fraction of a degree from the nominal orientation, about an axis perpendicular to the substrate growth surface. Edge dislocations, which can be thought of as the line defining the end of an extra atomic plane inserted into the lattice, act to accommodate grain misorientation. Twist boundaries, on the other hand, occur when two adjacent grains are rotated out of alignment about the axis perpendicular to the grain boundary [45]. Screw dislocations, which are much like spiral staircases formed around an imaginary pole coincident with the dislocation line direction, are formed by the lattice offsets resulting from twist boundaries Dislocations with screw components also occur in NLs. As is apparent in Fig. 9, NLs consist of a large density of small ('^10 nm) misoriented grains in which the c-axis for each grain is often not perpendicular to the substrate surface. Screw dislocations necessarily form at the boundaries of these adjacent misoriented grains. Dislocations with screw components are thought to serve as nucleation sites for HT growth [32]. Screw dislocations may also occur as 'pipes' (i.e hollow tubes wending their way through the GaN crystal) — the dislocation core remaining empty to eliminate the most highly strained part of the dislocation for the purpose of energy minimization [46]. 2.5. Inversion domain boundaries Like other compound semiconductors, GaN is polar. The existence of the cation and anion interpenetrating sublattices, offset in a direction perpendicular to the close-packed planes ((0001) for hexagonal; {111} for cubic), guarantees the polar nature of both wurtzite and zinc blende phases. In the TEM, this polar nature can be revealed by acquiring imaging and diffraction information from zone axes that include the {0002} reflections for the hexagonally indexed wurtzite phase. Although HRTEM elucidates the structure of the inversion domain boundaries (IDBs) that act as the interfaces between domains of differing polarity, the presence of such domains is more easily determined via dark field (DF) TEM imaging and convergent beam electron diffraction (CBED) [47]. For wurtzite and zinc blende materials, the convention for polar indexing regards the displacement from cation to anion along [0001] and [111] directions, respectively. Therefore, in following a given bond from gallium to nitrogen nearest neighbors in the wurtzite crystal, one imagines moving along the [0001] direction, in the positive sense

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M.E. Twigg et al.

Misoriented grains AIN nuclealition^ layer

AIN Nucleation Layer a-plane Sapphire Substrate AIN[2110] Sapphire [1100]

10 nm

Fig. 9. HRTEM of AIN-NL. NLs consist of a large density of small (-^10 nm) misoriented grains in which the c-axis for each grain is not quite perpendicular to the substrate surface. Screw dislocations form at the boundaries of these adjacent misoriented grains.

of the c-axis, as shown in Fig. 10. A GaN surface with the c-axis pointing outwards is necessarily Ga-terminated. Because the Ga atom terminating such a surface is held to that surface by three bonds, but linked to the next layer above it by only one bond, that surface has only one third the number of broken bonds as a similarly oriented crystal terminated by N. From an analogous argument, a surface with the c-axis directed inwards would be N-terminated. In Fig. 11, we see an example of such a determination using CBED. By recording the {0002} reflections of the CBED pattern as a function of XTEM specimen thickness, and matching them to the simulation of a CBED pattern [13,48], the polarity of the crystal can be determined. Using this procedure, we have determined that the film shown in Fig. 11 (like most of NRL's MOVPE-grown GaN films) is Ga-terminated. Ramachandran et al. have observed that high levels of Mg doping lead to the formation of inversion boundaries in both MBE and MOVPE-grown GaN [49]. We have also observed one N-terminated film under high Mg doping, as shown by dark-filed TEM in Fig. 12. This Mg-doped film has a rough morphology and a high oxygen concentration, as determined by secondary ion mass spectroscopy (SIMS). NRL's other Mg-doped samples, with lower levels of Mg doping, exhibited neither the elevated oxygen concentration, nor the presence of IDBs.

Structural defects in nitride heteroepitaxy

GaN Polarity

353

Ch. 10

Q^.^

Ga-terminated

^ I Q

N-terminated

[2TT0] Zone Axis

Fig. 10. Schematic definition of GaN polarity. For wurtzite and zinc blende materials, the convention for polar indexing regards the displacement from cation to anion along [0001] and [111] directions, respectively. Therefore, in going from gallium to nitrogen in the wurtzite crystal, one imagines moving in the [0001] direction, in the positive sense of the c-axis.

Convergent Beam Electron Diffraction (CBED) Determination of GaN Polarity XTEM Specimen Thickness

[2110] Zone Axis CBED Patterns

c-axis:

[0001]

Thus: Ga-terminated

120nm

140nm

# 1 > A l : i^i* i^i-^

'^WSim ^^pfP

160nm Fig. 11. Convergent beam electron diffraction (CBED) and GaN polarity. By recording the reflections of the CBED pattern as a function of thickness, and matching them to the simulation of a CBED pattern, the polarity of the crystal can be determined. Using this procedure, we have determined that this film is Ga-terminated.

354

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M.E. Twigg et al.

c-axis Inversion Boundary c-axis f

Mg-doped GaN g:{0002} Fig. 12. Dark-field XTEM image showing inversion domain boundaries (IDBs) in heavily Mg-doped GaN film. The IDBs cause an originally Ga-terminated film to switch to N-termination, as confirmed by CBED.

Z-contrast STEM reveals that a single AlO octahedral layer defines inversion domain boundaries in AIN [50]. The presence of oxygen at AIN domain boundaries has also been suggested by energy dispersive X-ray spectroscopy (EDXS) in the STEM [51]. These STEM-based measurements suggest that each interfacial aluminum atom is surrounded by six oxygen atoms, in a configuration similar to that of an aluminum atom within an oxygen octahedron in sapphire [52]. The conjecture that oxygen is necessary for the formation of IDBs in nitrides is also supported by our own observation of an anomalously high oxygen concentration in a heavily Mg-doped sample containing IDBs. There is also evidence for structure origins for IDBs. According to Wu et al., the presence of IDBs may also be traced to the morphology of the substrate surface [44]. Barbaray et al. have developed a sophisticated model, supported by detailed HRTEM imaging experiments, that addresses the role of c-plane sapphire surface steps of height c/3 in generating IDBs [53]. Rouviere et al. observe that IDBs may occur in GaN films grown on insufficiently thick AIN NLs grown on sapphire [54]. In this thin-NL condition, most of the HT film is found to be N-terminated rather than Ga-terminated. Such a film is characterized by a rough morphology as well as by the presence of IDBs. The latter of these two structural mechanisms for IDB formation, however, may be attributable to composition. Using X-ray photoelectron spectroscopy, Cho et al. have observed the presence of oxygen as well as gallium and nitrogen in nominally AIN

Structural defects in nitride heteroepitaxy

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355

layers (as identified by TEM) that form on sapphire during plasma source nitridation [55]. Using TEM-based EDXS measurements, Li and Zhu found that Al diffused up from the sapphire substrate and into the NL [56]. Because of the tendency for oxygen to promote the formation of IDBs in AIN, we conjecture that the polarity of some N-terminated GaN films is traceable to IDBs in the AIN NL. In the case explored by Rouviere et al., we might expect that thin NLs grown on sapphire substrates may be more easily saturated with oxygen and thereby give rise to IDBs and N-terminated HT GaN films. 3. Defect reduction strategies Because heteroepitaxial GaN films evolve as a large number of slightly misoriented and coalescing grains, the film must necessarily contain a high density of grain boundaries and threading dislocations. In order to reduce the density of extended defects in such a heteroepitaxial film, researchers have devised a variety of schemes. Each approach involves one of three basic strategies: improving grain alignment, increasing grain size, or filtering threading dislocations. Improving grain alignment reduces the density of threading dislocations needed to accommodate the misorientation between adjacent grains. Promoting larger grain size reduces the density of grain boundaries as well as the density of threading dislocations that help define the grain boundaries. Dislocation filtering is accomplished through the deposition of specially engineered layers for enhancing dislocation recombination, where dislocations combine or annihilate as they thread to the film surface. The approach to promoting grain size can be further divided into two rather different avenues: optimal pressure growth (OPG) and lateral epitaxial overgrowth (LEO). Both techniques rely on controlling grain nucleation at the onset of HT growth so that a lower density of grains succeed in nucleating. In the case of OPG, this control is effected by carefully controlling the growth parameters; in LEO, the growth surface is specially prepared to allow nucleation to occur upon only specific regions of the substrate. 3.1. Grain alignment via vicinal growth Because the substrate in heteroepitaxy functions as the template for subsequent growth, the morphology of the substrate surface may influence the structure of the deposited film. In GaAs on (100) Si, vicinal substrates provide steps that act as island nucleation sites [57]. In addition, steps on vicinal surfaces influence the structure of interfacial dislocations, as has been observed for silicon on {1012} sapphire or CdTe on c-plane sapphire [58]. Weeks et al. have grown GaN on vicinal SiC substrates and arrived at a similar conclusion [59]. In this case, growing on a vicinal c-plane SiC substrate resulted in sufficiently good grain alignment to prevent the actual definition of grain boundaries when viewed using XTEM. For GaN films grown on c-plane sapphire, however, there is an absence of any correlation of GaN film quality with vicinality [60,61]. For GaN grown on ^-plane sapphire, we have found that the structure of the heteroepitaxial GaN film is strongly influenced by substrate vicinality. A detailed X-ray diffraction (XRD) survey, of a large number of GaN films grown on a-plane sapphire

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M.E. Twiggetal.

GaN on a- pi ane sapphi re: Effect of substrate vicinal angle on X- ray FWHM and Mobi I i ty C JI

>
|400h >5 200 (C)

(D)

(E)

(F)

Fig. 13. X-ray diffraction (XRD) FWHM and mobility vicinality experiment. For GaN grown on a-plane sapphire, the structure of the heteroepitaxial GaN film is strongly influenced by substrate vicinality. XRD reveals that films grown on vicinal a-plane substrates have a lower (0001) FWHM. Vicinally grown films also enjoy higher mobilities.

in the CV reactor at 50 Torr, reveals that films grown on vicinal a-plane substrates have a lower (0001) full-width at half maximum (FWHM) [62]. (Note that the orientation relationships for GaN on a-p\ane sapphire are not given correctly in [62]. The correct relationships are given in [30].) Furthermore, as shown in Fig. 13, these vicinally grown films also enjoy higher mobilities. XTEM observations (shown in Fig. 14) indicate that the reduction in the XRD FWHM may be traced to better grain alignment in GaN films grown on vicinal a-p\a.nc substrates [30,62]. For samples grown in the CV reactor at 50 Torr, the density of edge dislocations in vicinally grown samples is less than 10^/cm^, as compared with an edge dislocation density of 5xlO^/cm^ for films deposited upon on-axis substrates. Because the density of screw dislocations is 5 x 10^/cm^ for both vicinal and on-axis films, the dislocation density in the former (5 x 10^/cm^) is half that of the latter (10^/cm^). It is our conjecture that steps on the vicinal a-plane sapphire surface provide a better template for grain alignment, which in turn leads to a lower density of the edge dislocations at the low-angle grain boundaries between adjacent grains. 3.2. Optimal pressure growth Optimal pressure growth (OPG) improves film quality by increasing grain size in the HT layer. In an XTEM study of GaN films grown over a range of reactor pressures in the CSS reactor, grain sizes are found to be approximately 0.2 |xm for 39 Torr, 1 |xm for

Structural defects in nitride heteroepitaxy

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Edge Dislocations

Screw Dislocations

On Axis

Vicinal

0110

1 \im

Fig. 14. Dark-field XTEM of GaN films grown on both vicinal and on-axis fl-plane sapphire substrates, (a) g = 0110, revealing 5 x 10^/cm^ edge dislocations in on axis growth, (b) g = 0002, revealing 5 x 10^/cm^ screw dislocations in on-axis growth, (c) g = 0110, revealing less than 10^/cm^ edge dislocations density in vicinal growth. (d)g = 0002, revealing 5 x 10^/cm^ screw dislocations in vicinal growth.

65 Torr, and 2 |xm for both 130 and 200 Torr as shown in Fig. 15 [12]. This trend is also followed in the CV reactor, where the grain size averages less than 0.5 |xm at a pressure 50 Torr or less, with a grain size of 1 ixm or larger at a pressure of 100 Torr or greater. As shown in Table 1, XRD measurements of the FWHM for both {0001} and {1102} planes also reveal the tendency for film quality to improve from 39 to 130 Torr. At 200 Torr, however, the (0002) XRD FWHM is seen to increase. The increase of the (0002) FWHM suggests the formation of screw dislocations and twist boundaries in the GaN film. Table 1.

Correlation of reactor pressure with X-ray diffraction data

Growth pressure (Torr) 39 65 130 200

FWHM (arc-s) ± 10

FWHM (arc-s) ± 10

326 325 340 420

610 608 517 510

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M.E. Twigg et al.

Correlation of GaN Grain Size w i t h Reactor Pressure 39 torr

65 torr

130 torr

200 torr

1 urn

0110

Fig. 15. XTEM grain size and pressure. Optimal pressure growth improves film quality by increasing grain size in the HT layer. Grain sizes are found to be approximately 0.2 ixm for 39 Torr, 1 |xm for 65 Torr, and 2 |xm for both 130 and 200 Torr.

An understanding of the increase in grain size, the corresponding decrease in the density of tilt grain boundaries, and the evolution of twist grain boundaries can be understood in terms of the influence of reactor conditions on grain size and morphology. According to Koleske et al. [43], higher hydrogen pressure promotes GaN decomposition, with hydrogen reacting with nitrogen on the GaN surface to form anmionia. Thus, enhanced desorption at higher pressures may retard grain nucleation, thereby resulting in larger grain size [11]. The dependence of growth rate on H2 pressure is shown in Fig. 16. The presence of twist boundaries in the 200 Torr growth, suggested by the XRD data in Table 1, may be explained in part by the increasing diameter of HT GaN islands at higher pressure as well as by enhanced faceting. The enhanced faceting at higher

Structural defects in nitride heteroepitaxy 1

"kT*

=L

1 1 r~t

Ch. 10

359

T~m "1^

1 1 1 1 ~i

1 1

i 1 1 1

I I I

11 11i_

0.8

_ 0.6

B CO

3 0.4

2 O

^ 0.2 " 1 1 1 1

)

50

1 1

100

t i l l

150

' ' M "

200

250

Reactor Pressure (torr) Fig. 16. Growth rate and pressure. Higher hydrogen pressure promotes GaN decomposition, with hydrogen reacting with nitrogen on the GaN surface to form ammonia. Enhanced desorption at higher pressures may retard grain nucleation, thereby resulting in larger grain size in GaN films.

pressures is apparent from Nomarski micrographs (Fig. 17) of GaN films grown directly on (2-plane sapphire (i.e. without a NL). Large faceted islands have a tendency to draw threading dislocations to the facets, thereby directing bundles of threading dislocations laterally. The extra atomic planes inserted (or removed) by these dislocation bundles give rise to crystallographic tilting [63]. Under the diffraction conditions employed in the dark-field XTEM images in Fig. 15, edge-type threading dislocations are in contrast. These diffraction contrast conditions are also sensitive to rotations of GaN grains about the axis perpendicular to the substrate surface. Such TEM imaging experiments resolve individual GaN grains flanked by tilt boundaries, and outlined by edge-type threading dislocations accommodating these in-plane rotations [45]. The dislocation density was seen to vary by less than a factor of two in the films, at a level near 10^/cm^. XTEM analysis of a Si-doped GaN film grown at 200 Torr indicated grains (mainly defined by tilt boundaries) of the same large size as the 130 Torr film. The GaN growth rate was observed to decrease with increasing growth pressure in this study, ranging from 0.5 to 0.7 |xm/h in the 39 and 65 Torr films, 0.5-0.6 |xm/h for the 130 Torr films, and 0.3-0.4 |jim/h for the 200 Torr films. The variation in growth rate has been attributed in part to GaN decomposition, which is enhanced for pressures above 100 Torr in the CSS reactor geometry [11]. For other reactor configurations the optimal pressure for MOVPE growth may be as high as one atmosphere [64]. Enhanced GaN decomposition has been related to increased grain size by Koleske et al. [43]. It is suggested that small GaN nuclei suffer decomposition soon after their initial growth, bringing about a reduction in nuclei density and resulting in the lateral growth of large grains. The same mechanism would serve to limit GaN renucleation on the growing film surface. In addition to the decomposition mechanism, gas phase depletion of reactants at increased pressure may also be influencing the growth rate, and is a function of reactor geometry. The point at which the GaN growth rate decreases noticeably (e.g. by a factor of two) in the CV reactor is significantly higher, at pressures above 300 Torr. In both CSS and CV reactors, substantial sidewall deposits are seen at increased pressures. In the case of the CSS reactor geometry, the proximity

Ch. 10

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M.E. Twigg et al.

39 torr

130 torr

200 torr

300 torr lOO^im

Fig. 17. Un-nucleated growth and reactor pressure. Larger grain size and enhanced faceting at higher pressures are apparent from Nomarski micrographs of GaN films grown directly on (3-plane sapphire (i.e. without a NL).

of the gas injection showerhead to the heated susceptor may induce gas-phase depletion reactions at lower pressures than in the CV reactor geometry. These observations suggest a practical limit on the growth pressure that can be used to achieve large-grained film growth in the CSS reactor geometry, and a need to compensate for reduction in growth rate at higher pressures by increasing the total molar flows of the reactants. While higher pressures are desirable for large GaN grains, this growth pressure regime is not optimal for controlled AlGaN growth. Fig. 18 illustrates the measured alloy concentration (as determined by cathodoluminescence spectroscopy) of 0.5-1.0 |xm thick AlGaN films grown at 1020°C, at pressures of 130 Torr and 65 Torr, with varying TMAl molar flow [12]. The films grown at 130 Torr are found to deviate from the expected gas phase composition [65] by a factor of two, and the growth rates were

Structural defects in nitride heteroepitaxy

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Ch. 10

I I t I I I I I I I I I I I I I I I I I I I I [ I I I I I I I I I

vapor composition

^

^-P(growth) = 65torr -A

0

5

10

15

20

25

30

35

p.mol TI\^AI Fig. 18. AlGaN growth rate with pressure. While higher pressures are desirable for large GaN grains, the growth pressure regime is not optimal for controlled AlGaN growth. This figure shows the measured alloy concentration of 0.5-1.0 |xm thick AlGaN films grown at 10200°C, at pressures of 130 Torr and 65 Torr, with varying TMAl molar flow. The films grown at 130 Torr are found to deviate from the expected gas phase composition by a factor of two, and the growth rates were half of those measured for growth of GaN at 65 Torr.

half of those measured for growth of GaN at 65 Torr. ^ A white deposit was observed in the reactor for the 130 Torr AlGaN growths, and increases as a function of TMAl molar flow. This deposit is ascribed to adduct formation between the ammonia and TMAl precursors [66-69,133]. Growth at 65 Torr pressure provides a reasonable fit to the expected gas phase aluminum content, with no evidence of adduct-type deposits. The fact that growth of AlGaN at 65 Torr proceeds without deposits, suggests that the aluminum is more effectively incorporated into the growing film at 65 Torr than for 130 Torr AlGaN growth. As a result of this study, the AlGaN films in recent AlOo.aGaojN/SiiGaN HEMT devices were grown at 65 Torr, upon highly resistive (HR) GaN films grown at 130 Torr. Device structures have been successfully grown using different reactor pressures for GaN and AlGaN layers [12]. The transport characteristics of these devices will be discussed later in this chapter. 3.3. Lateral epitaxial overgrowth Similar in objective to OPG is the growth technique of lateral epitaxial overgrowth (LEO). In both cases the grower is trying to reduce the incidence of HT grain nucleation. In the case of OPG, this end is pursued rather subtly, by increasing the reactor pressure to a point where GaN decomposition frustrates HT grain nucleation. In LEO, the same end is achieved in a more obvious fashion, by masking off most of the nucleating surface [70]. As shown in Fig. 19, GaN grains are only able to nucleate on the

^ Gas phase composition was calculated using the vapor pressure equation: /oglOP(mmHg) = 8.224-2.134.83/r(K).

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M.E. Twigg et al.

SiO, stripes

[xdtialGaMsabstiate

1). Grow GaN on sapphire

2). Pattern GaN with SiQ 7oids «3 gsBtinscoeitosce

GftNgrovth

3). Regrow GaN on S i q

4), Grow GaN until coalescence

Fig. 19. Schematic of LEO growth. In LEO GaN grains are only able to nucleate on the unmasked growth template, followed by lateral growth over the masked region until coalescence occurs.

unmasked growth template, followed by lateral growth over the masked region until coalescence occurs. LEO in GaN is usually configured so that the lateral growth advances along the direction, which allows faster lateral growth than the direction [70]. LEO shares the advantages of large grain size with OPG growth, namely that the density of grain boundaries, and the formation of dislocations at the grain boundaries are correspondingly reduced. There is an added potential advantage of LEO over OPG, however, in that the mask prevents threading dislocations originating at the NL and substrate interfaces from moving up into the HT layer; as a result these threading dislocations are completely blocked off. Most such threading dislocations then occur in large densities only in the immediate vicinity of the windows in the mask. Some dislocations originating in the unmasked region, however, seek the sidewalls rather than threading to the surface of the coalesced film [71,72]. In part, this circumstance can be traced to the general tendency for dislocations to seek out the nearest free surface in order to minimize strain energy. As in OPG growth, laterally directed dislocations act to induce lattice tilt, a tendency which increases with the overgrowth width (u;) to height (/i) ratio (w;//i) [63,73]. The lateral growth rate and the tendency to form sidewall facets is influenced by the V/III ratio. At a low V/III ratio, the sidewalls consist of inclined {1122} facets and the lateral growth rate is small. As the V/III ratio is increased, smooth vertical {1120} facets appear and the lateral growth rate increases. Continuing to increase the V/III ratio, however, leads to the formation of {1011} facets, a jagged morphology, and a fall in

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growth rate [74]. A large lateral growth rate and smooth {1120} sidewalls are necessary for successful LEO growth of GaN, so that a value of the V/III ratio must be chosen that encourages both of these conditions. The most technologically important aspect of LEO nitride growth, that of reducing the threading dislocations density, is illustrated by the AFM images in Fig. 20, where the surface at a LEO grain boundary is shown to be free of mixed dislocations. Dislocations with screw components act to terminate steps, a feature that is easily observable in GaN using AFM [73]. Unlike other semiconductors, GaN is relatively inert and is therefore without a thick native oxide that could mask surface structure [27]. AFM observations suggest that the dislocation density in regions of the LEO sample away from the windows in the mask may be less than 10^/cm^, although scanning electron microscopy (SEM), of some LEO samples treated with an UV-assisted KOH etch (i.e. photo-electrochemical etching, PEC) [75,76], suggests that 10^/cm^ is a more realistic estimate [77]. Thus, LEO may not always result in a significant improvement in film quality. It is apparent that a study using both PEC and AFM is needed to completely judge the efficacy of LEO. These two imaging techniques are complementary in that

Bulk GaN 10®- 10^° Dislocations/cm^

LEO GaN < 1 0 ® - 10^ Dislocations/cm^

No Step Terminations

Step Terminations

lum Fig. 20. AFM of LEO growth and step terminations. The surface at a LEO grain boundary is shown to be free of mixed dislocations, whereas near the mask window the dislocations density is high. Dislocations with screw components act to terminate steps, a feature that is easily observable in GaN using AFM. AFM observations suggest that the dislocation density in regions of the LEO sample away from the windows in the mask may be less than 10^/cm^.

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AFM is most sensitive to screw and mixed threading dislocations, whereas PEC is sensitive to edge and mixed threading dislocations [73,75,76]. Even in the case where none of the dislocations at the coalesced boundary thread to the film surface, LEO growth is faced with the problem of residual strains due to slight misorientations between coalescing grains. One approach to reducing such strains is that of Pendeo-epitaxy, a technique where lateral growth is seeded from -oriented stripes etched out of a conventionally grown GaN film [78]. The etching process removes several hundred nanometers of the SiC substrate as well, so that the growth proceeds from the {1120} sidewalls and remains suspended above the substrate, even after the film coalesces. In naming this approach Zheleva et al. adopted the Latin prefix pendeo, which is derived from the werh pendere, to hang on [78]. 3.4. Dislocation filtering Another novel approach to improving film quality is that of interrupting high-temperature growth with a series of low-temperature interfacial layers (ILs) grown under the same conditions as conventional NLs [79]. Weak-beam XTEM images of a GaN film, grown in NRL's CSS reactor at 130 Torr with AlN-ILs, are shown in Fig. 21 [80]. Diffraction contrast (g-b) analysis of the XTEM images indicates that the ILs primarily

1|lim Fig. 21. Weak-beam XTEM images of a GaN film grown using multi-interfacial layer (IL) growth. Diffraction contrast {gb) analysis of the XTEM images reveals that the IL filters screw dislocations.

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1 ^im Fig. 22. Weak-beam XTEM images of GaN/AlN IL interface of multi-IL structure. The orientation of the g vector (0002, 0110 and 0112, respectively) was varied to image: (a) threading screw dislocations, (b) threading edge dislocations, and (c) both screw and edge threading dislocations. Contrast if dislocations in the IL is seen in (a) and (c), but not in (b), indicating that the Burgers vectors of these dislocations are parallel to the c-axis (i.e. ).

consist of dislocations with the Burgers vector perpendicular to the growth plane. This array of IL dislocations then act to annihilate threading screw dislocations, thereby reducing screw dislocation density to less than 10^/cm^. Weak-beam XTEM images of the GaN film above the last AIN-IL of the 5 AIN-IL structure are shown in Fig. 22. Imaging conditions which highlight dislocations with , 1/3, or either of these two Burgers vector components are shown in Fig. 22 (a, b and c, respectively). Diffraction contrast analysis of the XTEM images indicates that the AlN-ILs consist primarily of dislocations, which, like threading screw dislocations, have Burgers vectors perpendicular to the growth plane (i.e Burgers vectors). This array of AIN-IL dislocations then act to annihilate threading screw dislocations, thereby reducing their density to less than 10^/cm^, as shown in Fig. 22a. A similar reduction in the screw dislocation density, using the IL approach, was also noted by Iwaya et al. [79]. Despite the large (2-6 |xm) GaN grain size in this film [11], the edge dislocation density measured in Fig. 22b is approximately lOVcml In Fig. 22c, where dislocations with either or 1/3 Burgers vector components are in contrast, a dislocation density of greater than 10^^/cm^ is revealed within the AIN-IL. The dislocations within the AIN-IL, however, arenot in contrast in Fig. 22b, indicating that the AIN-IL dislocations must not have 1/3 components. Similarly, the dislocations that are incontrast in Fig. 22b, in the GaN layer just above the last AIN-IL, must have only l/3 Burgers vector components and are therefore threading edge dislocations. The screw dislocations appear to annihilate as they attempt to thread through the AIN-IL interfaces, thereby removing the screw dislocations

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from the GaN film. As observed by Rouviere et al., for MOVPE-grown GaN, screw dislocations of opposite -type Burgers vector easily annihilate [54]. Despite the large (2-6 |xm) grain size in the 5 IL film, however, the edge dislocation density is ^10^/cm^. In contrast to screw dislocations, annihilation reactions involving edge dislocations seldom occur [81]. It was also observed that the XRD FWHM increased with the number of ILs. It may be that the lack of screw dislocations prevents strain relief between adjacent twist boundaries, with a corresponding increase in the XRD FWHM. 4. Defects and electrical properties In contrast to essentially covalent semiconductors like GaAs and Si, GaN is strongly ionic [82]. One consequence of this strong ionicity is the wurtzite structure of the GaN lattice (as opposed to zinc blende of more covalent semiconductors). In wurtzite the distance between third-order Ga and N nearest neighbors is less than in zinc blende, which reduces the configurational energy derived from electrostatic forces [37]. For strongly covalent semiconductors, discontinuities such as surfaces result in dangling covalent bonds [83]. In strongly ionic materials like GaN, states associated with the lattice discontinuity at the surface are either few or energetically outside the band gap, so that the surfaces of GaN are not subject to fermi-level pinning [84]. Extended defects, such as dislocations, also act as lattice interruptions, and, like surfaces, do not generally have states within the band gap of strongly ionic materials [85]. Therefore, significant carrier recombination in ionic semiconductors like GaN is not expected to occur at dislocations. That is, extended defects in GaN should not act as deep electron traps. A possible consequence of such relatively benign extended defects is the ability of GaN-based light-emitting diodes (LEDs) to function despite large threading dislocation densities ('^lO^^/cm^) [86]. Although dislocations in ionic semiconductors are not efficient carrier recombination centers [87], they are highly negatively charged (as revealed by scanning capacitance microscopy [88] and therefore strongly scatter carriers [89,90]. This scattering, of course, acts to reduce carrier mobility in electrical devices. 4.L Point defects The tendency for point defects to segregate to extended defects (and thereby influence the electrical activity of such defects) has been observed in other electronic materials [91]. Our objective is therefore to move from a general understanding of the role of extended defects in the electrical properties of heteroepitaxial GaN, to consider how specific problems due to extended defects affect electrical properties in GaN films, and develop strategies for minimizing their deleterious contributions. Given the well argued conjecture that many of the extended defects in GaN are not intrinsically electrically active, we need to further examine the possibility that extended defects in GaN derive their electronic properties from associated point defects. There is a significant drawback to this approach, however, in that the role of point defects in the optical properties of GaN is not well understood. The configuration and

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composition of the point defects responsible for yellow (2.2 eV) luminescence in GaN films, for example, are not clear, although there are a number of theories addressing the mechanism. Neugebauer and Van de Walle have used density-functional theory to calculate the formation energy of a number of defect configurations and have concluded that the Ga vacancy complexes Voa-Sica and Voa-ON are stable in n-type GaN and capable of functioning as the deep acceptor needed to generate yellow luminescence [92]. The photoluminescence study of Kaufmann et al. advances a convincing argument that yellow luminescence in their GaN films can be traced to Si [93]. In addition Kaufmann et al. show how blue (2.8 eV) luminescence can be traced to Mg in GaN and red (1.8 eV) luminescence to both Si and Mg in GaN [93]. 4.2. Dislocations To some degree dislocations can be thought of as internal surfaces. Eisner et al. adopt this viewpoint and observe that the low-energy {1010} plane serves as the internal surface for open-core screw dislocations and threading edge dislocations in GaN [94]. These two types of dislocations with {1010} internal surfaces are essentially benign and should not give rise to deep states within the band gap. There is also, however, a species of screw dislocations with a full (i.e. not open) core, as determined by the Z-contrast scanning transmission electron microscopy (STEM) imaging study of Xin et al. [95]. The strong distortion of the bonds at the core of a full-core screw dislocation are expected to give rise to associated states within the band gap [96]. Some of the attributes of dislocations in GaN have been addressed by SEM-based cathodoluminescence (CL) imaging of GaN films. Suguhara et al. used plan-view TEM and SEM/CL to study dislocations in MOVPE-grown GaN thin films [97]. Using panchromatic CL, Suguhara et al. imaged electron-transparent TEM samples held at ambient temperature and found that dark regions in the CL image are due to dislocations in the corresponding TEM image [97], indicating that these dislocations act as non-radiative recombination centers in GaN. From CL imaging experiments, Rossner et al. [98,99] and Salvanti et al. [100] conclude that dislocations act as non-radiative recombination centers in MOVPE and Hydride vapor phase epitaxy (HVPE) GaN, respectively. It should be noted that the SEM/CL experiment using an electron-transparent TEM sample, as conducted by Suguhara et al., has two advantages over CL measurements performed on a conventional bulk film: (1) the dislocations can be identified by TEM; (2) the thinner TEM sample allows for less broadening of the electron-irradiated area and hence better spatial resolution of the CL image [97]. Suguhara et al. estimated the hole diffusion length in n-type GaN as 50 nm by noticing that the loss of luminescence was most pronounced for regions where the spacing between adjacent dislocations was less than 50 nm [97]. This value stands in contrast to the 200 nm electron diffusion lengths measured in p-type GaN using electron beam induced conductivity (EBIC) measurements [101]. This small hole diffusion length may contribute to the ability of LEDs to function despite large dislocation densities. In contrast to studies where dislocations are identified as non-radiative recombination centers, the CL observations of Ponce et al. indicate that yellow luminescence delineates grain boundaries in MOVPE GaN films [102]. The CL study of de Mierry et al. also

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found that yellow luminescence is strongest at grain boundaries [103]. A CL study of grains in GaN grown by the sublimation sandwich method also found evidence for this tendency [104]. The CL observations of Christiansen et al., however, indicate that the intensity of yellow luminescence is uniform across GaN films grown by gas source molecular beam epitaxy (GSMBE) rather than concentrated at grain boundaries [105]. The rather great variety of outcomes in CL imaging of GaN films, especially regarding the optical signature of extended defects such as dislocations and grain boundaries, certainly deserves some comment. Even among GaN films grown by MOVPE, there is a lack of consensus on the identity of optical signatures for extended defects. One obvious explanation for the differences in these CL observations is that it is the impurities associated with the extended defects, rather than the extended defects themselves, which give rise to such optical features as yellow luminescence. Indeed, the calculations of Eisner et al., based on density-functional theory, indicate that most types of extended defects are not expected to generate the deep traps within the band gap that are necessary for these optical signatures [94,96]. These observations are in accord with the conjecture of Liliental-Weber et al., that screw dislocations configured as {1010}-faceted nanotubes derive their internal structure from the segregation of oxygen to the walls of the nanotube [106]. It should also be noted that optical properties improve with the lower threading dislocation density of LEO-grown GaN [107]. The use of LEO GaN has augmented the operating lifetime for laser diodes [69]. Furthermore, a study of p-n diodes fabricated on LEO GaN reveals a significant reduction in reverse-bias leakage current [108]. 4.3. Grain boundaries Scanning capacitance microscopy reveals that the edge and mixed-character dislocations, as well as the associated grain boundaries, are negatively charged [88]. This observation suggests that acceptors lie at these grain boundaries as well as at the dislocations defining these grain boundaries. The electrical properties of a special class of grain boundaries in GaN have also been addressed by the TEM studies of Humphreys and coworkers [109-111]; in particular they have focused on double-positioning domain boundaries associated with the {1120} and {1010} habit planes, which are designated as DBl and DB2, respectively. Using electron energy loss spectroscopy (EELS) in the TEM, Humphreys and coworkers have compared spectra from DBl and DB2 with that of defect-free GaN. Like the dislocations built on {1010} surfaces, DB2 is benign and appears identical to bulk GaN in the EELS spectra. EELS analysis indicates that the {1120}-oriented DBl is heavily charged so that 1.5 electrons are bound to each atom at the boundary interface. It is the conjecture of Eisner et al. that these charges are the result of the trapping of Ga vacancies at DBl boundaries [94]. 4.4. Carrier mobility Although microscopy of individual extended defects and optical spectroscopy of point defects advance the understanding of the electro-optical properties of GaN, the mea-

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surement of the aggregate properties of mobility and carrier concentration must have the final word on the suitability of such materials for electrical device applications. There is evidence that empirically derived values of carrier mobility and concentration values are consistent with carrier scattering by negatively charged dislocations defining the GaN grain boundaries [89,90,112]. The etching study of Youtsey et al. also suggests that dislocations in GaN are charged [75,76]. That GaN edge dislocations are negatively charged is supported by recent Z-contrast STEM and EELS measurements of Xin et al. [113]. Analysis of the Z-contrast images, however, suggests that the fraction of Ga vacancies in threading edge dislocation cores [114,115] is too small for the mobility reduction suggested by an analysis of electrical measurements [89,90,112]. Maximum entropy analysis of Z-contrast STEM images indicates that less than 15% of all possible Ga sites at the edge dislocation core are vacant [113]. This small fraction of Ga vacancies at edge dislocation cores therefore suggests that other impurities and point defects associated with the dislocation may be responsible for carrier scattering and the resulting reduction in mobility. It is also conceivable that carriers may be scattered by charged point defects that segregate to grain boundaries, as argued by Fehrer et al. [116]. As suggested by models of scattering by charged defects, the dislocation density must be less than 10^/cm^ before dislocations cease to significantly limit mobility [89, 90,112]. The existence of this threshold is supported by the observations of Watanabe et al. [97,117]. Using the PEC etching procedure of Youtsey et al., individual whiskers surrounding edge and mixed dislocations were revealed [75,76]. By determining the density of such whiskers using SEM observations, the density of edge and mixed dislocations can be accurately determined. Correlation of Hall mobility measurements and PEC/SEM observations agree with the claim that mobility does not increase significantly as the dislocation density falls below 10^/cm^. When the dislocation density falls below the 10^/cm^ level, other scattering mechanisms (such as those associated with point defects) have the opportunity to dominate [89].Changing the substrate nitridation procedure prior to NL growth has been shown to significantly alter carrier mobility as well as threading dislocation density [28,31,90]. It was found that reducing substrate nitridation time reduces the dislocation density from >10^^/cm^ tolO^/cm^. This reduction in the dislocation density leads to an increase in the carrier mobility at 300 K from 149 to 592 cm^/Vs. The effect of nitridation procedure on dislocation density and carrier mobility has also been investigated by Wickenden et al. [ll]._According to Wickenden et al., the preferred crystallographic configuration, GaN[2110]/sap[1100]; GaN(0001)/sap(ii20), for nitride growth on a-plane sapphire is brought about by nitriding at elevated temperatures (e.g. 1065°C). GaN films with this orientation were observed to have carrier mobilities of 500 cm^/Vs at ambient temperature [11,12]. Lower temperature nitridation (e.g. 625°C)_ results in the other observed configuration, GaN[liOO]/sap[liOO]; GaN(0001)/sap(li20), which suffers from poor grain alignment, with a resulting large dislocation density (>10^^/cm^) at the grain boundaries and carrier mobilities as low as 60 cm^/Vs. Similarly, Wu et al. found that c-plane sapphire substrates exposed to shorter nitridation times result in larger grains, fewer dislocations, and higher carrier mobilities as dislocation densities dropped from 10^^/cm^ to lOVcm^ [32]. It has also been shown by Fatemi et al. that by reducing the edge dislocation density from 5 x lOVcm^ to lOVcm^, while holding

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screw dislocations density at 5 x 10^/cm^ the carrier mobility increases from 300 to 600cmVVs[62]. It is also conceivable that grain size may effect carrier mobility independently of dislocation density. For Si-doped GaN films grown in the NRL CV reactor, with dislocation densities that appear uniformly on the order of 10^/cm^, significant center-to-edge differences were found in mobility and carrier concentration at the center of a 2-inch diameter wafer recorded at ambient temperature (e.g. /^ = 83 cm^/V s and n = 2.34 X lO^Vcm^ at the wafer center; JJL = 192 c m ^ V s and n = 6.0 x lO^Vcm^ at the wafer edge). The grain size at the sample edge was approximately 1 |xm, and 0.5 jxm or less at the wafer center. Smaller grain size may be the cause of the lower carrier mobility in the wafer center, due to enhanced carrier scattering at the grain boundaries [42]. It is not only in center-to-edge differences in electrical properties where grain size appears to play a role in electrical properties of GaN films. A characteristic relationship between growth pressure and structural morphology has been observed in films grown in both CSS and CV MOVPE reactor geometries by Wickenden et al. [11], with increased pressure resulting in larger grain growth. Si-doped GaN films grown at higher pressures exhibit increased mobility, within a specific range of pressure, as shown in Fig. 23. The Hall electron mobilities are plotted against temperature in Fig. 24. for samples grown at 39, 65, 130, and 200 Torr. The two higher-pressure films, in which similar large grain size was observed, appear to exhibit normal ionized impurity scattering behavior in the low-temperature regime. The two lower-pressure films exhibit dramatically reduced mobility, which can be correlated to smaller grain structure of these films. The temperature dependence of the mobility of the lower-pressure films is consistent with models of charged edge dislocation screening [89,90,112]. The effect of screw dislocations on carrier mobility can be assessed from Hall measurements of GaN films grown with multiple AIN interlayers. Because of the significant decrease in the screw dislocation density in films grown using multiple AlN-ILs, the influence of screw dislocations on electrical and optical properties may be addressed by the study of these structures. Mobilities in excess of 700 cm^/Vs and carrier concentrations of ^ 2 x 10^^/cm^ were obtained in n-type Si-doped GaN

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films grown using this multiple-NL approach. The relatively small density of screw dislocations may explain the superior electrical properties of this material. Similarly for Wu et al., the GaN material with the better electrical properties had a screw dislocation density of less than 10^/cm^ [32]. These data suggest that screw dislocations are deleterious to carrier mobility, as are edge dislocations. Because Hall measurements reveal the bulk-like behavior of electrical conduction as a function of temperature in the Si-doped GaN, the improved electrical properties can be ascribed to improvement in the bulk GaN and are not due to the formation of a 2-dimensional electron gas (2DEG) at the AlN/GaN interface [118]. Over a narrow doping range {n ranging from 0.55 to 1.47 x 10^^/cm^), the mobility increases as the number of the AIN-NL increases. Yang et al. have also observed an increase in /x from 267 to 446 cm^/V s as the number of GaN IL increases from 1 to 4 [119]. 4.5. Film resistivity Because electrical devices such as field-effect transistors (FETs) and high-mobility electron transistors (HEMTs) require high-resistivity buffers to achieve pinch-off, the GaN buffer adjacent to the channel region must be highly resistive. Highly resistive GaN films are also important for device isolation. Growing highly resistive GaN films, however, is frustrated by unintentional doping (UID): the incorporation of impurities which act as dopants. In the case of GaN these unintentional dopants act as shallow donors. In order to achieve high-resistivity films, the deep acceptor concentration must exceed the shallow donor concentration. If the deep acceptor concentration greatly exceeds the shallow donor concentration in the HEMT, however, the 2DEG sheet carrier concentration will be lowered and device performance will be adversely affected. Above a given growth pressure in MOVPE, which is reactor dependent, UID GaN films lose their highly resistive nature. In the NRL CSS reactor, this loss of high resistivity occurs as the growth pressure is increased from 39 to 200 Torr [12]. The

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growth rate (jim/hr) Fig. 25. Electron concentration vs. growth rate. The 300°K Hall electron concentration was observed to fall linearly with growth rate of the GaN/Si-doped films grown in the CSS reactor. The electron concentration would be expected to double as growth rate decreases from 0.72 |xm/h (at 39 Torr) to 0.38 mm/h (at 200 Torr), given a simple volume incorporation argument and a constant SiH4 dopant flow. The fact that the electron concentration at 200 Torr is six times that of the 39 Torr value suggests increased compensation and reduced donor concentrations in the films grown at lower pressure.

300 K Hall electron concentration was observed to fall linearly with the growth rate of Si-doped GaN films grown in the CSS reactor, as shown in Fig. 25. The electron concentration would be expected to double as growth rate decreases from 0.72 |xm/h (at 39 Torr) to 0.38 |xm/h (at 200 Torr), given a simple volume incorporation argument and a constant SiH4 dopant flow. The fact that the electron concentration at 200 Torr is six times that of the 39 Torr value suggests increased compensation or reduced donor concentrations in the films grown at lower pressure. Analysis of variable temperature Hall data for compensation levels was inconclusive in the Si-doped GaN films, due to the relatively high dopant concentration. The Hall electron concentrations are plotted against temperature in Fig. 26. The temperature dependence of the electron concentration is similar for the 130 Torr and 200 Torr films, but does not follow a simple exponential relationship in the 65 Torr and 39 Torr samples which were found to be much more resistive, even with relatively high 300 K electron concentrations. The variation of resistivity as a function of NL thickness has also been observed by Briot et al. [120]. The fact that GaN resistivity may be influenced by both growth pressure or NL thickness suggests that morphological structure is a common factor, in agreement with the grain growth mode of GaN growth proposed by Hersee et al. [121]. Edge dislocations defining grain boundaries may not directly affect compensation, but it has been suggested that their associated stress field may play a role in trapping effects [122]. The possible mechanisms responsible for the modulation of carrier mobility, carrier concentration, and donor compensation have been addressed by photoluminescence (PL) studies. In the series of Si-doped GaN films discussed above, yellow band emission (centered at 2.25 eV) is seen to be very strong in the 39 Torr film, less strong in the 65 Torr film, and very weak in the 130 Torr and 200 Torr films. Broad band emission centered at 3.0 eV is only significant in the 39 Torr film. These PL data suggest the presence of a deep acceptor that falls off with increasing growth pressure [12]. Yellow

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luminescence could be derived from electron recombination with deep acceptors trapped at threading edge dislocations as suggested by Eisner et al. [122]. The combined results of Hall and PL analysis suggest that the acceptor-type defects associated with the 2.25 and 3.0 eV bands are reduced at 130 Torr relative to the 39 Tonfilm to a level that just compensates the intrinsic donor concentration, minimizing carrier scattering and increasing mobility in intentionally Si-doped films. SIMS measurements of the impurity levels in these samples indicate that the carbon concentration falls from 3 X 10^^/cm^ to 8 X 10^^/cm^ as the reactor pressure rises from 39 to 130 Torr. This fall in carbon concentration with increasing reactor pressure can be understood in terms of the enhanced probability that hydrogen reacts with the carbon on the film surface to form methane (CH4), thereby removing carbon from the film surface. As the compensating acceptor (possibly carbon) is further reduced at higher pressure, n-type conduction is enhanced, as seen by many groups in GaN films grown near atmospheric pressure. Because the carbon concentration is seen to decrease as the concentration of compensating acceptors decreases, it is reasonable to suggest that the carbon is acting as the compensating acceptor [123]. In a similar study of UID GaN films grown at varying pressures in the CV reactor, we observed that the conductivity of the films increased with pressure. When the HT layer was grown at 45 Torr, the films were found to be highly resistive, with a break-down voltage of greater than 1000 V. When the HT layer was grown at 250 Torr, however, the GaN film was found to be n-type (1 x lO^Vcm^) with high mobility (600 cm^/V s). XTEM analysis of these films also demonstrated that the films grown at higher pressure had larger grain size. The correlation between resistance and grain size is again in agreement with the multi-grained model of GaN growth [122]. Carbon concentration in GaN films grown in NRL's CV reactor is also seen to fall with increasing pressure. SIMS analysis indicates that the carbon concentration decreases from 4 x 10^^/cm^ to 1 x 10^'^/cm^ as the reactor pressure rises from 49 to 350

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Torr. In a separate experiment GaN was grown in the CV reactor using variable pressure growth (VPG) such that high-pressure (250 Torr) growth was followed by low-pressure (49 Torr) growth. SIMS measurements of the VPG film indicate that the carbon level increased from 8 x 10^^/cm^ to 2 x 10^'^/cm^ with the fall in pressure. The Si concentration also decreased from 2 x 10^'^/cm^ to less than 1 x 10^^/cm^ whereas the grain structure and dislocation density of the film were unaffected by the change in pressure. This film was found to have a significantly higher breakdown voltage than in other films grown at 250 Torr in the CV reactor. In this case, the high breakdown voltage may be due to the fall in the Si concentration as well as to a decrease in the carbon concentration. The effect of dislocations on film resistivity can be addressed by Hall measurements performed on GaN films with multiple ILs. Because the density of screw dislocations falls off with the number of AlN-ILs, carrier compensation due to screw dislocations can be assessed, to some degree by the way the calculated acceptor concentration A^A decreases with the number of IL layers [80,124] in Si-doped structures. As the number of ILs increases from 1 to 5, A^A falls from 1.74 x 10^^/cm^ to 0.51 x lO^Vcm^; the compensation ratio A^A/A^D falls from 0.760 to 0.256. In the 5-IL film, PL measurements detect a lower intensity of yellow luminescence in the top 2 ixm layer, than in conventional MOVPE-grown GaN films. These PL observations then suggest that threading screw dislocations in this film (or the point defects surrounding these dislocations) contribute to yellow luminescence. 4.6. High-power device requirements Requirements for nitride high-power microwave devices mandate highly resistive isolation layers, high mobility, and low trap density. Ideally, the GaN film is highly resistive (HR) when unintentionally doped (so that there are no significant shunting paths from source to drain [125]), and exhibits high mobility when intentionally doped. We have observed that MOVPE growth pressure profoundly influences the morphological structure and growth rate of GaN films, with a resultant influence on dopant incorporation and compensation level [123]. The growth rate and alloy composition of AlGaN films in HEMTs are also strongly influenced by the growth pressure, in agreement with reports of several groups [123]. Ambient temperature Hall measurements indicate that HEMT device structures fabricated on large-grained GaN films grown at NRL have been able to achieve high mobility (1500 cm^/Vs) and high sheet carrier concentration (1.2 x 10^^/cm^), which are necessary conditions for high transconductance [123,126]. Recently fabricated HEMT devices have achieved a transconductance of over 200 mS/mm [127,128]. The resistivity of the underlying HR-GaN buffer was found to be 10^ ^ c m , allowing sharp device pinch-off [123,127]. On-wafer small-signal measurements have yielded a cut-off frequency ifj) of 90 GHz with a maximum oscillation frequency (/max) of 145 GHz: the highest values reported to date for a 0.15 |xm gate-length GaN HEMT [128]. In addition, trapping effects that have been known to cause drain lag (drain current transients in response to a drain voltage pulse) and current collapse (limitation of drain current due to electron trapping in the channel region) were significantly reduced in fabricated microwave devices [127].

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In both of NRL's MOVPE reactors (CSS and CV), UID GaN films grown at low pressure (e.g. 40 Torr) are highly resistive, with typical breakdown voltages greater than 1200 V. When films grown at these low pressures are intentionally silicon-doped, however, they suffer from characteristically low mobilities. XTEM diffraction contrast imaging of these films shows small grains which are defined by threading dislocations. Within a certain pressure range, growth at increasing pressure results in larger grains and increased mobility of GaN:Si films, while simultaneously maintaining the capability for UID HR-GaN growth. At higher pressures, UID films become n-type, with high mobilities and low measured compensation [123]. AlGaN:Si/GaN HEMT devices have been grown with the HR-GaN layers deposited at 130 Torr in order to achieve large-grained films. As shown in Fig. 27, the GaN layer of the HEMT device has a large ('--5 jxm) grain size. The elimination of drain lag and the reduction in current collapse in this device structure may be due to the reduction of the density of grain boundaries, dislocations, or carbon contamination. The structure and composition of the AlGaN layer itself should influence the electrical properties of the HEMT as well. Many of the structural properties of the AlGaN layer can be determined by XTEM, as shown in Fig. 28. Here it is apparent that GaN/AlGaN interface suffers from approximately 5 nm of roughness. The lateral variation in the contrast of the

Fig. 27. XTEM of HEMT grain size. AlGaN:Si/GaN HEMT devices have been grown the HR-GaN under the 130 Torr pressure conditions favoring large-grained material. The GaN layer of the HEMT device has a large (~5 |xm) grain size. In the HEMT based on this material, drain lag has been eliminated and current collapse has been significantly reduced in fabricated devices.

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0002

Fig. 28. XTEM imaging indicates that GaN/AlGaN interface suffers from approximately 5 nm of roughness in this HEMT device structure. The lateral variation in the contrast of the AlGaN layer suggests segregation or clustering effects, such as would occur during spinoidal decomposition.

AlGaN layer suggests segregation or clustering effects, such as would occur during spinoidal decomposition [129-132,134]. 5. Conclusions Extended defects in heteroepitaxial GaN films grown by MOVPE scatter carriers, resulting in lower mobility, appear to surround themselves with point defects and impurities which act to compensate dopants. It also appears that point defects may be able to compensate dopants without associating with extended defects; the SIMS and TEM study of carbon in GaN films deposited by variable pressure growth supports this contention. In particular, it is interesting to consider carbon as a point defect involved in compensation, since it is an inevitable by-product of the MOVPE process which can be controlled, to some degree, by altering the reactor pressure. Reactor pressure influences grain size as well as carbon concentration and there appears to be a reactor-dependent optimal pressure for growing grains that are large without the onset of faceting, or the onset of associated lattice tilting and twist boundaries. These reactor parameters for growing a film with the minimum extended defect density on a nucleation layer are similar to growth via LEO in that the lateral growth rate must be as large as possible without the onset of faceting. There is also reason to believe that both LEO and conventional growth can be optimized by the use of vicinal c-plane SiC or ^-plane sapphire substrates, in order to improve grain alignment and thereby reduce the edge dislocation density occurring at grain boundaries.

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The role of the nucleation layer in heteroepitaxial GaN growth and the procedures for optimizing this layer are still not well understood. For some reactors, at least, it appears that the optimal nucleation layer goes down with a significant fraction of the film consisting of the zinc blende polymorph, which then transforms into the wurtzite phase upon annealing. Although there has been a preliminary effort to explain these structural constraints, there is not yet a sufficiently general understanding to guide a grower in achieving a good nucleation layer. There is some indication that optimizing the nucleation layer results in defining a specific film polarity (i.e. Ga-terminated) and that this desirable result may be achieved by reducing the oxygen composition and thereby eliminate oxygen-rich IDBs in the NL. It also appears that achieving a film with no inversion boundaries is frustrated by a rough substrate morphology. Acknowledgements This work was supported by the Office of Naval Research. We thank Larry Ardis and Bob Gorman for expert technical assistance. We also thank Evan Glaser and Steve Binari for helpful suggestions regarding the preparation of the manuscript. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

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J.W. Cahn, Acta Metall. 9, 795 (1961). G.B. Stringfellow, J. Cryst. Growth 58, 194 (1982). S.N.G. Chu, S. Nakahara, K.E. Strenge and W.D. Johnson Jr., J. Appl. Phys. 57, 4610 (1985). M.M. Treacy, J.M. Gibson and A. Howie, Philos. Mag. A 51, 389 (1985). S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Tamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano and K. Chocho, Appl. Phys. Lett. 72, 211 (1998). J.W. Cahn, Acta Metall. 10(1962).

III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 10

Structural defects in nitride heteroepitaxy M.E. Twigg, D.D. Koleske, A.E. Wickenden, R.L. Henry, M. Fatemi and J.C. Culbertson

1. Introduction Gallium-nitride-based semiconductors have demonstrated the potential to serve as the basis of a new generation of optoelectronic, high-temperature, and high-power microelectronic devices [1-5]. Because of the difficulty in growing sufficiently large GaN substrates [6], GaN films must be grown heteroepitaxially on a variety of alternative substrates. Despite large differences in lattice parameters and thermal expansion coefficients, technologically promisingGaN thin films have been grown on c-plane (i.e. {0001}) sapphire [7-10], a-plane {1120} sapphire [11,12], and {0001} SiC [13,14]. As a consequence of heteroepitaxy, however, the resulting film suffers from a large density of extended defects. Differences in lattice parameter and coefficient of thermal expansion necessarily lead to large dislocation densities, whereas differences in surface and interfacial energies often lead to the formation of islands and planar defects. Heteroepitaxial c-axis growth of a polar material like GaN also introduces the problem of inversion domain boundaries (IDBs), as well as the possibility that the deposited film may have one of two polarities: Ga-terminated or N-terminated [15]. Properly optimized MOVPE (metalorganic vapor phase epitaxy) growth of GaN has succeeded in producing GaN films with dislocation densities between 10^ and 10^/cm^. Advances in the understanding of the effects of substrate nitridation and vicinality, reactor pressure, and dislocation filtering have led to strategies for reducing dislocation density and increasing grain size. These strategies, in turn, have contributed to the growth of uniform GaN films with properties suitable for electronic and electro-optic devices. 2. Growth and microstructure The group III nitrides have stronger chemical bonds than other III-V semiconductors. The Ga-N bond, for example, is estimated to be 4.2 eV [16], which is comparable to the C-C bond strength of 3.6 eV bond for diamond [17] and much larger than that of Ga-As or In-P, which is 2.0 eV for both semiconductors [16]. Because of these strong and largely ionic bonds, nitride lattice parameters are relatively small. The lattice parameter of zinc blende GaN is 0.451 nm [18], as compared with that of 0.565 for GaAs. This strong bonding results in the wide band gap characteristics, making nitrides useful in a wide range of electro-optical [1,2] and power semiconductor devices [3-5]. Such strong

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bonds also result in small cation surface diffusion lengths, so that step-flow growth in MOVPE can only be achieved at high growth temperatures (--lOOO^C) [19,20]. High growth temperatures are also mandated by the kinetic constraints of MOVPE growth, in that high temperatures are required for ammonia (NH3) cracking. Growing GaN directly on sapphire at elevated temperatures, however, results in a large-grained (~1 [xm grain size) film with a hexagonally faceted surface. This rough morphology can be traced, in turn, to nucleation of GaN islands with widely varying heights. This wide range in island height is due to the tendency for GaN islands to nucleate at different moments over the course of growth as well as to differences in island polarity (Ga or N termination). For GaN films grown on c-plane sapphire substrates, N-terminated films tend to be rough whereas Ga-terminated films have smoother surfaces [21]. MOVPE growth of GaN on sapphire at lower temperatures ('^SOO^C) results in a fine-grained (~10 nm grain size) film with a smoother surface morphology. Smaller grains are expected at lower growth temperatures, since the cation diffusion length is smaller. A fine-grained film, however, suffers from an extremely large density of extended defects, and is therefore unsuitable for electronic and electro-optical applications. Ultimately, it has become apparent that neither low-temperature nor high-temperature heteroepitaxial growth of GaN, directly on a sapphire or SiC, is suitable for depositing GaN films with good surface morphology. Thus Akasaki et al. and Nakamura et al. adopted a two-step growth process for GaN thin films [22,23]. The first step consists of AIN or GaN growth at lower temperatures (~600°C) in order to achieve a smooth, fine-grained film; the second step consists of GaN growth at higher temperatures (~1100°C). This initial low-temperature deposition, although extremely defective, establishes a growth template with a surface energy much closer to that of the desired large-grained GaN film; the resulting interfacial energy should be significantly less than that for heteroepitaxial growth of GaN on sapphire or SiC substrates. Because the initial low-temperature GaN or AIN layer has a surface energy similar to the subsequent high-temperature (HT) layer, the tendency for islanding associated with Volmer-Weber growth would be minimized [24,25]. Because the low-temperature layer provides an array of properly optimized nucleation sites for subsequent HT growth, it is often referred to as the nucleation layer (NL), although some authors refer to it as a buffer layer. 2.1. MOVPE growth conditions In order to address the problem of extended defects in heteroepitaxial MOVPE-grown GaN with sufficient generality, we need to make a few observations regarding the reactors used in growing the films discussed in this chapter. MOVPE growth of GaN films at the Naval Research Laboratory (NRL) has been conducted in two types of vertical reactors: a conventional vertical (CV) reactor consisting of a water-cooled, inductively heated, quartz tube with the gas inlet located 10 cm above the sample, and a resistively heated, close-spaced showerhead (CSS) reactor with the gas inlet 1 cm above the sample (Fig. 1). In both reactors, trimethylgallium (TMG) is the group III precursor for GaN growth. The group III precursors for AIN growth in the CSS and CV

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"showerhead" Injector group III water cooling group V

Advantages quartz rf-heated - Higher growth rates - Increased flexibility - Better nucleation layers - Higher temperatures TMG + NH3 + H2

graphite susceptor heater quartz liner water cooled steinless steel wall

pyrometer

I

/

quartz glass tube

quartz tube

Advantages close-spaced showerhead - Avoid pre-mixing of alkyls and NH3 - Fixed boundary layer - More uniform film growth - Large grain size - Better high temperature growth

rf coil

exhaust rotation

Fig. 1. Schematic diagrams of NRL's close-spaced showerhead (CSS) and conventional vertical (CV) MOVPE reactors.

reactors are trimethylaluminum (TMA) and triethylaluminum, respectively. Ammonia is the group V source, and hydrogen is the carrier gas. Silane or disilane serve as the dopant source for Si-doped films. Prior to growth of the high-temperature GaN layer, a --20-50 nm nucleation layer (NL) is deposited. For the CV reactor, only AIN NLs are used, whereas in the CSS reactor both AIN and GaN NLs have been investigated [26]. Typically, NRL's CV and CSS MOVPE reactors operate at a total pressure of 4 0 300 Torr. The sapphire substrate is annealed for 10 min in H2 at --UOO^C prior to growth. The substrate is then cooled to a temperature of 500-600°C for 4-5 min of nitridation using 1-2 SLM (standard liters per minute) of ammonia (NH3). At this same temperature the AIN NL is then deposited using 1.5 |imole/min TMA (or TEA), 1-2 SLM NH3, and 2.0 SLM H2. The growth of the NL is followed by a 2-min ramp to 1020°C, after which the NL is annealed in this same temperature range for 10 min. A GaN film is then grown at 1020°C using 26 |xmole/min of TMG, 1 SLM NH3, and 2 SLM H2. The GaN film is doped using 8 ppm Si2H6 in H2, at a flow rate of 0.2 seem (standard cubic centimeters per minute). The V/III ratio for GaN growth must lie in a range where the desorption rate of N does not greatly exceed that of Ga, thereby achieving the so-called nitrogen-rich growth condition. The V/III ratio at 1030°C, for example, must exceed 10^ in order to prevent GaN decomposition and the formation of Ga droplets. Because desorption rates exhibit Arrhenius exponential behavior with respect to temperature, the logarithm

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of the V/III threshold can be plotted as a linear function of inverse temperature. This threshold has been shown to be well defined for a wide range of reactors and growth conditions. Above this threshold, the GaN surface of an MOVPE-grown film is capable of maintaining a smooth morphology. Below this threshold the surface is invariably rough [20]. According to the atomic force microscopy (AFM) study of Keying et al., this change in morphology is traceable to dislocation-mediated growth (i.e. the effect of dislocation pinning on step flow) [27]. We should also note that other research efforts, notably those at Nichia [23] and University of CaUfomia at Santa Barbara (UCSB) [28], have been carried out using horizontal-flow MOVPE reactors. Although these reactors use the same reagents as those at NRL, some of the gas jets are directed horizontally across the substrate wafer. Nevertheless, there are a number of similarities between GaN films grown in vertical reactors and those grown using horizontal reactors. There are also common features among GaN films grown on different substrates. The concepts explored here are therefore sufficiently general to be useful to most growers of MOVPE GaN films. It is with these thoughts in mind that we seek to provide growers with a number of microstructural landmarks to guide them through the welter of parameters that describe MOVPE nitride growth and the constantly changing reactor environment. 2.2, The nucleation layer Because the nucleation layer plays a very important role in determining the morphology of the HT layer, the configuration of the nucleation layer is a topic of considerable interest. Much that is known about the NL comes from the study of its influence on the morphology of the HT layer. As shown in Fig. 2, we have used cross-sectional transmission electron microscopy (XTEM) to study the resulting thin (50 nm) HT film for two differently prepared NLs grown in the CSS reactor. The two growth sequences shown in Fig. 2 differ in the temperature at which the a-plane sapphire substrate [29] is initially exposed to ammonia (i.e. the nitridation temperature). In each case, the nitridation procedure lasts for 10 min and is followed by the growth of a GaN NL at 550°C [11]. A smoother and larger-grained HT morphology, indicative of successful lateral growth, was obtained by nitriding at the higher temperature of 1065°C. The rougher and smaller-grained HT morphology was obtained by nitriding at 625°C. From the corresponding diffraction patterns shown in Fig. 2, we determined that the two nitridation conditions result in two distinctly different orientations for nitride growth on (2-plane sapphire. The 1065°C nitridation resulted in the orientation relationship GaN[2ll0]/sap [ll20]; GaN(0001)/sap(ll20). The 625°C nitridation resulted in the configuration GaN[1100]/sap[1100]; GaN(0001)/sap(li20) [30]. (Please note that the effects of nitridation on orientation relationships, in GaN films grown on a-plane sapphire, are given correctly in [30], but not in [11].) In a second set of samples, the effects of different nitridation procedures were found to result in significant differences in the structure of the thicker coalesced films, as shown in Fig. 3. XTEM of the film using the higher-temperature nitridation process (800°C) reveals a dislocation density of less than 10^/cm^, as shown in Fig. 3a. The HT film grown following the lower-temperature nitridation condition (500°C), and subsequent

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NitrJdation Crystallography and Temperature GaN[2 T T0]/Sap[1 ToO]

GaN[1 T00]/Sap[1 ToO]

Fig. 2. DF XTEM images of GaN films after 10 min of HT deposition, (a) HT deposition after high-temperature nitridation. Diffraction pattern corresponding to GaN[2iiO]; sapphire[1100]. (b) HT deposition after low-temperature nitridation. Diffraction pattern corresponds to GaN[ll00] zone axis.

NL deposition and annealing, suffers from poor grain alignment, with large dislocation densities (> 10^^/cm^) at the grain boundaries, as shown in Fig. 3b. There are additional differences in growth conditions between these two films: the film with the higher nitridation temperature was also grown at a higher reactor pressure (150 Torr) than the film with the lower nitridation temperature (76 Torr). Nevertheless, it is only in films nitrided at low temperatures (shown in Fig. 2 and Fig. 3b) that the GaN[1100]/sap[ll00] orientation was observed. All of NRL's MOVPE GaN films that were grown on ^-plane sapphire using the high-temperature nitridation procedure were found to have the orientation relationship GaN[2i 10]/sap[l 100]; GaN(0001)/sap(l 120) [30]. Further evidence of the impact of nitridation on film structure has been observed by researchers at UCSB, who have traced the effect of nitridation time on c-plane sapphire (i.e. the ammonia dose prior to NL growth). Sample A, the film with the lower ammonia dose (3 SLM for 60 s), was found to form well oriented grains giving rise to a film with a dislocation density of less than 10^/cm^. Sample B, the film resulting from the larger dose (3 SLM for 400 s), suffered from a dislocation density greater than 10^^/cm^, which appeared to have resulted from both larger grain misorientation and

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Fig. 3. XTEM of coalesced GaN films, (a) Following high-temperature nitridation: GaN[2ilO]/ sapphire[liOO]; dislocation density 10^^/cm^.

smaller grain size [28,31,32]. Both films exhibited the familiar GaN[2110]/sap[li00]; GaN(0001)/sap(0001) epitaxial relationship. Preliminary TEM observations of Wu et al. indicated that the as-grown GaN NL of sample A consisted of well oriented faceted islands predominantly of the cubic zinc blende crystal structure, which transformed into

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the hexagonal wurtzite phase upon annealing [33,34]. The as-grown NL for sample B, however, had a 2-5 nm thick wurtzite 'wetting layer' which covered the sapphire substrate; upon this layer a rough layer of faceted islands grew of mixed wurtzite and zinc blende polymorphs with significant stacking disorder [32]. A recent study of UCSB's A and B NLs using grazing incidence X-ray scattering, indicated that the NL of sample A is a mix of zinc blende and wurtzite phases, with a zinc blende to wurtzite ratio of 0.56 [35]. The large fraction of the zinc blende phase was ascribed, in part, to a high density of stacking faults, which are clearly observable in XTEM. The NL associated with sample B, however, was found to have a zinc blende to wurtzite ratio of only 0.17. According to both theory and experiment, GaN has a low stacking fault energy [36,37]: 20 mJ/m^, as compared with 45 mJ/m^ for GaAs and 55 mJ/m^ for Si. The stacking fault energy indicates the cost in energy that must be paid when an atom assumes a position on a close-packed plane (i.e. (0001) for wurtzite; {111} for zinc blende) that does not correspond to the equilibrium crystal structure. A low stacking fault energy would allow deposited atoms to more easily sustain such a metastable configuration. A large stacking fault density, and the significant presence of the metastable zinc blende polymorph in a NL that is wurtzite in structure at equilibrium, suggest that the NL was deposited at a relatively low temperature. Therefore, the presence of the zinc blende polymorph in a nitride NL may be regarded as evidence of a suitably low deposition temperature for a given set of growth conditions. It has been observed by Suda et al. that GaN deposited by metalorganic molecular beam epitaxy (MOMBE) on c-plane SiC favors the zinc blende phase when the surface is Ga-stabilized [38]. The Ga-stabilized surface is thought to result in a difference in the charge distribution at the film surface so that a very thin Ga-stabilized GaN layer is less ionic than in the bulk. Because it is the ionic nature of GaN that is thought to be responsible for the stability of the wurtzite polymorph [39], any tendency to reduce ionicity would contribute the formation of the zinc blende polymorph favored by less strongly ionic semiconductors (e.g. Si and GaAs). The presence of the zinc blende nitride polymorph in the NL may also result from its tendency to reduce the polarization field. Spontaneous polarization (i.e. pyroelectricity) is absent in zinc blende nitrides. A polarization field cannot be maintained in an unstrained cubic crystal, such as in the zinc blende nitride polymorph, since such a direction would have to be a unique direction of high symmetry [40]. In wurtzite nitrides, the [0001] is indeed a unique direction of high symmetry, whereas the analogous zinc blende directions are not. The presence of the zinc blende polymorph in a NL would reduce the polarization field because of its own lack of a spontaneous field, as well as the tendency for its piezoelectric field to counter the spontaneous field of adjacent wurtzite GaN for some cases of pseudomorphic strain [41]. The TEM study of Twigg et al. also linked the presence of the zinc blende phase in the as-grown NL to the quality of the subsequent HT layer [42]. In this study, an AIN NL was grown on a-plane sapphire by MOVPE in the CV reactor. Unlike the NLs described by Wu et al. [33], these NLs were flat from center to edge, rather than consisting of separate islands. The NL at the wafer edge was found to have a greater presence of the zinc blende phase than at the wafer center. Because the HT grain size

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was larger at the wafer edge than at the wafer center, these observations support the conjecture that a successful NL should have a significant volume fraction of the zinc blende phase. It should be noted, however, that in these NLs, the wurtzite polymorph was always predominant over zinc blende, possibly because the AIN stacking fault energy of 200 mJ/cm^ is much larger than that of GaN at 20 mJ/cm^ [36,37]. 2.3. Film uniformity and grain size

Many important aspects of extended defect formation in heteroepitaxial GaN films can be understood by considering center-to-edge differences in films grown on a-plane sapphire in the CV reactor. The sources of these differences are thought to be the variations in temperature and deposition conditions (i.e. gas flow dynamics) from wafer center to wafer edge, and which may be attributable to the geometry of the CV reactor: namely that the reactants are delivered by a single inlet directed at the wafer center. Throughout the wafer the dislocation density was found to be approximately 10^/cm^. It is apparent from XTEM, however, that the GaN grain size at the wafer edge is approximately 1 |xm, whereas the GaN grain size at the wafer center ranges from 0.1 to 0.5 |xm, as shown in Fig. 4 [42].

Wafer Edge

Wafer Center

1 [Am

0110

Fig. 4. XTEM of edge-to-center coalesced film grown in CV MOVPE reactor. GaN grain size at the wafer edge is approximately 1 jxm, whereas the GaN grain size at the wafer center ranges from 0,1 to 0.5 |xm.

Structural defects in nitride heteroepitaxy

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Using XTEM, we have studied the as-grown NL as well as the NL following the 2-min ramp to 1030°C. From transmission electron diffraction observations, we have determined that at the wafer center both as-grown and ramped NLs are polycrystalline with little tendency towards the preferred orientation. In the as-grown and ramped NLs at the wafer edge, however, we find evidence of properly oriented zinc blende and wurtzite AIN. At the wafer edge, the as-grown NL is a mixture of zinc blende and wurtzite polymorphs, and becomes more predominantly wurtzite upon annealing. The apparent necessity for some fraction of the zinc blende polymorph in the as-grown NL, for high-mobility GaN films grown on differently oriented substrates (c-plane and a-plane sapphire) in differently configured reactors, suggests the importance of NL crystallinity over that of the nitride/sapphire epitaxial relationship. In order to develop a better understanding of the influence of the NL on the subsequent GaN growth, we grew a nominally 20 nm HT GaN layer on a fully annealed 50 nm AIN NL. From XTEM observations, as shown in Fig. 5, we see that the HT GaN film nucleates in the form of 100-200 nm wide islands at the wafer center, while no HT GaN growth appears to occur at the wafer edge. This difference in island density, from center to edge, is also observed in AFM, as shown in Fig. 6. Although the NL layer in

Wafer Center

Wafer Edge

100 nm

0110

Fig. 5. XTEM of edge-to-center 10-min islands from CV reactor. A 20-nm HT GaN film nucleates in the form of 100-200 nm wide islands at the wafer center, while no HT GaN growth appears to occur at the wafer edge.

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10 mm

0.4 mm

1 7 mm

1 ^im Fig. 6. AFM of edge-to-center 10-min islands from CV reactor. It is clear that islands only nucleate near the wafer center.

this film is seen to consist of properly oriented wurtzite AIN, the extended defect density is extremely high. At the wafer edge the extended defect density is 10^°/cm^, which is still drastically lower than that found at the wafer center, where the extended defect density is over 10^ Vcm^As shown by XTEM in Fig. 7, the islands at the wafer center appear to form at clusters of extended defects in the underlying NL, suggesting that these defect clusters are responsible for GaN island nucleation. The absence of such nucleation sites at the

Fig. 7. Island at wafer center nucleating on defect cluster, (a) XTEM of islands formed at cluster of extended defects in the underlying NL. The absence of such nucleation sites at the wafer edge allows the formation of a large-grained GaN film, (b) HRTEM image showing the defect clusters responsible for the island nucleation.

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10 nm

10 nm

GaN Nucleation Site in AIN NL

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Twiggetal

wafer edge allows the formation of a large-grained GaN film, whereas the presence of these clusters at the wafer center results in the formation of a smaller-grained GaN film. These observations are also consistent with recent studies addressing the influence of reactor pressure on GaN grain size [11,43]. Growing at higher pressures effectively suppresses grain nucleation in the HT GaN to such an extent that the overall grain size increases to well over 1 |xm, with the result that center-to-edge variation of film structure and electrical properties are effectively eliminated. Another important observation relates to the nature of grain morphology. As shown in Fig. 8, the grain structure is well defined up to 1 [xm above the NL. In the region of the HT film greater than 1 |xm above the NL layer, however, the definition of the grains in the XTEM image begins to fade. In part, this loss of grain definition is due to dislocation annihilation with film thickness, since it is largely the threading dislocations

1 |im

0110

Fig. 8. Dark-field XTEM image of coalesced GaN film. Grain structure is well defined in the first 1 jjim from the NL. Farther from the NL layer the definition of the grains in the XTEM image begins to fade. This loss of grain definition is due to dislocation annihilation with film thickness.

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that define grain boundaries in GaN films [32,44]. For this reason, GaN device structures are best grown on thicker and therefore relatively dislocation-free GaN films, at least to the degree allowed by the constraints imposed by thermal mismatch and the associated hazards of crack formation. 2.4. Threading dislocations The line direction of threading dislocations in GaN films usually runs parallel to the c-axis. The Burgers vector for these dislocations may be 1/3 (edge type), (screw type), or mixed (e.g. l/3). Edge dislocations occur at tilt grain boundaries, whereas screw dislocations occur at twist grain boundaries. A tilt boundary is defined as the interface between two grains that are rotated in a plane perpendicular to the grain boundary [45]. For the case of GaN grains in a heteroepitaxial film, tilt boundaries are formed when grains rotate a fraction of a degree from the nominal orientation, about an axis perpendicular to the substrate growth surface. Edge dislocations, which can be thought of as the line defining the end of an extra atomic plane inserted into the lattice, act to accommodate grain misorientation. Twist boundaries, on the other hand, occur when two adjacent grains are rotated out of alignment about the axis perpendicular to the grain boundary [45]. Screw dislocations, which are much like spiral staircases formed around an imaginary pole coincident with the dislocation line direction, are formed by the lattice offsets resulting from twist boundaries Dislocations with screw components also occur in NLs. As is apparent in Fig. 9, NLs consist of a large density of small ('^10 nm) misoriented grains in which the c-axis for each grain is often not perpendicular to the substrate surface. Screw dislocations necessarily form at the boundaries of these adjacent misoriented grains. Dislocations with screw components are thought to serve as nucleation sites for HT growth [32]. Screw dislocations may also occur as 'pipes' (i.e hollow tubes wending their way through the GaN crystal) — the dislocation core remaining empty to eliminate the most highly strained part of the dislocation for the purpose of energy minimization [46]. 2.5. Inversion domain boundaries Like other compound semiconductors, GaN is polar. The existence of the cation and anion interpenetrating sublattices, offset in a direction perpendicular to the close-packed planes ((0001) for hexagonal; {111} for cubic), guarantees the polar nature of both wurtzite and zinc blende phases. In the TEM, this polar nature can be revealed by acquiring imaging and diffraction information from zone axes that include the {0002} reflections for the hexagonally indexed wurtzite phase. Although HRTEM elucidates the structure of the inversion domain boundaries (IDBs) that act as the interfaces between domains of differing polarity, the presence of such domains is more easily determined via dark field (DF) TEM imaging and convergent beam electron diffraction (CBED) [47]. For wurtzite and zinc blende materials, the convention for polar indexing regards the displacement from cation to anion along [0001] and [111] directions, respectively. Therefore, in following a given bond from gallium to nitrogen nearest neighbors in the wurtzite crystal, one imagines moving along the [0001] direction, in the positive sense

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Misoriented grains AIN nuclealition^ layer

AIN Nucleation Layer a-plane Sapphire Substrate AIN[2110] Sapphire [1100]

10 nm

Fig. 9. HRTEM of AIN-NL. NLs consist of a large density of small (-^10 nm) misoriented grains in which the c-axis for each grain is not quite perpendicular to the substrate surface. Screw dislocations form at the boundaries of these adjacent misoriented grains.

of the c-axis, as shown in Fig. 10. A GaN surface with the c-axis pointing outwards is necessarily Ga-terminated. Because the Ga atom terminating such a surface is held to that surface by three bonds, but linked to the next layer above it by only one bond, that surface has only one third the number of broken bonds as a similarly oriented crystal terminated by N. From an analogous argument, a surface with the c-axis directed inwards would be N-terminated. In Fig. 11, we see an example of such a determination using CBED. By recording the {0002} reflections of the CBED pattern as a function of XTEM specimen thickness, and matching them to the simulation of a CBED pattern [13,48], the polarity of the crystal can be determined. Using this procedure, we have determined that the film shown in Fig. 11 (like most of NRL's MOVPE-grown GaN films) is Ga-terminated. Ramachandran et al. have observed that high levels of Mg doping lead to the formation of inversion boundaries in both MBE and MOVPE-grown GaN [49]. We have also observed one N-terminated film under high Mg doping, as shown by dark-filed TEM in Fig. 12. This Mg-doped film has a rough morphology and a high oxygen concentration, as determined by secondary ion mass spectroscopy (SIMS). NRL's other Mg-doped samples, with lower levels of Mg doping, exhibited neither the elevated oxygen concentration, nor the presence of IDBs.

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Q^.^

Ga-terminated

^ I Q

N-terminated

[2TT0] Zone Axis

Fig. 10. Schematic definition of GaN polarity. For wurtzite and zinc blende materials, the convention for polar indexing regards the displacement from cation to anion along [0001] and [111] directions, respectively. Therefore, in going from gallium to nitrogen in the wurtzite crystal, one imagines moving in the [0001] direction, in the positive sense of the c-axis.

Convergent Beam Electron Diffraction (CBED) Determination of GaN Polarity XTEM Specimen Thickness

[2110] Zone Axis CBED Patterns

c-axis:

[0001]

Thus: Ga-terminated

120nm

140nm

# 1 > A l : i^i* i^i-^

'^WSim ^^pfP

160nm Fig. 11. Convergent beam electron diffraction (CBED) and GaN polarity. By recording the reflections of the CBED pattern as a function of thickness, and matching them to the simulation of a CBED pattern, the polarity of the crystal can be determined. Using this procedure, we have determined that this film is Ga-terminated.

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c-axis Inversion Boundary c-axis f

Mg-doped GaN g:{0002} Fig. 12. Dark-field XTEM image showing inversion domain boundaries (IDBs) in heavily Mg-doped GaN film. The IDBs cause an originally Ga-terminated film to switch to N-termination, as confirmed by CBED.

Z-contrast STEM reveals that a single AlO octahedral layer defines inversion domain boundaries in AIN [50]. The presence of oxygen at AIN domain boundaries has also been suggested by energy dispersive X-ray spectroscopy (EDXS) in the STEM [51]. These STEM-based measurements suggest that each interfacial aluminum atom is surrounded by six oxygen atoms, in a configuration similar to that of an aluminum atom within an oxygen octahedron in sapphire [52]. The conjecture that oxygen is necessary for the formation of IDBs in nitrides is also supported by our own observation of an anomalously high oxygen concentration in a heavily Mg-doped sample containing IDBs. There is also evidence for structure origins for IDBs. According to Wu et al., the presence of IDBs may also be traced to the morphology of the substrate surface [44]. Barbaray et al. have developed a sophisticated model, supported by detailed HRTEM imaging experiments, that addresses the role of c-plane sapphire surface steps of height c/3 in generating IDBs [53]. Rouviere et al. observe that IDBs may occur in GaN films grown on insufficiently thick AIN NLs grown on sapphire [54]. In this thin-NL condition, most of the HT film is found to be N-terminated rather than Ga-terminated. Such a film is characterized by a rough morphology as well as by the presence of IDBs. The latter of these two structural mechanisms for IDB formation, however, may be attributable to composition. Using X-ray photoelectron spectroscopy, Cho et al. have observed the presence of oxygen as well as gallium and nitrogen in nominally AIN

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layers (as identified by TEM) that form on sapphire during plasma source nitridation [55]. Using TEM-based EDXS measurements, Li and Zhu found that Al diffused up from the sapphire substrate and into the NL [56]. Because of the tendency for oxygen to promote the formation of IDBs in AIN, we conjecture that the polarity of some N-terminated GaN films is traceable to IDBs in the AIN NL. In the case explored by Rouviere et al., we might expect that thin NLs grown on sapphire substrates may be more easily saturated with oxygen and thereby give rise to IDBs and N-terminated HT GaN films. 3. Defect reduction strategies Because heteroepitaxial GaN films evolve as a large number of slightly misoriented and coalescing grains, the film must necessarily contain a high density of grain boundaries and threading dislocations. In order to reduce the density of extended defects in such a heteroepitaxial film, researchers have devised a variety of schemes. Each approach involves one of three basic strategies: improving grain alignment, increasing grain size, or filtering threading dislocations. Improving grain alignment reduces the density of threading dislocations needed to accommodate the misorientation between adjacent grains. Promoting larger grain size reduces the density of grain boundaries as well as the density of threading dislocations that help define the grain boundaries. Dislocation filtering is accomplished through the deposition of specially engineered layers for enhancing dislocation recombination, where dislocations combine or annihilate as they thread to the film surface. The approach to promoting grain size can be further divided into two rather different avenues: optimal pressure growth (OPG) and lateral epitaxial overgrowth (LEO). Both techniques rely on controlling grain nucleation at the onset of HT growth so that a lower density of grains succeed in nucleating. In the case of OPG, this control is effected by carefully controlling the growth parameters; in LEO, the growth surface is specially prepared to allow nucleation to occur upon only specific regions of the substrate. 3.1. Grain alignment via vicinal growth Because the substrate in heteroepitaxy functions as the template for subsequent growth, the morphology of the substrate surface may influence the structure of the deposited film. In GaAs on (100) Si, vicinal substrates provide steps that act as island nucleation sites [57]. In addition, steps on vicinal surfaces influence the structure of interfacial dislocations, as has been observed for silicon on {1012} sapphire or CdTe on c-plane sapphire [58]. Weeks et al. have grown GaN on vicinal SiC substrates and arrived at a similar conclusion [59]. In this case, growing on a vicinal c-plane SiC substrate resulted in sufficiently good grain alignment to prevent the actual definition of grain boundaries when viewed using XTEM. For GaN films grown on c-plane sapphire, however, there is an absence of any correlation of GaN film quality with vicinality [60,61]. For GaN grown on ^-plane sapphire, we have found that the structure of the heteroepitaxial GaN film is strongly influenced by substrate vicinality. A detailed X-ray diffraction (XRD) survey, of a large number of GaN films grown on a-plane sapphire

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GaN on a- pi ane sapphi re: Effect of substrate vicinal angle on X- ray FWHM and Mobi I i ty C JI

>
|400h >5 200 (C)

(D)

(E)

(F)

Fig. 13. X-ray diffraction (XRD) FWHM and mobility vicinality experiment. For GaN grown on a-plane sapphire, the structure of the heteroepitaxial GaN film is strongly influenced by substrate vicinality. XRD reveals that films grown on vicinal a-plane substrates have a lower (0001) FWHM. Vicinally grown films also enjoy higher mobilities.

in the CV reactor at 50 Torr, reveals that films grown on vicinal a-plane substrates have a lower (0001) full-width at half maximum (FWHM) [62]. (Note that the orientation relationships for GaN on a-p\ane sapphire are not given correctly in [62]. The correct relationships are given in [30].) Furthermore, as shown in Fig. 13, these vicinally grown films also enjoy higher mobilities. XTEM observations (shown in Fig. 14) indicate that the reduction in the XRD FWHM may be traced to better grain alignment in GaN films grown on vicinal a-p\a.nc substrates [30,62]. For samples grown in the CV reactor at 50 Torr, the density of edge dislocations in vicinally grown samples is less than 10^/cm^, as compared with an edge dislocation density of 5xlO^/cm^ for films deposited upon on-axis substrates. Because the density of screw dislocations is 5 x 10^/cm^ for both vicinal and on-axis films, the dislocation density in the former (5 x 10^/cm^) is half that of the latter (10^/cm^). It is our conjecture that steps on the vicinal a-plane sapphire surface provide a better template for grain alignment, which in turn leads to a lower density of the edge dislocations at the low-angle grain boundaries between adjacent grains. 3.2. Optimal pressure growth Optimal pressure growth (OPG) improves film quality by increasing grain size in the HT layer. In an XTEM study of GaN films grown over a range of reactor pressures in the CSS reactor, grain sizes are found to be approximately 0.2 |xm for 39 Torr, 1 |xm for

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Edge Dislocations

Screw Dislocations

On Axis

Vicinal

0110

1 \im

Fig. 14. Dark-field XTEM of GaN films grown on both vicinal and on-axis fl-plane sapphire substrates, (a) g = 0110, revealing 5 x 10^/cm^ edge dislocations in on axis growth, (b) g = 0002, revealing 5 x 10^/cm^ screw dislocations in on-axis growth, (c) g = 0110, revealing less than 10^/cm^ edge dislocations density in vicinal growth. (d)g = 0002, revealing 5 x 10^/cm^ screw dislocations in vicinal growth.

65 Torr, and 2 |xm for both 130 and 200 Torr as shown in Fig. 15 [12]. This trend is also followed in the CV reactor, where the grain size averages less than 0.5 |xm at a pressure 50 Torr or less, with a grain size of 1 ixm or larger at a pressure of 100 Torr or greater. As shown in Table 1, XRD measurements of the FWHM for both {0001} and {1102} planes also reveal the tendency for film quality to improve from 39 to 130 Torr. At 200 Torr, however, the (0002) XRD FWHM is seen to increase. The increase of the (0002) FWHM suggests the formation of screw dislocations and twist boundaries in the GaN film. Table 1.

Correlation of reactor pressure with X-ray diffraction data

Growth pressure (Torr) 39 65 130 200

FWHM (arc-s) ± 10

FWHM (arc-s) ± 10

326 325 340 420

610 608 517 510

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Correlation of GaN Grain Size w i t h Reactor Pressure 39 torr

65 torr

130 torr

200 torr

1 urn

0110

Fig. 15. XTEM grain size and pressure. Optimal pressure growth improves film quality by increasing grain size in the HT layer. Grain sizes are found to be approximately 0.2 ixm for 39 Torr, 1 |xm for 65 Torr, and 2 |xm for both 130 and 200 Torr.

An understanding of the increase in grain size, the corresponding decrease in the density of tilt grain boundaries, and the evolution of twist grain boundaries can be understood in terms of the influence of reactor conditions on grain size and morphology. According to Koleske et al. [43], higher hydrogen pressure promotes GaN decomposition, with hydrogen reacting with nitrogen on the GaN surface to form anmionia. Thus, enhanced desorption at higher pressures may retard grain nucleation, thereby resulting in larger grain size [11]. The dependence of growth rate on H2 pressure is shown in Fig. 16. The presence of twist boundaries in the 200 Torr growth, suggested by the XRD data in Table 1, may be explained in part by the increasing diameter of HT GaN islands at higher pressure as well as by enhanced faceting. The enhanced faceting at higher

Structural defects in nitride heteroepitaxy 1

"kT*

=L

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T~m "1^

1 1 1 1 ~i

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Reactor Pressure (torr) Fig. 16. Growth rate and pressure. Higher hydrogen pressure promotes GaN decomposition, with hydrogen reacting with nitrogen on the GaN surface to form ammonia. Enhanced desorption at higher pressures may retard grain nucleation, thereby resulting in larger grain size in GaN films.

pressures is apparent from Nomarski micrographs (Fig. 17) of GaN films grown directly on (2-plane sapphire (i.e. without a NL). Large faceted islands have a tendency to draw threading dislocations to the facets, thereby directing bundles of threading dislocations laterally. The extra atomic planes inserted (or removed) by these dislocation bundles give rise to crystallographic tilting [63]. Under the diffraction conditions employed in the dark-field XTEM images in Fig. 15, edge-type threading dislocations are in contrast. These diffraction contrast conditions are also sensitive to rotations of GaN grains about the axis perpendicular to the substrate surface. Such TEM imaging experiments resolve individual GaN grains flanked by tilt boundaries, and outlined by edge-type threading dislocations accommodating these in-plane rotations [45]. The dislocation density was seen to vary by less than a factor of two in the films, at a level near 10^/cm^. XTEM analysis of a Si-doped GaN film grown at 200 Torr indicated grains (mainly defined by tilt boundaries) of the same large size as the 130 Torr film. The GaN growth rate was observed to decrease with increasing growth pressure in this study, ranging from 0.5 to 0.7 |xm/h in the 39 and 65 Torr films, 0.5-0.6 |xm/h for the 130 Torr films, and 0.3-0.4 |jim/h for the 200 Torr films. The variation in growth rate has been attributed in part to GaN decomposition, which is enhanced for pressures above 100 Torr in the CSS reactor geometry [11]. For other reactor configurations the optimal pressure for MOVPE growth may be as high as one atmosphere [64]. Enhanced GaN decomposition has been related to increased grain size by Koleske et al. [43]. It is suggested that small GaN nuclei suffer decomposition soon after their initial growth, bringing about a reduction in nuclei density and resulting in the lateral growth of large grains. The same mechanism would serve to limit GaN renucleation on the growing film surface. In addition to the decomposition mechanism, gas phase depletion of reactants at increased pressure may also be influencing the growth rate, and is a function of reactor geometry. The point at which the GaN growth rate decreases noticeably (e.g. by a factor of two) in the CV reactor is significantly higher, at pressures above 300 Torr. In both CSS and CV reactors, substantial sidewall deposits are seen at increased pressures. In the case of the CSS reactor geometry, the proximity

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39 torr

130 torr

200 torr

300 torr lOO^im

Fig. 17. Un-nucleated growth and reactor pressure. Larger grain size and enhanced faceting at higher pressures are apparent from Nomarski micrographs of GaN films grown directly on (3-plane sapphire (i.e. without a NL).

of the gas injection showerhead to the heated susceptor may induce gas-phase depletion reactions at lower pressures than in the CV reactor geometry. These observations suggest a practical limit on the growth pressure that can be used to achieve large-grained film growth in the CSS reactor geometry, and a need to compensate for reduction in growth rate at higher pressures by increasing the total molar flows of the reactants. While higher pressures are desirable for large GaN grains, this growth pressure regime is not optimal for controlled AlGaN growth. Fig. 18 illustrates the measured alloy concentration (as determined by cathodoluminescence spectroscopy) of 0.5-1.0 |xm thick AlGaN films grown at 1020°C, at pressures of 130 Torr and 65 Torr, with varying TMAl molar flow [12]. The films grown at 130 Torr are found to deviate from the expected gas phase composition [65] by a factor of two, and the growth rates were

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I I t I I I I I I I I I I I I I I I I I I I I [ I I I I I I I I I

vapor composition

^

^-P(growth) = 65torr -A

0

5

10

15

20

25

30

35

p.mol TI\^AI Fig. 18. AlGaN growth rate with pressure. While higher pressures are desirable for large GaN grains, the growth pressure regime is not optimal for controlled AlGaN growth. This figure shows the measured alloy concentration of 0.5-1.0 |xm thick AlGaN films grown at 10200°C, at pressures of 130 Torr and 65 Torr, with varying TMAl molar flow. The films grown at 130 Torr are found to deviate from the expected gas phase composition by a factor of two, and the growth rates were half of those measured for growth of GaN at 65 Torr.

half of those measured for growth of GaN at 65 Torr. ^ A white deposit was observed in the reactor for the 130 Torr AlGaN growths, and increases as a function of TMAl molar flow. This deposit is ascribed to adduct formation between the ammonia and TMAl precursors [66-69,133]. Growth at 65 Torr pressure provides a reasonable fit to the expected gas phase aluminum content, with no evidence of adduct-type deposits. The fact that growth of AlGaN at 65 Torr proceeds without deposits, suggests that the aluminum is more effectively incorporated into the growing film at 65 Torr than for 130 Torr AlGaN growth. As a result of this study, the AlGaN films in recent AlOo.aGaojN/SiiGaN HEMT devices were grown at 65 Torr, upon highly resistive (HR) GaN films grown at 130 Torr. Device structures have been successfully grown using different reactor pressures for GaN and AlGaN layers [12]. The transport characteristics of these devices will be discussed later in this chapter. 3.3. Lateral epitaxial overgrowth Similar in objective to OPG is the growth technique of lateral epitaxial overgrowth (LEO). In both cases the grower is trying to reduce the incidence of HT grain nucleation. In the case of OPG, this end is pursued rather subtly, by increasing the reactor pressure to a point where GaN decomposition frustrates HT grain nucleation. In LEO, the same end is achieved in a more obvious fashion, by masking off most of the nucleating surface [70]. As shown in Fig. 19, GaN grains are only able to nucleate on the

^ Gas phase composition was calculated using the vapor pressure equation: /oglOP(mmHg) = 8.224-2.134.83/r(K).

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SiO, stripes

[xdtialGaMsabstiate

1). Grow GaN on sapphire

2). Pattern GaN with SiQ 7oids «3 gsBtinscoeitosce

GftNgrovth

3). Regrow GaN on S i q

4), Grow GaN until coalescence

Fig. 19. Schematic of LEO growth. In LEO GaN grains are only able to nucleate on the unmasked growth template, followed by lateral growth over the masked region until coalescence occurs.

unmasked growth template, followed by lateral growth over the masked region until coalescence occurs. LEO in GaN is usually configured so that the lateral growth advances along the direction, which allows faster lateral growth than the direction [70]. LEO shares the advantages of large grain size with OPG growth, namely that the density of grain boundaries, and the formation of dislocations at the grain boundaries are correspondingly reduced. There is an added potential advantage of LEO over OPG, however, in that the mask prevents threading dislocations originating at the NL and substrate interfaces from moving up into the HT layer; as a result these threading dislocations are completely blocked off. Most such threading dislocations then occur in large densities only in the immediate vicinity of the windows in the mask. Some dislocations originating in the unmasked region, however, seek the sidewalls rather than threading to the surface of the coalesced film [71,72]. In part, this circumstance can be traced to the general tendency for dislocations to seek out the nearest free surface in order to minimize strain energy. As in OPG growth, laterally directed dislocations act to induce lattice tilt, a tendency which increases with the overgrowth width (u;) to height (/i) ratio (w;//i) [63,73]. The lateral growth rate and the tendency to form sidewall facets is influenced by the V/III ratio. At a low V/III ratio, the sidewalls consist of inclined {1122} facets and the lateral growth rate is small. As the V/III ratio is increased, smooth vertical {1120} facets appear and the lateral growth rate increases. Continuing to increase the V/III ratio, however, leads to the formation of {1011} facets, a jagged morphology, and a fall in

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growth rate [74]. A large lateral growth rate and smooth {1120} sidewalls are necessary for successful LEO growth of GaN, so that a value of the V/III ratio must be chosen that encourages both of these conditions. The most technologically important aspect of LEO nitride growth, that of reducing the threading dislocations density, is illustrated by the AFM images in Fig. 20, where the surface at a LEO grain boundary is shown to be free of mixed dislocations. Dislocations with screw components act to terminate steps, a feature that is easily observable in GaN using AFM [73]. Unlike other semiconductors, GaN is relatively inert and is therefore without a thick native oxide that could mask surface structure [27]. AFM observations suggest that the dislocation density in regions of the LEO sample away from the windows in the mask may be less than 10^/cm^, although scanning electron microscopy (SEM), of some LEO samples treated with an UV-assisted KOH etch (i.e. photo-electrochemical etching, PEC) [75,76], suggests that 10^/cm^ is a more realistic estimate [77]. Thus, LEO may not always result in a significant improvement in film quality. It is apparent that a study using both PEC and AFM is needed to completely judge the efficacy of LEO. These two imaging techniques are complementary in that

Bulk GaN 10®- 10^° Dislocations/cm^

LEO GaN < 1 0 ® - 10^ Dislocations/cm^

No Step Terminations

Step Terminations

lum Fig. 20. AFM of LEO growth and step terminations. The surface at a LEO grain boundary is shown to be free of mixed dislocations, whereas near the mask window the dislocations density is high. Dislocations with screw components act to terminate steps, a feature that is easily observable in GaN using AFM. AFM observations suggest that the dislocation density in regions of the LEO sample away from the windows in the mask may be less than 10^/cm^.

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AFM is most sensitive to screw and mixed threading dislocations, whereas PEC is sensitive to edge and mixed threading dislocations [73,75,76]. Even in the case where none of the dislocations at the coalesced boundary thread to the film surface, LEO growth is faced with the problem of residual strains due to slight misorientations between coalescing grains. One approach to reducing such strains is that of Pendeo-epitaxy, a technique where lateral growth is seeded from -oriented stripes etched out of a conventionally grown GaN film [78]. The etching process removes several hundred nanometers of the SiC substrate as well, so that the growth proceeds from the {1120} sidewalls and remains suspended above the substrate, even after the film coalesces. In naming this approach Zheleva et al. adopted the Latin prefix pendeo, which is derived from the werh pendere, to hang on [78]. 3.4. Dislocation filtering Another novel approach to improving film quality is that of interrupting high-temperature growth with a series of low-temperature interfacial layers (ILs) grown under the same conditions as conventional NLs [79]. Weak-beam XTEM images of a GaN film, grown in NRL's CSS reactor at 130 Torr with AlN-ILs, are shown in Fig. 21 [80]. Diffraction contrast (g-b) analysis of the XTEM images indicates that the ILs primarily

1|lim Fig. 21. Weak-beam XTEM images of a GaN film grown using multi-interfacial layer (IL) growth. Diffraction contrast {gb) analysis of the XTEM images reveals that the IL filters screw dislocations.

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365

0112

1 ^im Fig. 22. Weak-beam XTEM images of GaN/AlN IL interface of multi-IL structure. The orientation of the g vector (0002, 0110 and 0112, respectively) was varied to image: (a) threading screw dislocations, (b) threading edge dislocations, and (c) both screw and edge threading dislocations. Contrast if dislocations in the IL is seen in (a) and (c), but not in (b), indicating that the Burgers vectors of these dislocations are parallel to the c-axis (i.e. ).

consist of dislocations with the Burgers vector perpendicular to the growth plane. This array of IL dislocations then act to annihilate threading screw dislocations, thereby reducing screw dislocation density to less than 10^/cm^. Weak-beam XTEM images of the GaN film above the last AIN-IL of the 5 AIN-IL structure are shown in Fig. 22. Imaging conditions which highlight dislocations with , 1/3, or either of these two Burgers vector components are shown in Fig. 22 (a, b and c, respectively). Diffraction contrast analysis of the XTEM images indicates that the AlN-ILs consist primarily of dislocations, which, like threading screw dislocations, have Burgers vectors perpendicular to the growth plane (i.e Burgers vectors). This array of AIN-IL dislocations then act to annihilate threading screw dislocations, thereby reducing their density to less than 10^/cm^, as shown in Fig. 22a. A similar reduction in the screw dislocation density, using the IL approach, was also noted by Iwaya et al. [79]. Despite the large (2-6 |xm) GaN grain size in this film [11], the edge dislocation density measured in Fig. 22b is approximately lOVcml In Fig. 22c, where dislocations with either or 1/3 Burgers vector components are in contrast, a dislocation density of greater than 10^^/cm^ is revealed within the AIN-IL. The dislocations within the AIN-IL, however, arenot in contrast in Fig. 22b, indicating that the AIN-IL dislocations must not have 1/3 components. Similarly, the dislocations that are incontrast in Fig. 22b, in the GaN layer just above the last AIN-IL, must have only l/3 Burgers vector components and are therefore threading edge dislocations. The screw dislocations appear to annihilate as they attempt to thread through the AIN-IL interfaces, thereby removing the screw dislocations

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from the GaN film. As observed by Rouviere et al., for MOVPE-grown GaN, screw dislocations of opposite -type Burgers vector easily annihilate [54]. Despite the large (2-6 |xm) grain size in the 5 IL film, however, the edge dislocation density is ^10^/cm^. In contrast to screw dislocations, annihilation reactions involving edge dislocations seldom occur [81]. It was also observed that the XRD FWHM increased with the number of ILs. It may be that the lack of screw dislocations prevents strain relief between adjacent twist boundaries, with a corresponding increase in the XRD FWHM. 4. Defects and electrical properties In contrast to essentially covalent semiconductors like GaAs and Si, GaN is strongly ionic [82]. One consequence of this strong ionicity is the wurtzite structure of the GaN lattice (as opposed to zinc blende of more covalent semiconductors). In wurtzite the distance between third-order Ga and N nearest neighbors is less than in zinc blende, which reduces the configurational energy derived from electrostatic forces [37]. For strongly covalent semiconductors, discontinuities such as surfaces result in dangling covalent bonds [83]. In strongly ionic materials like GaN, states associated with the lattice discontinuity at the surface are either few or energetically outside the band gap, so that the surfaces of GaN are not subject to fermi-level pinning [84]. Extended defects, such as dislocations, also act as lattice interruptions, and, like surfaces, do not generally have states within the band gap of strongly ionic materials [85]. Therefore, significant carrier recombination in ionic semiconductors like GaN is not expected to occur at dislocations. That is, extended defects in GaN should not act as deep electron traps. A possible consequence of such relatively benign extended defects is the ability of GaN-based light-emitting diodes (LEDs) to function despite large threading dislocation densities ('^lO^^/cm^) [86]. Although dislocations in ionic semiconductors are not efficient carrier recombination centers [87], they are highly negatively charged (as revealed by scanning capacitance microscopy [88] and therefore strongly scatter carriers [89,90]. This scattering, of course, acts to reduce carrier mobility in electrical devices. 4.L Point defects The tendency for point defects to segregate to extended defects (and thereby influence the electrical activity of such defects) has been observed in other electronic materials [91]. Our objective is therefore to move from a general understanding of the role of extended defects in the electrical properties of heteroepitaxial GaN, to consider how specific problems due to extended defects affect electrical properties in GaN films, and develop strategies for minimizing their deleterious contributions. Given the well argued conjecture that many of the extended defects in GaN are not intrinsically electrically active, we need to further examine the possibility that extended defects in GaN derive their electronic properties from associated point defects. There is a significant drawback to this approach, however, in that the role of point defects in the optical properties of GaN is not well understood. The configuration and

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composition of the point defects responsible for yellow (2.2 eV) luminescence in GaN films, for example, are not clear, although there are a number of theories addressing the mechanism. Neugebauer and Van de Walle have used density-functional theory to calculate the formation energy of a number of defect configurations and have concluded that the Ga vacancy complexes Voa-Sica and Voa-ON are stable in n-type GaN and capable of functioning as the deep acceptor needed to generate yellow luminescence [92]. The photoluminescence study of Kaufmann et al. advances a convincing argument that yellow luminescence in their GaN films can be traced to Si [93]. In addition Kaufmann et al. show how blue (2.8 eV) luminescence can be traced to Mg in GaN and red (1.8 eV) luminescence to both Si and Mg in GaN [93]. 4.2. Dislocations To some degree dislocations can be thought of as internal surfaces. Eisner et al. adopt this viewpoint and observe that the low-energy {1010} plane serves as the internal surface for open-core screw dislocations and threading edge dislocations in GaN [94]. These two types of dislocations with {1010} internal surfaces are essentially benign and should not give rise to deep states within the band gap. There is also, however, a species of screw dislocations with a full (i.e. not open) core, as determined by the Z-contrast scanning transmission electron microscopy (STEM) imaging study of Xin et al. [95]. The strong distortion of the bonds at the core of a full-core screw dislocation are expected to give rise to associated states within the band gap [96]. Some of the attributes of dislocations in GaN have been addressed by SEM-based cathodoluminescence (CL) imaging of GaN films. Suguhara et al. used plan-view TEM and SEM/CL to study dislocations in MOVPE-grown GaN thin films [97]. Using panchromatic CL, Suguhara et al. imaged electron-transparent TEM samples held at ambient temperature and found that dark regions in the CL image are due to dislocations in the corresponding TEM image [97], indicating that these dislocations act as non-radiative recombination centers in GaN. From CL imaging experiments, Rossner et al. [98,99] and Salvanti et al. [100] conclude that dislocations act as non-radiative recombination centers in MOVPE and Hydride vapor phase epitaxy (HVPE) GaN, respectively. It should be noted that the SEM/CL experiment using an electron-transparent TEM sample, as conducted by Suguhara et al., has two advantages over CL measurements performed on a conventional bulk film: (1) the dislocations can be identified by TEM; (2) the thinner TEM sample allows for less broadening of the electron-irradiated area and hence better spatial resolution of the CL image [97]. Suguhara et al. estimated the hole diffusion length in n-type GaN as 50 nm by noticing that the loss of luminescence was most pronounced for regions where the spacing between adjacent dislocations was less than 50 nm [97]. This value stands in contrast to the 200 nm electron diffusion lengths measured in p-type GaN using electron beam induced conductivity (EBIC) measurements [101]. This small hole diffusion length may contribute to the ability of LEDs to function despite large dislocation densities. In contrast to studies where dislocations are identified as non-radiative recombination centers, the CL observations of Ponce et al. indicate that yellow luminescence delineates grain boundaries in MOVPE GaN films [102]. The CL study of de Mierry et al. also

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found that yellow luminescence is strongest at grain boundaries [103]. A CL study of grains in GaN grown by the sublimation sandwich method also found evidence for this tendency [104]. The CL observations of Christiansen et al., however, indicate that the intensity of yellow luminescence is uniform across GaN films grown by gas source molecular beam epitaxy (GSMBE) rather than concentrated at grain boundaries [105]. The rather great variety of outcomes in CL imaging of GaN films, especially regarding the optical signature of extended defects such as dislocations and grain boundaries, certainly deserves some comment. Even among GaN films grown by MOVPE, there is a lack of consensus on the identity of optical signatures for extended defects. One obvious explanation for the differences in these CL observations is that it is the impurities associated with the extended defects, rather than the extended defects themselves, which give rise to such optical features as yellow luminescence. Indeed, the calculations of Eisner et al., based on density-functional theory, indicate that most types of extended defects are not expected to generate the deep traps within the band gap that are necessary for these optical signatures [94,96]. These observations are in accord with the conjecture of Liliental-Weber et al., that screw dislocations configured as {1010}-faceted nanotubes derive their internal structure from the segregation of oxygen to the walls of the nanotube [106]. It should also be noted that optical properties improve with the lower threading dislocation density of LEO-grown GaN [107]. The use of LEO GaN has augmented the operating lifetime for laser diodes [69]. Furthermore, a study of p-n diodes fabricated on LEO GaN reveals a significant reduction in reverse-bias leakage current [108]. 4.3. Grain boundaries Scanning capacitance microscopy reveals that the edge and mixed-character dislocations, as well as the associated grain boundaries, are negatively charged [88]. This observation suggests that acceptors lie at these grain boundaries as well as at the dislocations defining these grain boundaries. The electrical properties of a special class of grain boundaries in GaN have also been addressed by the TEM studies of Humphreys and coworkers [109-111]; in particular they have focused on double-positioning domain boundaries associated with the {1120} and {1010} habit planes, which are designated as DBl and DB2, respectively. Using electron energy loss spectroscopy (EELS) in the TEM, Humphreys and coworkers have compared spectra from DBl and DB2 with that of defect-free GaN. Like the dislocations built on {1010} surfaces, DB2 is benign and appears identical to bulk GaN in the EELS spectra. EELS analysis indicates that the {1120}-oriented DBl is heavily charged so that 1.5 electrons are bound to each atom at the boundary interface. It is the conjecture of Eisner et al. that these charges are the result of the trapping of Ga vacancies at DBl boundaries [94]. 4.4. Carrier mobility Although microscopy of individual extended defects and optical spectroscopy of point defects advance the understanding of the electro-optical properties of GaN, the mea-

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surement of the aggregate properties of mobility and carrier concentration must have the final word on the suitability of such materials for electrical device applications. There is evidence that empirically derived values of carrier mobility and concentration values are consistent with carrier scattering by negatively charged dislocations defining the GaN grain boundaries [89,90,112]. The etching study of Youtsey et al. also suggests that dislocations in GaN are charged [75,76]. That GaN edge dislocations are negatively charged is supported by recent Z-contrast STEM and EELS measurements of Xin et al. [113]. Analysis of the Z-contrast images, however, suggests that the fraction of Ga vacancies in threading edge dislocation cores [114,115] is too small for the mobility reduction suggested by an analysis of electrical measurements [89,90,112]. Maximum entropy analysis of Z-contrast STEM images indicates that less than 15% of all possible Ga sites at the edge dislocation core are vacant [113]. This small fraction of Ga vacancies at edge dislocation cores therefore suggests that other impurities and point defects associated with the dislocation may be responsible for carrier scattering and the resulting reduction in mobility. It is also conceivable that carriers may be scattered by charged point defects that segregate to grain boundaries, as argued by Fehrer et al. [116]. As suggested by models of scattering by charged defects, the dislocation density must be less than 10^/cm^ before dislocations cease to significantly limit mobility [89, 90,112]. The existence of this threshold is supported by the observations of Watanabe et al. [97,117]. Using the PEC etching procedure of Youtsey et al., individual whiskers surrounding edge and mixed dislocations were revealed [75,76]. By determining the density of such whiskers using SEM observations, the density of edge and mixed dislocations can be accurately determined. Correlation of Hall mobility measurements and PEC/SEM observations agree with the claim that mobility does not increase significantly as the dislocation density falls below 10^/cm^. When the dislocation density falls below the 10^/cm^ level, other scattering mechanisms (such as those associated with point defects) have the opportunity to dominate [89].Changing the substrate nitridation procedure prior to NL growth has been shown to significantly alter carrier mobility as well as threading dislocation density [28,31,90]. It was found that reducing substrate nitridation time reduces the dislocation density from >10^^/cm^ tolO^/cm^. This reduction in the dislocation density leads to an increase in the carrier mobility at 300 K from 149 to 592 cm^/Vs. The effect of nitridation procedure on dislocation density and carrier mobility has also been investigated by Wickenden et al. [ll]._According to Wickenden et al., the preferred crystallographic configuration, GaN[2110]/sap[1100]; GaN(0001)/sap(ii20), for nitride growth on a-plane sapphire is brought about by nitriding at elevated temperatures (e.g. 1065°C). GaN films with this orientation were observed to have carrier mobilities of 500 cm^/Vs at ambient temperature [11,12]. Lower temperature nitridation (e.g. 625°C)_ results in the other observed configuration, GaN[liOO]/sap[liOO]; GaN(0001)/sap(li20), which suffers from poor grain alignment, with a resulting large dislocation density (>10^^/cm^) at the grain boundaries and carrier mobilities as low as 60 cm^/Vs. Similarly, Wu et al. found that c-plane sapphire substrates exposed to shorter nitridation times result in larger grains, fewer dislocations, and higher carrier mobilities as dislocation densities dropped from 10^^/cm^ to lOVcm^ [32]. It has also been shown by Fatemi et al. that by reducing the edge dislocation density from 5 x lOVcm^ to lOVcm^, while holding

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screw dislocations density at 5 x 10^/cm^ the carrier mobility increases from 300 to 600cmVVs[62]. It is also conceivable that grain size may effect carrier mobility independently of dislocation density. For Si-doped GaN films grown in the NRL CV reactor, with dislocation densities that appear uniformly on the order of 10^/cm^, significant center-to-edge differences were found in mobility and carrier concentration at the center of a 2-inch diameter wafer recorded at ambient temperature (e.g. /^ = 83 cm^/V s and n = 2.34 X lO^Vcm^ at the wafer center; JJL = 192 c m ^ V s and n = 6.0 x lO^Vcm^ at the wafer edge). The grain size at the sample edge was approximately 1 |xm, and 0.5 jxm or less at the wafer center. Smaller grain size may be the cause of the lower carrier mobility in the wafer center, due to enhanced carrier scattering at the grain boundaries [42]. It is not only in center-to-edge differences in electrical properties where grain size appears to play a role in electrical properties of GaN films. A characteristic relationship between growth pressure and structural morphology has been observed in films grown in both CSS and CV MOVPE reactor geometries by Wickenden et al. [11], with increased pressure resulting in larger grain growth. Si-doped GaN films grown at higher pressures exhibit increased mobility, within a specific range of pressure, as shown in Fig. 23. The Hall electron mobilities are plotted against temperature in Fig. 24. for samples grown at 39, 65, 130, and 200 Torr. The two higher-pressure films, in which similar large grain size was observed, appear to exhibit normal ionized impurity scattering behavior in the low-temperature regime. The two lower-pressure films exhibit dramatically reduced mobility, which can be correlated to smaller grain structure of these films. The temperature dependence of the mobility of the lower-pressure films is consistent with models of charged edge dislocation screening [89,90,112]. The effect of screw dislocations on carrier mobility can be assessed from Hall measurements of GaN films grown with multiple AIN interlayers. Because of the significant decrease in the screw dislocation density in films grown using multiple AlN-ILs, the influence of screw dislocations on electrical and optical properties may be addressed by the study of these structures. Mobilities in excess of 700 cm^/Vs and carrier concentrations of ^ 2 x 10^^/cm^ were obtained in n-type Si-doped GaN

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films grown using this multiple-NL approach. The relatively small density of screw dislocations may explain the superior electrical properties of this material. Similarly for Wu et al., the GaN material with the better electrical properties had a screw dislocation density of less than 10^/cm^ [32]. These data suggest that screw dislocations are deleterious to carrier mobility, as are edge dislocations. Because Hall measurements reveal the bulk-like behavior of electrical conduction as a function of temperature in the Si-doped GaN, the improved electrical properties can be ascribed to improvement in the bulk GaN and are not due to the formation of a 2-dimensional electron gas (2DEG) at the AlN/GaN interface [118]. Over a narrow doping range {n ranging from 0.55 to 1.47 x 10^^/cm^), the mobility increases as the number of the AIN-NL increases. Yang et al. have also observed an increase in /x from 267 to 446 cm^/V s as the number of GaN IL increases from 1 to 4 [119]. 4.5. Film resistivity Because electrical devices such as field-effect transistors (FETs) and high-mobility electron transistors (HEMTs) require high-resistivity buffers to achieve pinch-off, the GaN buffer adjacent to the channel region must be highly resistive. Highly resistive GaN films are also important for device isolation. Growing highly resistive GaN films, however, is frustrated by unintentional doping (UID): the incorporation of impurities which act as dopants. In the case of GaN these unintentional dopants act as shallow donors. In order to achieve high-resistivity films, the deep acceptor concentration must exceed the shallow donor concentration. If the deep acceptor concentration greatly exceeds the shallow donor concentration in the HEMT, however, the 2DEG sheet carrier concentration will be lowered and device performance will be adversely affected. Above a given growth pressure in MOVPE, which is reactor dependent, UID GaN films lose their highly resistive nature. In the NRL CSS reactor, this loss of high resistivity occurs as the growth pressure is increased from 39 to 200 Torr [12]. The

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growth rate (jim/hr) Fig. 25. Electron concentration vs. growth rate. The 300°K Hall electron concentration was observed to fall linearly with growth rate of the GaN/Si-doped films grown in the CSS reactor. The electron concentration would be expected to double as growth rate decreases from 0.72 |xm/h (at 39 Torr) to 0.38 mm/h (at 200 Torr), given a simple volume incorporation argument and a constant SiH4 dopant flow. The fact that the electron concentration at 200 Torr is six times that of the 39 Torr value suggests increased compensation and reduced donor concentrations in the films grown at lower pressure.

300 K Hall electron concentration was observed to fall linearly with the growth rate of Si-doped GaN films grown in the CSS reactor, as shown in Fig. 25. The electron concentration would be expected to double as growth rate decreases from 0.72 |xm/h (at 39 Torr) to 0.38 |xm/h (at 200 Torr), given a simple volume incorporation argument and a constant SiH4 dopant flow. The fact that the electron concentration at 200 Torr is six times that of the 39 Torr value suggests increased compensation or reduced donor concentrations in the films grown at lower pressure. Analysis of variable temperature Hall data for compensation levels was inconclusive in the Si-doped GaN films, due to the relatively high dopant concentration. The Hall electron concentrations are plotted against temperature in Fig. 26. The temperature dependence of the electron concentration is similar for the 130 Torr and 200 Torr films, but does not follow a simple exponential relationship in the 65 Torr and 39 Torr samples which were found to be much more resistive, even with relatively high 300 K electron concentrations. The variation of resistivity as a function of NL thickness has also been observed by Briot et al. [120]. The fact that GaN resistivity may be influenced by both growth pressure or NL thickness suggests that morphological structure is a common factor, in agreement with the grain growth mode of GaN growth proposed by Hersee et al. [121]. Edge dislocations defining grain boundaries may not directly affect compensation, but it has been suggested that their associated stress field may play a role in trapping effects [122]. The possible mechanisms responsible for the modulation of carrier mobility, carrier concentration, and donor compensation have been addressed by photoluminescence (PL) studies. In the series of Si-doped GaN films discussed above, yellow band emission (centered at 2.25 eV) is seen to be very strong in the 39 Torr film, less strong in the 65 Torr film, and very weak in the 130 Torr and 200 Torr films. Broad band emission centered at 3.0 eV is only significant in the 39 Torr film. These PL data suggest the presence of a deep acceptor that falls off with increasing growth pressure [12]. Yellow

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luminescence could be derived from electron recombination with deep acceptors trapped at threading edge dislocations as suggested by Eisner et al. [122]. The combined results of Hall and PL analysis suggest that the acceptor-type defects associated with the 2.25 and 3.0 eV bands are reduced at 130 Torr relative to the 39 Tonfilm to a level that just compensates the intrinsic donor concentration, minimizing carrier scattering and increasing mobility in intentionally Si-doped films. SIMS measurements of the impurity levels in these samples indicate that the carbon concentration falls from 3 X 10^^/cm^ to 8 X 10^^/cm^ as the reactor pressure rises from 39 to 130 Torr. This fall in carbon concentration with increasing reactor pressure can be understood in terms of the enhanced probability that hydrogen reacts with the carbon on the film surface to form methane (CH4), thereby removing carbon from the film surface. As the compensating acceptor (possibly carbon) is further reduced at higher pressure, n-type conduction is enhanced, as seen by many groups in GaN films grown near atmospheric pressure. Because the carbon concentration is seen to decrease as the concentration of compensating acceptors decreases, it is reasonable to suggest that the carbon is acting as the compensating acceptor [123]. In a similar study of UID GaN films grown at varying pressures in the CV reactor, we observed that the conductivity of the films increased with pressure. When the HT layer was grown at 45 Torr, the films were found to be highly resistive, with a break-down voltage of greater than 1000 V. When the HT layer was grown at 250 Torr, however, the GaN film was found to be n-type (1 x lO^Vcm^) with high mobility (600 cm^/V s). XTEM analysis of these films also demonstrated that the films grown at higher pressure had larger grain size. The correlation between resistance and grain size is again in agreement with the multi-grained model of GaN growth [122]. Carbon concentration in GaN films grown in NRL's CV reactor is also seen to fall with increasing pressure. SIMS analysis indicates that the carbon concentration decreases from 4 x 10^^/cm^ to 1 x 10^'^/cm^ as the reactor pressure rises from 49 to 350

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Torr. In a separate experiment GaN was grown in the CV reactor using variable pressure growth (VPG) such that high-pressure (250 Torr) growth was followed by low-pressure (49 Torr) growth. SIMS measurements of the VPG film indicate that the carbon level increased from 8 x 10^^/cm^ to 2 x 10^'^/cm^ with the fall in pressure. The Si concentration also decreased from 2 x 10^'^/cm^ to less than 1 x 10^^/cm^ whereas the grain structure and dislocation density of the film were unaffected by the change in pressure. This film was found to have a significantly higher breakdown voltage than in other films grown at 250 Torr in the CV reactor. In this case, the high breakdown voltage may be due to the fall in the Si concentration as well as to a decrease in the carbon concentration. The effect of dislocations on film resistivity can be addressed by Hall measurements performed on GaN films with multiple ILs. Because the density of screw dislocations falls off with the number of AlN-ILs, carrier compensation due to screw dislocations can be assessed, to some degree by the way the calculated acceptor concentration A^A decreases with the number of IL layers [80,124] in Si-doped structures. As the number of ILs increases from 1 to 5, A^A falls from 1.74 x 10^^/cm^ to 0.51 x lO^Vcm^; the compensation ratio A^A/A^D falls from 0.760 to 0.256. In the 5-IL film, PL measurements detect a lower intensity of yellow luminescence in the top 2 ixm layer, than in conventional MOVPE-grown GaN films. These PL observations then suggest that threading screw dislocations in this film (or the point defects surrounding these dislocations) contribute to yellow luminescence. 4.6. High-power device requirements Requirements for nitride high-power microwave devices mandate highly resistive isolation layers, high mobility, and low trap density. Ideally, the GaN film is highly resistive (HR) when unintentionally doped (so that there are no significant shunting paths from source to drain [125]), and exhibits high mobility when intentionally doped. We have observed that MOVPE growth pressure profoundly influences the morphological structure and growth rate of GaN films, with a resultant influence on dopant incorporation and compensation level [123]. The growth rate and alloy composition of AlGaN films in HEMTs are also strongly influenced by the growth pressure, in agreement with reports of several groups [123]. Ambient temperature Hall measurements indicate that HEMT device structures fabricated on large-grained GaN films grown at NRL have been able to achieve high mobility (1500 cm^/Vs) and high sheet carrier concentration (1.2 x 10^^/cm^), which are necessary conditions for high transconductance [123,126]. Recently fabricated HEMT devices have achieved a transconductance of over 200 mS/mm [127,128]. The resistivity of the underlying HR-GaN buffer was found to be 10^ ^ c m , allowing sharp device pinch-off [123,127]. On-wafer small-signal measurements have yielded a cut-off frequency ifj) of 90 GHz with a maximum oscillation frequency (/max) of 145 GHz: the highest values reported to date for a 0.15 |xm gate-length GaN HEMT [128]. In addition, trapping effects that have been known to cause drain lag (drain current transients in response to a drain voltage pulse) and current collapse (limitation of drain current due to electron trapping in the channel region) were significantly reduced in fabricated microwave devices [127].

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In both of NRL's MOVPE reactors (CSS and CV), UID GaN films grown at low pressure (e.g. 40 Torr) are highly resistive, with typical breakdown voltages greater than 1200 V. When films grown at these low pressures are intentionally silicon-doped, however, they suffer from characteristically low mobilities. XTEM diffraction contrast imaging of these films shows small grains which are defined by threading dislocations. Within a certain pressure range, growth at increasing pressure results in larger grains and increased mobility of GaN:Si films, while simultaneously maintaining the capability for UID HR-GaN growth. At higher pressures, UID films become n-type, with high mobilities and low measured compensation [123]. AlGaN:Si/GaN HEMT devices have been grown with the HR-GaN layers deposited at 130 Torr in order to achieve large-grained films. As shown in Fig. 27, the GaN layer of the HEMT device has a large ('--5 jxm) grain size. The elimination of drain lag and the reduction in current collapse in this device structure may be due to the reduction of the density of grain boundaries, dislocations, or carbon contamination. The structure and composition of the AlGaN layer itself should influence the electrical properties of the HEMT as well. Many of the structural properties of the AlGaN layer can be determined by XTEM, as shown in Fig. 28. Here it is apparent that GaN/AlGaN interface suffers from approximately 5 nm of roughness. The lateral variation in the contrast of the

Fig. 27. XTEM of HEMT grain size. AlGaN:Si/GaN HEMT devices have been grown the HR-GaN under the 130 Torr pressure conditions favoring large-grained material. The GaN layer of the HEMT device has a large (~5 |xm) grain size. In the HEMT based on this material, drain lag has been eliminated and current collapse has been significantly reduced in fabricated devices.

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Fig. 28. XTEM imaging indicates that GaN/AlGaN interface suffers from approximately 5 nm of roughness in this HEMT device structure. The lateral variation in the contrast of the AlGaN layer suggests segregation or clustering effects, such as would occur during spinoidal decomposition.

AlGaN layer suggests segregation or clustering effects, such as would occur during spinoidal decomposition [129-132,134]. 5. Conclusions Extended defects in heteroepitaxial GaN films grown by MOVPE scatter carriers, resulting in lower mobility, appear to surround themselves with point defects and impurities which act to compensate dopants. It also appears that point defects may be able to compensate dopants without associating with extended defects; the SIMS and TEM study of carbon in GaN films deposited by variable pressure growth supports this contention. In particular, it is interesting to consider carbon as a point defect involved in compensation, since it is an inevitable by-product of the MOVPE process which can be controlled, to some degree, by altering the reactor pressure. Reactor pressure influences grain size as well as carbon concentration and there appears to be a reactor-dependent optimal pressure for growing grains that are large without the onset of faceting, or the onset of associated lattice tilting and twist boundaries. These reactor parameters for growing a film with the minimum extended defect density on a nucleation layer are similar to growth via LEO in that the lateral growth rate must be as large as possible without the onset of faceting. There is also reason to believe that both LEO and conventional growth can be optimized by the use of vicinal c-plane SiC or ^-plane sapphire substrates, in order to improve grain alignment and thereby reduce the edge dislocation density occurring at grain boundaries.

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The role of the nucleation layer in heteroepitaxial GaN growth and the procedures for optimizing this layer are still not well understood. For some reactors, at least, it appears that the optimal nucleation layer goes down with a significant fraction of the film consisting of the zinc blende polymorph, which then transforms into the wurtzite phase upon annealing. Although there has been a preliminary effort to explain these structural constraints, there is not yet a sufficiently general understanding to guide a grower in achieving a good nucleation layer. There is some indication that optimizing the nucleation layer results in defining a specific film polarity (i.e. Ga-terminated) and that this desirable result may be achieved by reducing the oxygen composition and thereby eliminate oxygen-rich IDBs in the NL. It also appears that achieving a film with no inversion boundaries is frustrated by a rough substrate morphology. Acknowledgements This work was supported by the Office of Naval Research. We thank Larry Ardis and Bob Gorman for expert technical assistance. We also thank Evan Glaser and Steve Binari for helpful suggestions regarding the preparation of the manuscript. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

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III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 11

Optical phonon confinement in nitride-based heterostructures N.A. Zakhleniuk, C.R. Bennett, M. Babiker and B.K. Ridley

1. Introduction The physics of semiconductor heterostructures and devices constituted, over the last two decades or so, one of the most exciting and rapidly developing research fields [1]. An important area of investigation, which was identified at the outset, concerned the main properties of the charge carriers and the lattice vibrations in heterostructures, as could be revealed experimentally, for example, using Raman measurements [2]. From a device application point of view, however, much effort was also devoted to understanding carrier-phonon interactions. Optical phonon scattering, in particular, has long been known to play the dominant role in determining the mobility in bulk III-V semiconductors [3] and it was only natural to contemplate how this key property would be modified in heterostructures. At the nanoscale level, heterostructures present strongly inhomogeneous environments in which charge carriers and phonons coexist. This can cause confinement effects which should, in principle, lead to modifications of the physics relative to the homogeneous bulk. However, under these conditions not only that the gross properties of the charge carriers and the phonons would be subject to modifications, but, more importantly the carrier-phonon interactions themselves should suffer changes. The purpose of this chapter is to provide an account of carrier-phonon interactions and their manifestations in heterostructures with special emphasis on applications in the context of structures made of large-band gap semiconductors, most notably the nitride-based systems [4]. The characterisation of non-interacting carriers in heterostructures is relatively trouble free and has been successfully dealt with in terms of envelope function models involving an effective mass approximation [5]. In order to deal conveniently and practicably with phonons in heterostructures it seems reasonable to seek a continuum model which should be valid for long-wavelength vibrations and should essentially be analogous to the envelope-function model adopted for electrons. It turns out that in contrast with the case of electrons, constructing a continuum model for phonons in heterostructures is far from a straightforward matter. The continuum model we must seek to obtain should correspond closely to the microscopic atomic models of lattice vibrations. This implies that within the limits

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where both theories are valid, the descriptions of a given phonon mode arising from the two separate (microscopic and continuum) frameworks should have the same frequency and the same field distribution, exhibiting the same spatial symmetry. Only when these basic requirements have been met can a continuum description of lattice vibrations be self-consistent and be confidently used as the basis for a broad range of phenomena, such as exist in Raman scattering or carrier-phonon interactions. A continuum model in the context of inhomogeneous systems has long been available for acoustic lattice vibrations [6], but not for polar optical (PO) phonons. As we explain later, dealing with polar optical vibrations presents analytical problems arising from the fact that these vibrations possess mechanical as well as electrical properties. The optical phonon fields must then experience jump conditions of both mechanical and electrical kinds at heterostructure interfaces. This necessitates specifying the correct forms of boundary conditions and applying them in derivations of the modes. To understand the basic issues involved in the construction of a consistent continuum model, it is useful to review briefly the development of the relevant work in this area. The first significant work on polar systems was the phenomenological macroscopic theory of polar optical phonons in a homogeneous bulk polar material developed by Bom and Huang [7]. As is well known, the primary outcome of this theory was the derivation of the frequency-dependent dielectric function of the material. Once the dielectric function has been specified, the form of the electromagnetic modes can be found directly as solutions of a pure electromagnetic problem based entirely on Maxwell's equations and involving only electromagnetic boundary conditions. Because of this, the Bom and Huang model is often referred to as the dielectric continuum (DC) model. It should be noted that in the Bom and Huang theory the mechanical effects do play a role as they enter through the associated polarisation fields contributing to the dielectric function. In fact the treatment allows one to straightforwardly deduce the mechanical fields once the electromagnetic fields are known. The Bom and Huang DC model was subsequently employed by Fuchs and Kliewer [8] to derive the modes of vibration for the inhomogeneous case of a layered medium. The central assumption of the Fuchs and Kliewer theory was that the dielectric function within a given layer is the same as that of the corresponding infinite medium, with adjacent layers possessing different dielectric functions. The allowed modes which are solutions of the wave equation in each region are specified in both spatial distribution and frequency after the imposition of electromagnetic boundary conditions which match the general solutions in adjacent layers. The main results of the Fuchs and Kliewer DC theory is the optical phonon confinement effect, which means that waves of specific frequencies can propagate only within the layers for which the frequencies are the bulk longitudinal or transverse eigenfrequencies of that material. A given wave in a layer of one material does not propagate in layers of the other type of material. Another important prediction of the Fuchs and Kliewer work is the presence of interface modes which have frequencies in the reststrahl bands of the materials and whose amplitudes decay away with distance on both sides of interfaces. The Fuchs and Kliewer DC modes have been used in calculations involving electronpolar optical phonon interactions in layered semiconductor quantum well stmctures [9] and the theoretical results were compared with the corresponding results emerging

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from the bulk phonon model in which the quantum well electrons interact with the bulk phonons of one of the quantum well materials. It has been found that the Fuchs and Kliewer modes give rise to results exhibiting a better agreement with experimental results than do those emerging from the use of bulk phonons instead. This apparent success of the Fuchs and Kliewer theory should be contrasted with their failure when used to explain Raman scattering data. It has been found [10] that this theory failed to provide the correct interpretation of the Raman spectra from layered structures. In particular, the theory predicted the wrong symmetry of the confined modes identified in Raman scattering measurements [10]. It can thus be said that the Fuchs-Kliewer DC theory provides an adequate description of the phenomena in which individual separate modes do not play the key role but, rather, it is the total contribution from the entire set of allowed modes that is of significance. In the opposite case where single mode processes are observed, for example in Raman scattering, the Fuchs-Kliewer theory does not, in general, provide a reliable basis for comparison with experiment. It has been suggested [10] that the conflicting roles played by the Fuchs-Kliewer theory in different physical contexts is due to employing macroscopic electromagnetic boundary conditions in the theory [8]. For confined modes such a step has the effect of imposing a zero electric potential at the interfaces with no restriction imposed on the mechanical field. Because the DC model does not incorporate any spatial dispersion effects, the mechanical equations of motion do not include any space derivatives of the ionic displacement field and so no mechanical boundary conditions need be specified. This is the reason why in the DC model the mechanical field is directly dependent on the electromagnetic field which is subject to the familiar electromagnetic boundary conditions. On the other hand, it is physically obvious that at the microscopic level the mechanical motion of the atoms and ions at interfaces between different materials must differ from their motion away from these interfaces. At the continuum level, the influence of the interface must appear as boundary conditions imposed on the corresponding mechanical field. It turns out that these features can be taken into account by introducing spatial dispersion into the mechanical field equations [11] which then become differential equations and so have associated boundary conditions. This step puts the electromagnetic and mechanical fields in a polar medium on an equal footing and it also renders the model internally self-consistent and more advanced than the DC model. Because of the role played by spatial dispersion in this model it is appropriate to refer to it at this stage as the dispersive continuum model. As we explain later, when the dispersive continuum model is applied to heterostructures we obtain vibration PO modes which are, in general, a linear combination (hybrid) of longitudinal, transverse and interface-like solutions of the wave equation. This version of the dispersive continuum model has been referred to as the hybrid model. The dispersive continuum model was initially applied to the GaAs/AlAs system [12-14] to evaluate the vibrational modes. This was followed by evaluations (based on the hybrid model) for electron-polar optical phonon interactions in quantum wells [15] and in the analysis of Raman spectra in GaAs/AlAs superlattices [16]. The results of these calculations turned out to be in very good agreement with the results of fully microscopic analyses of the PO phonons in GaAs/AlAs heterostructures [17].

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As we discussed at the outset, the general aim of the continuum theories is not just the enumeration of the vibrational modes, the derivation of their dispersion relations and the specification of their spatial distributions. In the context of semiconductor heterostructures the primary concern must be quantifying the carrier interactions with these modes, which is of importance for an adequate description of the performance of optoelectronic devices. For these reasons, both the carriers and the lattice vibrations need to be treated quantum mechanically. A rigorous quantization procedure for the PO vibrations using the DC model has already been developed [18], but there is need to extend the treatment to include the effects of the spatial dispersion in the theory, as contained in the dispersive continuum model mentioned above. In this chapter we systematize the theory underlying the dispersive continuum model and apply it to describe the lattice vibrations in layered heterostructures, with particular emphasis on heterostructures based on III-V nitride materials. As we shall see, the nitride-based heterostructures have, in general, very special dynamical properties which distinguish them from the more traditional GaAs/AlAs heterostructures. The differences in properties between the two types of heterostructure are so significant that a more in-depth analysis of macroscopic lattice dynamics is required to deal correctly with the situation in nitride-based heterostructures. Another important question that we wish to address here concerns the mechanical boundary conditions. It turns out that the only rigorous self-consistent route to arrive at physically acceptable boundary conditions is to start from the microscopic mechanical equations which describe the vibrations of the separate ions and then carefully proceed to obtain the continuum limit. This is done here using the Keating model approach [19]. The general organization of this chapter is as follows. In Section 2 we present a brief description of the essential features of bulk nitride materials, particularly in relation to lattice vibrations and dielectric properties. In Section 3 we systematize a treatment of the quantum field theory of dispersive PO continuum modes in bulk nitrides, emphasizing the additional features introduced by the incorporation of spatial dispersion. This rigorous theory is presented here for the first time and applied in the context of electron-phonon interactions in the bulk. Section 4 deals with the application of the dispersive continuum theory to the situation in a heterostructure. Once more the inclusion of dispersion in the theory makes this section an original account presented here for the first time. In Section 5 we explore the microscopic origin of the continuum theory of PO phonons in heterostructures. In particular, we seek to shed some light on how the boundary conditions to be satisfied by PO modes at interfaces between different media emerge from a microscopic treatment when the continuum limit is carefully applied. In Section 6 we give a description of results emerging from the hybrid models, the double hybrid and extended hybrid models, in the context of electron-PO phonon interactions in double heterostructures and superlattices based on GaN systems. In Section 7 we highlight the existence of a sum-rule which holds whenever one is concerned with total contributions from the entire spectrum of allowed modes. This treatment too is presented here for the first time. The relationship between the dispersive continuum theory (in its hybrid model form) and the DC model is clarified. Section 8 contains a brief summary of the material presented.

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2. Polar optical phonons in bulk nitride crystals The very promising electronic and optoelectronic applications of nitride materials have fuelled many investigations of their physical properties particularly in low dimensional heterostructures. As far as the lattice dynamics of nitrides are concerned, much published research on the subject has appeared in recent years and it would be a difficult task to provide a complete review of all the current literature. In fact the number of publications continues to grow. Instead we shall aim to present here a general theoretical account of the macroscopic description of lattice vibrations in nitride-based heterostructures. We begin by outlining a brief description of the PO phonons in bulk nitride materials. The most interesting structural property of the III-V nitride materials, such as GaN, AIN, InN, etc, is their ability to crystalize into two different crystal structures with different symmetries, namely, the cubic (zinc-blende ZB) and hexagonal (wurzite WZ) structures. Both of these crystal phases of nitrides have been successfully grown using Si or GaAs substrates for the cubic nitrides and sapphire substrates for hexagonal nitrides. The cubic crystals have two atoms per unit cell, whereas the hexagonal crystals have four atoms per unit cell. Due to the cubic symmetry, the macroscopic parameters of the ZB crystals are isotropic. As a result of this the dielectric function S{(JO) is a scalar function: 2 2 CO^ — CO J

£(o}) = Soo-i

f.

(1)

Eq. (1) follows straightforwardly from the Bom-Huang model [7]. Here Soo is the high frequency dielectric constant, coi is the zone centre longitudinal optical (LO) phonon frequency which is related to the transverse optical (TO) phonon frequency CL>T by SOQCOI = Ssco^, with Ss the static dielectric constant. Substitution of the dielectric function in Eq. (1) in Maxwell's equations results in two PO phonon modes: a LO mode, whose frequency COL is given by the dispersion relation £((o) = 0, and a TO mode of frequency coj, which is given by the dispersion equation s~^(a)) = 0. There is nothing special here in the description of the properties of cubic GaN in comparison with, for example, GaAs besides the differences in the magnitudes of the dielectric constants and the values of the phonon frequencies. However, it is important to bear in mind that the difference in the numerical values of the corresponding parameters in these materials could have dramatic consequences for the electronic and optoelectronic device applications. For example, the Frohlich coupling constant and the LO phonon energy for GaN are af = 0.45 and hcoi = 92.8 meV, respectively. For GaAs we have Qf/r = 0.079 and Hco^ = 36.25 meV. The nitrides are then much more polar materials than the arsenides. As a result, the electron-PO phonon interaction in nitrides is almost an order of magnitude stronger than in GaAs. The WZ crystals exhibit a uniaxial structure and have anisotropic properties. Due to the crystal anisotropy, the mechanical vibrations in which the atoms (ions) are displaced parallel to the c-axis have the frequencies COL (COT ) for the LO (TO) phonons and for the vibrations in which the atomic displacements are perpendicular to the c-axis

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the corresponding frequencies are (JOIX_ {COTI) for the LO (TO) phonons. As a result the dielectric function e{(o) in the WZ crystal is a tensor function which is given by (e^{co) e^{(o) 8{a)) = 0 0

0 ex_{(o) ex_{(o) 0

0 0

\ ,

(2)

8 {(O)

with % ,..2 (O"- — (O

£ ± M = £oo±^

7^,

(3)

ft;;

'r_L

,2 _ ,..2 ft;^ — ft;;'L e (ft>) = fioo - ; 2~'

(4)

where foo± and Soo are the corresponding components of the high frequency dielectric tensor. It is obvious that the description of the lattice vibrations using the dielectric function in Eqs. (2)-(4) in Maxwell's equations is far more complicated than in the isotropic case of cubic crystals. The bulk wurzite-type crystals (mostly dielectrics like ZnO, ZnS, CdS, etc) have long been a subject for Raman light scattering analysis. As a result, the PO phonon modes in WZ crystals have been identified and extensively investigated both theoretically and experimentally. Much of the work done in the 1960s for wurzite crystals has now become relevant to WZ nitride crystals, like GaN, AIN, InN, etc. An excellent general analysis of PO phonons in WZ crystals was carried out in [20,21]. In these works, the Bom-Huang theory [1] was modified by including the anisotropy of the LO and TO optical phonon frequencies. The main result of this analysis of long- wavelength PO lattice vibrations in WZ uniaxial crystals is the identification of two types of phonons: one is the so-called ordinary phonon and there are two others called extraordinary phonons. The ordinary wave has zero electric field E(r) = 0 (in the non-retarded limit) and the mechanical displacement vector u and polarization vector P are parallel to each other with both u and P simultaneously perpendicular to the phonon wavevector q and to the c-axis for any relative orientation of q and the c-axis. The ordinary phonons are transverse and their frequency isft>= ft^j-x given by el^ioS) = 0. Because the electric field of the ordinary phonons is zero, they do not couple to electrons. For the extraordinary wave, the electric field E is always parallel to the phonon wavevector q (again this is true only in the non-retarded limit), the mechanical displacement vector u and polarization vector P have arbitrary orientation with respect to q and the c-axis and the dielectric displacement vector D is always perpendicular to q. The frequencies of both extraordinary phonons depend on the orientation of q with respect to the c-axis. In the non-retarded limit the angular dispersion of the extraordinary phonons is given by [20]: 6 (co) cos^((9) + 6^(0)) sin^(6>) = 0,

(5)

where 0 is the angle between q and the c-axis. This equation has two roots, in general.

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which correspond to the two extraordinary phonon modes: ^1,2 = I [(^i + ^ r i ) cos^(6>) + (0)1^ + col ) sin^(^w(r, 0 + yi2E(r, t) - vlv (V • w(r, t)) + vjv x (V x w(r, 0 ) • (26) Substituting the Hamiltonian density given in Eq. (21) into Eq. (23) and using the first Maxwell's equation in Eq. (25) as well as Eq. (26) in the non-retarded limit (c -> oo, A = 0 and H = 0) we obtain H = \ / [ i b ^ - w - w - vlV • (w(V . w)) - v^V • (w X (V X w))] d r.

(27)

In deriving the above equation we have also used the relations [33]: V . (w(vlV ' w)) = vl(W . w)2 + w • V(i;2 V • w), V • (w X (vjV X w)) = vj(V X w)^ + w • V X (u|V x w).

(28)

Within the bounds of isotropic continuum theory, the Hamiltonian in Eq. (27) is an exact result obtained taking into account the bulk dispersion of the optical vibrations. The interesting point about this result is that the integration of the last two terms in Eq. (27) gives exactly zero. To see this we need to use Gauss's theorem / V • Fd^r = ^^ F • da and the condition that F ^- 0 at the integration surface S which is taken at infinity where all the fields are zero. The final result for the Hamiltonian is H=\

( [ii;2(r, 0 - w(r, t) • w(r, r)]

d\.

(29)

Since the above expression contains not only w(r, 0 but also its time derivatives, w(r, t) and w(r, t), it is essential to work in reciprocal (Fourier) space. This is also important for the subsequent solution of the field equations. In the case of bulk homogeneous systems we use three dimensional Fourier transforms for all the fields which we denote as F(r, t) in the form F(r,r) = - i - r/*F(q)^'(^--"«''^j3^ + f

¥Hq)e-'^'^'-''''^d^q

(30)

Using Eq. (30) we obtain for the Hamiltonian H = - ^

j a>>(q) • y^*iq)d'q.

(31)

The components of the phonon wavevector q are quasi-continuous and take multiple values of the steps A^^ = In/La, a = x,y,z where Vb = L^LyL^ is the quantization

Optical phonon confinement in nitride-based heterostructures

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397

volume of the system. Thus we can apply Bom-von Karman substitutions (27r)-

j d'q 5 ] ,

5(q - qO ^=^ (^^Q^Q''

(32)

and present the Hamiltonian in Eq. (31) in the form H = ^y]a>^w(q).w*(q).

(33)

The Hamiltonian in Eq. (33) has exactly the same form as the Hamiltonian in Eq. (6.23) in [18] obtained for bulk non-dispersive homogeneous polar material. Of course, the vibrational frequencies coq are different in the cases of dispersive and nondispersive media. The fact that the total Hamiltonian of the dispersive system does not contain explicitly the dispersion characteristics of the medium {vi and fr) is a reflection of the physical meaning of spatial dispersion. In general, the spatial dispersion is responsible for the redistribution of vibrational energy between all allowed modes, but it does not affect the total energy of all the modes within the medium. The quantization of this Hamiltonian and the normalization condition for the mechanical displacement mode amplitude can be obtained by applying the following linear transformations w(q) = K e ( q ) + « n ( q ) ] w;o(q), w*(q) = K e ( q ) - /n(q)] w;*(q). Imposing the mode amplitude normalization condition in the form w^o(q)-it;o*(q) = ^ ,

(35)

we obtain the Hamiltonian

^ = iEK2'(q) + n2(q)].

(36)

q

This is the Hamiltonian for a system of independent classical oscillators and its quantization follows simply by the conversion of j2(q) and n(q) into the quantummechanical position-like and momentum-like operators + u;*(q )aHq )^-'^^ ''-^^ ^>]. ' ^

(64)

4.3. Electron-phonon interaction hamiltonian in layered heterosystems Our aim here is to derive the interaction Hamiltonian Heir, t) = ~^0(r, 0- To this end it is necessary to obtain the Coulomb potential operator 0(r, t). There is a fundamental

Optical phonon confinement in nitride-based heterostructures Ch. 11

403

difference between solving this problem for the case of a polar inhomogeneous layered system and solving it for the case of a bulk polar homogeneous medium. As we have already pointed out in the case of a bulk homogeneous system, the problem of evaluating the lattice vibrational modes can be solved as a pure electrodynamical problem. This was possible because we were able to derive an explicit expression for the dielectric function of the dispersive medium which is given by Eq. (48). In turn, this equation was derived using the field equation Eq. (46) for the Fourier amplitudes, which provides a relation linking Wx(q) to Ex(q). This relation shows that the connection between Wx(q) and Ex(q) is local, which means that the mechanical displacement Wx(q) at any point q of the Fourier space is expressed in terms of the electric field Ex(q) at the same point q. This is not the case for the inhomogeneous heterosystem which possesses interface boundaries. In this case the relation between Wx(q) and Ex(q) is non-local, i.e. the displacement field w^ at a given point z is determined by the electric field values E^ evaluated at every point z in real space. In order to see this explicitly, we need to decompose all the fields in Eq. (26) into longitudinal and transverse parts, as in Eqs. (44) and (45) and take the Fourier transform of the equation obtained. This gives rise to the relation ^2 1 2 2 2 2 2 Ex(q,z) = w,(q,z), (X = L,7). (65) Yn We see that Wx(q , z) is expressible in terms of ^x{q , z) by an integral relation. This is clearly different from what we had in Eq. (46) for the inhomogeneous infinite medium. The non-local form of the relation between Wx(q , z) and EA(q , z) does not permit one to introduce the dielectric function for the inhomogeneous system under consideration. As a result, the problem of calculating the lattice vibrational modes can no longer be presented as a pure electrodynamical problem. The solution of the mechanical displacement field equation is required in the first instance in order to determine the corresponding electric field modes. This problem will be considered in the next section. It will be shown that the longitudinal (A = L) and transverse {k = T) lattice vibrations are governed by the wavevector Q with components (q ,qx) where the confinement wavevector qx is defined by 2

ql =

2 2

2

5

(66)

.

Using Eq. (66) we can present Eq. (65) in the following form -,-1/2

,

1 8ex(a)a , Q) wx(q ,2) + -^Ux^ + ^ j W x ( q , z ) , (67) Ex(q , z) = 47r dcol where the derivative in thefirstterm should be taken at the frequency satisfying 4 =col,=col-vlQ\ (68) where Q^ = q^ -^ ql- In writing Eq. (67) we have formally introduced the following notation col -^] ^^IQ^

s,{

Ch. 11

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N.A. Zakhleniuk et al.

It should be emphasised that the expression in Eq. (69) is not the dielectric function of the inhomogeneous heterosystem. This is just a formal expression written here in a form similar to the dispersive dielectric function of the bulk polar medium given in Eq. (48). The reason for introducing ex(coq , Q) in Eq. (69) is that it allows a straightforward transition in Eq. (67) to the case of the bulk homogeneous medium. In this case d^/dz^ -> —q^ = -ql and, on making use of the relation Q^ = q^ -{-q^ = q^^ the last term in Eq. (67) becomes identical to the expression from Eq. (46) for the bulk homogeneous system. It follows from Eq. (67) that both the longitudinal EL(q , z) and the transverse ET(q , z) fields are not equal to zero for the inhomogeneous system (in the case of the bulk homogeneous system ET(q , z) = 0, see Eq. (49)). The explicit forms of these fields are as follows -1/2

1 a^x(^q,Q) EL(q ,z) = 80.2 An ET(q , z) = — U r + ^

WL(q , z) +

K^'^S)

WL(q ,z), (70)

) ^T(q , z).

In the polar medium the electric fields are created by the mechanical lattice displacements and, therefore, the electric fields are zero if the displacements are zero. Note that the opposite is not necessarily true. For example, in the bulk homogeneous medium E j = 0 as can be seen from Eqs. (46), (49) and (51). In the case of an inhomogeneous medium the transverse electric field ET(q , z) is not equal to zero precisely because the dispersion of the lattice vibrations is taken into account (vj 7«^ 0). If the dispersion is ignored, then for both homogeneous and inhomogeneous media we h a v e E T ( q , z) = 0. The Coulomb potential 0 ( q , z ) is obtained using Maxwell's equation V x E ( q , z ) = 0, which gives E(q , z) = - V 0 ( q , z ) . The Fourier amplitudes are such that £ (q , z ) = -iq 0 ( q , z ) ; £^(q , z ) = -9(q .z)l^z where E (q , z ) = q • E ( q ,z)lq . Using Eqs. (64) and (70) we obtain the required expression for the interaction Hamiltonian operator for an arbitrary polar layered heterosystem in the form -1/2

1 a£x(<Wq , Q )

^.(r,0 = -Ao/ i E

yJ^hXD^

%co\

An

'WL

(q , z , x )

2 2

-

V

(71)

^^fAa)iix(q,z,x)

The subscript L in the first term indicates that the derivative is taken at tWq = o),'qL (see Eq. (68)). Here we have introduced the following notation Wx(q , z, X) = «;ox(q . z)a(q )e'*'' "-'"'- " - wl^aHq )e-'/(q , z) can be found using Eqs. (81) and (93). We have Di(q , z) = e (A/^^ ' + Bie'"^') - ieAAje"^' - Bie'"^'),

(94)

where we have introduced new constants A/ and B/ instead of A^ and Bx such that Ai = AL -h e(cOq)AT and Bj = Bi+ s{a)q )BT. Because the equations of motion are linear and homogeneous, the solutions of these equations contain arbitrary multiplication factors which we denote as C^o and CSQ for the p- and s-polarized, respectively. Since the boundary conditions give only the ratios between the constants in the solutions without specifying the constants themselves, we can put Ci = Cpo, CTS = Qo» ^ L = kiCpo, KT = kfCpo, AI = ajCpo, Bj = bjCpo and Bjs = ^^Qo- The constants ki^kr^ai, bi and bs should be found from the boundary conditions and the constants C^o and C^o are found from the normalization condition in Eq. (62). The s- and p-polarized solutions are decoupled from each other, so the s- and p-modes are normalized separately.

Optical phonon confinement in nitride-based heterostructures

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Using Eq. (93) we obtain for the total field modes w\,'\q^ , z) = G['l{q , z) + G^^^iq , z) -

^'^ ^(^q ){0)\

,M) wi;\q,z)

=

(95)

G'o'i(q,z), (Or

7(P)

-0)^)

(s),

Yn

i(p)

"^Gl^li^^z)^

e{coQ )

Doi(q ,z),

(96)

(P)/

(97) D^o^(q,z)=4nynG^^liq,z), Here we have used the notation F^^'^^q , z) = F^^'^Hq , z)/C(s,p)o for all the above modes. The above expressions for the total fields represent a general solution for the vibrational modes in an arbitrary polar layered heterostructure. These expressions are also needed in the boundary conditions in order to fix the numerical coefficients in Eqs. (86), (87) and (94).This is because the boundary conditions are imposed on the total fields rather than their longitudinal or transverse components. 4.5. An explicit form of the interaction Hamiltonian and the electron-phonon scattering rate It is important from a practical point of view, to derive the explicit form of the interaction Hamiltonian using the solution obtained above for w(q , z) in Eqs. (83) and (95). We obtain from Eq. (71) the interaction Hamiltonian for the vibrational mode specified by q andcoq

HArj) =

-ij:^^^^ (q.z)-

(q,^)

Yn

^(^q)(^q

-Ci>\)

m)e'''^-^'-HC

(98)

^^

where the interaction parameter ap{q ) is otp{q ) =

Ine'^ 0)] Ao o)}q

V^oo

^s /

^ q 0 in the mechanical field equation, this would mean a change in the type of the equation, i.e. a transition from the differential equation to an algebraic equation. Obviously, the solution of this non-dispersive algebraic equation (from Eq. (26) with v\ = 0 and i;^ = 0) and the solution obtained as a limit of the general solution of the differential equation (Eq. (26) with vl ^ 0 and v^ 92^ 0) assuming i;^ -> 0 and Vj ~> 0, are, in general, completely different. They may coinside only in very special and particular cases. This is why one should treat with caution any theoretical analysis in the literature which considers the DC model results as a limit (vf -^ 0 and Vj -> 0) of the dispersive theory. The DC theory of lattice vibrations is simpler than the dispersive theory which we considered here and it is very useful for applications as well. For example, we have considered here materials which have a cubic synmietry. The dispersive theory of nitride-based materials with wurzite synmietry has yet to be developed. The main problem with wurzite bulk materials and heterostructures is the anisotropy of the frequency spectrum [20]. Our present theory sets out a general method for quantizing the vibrational dispersive modes and, in this respect, it will be of direct importance when applying the theory to bulk materials and heterostructures with wurzite symmetry. At the same time, the DC model has been applied very recently to the study of anisotropy effects on polar optical phonons in quantum wells and superlattices based on GaN/AlN wurzite materials and also to the analysis of the electron scattering rate due to the interaction with PO phonons in these heterostructures [44,45]. These results will also be very useful for the future development of a self-consistent dispersive theory of phonon confinement in wurzite heterosystems. 5. Microscopic theory and continuum models We have emphasized that a continuum model which is expected to accurately reflect the conditions at an interface must include dispersion — the variation of frequency with wavevector. Fortunately the acoustic-mode theory automatically has dispersion built in, leading to the familiar mechanical boundary conditions (BCs) of the continuity of both amplitude and stress (see, for example, [46]). Since a rigorous dispersive theory for optical modes, applicable to heterostructures as in Section 4, has not previously been available, the question of correct mechanical BCs for optical modes has remained unresolved. This section aims to provide an account of work exploring the microscopic origin of the continuum theory as applicable to lattice vibrations in polar media and consider the problem of the optical boundary conditions that are required in the context of heterostructures. It is by no means obvious that a continuum model can ever be adequate to describe optical modes in an inhomogeneous solid containing spatially abrupt interfaces. It would seem that any description of ionic motion in terms of continuous envelope functions obeying a second-order differential equation where reduced mass and force constants change discontinuously cannot possibly provide an adequate description. Using the theory of microscopic lattice dynamics is in principle exact and it avoids the problem of BCs, though it is admittedly computer-intensive but, as we emphasized at the outset.

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N.A. Zakhleniuk et al

100 - ]

80 H 60 40 H

20 A

o4 -20 4 20

40

60

20

1^ 40

1^ 60

"T" 80

100

120

1^ 80

100

I 120

0.12 - i

0.10 A 0.08 A 0.06 4 0.04 4 0.02 4 0.00 4

-0.02

4

Fig. 2. Quasicontinuum functions: (a) showing the displacement of one atom; (b) showing the variation of some property across an interface.

there are good reasons for constructing a continuum theory. The same perception applies to the use of envelope-function theory for electrons, yet there is good evidence that it works extremely well. Examples of envelope functions for an ionic lattice in a bulk medium and at an interface are shown in Fig. 2. In fact, an exact envelope-function formalism can be developed to describe electron states [47]. The same is true for lattice vibrations as [48-50] have shown. In this case it is clear that any interpolation of ionic motion should not involve variations more rapid than the ionic spacing, which means restricting the envelope function to wavevectors within the first Brillouin zone. If this is done then it can be exactly and uniquely related to the ionic motion. The physical space of such functions is known as the quasicontinuum. Thus, quasicontinuum theory is capable of describing exactly the motion of ions in terms of envelope functions whose wavevectors are restricted to the first Brillouin zone. That being the case, continuum (or more strictly, quasicontinuum)

Optical phonon confinement in nitride-based heterostructures

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413

theory, being in principle as accurate as microscopic theory, is much more versatile and more generally useful, provided that valid mechanical BCs can be deduced. Certainly, there need be no qualms about its validity. The classic theory of long-wavelength optical modes in polar material of Bom and Huang [7] does not include dispersion and so could not provide mechanical BCs. Fortunately, in the case of the most investigated system — AlAs/GaAs — the large difference of optical-mode frequencies suggested that the true mechanical BCs could be approximated by entailing that the amplitude vanish at the interface (u = 0), and this plausible approximation received support from the results of Raman scattering experiments [51-54] and from numerical models [55]. Combining this condition with the classic electrical BCs, continuity of both tangential electric field and normal electric displacement, led to the necessity for the optical modes to become hybrids of longitudinally-polarized (LO), transversely-polarized (TO) and polariton-like interface modes [14,56,57]. But the mechanical boundary condition u = 0 [14,56,57] could not be used for systems such as AlxGai_xAs, with x small, in which the frequency bands overlap. There were also earlier attempts to model mechanical BCs in terms of hydrodynamic BCs [11] in the context of Raman scattering theory or acoustic-like BCs [2,58]. However, investigations of this system have had to rely on the heavily numerical calculation of the microscopic lattice dynamics [59]. More recently, the increasing interest in the AlN/GaN system, where the frequency bands overlap, has added urgency to the problem of mechanical BCs. Other systems also pose problems. For example, the interface in the InAs/GaSb system can have the molecular character of InSb or GaAs, quite different from either binary, implying the existence of quite novel mechanical BCs [60,61] involving delta-function-like terms in the reduced mass of the ions and zone-centre force constants. A further characteristic of optical modes that make their mechanical BCs different from those of acoustic modes is that the optical stress tensor is not symmetric [61]. In the case of acoustic modes the stress tensor is symmetric as a result of the requirement for rotational invariance, but no such constraint applies for optical modes. As a result, optical-mode elasticity in zinc-blende materials requires 4 independent elastic constants instead of 3. This extra elastic constant does not play a role in a homogeneous material, but has to be taken into account in determining the boundary conditions. It is clear that a continuum theory of optical-mode elasticity had to be significantly more complex than the equivalent for acoustic modes. In the next section we give the results of a three-dimensional analysis of optical-mode elasticity [62] which, although it contains simplifications for clarity's sake, successfully describes the principal features that makes optical-mode elasticity unique. 5.1. Long-wavelength vibrations In order to focus on the mechanical aspects we ignore Coulomb effects and, for simplicity and convenience, take the two-parameter Keating potential for the zinc-blende lattice to describe the lattice dynamics [19]. This potential takes into account only the nearest-neighbour interaction via a central-force constant a and a second-neighbour

414

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interaction via a non-central force constant p. Quasicontinuum theory is used to describe the discrete displacements of the atoms in terms of envelope functions and equations of motion for the two atoms A and B in the unit cell are derived from the Lagrangian. These equations are then converted to equations for acoustic displacement U and optical displacement u, where: (102) and m is the atomic mass and M is the total mass. This procedure entails that we extend the envelope function description to the mass parameters and the force constants in order to take account of their variation at an interface. A commonly used simplification is to assume that the force constants of different Group IV and III-V semiconductors do not vary significantly and that the parameter principally responsible for the difference in zone-centre optical-mode frequencies is the reduced mass. This simplification — the mass approximation — is assumed here. The equations are actually coupled, each involving acoustic and optical displacements, but they can be decoupled in the longwavelength limit. When this is done the equation of motion for acoustic modes becomes: 0) pUa

=

—(CaXPti^p,fM),Xy

where p is the total-mass density, f/^,^ = dU^/dx^, A = 1 provided the subscripts occur in matched pairs, e.g. xxyy, xyxy, etc., and is zero otherwise and |£| = 1 provided the subscripts are all different, and zero otherwise. The nearest-neighbour separation is y/3a and the force constant P = (fi^ + P^)/2, i.e. the average of the force constants associated with each type of ion. Explicit results are:

r

- . __^±^ 4a

C

- c. = ^ " ^

^xyxy

— ^xyyx

(104)

afi

— ^44

a((x-^P)' which are the elastic constants derived by Keating [19]. The equation of motion for optical vibrations is:

a-\-B + ^ak^fifi +

a-fi

1

^afi^^x)

Cax^^ = ^ ( - ^ ) [(« - P)Kfix^ + Pi28^^Sx^ + 8^xh^ + 8^^8px)]

^' -

-^(^aX^fin

(a - ^f + ^an^^k)

iTf^^

~ ^(xx)(^aphn

+ ^otn^fik).

(105)

Optical phonon confinement in nitride-based hetewstructures

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415

where /x is the reduced mass, pr is the reduced-mass density and p' = ^ -{- rAyS, The optical elastic tensor has the symmetry c^x^^ = c^^ax but, unhke the acoustic tensor, there is no rotational invariance, i.e. c^x^^j^ ^ Cax^^. Explicit results are:

_ / ^ \ ct + 3p _

^

_ (j^\ ^ _ ^ (106) _ /ju X a 4 ^ ^ _ (a - pf ''^y^y -\M) Aa aco^M ' <M/ 4a

^'

{ot - P)2

Sa

aco^M

The tensor c^^ reduces to a straightforward force- constant in homogeneous material:

For a crystal inhomogeneous in the z-direction, the non-zero elements are:

__ a + P

a + /6

(^)...-«-'' 4a^ 8a a + fi a + 3)g / / x x ^, ,2-. ^^ 4a3 - ^ < ^ ) - ^ < - > ^ ' - ^ -

a- P C^y -

^3,^ -

^^2

^'^

5.2. Homogeneous material In what follows, it will be convenient to recast Eqs. (104) and (105) explicitly in terms of the non-zero elastic coefficients:

+ [Cl4(U,,y 4- Uy,,)ly + [Cl4(U,,Z + ^Z,.)],., CO^PrU,^ = CxxUx

H- CjcyUy + C;,^^^ + [CnUx,x

+ Cl2(W3;,>; +

+ kfll4Wjc,j +

-h//C (135)

Optical phonon confinement in nitride-based heterostructures

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425

Hereof = 47TPi((jol.-ojli),a/ = col^-vl^iq^ + ql^), fs = H-3sin(^z.i^)/^Li^ + 4sm'^(qiid/2) coth(qd/2)/qd + (q/qiO^U + sin(^£iJ)/^£i J ] and all the other parameters are those for material 1 as defined in Section 4. For the antisymmetric modes in material 1 the dispersion relation is ^L\Sl

-'(¥)[|-(f)-]—(T)=«'

(136)

and the corresponding Coulomb potential is given by ,(x,2) = siniqiiz)

E

qii

XPiVoicofAj

-

qiisi

cos(qd/2)

q cosh(qd/2)

sinh(^z) |z| q.^Li > a,

^'^^''^^gna)cos(^J/2)^-^(l^'-^/2) qsi +HC

\z\> (137)

fA = l-3sin(qud)qLid

+

4cos^iqud/2)tSinh{qd/2)/qd

+ (q/qu)^ [1 - sin(^z.i^)/^ii^] • Fig. 5 shows the dispersion of the double hybrid modes due to material 1. The curves form straight lines joining the frequency values where the mechanical wave fits the quantum well width at small wavevector to frequency values where the Coulomb potential wave fit the quantum well width at large wavevector [15]. The value (and the boundary condition that produces it) at small wavevector is the same as in the hydrodynamic model [11] while the value at large wavevector is that given by the

0.98 h

0.96 h

0.94

0.92

Fig. 5. The frequencies against qd of the double hybrid modes due to material 1, the well material, for a GaAs/AlAs double heterostructure. The dashed curves are the symmetric modes and the solid curves are the antisymmetric modes. The dotted curves are the DC interface phonons for the same system.

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N.A. Zakhleniuk et al.

condition used in the DC model [15]. The only deviation from this is where the curves cross a DC interface phonon dispersion of the same synmietry where anti-crossings occur [15]. The modes due to material 2 are given in terms of an incoming amplitude, ALI^ of the Coulomb potential wave which is normalized in the same way as a bulk wave (see Section 4.2), thus [65] hej 42 (138) 2p2Vo2Coiq^-hql2)' where co^ = C0I2 ~ '^lii^'^ + ^L2)- Hence, after applying the boundary conditions, the electric potential is given by y+e

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From Eq. (139) we may find reflection and transmission coefficients [65]. For brevity the scattering rates are not displayed or discussed here since a full account can be found in [15] [65]. The main conclusion was that the hybrid model provides results for the scattering rates which are very close to those obtained from the DC model. The agreement is attributed to the negligible effects of spatial dispersion in the GaAs/AlAs system [15]. This situation will be contrasted with that in the GaN/AlN system, which we discuss next. 6.3. The extended hybrid model We now apply the hybrid model to the case of GaN/AlN heterostructures. The theory in this case becomes quite involved and it is more instructive to provide an outline description of the essential steps. For further details the reader is referred to [66,67]. First we must determine the bulk dispersion curves. For this we have taken the frequencies at the F and X points from [68] and fitted a parabolic negative dispersion relation. The appropriate parameters are shown in Table 2 and the corresponding bulk dispersion curves are presented in Fig. 6. Note that this step of fixing the bulk dispersion is essential, but need not be accurate. The parabolic approximation is only made here because it is consistent with the order of the equation of motion. Also, some papers display the TO branch of GaN exhibiting a positive dispersion [33,69]. Again this feature does not affect the overall essential structure of the solution.

Optical phonon confinement in nitride-based heterostructures

Ch. 11

All

Table 2. The parameters associated with bulk GaN and AIN phonons assuming a parabolic dispersion. The values at the T and X points are taken from [68]. Material

GaN

VL (ms"') 10600

VT

(ms'O

2080

Symmetry Point

hcDL (meV)

h bar COT (meV)

r r

92.76 79.24 114.08 86.92

69.69 69.19 83.08 76.14

X

AIN

16000

7380

X

It turns out that we cannot ignore any component of the solution as done in the double hybrid case. Hence, in every region we must include ionic displacements for the LO, TO and interface-like (IF) components with the associated electric and electric displacement fields. If the frequency of the mode lies outside the bulk dispersion band of a particular component of the solution, the wavevector becomes imaginary and the solution evanescent. For example, if coij(X) < co < coijir) then kij is real and a propagating solution is taken but if COL,T(X) > co > coLj{T),kij becomes imaginary and an evanescent solution should be included for that component. If the frequency lies above the bulk dispersion curve, the nature of the solution is determined automatically through the dispersion relation; for a frequency lying below the bulk dispersion curve an evanescent solution must be included artificially, i.e. by writing a decaying or growing exponential rather than a plane wave solution. The extended hybrid model demands fixing six boundary conditions at each interface. Four of these are provided by the electromagnetic boundary conditions and the continuity of the perpendicular and parallel components of the relative displacement at each interface. In the preceding section we have seen how microscopic theory was used to try to find the two additional boundary conditions from the mechanical field equation. This work is still ongoing, so in order to investigate the importance of these boundary conditions we will consider two separate possibilities. It has been shown that the two

q(7t/a^) Fig. 6. The bulk dispersion curves using a parabolic approximation and the parameters in Table 2 for GaN and AIN for the entire Brillouin zone. The shaded region is where the reststrahl bands overlap.

Ch. 11

428

NA. Zakhleniuk et al.

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