Functional structure design of new

high-performance materials via atomic

design and defect engineering (ADDE)

edited by

Prof. David Rafaja

Imprint

Copyright: Technische Universität Bergakademie Freiberg, Spitzentechnologiecluster ADDE

Publishing: SAXONIA Standortentwicklungs- und -verwaltungsgesellschaft mbH

Technical editing: Alexander Eisenblätter, Dr. Uta Rensch

Layout: Alexander Eisenblätter, Susann Müller

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No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recpording or otherwise, without written permission from the Publisher.

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ISBN 978-3-934409-68-2

Preface

Modern industry requires instantly new materials with tailored properties and energy efficient technologies for their production. Technical University Bergakademie Freiberg is one of the European universities, which are permanently active both in the materials science and engi-neering and in the development of modern technologies for the advanced materials produc-tion. Based on this long-time tradition of the Freiberg University, the development of modern high-performance materials with high functionality and efficiency for applications in the fields of communication, mobility, energy and environment was naturally the main goal of the Centre of Excellence “Functional structure design of new high-performance materials via atomic de-sign and defect engineering (ADDE)”, which was established in 2009 and funded until the end of 2014 by the European Regional Development Fund (ERDF) and by the Ministry of Science and Art of Saxony.

The main idea of the Cluster of Excellence ADDE was to control the crystal structure and mi-crostructure defects in order to tailor the properties of materials. This book presents an over-view of the results of 19 interdisciplinary projects, which dealt with the generation and manip-ulation of desired microstructure features in functionalised materials like metastable phases, controlled phase decomposition, precipitation and nano-sized structures, or with the elimina-tion of unwanted defects in large crystals intended for special electronic applications like for-eign atoms or dislocations. The main aim of the Cluster of Excellence ADDE was to understand the interactions between individual crystal defects and microstructure features as a first step towards targeted defect engineering. The choice of the materials was stimulated by the topics, which are established at the TU Bergakademie Freiberg and at the principal cooperation part-ners, which were the Helmholtz Centre Dresden Rossendorf and the Leibnitz Institute for Solid State and Materials Research Dresden. As the education and training of young professionals and academics for the Saxonian industry and research was one of the central tasks of the Centre of Excellence ADDE, a close cooperation with the local industry played a very important role.

The contributions in this book are divided into four groups. The first one is devoted to the technologies for production of thin silicon solar cells. It comprises the growth and processing of silicon ingots, the methods for their characterisation and the technologies for recycling of sawing slurries. In the second group of the contributions, selected materials for microelectron-ics, information storage and sensor technology are presented like the wide-gap semiconductor GaN, the dielectrics TiO2, SrTiO3, ZrO2 and TaZrOx, the azulene and anthraquinone structures for information storage and the conductive coordination polymers for transducers in sensor applications. In the third part of this book, protective coatings for wear reduction and corrosion protection are discussed with a special focus on the use of metastable phases. The last group of the contributions is dedicated to the mechanical properties and thermodynamics of light metal alloys.

David Rafaja November 2015Coordinator of the ADDE project

Contents

TECHNOLOGIES FOR PRODUCTION OF SILICON SOLAR CELLS

Ultra-short time processing of silicon solar cellsS. Prucnal, F. L. Bregolin, K. Krockert, H. J. Möller, W. Skorupa

Growth and characterization of multi-crystalline silicon ingotsE. Schmid, C. Funke, Th. Behm, S. Würzner, O. Pätzold, V. Galindo, M. Stelter, H. J. Möller

Experimental and numerical investigations of the formation of surface defects during machining of silicon wafersM. Budnitzki, T. Behm, M. Kuna, H. J. Möller

Development of a new process for recycling of used sawing slurries from solar industryI. Nitzbon, A. Obst, U. Šingliar, M. Bertau

MATERIALS FOR MICROELECTRONICS AND SENSOR TECHNOLOGY

Defect engineering in GaN layers grown by hydride vapor phase epitaxyG. Lukin, O. Pätzold, M. Stelter, M. Barchuk, D. Rafaja, C. Röder, J. Kortus

Strontium titanate – Breaking the symmetryH. Stöcker, J. Hanzig, F. Hanzig, M. Zschornak, E. Mehner, S. Jachalke, D. C. Meyer

Atomic layer deposition of dielectric thin films in the ternary system TiO2-SrTiO3B. Abendroth, S. Rentrop, W. Münchgesang, H. Stöcker, J. Rensberg, C. Ronning, S. Gemming, D. C. Meyer

Synthesis and characterization of Ge nanocrystals embedded in high-k materials for alternative non-volatile memory devicesD. Lehninger, P. Seidel, M. Geyer, F. Schneider, A. Schmid, V. Klemm, D. Rafaja, J. Heitmann

Novel molecular materials for information storage – Synthesis, electronic properties and electrode designM. Mazik, E. Weber, N. Seidel, S. Förster, E. Kroke, J. Wagler, A. Kämpfe, J. Kortus, T. Hahn, S. Liebing, Y. Joseph, R. Dittrich

Development of an electrically conductive coordination polymer based transducer for sensor applicationsM. Günthel, J. Hübscher, F. Katzsch, R. Dittrich, Y. Joseph, E. Weber, F. Mertens

6

26

42

64

78

100

118

134

146

166

PROTECTIVE COATINGS AND HARD MATERIALS

On the thermal stability of nanoscaled Cr/ta-C multilayersU. Ratayski, Ch. Schimpf, T. Schucknecht, U. Mühle, C. Baehtz, M. Leonhardt, H.-J. Scheibe, D. Rafaja

Defect engineering in Ti-Al-N based coatings via energetic particle bombardment during cathodic arc evaporationCh. Wüstefeld, M. Motylenko, D. Rafaja, C. Michotte, Ch. Czettl

Experimental and numerical assessment of protective coatings deposited by high velocity oxygen fuel flame spraying: Spraying process and thermo-mechanical behaviorS. Roth, M. Hoffmann, C. Skupsch, M. Kuna, H. Biermann, H. Chaves

Synthesis, properties and potential applications of rocksalt-type aluminium nitride (rs-AlN)K. Keller, M. R. Schwarz, S. Schmerler, E. Kroke, G. Heide, D. Rafaja, J. Kortus

MECHANICAL PROPERTIES AND THERMODYNAMICS OF LIGHT METAL ALLOYS

Influence of multi-pass roll-bonding on the mechanical properties of twin roll cast magnesium sheetsF. Schwarz, St. Reichelt, L. Krüger, R. Kawalla

Mg-Al composite wiresE. Knauer, J. Freudenberger, A. Kauffmann, L. Schultz

A unified approach to identify material properties from small punch test experimentsM. Abendroth

Atomistic modeling of defects in the framework of the modified embedded-atom methodS. Groh

Thermodynamic investigations in the ternary Al-Ti-Cr systemM. Kriegel, O. Fabrichnaya, D. Heger, D. Chmelik, D. Rafaja, H. J. Seifert

List of authors

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278

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306

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Defect engineering in GaN layers grown by hydride vapor phase epitaxy

G. Lukin,1 O. Pätzold,1 M. Stelter,1 M. Barchuk,2 D. Rafaja,2 C. Röder 3 and J. Kortus 3

1 TU Bergakademie Freiberg, Institute of Nonferrous Metallurgy and Purest Materials, Leipziger Str. 34, 09599 Freiberg, Germany

2 TU Bergakademie Freiberg, Institute of Materials Science, Gustav-Zeuner-Str. 5, 09599 Freiberg, Germany

3 TU Bergakademie Freiberg, Institute of Theoretical Physics, Leipziger Str. 23, 09599 Freiberg, Germany

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AbstractThe impact of kinetic effects on the homoepitaxial and heteroepitaxial growth of GaN by Hydride Vapor Phase Epitaxy (HVPE) has been studied. It was shown that kinetically limited growth conditions strongly affect the defect formation and stress evolution in GaN, and can be used as an in-situ method of defect engineering in order to control the material properties by HVPE. Application of kinetically limited growth during the homoepitaxy of GaN induces the generation of inverse pyramids (V-pits), which affect the threading dislocation density in deposited layers. The heteroepitaxial, kinetically limited growth of GaN in the temperature range of 750 - 900 °C resulted in a novel approach to deposit GaN layers directly on sapphire substrates by HVPE. The two-step deposition process includes the growth of GaN nucleation layers at in- termediate temperatures (750 - 900 °C) and a subsequent high-temperature overgrowth. The results of first experiments demonstrate the possibility to grow 10 - 15 µm thick, crack-free GaN layers of high crystalline quality direct on sapphire. Furthermore, the correlation between the residual stress and the density of threading dislocations was investigated. It was found that the increase of the threading dislocation density with the increasing compressive residual stress is different in dependence on the nucleation procedure. Still, some differences in the character of the dislocations were observed for the studied sample groups. The structural properties of grown GaN layers were characterized by scanning and transmission electron microscopy. The residual stress was determined using micro-Raman spectroscopy and high-resolution X-ray diffraction. The density of threading dislocations was concluded from the broadening of the reciprocal lattice points that was measured using high-resolution X-ray diffraction as well. The fitting of the reciprocal space maps allowed the character of the threading dislocations to be described quantitatively in terms of the fractions of edge and screw dislocations.

Keywords: gallium nitride, HVPE, kinetically limited growth, microstructure defects, residual stress

Introduction Gallium nitride (GaN) based materials are widely used for opto- and microelectronic applications, e.g. light emitting diodes, blue lasers, solar cells [1]. Due to the lack of na-tive substrates, GaN is typically grown he-teroepitaxially on foreign materials, such as sapphire (Al2O3), silicon carbide or silicon. The heteroepitaxial growth still remains one of the main factors limiting the performance of GaN-based devices. Owing to the high growth rate, the Hydride Vapor Phase Epitaxy (HVPE) is ascribed a great potential for pro-ducing free-standing GaN substrates to over-come this problem [2]. Several routes to ob-tain thick, high-quality HVPE layers starting from sapphire substrates are currently under investigation, such as (i) HVPE overgrowth of GaN templates produced by Metalorganic Va-por Phase Epitaxy (MOVPE) on sapphire [3], and (ii) the deposition of GaN layers direct-

ly on sapphire in a closed HVPE process [4]. An inherent drawback of the MOVPE/HVPE method is the combination of different growth techniques involving separate reactors and sample preparation. Furthermore, reproduc- ible quality of HVPE layers depends strongly on the parameters of the MOVPE templates, such as their stress level, which is difficult to be specified precisely [5]. Nevertheless, MOVPE/HVPE grown GaN substrates are already commercially available, although at very high prices.

Concerning the direct deposition of GaN on sapphire, the large lattice misfit [6] promotes the nucleation and growth of individual and isolated islands instead of the growth of a closed film. Böttcher et al. correlated the av- erage diameter of the islands with the residual stress in the layer [7]. In-situ wafer curvature

79

measurements performed at growth tem- peratures revealed the presence of tensile stress in GaN up to hundreds of MPa in many cases [8], which can result in the formation of cracks in the GaN [9]. The tensile stress was explained by the coalescence of GaN islands at initial growth stages [9]. Due to the dif-ferent thermal expansion of GaN and Al2O3 [10], the low tensile residual stress in GaN turns to be compressive upon cooling from the deposition temperature to room tem- perature. For GaN layers with a thickness between 1 and 2 µm and grown by MOVPE at 1050°C and cooled down to room tem- perature, Hearne et al. [8] and Böttcher et al. [7] reported the contribution of the thermally induced stress of about -(660 ± 100) MPa and -(710 ± 100) MPa, respectively. In thick GaN layers, the residual stress can be compensated by structural defects. A lot of studies reveal that polar GaN heteroepitaxial layers grown by HVPE possess a huge number of threading dislocations (TDs) [6, 11].

To overcome the problems related to the large lattice misfit, e.g. formation of incoherent nu-clei as well as threading dislocations, multiple step HVPE processes consisting of the growth of a low-temperature (LT) nucleation layer on sapphire followed by HVPE overgrowth have been applied (e.g. Ref. 12–17). The nucleation layer acts as a buffer to compensate the lat-tice misfit and provides more or less coherent GaN nucleation sites leading to a rapid coa- lescence of the overgrowing layer. Usually, nu-cleation layers are grown at 450 - 600 °C. In this temperature range, a high nucleation density with a narrow lateral size distribution of the nuclei is typically achieved [12, 13, 16, 17]. The poor crystalline quality of the LT layers is im- proved by an additional high-temperature (HT) treatment at 950 - 1080 °C, which is assumed to result in a complete recrystalliza-tion of the layers, i.e. in the formation of fully hexagonal structures of the deposited nuclei [18]. In a final step, thick GaN layers are ob- tained by HT HVPE overgrowth. Despite of large effort, an established LT nucleation proce-dure to deposit high-quality HVPE layers is not yet available [15]. As reported by Prazmowska

et al. [16], the quality of HT HVPE layers is strongly impacted by small variations of nucleation layer growth conditions such as growth rate and growth time. A typical growth rate of LT nucleation layers is lower than 5 µm/h [12, 17] and is hard to be controlled during the HVPE process. Despite of the tremendous progress in HVPE growth of GaN in the last years, some important aspects of this growth method are not well studied and understood. One of these issues is the role of a kinetically limited growth regime in HVPE process and its impact on the defect for- mation in different stages of the GaN growth.

This paper describes the homoepitaxial HVPE growth on MOVPE templates as well as the heteroepitaxial HVPE growth on sapphire under kinetically limited growth conditions, and their impact on the defect formation and stress evolution in GaN layers. The kineti-cally limited growth mode by HVPE can be achieved in the temperature range between 750 °C and 930 °C without a significant loss of the material quality. This temperature range can be understood as intermediate between the temperature ranges of the LT nucleation and HT GaN growth mentioned above. Re-garding studies of the GaN growth by HVPE in this temperature range to our knowledge, no reports can be found in literature. From a technological point of view, this effort may result in a novel approach (i) to a closed pro-cess for depositing high-quality GaN layers on sapphire which can be more suitable for the HVPE growth process as the LT nucle-ation as well as (ii) to in-situ defect and stress engineering during the HVPE deposition. Hereinafter, the homoepitaxial deposition and the formation of nucleation layers are studied in dependence on the process temperature and duration of growth. The surface morphol-ogy, crystal quality, and residual stress of the layers are investigated in detail. The results on HVPE overgrowth of nucleation layers formed under intermediate temperatures are presented. Furthermore, we describe the in-terplay between the layer thickness, the den-sity of threading dislocations and the residual stress in grown GaN layers. The residual stress

80

(1)

was determined at room temperature by means of high-resolution X-ray diffraction (HRXRD) and micro-Raman spectroscopy. The density of threading dislocations was obtained from the XRD line broadening that was measured via reciprocal space mapping using HRXRD.

Experimental HVPE sample preparation The GaN layers were grown in a commercial, vertical HVPE reactor from Aixtron using the conventional HVPE process with elemental gallium, hydrogen chloride (HCl), and am-monia (NH3) as precursors. All experiments were performed at 900 mbar. The homoep-itaxial growth was performed in nitrogen atmosphere on (0001) oriented, 2 inch com-mercial MOVPE templates. The kinetically limited growth conditions were achieved using reduced substrate temperatures as well as high V/III ratios. The heteroepitaxial GaN layers were grown on exactly (0001) orient-ed, 2 inch sapphire substrates. Nitrogen or a N2/H2 mixture with a ratio of nearly 1:1 was used as carrier gas during the nucleation step. Prior to nucleation, the substrates were hea-ted up to 1050 °C and annealed for 5 min- utes under carrier gas atmosphere. Nucleation layers with a thickness up to 2 µm were depos-ited at different temperatures between 765 °C and 900 °C under a constant HCl flux as well as under a constant V/III ratio of 20. Mean growth rates during the nucleation calcu- lated from the GaN mass gain were higher than 200 µm/h. The overgrowth of nucleation layers was performed at 1040 - 1050 °C using N2/H2 mixture as carrier gas.  Sample characterization The surface morphology of the GaN layers was studied by scanning electron microscopy (SEM). The high-resolution X-ray diffraction (HRXRD) measurements were carried out at a triple-axis diffractometer (Seifert/FPM) with an Eulerian cradle which was equipped

with a sealed X-ray tube with copper anode and two perfect, i. e. dislocation-free, (111) oriented Si crystals. The first Si crystal was used as a monochromator in the pri- mary beam, the second one as an analyzer of the diffracted beam. The cross section of the pri- mary X-ray beam was reduced by a set of slits to 0.09 × 2 mm2. The instrumental line broaden-ing of the diffractometer was below 10 arcsec. The penetration depth of the X-rays was estimated as 5 µm. The density of threading dislocations (TDs) was determined from the reciprocal space maps (RSMs) that were recorded in copla-nar diffraction geometry on the symmetri-cal reflection 0004 and on the asymmetrical reflections 1014 and 1015. During the recip- rocal space mapping, a set of radial (2θ/ω) scans was measured for different values of ω. The quantity 2θ denotes the detector angle, ω the angle between the primary beam and the sample surface. As a result of the reciprocal space mapping, a distribution of the meas-ured intensity in the angular (ω,2θ) space was obtained for each diffraction line that was converted into the (qx,qz) representation of the reciprocal space using the transformation

where λ = 0.154056 nm refers to the wave-length of the X-ray beam. In addition to RSMs, radial (2θ/ω) and azimuthal (ω) scans were performed through the intensity maxima of the symmetrical diffractions 0002, 0004, and 0006 as well as asymmetrical diffractions 1014, 1015, and 1124 or 2024 for each sample. These radial and azimuthal scans were used in order to obtain exact line positions in the qx and qz coordinates (see Eq. (1)) and inter-planar spacings that are needed for the residual stress calculation (see below).

The threading dislocations were visualized on the cross section of the samples by means of transmission electron microscopy (TEM).

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During the cross section preparation, a thin lamella was cut out of the samples and dimpled in a precision ion polishing system. The TEM experiments were performed on a JEM2200FS from JEOL that was equipped with an illumi-nation system corrected for spherical aberra-tion (CS correction), an ultra-high resolution objective lens (CS = 0.5 mm), and an in-col-umn energy filter. The acceleration voltage was 220 kV. As detector, a 2k × 2k CCD camera from Gatan was used.

The Raman measurements were performed at room temperature in backscattering ge-ometry using a Labram HR 800 Horiba Jobin Yvon (Villeneuve d’Asq, France) spectrome-ter with a thermoelectrically cooled charge- coupled device (CCD) detector. The spectral calibration was realized by employing a mer-cury vapor lamp. Raman scattering was ex- cited with the 532 nm (2.33 eV) line of a frequency-doubled Nd:YAG laser. By pass-ing the laser beam through a 100x Olympus microscope objective, the linearly polarized laser light was focused on the surface of the GaN specimens. This provided a lateral resolution of 1 µm. The scattered light was collected by the same objective and contains both the z(yx)z and z(yy)z configurations with the z directions oriented parallel to the c axis of the samples which enabled the detec-tion of the GaN E2 and A1(LO) modes [19]. The spectral resolution of the Raman mea-surements was better than 1 cm−1. Since GaN is transparent in the visible spectral range, it is possible to obtain depth dependent in-formation by using the confocal technique [20, 21]. Moving the focal plane within the GaN layer allows monitoring the spectral position of the observable Raman modes as function of the distance from the GaN surface. The diam-eter of the confocal hole was adjusted in order to have a depth resolution of about 2.5 µm.

Calculation of the threading dislocation density and residual stress

Several X-ray based methods appropriate for the determination of the threading dis-location density have been developed in the past [22–24]. Recently, a Monte Carlo method established by Holy et al. [25] for simulation of the intensity distribution in the reciprocal space was applied to determine the TD den-sity in a series of polar GaN layers grown by MOVPE on sapphire substrates [26]. Later on, this technique was successfully applied to more complicated AlGaN two-layer systems [27]. The approach from Barchuk et al. [26] is based on fitting of RSMs simulated by the Mon-te Carlo method [25] to the measured RSMs. The free parameters of the model used for the Monte Carlo simulation are the densities of the edge and screw TDs with given Burgers vectors. During the refinement of the free pa-rameters, first the density of screw TDs (ρs) with the Burgers vector [ 22] is determined from the symmetrical RSM measured on the reflection 0004, which is not affected by the edge dislocations with the Burgers vector [22]. Sub-sequently, the asymmetrical RSMs measured on the reflections 1014 and 1015 are employed to determine the density of edge TDs (ρe). During the fitting of the asymmetrical RSMs, the density of screw TDs obtained from the symmetrical reflection is taken into account but not refined. All calculated RSMs were convoluted with the resolution function which takes into account the azimuthal divergence of the primary beam and the angular acceptance of the detector [28] as well as an additional line broadening caused by the sample bowing. The crystal truncation rod (CTR) and the effect of the surface stress relaxation on the RSMs were neglected in the calculations in order to reduce the computation time [29].

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(2)

(3)

For calculation of the residual stress in HVPE GaN from the XRD data, a modification of the sin2 ψ method [30, 31] was employed that was derived for hexagonal single-crystalline layers (with the point group 6mm) assuming that the residual stress acts perpendicular to the <0001> direction, i.e. in the plane of the GaN layers. For this orientation of the resid-ual stress, a straightforward application of the Hookes law reveals that the residual stress (σ) causes elastic lattice deformation (εψ ), which is a linear function of sin2 ψ,

In Eq. (2), ψ refers to the angle between the diffracting lattice planes and the sample surface, i.e. the lattice planes (0001); S11 = 3.086 TPa−1, S12 = -0.996 TPa−1 and S13 = -0.557 TPa−1 are single-crys-talline elastic constants of GaN as tak-en from Polian et al. [32]. The elastic lattice deformations were determined for three symmetrical (0002, 0004, and 0006) and three asymmetrical diffraction lines (1014, 1015, and 1124 or 2024) using

where dψ = λ/(2 sin θ) denotes the interpla-nar spacing measured in the ψ direction and

refers to the intrinsic (stress-free) interplanar spacing calculated using the lattice parameters a = 0.31895 nm and c = 0.51861 nm [33].

(4)

According to Davydov et al. [37], the intrinsic position of the E2(high) Raman mode in un-strained bulk GaN is , the linear stress coefficient assuming biaxial stress in the c plane is The precise spectral position of the E2(high) mode, ,was obtained within an error of ±0.03 cm−1 by fitting the measured data by a Lorentzian function. As mentioned above, the use of the confocal technique in conjunction with Raman spectroscopy allowed the resid-ual stress to be determined in different depths under the sample surface. However, in order to be able to compare residual stress values obtained from XRD and Raman spectros- copy, the residual stress calculated from the Raman shift was averaged over the uppermost 5 µm, which corresponds approximately to the penetration depth of X-rays.

.

As a complementary method, confocal mi-cro-Raman spectroscopy has been used to determine the residual stress. This technique allows the residual stress to be measured in different depths below the surface of the GaN samples. Thus, it can detect possible depth gra-dients of the residual stress. The residual stress measurement using the Raman spectroscopy is based on the analysis of the peak position shift of observable Raman modes, which is directly proportional to the lattice strain. For elastic deformation, the change in the wave-number is consequently directly proportional to the residual stress [34–36]. Although three optical phonon modes, i.e. E2(low), E2(high), and A1(LO), are allowed in GaN c plane back-scattering according to the selection rules [19], we selected the non-polar E2(high) phonon for our study, because it is sensitive to the strain in the basal plane (c plane) and thus directly to the in-plane residual stress in the (0001) ori-ented GaN layers:

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Results and Discussion

Homoepitaxial HVPE growth under ki-netically limited growth conditions

The deposition of high-quality GaN layers typ-ically requires transport limited process condi-tions with a sufficiently fast surface kinetics, which is determined mainly by the substrate temperature. Moreover, the surface diffusivi-ty is also affected by other process parameters such as growth rate, V/III ratio or carrier gas composition. Its reduction can be realized in different ways. For instance, in case of nitro-gen-rich growth conditions (high V/III ra-tios) and nitrogen atmosphere the surface dif-fusivity is decreased owing to the enhanced

growth rate. In the present work the influence of reduced surface kinetics on the surface morphology and on the defect formation in HVPE GaN layers was studied. For this pur-pose, MOVPE templates were used for the homoepitaxial HVPE growth of GaN using process conditions promoting the limitations of the surface kinetics. The experimental pa-rameters as well as the results of rocking curve measurements of the investigated samples are summarized in Table I.

Table I: Growth conditions and full width at half maximum (FWHM) of 0002 and 1015 rocking curves for GaN layers grown homoepitaxially on MOVPE templates.

Figure 1a shows the surface morphology of sample S1 which was grown at a temperature of 1050 °C, but in comparison to the standard process at a higher V/III ratio and with an enhanced growth rate. The sample reveals a smooth, mirrored surface without inverse pyr-amids. However, a noticeable step bunching which is well recognizable in the SEM image in-dicates a reduced surface diffusivity during the growth. Further slowdown of the surface ki-netics by decreasing the growth temperature results in an enhanced formation of V-pits on the layer surface, as it is clearly seen in Fig. 1b of sample S2. In comparison to S2, sample S3 grown at 880 °C (Fig. 1c) is more than twice thinner, but its surface is completely built of inverse pyramids with much smaller lateraldimensions. The full width at half maximum (FWHM) of the rocking curves (0002) and

(1015) is similar to that of used MOVPE tem-plates for samples S1 and S3, but slightly lower in case of sample S2. The excellent FWHM values of all samples reveal that the applied kineti-cally limited growth conditions do not lead to degradation of the crystal quality. Moreover, the decreased FWHMs of sample S2 indicate the reduction of the threading dislocation density. Similarly, the impact of V-pits formed during coalescence of ELO islands at 1030 °C on GaAs was observed by Motoki [38]. Taking stress relations into account, this effect can be used as in-situ method for the additional reduction of the threading dislocation density during HVPE growth.

Sample Thickness(µm)

Temperature(◦C)

V/IIIratio Growth rate(µm/h)

FWHM (0002)(arcsec)

FWHM (1015)(arcsec)

S1 50 1050 40 150 238 182

S2 12 930 320 60 196 158

S3 5 880 640 65 241 155

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Figure 1: SEM images of sample (a) S1, (b) S2, and (c) S3 grown on MOVPE templates.

Furthermore, we consider some issues of the V-pit structure. Figure 2a shows the plane view of a typical V-pit in HVPE growth which consists of a six facetted {1101} surfaces with a V-shape angle of about 56°. On the contrary, considering sample S2 in more detail (Fig. 2b) it is recognizable that all V-pits appear nearly round. A cross section SEM image of sample S2 in Fig. 2c supplies the V-shape an-gle value of about 90°. According to Du et al. [39] a rounding of the facetted corners occurs due to the fast growth of corners between, e.g. two slow {1101} facets at kinetically limited growth conditions. Thus, varying the growth conditions, from the form of V-pits conclu-sions about the dominating growth regime can be drawn. Apart from a lot of V-pits, the surface of sample S2 reveals some small 3D is-lands which are marked by red arrows in Fig. 2b. These islands indicate a sufficiently re-duced surface diffusivity as well.

Growth of nucleation layers by intermedi-ate temperatures

Similar growth conditions ensuring a reduced surface diffusivity have been applied for the direct deposition of GaN on sapphire. Table II shows growth parameters of the experiments which resulted in the deposition of non-closed nucleation layers A-D and some identical closed layers grown under same growth condi-tions and denoted as nucleation layer E. Fur-ther details of these experiments are described in the article by Lukin et al. [40]. SEM images of two non-closed nucleation layers A and B grown at 900 °C and 780 °C under nitrogen atmosphere and otherwise identical conditions are shown in Figs. 3a and 3b. Owing to the short growth time, the sapphire substrate is only partly covered by deposited GaN islands. Due to the large lattice misfit between sapphire and GaN, the 3D growth dominates.

Figure 2: SEM images of inverse pyramids (V-pits) on the surface of HVPE layers. (a) Typical, hexagonal pit usually appearing on the surface of HVPE layers. (b) Round shaped V-pits on the surface of S2. Red arrows mark 3D small islands. (c) Cross section of a V-pit on S2 reveals the V-shape angle of 90°.

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Table II: Process parameters and FWHM of the 0002 rocking curve of the deposited nucleation layers.

Two in-plane crystal directions in GaN [1100] and [1120] are shown in Fig. 3a as deter-mined from the flat direction of the sapphire substrate. Mainly hexagonally shaped GaN is-lands with edges parallel to the <1120> crystal direction in GaN are observed, indicating a high degree of crystallinity. XRD measure-ments confirmed the predominant hexagonal lattice structure with the (0001) orientation of the islands. However, a large FWHM of the rocking curve (0002), which was equal to 2180 arcsec and 1580 arcsec as measured for the nucleation layers A and B, respectively, indicated a high mutual tilting and/or mosaicity of the crystallites.

The density and size distribution of the GaN islands were found to depend strongly on the growth temperature as well. At 900 °C relatively extended islands with varying size and mutual distance are observed (Fig. 3a). When growing at 780 °C (Fig. 3b), the islands are smaller, whereas the nucleation density is higher and the lateral and size distributions are more uniform. Regarding the different widths of the rocking curves discussed above, this re-sult supports the hypothesis that the mosaicity increases with increasing lateral size of the is-lands and that the width of the rocking curves is mainly controlled by the mosaicity of indi-vidual islands. The high nucleation density and

Figure 3: Surface morphology of nucleation layers (SEM images) grown for the same duration: (a) at 900 °C using N2 carrier gas, (b) at 780 °C using N2 carrier gas, (c) at 780°C using N2/H2 mixture, (d) at 780 °C using N2/H2 mixture and increased V/III ratio.

Nucleation layer Carrier gas Temperature (◦C) V/IIIratio FWHM (0002)(arcsec)

A N2 900 20 2180

B N2 780 20 1580C N2/H2 780 30D N2/H2 780 60

E N2 780 20 1134

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the high grade of the island size homogeneity of nucleation layer B favor the coalescence of islands and hence, the formation of a closed GaN layer. Decreasing the growth temperature to about 765 °C, in turn, leads to a further de-crease of the island size and to an increase of the defect density by coalescence (mainly thread-ing dislocations) [7] in subsequent stages of growth. The addition of hydrogen to the car-rier gas at similar growth parameters results in a drastical reduction of the nuclei density (see surface morphology of sample C in Fig. 3c). A sufficiently high nucleation density can be partially restored by increasing the V/III ratio as in the case of nucleation layer D (Fig. 3d). Therefore, further growth experiments have been performed at temperatures around 780 °C using nitrogen as carrier gas.

Figure 4: SEM images of a non-closed nucleation layer B show the surface morphology of the type 1 and type 2 islands as well as the surface evolution at the very first stage of lateral growth (dashed circle in (b)) of the second layer. The dashed arrow in (a) indicates a side facet of a second layer island. The solid arrow in (b) displays the inverse pyramids (V-pits) appearing during the coalescence of second layer nuclei.

In Fig. 4 the surface morphology of a non-closed nucleation layer B is presented in more detail. The structure of GaN islands and their evolution to closed layers at temperatures around 780 °C reveal some interesting features. The results and the developed structure model have been published recently by Lukin et al. [40]. According to this structure model the island shapes can be attributed to two differ-ent types (Fig. 4a). Except for the predominant type 2, some islands of type 1 are observed. Grown at 780 °C, type 2 islands possess a com-plex polyhedron form, hexagonal in projection on the substrate plane. For simplicity of the following discussion we denote this island part as the first layer. The top [0001] surface of such first layer islands might act as a preferred nucleation site for the subsequent deposition.

The dashed arrow in Fig. 4a indeed indicates, e.g. a separated hexagonal structure with smooth {1101} side facets on the top sur-face of the first layer islands. We denote these structures as the second layer islands. Several of these structures (marked by dashed circle in Fig. 4b) seem to be already coalesced forming a first fragment of a closed second layer. Obvi-ously, the second layer can rapidly grow in the lateral directions in contrast to the previous 3D growth modus during direct deposition of GaN on sapphire. Thus, the surface pattern shown in Fig. 4 is assumed to represent a very early stage of closed GaN layer formation by lateral growth.

The coalescence of second layer nuclei is asso-ciated with the appearance of distinct, facetted pits having the form of an inverse pyramid. Such kind of defects are already observed at the very beginning of lateral growth as indicated by the solid arrows in Fig. 4b, whereas the first layer islands reveal no pits at all on coalescing (see Fig. 4c). On the basis of results reported by Liliental-Weber et al. [41], second layer pit formation is supposed to be initiated by threading dislocations (or bundles of threading dislocations) occurring in the grain boundaries of underlying clus-ters of nuclei. This is also suggested by the ar-rangement of pits detected in subsequent layer growth (see Fig. 6 below).

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Figure 5 shows a cross section of two coalesced islands of the non-closed nucleation layer in a bright-field TEM image. The dark contrast between the islands indicated by the dashed arrow shows the common grain boundary. The horizontal patterns visible in the TEM micro-graph of the individual islands stems from the diffraction contrast on local strain fields and can be explained by a series of laterally extend-ed stacking faults. The streaks along the [0001] direction and twin spots clearly seen in the

Figure 5: Bright-field cross section TEM image of a non-closed nucle-ation layer B grown at 780 °C showing the microstructure of two coalesced islands. The direction of the prima-ry electron beam was [1120]. The dashed arrow indicates the grain boundary. Islands are primarily free of threading dislocations, but con-tain a lot of stacking faults. The corresponding diffraction pattern reveals the reflex splitting and the streaks due to basal stacking faults.

corresponding diffraction pattern confirm the presence of basal stacking faults [42]. Hence, initial islands on sapphire obviously contain a high density of stacking faults, whereas they appear to be free of threading dislocations. On the contrary, dislocations are concentrated in the grain boundaries between the islands. In addition to the threading dislocations, a signifi-cant density of partial dislocations terminating the stacking faults in the basal planes of GaN [43] is assumed to exist in the grain boundary.

Rapid lateral coalescence of the second layer was confirmed by experiments with a longer growth time. As an example, Fig. 6a shows the sur-face morphology of nucleation layer E when the growth time at 780 °C was three times lon-ger as compared to sample B. The FWHM of the (0002) rocking curve was 1134 arcsec indi-cating a reduced mosaicity in comparison with the early stages of nucleation layer growth (see Fig. 3b). An almost closed GaN layer with a thickness of about 0.8 µm has formed with the only obvious indication of non-complete-ly buried type 2 island being marked by the dashed arrow in Fig. 6a. The enhanced lateral growth of the second layer seems to be analog to the rapid coalescence of GaN islands ob-served on a AlN buffer layer by MOVPE [44].

In the case of the nucleation at 780 °C, the role of the buffer layer plays, obviously, the first layer. On the basis of the non-closed nucleation layer structure discussed above, we propose a

model (see Fig. 6b) which can explain the for-mation of the surface morphology shown in Fig. 6a. The islands of the second layer grow mainly in lateral directions forming pits by co-alescence. In contrast to the individual facetted pits, already described in the context of Fig. 4 above, a lot of pits with mainly continuously curved sides (not facetted) are found to be the dominating surface defects. Often, pits are linearly arranged as indicated by solid arrows in Fig. 6a. These rows of pits probably partly represent the grain boundaries of underlying type 2 islands, because the boundaries consist of threading dislocations, which, in turn, lead to the formation of pits as already mentioned. Assuming that a pit is caused by just one threading dislocation, a minimal threading dislocation density of approx. 1.5×10

9 cm−2 can

be estimated for the nucleation layer shown in Fig. 6a.

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Figure 6: Surface morphology of closed nucleation layers E (SEM images) at 780 °C: Solid arrows in (a) show rows of pits, which probably represent grain boundaries between underlying nuclei. The dashed arrow indicates a hexagonally shaped nucleation island that is non-completely buried during growth. (b) Schematic model representing the structure of closed nucleation layer.

The micro-Raman spectroscopy has been used to determine the residual stress of the nucle-ation layers, which is an important criterion for evaluation of the relaxation behavior. The SEM image in Fig. 7a illustrates the spot size of the focused laser beam in relation to the surface morphology of the investigated closed nucleation layer (cf. Fig. 6a). In Fig. 7b, the volume-averaged Raman shift of the E2(high) mode at several neighboring positions on the surface of the closed nucleation lay-er is plotted. The zero stress frequency is marked by the horizontal dashed line.

Figure 7: (a) Surface morphology of the closed nucleation layer E deposited at 780 °C. The SEM image illustrates the spot size of the focused laser beam in relation to the surface morphology of the sample. (b) Raman shift of the E2(high) mode from different positions of the sample surface. Raman shift of unstrained GaN is marked by the dashed horizontal line.

It was found that the layer is nearly unstrained on average with a mean E2(high) frequency of (567.63 ± 0.12) cm−1. The significant variations of the frequency of up to 0.37 cm−1 represent a maximum residual stress of about 137 MPa. It is important to note that Raman investigations of non-closed and closed nucleation layers give similar results independent of growth time and layer thickness of up to 2 µm as well as growth temperatures in the range of 765 - 800 °C. The FWHM of the E2(high) Raman mode in the range of 3.7 - 4.7 cm−1 indicates a low crystal quality and/or a high defect density.

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To explain the results obtained from the closed nucleation layers, we refer to the strain-stress relations in MOVPE-grown templates sys-tematically studied, e.g. by Hearne et al. [8]. Comparing stress values of about -660 MPa for closed, 1 - 3 µm thick MOVPE grown lay-ers with the samples under consideration here, the nearly zero residual stress of the nucle-ation layers would correspond to an unrealistic high level of tensile stress at growth tempera-tures. The residual stress relaxation is assumed to arise from the lateral growth of islands.

Stresses can be strongly reduced as direct con-nection to the substrate is limited to the center of the domains. As a consequence, threading dislocations are virtually only present near/at domain boundaries. The significant stress inho-mogeneity reflects this. Further investigation is required to understand potential relaxation mechanisms which reduce the thermal stress on cooling the samples down from growth temperatures including the impact of disloca-tions, mosaicity, and surface roughness.

Nucleation layer overgrowth

The results on the HT overgrowth of our HVPE nucleation layers are presented in Table III. The non-closed nucleation layer B and almost closed layers E, respectively, have been used as tem-plates for the overgrowth by HVPE, which was carried out at 1040 - 1050 °C resulting in closed GaN layers with a thickness of up to

Table III: Results of overgrowth experiments using nucleation layers as templates. Sample S4 is marked by an asterisk because it was grown at a three-time lower V/III ratio than the other samples.

15 µm. Thereby, sample S4 was grown at three-time lower V/III ratio than the other samples. The overgrowth of nucleation layer D grown using hydrogen/nitrogen mixture as carrier gas provided similar results as for nucleation layer B, and will be not discussed here.

As can be seen from the SEM image (Fig. 8a), the deposition on the non-closed nucleation layer gives a rough surface with a typical thickness variation of 1 - 2 µm. Furthermore, a high defect density dominated by small pits of up to 1 µm in lateral size and some small holes left after HT coalescence at the GaN/sapphire interface are found. The FWHM of the (0002) and (1015) rocking curve was de-tected to be 770 arcsec and 575 arcsec, re-spectively. In contrast to sample S7 grown on the non-closed nucleation layer, samples S5 - S6 grown on closed nucleation layers appears

smooth and mirroring, e.g. Fig. 8b shows a cross section of sample S5. Besides, they re-veal a very good crystal quality (see FWHM values in Table III), which is even comparable with typical values of HVPE layers grown on MOVPE templates (e.g. Ref. 14 and 45). Conse-quently, the full coalescence of the second layer and the formation of the pit-like surface mor-phology (Fig. 6) by nucleation at about 780°C provide the fast smoothing of the GaN layers by HT overgrowth (Fig. 8b), and results in high crystal quality.

Sample Nucleation layer Thickness(µm)

FWHM (0002)(arcsec)

FWHM (1015)(arcsec)

S4∗ E 13 247 195

S5 E 9 257 142S6 E 15 276 152

S7 B 8 770 575

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Figure 8: SEM images of overgrown GaN layers. Image (a) shows the layer produced by HT HVPE overgrowth of the non-closed nucleation layer B. Image (b) shows the cross section of sample S5.

Threading dislocation density

Further, a comprehensive study of threading dislocations density and residual stress was performed on grown samples. According to the nucleation procedure, the studied sam-ples can be divided in three groups. Samples S1 - S3 were grown homoepitaxially on 2 inch (0001) oriented MOVPE GaN templates. The second sample series comprising samples S4 - S6 was deposited on closed HVPE GaN tem-plates. The last sample (S7) was deposited at similar deposition conditions like S5 and S6,

Table IV: Characteristics of the samples under study: template type, average sample thickness (t), screw TD density (ρs), edge TD density (ρe), total TD density (ρtot), residual stress determined from XRD data (σXRD) and Raman measurements (σRaman). The densities of screw and edge TDs from Monte Carlo simulation were determined with an error of ±15%. The values of residual stress from X-ray and micro-Raman experiments possess an error of approx. ±50 MPa. The asterisks mark those samples, which were grown at a lower V/III ratio.

but the non-closed HVPE GaN nucleation layer grown at 780 °C was employed directly as template for the further growth. Addition-ally, a commercial, nearly unstressed HVPE layer with a thickness of 900 µm (S0) grown on a MOVPE template was used for comparison. This thick layer was deposited at low V/III ra-tio as well as sample S4. The results are sum-marized in Table IV. Additional results and details can be found in Barchuk et al. [46].

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Sample Templatet

(µm)ρs

(10−8 cm−2)ρe

(10−8 cm−2)ρtot

(10−8 cm−2)σXRD

(MPa)

σRaman

(MPa)S0∗ MOVPE 900 0.13 0.38 0.5 -55.1 -44.4

S1 MOVPE 50 0.28 1.04 1.3 -190.6 -274.1S2 MOVPE 12 0.09 0.84 0.93 -504.0 -222.0S3 MOVPE 5 0.77 1.9 2.7 -566.4 -496.3

S4∗ E 13 0.68 3.3 4.0 -231.2 -203.7S5 E 9 0.90 8.9 9.8 -496.6 -444.4S6 E 15 0.86 5.4 6.3 -366.5 -348.1S7 B 8 6.7 17.6 24.3 -658.9 -507.5

For all samples under study, the intensities of the diffuse scattering in the vicinity of the dif-fraction maxima, which were measured us- ing the ω scans and/or extracted from the qx scans, can be described by qx

−n function with n being between 2 and 3. One example of the I vs. qx scans, which was measured on the reflec-tions 0004 and 1014 in sample S5 and displayed in the double-logarithmic representation, is shown in Fig. 9a. Such dependence indicates the presence of mixed (screw and edge) dislo-cations [24, 25]. The refinement of the density of screw and edge TDs using the Monte Carlo method described above revealed the dislo-cation densities summarized in Tab. IV. The

Figure 9: Reciprocal-space maps simulations of the reflections 0004 and 1014 for S5. (a) Comparison of experimental (dots) and simulated (solid lines) qx cuts in the reciprocal space. (b) Experimental (solid blue lines) and simulated (dot-ted red lines) reciprocal-space maps. The step of intensities is 100.5 in a logarithmic scale.

quality of the refinements is illustrated in Fig. 9b, where the RSMs measured on the symmet-rical 0004 and the asymmetrical 1014 diffrac-tions as well as the corresponding simulated RSMs are shown. An excellent agreement be-tween the measured and simulated RSMs was achieved for the qx cuts in the reciprocal space (cf. also Fig. 9a) that are directly influenced by the TDs density. Some disagreements in the intensity levels between experimental and sim-ulated data (mainly in the qz direction) stem possibly from the neglected strain relaxation towards the sample surface and from the cor-relation of the dislocation positions that was not regarded in our calculations.

Depending on the template type and on the GaN layer thickness, the TD densities range between 107 and 2×109 cm−2 (cf. Tab. IV). In general, the TD densities are lower for MOVPE GaN templates (samples S0 - S3) than for HVPE GaN templates (samples S4 - S7). Furthermore, the TD densities decrease with increasing thickness of the GaN layers (Fig. 10). The dislocation density in sample S2 was strongly affected by the V-pits formation. It is first of all noticeable for the density of screw dislocations. According to Motoki et al. [38], V-pits provide annihilation of TDs due to their interaction with the facets of V-pits. Both, screw and edge threading dislocation density of sample S2 indicate that the annihilation of

screw TDs proceeds on the V-pits facets faster than that of edge TDs. The reduction of the TD density in thicker GaN layers can be ex-plained by dislocation bunching [47, 48]. These studies showed that the dislocation bunching takes place typically in the first ten microme-ter above the GaN/template interface. Since the penetration depth of X-rays is about 5 µm, only the near-surface region of the thick GaN layers is probed by XRD. In this region, the TDs are already bunched. As XRD quantifies the TD density from the extent of the local strain fields caused by TDs, the decrease of the TD density with increasing GaN layer thickness and thus with advancing TD bunching can be interpret-ed as a gradual decay of the mean strain field

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around bunched TDs. The reasons for this phenomenon can be (i) the interaction of TDs within the TD bunches and the consequent interference of their strain fields, (ii) too large atomic displacements within the TD bunches

Our TEM experiments confirmed the presence of bunched edge TDs in the samples under study (not shown here).

The determined TD densities (Fig. 10) reveal that the density of edge dislocations is larger than the density of screw dislocations. This effect was already reported for other GaN lay-ers grown by different processes [4, 11, 38]. However, the character of the threading dis-locations, which is given by the ratio between edge and screw TDs, depends significantly on the template type. For the GaN layers grown on MOVPE templates (samples S0, S1, S3) ρe/ρs approaches 3. In the GaN layers grown on closed HVPE GaN templates (samples S4 - S6), mainly the density of edge TDs increases (ρe/ρs ≈ 10) raising the total TD density in these GaN layers. The dependence ρs t−0.32

where t refers to the thickness of the GaN lay-er was determined for screw TDs in samples S0, S1, and S3. The density of screw TDs in samples S4 - S6 approaches this relation which is plotted by the solid line in Fig. 10. The higher density of edge TDs observed in GaN

Figure 10: Densities of screw (squares) and edge (circles) thread-ing dislocations as well as the total threading dislocation density (tri-angles) plotted as function of the GaN layer thickness.

that produce widespread diffuse scattering, which is not fully recognized in the HRXRD experiment, and (iii) the annihilation of TDs at the vertical boundaries of the mosaic GaN blocks [47, 48] or at the bottom of the pits [38].

layers grown on closed HVPE templates is related to a higher mosaicity of these layers. The boundaries of the mosaic blocks contain a large number of edge TDs that are responsi-ble for a mutual disorientation of the adjacent blocks. The highest density of edge and screw TDs was found in the GaN layer grown on the non-closed HVPE GaN nucleation layer (sample S7). Due to the high density of screw TDs, the ratio of the TD densities was com-parable with the ρe/ρs ratio in the GaN layers grown on the MOVPE templates (ρe/ρs ≈ 3). Such unusually high density of screw TDs is obviously related to the non-closed nature of the nucleation layer B that was used as a template in this particular case. Probably, the island coalescence at high temperatures results in the enhanced formation of screw threading dislocations. The screw dislocations probably compensate the lattice misfit between the ac-tual HVPE GaN layer and the uncovered sap-phire substrate as well as the larger surface roughness of the HVPE GaN nucleation layer, which is similar to the phenomena observed by Kawamura et al. [47] in staircase structures.

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In contrast to screw TDs, the density of edge TDs measured in S7 is comparable with the densities of edge TDs in samples S4 - S6.

Residual stress

The confocal micro-Raman spectroscopy and the XRD measurements revealed that all in-vestigated GaN layers are under compressive residual stress (see Table IV). The comparison of residual stresses in individual samples shows that the compressive residual stress decreases with increasing GaN layer thickness. As com-pared to the general trend, the compressive residual stress is smaller in samples S0 and S4, which were deposited at the lowest V/III ratio, and slightly higher in sample S7, which was deposited on a non-closed HVPE GaN nucleation layer. The low stress value for the sample S2 obtained by micro-Raman spectros-copy must be treated carefully. Obviously, large V-pits on the surface lead to the surface relax-ation and to a very low stress values measured by micro-Raman spectroscopy. In contrast, the HRXRD intensity was collected from the much larger area and provides a stress value comparable to other samples grown at higher V/III ratios.

The residual stresses for other samples obtained using micro-Raman spectroscopy and HRXRD are in a very good agreement, i.e. within the error bars in most samples. The largest discrep-ancies were observed for GaN layers with a steep depth gradient of the residual stress (as recognized by confocal micro-Raman spectros-copy), although the micro-Raman data were averaged over the penetration depth of X-rays as described above. Whereas sample S5 grown on the closed HVPE GaN template possessed no stress gradient, the residual stress in sam-ple S7, which was grown on the non-closed HVPE GaN nucleation layer, decreased from -590 MPa at the GaN/template interface to -475 MPa at the surface of the GaN layer (see Fig. 7 in Ref. 46). For such a gradient of the residual stress, the assumptions of Eq. (2) are not valid any more. Furthermore, a steep depth gradient of the residual stress mimes sheer stress components [30], which are not considered in Eq. (2).

Correlation between threading dislocation density and residual stress

The simultaneous decrease of the dislocation density and residual stress with increasing GaN layer thickness, which is moreover de-scribed by similar power function of sample thickness for S0, S1, S3, indicates some cor-relation between the total TDs density and the residual stress in the HVPE GaN layers. This correlation is shown in Fig. 11 and dis-cussed below in more details. For all template types, the compressive residual stress increas-es with increasing total TD density, which was calculated as a sum of the densities of edge and screw TDs. For individual templates, the de-pendence of the residual stress on the total TD density can be described by power functions, where the power n is characteristic for each template. For the MOVPE GaN template, n = 1.43, for the closed HVPE GaN template, n = 0.80, and for the non-closed HVPE GaN nucleation layer, n ≈ 0.69.

This correlation between the residual stress and the total TD density leads to the hy-pothesis that the compressive residual stress is caused by uncompensated strain fields of the dislocations. However, the uncompensated strain fields cannot be generated by non-in-teracting dislocations, as they cause strain fields with zero mean atomic displacement (see, e.g., Ref. 49 and/or 50) and thus with no macroscopic change of the interplanar spac-ing, which is recognized as zero residual stress.On the contrary, the strain fields of interact-ing dislocations overlap, which can break the symmetry of the strain fields, especially if the dislocations are not randomly distrib- uted. Consequently, the mean value of lattice deformation is non-zero, which leads to a shift of the diffraction maxima from their intrinsic positions that is recognized as residual stress. The effect of the broken symmetry of the strain fields of TDs on the X-ray diffuse scattering was shown by Holy et al. [25], who simulat-ed the simultaneous broadening and shift of diffraction lines caused by threading disloca-tions that were non-uniformly distributed in a limited diffracting volume. A special case

94

Figure 11: The dependence of the residual stress on the total density of threading dislocations. The resid-ual stresses were determined using the sin2 ψ method (black squares) and micro-Raman spectroscopy (red circles).

of the inhomogeneous distribution of TDs is the dislocation bunching, which leads to the formation of local lateral gradients of the TD density within individual crystallites [48, 51, 52]. Such gradients of TD density would be responsible for the formation of compressive residual stresses in HVPE GaN layers. However, the dislocation bunching must be accompanied by the annihilation of the dislocations during the HVPE GaN layer growth, as both the TD density and the resid-ual stress decreases with increasing GaN lay-er thickness. The annihilation of TDs at the vertical boundaries of the mosaic GaN blocks was reported by Datta et al. [48] and Kawamura et al. [47], the annihilation of TDs at the bottom of the pits by Motoki et al. [38]. If the residual stresses result from the uncompensated strain fields of bunched TDs, it can be expected that the kind of the dislocation bunching strongly influences the dependence of the residual stress on the TD density. From Fig. 11, it can be concluded that the kind of the TD bunching is characteristic for each template. In the HVPE GaN layers grown on MOVPE GaN templates (samples S0 - S3), the compressive residual stress increases steeply with increasing TD density, although the TD density is relatively low in these GaN layers. This effect can be explained by an in-tense dislocation bunching. The HVPE GaN layers grown on closed HVPE GaN templates

(S4 - S6) possess similar compressive residual stress like samples S0 - S3, despite a higher TD density. Some part of TDs remains probably “unbunched”, i.e. more or less randomly distributed over the crystallites in samples S4 - S6.

Conclusion

The impact of the kinetically controlled HVPE growth on the defect formation in GaN layers has been studied. Application of the kinetically limited growth during the ho-moepitaxy of GaN induce the generation of inverse pyramids (V-pits), which promote the reduction of the threading dislocations densi-ty in grown layers. The density of screw thread-ing dislocations will be decreased considerably more than that of edge threading dislocations. The initial stages of HVPE growth on sapphire at intermediate temperatures in the range of 750 - 900 °C are accompanied by the formation of a lot of stacking faults in nucleation islands, and results in the rapid formation of a closed uniform structured GaN layer based on a form of epitaxial lateral overgrowth, which can be used as a nucleation/buffer layer for further high-temperature HVPE growth of smooth, high quality GaN layers. The homoepitaxial-ly and heteroepitaxially grown samples were investigated by using high-resolution X-ray diffraction and micro-Raman spectroscopy.

95

Acknowledgement

The authors gratefully acknowledge the fruitful cooperation with Freiberger Compound Ma- terials GmbH. This work was performed within the Cluster of Excellence “Structure Design of Novel High-Performance Materials via Atomic Design and Defect Engineering (ADDE)” which is financially supported by the European Union (European regional de-velopment fund) and by the Ministry of Sci-ence and Art of Saxony (SMWK).

In all samples, the density of edge threading dislocations was higher than the density of screw dislocations. The residual stresses in the GaN layers were always compressive; their amount increased with increasing thread-ing dislocation density. The correlation between the residual stress and the dislocation density was explained by the formation of uncompensated strain fields around bunched threading dislocations, and was strongly af- fected by the nucleation procedure. For the same layer thickness, the lowest density of edge and screw threading dislocations was achieved in the HVPE GaN layers grown on MOVPE GaN templates. The dislocation density in the GaN layers grown on HVPE GaN templates was 2-3 times higher. Furthermore, the characteristic of the template affected the dislocation bunching and thus the depen-dence of the residual stress on the threading dislocation density. The interplay between the dislocation bunching and the residual stress formation restrained the compressive re- sidual stresses to be below 600 MPa in most GaN layers under study.

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