Coalescence aspects of III-nitride epitaxy

J. Appl. Phys. 101, 054906 (2007); https://doi.org/10.1063/1.2464195 101, 054906 © 2007 American Institute of Physics. Coalescence aspects of III-nitride epitaxy Cite as: J. Appl. Phys. 101, 054906 (2007); https://doi.org/10.1063/1.2464195 Submitted: 26 October 2006 . Accepted: 21 December 2006 . Published Online: 09 March 2007 V. Lebedev, K. Tonisch, F. Niebelschütz, V. Cimalla, D. Cengher, I. Cimalla, Ch. Mauder, S. Hauguth, O. Ambacher, F. M. Morales, J. G. Lozano, D. González, et al. ARTICLES YOU MAY BE INTERESTED IN Adatom diffusion at GaN (0001) and (0001) surfaces Applied Physics Letters 73, 487 (1998); https://doi.org/10.1063/1.121909 Dislocation mediated surface morphology of GaN Journal of Applied Physics 85, 6470 (1999); https://doi.org/10.1063/1.370150 On the origin of threading dislocations in GaN films Journal of Applied Physics 106, 073513 (2009); https://doi.org/10.1063/1.3225920 Coalescence aspects of III-nitride epitaxy V. Lebedev,a兲K. Tonisch, F. Niebelschütz, V. Cimalla, D. Cengher, I. Cimalla, Ch. Mauder, S. Hauguth, and O. Ambacher Institute of Microand Nanotechnologies, Technical University Ilmenau, D-98684 Ilmenau, Germany F. M. Morales, J. G. Lozano, and D. González Departamento de Ciencia de los Materiales e Ingeniería Metalúrgica y Química Inorgánica, Facultad de Ciencias, Universidad de Cádiz, 11510 Puerto Real-Cádiz, Spain 共Received 26 October 2006; accepted 21 December 2006; published online 9 March 2007兲 In this work, coalescence aspects of wurtzite-III-nitride epitaxy are addressed. The coalescence phenomena have been studied in thin epilayers by means of electron and atomic force microscopies, and electron and x-ray diffractions. This study generalizes the growth parameters responsible for the rapid coalescence of III-nitride films, and describes the coalescence qualitatively and, partly, analytically for the case of heteroepitaxy in nonequilibrium conditions. Coalescence time and the corresponding diffusion coefficients at elevated temperatures were estimated for GaN and InN depositions. The rate of coalescence has been found to impact on the structure and morphology of III-nitride epilayers. A simple growth model was suggested to explain the formation of domain boundaries and 共0001兲stacking faults formed during the coalescence. In particular, it is shown that two adjacent and tilted, hexagonal-shaped 2Hdomains may form a noncoherent boundary explicitly along a 兵11 ¯ 00其plane. We also suggest that the interaction between tilted domains induces the localized lateral growth of the most epitaxially oriented domain forming a basal 共0001兲stacking fault followed by the formation of surface macrosteps, and consequently the termination of a threading dislocation by its dissociation and propagation under the formed 共0001兲stacking fault. ©2007 American Institute of Physics.关DOI: 10.1063/1.2464195兴 I. INTRODUCTION Recently, great progress in fabricating highly efficient III-nitride-based devices has been achieved.1Extensive studies of material and device properties have been accomplished by a number of studies concerning defects and impurities,2,3 surface structures,4and associated growth mechanisms.5–8 However, a lack of lattice-matched substrate remains the main challenge hindering the progress on the practical side. Moreover, there are still substantial problems concerning a deep understanding of the fundamental mechanisms of the III-nitride heteroepitaxy. Epitaxial wurtzite 共2H-兲III-nitride layers used for device fabrication are usually highly faulted single crystals and typically adopt a mosaic structure with subgrain boundaries delineated by threading dislocations 共TDs兲.9,10 The origin of this structure lies on surface atomic processes under growth. It was recently shown11,12 that heteroepitaxy of III nitrides on highly mismatched substrates can be divided into four stages, each of them having a critical impact on the crystal quality of the epilayer. They are 共i兲three-dimensional 共3D兲nucleation, 共ii兲subsequent growth of misoriented islands in the VolmerWeber mode, 共iii兲partial coalescence of the islands into a continuous film, and 共iv兲long-term epitaxy followed by gradual improvements of the surface morphology. 3D nucleation and subsequent coalescence are interesting and important problems, which control a number of physical and mechanical properties of thin films. It has been extensively studied for decades using a variety of theoretical approaches mostly based on theory of phase-ordering kinetics.13,14 However, most of the studies were devoted to computer simulations of the grain growth in the isotropic limit 共i.e., when both energy and mobility of grain boundaries are isotropic兲, with rare attempts on anisotropy calculations.15,16 In the case of the heteroepitaxy of thin IIInitride films, both energy and mobility are strongly anisotropic, e.g., their values depend on the misorientation between two neighboring crystals and the spatial orientation of their boundaries. In addition, nonequilibrium growth conditions and the presence of liquid phase at the grain boundaries, usual for a group-III-rich growth, may also result in a strong anisotropy of both energy and mobility. Due to their complexity, either analytical or computational studies of the coalescence in III nitrides have been rarely addressed. So far, III-nitride nanodomain coalescence has not been studied in great detail also experimentally. However, this knowledge is extremely important due to the dependence of the crystal structure on particle sizes, which further influences the performance of devices. In general the shape and size of nucleated nanocrystals depend on the crystal structure, temperature, and composition 共e.g., stoichiometry兲.7In many cases, the III-nitride islands have a hexagonal form with small degrees of truncation 共see Fig. 1兲. This shape occurs since it leads to surface energy minimization for nuclei formed at equilibrium, and because of kinetics where the shape is determined by the rate at which different crystal faces grow.17 However, the combination of factors such as a兲Electronic mail: [email protected] JOURNAL OF APPLIED PHYSICS 101, 054906 共2007兲 0021-8979/2007/101共5兲/054906/12/$23.00 © 2007 American Institute of Physics101, 054906-1 temperature, kinetics, impurities, and surface energy effects could lead to unusual nanoparticle size-shape distributions, which influences on the particle coalescence. In order to improve growths in a systematic way it is essential to understand the underlying kinetic processes such as adsorption, desorption, and surface diffusion. In particular, adatom diffusion on the growing surfaces is considered to be a key parameter controlling the coalescence and consequently the material quality and the surface morphology.5 Recently, we have proposed12 that the coalescence process is a dominating factor controlling key crystal properties as polytype, dislocation density, and surface morphology of 2H-InN. The present work attempts to generalize this idea for the whole family of binary III nitrides and describe the coalescence 共at least, qualitatively兲for the cases of plasmainduced molecular beam epitaxy 共PIMBE兲and metal-organic chemical vapor deposition 共MOCVD兲. Coalescence times and the corresponding diffusion coefficients at elevated temperatures were estimated for both cases and compared with theoretical predictions. Additionally, a simple growth model is proposed to explain the formation of domain boundaries and stacking faults during the coalescence stage. 2H-AlN and 2H-GaN buffer layers are usually involved in the heteroepitaxial growth of III-nitride heterostructures on conventional substrates, e.g., sapphire, silicon, and silicon carbide. Consequently, the grain structure of such films plays a crucial role in the achievement of functional III-nitride devices determining the mosaic structure of the subsequent epilayers. Therefore, our discussion is extensively developed for the case of highly mismatched wurtzite heterosystems, e.g., GaN and AlN on sapphire and InN on AlN and GaN, having the lattice mismatch f⬎10%. Additionally, particular examples of AlGaN thin film deposition are also used for supporting our statements which generalize the III-N heteroepitaxy. II. EXPERIMENTAL DETAILS The MOCVD of GaN and AlN was performed at 1120 and 1190 °C, respectively, at 15 mbar pressure using a commercial Aixtron AIX200RF reactor. Triethylgallium 共TEGa兲, trimethylaluminum 共TMAl兲, and ammonia in hydrogen served as precursors with a V-III ratio of ⬃2000. The sapphire surface was cleaned in situ by etching in a hydrogen atmosphere at 1180 °C. The growth was initiated by a low temperature by either a 20 nm thick AlN or GaN nucleation layer. Afterwards a thicker epilayer was deposited to reach the structural quality required. The detailed description of the MOCVD experiments can be found elsewhere.18,19 Other heterostructures discussed in this work were grown in a Balzer’s PIMBE system with a base pressure of ⬃1⫻10−10 mbar. Standard Knudsen cells were used for Ga, Al, and In evaporations. An Oxford Applied Research radiofrequency nitrogen plasma source has been used to supply active N radicals from purified 6N5 N2gas. The substrate temperatures were calibrated by an infrared pyrometer. The growth process was monitored by digitized patterns of reflection high-energy electron diffraction 共RHEED兲. Molecular fluxes were monitored in situ by a quadrupole mass spectrometer and calibrated using RHEED oscillations. The PIMBE growth conditions of 2H-AlN 共Ref. 20兲and 2HInH 共Ref. 12兲thin films are described elsewhere. The growth temperatures of 670 and 370 °C were used for GaN and InN depositions, respectively. In these conditions, the growth rate is proportional to the impinging group-III flux, thus getting sticking coefficients approximately equal to the unity.21 Unlike that, AlN epitaxy has been performed at rather higher temperatures of ⬃910 °C and excess of Al has been used to keep the two-dimensional 共2D兲growth as the active mode of deposition. For structural characterization, transmission electron microscopy 共TEM兲was performed in electron microscopes operating at 200 keV 关TECNAI 20S-TWIN 共FEI兲and JEM2011 from JEOL兴. Mechanical thinning and ion milling were used to prepare specimens for cross-section TEM 共XTEM兲 and plan-view FEM 共PVTEM兲inspection. Electron diffraction patterns and micrographs obtained in bright-field 共BF兲 FIG. 1. Examples of the mosaic structure of III-nitride films grown on 共0001兲sapphire by PIMBE: 共a兲2⫻2 ␮ m2AFM image of a 40 nm thick AlN epilayer grown at 700 °C and associated roughness profile; 共b兲SEM image of the lateral interface between the Ga and N faces of an ⬃500 nm thick GaN共0001兲LPH shows a completed coalescence on the Ga-face side and the result of a partial coalescence on the N-face side 共the surface is covered by a 10 nm thick Au layer for better imaging conditions兲;关共c兲and 共d兲兴 DF 共c兲and BF 共d兲PVTEM micrographs of the same region of a 70 nm thick 2H-InN layer grown on GaN共0001兲/sapphire template. In these 2B conditions using the 共112 ¯ 0兲reflection near the 关0001兴zone axis, TDs with an edge component are visible. These images demonstrate the mosaic structure of the film and the TD distribution within the domain boundary 共marked by the dashed line兲. 054906-2 Lebedev et al. J. Appl. Phys. 101, 054906 共2007兲 and dark-field 共DF兲modes by conventional two-beam 共2B兲 conditions and high resolution TEM 共HRTEM兲were obtained and analyzed. Structural analysis was also performed by high resolution x-ray diffraction 共XRD兲using a Bruker D8 diffractometer. Rocking curves at the symmetric 共0002兲and reciprocal space maps at the symmetric 共0002兲and the asymmetric 共202 ¯ 5兲2Hreflections were taken to evaluate the crystal quality and the residual strain in the III-nitride epilayers, respectively. III. RESULTS A. Mosaic structure of III-nitride epilayers So far, heteroepitaxial thin 2H-III-nitride layers are characterized by a mosaic structure with an average subgrain size of 50–250 nm arising as the result of initial threedimensional 共3D兲nucleation and partial coalescence of the islands. Moreover, a mean grain size has been found to be a function of the growth conditions and the mismatch strain induced in the heterosystem representing the wetting properties of the epilayer deposited onto the substrate. In this part, some examples of the mosaic structures of thin binary IIInitride films will be considered to provide characteristic domain sizes for the numerical estimations and the forthcoming discussion. In Fig. 1, atomic force microscopy 共AFM兲, scanning electron microscopy 共SEM兲, and PVTEM micrographs of PIMBE III-nitride epilayer surfaces exhibiting a characteristic domain structure are presented. AFM image in Fig. 1共a兲 shows a mosaic surface of a 40 nm thick 2H-AlN layer nucleated on 共0001兲sapphire at 700 ° C and annealed at 1100 °C for 2 min. Typical layers have pronounced grain structures with the mean grain size of ⬃100 nm and the root mean square 共rms兲roughness of ⬃1.5 nm. In Fig. 1共b兲, SEM micrograph of the lateral interface between Ga and N faces of an ⬃500 nm thick GaN共0001兲 lateral polarity heterostructure22 共LPH兲shows a complete coalescence on the Ga-face side and the result of a partial coalescence on the N-face side. Due to the large GaN/ sapphire lattice mismatch and a reduced diffusion of Ga atoms on the N-face surface the coalescence of the N-face domains cannot be completed, leading to the specific mosaic structure of the film grown directly on sapphire with an average grain size of ⬃250 nm. Figures 1共c兲and 1共d兲show PVTEM images of a 70 nm thick 2H-InN layer grown on GaN共0001兲template demonstrating the partial coalescence between in-plane misoriented InN domains having the mean grain size ranging from 50 to 100 nm. It was demonstrated elsewhere12 that the lateral interaction of such domains leads to the formation of the b=1/3具112 ¯ 3典TDs distributed along the domain boundary with a spacing ranging from 20 to 50 nm. In contrast to PIMBE, MOCVD is capable of providing nucleation epilayers having larger domains. In Fig. 2,5 ⫻5 ␮ m2AFM images demonstrate an evolution of the mean grain size with respect to the epilayer thickness for 70, 140, and 210 nm thick GaN epilayers grown by MOCVD on AlN共20 nm兲/sapphire templates. The gradual increase of the characteristic domain size from 300 nm to ⬃2 ␮ m for 70 and 210 nm thick epilayers, respectively, corresponds to the long-term coalescence process of the nucleated islands into the continuous single crystalline film. The mosaic structure of AlN layers grown by MOCVD and PIMBE on sapphire was compared elsewhere.23 In particular, it was shown that the characteristic mean grain size depends on the deposition technology used, being a function of actual growth conditions provided by the specific method, i.e., deposition temperature, arrival flux of the species, group-III/group-V flux ratio, etc. The epitaxy of AlN thin films results in domain sizes of 80–120 nm and of 150–300 nm for PIMBE and MOCVD methods, respectively. In both cases, however, the mean domain size is limited by both kinetics and thermodynamics of the heterogeneous crystal growth addressed in the Discussion section. B. Coalescence dynamics 1. GAN/sapphire and GaN/AIN „ 0001 … heterosystems To study the dynamics of the coalescence in detail, a selective MOCVD of Ga-face GaN共0001兲nanostripes has been carried out on nanopatterned Al2O3共0001兲substrates. 100 nm wide and 10 ␮ m long nanogrooves have been created in SixNy/Al2O3templates by using e-beam lithography and reactive ion-etch techniques. The grooves were prepared along 具112 ¯ 0典and 具101 ¯ 0典directions of the sapphire surface to study the coalescence on the orthogonal facets. The etch process parameters were chosen to establish dashed-trench geometry of the grooves. In Fig. 3共a兲, it is shown that the etched grooves are not homogeneous in depth and, as a result, functional windows are opened in the SixNymask providing circular spots of open sapphire surface. These funcFIG. 2. 5⫻5 ␮ m2AFM images of 共a兲70, 共b兲140, and 共c兲210 nm thick GaN epilayers grown by MOCVD on a 20 nm thick AlN nucleation layer deposited on 共0001兲sapphire. 共d兲The surface profiles extracted from the AFM images. 054906-3 Lebedev et al. J. Appl. Phys. 101, 054906 共2007兲 tional windows with a diameter of ⬃50–60 nm are ideal nucleation sites for single GaN isolated islands—as it was discussed above; the thin GaN layers grown by MOCVD have a domain structure with domain sizes of 200–300 nm. The characteristic dimensions of the nucleation spots ensure that homogeneous, single islands will be formed at every nucleation point. Moreover, the short average distance between these spots allows growing GaN domains to coalesce within a short time of deposition. Figure 3shows various stages of nucleation and coalescence of 2H-GaN domains during the deposition. An estimation of the coalescence time 共 ␶ C兲for islands of average radius of ⬃200 nm yields a value of about 90 s, if we assume that the coalescence starts in a state similar to that shown in Fig. 3共b兲and is completed when a total junction between nuclei happens along grooves as shown in Fig. 3共d兲. The driving forces for the high rate of lateral growth and, consequently, of the coalescence are a surface diffusion of the adsorbed species. Adatoms diffuse on the island surface from the regions of high curvature 共fewer neighbors and therefore less strongly bound兲towards the regions of lower curvature 共e.g., facets兲, providing lateral growth of the initial nuclei.17 It is necessary to note that used pseudo-onedimensional growth geometry simplifies significantly the physical picture of the coalescence. The artificial structures used allow studying the coalescence in both orthogonal directions 共具112 ¯ 0典and 具101 ¯ 0典兲 of the hexagonal structure separately 关see Fig. 3共d兲兴. Macroscopic theories of coalescence via atomic surface diffusion predict a coalescence time,24 ␶ c=kT CDs共T兲 ␥ 冉 R a 冊 4 ,共1兲 where R⬃250 nm is the domain radius, ␥ is the surface energy of GaN共0001兲,C⬇25 is a numerical constant, Ds共T兲 is the surface diffusion coefficient, T=1120 °C is the growth temperature, and a⬃0.3 nm is the atomic dimension. The surface energies of the minimum energy GaN are nearly equal for various surfaces of GaN: ␥ 共112 ¯ 0兲⬃123 meV/Å2, ␥ 共101 ¯ 0兲⬃110 meV/Å2, and ␥ 共0001兲⬃125 meV/Å2.25 Thus, we assumed ␥ =1.89 J/m2for the whole island surface area. For the case shown in Fig. 3共Ga-face GaN兲we obtain Ds共1120 °C兲=2.2⫻10−12 m2s−1 using the experimental value of ␶ c=90 s. Thus, the estimated distance that an atom travels within the coalescence time ␶ cis Ddif=共Ds ␶ c兲1/2 ⬃14 ␮ m which is much higher than the particle size after the coalescence. Additionally, the observed flattop pyramids indicate a high lateral growth rate. Such a shape favors a rapid coalescence and a flatter morphology of the thicker films.17 One can see it in Fig. 3共e兲, where a larger window was used as a nucleation test area for a conventional 2D coalescence. In these series of experiments, it was also observed that the grain boundaries between interacting GaN共0001兲islands are predominantly formed along the 兵11 ¯ 00其planes 关Fig. 3共d兲兴. The analyses of the controlled coalescence process do not indicate that the hexagonal-shaped domains interact by the 兵112 ¯ 0其planes. The domain interaction on this plane family is rather poor, leading to the degeneration of the 兵112 ¯ 0其 contact interfaces to the grain boundaries along the 兵11 ¯ 00其 plane 关Fig. 3共d兲兴. This can be explained by the fact that boundaries along the 兵11 ¯ 00其planes have the lowest energies as well as the lowest mobilities.25,26 Therefore, energy minimization would make nuclei tend to bond by low-energy boundaries.15,16 Additionally, to compare the coalescence of Gaand N-face films directly, GaN LPHs 共Ref. 22兲were grown on patterned 2H-AlN/sapphire共0001兲templates by PIMBE. The LPHs contained a periodic lateral structure consisting of ⬃100 ␮ m wide Gaand N-face GaN stripes. The lateral interface between two faces is shown in SEM and AFM images 关Fig. 1共b兲and Figs. 4共a兲and 4共b兲兴. Here, the Ga-face GaN共0001兲has been grown on the developed AlN stripes 共lattice mismatch f⬍1%兲, while the N-face 共0001 ¯ 兲layer was nucleated directly on the sapphire surface 共f⬃14%兲.Asa result of lateral interaction of inverted domains, inversion domain boundaries 共IDBs兲are formed at vertical interfaces between two phases of 2H-GaN.22 The GaN epitaxy was initiated at ⬃650 °C, which is a typical growth condition for the Ga-face material. As one can see in Figs. 1共b兲and 4, due to the large mismatch between sapphire and GaN as well as FIG. 3. SEM micrographs of 共a兲a nanopatterned SixNy/sapphire template 共the triangles point to the open sapphire surface兲and 关共b兲–共d兲兴 various stages of nucleation and coalescence of 2H-GaN domains during the selective MOCVD. The Draws in 共d兲show the characteristic shape and interaction planes for GaN nuclei. 共e兲A fragment of a large reference window used for 2D nucleation. 054906-4 Lebedev et al. J. Appl. Phys. 101, 054906 共2007兲 due to the low mobility of Ga adatoms on the N-face GaN,5,21,27,28 the N-face side exhibits a very faceted growth surface with the mean grain size of ⬃200 nm, while Ga-face stripes are single-crystalline, smooth films. 2. InN/GaN „ 0001 … heterosystem Figure 5shows an initial stage of nucleation and partial coalescence of 2H-InN domains during the deposition on GaN共0001兲by PIMBE at 370° C 共f⬃13%兲. An estimation of the coalescence time 共 ␶ C兲for islands of average diameter of ⬃60 nm yields a value of about 35 s. For the case shown in Fig. 5we obtain very low Ds共370 °C兲⬃6⫻10−16 m2s−1 using the experimental value of ␶ c=35 s. The estimated distance that an atom travels within the coalescence time ␶ cis Ddif⬃0.14 ␮ m, which is only slightly larger than the average crystal size after the coalescence. In this particular case, a small mean grain size of the nucleated domains as well as a partial character of the coalescence are determined by low temperature of the deposition. The latter is illustrated by the SEM micrograph of a 70 nm thick InN epilayer shown in Fig. 5共b兲. For this sample, the coalescence is not completed and the surface structure is still dominant by large hexagonal domains with an average size of ⬃200 nm. A partial character of the coalescence results in slow improvements of the material quality with increasing thickness of the epilayer. In Fig. 5共c兲, the full width half maximum 共FWHM兲of the XRD rocking curves measured on IIInitride epilayers is plotted as a function of the epilayers thickness. Among the selected systems, InN on GaN shows the lowest rate of crystal quality improvements reflecting specific conditions of the InN growth, i.e., low growth temperature of In-face InN, which is limited by the thermal decomposition of InN at ⬃500 °C in vacuum. 3. AlN/sapphire heterosystem 2H-AlN buffer layers are commonly used in the heteroepitaxial growth of III-nitride heterostructures on conventional substrates. It was found that the heteroepitaxial growth across the III-nitride/sapphire interface is dictated by the Al–O bonding, which results in a 30° in-plane rotation of the nitride lattice with respect to the sapphire substrate.29 It delineates the epitaxial relationship between the film and subFIG. 4. 3⫻3 ␮ m2AFM 共a兲, and SEM 关共b兲and 共c兲兴 images of the GaN LPH demonstrating the impacts of surface diffusion and of low-temperature buffer layer on the morphology of N-face polarity 2H-GaN stripes. FIG. 5. 关共a兲and 共b兲兴 The mosaic structure of 2H-InN grown on GaN/ sapphire by PIMBE: 共a兲the PVTEM image of a 10 nm thick InN layer shows a typical domain size of ⬃50 nm. The moiré contrast is due to the overlapping of the InN and GaN related atomic planes. 共b兲SEM image of a 70 nm thick InN layer after the partial coalescence stage. 共c兲FWHM of XRD rocking curves taken at the 共0002兲reflex measured on MOCVD GaN, and PIMBE InN and AlN samples as a function of the epilayers thickness. 054906-5 Lebedev et al. J. Appl. Phys. 101, 054906 共2007兲 strate as follows: 共0001兲f 储 共0001兲s,关011 ¯ 0兴f 储 关1 ¯ 21 ¯ 0兴s, and 关1 ¯ 21 ¯ 0兴f 储 关011 ¯ 0兴s. The 30° rotation results in a mismatch of about 12% between the substrate 共as/冑3兲and the film 共af兲. The large lattice mismatch is accommodated by domain matching of the lattice constants 共7as/冑3=6af兲, where seven 共1 ¯ 21 ¯ 0兲planes of sapphire match six 共011 ¯ 0兲planes of the AlN film.30 In general, the quality of the AlN films grown directly 共i.e., without a low-temperature buffer layer兲on any plane of sapphire is poor as a result of the large lattice mismatch and difference in the coefficients of thermal expansions between the epilayer and the substrate. A low-temperature growth of AlN 共⬍700 °C for PIMBE兲allows full coverage of the substrate to be quickly achieved, and the subsequent layers can be grown at the optimal pseudohomoepitaxial conditions.31 It was also shown that the properties of the subsequent epilayers are strongly influenced by the thickness and growth temperature of the buffer layer. C. Effect of a low-temperature nucleation layer Any kind of deposition of III-nitride epilayers yields low-energy-deposited particles, which preserve their integrity upon impact onto the substrate at high temperatures. To overcome this repulsion, an initiation of the growth at low temperatures is widely used in III-nitride epitaxy resulting in formation of highly disordered 共textured兲“buffer” layers. In this stage, neither coalescence nor ripening processes occur. The growth of such layer can overcome the problems related to the high lattice mismatch32 and even to the differences in the crystal cell symmetry.33,34 It allows a full coverage of the substrate surface, but leads to a coarsening of the growing layer 关see Fig. 1共a兲兴. The low-temperature deposition is usually followed by annealing and long-term epitaxy at higher temperatures to achieve crystal quality and surface morphology suitable for device applications. Obviously, the temperature increase leads to the coalescence of the deposited textured aggregate. One illustration of this phenomenon is the time evolution of RHEED patterns during PIMBE nucleation and growth of AlN共0001兲on a Si共111兲substrate 共Fig. 6兲. The film was nucleated with the growth rate of ⬃0.5 ML s−1 共ML denotes monolayer兲at a low temperature of ⬃700 °C and at a high Al supersaturation 关Fig. 6共a兲兴. Then, after a short time of ⬃60 s of nucleation, the substrate temperature was increased rapidly 共50 °C/min兲till the growth point at ⬃910 °C 关see Figs. 6共b兲and 6共c兲兴. As one can see in these RHEED patterns, the nucleated film consists of highly misoriented nuclei of 2Hpolytype at the beginning of the process. A mean degree of the tilt is as high as 20° 关volume angle corresponding to an angular width of the arc shown in Fig. 6共a兲兴.Ifthe growth is continued at 910 °C, a well developed, “streaky” pattern is formed after approximately 50 nm of material deposition indicating a completed coalescence of the islands. In this case, both low diffusion and relatively high deposition rates increase, resulting in a high 2H-AlN nuclei density at low temperature. Additionally, it is generally assumed that the evolution of the average grain area obeys the time power law growth 具A典⬃tk.13 In accordance with theoretical predictions,16 in the case of highly textured polycrystalline aggregates, the average area of the grains is growing linearly with time 共k⬃1兲, allowing a full coverage of the substrate surface to be quickly achieved. A subsequential increase in the temperature leads to the partial coalescence of the domains into a continuous film. In fact, after ⬃10 nm 共2 min兲 of a high-temperature 共910 °C兲growth, the surface gets rough but single crystalline indicating a partially completed coalescence and a pseudo-2D growth 关Fig. 6共b兲兴. A longterm epitaxy at 910 °C results in a smoother surface 关Fig. 6共c兲兴with a rms roughness of ⬃1 nm as measured by AFM. The impact of coalescence on the crystal quality of AlN epilayers is shown in Fig. 6共c兲. The crystal quality of the layers of variable thickness has been evaluated by means of XRD rocking curves reflecting angular misorientation of the islands in 关0001兴direction. One can see that the maximum rate of reduction of the FWHM occurs in the range of 50–100 nm corresponding to the active phase of the coalescence process. Another example of the effect of the low-temperature buffer on material quality is the growth of GaN LPHs by PIMBE. In Fig. 4共c兲, the SEM image of GaN LPH grown on a low-temperature GaN buffer layer is shown. The obvious improvements in the N-face material morphology are the result of a 40 nm thick GaN buffer layer deposited at ⬃500 °C, which ensures a full coverage of the sapphire surface. The initial deposition is followed by the annealing step at 650 °C, leading to the improvements of the GaN crystal quality due to the island coalescence. In turn, the subsequent deposition at high temperature improves the surface morphology. FIG. 6. RHEED pattern time evolution for PIMBE of 2H-AlN共0001兲film nucleated on Si共111兲surface: 共a兲nucleation of the slightly misoriented islands, 共b兲coalescence of the islands into the continuous film at the elevated temperature, and 共c兲long-term 2D AlN epitaxy. 054906-6 Lebedev et al. J. Appl. Phys. 101, 054906 共2007兲 IV. DISCUSSION Despite the differences in mechanical properties, primary mismatch strains, and deposition methods used, all the investigated hexagonal heterosystems show nearly similar initial surface morphology and dynamics of the material quality improvements. It indicates that the residual misfits remaining in the heterosystems after nucleation stage do not differ significantly for the heterosystems discussed above. In highly mismatched hexagonal systems, it is generally not possible to strain the film lattice elastically to fit onto the template lattice at the interface. Instead there is an approximate matching of m共hkl兲fplanes of the film with n共hkl兲s planes of the template with m=n+1 for f⬍0, where 共hkl兲fis parallel to 共hkl兲sand both sets are normal to the interface.36 Since m=n±1, there is an extra half plane either in the film 共for f⬍0兲or in the substrate 共for f⬎0兲. Namely, these planes define a geometrical misfit dislocation 共GMD兲, a 60° dislocation with Burgers vector band line parallel to 具21 ¯ 1 ¯ 0典 directions and lying on the 共0001兲basal plane, which exists in a high percentage from the very start of the film growth. In the discussed cases, GMDs are the only mechanism to relief a huge primary strain in the heterosystem down to the value allowing epitaxial growth. In Table I, the values of the primary and residual in plane strains for the investigated systems are listed. One can see that for the majority of the heterosystems residual misfit does not exceed 1.5%, while 2H-InN epilayers grown on GaN and AlN templates show the highest residual strain of ⬃4% measured dynamically by in situ RHEED.12 In particular, this fact explains a low rate of improvements in the material quality of InN epilayers represented by the FWHM versus thickness curves shown in Fig. 5共c兲. A. The origin of the mosaic structure Besides the accommodation of the initial misfit by introduction of GMDs at the heterointerface,12,32 there is another way to relax misfit strain within the nucleated epilayer destabilizing the growth front.11 Indeed, in the simplified case, the wetting conditions for the epilayer are defined by the balance between the formation energies of the film surface ␴ film, the template surface ␴ sub, and the formation energy of the epilayer Ef,37 which is a function of the actual growth conditions 共e.g., the supersaturation Sand temperature T兲 and the stress energy Estr arising from the mismatch between template and epilayer, Ef共S,T,Estr兲⬎ ␴ film − ␴ sub −⌬E.共2兲 In other words, the residual misfit strain can destabilize the growth front by producing surface modulation20 关Fig. 7共a兲兴 or eventually forming islands 关Fig. 7共b兲兴.12 The last term in Eq. 共2兲,⌬E, represents the reduction in the total energy of the system due to such pseudoperiodical undulations at the growing surface.20,37 Consequently, the nucleation step can result in a second-order elastic relaxation of the epilayer within the nucleated nanoislands. As an example, we will compare three heterosystems grown by PIMBE representing the boundary cases for the wurtzite III nitrides. After initial misfit relaxation via GMDs, InN/AlN and AlN/Al2O3heterosystems have residual strains of ⬃4.1% and of ⬃2%, respectively, as it was shown by in situ RHEED and HRTEM observations.12 In contrast, Al0.3Ga0.7N layer grown on GaN pseudomorphically has to accommodate the residual strain of ⬃0.8%. Approximated analytical solutions for the equilibrium strains have been discussed in the literature for a periodic set of thin deposits.11,12,38 It was shown that the surface stress may enhance, compensate, or decrease the epitaxial misfit. Moreover, the island relaxes by its free borders so that the lateral stress becomes height dependent. In the frame of a 2D thick ribbon model,38 a simple isotropic approximation for TABLE I. Primary and residual strains in the investigated heterosystems. Heterosystem Primary strain 共%兲 m:n ratio Residual strain 共%兲 AlN/Si共111兲23 5:4a1.3a GaN/Al2O316 7:8a⬃2b AlN/Al2O313 6:7a⬃2b Al0.3Ga0.7N/GaN 0.8 1:1c0.8c InN/GaN 11 8:9a⬃4b InN/AlN 13 7:8a⬃4b aHRTEM, see Refs. 12,32,35,and36. bIn situ RHEED, see Ref. 12 for method description. cHRTEM, this work. FIG. 7. HRTEM images 共a兲Al0.3Ga0.7N/GaN hetorostructure and 共b兲of 2H-InN island nucleated on an AlN template; 共c兲calculated in-plane strain due to the island growth as a function of the characteristic island size lfor different 2Hheterosystems. 054906-7 Lebedev et al. J. Appl. Phys. 101, 054906 共2007兲 the relaxation of the topmost layers of the 2Hislands can be obtained. The model assumes that the strain in an infinitely long ribbon of height hand width l, deposited coherently on a substrate having a misfit f0, is given by Iyy共x,N兲=Iyy共x,0兲具M1典N−1,共3兲 具M1典=1−2 ␲ a l+ 冉 1+冑2 ␲ a l 冊 2 exp 冉 −冑2l a ␲ 冊 ,共4兲 where Ndefines the number of monolayers and varies from 0 to h/a—the total number of monolayers included in the ribbon of height h. The dependence of the residual strain remaining in the system on the characteristic island width lbased on Eq. 共3兲is presented in Fig. 7共c兲. Using this approximation, we can interpret the experimental results obtained by TEM 共Fig. 7兲in the following way. One can assume a critical value of the residual strain, fc, which is a boundary between an island and continuous film growth. The value of fcdepends on the elastic stiffness constants of the deposit and the actual growth parameters 共e.g., supersaturation兲. However, the typical experimental values of fclie in the range of 1%–2%. Accepting fc⬃1.5% as a boundary between the 2D and 3D growth modes, we can confirm that for the Al0.3Ga0.7N/GaN system, lis infinitely large providing continues film growth. The residual strain relief is achieved by destabilization of the growth front resulting in the periodical undulations of the growing surface 关Fig. 7共a兲兴. On the other hand, PIMBE of the InN/AlN and AlN/Al2O3heterosystems can be stabilized only by the reduction of the characteristic domain size resulting in the formation of the mosaic structure of the film with lof ⬃50–100 nm. These values correspond well to the experimentally observed characteristic size of the III-nitride islands taking part in the subsequent coalescence. According to the suggested model, the residual strain in the epilayer determines the characteristic size of the growing islands preventing the growth of large area domains during the nucleation stage. However, two important notes concerning the model restrictions have to be made. The model does not take into account a plastic deformation of the islands as well as kinetic parameters governing island growth.11 Since surface stresses are adsorption sensitive, a surface adsorption may force the equilibrium strains and stresses to change in a reversible fashion. The latter is the case for MOCVD grown III-nitride films, where significantly larger domain sizes governed by high pressures and high temperatures characteristic for the growth can be reached. B. Coalescence kinetics In general, the growth mode of an epilayer is determined by both bulk thermodynamics and surface kinetics. However, in the nonequilibrium conditions characteristic for III-nitride growth, surface kinetics plays often a dominant role, especially during the early stages of nucleation and growth. Using a Peclet number 共the ratio between the system length and the diffusion length兲39,40 Pe= ␶ diffusion ␶ arrival =L2F Ds ,共5兲 as a criterion, we can define the growth conditions for a required rapid coalescence 共PeⰆ1兲. For Pe⬎1, the surface mobility is low, promoting sticking of the species on top of the islands. As an example, we can consider the MOCVD GaN nanostripes discussed in the experimental part 共Fig. 3兲. For this structure, L⬃50 nm is the mean distance between nucleation sites on the surface and Fis the arrival rate of the species on the surface 共⬃2MLs −1 for the MOCVD growth rate ⬃16 nm min−1兲. In this particular case, Pe⬃0.002Ⰶ1 indicates that the surface diffusion is a dominant process providing a high rate of the lateral growth of initial nuclei. The Peclet number as a function of GaN growth temperature is shown in Fig. 8共a兲. One can see that conditions for the rapid coalescence for MOCVD growth are rather easily achievable than those for the case of PIMBE. It leads to a higher characteristic domain size during MOCVD growth usually resulting in a better device performance. Similar consideration performed for the InN epilayer PIMBE growth 关see Figs. 5共a兲and 5共b兲兴gives principally different results. Due to the low diffusion at the characteristic growth temperature ⬃370–400 °C, the condition Pe⬃0.1 can be fulFIG. 8. The Peclet number as a criterion of the rapid coalescence process for 共a兲PIMBE and MOCVD of GaN and 共b兲PIMBE of InN. 054906-8 Lebedev et al. J. Appl. Phys. 101, 054906 共2007兲