In this review, the structural, mechanical, thermal, and chemical properties of substrates used for gallium nitride (GaN) epitaxy are compiled, and the properties of GaN films deposited on these substrates are reviewed. Among semiconductors, GaN is unique; most of its applications uses thin GaN films deposited on foreign substrates (materials other than GaN); that is, heteroepitaxial thin films. As a consequence of heteroepitaxy, the quality of the GaN films is very dependent on the properties of the substrate—both the inherent properties such as lattice constants and thermal expansion coefficients, and process induced properties such as surface roughness, step height and terrace width, and wetting behavior. The consequences of heteroepitaxy are discussed, including the crystallographic orientation and polarity, surface morphology, and inherent and thermally induced stress in the GaN films. Defects such as threading dislocations, inversion domains, and the unintentional incorporation of impurities into the epitaxial GaN layer resulting from heteroepitaxy are presented along with their effect on device processing and performance. A summary of the structure and lattice constants for many semiconductors, metals, metal nitrides, and oxides used or considered for GaN epitaxy is presented. The properties, synthesis, advantages and disadvantages of the six most commonly employed substrates (sapphire, 6H-SiC, Si, GaAs, LiGaO 2 , and AlN) are presented. Useful substrate properties such as lattice constants, defect densities, elastic moduli, thermal expansion coefficients, thermal conductivities, etching characteristics, and reactivities under deposition conditions are presented. Efforts to reduce the defect densities and to optimize the electrical and optical properties of the GaN epitaxial film by substrate etching, nitridation, and slight misorientation from the (0 0 0 1) crystal plane are reviewed. The requirements, the obstacles, and the results to date to produce zincblende GaN on 3C-SiC/Si(0 0 1) and GaAs are discussed. Tables summarizing measures of the GaN quality such as XRD rocking curve FWHM, photoluminescence peak position and FWHM, and electron mobilities for GaN epitaxial layers produced by MOCVD, MBE, and HVPE for each substrate are given. The initial results using GaN substrates, prepared as bulk crystals and as free-standing epitaxial films, are reviewed. Finally, the promise and the directions of research on new potential substrates, such as compliant and porous substrates are described.

Substrates for gallium nitride epitaxy

Introduction Properties of Semiconductors Introduction Crystallographic Properties Lattice Constants and Thermal Expansion Coefficients Elastic Properties Surface Free Energy Dislocations Planar Defects Problems References Heteroepitaxial Growth Introduction Vapor Phase Epitaxy (VPE) Molecular Beam Epitaxy (MBE) Silicon, Germanium, and Si1-xGex Alloys Silicon Carbide III-Arsenides, III-Phosphides, and III-Antimonides III-Nitrides II-VI Semiconductors Conclusion Problems References Surface and Chemical Considerations in Heteroepitaxy Introduction Surface Reconstructions Nucleation Growth Modes Nucleation Layers Surfactants in Heteroepitaxy Quantum Dots and Self-Assembly Problems References Mismatched Heteroepitaxial Growth and Strain Relaxation Introduction Pseudomorphic Growth and the Critical Layer Thickness Dislocation Sources Interactions between Misfit Dislocations Lattice Relaxation Mechanisms Quantitative Models for Lattice Relaxation Lattice Relaxation on Vicinal Substrates: Crystallographic Tilting of Heteroepitaxial Layers Lattice Relaxation in Graded Layers Lattice Relaxation in Superlattices and Multilayer Structures Dislocation Coalescence, Annihilation, and Removal in Relaxed Heteroepitaxial Layers Thermal Strain Cracking in Thick Films Problems References Characterization of Heteroepitaxial Layers Introduction X-Ray Diffraction Electron Diffraction Microscopy Crystallographic Etching Techniques Photoluminescence Growth Rate and Layer Thickness Composition and Strain Determination of Critical Layer Thickness Crystal Orientation Defect Types and Densities Multilayered Structures and Superlattices Growth Mode Problems References Defect Engineering in Heteroepitaxial Layers Introduction Buffer Layer Approaches Reduced Area Growth Using Patterned Substrates Patterning and Annealing Epitaxial Lateral Overgrowth (ELO) Pendeo-Epitaxy Nanoheteroepitaxy Planar Compliant Substrates Free-Standing Semiconductor Films Conclusion Problems References Appendix A: Bandgap Engineering Diagrams Appendix B: Lattice Constants and Coefficients of Thermal Expansion Appendix C: Elastic Constants Appendix D: Critical Layer Thickness Appendix E: Crystallographic Etches Appendix F: Tables for X-Ray Diffraction Index

Heteroepitaxy of Semiconductors: Theory, Growth, and Characterization

Nuclear resonant scattering techniques with synchrotron radiation (SR) are introduced on a basic level. We focus on the theoretical background and on experimental aspects of two popular methods with a widening range of applications, nuclear resonant inelastic x-ray scattering and synchrotron Mossbauer spectroscopy. The inelastic method provides specific vibrational information, e.g., the phonon density of states. The Mossbauer method permits determination of hyperfine interactions. All nuclear resonance techniques take full advantage of the unique properties of SR: intensity, collimation, time structure, and polarization. As a result both methods discussed here have led to novel applications for materials under extreme conditions, proteins with biological functionality, and magnetic nanostructures.

https://iopscience.iop.org/article/10.1088/0953-8984/16/5/009/pdf

Nuclear resonant spectroscopy

http://www.nims.go.jp/NFM/paper1/SuperconductingDiamond/09SolidStateCommun133(2005)3-18.pdf

Electron-phonon interaction in tetrahedral semiconductors

Mirror-turn axis of the sixth order (ternary inversion axis)


Three axes of the second order normal to it


Three symmetry planes normal to the axes of the second order and intercrossing along the axis of the highest order


Symmetry center

Properties of Sapphire

The lattice parameters of α-Al2O3 have been measured in a temperature range from 4.5 to 250 K with a relative accuracy of better than 6 × 10−6. The experimental method uses Bragg backscattering and the recently proposed Mossbauer wavelength standard, i.e. the wavelength λM = 86.025474 (16) pm of the nuclear resonance radiation of 57Fe (Shvyd'ko et al., 2000), which has previously been applied successfully to measure the lattice parameters of α-Al2O3 at temperatures between 286 and 374 K (Shvyd'ko et al., 2002). The experimental data in the range from 4.5 to 374 K are consistent with the Debye model of thermal expansion. At 4.5 K, the thermal expansion coefficient is as low as 1.2 (9) × 10−10 K−1 in the a direction.

Precise measurement of the lattice parameters of α-Al2O3 in the temperature range 4.5–250 K using the Mössbauer wavelength standard

We demonstrate an interferometer for hard x rays with two back-reflecting sapphire crystal mirrors---a prototype x-ray Fabry-P\'erot interferometer. A finesse of $15$ and $0.76\text{ }\text{ }\ensuremath{\mu}\mathrm{e}\mathrm{V}$ broad Fabry-P\'erot transmission resonances are measured by the time response of the interferometer. Interference patterns are observed directly in spectral dependences of reflectivity.

/pdf/x-ray-interferometry-with-microelectronvolt-resolution-43y7exiahm.pdf

X-Ray Interferometry with Microelectronvolt Resolution

The wavelength of the ${}^{57}\mathrm{Fe}$ M\"ossbauer radiation is measured with a relative uncertainty of 0.19 ppm by using almost exact Bragg backscattering from a reference silicon crystal. Its value is determined as ${\ensuremath{\lambda}}_{\mathrm{M}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.86025474(16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ m. The corresponding M\"ossbauer photon energy is ${E}_{\mathrm{M}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}14412.497(3)$ eV. The wavelength of the ${}^{57}\mathrm{Fe}$ M\"ossbauer radiation is easily reproducible with an accuracy of at least ${10}^{\ensuremath{-}11}{\ensuremath{\lambda}}_{\mathrm{M}}$ and could be used as a length standard of atomic dimensions.

γ -Ray Wavelength Standard for Atomic Scales

The difference $\ensuremath{\Delta}a={a}_{(30)}\ensuremath{-}{a}_{(28)}$ of the lattice parameter of $^{\mathrm{30}}\mathrm{S}\mathrm{i}$ and $^{\mathrm{28}}\mathrm{S}\mathrm{i}$ crystals is measured over a temperature range from 4.7 to 700 K. In disagreement with existing knowledge, the strongest isotopic effect is not detected at the lowest achieved temperature $T=4.7\text{ }\text{ }\mathrm{K}$. An anomalous behavior is observed: The relative difference $|\ensuremath{\Delta}a/a|$ attains its maximum value of 56.8(5) ppm at $T=75(10)\text{ }\text{ }\mathrm{K}$. The anomalous behavior is attributed to the influence of phonon modes with negative Gr\"uneisen parameters. At $T=700\text{ }\text{ }\mathrm{K}$ the effect still amounts to 30% of the maximal value. The experimental data are consistent with an approach based on the density-functional perturbation theory.

/pdf/anomalous-isotopic-effect-on-the-lattice-parameter-of-1jx8t43wkq.pdf

Anomalous isotopic effect on the lattice parameter of silicon.

The newly proposed atomic-scale length standard, the wavelength of the 57Fe Mossbauer radiation [Shvyd'ko et al. (2000). Phys. Rev. Lett. 45, 495–498], is used to measure the wavelengths of the Mossbauer radiation of 151Eu, 57.556185 (27) pm, 119Sn, 51.920811 (39) pm, and 161Dy, 48.334336 (19) pm, with a relative accuracy of ∼0.5 p.p.m. Also, the lattice constants of Al2O3 are measured in a temperature range from 286 K to 374 K. At room temperature, T = 295.65 K, their values are a = 4.759213 (8) A, c = 12.991586 (4) A.

M. Lerche

Papers

Precise measurement of the lattice parameters of α-Al2O3 in the temperature range 4.5–250 K using the Mössbauer wavelength standard

X-Ray Interferometry with Microelectronvolt Resolution

γ -Ray Wavelength Standard for Atomic Scales

Anomalous isotopic effect on the lattice parameter of silicon.

Measuring wavelengths and lattice constants with the Mössbauer wavelength standard