- Open Access
DFT modeling of stacking faults in hexagonal and cubic GaN
Phys. Rev. B 114, 115303 – Published 11 August, 2026
DOI: https://doi.org/10.1103/cb62-j7t7
Abstract
We have performed density functional theory (DFT) calculations to characterize the energetics, and the atomic and electronic structure, of stacking faults in GaN, both in the stable hexagonal wurtzite (wz) phase and in the metastable cubic zincblende (zb) phase. In wz GaN, SFs on the planes can be divided into three different intrinsic stacking faults (, and ) and one extrinsic stacking fault (E). Based on the calculated formation energy, is the most stable SF of wz GaN in agreement with experiment. In zb GaN, SFs form on planes, giving one type each of intrinsic, extrinsic, and twin SFs. In our calculations, the three types of SFs have similar formation energy. To characterize the effect of the stacking faults on the electronic structure of the material, we examined the band density. We found that the bands near the valence band maximum in wz GaN are localized on the Ga-polar side of the stacking fault (i.e., on the Ga side of the Ga-N bonds perpendicular to the SF), with the bands near the conduction band minimum more on the N-polar side, though somewhat delocalized. We found the opposite trend in zb GaN; this behavior is caused by a redistribution of charge near the interface. We also show the band offsets for the stacking faults, finding that they are very sensitive to local conditions, but can all be described as type II interfaces, with the presence of a stacking fault reducing the gap locally in both wz and zb.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (48)
- B. Ding, Improving radiative recombination efficiency of green light-emitting diodes, Mater. Sci. Technol. 34, 1615 (2018).
- T. Ito, T. Araki, T. Akiyama, and K. Nakamura, A simple approach to temperature dependence of strain energy: Application to GaN-based semiconductors, J. Cryst. Growth 301-302, 62 (2007).
- S. Lester, F. A. Ponce, M. G. Craford, and D. A. Steigerwald, High dislocation densities in high efficiency GaN-based light-emitting diodes, Appl. Phys. Lett. 66, 1249 (1995).
- M. Moram, C. Ghedia, D. Rao, J. Barnard, Y. Zhang, M. Kappers, and C. Humphreys, On the origin of threading dislocations in GaN films, J. Appl. Phys. 106, 073513 (2009).
- M. Häberlen, T. J. Badcock, M. A. Moram, J. L. Hollander, M. J. Kappers, P. Dawson, C. J. Humphreys, and R. A. Oliver, Low temperature photoluminescence and cathodoluminescence studies of nonpolar GaN grown using epitaxial lateral overgrowth, J. Appl. Phys. 108, 033523 (2010).
- D. N. Zakharov, Z. Liliental-Weber, B. Wagner, Z. J. Reitmeier, E. A. Preble, and R. F. Davis, Structural TEM study of nonpolar -plane gallium nitride grown on by organometallic vapor phase epitaxy, Phys. Rev. B 71, 235334 (2005).
- W. Z. Tawfik, G. Y. Hyeon, and J. K. Lee, Stress-induced piezoelectric field in GaN-based 450-nm light-emitting diodes, J. Appl. Phys. 116, 164503 (2014).
- F. Bernardini, V. Fiorentini, and D. Vanderbilt, Spontaneous polarization and piezoelectric constants of III-V nitrides, Phys. Rev. B 56, R10024 (1997).
- H. Morkoç, R. Cingolani, W. Lambrecht, B. Gil, H.-X. Jiang, J. Lin, D. Pavlidis, and K. Shenai, Material properties of GaN in the context of electron devices, MRS Internet J. Nitride Semic. Res. 4, 18 (1999).
- H. Yang, O. Brandt, A. Trampert, and K. Ploog, Initial stage of growth of in plasma-assisted molecular beam epitaxy, Appl. Surf. Sci. 104-105, 461 (1996).
- A. Trampert, O. Brandt, H. Yang, and K. Ploog, Direct observation of the initial nucleation and epitaxial growth of metastable cubic GaN on (001) GaAs, Appl. Phys. Lett. 70, 583 (1997).
- S. A. Church, M. Quinn, K. Cooley-Greene, B. Ding, A. Gundimeda, M. J. Kappers, M. Frentrup, D. J. Wallis, R. A. Oliver, and D. J. Binks, Photoluminescence efficiency of zincblende InGaN/GaN quantum wells, J. Appl. Phys. 129, 175702 (2021).
- D. J. Binks, P. Dawson, R. A. Oliver, and D. J. Wallis, Cubic GaN and InGaN/GaN quantum wells, Appl. Phys. Rev. 9, 041309 (2022).
- B. Ding, M. Frentrup, S. Fairclough, M. Kappers, M. Jain, A. Kovács, D. Wallis, and R. Oliver, Alloy segregation at stacking faults in zincblende GaN heterostructures, J. Appl. Phys. 128, 145703 (2020).
- C. Stampfl and C. G. Van de Walle, Density-functional calculations for III-V nitrides using the local-density approximation and the generalized gradient approximation, Phys. Rev. B 59, 5521 (1999).
- I. G. Batyrev, W. L. Sarney, T. S. Zheleva, C. Nguyen, B. M. Rice, and K. A. Jones, Dislocations and stacking faults in hexagonal GaN, Phys. Stat. Sol. A 208, 1566 (2011).
- A. Benbedra, S. Meskine, A. Boukortt, R. Hayn, M. Texier, O. Thomas, and T. W. Cornelius, Energetics, electronic structure and electric polarization of basal stacking faults in wurtzite GaN and ZnO, Comp. Cond. Matter 43, e01033 (2025).
- Z. Antoš, P. Vacek, and R. Gröger, Intersections of two stacking faults in zincblende GaN, Comput. Mater. Sci. 180, 109620 (2020).
- M. Barchuk, V. Holý, D. Kriegner, J. Stangl, S. Schwaiger, and F. Scholz, Diffuse x-ray scattering from stacking faults in -plane GaN epitaxial layers, Phys. Rev. B 84, 094113 (2011).
- M. Moram, C. Johnston, J. Hollander, M. Kappers, and C. Humphreys, Understanding x-ray diffraction of nonpolar gallium nitride films, J. Appl. Phys. 105, 113501 (2009).
- E. Yücelen, I. Lazić, and E. G. Bosch, Phase contrast scanning transmission electron microscopy imaging of light and heavy atoms at the limit of contrast and resolution, Sci. Rep. 8, 2676 (2018).
- H. Xiu, S. M. Fairclough, A. Gundimeda, M. J. Kappers, D. J. Wallis, R. A. Oliver, and M. Frentrup, Polarity determination of crystal defects in zincblende GaN by aberration-corrected electron microscopy, J. Appl. Phys. 133, 105302 (2023).
- D. R. Bowler, T. Miyazaki, and M. J. Gillan, Recent progress in linear scaling ab initio electronic structure techniques, J. Phys.: Condens. Matter 14, 2781 (2002).
- T. Miyazaki, D. R. Bowler, R. Choudhury, and M. J. Gillan, Atomic force algorithms in density functional theory electronic-structure techniques based on local orbitals, J. Chem. Phys. 121, 6186 (2004).
- A. Nakata, J. S. Baker, S. Y. Mujahed, J. T. L. Poulton, S. Arapan, J. Lin, Z. Raza, S. Yadav, L. Truflandier, T. Miyazaki, and D. R. Bowler, The journal of chemical physics, large scale and linear scaling DFT with the CONQUEST code, J. Chem. Phys. 152, 164112 (2020).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
- M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G. M. Rignanese, The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table, Comput. Phys. Commun. 226, 39 (2018).
- D. R. Bowler, J. S. Baker, J. T. L. Poulton, S. Y. Mujahed, J. Lin, S. Yadav, Z. Raza, and T. Miyazaki, Highly accurate local basis sets for large-scale DFT calculations in conquest, Jpn. J. Appl. Phys. 58, 100503 (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/cb62-j7t7 for details of calculations and further results for all types of stacking fault.
- B. Schaefer, S. Alireza Ghasemi, S. Roy, and S. Goedecker, Stabilized quasi-Newton optimization of noisy potential energy surfaces, J. Chem. Phys. 142, 034112 (2015).
- The stacking sequence of the layers in bulk GaN are often notated AaBb (wz) and AaBbCc (zb) with Aa indicating the alternation of planes of Ga and N along the [0001] direction (wz) or [111] direction (zb). We will shorten this to AB and ABC, respectively, for simplicity of notation.
- B. Ding, Study of wurtzite and zincblende GaN based green LED heterostructure, Ph.D. thesis, University of Cambridge, 2021.
- H. Schulz and K. Thiemann, Crystal structure refinement of AlN and GaN, Solid State Commun. 23, 815 (1977).
- M. Frentrup, L. Y. Lee, S.-L. Sahonta, M. J. Kappers, F. Massabuau, P. Gupta, R. A. Oliver, C. J. Humphreys, and D. J. Wallis, X-ray diffraction analysis of cubic zincblende III-nitrides, J. Phys. D: Appl. Phys. 50, 433002 (2017).
- Y. Gao, D. Sun, X. Jiang, and J. Zhao, Point defects in group III nitrides: A comparative first-principles study, J. Appl. Phys. 125, 215705 (2019).
- L. C. De Carvalho, A. Schleife, and F. Bechstedt, Influence of exchange and correlation on structural and electronic properties of AlN, GaN, and InN polytypes, Phys. Rev. B 84, 195105 (2011).
- M. Moram and M. Vickers, X-ray diffraction of III-nitrides, Rep. Prog. Phys. 72, 036502 (2009).
- S. Takeuchi and K. Suzuki, Stacking fault energies of tetrahedrally coordinated crystals, Phys. Status Solidi (A) 171, 99 (1999).
- J. Lähnemann, O. Brandt, U. Jahn, C. Pfüller, C. Roder, P. Dogan, F. Grosse, A. Belabbes, F. Bechstedt, A. Trampert, and L. Geelhaar, Direct experimental determination of the spontaneous polarization of GaN, Phys. Rev. B 86, 081302(R) (2012).
- R. Resta and D. Vanderbilt, Theory of polarization: A modern approach, in Physics of Ferroelectrics: A Modern Perspective (Springer, Berlin, Heidelberg, 2007), pp. 31–68.
- R. Resta, Macroscopic polarization from electronic wave functions, Int. J. Quantum Chem. 75, 599 (1999).
- M. A. Caro, S. Schulz, and E. P. O'Reilly, Theory of local electric polarization and its relation to internal strain: Impact on polarization potential and electronic properties of group-III nitrides, Phys. Rev. B 88, 214103 (2013).
- I. Vurgaftman and J. R. Meyer, Band parameters for nitrogen-containing semiconductors, J. Appl. Phys. 94, 3675 (2003).
- X. H. Lu, P. Y. Yu, L. X. Zheng, S. J. Xu, M. H. Xie, and S. Y. Tong, Evidence for a type-II band alignment between cubic and hexagonal phases of GaN, Appl. Phys. Lett. 82, 1033 (2003).
- Y. J. Sun, O. Brandt, U. Jahn, T. Y. Liu, A. Trampert, S. Cronenberg, S. Dhar, and K. H. Ploog, Impact of nucleation conditions on the structural and optical properties of -plane grown on -LiAlO2, J. Appl. Phys. 92, 5714 (2002).
- R. Liu, A. Bell, F. A. Ponce, C. Q. Chen, J. W. Yang, and M. A. Khan, Luminescence from stacking faults in gallium nitride, Appl. Phys. Lett. 86, 021908 (2005).
- D. R. Bowler, Z. Wang, and M. M. Islam, Input files for GaN stacking faults, Zenodo, 2026, https://doi.org/10.5281/zenodo.18259436.