DFT modelling of stacking faults in hexagonal and cubic GaN

TL;DR

This work addresses how stacking faults in GaN affect structure and electronic properties across the two allotropes, wz and zb. Using large-scale periodic DFT with a consistent band-edge reference, the authors compute formation energies and map local electronic structure for all fault types, revealing phase-dependent charge localization and band-edge shifts. The key findings are that wz I1 is the most stable fault while zb faults have very low formation energies, and that all faults induce type II band offsets with local band-gap reductions. These insights inform defect engineering in GaN-based devices and interpretation of high-resolution imaging and spectroscopy data, with the full dataset made openly available.

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 (0001) planes can be divided into three different intrinsic stacking faults (I1, I2, and I3) and oneextrinsic stacking fault (E). In zb GaN, SFs form along (111) directions, giving one type each of intrinsic, extrinsic and twin SFs. Based on the calculated formation energy, I1 is the most stable SF of wz GaN in agreement with experiment. For zb GaN, the intrinsic stacking fault is the most dominant planar defect. 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 localised 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 delocalised. We found the opposite trend in zb GaN; this behaviour 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.

Figures (20)

• Figure 1: Stacking faults in wurtzite GaN. (a) Intrinsic 1 (I$_{1}$) /AB/CBCB/AB/, (b) Intrinsic 2 (I$_{2}$) /AB/CACA/C/AB/, (c) Intrinsic 3 (I$_{3}$) /AB/C/BABA/C/AB/ and (d) Extrinsic /ABAB/C/ABAB/. Note that these are highly shortened cells for illustration only.
• Figure 2: Stacking faults in Zincblende GaN. (a) Extrinsic /ABC/B/ABC/, (b) Intrinsic /ABC/BC/ABC/ and (c) Twin /ABC/BAC/ABC/. Note that these are highly shortened cells for illustration only.
• Figure 3: Band resolved densities of Intrinsic-1 stacking fault of wz GaN, here shown with six layers between stacking faults (/3AB/6CB/3AB/). The bands below the Fermi energy are shown in panels (a-d), and the bands above the Fermi energy are shown in panels (e-h). The isosurfaces were plotted at a density of 0.0005 electrons per Bohr$^{3}$. Note that there are two stacking faults in the simulation cell, 25% and 75% of the way along the cell.
• Figure 4: Band resolved densities of Intrinsic stacking fault for zb GaN along (111), here shown with eight layers between stacking faults (/4ABC/BC/4ABC/). The bands below the Fermi energy are shown in panels (a-d), and the bands above the Fermi energy are shown in panels (e-h). The isosurfaces were plotted at a density of 0.0005 electrons per Bohr$^{3}$. There is one stacking fault, halfway along the simulation cell.
• Figure 5: Potential difference between faulted and perfect material, averaged in the x-y plane (top), density difference found in the same way (middle) and density difference integrated along z (bottom) for (a) I$_{1}$ SF in wz and (b) Intrinsic SF in zb.