DFT modelling of stacking faults in hexagonal and cubic GaN

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.

💡 Research Summary

In this work the authors employ large‑scale density‑functional theory (DFT) calculations, implemented in the Conquest code, to investigate stacking faults (SFs) in both the stable wurtzite (wz) and the metastable zincblende (zb) polytypes of GaN. Using the GGA‑PBE exchange‑correlation functional together with norm‑conserving pseudopotentials and a double‑zeta plus polarization (DZP) real‑space orbital basis, they achieve sub‑µHa energy convergence and stress convergence better than 0.01 GPa. The crystal geometries are modelled in orthorhombic supercells that preserve the correct a/b ratio (√3) for each polytype. For the wurtzite phase, four SF types are considered on the (0001) plane: three intrinsic faults (I1, I2, I3) and one extrinsic fault (E). For the zincblende phase, three planar defects are examined on the (111) direction: intrinsic, extrinsic and twin. Periodic boundary conditions require two faults per cell for the wurtzite models and one for the zincblende models; the authors systematically increase the number of bulk layers separating the faults to verify convergence of the formation energies.

The formation energy per unit area is defined as ΔE = E_SF – n E_ref, where E_ref is the energy per layer of the perfect bulk. Converged values (in mJ m⁻²) are reported after testing supercells with up to 34 layers. In wurtzite GaN, I1 has the lowest formation energy (≈ 17 mJ m⁻²), followed by I2 (≈ 28 mJ m⁻²), I3 (≈ 36 mJ m⁻²) and finally the extrinsic fault (≈ 55 mJ m⁻²). This hierarchy matches experimental observations that about 90 % of basal‑plane SFs in wz‑GaN are of the I1 type. In zincblende GaN all three faults have essentially the same negative formation energy (≈ –33 mJ m⁻²), reflecting that a wurtzite insertion is energetically favorable in the zb matrix; the intrinsic fault is experimentally the most abundant.

Electronic structure is probed by plotting band‑resolved charge densities ρ_n(r) for states near the Fermi level. In both polytypes the valence‑band edge states localise on one side of the fault while the conduction‑band edge states localise on the opposite side, but the polarity of the localisation is opposite in the two structures. In wurtzite GaN the valence‑band charge resides on the Ga‑polar side of the fault and the conduction‑band charge on the N‑polar side. In zincblende GaN the situation is reversed. The authors attribute this behaviour to a redistribution of the electrostatic potential across the fault, which they extract by planar averaging along the c‑axis. The resulting potential step produces a type‑II band alignment for all faults: the valence‑band maximum (VBM) and conduction‑band minimum (CBM) are situated in different polar regions, effectively forming a quantum‑well‑like potential that locally narrows the band gap.

Band offsets are found to be highly sensitive to the local atomic configuration, but all faults can be described as type‑II interfaces. The calculated inter‑planar spacings within the faults (≈ 2.64 Å for both polytypes) are essentially identical to bulk values, confirming that the faults do not introduce significant strain. The authors also report the fault thickness l, defined as the number of disrupted layers, which is consistent with recent high‑resolution STEM measurements.

Overall, the paper delivers a comprehensive first‑principles picture of stacking‑fault energetics and electronic effects in GaN. It clarifies why I1 dominates in wurtzite GaN, why intrinsic faults are prevalent in zincblende GaN, and how these planar defects generate type‑II band offsets that can act as quantum wells. These insights are directly relevant to the design of GaN‑based optoelectronic devices: they suggest routes to mitigate the quantum‑confined Stark effect in wurtzite structures, to exploit the non‑polar character of zincblende GaN for longer‑wavelength emission, and to engineer fault‑induced quantum‑confined states for novel light‑emitting or carrier‑confinement applications. Future work extending the present methodology to alloyed systems (e.g., InGaN, AlGaN) and to defect‑mediated carrier recombination will further enhance the utility of these findings for high‑efficiency LEDs, laser diodes, and quantum‑well devices.