Spin-orbit coupling effects on predicting defect properties with hybrid functionals: A case study in CdTe

Abstract

Defect formation energies and transition levels are critical in determining doping behavior and recombination in semiconductor applications. Hybrid functionals are often used to overcome the band gap and delocalization errors of standard density-functional theory, and it is tempting to presume that the defect properties are correctly predicted once the hybrid functional mixing parameter reproduces the experimental band gap. However, pronounced spin-orbit coupling (SOC) effects can have an additional important role, which is clearly shown in this work by analyzing SOC effects originating from the $\mathrm{Te}\ensuremath{-}p$ orbitals in CdTe. In this work, we therefore use a hybrid functional that reproduces the experimental band gap when SOC is included, requiring a larger mixing parameter $\ensuremath{\alpha}=0.33$ compared to the conventional choice of $\ensuremath{\alpha}=0.25$. This hybrid functional was then used to predict defect properties, e.g., formation energy, transition level, and defect equilibrium. For defect states that do not directly involve the $\mathrm{Te}\ensuremath{-}p$ orbitals, such as the Cd interstitial (${\mathrm{Cd}}_{\mathrm{i}}$), we find that the effect of SOC on the defect levels can be captured by simply considering the SOC-induced band-edge shift. This is not the case for the A center ($\mathrm{C}{\mathrm{l}}_{\mathrm{Te}}\ensuremath{-}{V}_{\mathrm{Cd}}$ defect pair), where the localized acceptor state formed by $\mathrm{Te}\ensuremath{-}p$ orbitals is more directly affected by the SOC. For this defect, a mixing parameter as large as $\ensuremath{\alpha}=0.40$ is required to reproduce the experimental acceptor level. Regarding the implications for photovoltaics, we suggest that the ${\mathrm{Cd}}_{\mathrm{i}}$, which is the dominant compensating donor, could play an important role as a recombination center. While $\mathrm{C}{\mathrm{d}}_{\mathrm{i}}$ is usually thought of as a benign shallow donor, our predicted defect levels in the fully band-gap-corrected calculations are deep enough to raise a concern, and we propose a recombination mechanism for electron capture by $\mathrm{C}{\mathrm{d}}_{\mathrm{i}}$.