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While point defects in elemental (Si) and compound (GaAs, GaN, AlN) semiconductors have been extensively studied both experimentally and theoretically, only limited theoretical studies of these defects exist for technologically important binary $(\mathrm{S}{\mathrm{i}}_{x}\mathrm{G}{\mathrm{e}}_{1\text{\ensuremath{-}}x})$ and pseudobinary $(\mathrm{I}{\mathrm{n}}_{x}\mathrm{G}{\mathrm{a}}_{1\text{\ensuremath{-}}x}\mathrm{As}$, $\mathrm{I}{\mathrm{n}}_{\mathrm{x}}\mathrm{G}{\mathrm{a}}_{1\text{\ensuremath{-}}x}\mathrm{N}$, $\mathrm{A}{\mathrm{l}}_{x}\mathrm{G}{\mathrm{a}}_{1\text{\ensuremath{-}}x}\mathrm{N})$ semiconductor alloys. Here, we use density-functional theory and a recently developed bounds-analysis approach to survey the atomic structures, formation energies, and charge-state transition levels of the stable and metastable states of As interstitials in the pseudobinary alloy $\mathrm{I}{\mathrm{n}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}\mathrm{As}$. Our studies consider seven different candidate defect structures for the As interstitial, with calculations performed for selected defect charge states in the range $q=\ensuremath{-}2$ to $+3$. In each case, the mean and standard deviations of the defect-formation energy are determined using statistical sampling methods that place the defect into a wide variety of differing local-alloy environments. When examined from the point of view of the mean formation energy of the defect, the stable configurations of the As interstitial in $\mathrm{I}{\mathrm{n}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}\mathrm{As}$ are found to resemble previous findings for GaAs, with a ${\mathrm{C}}_{1\mathrm{h}}\text{\ensuremath{-}}\mathrm{p}{001}_{\mathrm{III}}$ interstitial structure in a $q=+1$ charge state favored near midgap and below, and a ${\mathrm{C}}_{2\mathrm{v}}\text{\ensuremath{-}}11{0}_{\mathrm{a}}$ split-interstitial structure in a $q=\ensuremath{-}1$ charge state favored above midgap (the named point-group symmetries refer to the underlying symmetry that the alloy defect would possess if within GaAs). The statistical sampling reveals a strong dependence of the defect-formation energy on the local-alloy environment, with the standard deviation $\ensuremath{\sigma}$ of the formation energy approaching 0.21 eV for the most stable As-interstitial structures. Because the range of ground-state energies encountered by an As-interstitial defect when moving through the alloy is found to be quite large, approaching $\ensuremath{\sim}1.2\phantom{\rule{0.16em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}(\ifmmode\pm\else\textpm\fi{}3\ensuremath{\sigma})$, defect-diffusion pathways in $\mathrm{I}{\mathrm{n}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}\mathrm{As}$ will have spatial and temporal complexities not found in GaAs.

First-principles survey of the structure, formation energies, and transition levels of As-interstitial defects in InGaAs