Application of the bounds-analysis approach to arsenic and gallium antisite defects in gallium arsenide

A recently developed bounds-analysis approach has been used to interpret density-functional-theory (DFT) results for the As and Ga antisites in GaAs. The bounds analysis and subsequent processing of DFT results for the As antisite yielded levels—defined as the Fermi levels at which the defect charge state changes—in very good agreement with measurements, including the −1/0 level which is within 0.1 eV of the conduction-band edge. Good agreement was also obtained for the activation energies to transform the $\mathrm{A}{\mathrm{s}}_{\mathrm{Ga}}$ from its metastable state to its stable state. For the Ga antisite, the bounds analysis revealed that the −1 and 0 charge states are hole states weakly bound to a localized −2 charge state. The calculated levels are in good agreement with measurements.

Figure 1

Bounds and $EL2$ levels vs inverse supercell size $(1/L)$. The solid lines are cubic-spline fits of the bounds ${\Delta }^{B,\mathrm{fit}}\left(-1,L\right)$ and ${\Delta }^{B,\mathrm{fit}}\left(+1,L\right).$ The symbols are DFT levels ${\Delta }^D\left(q-1/q,L\right)$ from 216-, 512-, and 1000-atom supercells. The dashed lines are the supercell-size dependencies of the DFT defect levels ${\Delta }^{D,\mathrm{ssd}}\left(q-1/q,L\right),$ identified in the bounds analysis.

Figure 2

Bounds and $EL{2}^{*}$ levels vs inverse supercell size $(1/L)$. The solid lines are cubic-spline fits of the bounds ${\Delta }^{B,\mathrm{fit}}\left(-1,L\right)$ and ${\Delta }^{B,\mathrm{fit}}\left(+1,L\right).$ The symbols are DFT levels ${\Delta }^D\left(q-1/q,L\right)$ from 216-, 512-, and 1000-atom supercells. The dashed line is the supercell-size dependence of the DFT defect level ${\Delta }^{D,\mathrm{ssd}}\left(-1/0,L\right),$ identified in the bounds analysis.

Figure 3

Bounds and saddle-point level vs inverse supercell size $(1/L)$. The solid lines are cubic-spline fits of the bounds ${\Delta }^{B,\mathrm{fit}}\left(-1,L\right)$ and ${\Delta }^{B,\mathrm{fit}}\left(+1,L\right).$ The symbols are DFT levels ${\Delta }^D\left(q-1/q,L\right)$ from 216-, 512-, and 1000-atom supercells. The dashed lines are the supercell-size dependencies of the DFT defect levels ${\Delta }^{D,\mathrm{ssd}}\left(q-1/q,L\right),$ identified in the bounds analysis.

Figure 4

Bounds and ${\mathrm{Ga}}_{\mathrm{As}}$ levels vs inverse supercell size $1/L$. The symbols are DFT levels ${\Delta }^D\left(q-1/q,L\right)$ from 216-, 512-, and 1000-atom supercells.