Self-vacancies in gallium arsenide: An ab initio calculation

We report here a reexamination of the static properties of vacancies in GaAs by means of first-principles density-functional calculations using localized basis sets. Our calculated formation energies yields results that are in good agreement with recent experimental and ab initio calculation and provide a complete description of the relaxation geometry and energetic for various charge states of vacancies from both sublattices. Gallium vacancies are stable in the 0, −, $-2$, $-3$ charge states, but $V_{\mathrm{Ga}}^{-3}$ remains the dominant charge state for intrinsic and $n$-type GaAs, confirming results from positron annihilation. Interestingly, arsenic vacancies show two successive negative-$U$ transitions making only $+1$, $-1$, and $-3$ charge states stable, while the intermediate defects are metastable. The second transition $(-∕-3)$ brings a resonant bond relaxation for $V_{\mathrm{As}}^{-3}$ similar to the one identified for silicon and GaAs divacancies.

Figure 1

(Color online) Schematic representation of the convergence of ionization energies as function of the basis set. Due to the underestimation of the gap, as a consequence of LDA, it is usual to align the conduction band maximum (CBM) with the experimental value, at $1.52\mathrm{eV}$ from the valence band maximum (VBM). The left panel displays the ionization energies as functions of the basis set for the Ga vacancy that are all below the experimental midgap. The right panel shows the two ionization levels for the As vacancy located below and above the midgap and their convergence with respect to the different basis sets used. Refer to the text for the basis set description.

Figure 2

(Color online) Histogram of the change in the volume of the relaxed tetrahedron formed by atoms surrounding the vacancy in % of the ideal one for two densities of $k$ points in the Brillouin zone (refer to the text for details). For comparison, data for Ga and As vacancies in different charge states are plotted in the same figure.

Figure 3

(Color online) Formation energies as function of Fermi level in various charge states of Ga vacancies at $0\mathrm{K}$ calculated for stochiometric GaAs $(\Delta \mu =0)$. The Fermi level is defined by reference to the valence band maximum. Ionization levels are defined as the intersection between the formation energies of different defects. Defect with the lowest formation energy is dominant. Arrows point to the location of the ionization levels labeled (a) for $(0∕-)$, (b) for $(-∕-2)$, and (c) for $(-2∕-3)$.

Figure 4

(Color online) Formation energies as a function of the Fermi energy of various charge states of As vacancies at $0\mathrm{K}$. The Fermi level is calculated with respect to the valence band maximum. Arrows point to the location of the ionization levels labeled (a) for (+/−), (b) for $(-∕-3)$.

Figure 5

(Color online) Formation energies of Ga (solid line) and As (dashed line) vacancies in GaAs as a function of the growth conditions $\left(\Delta \mu \right)$. Different panels are for different critical values of the Fermi level or ionization levels identified earlier.