Relative concentration and structure of native defects in GaP

The native defects in the compound semiconductor GaP have been studied using a pseudopotential density functional theory method in order to determine their relative concentrations and the most stable charge states. The electronic and atomic structures are presented and the defect concentrations are estimated using calculated formation energies. Relaxation effects are taken into account fully and produce negative-U charge transfer levels for ${\mathrm{V}}_{\mathrm{P}}$ and ${\mathrm{P}}_{\mathrm{Ga}}$. The concentration of ${\mathrm{V}}_{\mathrm{Ga}}$ is in good agreement with the results of positron annihilation experiments. The charge transfer levels presented compare qualitatively well with experiments where available. The effect of stoichiometry on the defect concentrations is also described and is shown to be considerable. The lowest formation energies are found for ${\mathrm{P}}_{\mathrm{Ga}}^{+2}$ in $p$-type and ${\mathrm{V}}_{\mathrm{Ga}}^{-3}$ in $n$-type GaP under P-rich conditions, and for ${\mathrm{Ga}}_{\mathrm{P}}^{-2}$ in $n$-type GaP under Ga-rich conditions. Finally, the finite size errors arising from the use of supercells with periodic boundary conditions are examined.

Figure 1

Band structure of the neutral $\mathrm{P}$ antisite defect. The deep defect level is shown as the thick black line and its dispersion is presented for the 8, 64, and 216 atom supercells.

Figure 2

Schematic for the defect levels at $\mathbf{k}=(\frac{1}{4},\frac{1}{4},\frac{1}{4})$ for the neutral defects.

Figure 3

Formation energies as a function of the Fermi-level for all unrelaxed native defects under stoichiometric conditions $({\mu }_{\mathrm{Ga}}=-4.06\mathrm{eV})$. Values are only shown for the most stable charge state at any Fermi-level, the charge state given by the slope of the line. Charge transfer levels are labeled next to the vertical lines indicating their positions. The antisite defects are shown as dotted lines, vacancies as full lines and interstitials as broken lines. The alternative $y$ axis on the right gives the defect concentration in orders of magnitude at a temperature of $300\mathrm{K}$.

Figure 4

As Fig. 3, but for all the fully relaxed native defects under stoichiometric conditions $({\mu }_{\mathrm{Ga}}=-4.06\mathrm{eV})$. The most stable type of defect for each value of the Fermi-level is shown by the thick grey line.

Figure 5

As Fig. 4, but under P-rich conditions $({\mu }_{\mathrm{Ga}}=-4.50\mathrm{eV})$.

Figure 6

As Fig. 4, but under Ga-rich conditions $({\mu }_{\mathrm{Ga}}=-3.61\mathrm{eV})$.

Figure 7

Finite size scaling of formation energies for the most occurring defects. L is the length of the supercell side in unit s of the simple cubic 8 atom supercell side length, so that $1∕L=1$, $1∕L=\frac{1}{2}$, and $1∕L=\frac{1}{3}$ for the 8, 64, and 216 atom supercells, respectively.

Figure 8

The formation energies, extrapolated to the infinite supercell size limit, plotted as a function of the Fermi-level for all relaxed native defects under stoichiometric conditions $({\mu }_{\mathrm{Ga}}=-4.06\mathrm{eV})$. The grey curves are shown for comparison and correspond to the results of the 216 atom supercell (as in Fig. 4).