Self-compensation in semiconductors: The Zn vacancy in Ga-doped ZnO

Self-compensation, the tendency of a crystal to lower its energy by forming point defects to counter the effects of a dopant, is here quantitatively proven. Based on a new theoretical formalism and several different experimental techniques, we demonstrate that the addition of 1.4 × 10${}^{21}$-cm${}^{-3}$ Ga donors in ZnO causes the lattice to form 1.7 × 10${}^{20}$-cm${}^{-3}$ Zn-vacancy acceptors. The calculated $V_{\mathrm{Zn}}$ formation energy of 0.2 eV is consistent with predictions from density functional theory. Our formalism is of general validity and can be used to investigate self-compensation in any degenerate semiconductor material.

Figure 1

Experimental (points) and theoretical (solid and dashed lines) mobilities for Ga-doped ZnO samples grown at 200 °C in pure Ar and annealed at various temperatures in forming gas.

Figure 2

A comparison of donor concentrations determined by Hall mobility analysis (solid lines) and SIMS measurements of [Ga] + [H] + [Al] (dashed lines).

Figure 3

Cathodoluminescence spectra for Ga-doped ZnO samples grown at 200 °C in pure Ar and annealed at 300 and 550 °C, respectively, in forming gas. The dashed curve represents the 300 °C sample intensity normalized to that of the 550 °C sample in the near-band-edge region (3.5 eV) in order to compare the relative intensities of the peaks near 1.8 eV.