Native point defects and doping inZnGeN2

Abstract

A computational study within the framework of density functional theory in the local density approximation (LDA) is presented for native defects and doping in ${\mathrm{ZnGeN}}_{2}$. Gap corrections are taken into account using an LDA+$U$ approach and finite size corrections for charged defects are evaluated in terms of an effective charge model, introduced in this paper. The donor or acceptor characteristics of each of the cation and N vacancies and the two cation antisite defects are determined as well as their energies of formation under different chemical potential conditions. These are then used to determine defect concentrations and Fermi level pinning self-consistently. The cation antisite defects are found to have significantly lower formation energy than the cation vacancies. At a typical growth temperature of 1200 K, the charge neutrality condition pins the Fermi level close to the crossing of the formation energies of the ${\mathrm{Zn}}_{\mathrm{Ge}}^{\ensuremath{-}1}$ acceptor with the ${\mathrm{Ge}}_{\mathrm{Zn}}^{2+}$ shallow donor. Since this point lies closer to the valence-band maximum (VBM), intrinsic $p$-type doping would result at the growth temperature and will persist at room temperature if the defect concentrations are frozen in. It is the highest and of order ${10}^{16}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ for the most Ge-poor condition. On the other hand, for the most Ge-poor condition, it drops to ${10}^{13}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ at 1200 K and to almost zero at 300 K because then the Fermi level is too close to the middle of the gap. Oxygen impurities are found to strongly prefer the ${\mathrm{O}}_{\mathrm{N}}$ substitutional site and are found to be shallow donors with a very low energy of formation. It can only be suppressed by strongly reducing the oxygen partial pressure relative to that of nitrogen. At high temperatures, however, introduction of oxygen will be accompanied by compensating ${\mathrm{Zn}}_{\mathrm{Ge}}^{\ensuremath{-}2}$ acceptors and would lead to negligible net doping. The prospects for Ga base $p$-type doping are evaluated. While good solubility is expected, site competition between Zn and Ge sites is found to lead to a compensation problem similar to that of the two antisites and leads to $p$-type doping of the same level of ${10}^{16}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.