Hole conductivity and compensation in epitaxial GaN:Mg layers

Abstract

The concentration p and the mobility \ensuremath{\mu} of holes in metal-organic chemical vapor deposition (MOCVD) GaN:Mg layers were studied by room temperature Hall-effect measurements as a function of the Mg concentration ${N}_{A}$ in the range $3\ifmmode\times\else\texttimes\fi{}{10}^{18}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}<~{N}_{A}<~1\ifmmode\times\else\texttimes\fi{}{10}^{20}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ The hole density first increases with increasing ${N}_{A},$ reaches a maximum value ${p}_{\mathrm{max}}\ensuremath{\approx}6\ifmmode\times\else\texttimes\fi{}{10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at ${N}_{A}\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{19}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3},$ decreases for larger ${N}_{A}$ values, and drops to very small values at ${N}_{A}\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{20}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ The hole mobility decreases monotonically with increasing ${N}_{A}.$ The ${p(N}_{A})$ data provide strong evidence for self-compensation, i.e., for a doping driven compensation of the Mg acceptor by intrinsic donor defects. This effect becomes significant when ${N}_{A}$ exceeds a value of $2\ifmmode\times\else\texttimes\fi{}{10}^{19}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ A semiquantitative self-compensation model involving nitrogen vacancies is developed. It accounts satisfactorily for the measured ${p(N}_{A})$ dependence and suggests that self-compensation limits the hole conductivity in bulklike MOCVD GaN:Mg layers grown near 1300 K to about 1.2 (\ensuremath{\Omega} ${\mathrm{c}\mathrm{m})}^{\mathrm{\ensuremath{-}}1}$.