Equilibrium state of hydrogen in gallium nitride: Theory and experiment

Formation energies and vibration frequencies for H in wurtzite GaN were calculated from density-functional theory and used to predict equilibrium state occupancies and solid solubilities at elevated temperatures for p-type, intrinsic, and n-type material. The solubility of deuterium (D) was measured in p-type, Mg-doped GaN at 600, 700, and 800 °C as a function of D2 pressure and compared with theory. Agreement was obtained by reducing the H formation energies 0.22 eV from ab initio theoretical values. The predicted stretch-mode frequency for H bound to the Mg acceptor lies 5% above an observed infrared absorption attributed to this complex. More limited solubility measurements were carried out for nominally undoped material rendered n-type by donors provisionally identified as O impurities, and results agree well with theory after the aforementioned adjustment of formation energies. It is concluded that currently recognized H states and physical processes can account for the equilibrium, elevated-temperature behavior of H examined in this work.