Hydrogen in GaN: Novel Aspects of a Common Impurity

We have studied electronic structure, energetics, and migration of hydrogen and hydrogen complexes in GaN, based on first-principles total-energy calculations. Our calculations reveal a number of features very different from those exhibited by hydrogen in more traditional semiconductors such as Si or GaAs: a very large negative-$U$ effect ($U\approx 2.4$ eV), the instability of the bond-center site, high energies for hydrogen molecules, and an unusual geometry for the Mg-H complex. All of these features are shown to be a consequence of distinctive properties of GaN, namely, the strongly ionic nature and the large bond strength of the Ga-N bond. We propose a simple model for the negative-$U$ behavior, which should be valid for H in any semiconductor.