Comparative ab initio study of the hole mobility in AlN and GaN

Group-III nitrides are semiconductors crucial for power electronics and optoelectronics. Among them, AlN is particularly promising due to its ultrawide bandgap, high breakdown field, and excellent thermal conductivity. In anticipation of the experimental realization of p-doped AlN, we report a state-of-the-art first-principles study of the hole mobility in AlN, and compare it with the more established GaN to elucidate their differences. We compute hole mobilities limited by phonons and ionized impurities using the ab initio Boltzmann transport equation, and include spin-orbit coupling, long-range dipole and quadrupole corrections, and GW quasiparticle bands. We find that the hole mobility in AlN reaches 178 cm²/Vs at room temperature along the c axis, which is one order of magnitude higher than the hole mobility of GaN. The higher mobility of AlN originates from its negative crystal-field splitting, which places the split-off holes at the top of the valence bands and far above the heavy holes.