Microscopic Origin of Polarization Charges at GaN / (Al,Ga)N…

$\mathrm{Ga}\mathrm{N}$/$(\mathrm{Al},\mathrm{Ga})\mathrm{N}$ heterojunctions are at the heart of high-electron-mobility transistors that are being adopted for high-power and high-frequency applications. The strong polarization fields present at this interface significantly enhance the density of the two-dimensional electron gas (2DEG) that is confined on the $\mathrm{Ga}\mathrm{N}$ side of the junction. The microscopic origin of these electrons has been debated over the years: after excluding that they would be contributed by bulk donors, a model that identifies surface states on the $(\mathrm{Al},\mathrm{Ga})\mathrm{N}$ surface as the source of electrons has become widely adopted. Recently, it has become clear, however, that the measured density of surface states is insufficient to account for the high electron density in the 2DEG. Here we demonstrate, based on state-of-the-art first-principles calculations, that the source of electrons is intrinsic to the overall structure and that the negative charge in the 2DEG is balanced by fixed charge on the surface. We perform a rigorous study of polarization, using our recently developed methodology for quantifying polarization fields within the finite-sized systems that can be addressed with density-functional calculations. The results show that the electrons that appear in the 2DEG originate locally at the interface, and that the net charge at the interface is predominantly compensated by fixed charge on the surface, rather than surface states. We elucidate the source of this fixed charge and associate it with surface reconstructions or the presence of heterovalent impurities (such as oxygen). Our results force a reassessment of the impact of surface states on the density of the 2DEG: rather than serving as a supply of electrons, the surface states mainly act to pin the Fermi level. Our conclusions allow a fresh interpretation of experimental observations and allow devising guidelines for optimizing carrier densities in the 2DEG.