We present a systematic study of the sheet carrier density and valence-band offset in the GaN/Al x Ga 1Ϫx N(0001) heterostructure as a function of x from ab initio density-functional methods. We find that the calculated sheet carrier density increases rapidly with x for xр0.3 in good agreement with experiments, but beyond this concentration, it quickly saturates to a value of about 2ϫ10 13 cm Ϫ2 . The band offset shows a small asymmetry between the Ga-face and N-face interfaces and changes more

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... or less linearly with x, although a small bowing is found. The layer-projected densities of states indicate the formation of the two-dimensional electron gas at the Ga-face interface and confirm the absence of interface states in the gap.