Abstract
In this paper, we study the Schottky transport in a narrow-gap semiconductor and few-layer graphene in which the energy dispersions are highly nonparabolic. We propose that the contrasting current-temperature scaling relation of J proportional to T-2 in the conventional Schottky interface and J proportional to T-3 in graphene-based Schottky interface can be reconciled under Kane's k . p nonparabolic band model for narrow-gap semiconductors. Our model suggests a more general form of J proportional to (T-2 + gamma k(B)T(3)), where the nonparabolicty parameter gamma provides a smooth transition from T-2 to T-3 scaling. For few-layer graphene, we find that N-layer graphene with ABC stacking follows J proportional to T2/N+1, while ABA stacking follows a universal form of J proportional to T-3 regardless of the number of layers. Intriguingly, the Richardson constant extracted from the Arrhenius plot using an incorrect scaling relation disagrees with the actual value by 2 orders of magnitude, suggesting that correct models must be used in order to extract important properties for many Schottky devices.