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 $J\propto T^2$ in the conventional Schottky interface and $J\propto T^3$ in graphene-based Schottky interface can be reconciled under Kane’s $\mathbf{k}·\mathbf{p}$ nonparabolic band model for narrow-gap semiconductors. Our model suggests a more general form of $J\propto (T^2+\gamma k_B{T}^3)$, 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 $J\propto T^{2/N+1}$, while $ABA$ stacking follows a universal form of $J\propto T^3$ 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.

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• Electronic structure
• Thermionic emission
• Transport phenomena
• 2-dimensional systems
• Graphene
• Interfaces