On the diameter dependence of metal-nanowire Schottky barrier height

Bardeen's model for the non-ideal metal-semiconductor interface was applied to metal-wrapped cylindrical nanowire systems of 30–400 nm in diameter; a significant effect of the nanowire diameter on the non-ideal Schottky barrier height was found. The calculations were performed by solving Poisson's equation in the nanowire, self-consistently with the constraints set by the non-ideal interface conditions; in these calculations, the barrier height is obtained from the solution, and it is not a boundary condition for Poisson's equation. The main finding is that thin nanowires are expected to have $O(10−100)$ meV higher Schottky barriers compared to their thicker counterparts; an effect 3–4 times stronger than the diameter dependence of image-force barrier lowering in similar systems. What lies behind this effect is the electrostatic properties of metal-wrapped nanowires; in particular, since depletion charge is reduced with nanowire radius, the potential drop on the interfacial layer is reduced—leading to the increase of the barrier height with nanowire radius reduction.