On the diameter dependence of metal-nanowire Schottky barrier height

TL;DR

This paper investigates how the diameter of metal-wrapped nanowires influences the Schottky barrier height, revealing that thinner nanowires tend to have higher barriers due to electrostatic effects.

Contribution

It applies Bardeen's model to cylindrical nanowires and demonstrates the diameter dependence of Schottky barrier height through self-consistent Poisson's equation solutions.

Findings

Thinner nanowires have tens of meV higher Schottky barriers.

Barrier height increases as nanowire radius decreases.

Electrostatic properties explain the diameter dependence.

Abstract

Bardeen's model for the non-ideal metal-semiconductor interface was applied to metal-wrapped cylindrical nanowire systems; 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 tens of meV higher Schottky barriers compared to their thicker counterparts. 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.