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 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.
The boundary condition for the vanishing electric field at the onset of the depletion region is valid only for the depletion approximation; the more general condition, , is applicable also to both fully and partially depleted NWs. We use this condition in the numerical solution of the problem.
The subscript cyl denotes charge and capacitance per unit-length.
In fact, from an electrostatic stand-point, an interfacial layer of finite thickness is a necessity for the consideration of the voltage drop related to the interface states.