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.
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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.