Surface effects on nanowire transport: a numerical investigation using the Boltzmannequation

Abstract

A direct numerical solution of the steady-state Boltzmann equation in a cylindricalgeometry is reported. Finite-size effects are investigated in large semiconducting nanowiresusing the relaxation-time approximation. A nanowire is modelled as a combination of aninterior with local transport parameters identical to those in the bulk, and a finite surfaceregion across whose width the carrier density decays radially to zero. The roughness of thesurface is incorporated by using lower relaxation times there than in the interior.An argument supported by our numerical results challenges a commonly used zero-widthparametrization of the surface layer (Chambers 1950 Proc. R. Soc. A 202 378). In thenon-degenerate limit, appropriate for moderately doped semiconductors, a finite surfacewidth model does produce a positive longitudinal magneto-conductance, in agreementwith existing theory of Chambers. However, the effect is seen to be quite small(a few per cent) for realistic values of the wire parameters even at the highestpractical magnetic fields. Physical insights emerging from the results are discussed.