Surface effects on nanowire transport: a numerical investigation using the Boltzmann equation

A direct numerical solution of the steady-state Boltzmann equation in a cylindrical geometry is reported. Finite-size effects are investigated in large semiconducting nanowires using the relaxation-time approximation. A nanowire is modelled as a combination of an interior with local transport parameters identical to those in the bulk, and a finite surface region across whose width the carrier density decays radially to zero. The roughness of the surface is incorporated by using lower relaxation times there than in the interior. An argument supported by our numerical results challenges a commonly used zero-width parametrization of the surface layer (Chambers 1950 Proc. R. Soc. A 202 378). In the non-degenerate limit, appropriate for moderately doped semiconductors, a finite surface width model does produce a positive longitudinal magneto-conductance, in agreement with 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 highest practical magnetic fields. Physical insights emerging from the results are discussed