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

TL;DR

This study numerically solves the Boltzmann equation for semiconducting nanowires, revealing that finite surface width slightly influences transport properties and challenges the zero-width surface layer assumption.

Contribution

It introduces a finite surface width model for nanowire transport and demonstrates its effects using numerical solutions of the Boltzmann equation.

Findings

Finite surface width slightly affects magneto-conductance.

Zero-width surface layer assumption is challenged.

Surface roughness reduces relaxation times at the boundary.

Abstract

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. 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. 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.