Radial Dependence of the Carrier Mobility in Semiconductor Nanowires

TL;DR

This paper investigates how charge carrier mobility in semiconductor nanowires varies with radius, revealing non-monotonic behavior due to competing effects of cross-section increase and scattering channels, with implications for nanowire design.

Contribution

It provides a detailed analysis of the radius-dependent mobility considering impurity scattering and introduces improved models for transverse wavefunctions, highlighting the impact of impurity distribution assumptions.

Findings

Mobility exhibits non-monotonic dependence on nanowire radius.

Sharp mobility drops occur at radii where new scattering channels open.

Exponential mobility growth persists at intermediate radii with constant channel number.

Abstract

The mobility of charge carriers in a semiconductor nanowire is explored as a function of increasing radius, assuming low temperatures where impurity scattering dominates. The competition between increased cross-section and the concurrent increase in available scattering channels causes strongly non-monotonic dependence of the mobility on the radius. The inter-band scattering causes sharp declines in the mobility at the wire radii at which each new channel becomes available. At intermediate radii with the number of channels unchanged the mobility is seen to maintain an exponential growth even with multiple channels. We also compare the effects of changing the radial scaling of the impurity distribution. We use transverse carrier wavefunctions that are consistent with boundary conditions and demonstrate that the $\delta$-function approximate transverse profile leads to errors in the case of remote impurities.