Phonon-limited mobility in a quasi-one-dimensional semiconductor

Abstract

Phonon-limited mobility in a quasi-one-dimensional semiconductor is studied for scattering due to (i) acoustic phonons via deformation-potential coupling, (ii) acoustic phonons via piezoelectric coupling, and (iii) polar-optical phonons. In a simple model where the envelope wave function is assumed to be constant inside a cylindrical wire and zero outside, the mobility at low temperature can be expressed by analytical formulas for the three cases. Numerical calculations are performed over the whole range of temperature (liquid helium to room temperature) and comparison is made as far as possible to similar calculations in a two-dimensional semiconductor. The main conclusion is the following one: Contrary to scattering due to ionized impurities where the dimensionality, via the modulation doping, plays a fundamental role and can change the mobility by several orders of magnitude, the scattering due to phonons depends little on the dimensionality (three, two, or one) of the semiconductor for reasonable quantum-well widths (100 Å), whatever the temperature.