Characterization of very narrow quasi-one-dimensional quantum channels

Abstract

Narrow conducting channels are currently produced in, e.g., GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures by means of different lithographic methods. Depending on various factors associated with the fabrication process, problems arise as to how to characterize such channels in terms of electron concentration and effective width. Here we elaborate on a simple model designed for very narrow channels in which the lateral electrostatic confinement is assumed to be a parabolic well. The confinement gives rise to one-dimensional subbands, which gradually depopulate as an increasing, perpendicular magnetic field is applied. Because of the electrostatic confinement, a plot of sublevel index n versus inverse magnetic field is generally nonlinear. This nonlinearity is used here to extract an electron concentration and width for the channel.