Electron–impurity scattering in free-standing quantum wires: Effect of dielectric confinement

We calculate the impurity-scattering limited mobility of the one-dimensional electron gas in a rectangular GaAs quantum wire confined in the vertical (growth) direction by n-modulation doped AlGaAs layers and free-standing along the transverse direction. The Fourier-transformed scattering potential of the ionized impurity is obtained analytically by solving the Poisson equation with z-dependent electrostatic permittivity. An abrupt permittivity change at the GaAs(AlGaAs)/air interfaces gives rise to the image charge effect which strongly modifies the unperturbed scattering potential. We show that the “image impurity” scattering tends to drastically reduce the electron mobility for sufficiently small (∼10 nm) transverse wire widths.