Abstract
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 scattering potential of the ionized is obtained by solving the Poisson equation with z-dependent electrostatic permittivity in order to take into account the charge effect due to the abrupt permittivity change at the GaAs/air interfaces. We show that the image impurity scattering tends to drastically reduce the electron mobility for sufficiently small ( 10 nm) transverse wire widths.
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