Analogically, the electron - ionized impurity interaction can be expected to be enhanced. Nowadays there is a trend to produce the free-standing wires with transverse widths close to 10 nm in order to enhance the quantum confinement of the carriers. We compare the electron mobility in the free-standing GaAs wire with the mobility in the GaAs wire buried in the AlGaAs material, in which the image charge contribution to the scattering potential is negligible. To increase the electron mobility, the sublayer is separated from the GaAs wire by an undoped AlGaAs spacer layer of the vertical width L sp . It gives Differentiating Eq.
L z a set of two linear equations for is obtained.
This set of equations can be solved analytically. Performing the same calculation for our rectangular wire we have assessed the effect of the realistic wire cross section. The quantitative discrepancies between both calculations are due to the different cross sections of the wires. The mobility with image charge effect would show the same tendency for smaller L z than those considered in Fig. The obtained mobilities are qualitatively similar to those in Fig.