Born approximation versus the exact approach to carrier-impurity collisions in a one-dimensional semiconductor: Impact on the mobility

We study the collision of a one-dimensional (1D) electron with a screened C oulomb impurity in a single-subband GaAs quantum wire. The exact reflection probability is calculated and shown to drastically differ from the reflect ion probability in the Born approximation. As a result, both models also gi ve completly different 1D electron mobilities. Further, we introduce the ex act mean-field screening and show that except for high electron densities i t leads to a quite different reflection probability than the linear mean-fi eld (Lindhard) screening. Finally, we show that the Boltzmann 1D mobility C oncept has to be replaced by a more general semiclassical theory, if in a t ypical collision the backward reflection occurs with probability close to u nity. [S0163-1829(99)50716-9].