Effect of impurities on the two-dimensional electron gas polarisability

The polarisability for a two-dimensional electron gas is calculated in the presence of impurities by a Green function formalism. This leads to a system with finite mean free path due to electrons scattering off impurities. The calculated polarisability is found to be strongly dependent on the mean free path. The main feature is the suppression of the sharp corner at wavevector 2kF for finite mean free paths, and the pure metal result is recovered for the infinite mean free path. A possible application of the results of the transport properties of semiconductor inversion layers is discussed.