Theory for the Polarizability Function of an Electron Layer in the Presence of Collisional Broadening Effects and Its Experimental Implications

The polarizability function of a two-dimensional electron layer submerged in a threedimensional dielectric material and interacting with a random distribution of static charged impurity centers is calculated. Scattering and screening are treated self-consistently and each affects the other. The resultant scattering time is found to depend on the impurity density $N_i$ through the ${(a{N}_i+b{N_i}^2)}^{-1\mathrm{}}$ law which has been observed experimentally in silicon inversion layers. The theory is in good agreement with the experimental findings on the parameters $a$ and $b$.