Recently, experiments on the properties of electrons in semiconductor inversion layers have been carried out at very high electric fields. These fields correspond to electronic occupation of more than one of the discrete electric subbands created for motion perpendicular to the surface. Previous theoretical investigation on the problem was limited to the case when one subband is populated. In this paper we examine the more general case of having many subbands occupied, studying in detail two particular properties of the system. The first is the electron screening of an external potential described very conveniently by a matrix dielectric function. The second is the scattering of electrons by screened charged impurities and its contribution to the surface conductivity. © 1970 The American Physical Society.