Calculation of the average interface field in inversion layers using zero-temperature Green's function formalism

We investigate the dependence of the average interface field on the inversion and depletion charge density through the use of a zero-temperature Green's function formalism for the evaluation of the broadening of the electronic states and conductivity. Various models for the surface-roughness autocovariance function existing in the literature, including both Gaussian and exponential models, are studied in our calculations. Besides surface-roughness scattering, the dominant scattering mechanism at high electron densities, charged impurity, interface-trap and oxide charge scattering are also included. The position of the subband minima, as well as the electron wave functions, are obtained by a self-consistent solution of the Schrödinger, Poisson, and Dyson equations for each value of the inversion charge density. Many-body effects are included by considering the screened matrix elements for the scattering mechanisms and through inclusion of the exchange-correlation term. The dependence of the mobility and the effective field upon the inversion charge density is sensitive to the model chosen, and we discuss the manner in which this may be used to study the interface itself.