Dielectric response of an inhomogeneous quasi-two-dimensional electron gas

The solution of the integral equation required to invert the dielectric function of a confined quasi-two-dimensional electron gas is studied by means of a formal analysis which yields a convergent algorithm, The dielectric function can then be inverted in real space for an arbitrary number of populated subbands and taking into account the effect of intersubband excitations involving empty subbands to any desired degree of accuracy. Plasma modes and screened potential can then be easily studied by using a basis which bears out explicitly the consequences of symmetry in symmetric systems. A model calculation of dynamical screening at frequencies of the order of those of confined polar optical modes in usual GaAs wells indicates that the empty states may play a quite significant role and the screened potential, explicitly obtained in real space, may exhibit a great variety of behaviors: the sign of the potential may change and its magnitude may be either reduced (ordinary screening) or enhanced (antiscreening).