The dielectric function in Maxwell's equation

In a recent paper, Csavinszky (1978) has shown that when the spatial variation of the dielectric function of a semiconductor is taken into account, the screened impurity potential obtained in the Thomas-Fermi theory is considerably different when compared to the case where the spatial variation is not included. In the present work, the lidity of using the space dependent dielectric function epsilon(r) obtained for model semiconductors into Maxwell's equation is discussed. It is shown that when epsilon(r) is incorporated in Maxwell's equation, the resulting Thomas-Fermi equation has physically admissible solution only if depsilon/dr → 0 as r → 0. The need for Fourier analysing the Maxwell equation is brought out when one wants to obtain the screening of an impurity atom by an electron gas embedded in a semiconductor with dielectric function epsilon (q). The screened impurity potentials are obtained by solving the Thomas-Fermi equation with appropriate boundary conditions. The screened potentials are much weaker than those obtained by Csavinszky. (author)