![]() This additional screening in turn leads to the asymptotic incomplete screening form for the potential: φ(r)≊Ze/ ε 0r, where ε 0 is Z dependent and thus not equal to the bulk dielectric constant associated with the background. The partial filling of the conduction band near the point charge gives rise to a Z-dependent screening in addition to that of the usual form due to the background dipole density of the insulator (the latter is treated phenomenologically). The induced electron density in the conduction band near the point charge, expressed in terms of the electrostatic potential, is used in forming the Thomas-Fermi equation. In contrast to the corresponding familiar problem for a metal, the density of states, which enters into the Thomas-Fermi analysis, is here appropriate to a model band structure with two bands and a gap. Explicit results for the wave-number-dependent dielectric function (k) and for the spatial dielectric function (r) are obtained in simple analytical form. It is shown in this paper that the same TF equation can be handled with different boundary conditions to describe screening in semiconductors. The Thomas-Fermi treatment of screening of a point positive charge Ze in a model insulator is developed. Thomas-Fermi (TF) screening in metals has been widely studied in the literature many years ago. ![]()
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