A statistical model of a metallic inclusion in semiconducting media

Abstract

The properties of an isolated multicharged atom embedded into a semiconducting medium are discussed. The analysis generalizes the results of the known Thomas–Fermi theory for a multicharged (Z ≫ 1) atom in vacuum when it is immersed into an electron–hole gas of finite temperature. The Thomas–Fermi–Debye (TFD) atom problem is directly related to the properties of donors in low-doped semiconductors and is alternative in its conclusions to the ideal scenario of dissociation of donors. In the existing ideal statistics, an individual donor under infinitely low doping is completely ionized (a charged center does not hold its neutralizing counter-ions). A Thomas–Fermi–Debye atom (briefly, a TFD donor) remains a neutral formation that holds its screening “coat” even for infinitely low doping level, i.e., in the region of n_dλ₀³ ≪ 1, where n_d is the concentration of the doping impurity and λ₀ is the Debye length with the parameters of intrinsic semiconductor. Various observed consequences in the behavior of a TFD donor are discussed that allow one to judge the reality of the implications of the TFD donor model.