A model of how the thermal ionization energy of impurities in semiconductors depends on their concentration and compensation

Abstract

An electrostatic model is derived for the dependence of the thermal ionization energy of hydrogenic impurities E ₁ on their concentration N and degree of compensation K, with allowance for the screening of ions by electrons (holes) that hop from impurity to impurity. It is shown that the change in E ₁ with increasing N and K is connected with broadening of the impurity band and its shift toward the valence (v) band for acceptors and toward the conduction band (c) for donors. The shift in the impurity band is explained by a decrease in the affinity energy of an ionized acceptor for a hole (or a donor for an electron) due to screening of the ions. The impurity ion distribution density over the crystal is assumed to be Poisson-like, while its energy distribution is normal. The electron densities of states in the v-and c-bands are assumed to be those of the undoped crystal for the temperature interval in which E ₁ is determined. The values of E ₁(N,K) calculated using the expressions given here coincide with known experimental data for transmutation-doped Ge crystals. A description is given of the dependence on N and K of the thermal ionization energy of Zn atoms in p-type Ge as they change from a charge state (−1) to (−2).