Accurate expressions for optical coefficients, given in n(p)-type degenerate Ge-crystals, due to the impurity-size effect, and obtained from an improved Forouhi-Bloomer parameterization model (FB-PM)

Abstract

In the n(p)-type degenerate Ge-crystals, at low temperature T and high d(a)-density N, our expression for the static dielectric constant, ε rd a , expressed as a function of the donor (acceptor) radius, rd a , and determined by using an effective Bohr model, as that investigated in [1,2], suggests that, for an increasing rd a , due to such the impurity size effect, ε rd a decreases, affecting strongly the critical d(a)-density in the metal-insulator transition (MIT), NCDn(CDp)(rd(a)), determined by Eq. (3), and its values are reported in Table 1, and also our accurate expressions for optical coefficients, obtained in Equations (24, 25, 28, 29), and their numerical results are given in Tables 2-6. Furthermore, one notes that, as observed in Table 3c, our obtained results of those optical coefficients are found to be more accurate than the corresponding ones, obtained from the FB-PM [11], suggesting thus that our present model, used here to study the optical properties of the n(p)-type degenerate Ge-crystals, is a good improved FB-PM, as observed in Table 3c.