Determination of the impurity concentration in heavily doped inhomogeneous semiconductors from the measurement of the low-temperature conductivity

A method has been developed for determining the effective concentration of shallow impurities N^* reponsible for the low-temperature conductivity in the vicinity of the metal-insulator transition for inhomogeneous samples of n-Ge:As. The method is based on the measurement of two ratios of sample resistance γ-R(4.2 K)/R(300 K), β=R(2.0 K)/R(4.2 K) and the conductivity σ(4.2 K). The next step consists of plotting and σ(4.2) vs β. Assuming that β is the most reliable parameter, one can calculate, after an averaging procedare, the corrected values of γ^*, π^*(4.2) and the resistivity at room temperature ρ^*(300)=[γ^*π^*(4.2)]^-1. Finally, using the known dependence ρ(300)=f(N) for homogeneous samples, one can obtain the values of N^*. The dependences of N^* on β and on γ are plotted. The scaling behavior of the conductivity of the Ge:As samples with corrected values of π^*(4.2) and N^* has been observed down to T=100 mK.