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 impuritiesN ^* 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 -R(4.2 K)/R(300 K), =R(2.0 K)/R(4.2 K) and the conductivity (4.2 K). The next step consists of plotting and (4.2) vs . Assuming that is the most reliable parameter, one can calculate, after an averaging procedare, the corrected values of ^*, ^*(4.2) and the resistivity at room temperature ^*(300)= ^{* *}(4.2)]^–1. Finally, using the known dependence (300)=f(N) for homogeneous samples, one can obtain the values ofN ^*. The dependences ofN ^* on and on are plotted. The scaling behavior of the conductivity of the Ge:As samples with corrected values of ^*(4.2) andN ^* has been observed down toT=100 mK.