Low-Temperature Impurity Conduction and Magnetoresistivity inn-Type Germanium

The resistivity of several lightly doped (Sb) $n$-type germanium samples has been calculated and compared with values measured at 2.5°K. An order of magnitude agreement has been obtained for a span of five orders of magnitude in the resistivities. It has been assumed that the mechanism of conductivity consists of jumping of electrons from occupied to empty donors. The number of charge carriers has been determined by calculating the number of "free" donor ions. The "trapped" donor ions, due to the presence of charged compensating acceptors, have been assumed not to participate in the conduction process. The effect of a constant magnetic field on impurity conduction has also been investigated and a simple theory of magnetoresistivity is presented. The calculated magnetoresistive ratio is in order of magnitude agreement with the measured value.