Electrical Properties of Germanium Semiconductors at Low Temperatures

Low-temperature anomalies in the Hall coefficient and electrical resistivity—a steep maximum and a change of the slope of the log resistivity versus $\frac{1}{T}$ curve in germanium semiconductors—which were first observed by Hung and Gliessman, have been reinvestigated at temperatures between 1.5°K and 300°K using single crystals of $n$- and $p$-type germanium of various impurity concentrations. The influence of contacts and of various surface treatments has been studied. It was found that the effects observed cannot be explained by surface conduction. To exclude electrical field effects at low temperatures, fields well below the breakdown field have been used. The Hall coefficient was measured with magnetic fields ranging from 100 to 3500 gauss. Measurements on crystals cut in different crystal orientations show that the anomalies cannot be due to directional effects. In the same temperature region where the Hall effect and resistivity become anomalous, the magnetoresistive ratio also shows a drastic change. Throughout the whole temperature range the sample type, $n$ or $p$; is retained. The results indicate that in order to describe the observations it seems necessary to assume conduction in at least two bands, the regular conduction band (valence band in the case of $p$-type material) and one band with a very small mobility. Hung's model of impurity band conduction has to be refined considerably or altered to account for the complicated behavior of germanium samples with impurity contents between 2×${10}^{16}$ and 7×${10}^{16}$ acceptors/cc or between 3×${10}^{16}$ and 1×${10}^{17}$ donors/cc.