Resistivity and Hall Effect of Germanium at Low Temperatures

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Abstract
An experimental investigation of the Hall effect and the resistivity of germanium alloys at temperatures from room temperature down to the liquid helium temperature range is reported. Germanium samples with different kinds of impurity and different concentrations were used. At higher temperatures, satisfactory agreement between theory and experiment was found. The activation energy of the impurity states was found to be of the order of 10 millivolts. The scattering of the carriers in the conduction and filled bands consists mainly of lattice scattering and ionized impurity scattering. At low temperatures, however, anomalies in the Hall curves were observed. The Hall curve for every sample measured went through a maximum as the temperature was lowered. At the same time the resistivity approached a saturation value. The Hall curves of low resistivity samples finally became flat at very low temperatures. These anomalies are explained on the assumption of small but finite mobility of carriers in the impurity states. This conduction in the impurity states assumes importance at low temperatures when the concentration of carriers in the conduction band becomes very low. When this simultaneous conduction in the conduction band and the impurity band is considered, the behaviors in the Hall and the resistivity curves are satisfactorily explained. The mobility in the impurity band is found to increase with the impurity concentration, but is rather temperature-independent.

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