Electrical conductivity of high-purity germanium crystals at low temperature

The temperature dependence of electrical conductivity of single-crystal and polycrystalline high-purity germanium (HPGe) samples has been investigated in the temperature range from 7 to 100 K. The conductivity versus inverse of temperature curves for three single-crystal samples consist of two distinct temperature ranges: a high-temperature range where the conductivity increases to a maximum with decreasing temperature, and a low-temperature range where the conductivity continues decreasing slowly with decreasing temperature. In contrast, the conductivity versus inverse of temperature curves for three polycrystalline samples, in addition to a high- and a low-temperature range where a similar conductive behavior is shown, have a medium-temperature range where the conductivity decreases dramatically with decreasing temperature. The turning point temperature ( $${T_{\text{m}}}$$ ) which corresponds to the maximum values of the conductivity on the conductivity versus inverse of temperature curves are higher for the polycrystalline samples than for the single-crystal samples. Additionally, the net carrier concentrations of all samples have been calculated based on measured conductivity in the whole measurement temperature range. The calculated results show that the ionized carrier concentration increases with increasing temperature due to thermal excitation, but it reaches saturation around 40 K for the single-crystal samples and 70 K for the polycrystalline samples. All these differences between the single-crystal samples and the polycrystalline samples could be attributed to trapping and scattering effects of the grain boundaries on the charge carriers. The relevant physical models have been proposed to explain these differences in the conductive behaviors between two kinds of samples.