Non-Ohmic effects in hopping conduction in doped silicon and germanium between 0.05 and 1 K

We have studied non-Ohmic effects in hopping conduction in moderately compensated ion-implanted Si:P, B both nand p-type and neutron-transmutation-doped Ge:Ga,As over the temperature range 0.05–0.8 K and up to moderately strong electric fields. In the limit of small fields, where the current is proportional to applied voltage, the resistivities of these materials are approximated over a wide temperature range by the model of variable range hopping with a Coulomb gap: 0 exp(T0 /T) . The samples included in this study have characteristic temperatures T0 in the range 1.4–60 K for silicon, and 22–60 K for germanium. We have compared our data to exponential and ‘‘hyperbolic-sine’’ field-effect models of the electrical nonlinearity: (E) (0)e x and (E) (0)x/sinh(x), where x eEl/kT , and to an empirical hot-electron model. The exponential field-effect model tends to be a good representation for the samples with high T0 at low T . The sinh model can match the data only at low fields. The hot-electron model fits our data well over a wide range of power in the low-T0 –high-T regime. We discuss the quantitative implications of these results for the application of these materials as thermometers for microcalorimeters optimized for high-resolution spectroscopy. S0163-1829 98 05208-4