NONOHMIC EFFECTS IN HOPPING CONDUCTION IN DOPED SILICON AND GERMANIUMBETWEEN 0.05 AND 1 K

We have studied non-Ohmic effects In hopping conduction in moderately compensated ion-implanted Si:P, B (both n- and p-type) and neutron-tra nsmutation-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, w here 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: rho=rho(o) exp (T-o/T)(1/2). The samples included in this study have characteristic t emperatures T-o in the range 1.4-60 K for silicon, and 22-60 K for ger manium. We have compared our data to exponential and ''hyperbolic-sine '' field-effect models of the electrical nonlinearity: rho(E)=rho(0)e( -x) and rho(E)=rho(0)x/sinh(x), where x=eEl/kT, and to an empirical ho t-electron model. The exponential field-effect model tends to be a goo d representation for the samples with high T-o at low T. The sinh mode l can match the data only at low fields. The hot-electron model fits o ur data well over a wide range of power in the low-T-o-high-T regime. We discuss the quantitative implications of these results for the appl ication of these materials as thermometers for microcalorimeters optim ized for high-resolution spectroscopy. [S0163-1829(98)05208-4].