One-Parameter Scaling of the Conductivity of Si:B: A Temperature-Independent Variable-Range Hopping Prefactor

For insulating Si:B with dopant concentrations from 0.75 n_c to the critical concentration n_c, the conductivity ranging over five orders of magnitude collapses using a single scaling parameter T* onto a universal curve of the form $\sigma (T)={\sigma }_{0}f(T^{\ast }\mathrm{/}T)$ with a temperature-independent prefactor of the order of Mott’s minimum metallic conductivity. The function $f (T^/T) = e^{-(T^/T)^{\beta}}$ with \beta = 1/2 when T^/T>10, corresponding to Efros-Shklovskii variable-range hopping. For T^/T < 8 the exponent \beta = 1/3, a value expected for Mott variable-range hopping in two rather than three dimensions. The temperature-independent prefactor implies hopping that is not mediated by phonons.