Variable-Range Hopping in Si : B: A Temperature-Independent Prefactor in Three Dimensions

For Si : B with dopant concentrations ranging from 0.75n c to the critical concentration for the metal-insulator transition, the conductivity ranging over five orders of magnitude is shown to collapse onto a single universal curve of the form a(T) = σ 0 f(T * /T) with a prefactor σ 0 that is independent of temperature and dopant concentration. The function f(T * /T) = exp[-(T * /T) β ] with β = 1/2 when T * > 10T, corresponding to Efros-Shklovskii variable-range hopping. For T * < 8T the exponent β is 1/3, the 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.