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

Abstract

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 $\sigma (T)={\sigma }_{0}f(T^{\ast }/T)$ with a temperature-independent prefactor of the order of Mott's minimum metallic conductivity. The function $f(T^{\ast }/T)=e^{-(T^{\ast }/T{)}^{\beta }}$ with β= 1/2 when T^*/T>10, corresponding to Efros-Shklovskii variable-range hopping. For T^*/T < 8 the exponent β= 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.

4 pages, 4 figures