Deconvolution of activated and variable-range-hopping conduction for barely insulating arsenic-doped silicon

Abstract

An explanation, using the logarithmic derivative method, is given for some previously unexplained features of the temperature dependence of the conductivity for barely insulating Si:As for $10\mathrm{K}<T<78\mathrm{K}.$ The results and analysis suggest an important high-temperature correction to the prefactor of Mott variable range hopping, and also give more reliable values of the activation energy and the temperature-dependent prefactors of the activated conduction. The two samples closest to ${n}_{c}$ provide evidence for temperature-dependent activation energies. The activated contribution allows the determination of the mobility $\ensuremath{\mu}(n,T)$ for itinerant electrons above the mobility edge. This mobility is consistent with ionized impurity scattering in the impurity band. The logarithmic derivative method also provides a method for determining the fraction ${f}_{a}(n,T)$ of donor electrons thermally excited above the mobility edge. The activated conductivity results are compared with Manfield's expression for impurity scattering as adapted to the impurity band case.