Frequency-dependent conductivity of insulating Si:P and Si:As near the metal-insulator transition

Abstract

The microwave electrical conductivity \ensuremath{\sigma}(\ensuremath{\omega},N,T) of insulating Si:P has been measured for frequencies between 0.1 and 2.1 GHz in the density range 0.46/${N}_{c}$0.86 (${N}_{c}$=3.74\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) and for temperatures between 1.5 and 4.2 K. For T2 K \ensuremath{\sigma}(\ensuremath{\omega},N,T) was found to be nearly independent of temperature, and showed a frequency dependence of the form \ensuremath{\sigma}(\ensuremath{\omega},N)\ensuremath{\propto}${\ensuremath{\omega}}^{s(N)}$ with s(N) increasing rapidly with increasing donor density from s\ensuremath{\sim}1 to s2, and a very strong density dependence. These results are compared with similar measurements in Si:As and discussed in terms of pair photon-assisted hopping theories including and excluding electron-electron interactions. We also address the importance of extending these experiments into the dilution refrigerator temperature range.