Hopping conduction in a two-dimensional impurity band

The temperature dependence (380 mKT80 K) and electric field dependence (50 mV/cmF150 V/cm) of hopping conduction have been measured as a function of the impurity concentration, surface electric field, and carrier density in a quasi-two-dimensional impurity band formed in the inversion layer of a sodium-doped silicon metal-oxide--semiconductor field-effect transistor. The conductivity is found to be an exponential function of the temperature and applied electric field. Our observations can be accommodated by noninteracting, single-particle hopping models based on percolation theory in which the Coulomb repulsion between electrons on different sites is ignored. For impurity concentrations in the range 2×{}10¹¹ to 1.14×{}10¹² cm^-2 and localization lengths from 3.4 to 7.5 nm, the noninteracting theories accurately describe eight-orders-of-magnitude change in the conductivity of a half-filled impurity band observed for a factor-of-80 change in temperature, and three-orders-of-magnitude change in the non-Ohmic current observed for a factor-of-15 change in electric field. The observed temperature dependence of the conductivity is not consistent with the temperature dependence predicted by Efros and Shklovskii for a Coulomb gap in the single-particle excitation spectrum, although their theory was expected to predict the conductivity under the conditions examined in this experiment.