Hopping conductivity in lightly doped semiconductors. I. Two dimensions

We point out the existence of experimental results for lightly doped n-type GaAs and n-type InP in which the conductivity σ is & with s close to (1/4, indicating variable-range hopping. We show that the experimental range of temperatures T, 1≲T≲7 K, in which this behavior holds, is well in excess of the temperature range predicted for these materials by established theories of variable-range hopping, and that the experimental $T_0$ values are too small to be understood on the basis of these theories. As a first step toward understanding these experimental results, we consider a two-dimensional lightly doped semiconductor. We choose a flat density of states with width Δɛ. We model the semiconductor as a Miller-Abrahams-type resistor network; we use the full form of the resistance and do not take the low-temperature asymptotic form because we are interested in temperatures for which kT is of order Δɛ.