We report numerical simulations of hopping conduction in lightly doped semiconductors. We model the hopping using a Miller-Abrahams resistor network. We investigate the effect of the density of states (DOS) on the temperature dependence of the hopping conductivity σ(T) in a regime of temperature T well above the regime associated with variable-range hopping (VRH). In this ‘‘high-T ’’ regime, we study a ‘‘peaked’’ DOS and a ‘‘flat-flat’’ DOS. The ‘‘peaked’’ DOS has a maximum at the T=0 K chemical potential ${\mu }_0$ and decreases away from ${\mu }_0$.

The ‘‘flat-flat’’ DOS consists of two flat regions: an inner narrow region with density $g_{\mathrm{inner}}$ centered about ${\mu }_0$, and an outer broad region with density $g_{\mathrm{outer}>g_{\mathrm{inner}}}$. For the peaked DOS, we obtain at ‘‘high T ’’ results consistent with σ((T) =${\sigma }_0$exp[-($T_0$/T${)}^{1/4}$], where $T_0$ is much smaller than the $T_0$ for VRH. This behavior agrees with certain experimental results for the conductivity in lightly doped n-type GaAs and n-type InP, and thereby provides direct support for the explanation by Shegelski and Barrie [Phys. Rev. B 36, 7549 (1987); 36, 7558 (1987)] that such experimental behavior results from a peaked DOS. For the flat-flat DOS, we find σ(T) =${\sigma }_0$exp[-($T_0$/T${)}^{1/2}$] at ‘‘high T ’’ if the energy width of the inner region is a fraction γ≊0.1 of the total width of the DOS. This result indicates that a ‘‘filling in’’ of the Coulomb gap (i.e., the DOS is nonzero at ${\mu }_0$) is insufficient to destroy $T^{\mathrm{-}1/2}$ behavior. We suggest that the trend toward $T^{\mathrm{-}1/4}$ behavior evident in hopping-conduction experiments is due, not to a filling in of the Coulomb gap, but instead to a narrowing of the Coulomb gap (γ≲0.02). Such narrowing of the gap forces $T^{\mathrm{-}1/2}$ behavior down to very low T and allows $T^{\mathrm{-}1/4}$ behavior at high T.

• Received 31 October 1988

DOI:https://doi.org/10.1103/PhysRevB.39.13411