Analytical formulae for d.c. hopping conductivity

Abstract

Analytical formulae for d.c. hopping conductivity are derived from the conductance network analogue of the steady-state rate equations. The formulae provide valid approximations for both high and low site densities and for both degenerate and non-degenerate electron statistics. They are applied to the special case of non-degenerate hopping in narrow energy bands. The formulae are then particularly simple and are in excellent agreement with computer calculations in two and three dimensions. They yield hopping conductivities for n-–type and p–type Ge within about an order of magnitude of the experimental values. The prefactor in the conductivity is proportional to the inverse site density raised to the power (v – d + 1)/d in d dimensions where v is the power of the intersite separation in the prefactor to the hopping rate.