THEORETICAL-MODEL OF DISPERSIVE TUNNEL TRANSPORT IN DISORDERED MATERIALS

A differential equation is derived for the carrier density under the conditions of dispersive tunnel transport. This equation includes drift and diffusion terms and the relevant coefficients are expressed in terms of the parameters of the trap spectrum. For long times (t > t(tau), where t(tau) is the characteristic time governed by the energy spectrum of traps and rising strongly as a result of cooling), when the majority of the jumps is accompanied by thermal activation, this equation is in fact identical with the "dispersive" equation describing transport far from equilibrium derived by V. I. Arkhipov and A. I. Rudenko. In the opposite case (t < t(tau)) the equation has the same structure as before, but the diffusion kinetics is universal (it is independent of the nature of the trap spectrum and temperature), whereas the ratio of the diffusion coefficient to the mobility depends on the spectrum of traps and, generally speaking, it depends on time, differing in this respect from the usual Einstein relationship. For example, in the case of traps with an exponential energy distribution the ratio of the diffusion coefficient to the mobility includes a characteristic energy of the trap spectrum epsilon0 instead of the thermal energy kT.