Simulation of carrier transport and energy relaxation in a macroscopic hopping system of sites with a Gaussian energy distribution

Abstract

Abstract The transport properties within a cubic lattice consisting of 70 × 30 × 30 hopping sites subject to a Gaussian energy distribution [sgrave]=0.1 eV wide, have been simulated by a Monte Carlo technique. Transit pulse shapes, the time evolution of the energy of the hopping carrier and number of new sites visited as a function of time are analysed. It is found that within the time regime of dispersive transport the energy loss per carrier per jump is inversely proportional to the previous number of new sites visited. This is consistent with a t α-1 behaviour of the jump rate. After a time τe, dynamic equilibrium is established leading to Gaussian transport. For disordered molecular solids in which hopping transport dominates and which are characterized by [sgrave]/kT < 4, i.e. α > 0.5, τe is found to be less than 10−8 s. This value would prevent detection of the dispersive regime employing conventional electrical circuitry. The mean carrier displacement at t=τe is typically ten lattice planes. In the long-time limit, In μ ∼ -([sgrave]/T)2 is predicted.