Current injection from a metal to a disordered hopping system. I. Monte Carlo simulation

Abstract

Emission-limited charge-carrier injection in the dark from a metal into a random organic dielectric has been studied via Monte Carlo simulations. The dielectric has been modelled in terms of a regular lattice of point sites featuring a Gaussian distribution of energies to represent disorder. The essential input parameters are the zero-field energy barrier for injection $(\ensuremath{\Delta}),$ the variance $(\ensuremath{\sigma})$ of the distribution of the hopping states, electric field, and temperature. By varying the jump distance the unimportance of long-range tunneling transitions has been established. Therefore, Fowler-Nordheim type $j(F)$ charcteristics at high fields have to be considered accidental. The dependence of the injection yield resembles that of Richardson-Schottky (RS) thermionic emission. Quantitative differences are noted, however, concerning the RS coefficient and the temperature dependence. The latter tends to saturate at low temperatures, which is a signature of hopping among sites distributed in energy.