Electron-hole collision cross section in discrete hopping systems

Electron-hole collisions mediated by their Coulomb attraction are simulated for discrete hopping systems in the presence of a high electric field E. The collision cross section S is found to be field-dependent and sensitive to transport anisotropy. For microscopically isotropic systems S is well represented by SE = 4πe/ϵE, following from the Langevin recombination theory. For anisotropic systems it is demonstrated that S can be much larger or smaller than SE for current flow along the direction with the smaller or larger mobility, respectively. This effect is found to arise even in nominally isotropic systems because of the field-induced mobility anisotropy. Disorder, however, tends effectively to decrease the apparent degree of anisotropy.