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 S E = 4 πe / ϵE , following from the Langevin recombination theory. For anisotropic systems it is demonstrated that S can be much larger or smaller than S E 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.