Long-Range Hopping in Substitutionally Disordered Solids

A theoretical approach for studying charge-carrier and energy diffusion due to long-range hopping in substitutionally disordered solids is presented. Unlike some earlier theories, which invoke a pair approximation to treat back-transfer processes, the current theory makes use of the exact solution to an appropriate single-defect problemone in which long-range jumps into, out of, and between both the defect site and all other active sites in the lattice are explicitly included. From this exact solution a new long-range effective-medium theory is constructed to describe the configurationally averaged transport properties of the disordered system.