Theory of radiative recombination by diffusion and tunneling in amorphous Si:H

A theory for geminate electron-hole recombination in amorphous semiconductors is given, which includes the effects of both diffusion and tunneling. The exact solution of the model is obtained neglecting the Coulomb interaction, which is included later in the prescribed diffusion approximation. It is shown that any combination of diffusion and tunneling will lead to a $t^{-\frac{3}{2}}$ long-time behavior for the reaction rate. The model is used to carry out an analysis of the photoluminescence decay in plasma-deposited amorphous Si:H as a function of temperature. The $t^{-\frac{3}{2}}$ long-time decay is observed at intermediate temperatures ($T\sim 150$ K), and the calculated luminescence quenching is in good agreement with experiment. The initial thermalized pair distribution function of electron-hole separations obtained from the low-temperature ($T=8\mathrm{}$ K) luminescence data is used to determine the Onsager photogeneration efficiency at room temperature. The calculations are in good agreement with the corresponding quantum efficiency obtained from recent xerographic measurements on the same material.