Characteristic lengths for steady-state transport in illuminated, intrinsic a-Si:H

The steady-state transport equations are solved for a general small-signal case. This solution leads to the spatial distribution of the carriers in the bulk of undoped hydrogenated amorphous silicon (a-Si:H) under illumination. The general small-signal differential equations for electrons and holes, including a local and/or external electric field, are first established. Subsequently, the analysis is restricted to the case with a negligible external electric field. Two characteristic lengths appear in the analytical solution. They are interpreted for the lifetime regime as the ambipolar diffusion length and the dielectric relaxation length. Depending on the material parameters, one or the other of these lengths dominates the transport. Illustrative numerical examples for typical solar-cell-quality a-Si:H are given