Sensitivity of solutions of Poisson's equation to boundary values in p-type a-Si:H thin films

摘要

The sensitivity of the separation of the bottom edge of the conduction band and the Fermi level, E_c - E_F, in a p-type and intrinsic 5 Um thick a-Si:H layer, to the boundary values required for a solution to Poisson's equation has been investigated computationally. The bandgap of the a-Si:H is 1.89 eV and the boundary values considered vary from E_c - E_F = 0 to 1.89 eV These are extreme values; realistic values would lie within this range, but using such extreme values allows us to infer the sensitivity of the solution to all realistic boundary values. It was found that E_c - E_F near the surfaces is sensitive to the boundary values, but E_c - E_F in the interior of the layer is insensitive to the boundary values. The region of sensitivity is narrow for high boron dopant concentrations (1.12 × 10~19 cm~-3), and increases as the dopant concentration is decreased. For an intrinsic layer l Um thick, E_c - E_F exhibits sensitivity to the boundary values throughout the layer.