A generalized Scharfetter–Gummel scheme for degenerate and non-isothermal semiconductor

We present a highly accurate generalization of the Scharfetter–Gummel scheme for the discretization of the current densities in degenerate semiconductors under non-isothermal conditions. The underlying model relies on the Kelvin formula for the Seebeck coefficient, which has the intriguing property that the ∇T -term in the electrical current density expressions vanishes exactly when passing to the drift-diffusion form – even though the thermoelectric cross-coupling is fully taken into account.