Non-isothermal Scharfetter-Gummel scheme for electro-thermal transport simulation in degenerate semiconductors

Electro-thermal transport phenomena in semiconductors are described by the non-isothermal drift-diffusion system. The equations take a remarkably simple form when assuming the Kelvin formula for the thermopower. We present a novel, non-isothermal generalization of the Scharfetter-Gummel finite volume discretization for degenerate semiconductors obeying Fermi-Dirac statistics, which preserves numerous structural properties of the continuous model on the discrete level. The approach is demonstrated by 2D simulations of a heterojunction bipolar transistor.