Physical and Numerically Stable Linvill-Lump Compact Model of the pn -Junction

We present a compact model of the pn -junction for power device analysis using a physically based and numerically stable version of the approach proposed by Linvill in the 1950s. Problems with the original Linvill formulation have been eliminated by using quasi-Fermi potentials instead of mobile carrier densities as system unknowns and by adopting the Scharfetter–Gummel stable difference approximation. The model naturally accounts for high-level injection and reverse recovery effects and is based on physical parameters such as doping densities, recombination life-times, and geometry rather than empirical parameters such as knee current and relaxation time. The model is implemented in Verilog-A and is verified by dc, small-signal, and large-signal simulations.