A SOFT THRESHOLD LUCKY ELECTRON MODEL FOR EFFICIENT AND ACCURATE NUMERICAL DEVICE SIMULATION

Starting from Boltzmann's transport equation utilizing Shockley's idea for lucky electrons, a generalized expression of the impact ionizatio n generation rate for numerical device simulation is found. The deriva tion from Boltzmann's transport equation for inhomogeneous systems pro vides a solid basis for the physical and mathematical fromulation and removes the ambiguity of former heruistic approaches. The new model al lows the incorporation of different band structures and impact ionizat ion models. By comparison with Monte Carlo simulations, different leve ls of approximation are examined and the final model is chosen to be n umerically efficient without sacrificing physical accuracy too much. T he resulting generation rate model is nonlocal in the electric field a nd incorporates an impact ionization rate with a soft threshold behavi our. It is used in combination with a hydrodynamic device simulator an d is about three orders of magnitude faster than Monte Carlo, while yi elding comparable results for substrate currents of NMOSFETs. Even in the case of deep sub-mu m NMOSFETs with supply voltages of about 1.5 V the results agree well with Monte Carlo. Comparison with experimental data also show good agreement over a wide range of bias conditions. C opyright (C) 1996 IBRO.