A soft threshold lucky electron model for efficient and accurate numerical device simulation

Abstract

Starting from Boltzmann's transport equation utilizing Shockley's idea for lucky electrons, a generalized expression of the impact ionization generation rate for numerical device simulation is found. The derivation from Boltzmann's transport equation for inhomogeneous systems provides a solid basis for the physical and mathematical fromulation and removes the ambiguity of former heruistic approaches. The new model allows the incorporation of different band structures and impact ionization models. By comparison with Monte Carlo simulations, different levels of approximation are examined and the final model is chosen to be numerically efficient without sacrificing physical accuracy too much. The resulting generation rate model is nonlocal in the electric field and incorporates an impact ionization rate with a soft threshold behaviour. It is used in combination with a hydrodynamic device simulator and is about three orders of magnitude faster than Monte Carlo, while yielding comparable results for substrate currents of NMOSFETs. Even in the case of deep sub-μm 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.