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An exact SOI device simulator applicable to prediction of the transistor characteristics in high-current region is developed. In the simulator, the basic two-dimensional Poisson's and current continuity equations are numerically solved under steady-state condition. To obtain a stable and rapid convergence in the numerical scheme, a newly developed alternative step solving method is implemented. Using this simulator, the drain current kink effect, a typical phenomenon for substrate-floating devices, is exactly simulated for the first time. The physical mechanism of this phenomenon is also clarified. The simulated results indicate that kink effects are suppressed by using Iow-lifetime SOI substrates.