An accurate grid local truncation error for device simulation

One of the most important factors in achieving an accurate and efficient device simulation today is a good grid. However, an effective grid error indicator for the device simulation has been lacking; thus, it is very difficult to know how accurate the simulation results are. Previous papers have suggested that the local truncation error (LTE) is not a good indicator for grid discretization error. In this paper we show that the dominant factor in the LTE derivation has been ignored. With the correct formulation it is shown that LTE is a major source of the solution error. Since LTE is easy to calculate, our methodology provides up to orders of magnitudes savings in CPU time compared to other algorithms. This adaptive regridding on LTE provides overall simulation speedups of 10X for medium-sized examples. With little overhead, the LTE is extended to be an effective error indicator for device terminal characteristics, such as drive current and threshold voltage, which can only be obtained previously with large effort.