An accurate metric to control time step of transient device simulation by matrix exponential method

An accurate metric for the time step control in the power device transient simulation is proposed. This metric contains an exponential term of the dominant time constant of the whole device structure obtained by matrix exponential method. The proposed metric allows larger time step widths than the conventional metric of the 2
^nd
-order approximation of the local truncation error because it focuses on the dominant part of the transient response and its truncation error approximation is more accurate. Total CPU-time of the transient simulation of a silicon power DMOSFET by using the proposed method decreases down to 30% of that by the conventional metric with assuring the current accuracy of the dominant transient response.