The market for Insulated Gate Bipolar Transistor (IGBT) is growing and there is a need for techniques to improve the design, modeling and simulation of IGBT. In this thesis, we first developed a new method to optimize the layout and dimensions of IGBT circuits based on device simulation and combinatorial optimization. Our method leads to the optimal IGBT layout consisting of hexagons, which is 6 % more efficient in terms of performance (current per unit area) over that of squares, and up to 80 % more efficient than rectangles. We also explored several techniques to reduce the time used for device simulation. In particular, we developed an accurate Verilog-A description based on the Hefner model. For transient simulation, the time used by SPICE on the Verilog-A model is only 1/10000 of that used by device simulation on the device structure. The SPICE results, though contain some inaccuracies in the details, match device simulation in the general trend. Due to the effectiveness and efficiency of our methods, we propose their application in designing better power electronic circuits and shorter turn-around time.