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A one-dimensional analytic model for the insulated gate bipolar transistor (IGBT), which includes a high-doped buffer layer in the low-doped bipolar transistor base, is developed. The model is used to perform a theoretical trade-off study between IGBT's with and without the buffer layer. The study is performed for devices of equal breakdown voltages, and the critical parameters chosen to ``trade-off'' are turn-off switching energy loss (related to turn-off time) and on-state voltage, both at a given current. In this model, as in reality, the two critical parameters are varied by 1) adjusting the doping concentration and thickness of a buffer layer included as part of the bipolar transistor base, 2) adjusting the lifetime in the lowly doped bipolar transistor base with no buffer layer included, or by 3) a combination of 1) and 2). The results of the model predict that for equal breakdown voltages an optimized device with a buffer layer has less switching energy loss for a given on-state voltage than an optimized device with no buffer layer.