A variational thermodynamic approach for modeling internal capacitances of Trench Insulated Gate Bipolar Transistors (TIGBTs) to interpret measured capacitance-voltage characteristics

The Trench Insulated Gate Bipolar Transistor (TIGBT) is a device of great complexity consisting of a large number of interacting internal capacitances. It is imperative to understand these capacitances and interactions among them because of their direct implication in the device switching power loss and speed. Standard numerical modeling of the TIGBT using finite element (FE) methods is not completely satisfactory for a number of reasons. We here present a novel approach to modeling the static behavior of this device at a level of detail not otherwise available either experimentally or by standard methods of analysis. We base our model on evaluating the thermodynamic Free Energy of the device using parameterized `trial functions´ for the electrostatic potential in each of the seven electronically active regions of the transistor. Charge carrier concentrations are calculated using standard band gap theory. The resulting closed-form expression for Free Energy is minimized using the free parameters present in the trial functions. The results of this process can be employed to construct a terminal capacitance model by appropriately combining the internal capacitances distributed throughout the structure. The model can then be verified with measured terminal capacitance-voltage characteristics of the device to interpret individual contributions.