Modeling and Experimental Verification of TIGBT Detailed Internal Electric Fields Which Lead to Breakdown

Distribution and intensity of electrostatic field in a trench insulated gate bipolar transistor, a key factor in the breakdown of such power semiconductor devices, are investigated using the variational thermodynamic methodology based on device Helmholtz free energy yielding closed-form solutions. Attention is given to quantifying the detailed field effects due to curvature near the bottom of the gate. Our modeling of the bottom edge of the gate uses the shape of a published scanning electron microscopy image of an as-built trench gate. This necessitates an appropriate approach to represent subtle details of the system. We have also examined the modification of electrostatic field and potential in that region due to oxide charge. The electrostatic field is quantified and described for sheet charges of variable polarity, intensity, and position in the oxide. We have employed Fermi-Dirac statistics instead of Boltzmann statistics, which underconstrain mobile electron and hole populations at the operating conditions of the device studied. Our model results are consistent with the device gate breakdown experiments.