Modeling of detailed internal electric field in a Trench Insulated Gate Bipolar Transistor using variational thermodynamic methodology

The Trench Insulated Gate Bipolar Transistor (TIGBT) has become of central importance in high power high switching speed applications. Breakdown in these devices is strongly influenced, among other factors, by subtle details of trench geometry, especially at the bottom edge. Here, we apply the variational thermodynamic methodology to develop quantitative models for the electric potential relaxation distance into N
^-
-Si region adjacent to the trench gate oxide and the SiO
₂
/N
^-
-Si interface potential. From this we extract electric field in the gate oxide and at the SiO
₂
/N
^-
-Si interface for different sections of the trench as function of gate voltage.