A variational thermodynamic methodology applied to model critical smart grid electronic devices

The performance of the Trench Insulated Gate Bipolar Transistor is of special concern to the Smart Grid community. Here, a novel methodology for the quasi-static behavior of the device is introduced which is based on a firmly established law of classical thermodynamics, viz., the minimization of the Helmholtz Free Energy as a function of the internal fields, potential, and charge. The analysis begins with the expression of free energy density given by Landau. Then the ‘trial’ functions of the potential which are indexed to the parameter ‘interface potential’ and the parameter ‘penetration distance of interface potential’ into the doped silicon are introduced. Next, the minimum condition for Helmholtz Energy using these parameters by standard methods is found. Results of this analysis produce analytic closed-form expressions for ‘penetration distance of interface potential’ vs. ‘interface potential’ and ‘interface potential’ vs. ‘gate potential’ for both p-base and n-drift regions.