Variational thermodynamic and Finite Element analysis models of the Metal-Oxide-Semiconductor Capacitor

Finite Element modeling of the electrostatic behavior of semiconductor electronic devices has been a work-horse of top-level design for generations. Commercial off-the-shelf Finite Element code packages are readily available which afford the user convenient geometry options and post-processing tools. Recent effort at our Electron Devices Laboratory has been directed at approaching the problem from a thermodynamic perspective by implementing a Variational Thermodynamic method to the minimization of the Helmholtz Free Energy of the device. In this work we exercise both Variational Thermodynamic methodology and Finite Element analysis to model the static behavior of the Metal-Oxide-Semiconductor Capacitor under identical boundary conditions and assumptions to demonstrate how closely they agree.