Steady State Mathematical Theory for the Insulated Gate Field Effect Transistor

A two-dimensional mathematical analysis is presented of the mechanisms of operation for an insulated gate field effect transistor (IGFET). Included in this analysis are qualitative and quantitative comparisons between conventional one-dimensional theory and a rigorous two-dimensional computer solution for the IGFET. It is shown that many characteristics of device operation deduced from conventional theory cannot be verified on a two-dimensional basis because of mechanisms not presently taken into consideration by the theory. A modified one-dimensional mathematical theory is therefore proposed, to account for these mechanisms, that is in adequate agreement with a rigorous two-dimensional computer solution for this semiconductor problem.