Singular Perturbations and a Free Boundary Problem in the Modeling of Field-Effect Transistors

Abstract

The drift-diffusion equations of semiconductor physics, modeling the behavior of buried-channel field-effect transistors, are analyzed using formal perturbation techniques. For large aspect ratio devices, the potential distribution is essentially one-dimensional under the gate and has a boundary layer structure near the source and drain. By extending the results of Ward, Odeh, and Cohen [SIAM J. Appl. Math., 4 (1990), pp. 1099–1125], where a different class of devices was treated, the potential under the gate is resolved in the limit of large doping densities for various values of the gate voltage and implant depth. Using the asymptotic potential, the mobile charge, which is needed for the derivation of the long-channel current-voltage relations, is found using standard techniques in the asymptotic evaluation of integrals. The results of Ward, Odeh, and Cohen are also extended to analyze the potential distribution in the fully two-dimensional regions near the source and drain in equilibrium. In the limit ...