An interface boundary decision technique in laplace-poisson domain problems-a finite element analysis of junction FET

In treatment of problems of domains governed by either Laplace or Poisson type partial differential equations, such as in field-effect semiconductor devices, an important problem in practice is the determination of the boundary between the two domains. This paper presents a method using the finite-element approach to determine the Laplace-Poisson domain boundary. This method gives the solutions to the shape determination problems with high-order nonlinearity by adding a modification quantity in applying the sensitivity analysis for given initial boundary shape. Thus, it has the advantages of clear mathematical structure and convenience in applications. As a concrete application example, the two-dimensional junction FET is taken. Problems involving determination of the depletion layer (Poisson domain) and the current path (Laplace domain) are investigated. Results show that the boundary determination method presented here yields such FET characteristics as the field distribution, substrate effect and the pinch-off voltage and useful knowledge for design is obtained.