Shape optimization for a simulation of a semiconductor problem

This work gives a study of the Regier’s model by using the shape optimization techniques. Two formulations of this model are proposed with appropriate boundary conditions of the MESFET transistor. In each formulation the existence of a free boundary, separating the depletion and neutrality of charge regions, is proved with some hypothesis. The shape gradient is calculated for each formulation to approach the solution. To approximate the free boundary, two algorithms are presented. Numerical results obtained by implementing the last algorithm prove that this shape optimization techniques provide a reasonably smooth free boundary.