Date of Graduation
In this thesis, we investigate an inverse boundary value problem arising from the study of semiconductor transistors. The problem is to recover a number of parameters in the coefficient function from the knowledge of the solution at some accessible boundary. We first review the mathematical models that describe the current flow in a transistor into an integrated circuit. We then obtain the theoretical results pertaining to this inverse problem, such as existence, monotonicity, differentiability, asymptotic properties and identifiability. We also formulate the partial differential equation model into a boundary integral equation model. For the differential equation model, we employ both the finite difference method and finite element method to compute the numerical results. For the integral equation model, we obtain the numerical results by adopting a wavelet collocation method. Several iteration schemes are designed and implemented for parameter identification for both models. Examples are presented to illustrate the numerical results. Finally, some suggestions for future research in this topic are given. This work was partially supported by US Army Research Office Grant DAAG 55-98-1-0261.
Lu, Mingying, "An inverse boundary value problem from semiconductor modeling." (2003). Graduate Theses, Dissertations, and Problem Reports. 9326.