Nondestructive One- and Two-Dimensional Doping Profiling by Inverse Methods

摘要

In chapter 2, an overview is provided of the existing methods for doping profiling with some emphasis on those methods that use electrical measurement data, because they are most closely related to the new methods described in the thesis. Chapter 3 formulates doping profiling as an inverse Poisson problem, and introduces the two numerical methods that form the body of the work. Also, in chapter 3 design considerations for suitable profiling test structures are given. The abrupt depletion approximation, its use for the derivation of the traditional doping profiling equations and the literature on this subject are reviewed in appendix A. A method to enlarge the depletion range in MOS structures using DC voltages only is discussed in appendix B. The first new method uses nonlinear optimization techniques, an introduction to which is provided in appendix C. The implementation of the second new method, which uses the iterative solution of a dedicated linear least squares system, is described in chapter 4. Appendix E gives a numerical example of the scaling and solution by Single Value Decomposition of the least squares system of the second method.