In recent years, mixed-signal designs have become more pervasive, due to their efficient use of area and power. Unfortunately, with sensitive analog and fast digital circuits sharing a common, non-ideal substrate, such designs carry the additional design burden of electromagnetic coupling between contacts.This thesis presents a method that quickly extracts the electroquasistatic coupling resistances between contacts on a planar, rectangular, two-layer lossy substrate, using an FFT-accelerated multi-domain surface integral formulation. The multi-domain surface integral formulation allows for multi-layered substrates, without meshing the volume. This method has the advantages of easy meshing, simple implementation, and FFT-accelerated iterative methods. Also, a three-dimensional variant of this method allows for more complex substrate geometries than some other surface integral techniques, such as multilayered Green's functions; this three-dimensional problem and its solution are presented in parallel with the planar substrate problem and solution. Results from a C++ implementation are presented for the planar problem.Thesis Supervisor: Jacob K. White Title: Professor AcknowledgmentsAn Acknowledgements section is supposed to be one page long, but really, what is the cost of printing one extra page? I've been lucky enough to have many supporters, and I'd be remiss to omit one.I have Prof. Jacob White to thank for the inspiration of this thesis, as well as innumerable suggestions, encouragements and chastisements. Also to be thanked profusely is Xin Hu, a good friend, but more more importantly for the purposes of this thesis, a collaborator in much of the substrate coupling work, in particular the fundamentals and gruntwork of the two-dimensional problem. I must acknowledge that I couldn't have done it without our collaboration. It is imperative that 5I have my friends to thank for dragging me out of the lab, and keeping me sane.In particular, thank you to those of you who (horror!) are not in Engineering and/or (horror!) not at MIT. You guys have provided an amusing reality check, and great a cheerleading squad, even when you couldn't remember what my major is (it's Electrical Engineering, by the way). Speaking of sanity and reality, for the past nine months,

This paper describes an efficient method for solving an inverse optical scattering problem associated with the optical semiconductor process inspection. The method determines the geometric features of a fabricated structure, from spectroscopic ellipsometry measurements, by combining a parameterized low-order model with an optimization algorithm. We make improvements on the polynomial fittingbased parameterized moment matching technique to extract such model automatically. Since the resulting model is inexpensive to evaluate, the method shows large speedup without losing much accuracy: the examples show more than 1000 times speedup with less than 1% error in the final geometric parameter estimation.