T4 Inductance extraction and compact modeling of inductively coupled interconnects in the presence of process variations

In this tutorial, we will shed some light on an inductive extraction and compact modeling of inductively coupled interconnects, especially in the presence of unavoidable fabrication variations in the technology of 90 nm and below. The tutorial consists of two parts. The first part of the tutorial will describe the existing partial element equitant circuit (PEEC) based inductance extraction methods, and compact modeling techniques of inductively coupled interconnect circuits by means of second-order model order reduction techniques. For the inductive extraction part, we will review the concepts of partial inductances, PEEC extraction methods and latest susceptance-based inductance extraction and modeling. For the inductive modeling part, we will review the existing second-order model order reduction techniques and present the latest balanced truncation based second order model order reduction techniques. The second part of this tutorial will present a few of existing modeling and simulation approaches of interconnect circuits in the presence of process variations. We will review the latest model order reduction techniques of interconnects considering process variations. Those approaches include the parametric model order reduction by multi-dimension moment matching, interval-valued based reduction approaches, the sampling space based reduction methods and the statistical spectrum based approaches. We will give several specific examples for statistical spectrum based approaches and compare them with some existing approaches.