Boundary Value Problems in VLSI Modeling
The physical effects of importance in large VLSI circuits, whether localized in devices or global, are mostly governed by field equations of the Laplace and Poisson type. Our aim will be to derive physically sound reduced models for these effects. These models can then be used for design or verification purposes by appropriate tools such as a simulator or a network verifier. We are not so much interested in the solution of a single field equation, but in systematic modeling procedures. The result of our efforts will be a discretized and simplified system that mimics the essential parts of the behaviour of the given physical system. The most prominent effects that we shall encounter are resistive current transport (in interconnects and in MOS transistors) and interwire capacitance. In this chapter we review the basic equations governing these situations. In subsequent chapters we shall show how these equations can be discretized so as to produce sound approximate models and how these models can be reduced in turn.
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