Mathematics Colloquia and Seminars

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In 1965, Moore predicted that the number of transistors on a state-of-the-art integrated circuit could be doubled every two years. "Moore's law" has held up remarkably well for almost four decades, and today, it is possible to put about two billion transistors on a single chip. For the design of integrated circuits, simulation techniques have always been and still are indispensable. In fact, the design and analysis of integrated circuits is almost completely done with simulation, and despite the enormous complexity of today's chips, first-time correct silicon is still the norm.

In this talk, we describe some of the mathematical problems in VLSI circuit simulation and some of the computational methods that have been developed to efficiently solve these problems. In particular, we discuss how these problems have changed as the complexity of integrated circuits has grown from about 100 transistors per chip in 1965 to two billion transistors per chip today.