doi: 10.3850/978-3-9815370-4-8_0560

ABSTRACT

As CMOS technology continues to scale, the effects of variation inject a greater proportion of error and uncertainty into the design process. Ultra-deep submicron circuits require accurate modeling of gate delay in order to meet challenging timing constraints.With the lack of statistical data, designers are faced with a arduous task to optimize a circuit which is greatly affected by variability due to the mechanical and chemical manufacturing process. Discrete gate sizing is a complex problem which requires (1) accurate models that take into account random parametric variation and (2) a fair allocation of resources to maximize the solution in the delay-energy space. The GTFUZZ algorithm is presented which handles both of these tasks. Fuzzy games are used to model the problem of gate sizing as a resource allocation problem. In fuzzy games, delay is considered a fuzzy goal with fuzzy parameters to capture the imprecision of gate delay early in the design phase when empirical data is absent. Dynamic power is normalized as a fuzzy goal without varying coefficients. The fuzzy goals also provide a flexible platform for multimetric optimization. The robust GTFUZZ (Fuzzy Game Theory) algorithm is compared against fuzzy linear programming (FLP) and deterministic worstcase FLP (DWCFLP) algorithms. Benchmark circuits are first synthesized, placed, routed, and optimized for performance using the Synopsys University 32/28nm standard cell library and technology files. Operating at the optimized clock frequency, results show an average power reduction of about 20% versus DWCFLP and 9% against variation-aware gate sizing with FLP. Timing and timing yield are verified by both Synopsys PrimeTime and Monte Carlo simulations of the most critical paths using HSPICE.

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