An accurate sparse matrix based framework for statistical static timing analysis

ABSTRACT

Statistical Static Timing Analysis has received wide attention recently and emerged as a viable technique for manufacturability analysis. To be useful, however, it is important that the error introduced in SSTA be significantly smaller than the manufacturing variations being modeled. Achieving such accuracy requires careful attention to the delay models and to the algorithms applied. In this paper, we propose a new sparse-matrix based framework for accurate path-based SSTA, motivated by the observation that the number of timing paths in practice is sub-quadratic based on a study of industrial circuits and the ISCAS89 benchmarks. Our sparse-matrix based formulation has the following advantages: (a) It places no restrictions on process parameter distributions; (b) It embeds accurate polynomial-based delay model which takes into account slope propagation naturally; (c) It takes advantage of the matrix sparsity and high performance linear algebra for efficient implementation. Our experimental results are very promising.

References

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Index Terms

• Computing methodologies

  • Modeling and simulation

    • Model development and analysis

      • Model verification and validation

  • Symbolic and algebraic manipulation

    • Symbolic and algebraic algorithms

      • Linear algebra algorithms

• Hardware

  • Hardware validation

  • Integrated circuits

    • Digital switches

      • Logic families

• Mathematics of computing

  • Mathematical analysis

    • Numerical analysis

      • Computations on matrices