Hermite polynomial based interconnect analysis in the presence of process variations

Sarma Vrudhula, Janet Meiling Wang, Praveen Ghanta

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


Variations in the interconnect geometry of nanoscale ICs translate to variations in their performance. The resulting diminished accuracy in the estimates of performance at the design stage can lead to a significant reduction in the parametric yield. Thus, determining an accurate statistical description (e.g., moments, distribution, etc.) of the interconnect's response is critical for designers. In the presence of significant variations, device or interconnect model parameters such as wire resistance, capacitance, etc., need to modeled as random variables or as spatial random processes. The corner-based analysis is not accurate, and simulations based on sampling require long computation times due to the large number of parameters or random variables. This study proposes an efficient method of computing the stochastic response of interconnects. The technique models the stochastic response in an infinite dimensional Hubert space in terms of orthogonal polynomial expansions. A finite representation is obtained by projecting the infinite series representation onto a finite dimensional subspace. The advantage of the proposed method is that it provides a functional representation of the response of the system in terms of the random variables that represent the process variations. The proposed algorithm has been implemented in a procedure called orthogonal polynomial expansions for response analysis (OPERA). Results from OPERA simulations on a number of design test cases match well with those from the classical Monte Carlo simulation program with integrated circuits emphasis (SPICE) and from perturbation methods. Additionally, OPERA shows good computational efficiency: speedup of up to two orders of magnitude have been observed over Monte Carlo SPICE simulations.

Original languageEnglish (US)
Article number1677686
Pages (from-to)2001-2010
Number of pages10
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number10
StatePublished - Oct 2006


  • Galerkin projection
  • Hilbert space
  • Interconnects
  • Process variations
  • Stochastic finite elements
  • Very largescale integration (VLSI)

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering


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