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On a Generalized Framework for Modeling the Effects of Process Variations on Circuit Delay Performance Using Response Surface Methodology

TitleOn a Generalized Framework for Modeling the Effects of Process Variations on Circuit Delay Performance Using Response Surface Methodology
Publication TypeJournal Article
Year of Publication2007
AuthorsHarish, BP, Bhat, N, Patil, MB
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Date PublishedMarch
KeywordsCircuit simulation, Combinational circuits, delay circuits, delay distribution, Delay effects, design of experiments, design of experiments (DOE), Digital circuits, DOE, hybrid model, Hybrid power systems, integrated circuit design, least squares approximations, least squares method, least squares method (LSM), Least squares methods, mixed mode simulations, mixed-mode simulations, Monte Carlo analysis, Monte Carlo methods, process sensitivity, response surface methodology, response surface methodology (RSM), RSM, Software libraries, US Department of Energy

A generalized methodology for modeling the effects of process variations on circuit delay performance is proposed by directly relating the variations in process parameters to variations in delay metric of a digital circuit. The 2-input nand gate is used as a library element for 65 nm gate length technology, whose delay is extensively characterized by mixed-mode simulations. This information is then used in a general-purpose circuit simulator SEQUEL, by incorporating appropriate templates for the nand gate library. A 4-bit times 4-bit Wallace tree multiplier circuit, consisting of about 300 2-input nand gates, is used as a representative combinational circuit to demonstrate the proposed methodology. The variation in the multiplier delay is characterized by an extensive Monte Carlo analysis. To extend this methodology for a generic technology library with a variety of library elements, modeling of nand gate delays by response surface methodology (RSM), in terms of process parameters, is carried out using design of experiments (DOE). A simple piecewise quadratic model, based on the least squares method (LSM), is proposed for one-parameter variation to address significant cubic effects observed in the delay response function. Then, a hybrid model for gate delays is generated by superimposing the interaction terms of DOE-RSM model upon the quadratic model of one-parameter variation to address the generalized case of simultaneous variations in multiple process parameters. The proposed methodology has been demonstrated for nand gate library with 266 gates, and the simplicity and generality of the approach make it equally applicable to a large library of cells for both statistical timing analysis and statistical circuit simulation at the gate level