Modeling and Simulation of Deterministic and Stochastic Nano systems

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The relentless downscaling drive in the integrated Very Large Scale Integration (VLSI) circuit technology (from the deep submicron and down to the nano-scale level) has increased the level of challenges in predicting the system performance or estimating its basic figures-of-merit. The main reason for that difficulty stems from the increasing uncertainty that surrounds the actual (i.e., post Silicon-layout) values of the design parameters. Design parameters, in this context, refer to a wide range of circuit design parameters including geometrical and structural parameters, process parameters or electrical parameters. Traditional modeling and simulation approaches have treated those parameters as deterministic variables with well-specified numerical values. However, with the above-mentioned uncertainty surrounding their post-fabrication or actual values, those parameters must be regarded as random variables that are characterized with certain probability density functions (PDF), such as Gaussian or Uniform PDF. With this new development, system performance metrics are no longer deterministic functions in its design parameters, but need to be treated as stochastic processes whose full characterization can be best approached through calculating their PDFs. This goal of computing the PDF of a system is generally known in the mathematical literature as Uncertainty Quantification (UQ).