| 摘要 |
<p>Method and system for determining the effects of variation of N statistically distributed variables x1,...,xN (N≥1) in a fabrication process for semiconductor and other electronic devices by constructing and using an N-variable model function G(x1,...,xN) to model the process. A sequence of orthogonal polynomials Hi,ri(xi) is associated with each probability density function pi(xi) for each variable xi. These orthogonal polynomials, and products of these polynomials, are used to construct the model function G(x1,...,xN), having undetermined coefficients. Coefficient values are estimated by results of measurements or simulations with variable input values determined by the zeroes (collocation points) of selected orthogonal polynomials. A Monte Carlo process is applied to estimate a probability density function associated with the process or device. Coefficients whose magnitudes are very small are used to identify regions of (x1,...,xN)-space where subsequent Monte Carlo sampling may be substantially reduced. Monte Carlo sampling for the process is also made more transparent using the function G(x1,...,xN). The function G(x1,...,xN) can be used to calculate individual and joint statistical moments for the process.</p> |
