Abstract: A method for determining the movement of particles, particularly impurities, in a medium, under the influence of a changing interface between two neighboring phases. In a first step, the temporal and/or local evolution of said interface is determined. In a second step, the movement of said particles in dependence of the temporal and/or local evolution of the phase interface as determined in the first step is calculated. Optionally, the distribution of the particles within the medium at a certain time is then determined.

Abstract: Method and system for determining the effects of variation of N statistically distributed variables (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 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.