A Statistical Model Including Parameter Matching for Analog Integrated Circuits Simulation

Statistical analysis during the reliability simulation

“…A Monte-Carlo analysis is used by designers in order to assess the effect of the technological dispersions on the electrical performances of a circuit or system and thus, to determine its figures of merit and its absolute maximum ratings [3,4]. From this design point of view, this analysis gives no information about the evolution of these electrical performances during a given operating time t.…”

Relating statistical MOSFET model parameter variabilities to IC manufacturing process fluctuations enabling realistic worst case design

“…The number of principal components (m) generally required to adequately represent a set of correlated Parameters is much less than the original number of parameters which existed in the first place (i.e., m << n), thus making the principal components substantially easier to manipulate. The mathematical details associated with the derivation of the principal components are provided elsewhere [9], [lo], and [24]. Additionally we have found it necessary to further transform the selected principal components into a set of rotated components or factors (X's) using a VARIMAX [25] orthogonal rotation.…”

“…This can be done by constructing parameter sets where the parameters are allowed to vary independent of one another (randomly) in accordance with their measured distributions. However, a Monte Carlo analysis of a device or circuit performance using these "random" model parameter sets can lead to inaccurate results [9], [IO], and [26] because the parameter correlations are neglected. This problem can be overcome by randomly generating component sets (i.e., X's) and converting them to parameter sets, where measured parameter correlations are included, using (19).…”

“…Manipulation of this type of parametric data can enable the accurate and efficient prediction of device and circuit performance spreads which occur as a direct consequence of inevitable process disturbances. Ideally, in these schemes the measured correlated model parameter set is transformed into a much smaller and more workable set of independent factors either by a principal component analysis [6], [9]- [12] or by some related factor analysis [7]. Circuit simulation frameworks utilizing these factors and either a Monte Carlo analysis [6], gradient analysis [7], [13], or simply some worst case methodology will enable the accurate prediction of the required statistical circuit performance spreads.…”

An approach for relating model parameter variabilities to process fluctuations

“…Some such methodologies for obtaining this information involve statistical multivariate analyses of model parameter information, gathered over a period of time, from a stable manufacturing process. Manipulation of this data can enable the accurate and efficient prediction of circuit performance spreads which occur as a consequence of inevitable process disturbances [2,3,4,5,6]. In these schemes the measured correlated model parameter set is transformed into a much smaller and more workable set of independent factors either by a principal component analysis [2,3,4,5] or by some related factor analysis [6].…”