A Critical Enhancement in the Yield Analysis of Microsystems

Abstract

Yield analysis of microsystems is increasingly becoming important due to their decreasing feature sizes. Despite many ways and methods for statistical yield analysis, the contribution of worstcase methods in the yield analysis of microsystems is significant. Worst-case methods, in general, offer advantages like reduced number of simulations and a quantifiable yield metric in yield analysis of a system. However, the common yield analysis problems in MEMS and other microsystems have been identified to be falling into the category of non-linear specification boundaries. In this paper we present an enhancement to the yield analysis of microsystems using worst-case methods. The enhancement has been achieved in terms of accuracy of the parametric yield calculation process by considering non-linear metamodels in place of linear main-effect models. A function suite (WCAS) has been developed in order to implement the worst-case analysis and compare the results of the pre and post enhancements. The demonstrator used for comparing the results of pre and post enhanced worst-case analysis was a U-Shaped thermal actuator.

A Design Methodology for the Yield Enhancement of MEMS Designs with Respect to Process Induced Variations

“…In [3], we describe how to perform a worst-case analysis in order to analyze and calculate parametric yield using enhanced worst-case methods. In [3], we proposed a critical enhancement to increase the accuracy of the worst-case methods. The accuracy was increased by considering nonlinear specification boundaries rather than linearized boundaries.…”

“…The worst-case distance calculated during the worst-case analysis as stated in [3], serves as the quantifiable metric for design robustness / yield. On observing the worst-case distances of various performance specifications, it can be known about a particular performance or a particular set of performances causing reduced parametric yield of the design.…”

“…The model of the demonstrator has already been proven for its validity and conformation with fabrication data [13]. The WCAS function suite [3] has the capability to perform enhanced worst-case analysis as presented in [3]. Fig.4 exhibits a case where the WCAS function suite tracked the worst-case points from non-linear performance metamodels which include parameter interaction effects as well as the parameter quadratic effects.…”

“…This phase of the design practice method is therefore termed as yield conformance using Monte Carlo analysis. This step in the methodology is only advisory and not compulsory as we employed enhanced worst-case analysis which proved to have a reasonably good conformance with Monte Carlo Analysis [3]. After the conformance test of the design yield using Monte Carlo analysis, the design is either diverted back to the yield optimization routine or sent forward to a FEM simulator based on the degree of accordance.…”