Statistical diagnosis of unmodeled systematic timing effects

Abstract

Explaining the mismatch between predicted timing behavior from modeling and simulation, and the observed timing behavior measured on silicon chips can be very challenging. Given a list of potential sources, the mismatch can be the aggregate result caused by some of them both individually and collectively, resulting in a very large search space. Furthermore, observed data are always corrupted by some unknown statistical random noises. To overcome both challenges, this paper proposes a statistical diagnosis framework that formulates the diagnosis problem as a regression learning problem. In this diagnosis framework, the objective is to rank a set of features corresponding to the list of potential sources of concern. The rank is based on measured silicon path delay data such that a feature inducing a larger unexpected timing deviation is ranked higher. Experimental results are presented to explain the learning method. Diagnosis effectiveness will be demonstrated through benchmark experiments and on an industrial design.

Diagnosis of design-silicon timing mismatch with feature encoding and importance ranking - the methodology explained

“…The authors in [6], showed the superior capability of using the polynomial kernel to handle high-order timing effects due to combinations of occurrence-based features. For X,Y coordinates we can use the Gaussian kernel,…”

“…In this case, the two or all three should be ranked higher than X,Y. In the work [6], this is called a higher-order effect, where the effect depends on a combination of multiple features rather than just a feature individually. …”

“…Note that adding more features does not have a large effect on the learning algorithm in respect to accuracy nor runtime [6].…”

A volume diagnosis method for identifying systematic faults in lower-yield wafer occurring during mass production

“…There are many feature ranking methods [14][15][16]. In this work, we calculate an importance Sort NETS in descending order with the value of item; 7:…”

“…Model-based statistical diagnosis, which was proposed in [14] for speed-path analysis to identify systematic timing effects with design-silicon timing mismatch, can also be applied to volume diagnosis. The overview of the model-based volume diagnosis (MVD) method is shown in Fig.…”