Analog test metrics estimates with PPM accuracy

Abstract

ISBN 978-1-4244-8193-4International audienceThe high cost of analog circuit testing has sparked off intensified efforts to identify robust and low-cost alternative tests that could effectively replace the standard specification-based tests. Nevertheless, the current practice is still specification-based testing. One of the primary reasons is the lack of tools to evaluate in advance the indirect costs (e.g. parametric test escape and yield loss) associated with alternative tests. To this end, in this paper, we present a method to estimate test escape and yield loss that occur as a result of replacing one costly specification test by one low-cost alternative test. This evaluation is performed at the design or test development stage with parts per million (PPM) accuracy. The method is based on extreme value theory and on a fast simulation technique of extreme events called statistical blockade

Fast and Accurate DPPM Computation Using Model Based Filtering

“…A conceptually similar approach of using a model for sample selection has been employed as a part in a tail probability estimation method [12], [13]. However, this method is devised for single dimensional tail distribution fitting, and cannot be used for DPPM estimation.…”

“…However, this method is devised for single dimensional tail distribution fitting, and cannot be used for DPPM estimation. A simple classifier as a statistical blockade suffices in [12], [13] since missing samples that fall into the tail during the fitting phase is not catastrophic as long as these misses do not bias the samples in the tail. For our purpose of modelbased filtering, small model errors are acceptable.…”

“…Similarly, [13] employs an EVT based approach to estimate yield loss and test escape level for one of the tests that is replaced with an alternative test. But, these two methods cannot be applied to DPPM estimation for multiple dimensional output space, which requires multidimensional tail distribution estimation.…”

Statistical modelling of analog circuits for test metrics computation

“…For an n-dimensional random vector U = (U1, U2, ... , Un) on the unit cube, a copula C is a multivariate CDF such that: C(U1' U2,···, un) = Pr(Ul :S U1,···, Un :S un). (7) By applying Sklar's theorem [9], we can easily derive the expression of the joint CDF F(X1, ... , xn) associated with a copula C. Let X1,X2, ... ,Xn be n random variables with CDFs F1 (xd, F2(X2), ... , Fn(xn), respectively. Sklar's theorem states that there exists a copula C such that \/x (Xl,X2, ... ,xn)ElR n…”

“…For example, for circuits having 20 output parameters, a set of at least 20 million circuits must be generated. In a more recent work, [7] considered the use of Extreme Va lue Theory. Only circuits having extreme values of their output parameters are simulated by making use of the statistical blockade technique [8] in order to discriminate the process parameters that generate extreme circuits from those that generate the non-extreme ones.…”