Handling discontinuous effects in modeling spatial correlation of wafer-level analog/RF tests

Abstract

In an effort to reduce the cost of specification testing in analog/RF circuits, spatial correlation modeling of wafer-level measurements has recently attracted increased attention. Existing approaches for capturing and leveraging such correlation, however, rely on the assumption that spatial variation is smooth and continuous. This, in turn, limits the effectiveness of these methods on actual production data, which often exhibits localized spatial discontinuous effects. In this work, we propose a novel approach which enables spatial correlation modeling of wafer-level analog/RF tests to handle such effects and, thereby, to drastically reduce prediction error for measurements exhibiting discontinuous spatial patterns. The core of the proposed approach is a k-means algorithm which partitions a wafer into k clusters, as caused by discontinuous effects. Individual correlation models are then constructed within each cluster, revoking the assumption that spatial patterns should be smooth and continuous across the entire wafer. Effectiveness of the proposed approach is evaluated on industrial probe test data from more than 3,400 wafers, revealing significant error reduction over existing approaches.