3-D Probe: Low-Cost Variation Modeling Using Intertest-Item Correlations

Process variation models for variation tolerant designs are developed through expensive silicon characterization. This paper presents a low-cost variation characterization method that takes advantage of correlations between test items. The proposed method is based on compressed sensing (CS), a new innovative theory in signal processing and information theory, and we formulate the problem of accounting for the correlations in the form of standard CS problems, allowing us to leverage advances in CS theory. We consider wafer-level measurement results for multiple test items a 3-D signal and propose the sparsifying transform that combines the 2-D discrete cosine transform and the Karhunen-Loéve transform. Our experimental results show that the proposed method reduces the number of samples required for the same accuracy up to 2X compared to virtual probe when two test items are used.