Virtual Probe: Using Machine Learning and Bayesian Statistics to Understand Nanoscale Silicon

Group Researchers:   Wangyang Zhang (CMU)

Collaborators:  Xin Li, CMU:  Shawn Blanton, CMU;  Duane Boning, MIT;  Emrah Acar, IBM;  Frank Liu, IBM

At the nanoscale, nothing is deterministic.  Every behavior we want to model is a messy smear of correlated probability.  This creates major problems when trying to design modern integrated circuits.  Spatial variation – differences in the behavior of our designs based on where they are, how close they are – is a huge problem.   Things vary at the level of individual transistors, functional blocks, chips, wafer, and lots (different sets of wafers all manufactured together).  Where do we look for methods to attack such problems?   It turns out that Bayesian Statistics, and related methods from Machine Learning (ML) hold the key to building useful predictive models.

We have designed and validated a range of useful methods to deal with spatial variation.  This includes tools for predicting a minimum number of measurement samples from a wafer to predict behaviors at other non-measured locations (“virtual probes”);  tools for predicting where to put those samples for optimal results, in an information theoretic sense;  tools to decompose these variations intodecompose process variation into two different components: (1) spatially correlated variation, and (2) uncorrelated random variation; and tools for automatically clustering the spatial signatures of wafers to aid yield improvement.

Key Papers/Talks:

  • Xin Li, Rob A. Rutenbar, R. Shawn Blanton, “Virtual Probe: A Statistically Optimal Framework for Minimum-Cost Silicon Characterization of Nanoscale Integrated Circuits,”  Proc. ACM/IEEE Internaitonal Conference on CAD (ICCAD),  pp. 433-440, November 2009.
  • Wangyang Zhang, Xin Li and Rob A. Rutenbar, “Bayesian Virtual Probe: Minimizing variation characterization cost for nanoscale IC technologies via Bayesian inference,” Proc. ACM/IEEE Design Automation Conference (DAC), pp. 262-267, July 2010. (Winner of 2010 DAC Best Paper Award.)
  • Wangyang Zhang, Xin Li, Emrah Acar, Frank Liu, Rob A. Rutenbar, “ Multi-Wafer Virtual Probe: Minimum-cost variation characterization by exploring wafer-to-wafer correlation,” Proc. ACM/IEEE International Conference on CAD (ICCAD), pp. 47-54, November 2010.
  • W. Zhang, K. Balakrishnan, X. Li, D. Boning, R.A. Rutenbar, “Toward efficient spatial variation decomposition via sparse regression,” Proc ACM/IEEE International Conference on CAD (ICCAD), pp. 162-169, November 2011.
  • Wangyang Zhang, Karthik Balakrishnan, Xin Li, Duane Boning, Emrah Acar, Frank Liu and Rob A. Rutenbar, “Spatial Variation Decomposition via Sparse Regression,” Proc .IEEE  International Conference on Integrated Circuit Design & Technology (ICICDT), invited, June 2012.
  • Wangyang Zhang, Xin Li, Frank Liu, Emrah Acar,  Rob A. Rutenbar, R. Shawn Blanton, “Virtual Probe: A Statistical Framework for Low-Cost Silicon Characterization of Nanoscale Integrated Circuits,” IEEE Trans. On CAD, Vol. 30, No. 12, pp. 1814 – 1827, December 2011.


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