Statistical Characterization and Simulation of VLSI Circuits Considering Process Variations

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Principle Investigators:

Dr. Sheldon Tan (PI), UCR

Collaborators:

Dr. Yici Cai, Tsinghua University, China

Dr. Hao Yu, NTU, Singapore

Dr. Jinjun Xiong, IBM T. J. Watson Research Center, USA

Dr. Chandu Visweswariah, IBM, USA

Graduate Students (graduated):

David Hosson Shin, Yan Zhu

Graduate Students (graduated):

Ruijing Shen, Duo Li, Zhigang Hao, Ning Mi

Funding:

National Science Foundation, “SHF: Small: Variational and Bound Performance Analysis of Nanometer Mixed-Signal/Analog Circuits”, (CCF-1116882), 9/1/2011-8/30/2014, PI: Sheldon Tan

National Science Foundation, “IRES: Development of Global Scientists and Engineers by Collaborative Research on Variation-Aware Nanometer IC Design”, (OISE-1130402), 9/1/2011-8/30/2014, PI: Sheldon Tan, co-PI: Yici Cai

National Science Foundation, “US-Singapore Planning Visit: Collaborative Research on Design and Verification of 60Ghz RF/MM Integrated Circuits”, (OISE-1051797), 4/1/2011-3/30/2013, PI: Sheldon Tan, co-PI: Hao Yu.

2011 UC MEXUS-CONACYT Collaborative Research Grants, “Symbolic and Statistical Modeling and Analysis Techniques for Analog/Mixed-Signal Nanometer Integrated Circuits”, 2011-2013 academic year , 9/1/2011-2/31/2013, PI: Sheldon Tan

2009 UC MEXUS-CONACYT Collaborative Research Grant, “Symbolic modeling and reduction for analog/RF circuits and on-chip interconnect”, Aug 2009 to Jan 2011, PI, co-PI: Dr. Esteban Tlelo-Cuautle.

National Science Foundation, “IRES: Development of Global Scientists by Research Collaborations on Simulation and Optimization of Nanometer Integrated Systems”, (OISE-0623038), 9/1/2006-8/30/2009, PI: Sheldon Tan, co-PI: Yici Cai

National Science Foundation, “CAREER: Career Development Plan: Behavioral Modeling, Simulation and Optimization for Mixed-Signal System in a Chip”, (CCF-0448534, a number of REU supplements),  6/1/2005-5/31/2011. PI: Sheldon Tan.

Project Descriptions

This proposal tries to addresses the fundamental and emerging challenges in performance analysis under process parameter variability for analog/mixed-signal and VLSI circuits. The main goal of this program is to develop novel and efficient non-Monte-Carlo techniques for worst-case and statistical analysis of analog/mixed-signal circuits.

Specficially, we seek the following goals for the project

(1) Development of novel worst-case analysis methods for analog/mixed-signal circuits based on graph-based symbolic analysis, affine-like interval arithmetic and Kharitonov’s functions. The new method will first build variational transfer functions from linearized analog circuit by determinant decision diagram (DDD) based symbolic analysis and affine-like interval arithmetic. Then the performance bounds will be computed by Kharitonov’s functions from the variational transfer functions. We will investigate more conservative affine-like interval arithmetic to reduce conservation. We will investigate the performance bounds in the time domains given frequency domain bounds;

(2) Development of fast non-Monte-Carlo statistical analysis methods to calculate mismatch due to process variations. We model the problem as solving nonlinear stochastic differential-algebra-equations. Nonlinear stochastic methods (Galerkin or collocation methods) and trajectory-piecewise-linear macromodeling method with incremental subspace aggregation will be applied to solve the resulting problems.

(3) Fast Monto-Carlo or other statisitical methods for rate event (high sigma) and more variables (high dimentional) statistiical analysis.

Invited Presentations by Dr. Sheldon Tan

· IBM Watson Research Center, Yorktown Height, NY, “Variational Analysis for Large Power Delivery Networks and Full-Chip Leakage Powers of Nanometer VLSI Systems”, Nov. 5, 2008.

· Shanghai Jiao Tong University, School of Microelectronics, Shanghai, China, “Variational Analysis of Full-Chip Leakage Power in Nanometer VLSI Systems”, June 16, 2009.

· Xi'an Institute of Post & Telecommunications, Dept of Computer Science, Xi'an, Shaanxi Province, China, “Variational Analysis of Clock Networks Considering Environmental Uncertainty”, July 8, 2009.

· Xi’an Jiao Tong University, Dept of Electrical Engineering, Xi’an, Shaanxi Province, China, “Variational Analysis of Clock Networks Considering Environmental Uncertainty”, July 10, 2009.

· Fudan Univ. Shanghai, China, “Statistical Analysis of Full-Chip Leakage Power in Nanometer VLSI Systems”, July. 23, 2010.

· Shanghai Jiao Tong University, School of Microelectronics, Shanghai, China, “Performance bound analysis of analog circuits considering process variation”, May 30, 2011.

· The University of Hong Kong, Department of Electrical and Electronic Engineering, Hong Kong, China, “Graph-based Parallel and Statistical Analysis of Analog Circuits Based on GPU Platforms”, Hong Kong, Aug. 23, 2011.

· The EDA workshop, Department of Electrical Engineering, National Taiwan University, Taiwan, “Performance Bound Analysis for Analog Circuits Under Process Variations”, Sept 10, 2011.

· International Workshop on Emerging Circuits and Systems (IWECS’12), Shanghai Jiao Tong University, Shanghai, China, “Parallel Computing and Simulation for VLSI systems”, Aug. 9, 2012.

· INAOE (Institute National Astrophysics, Optical and Electrics), Department of Electrical Engineering, Puebla, Mexico , “Fast GPU-accelerated Sparse Matrix-Vector Multiplication”, May 3, 2013.

Software Download

As VLSI technology scales into the nanometer regime, chip design engineering face several challenges in maintaining historical rates of performance improvement and capacity increase with CMOS technologies. One profound change in the chip design business is that engineers can't put the design precisely into the silicon chips. Chip performance, manufacture yield and lifetime become unpredictable at the design stage. Chip performance, manufacture yield and lifetime can't be determined accurately at the design stage. The main culprit is that many chip parameters -- such as oxide thickness due to chemical and mechanical polish (CMP) and impurity density from doping fluctuations -- can't be determined precisely, and thus are unpredictable. The so-called manufacture process variations start to play a big role and their influence on the chip's performance, yield and reliability becomes significant.

As a result, how to efficiently and accurately assess the impacts of the process variations of interconnects in the various physical design steps are critical for fast design closure, yield improvement, cost reduction of VLSI design and fabrication processes. The design methodologies and design tools from system level down to the physical levels have to embrace variability impacts on the VLSI chips, which calls for statistical/stochastic based approaches for designing 90nm and beyond VLSI systems.

In this regard, it is imperative to develop new design methodologies to consider the impacts of various process and environmental uncertainties and elevated temperature on chip performance. Variational impacts and thermal constraints have to be incorporated into every steps of design process to ensure the reliable chips and profitable manufacture yields. The design methodologies and design tools from system level down to the physical levels have to consider variability and thermal impacts on the chip performance, which calls for new statistical and thermal-aware optimization approaches for designing nanometer VLSI systems.

The PI’s group at UCR has been working on statistical modeling and simulation of VLSI systems since 2006 and has made a number of contributions in this field. We have proposed statistical on-chip power grid analysis approaches based spectral stochastic method[ J1,J2,J5,C1,C3,C5,C7,C10], stochastic model order reduction methods [C2C4], stochastic capacitance and inductance extraction techniques [J3,C8, C15], statistical leakage and power (total and dynamic power) analysis techniques [J4,C11,C13,C14,C16,C17], performance bound and mismatch analysis of analog and mixed-signal circuits [C9, C12,C18], statistical timing analysis [J6,C9] and variational impact analysis on the on-chip cache design [C6]. A book summarized our works in a systemic way will be published by Springer in 2012 [B1].

Relevant Publications

Book and book chapter publications

B1. Ruijing Shen, Sheldon X.-D. Tan and Hao Yu, Statistical Performance Analysis and Modeling Techniques for Nanometer VLSI Designs, Springer Publisher, March 2012, ISBN-10: 1461407877.

B2. Sheldon X.-D. Tan, Ruijing Shen, “Chip-Level Statistical Leakage Modeling and Analysis”, Chapter in Recent Advancements in Modeling of Semiconductor Processes, Circuits and Chip-Level Interactions, Rasit Onur Topaloglu, and Peng Li (Editors), Bentham Publishing (www.ebook-engineering.org), 2010 (in press).

B3. Xue-Xin Liu, Hao Yu, Hai Wang, Sheldon X.-D. Tan, “Analog mismatch analysis by stochastic nonlinear macromodeling”, Chapter in “Analog Circuits: Applications, Design and Performances”, E. Tlelo-Cuautle (Editor), NOVA Science Publishers Inc. ISBN: 978-1-61324-355-8.

B4. Guoyong Shi, Sheldon X.-D. Tan, Esteban Tlelo-Cuautle, “Advanced Symbolic Analysis for VLSI Systems -- Methods and Applications”, Springer Publisher, 2014, ISBN 978-1-4939-1103-5

Journal publications

J1. N. Mi, J. Fan, S. X.-D. Tan, Y. Cai and X. Hong, “Statistical analysis of on-chip power delivery networks considering lognormal leakage current variations with spatial correlations”, IEEE Transaction on Circuit and System I (TCAS-I), vol. 55, no. 7, pp.2064-2075, August, 2008.

J2. N. Mi, S. X.-D. Tan, Y. Cai and X. Hong, “Fast variational analysis of on-chip power grids by stochastic extended Krylov subspace method”, IEEE Transaction on Computer-Aided Design of Integrated Circuits and Systems (TCAD), vol. 27, no. 11, pp. 1996-2006, 2008.

J3. R. Shen, S. X.-D. Tan, J. Cui, W. Yu, Y. Cai and G. Chen, “Variational capacitance extraction and modeling based on orthogonal polynomial method”, IEEE Transactions on Very Large Scale Integrated Systems (TVLSI), vol.18, no.11, pp1556-1565, 2010.

J4. R. Shen, S. X.-D. Tan, N. Mi and Y. Cai, “Statistical modeling and analysis of chip-level leakage power by spectral stochastic method”, Integration, The VLSI Journal, vol. 43, no. 1, pp. 156-165, January 2010. (online permanent DOI Link)

J5. D. Li, S. X.-D. Tan, “Statistical analysis of large on-chip power grid networks by variational reduction scheme”, Integration, The VLSI Journal, vol. 43, no. 2, pp.167-175, April, 2010.

J6. H. Wang, H. Yu, S. X.-D. Tan, “Fast timing analysis of clock networks considering environmental uncertainty”, Integration, The VLSI Journal, online available at http://dx.doi.org/10.1016/j.vlsi.2011.03.001

J7. Z. Hao, S. X.-D. Tan, E. Tlelo-Cuautle, J. Relles, C. Hu, W. Yu, Y. Cai and G. Shi, “Statistical extraction and modeling of inductance considering spatial correlation”, Analog Integr Circ Sig Process, July 2011. DOI: 10.1007/s10470-011-9720-8.

J8. F. Gong, X. Liu, H. Yu, S. X.-D. Tan, J. Ren and L. He, "A fast non-Monte-Carlo yield analysis and optimization by stochastic orthogonal polynomials", ACM Transactions on Design Automation of Electronic Systems (TODAES), vol. 17, no.1, pp10:1-10:23, January 2012. 10.1145/2071356.2071366

J9. Z. Hao, S. X.-D. Tan, G. Shi, “Statistical full-chip total power estimation considering spatially correlated process variations”, Integration, The VLSI Journal, Vol. 73, no. 1, 2012. doi:10.1016/j.vlsi.2011.12.004

J10. R. Shen, S. X.-D. Tan, H. Wang, J. Xiong, “Fast statistical full-chip leakage analysis for nanometer VLSI systems”, ACM Transactions on Design Automation of Electronic Systems (TODAES), vol. 17, no. 4, pp.51:1--51:19, Sept. 2012. 10.1145/2348839.2348855

J11. Z. Hao, G. Shi, S. X.-D. Tan, E. Tlelo-Cuautle, “Symbolic moment computation for statistical analysis of large interconnect networks”, IEEE Transactions on Very Large Scale Integrated Systems (TVLSI), vol. 21, no. 5, pp. 944-957, May 2013

J12. X. Liu, S. X.-D. Tan, A. Palma-Rodriguez, E. Tlelo-Cuautle, G. Shi, and Y. Cai, “Performance bound analysis of analog circuits in frequency and time domain considering process variations”, ACM Transactions on Design Automation of Electronic Systems (TODAES), vol. 19, no. 6, Dec. 2013.

Conference publications

C1 N. Mi, J. Fan, S. X.-D. Tan, “Statistical analysis of power grid networks considering lognormal leakage current variations with spatial correlation”, in Proc. Int. Conf. Computer Design (ICCD), pp.56-62, San Jose, CA 2006.

C2 J. Fan, N. Mi, S. X.-D. Tan, “Variational compact modeling and simulation for linear dynamic systems”, IEEE International Workshop on Behavioral Modeling and Simulation (BMAS), pp.17-22, San Jose, CA, Sept., 2006.

C3 N. Mi, J. Fan, S. X.-D. Tan, “Simulation of power grid networks considering wires and lognormal leakage current variations”, IEEE International Workshop on Behavioral Modeling and Simulation (BMAS), pp.73-78, San Jose, CA, Sept., 2006.

C4 J. Fan, N. Mi, S. X.-D. Tan, Y. Cai and X. Hong, “Statistical model order reduction for interconnect circuits considering spatial correlations”, Proc. Design, Automation and Test in Europe (DATE'07), pp. 1508-1513, Nice, France, April 2007.

C5 N. Mi, S. X.-D. Tan, P. Liu, J. Cui, Y. Cai and X. Hong, “Stochastic extended Krylov subspace method for variational analysis of on-chip power grid networks”, Proc. IEEE/ACM International Conf. on Computer-Aided Design (ICCAD), pp.48-53, San Jose, CA, Nov. 2007.

C6 W. Wu, J. Yang, S. X.-D. Tan, S.-L. Lu, “Improving the reliability of on-chip caches under process variations”, in Proc. Int. Conf. Computer Design (ICCD), Lake Tahoe, pp. 325-332, CA 2007. Best Paper Award (<2%).

C7 X. Yuan, J. Fan, B. Liu, S. X.-D. Tan, “Stochastic based extended Krylov subspace method for power/ground network analysis”, in Proc. 7th International Conference on ASIC (ASICON’07), Guilin, China, Oct. 2007. (Invited).

C8 J. Cui, G. Chen, R. Shen, S. X.-D. Tan, W. Yu, J. Tong, “Variational capacitance modeling using orthogonal polynomial method”, Proc. IEEE/ACM International Great Lakes Symposium on VLSI (GLSVLSI’08), pp. 23-28, Orlando, 2008.

C9 H. Wang, H. Yu, S. X.-D. Tan, “Fast analysis of non-tree clock network considering environmental uncertainty by parameterized and incremental macromodeling”, Proc. Asia South Pacific Design Automation Conference (ASP-DAC’09), pp. 379-384, Yokohama, Japan, Jan. 2009.

C10 D. Li, S. X.-.D. Tan, G. Chen and X. Zeng, “Statistical analysis of on-chip power grid networks by variational extended truncated balanced realization method” Proc. Asia South Pacific Design Automation Conference (ASP-DAC’09), pp. 272-277, Yokohama, Japan, Jan. 2009.

C11 R. Shen, N. Mi, S. X.-D. Tan, Y. Cai, X. Hong, “Statistical modeling and analysis of chip-level leakage power by spectral stochastic method”, Proc. Asia South Pacific Design Automation Conference (ASP-DAC’09), pp. 161-166, Yokohama, Japan, Jan. 2009.

C12 H. Yu, X. Liu, H. Wang, S. X.-D. Tan, “A fast analog mismatch analysis by an incremental and stochastic trajectory piecewise linear macromodel”, Proc. Asia South Pacific Design Automation Conference (ASP-DAC’10), pp.211-216, Taipei, Taiwan, Jan. 2010.

C13 R. Shen, S. X.-D. Tan, J. Xiong, “A linear statistical analysis for full-chip leakage power with spatial correlation”, Proc. IEEE/ACM International Great Lakes Symposium on VLSI (GLSVLSI’10), pp.27-232, Providence, RI, May, 2010.

C14 R. Shen, S. X.-D. Tan, J. Xiong, “A linear algorithm for full-chip statistical leakage power analysis considering weak spatial correlation”, Proc. IEEE/ACM Design Automation Conference (DAC’10), pp.481-486, Anaheim, CA, 2010.

C15 J. Relles, M. Ngan, E. Tlelo-Cuautle, S. X.-D. Tan, C. Hu, W. Yu and Y. Cai, “Statistical extraction and modeling of 3D inductance with spatial correlation”, IEEE International Workshop on Symbolic and Numerical Methods, Modeling and Applications to Circuit Design (SM2ACD), Tunisia, October 5-6, 2010.

C16 Z. Hao, R. Shen, S. X.-D. Tan, B. Liu, G. Shi and Y. Cai, “Statistical full-chip dynamic power estimation considering spatial correlations”, Proc. Int. Symposium. on Quality Electronic Design (ISQED’11), San Jose, CA, pp677-782, March 2011.

C17 Z. Hao, S. X.-D. Tan, G. Shi, “An efficient statistical chip-level total power estimation method considering process variations with spatial correlation”, Proc. Int. Symposium. on Quality Electronic Design (ISQED’11), pp.671-676, San Jose, CA, March 2011.

C18 Z. Hao, S. X.-D. Tan, R. Shen, G. Shi, “Performance bound analysis of analog circuits considering process variations”, Proc. IEEE/ACM Design Automation Conference (DAC’11) , pp.310-315, San Diego, CA, June 2011.

C19 X. Liu, S. X.-D. Tan, Z. Hao, G. Shi, “Time-domain performance bound analysis of analog circuits considering process variations”, ”, Proc. Asia South Pacific Design Automation Conference (ASP-DAC’12), Sydney, Australia, pp.535-540, Jan. 2012.

C20 X. Liu, S. X.-D. Tan, and H. Wang, “Parallel statistical analysis of analog circuits by GPU-accelerated graph-based approach”, Proc. Design, Automation and Test in Europe (DATE'12), pp.852-857, Dresden, Germany, March 2012.

C21 R. Shen, S. X.-D. Tan and X. Liu, “A new voltage binning technique for yield improvement based on graph theory”, Proc. Int. Symposium on Quality Electronic Design (ISQED’12), San Jose, CA, March 2012.

C22 S. Rodriguez-Chavez , E. Tlelo-Cuautle, A. Palma-Rodriguez, S. X.-D. Tan, “Symbolic DDD-based tool for the computation of noise in CMOS analog circuits”, 8^th International Caribbean Conf. on Devices, Circuits and Systems (ICCDCS), Playa del Carmen, Mexico, March 2012.

C23 A. Palma-Rodriguez, S. Rodriguez-Chavez , E. Tlelo-Cuautle, S. X.-D. Tan, “DDD-based symbolic sensitivity analysis of active filters”, 8^th International Caribbean Conf. on Devices, Circuits and Systems (ICCDCS), Playa del Carmen, Mexico, March 2012.

C24 X. Liu, A. Palma-Rodriguez , S. Rodriguez-Chavez, S. X.-D. Tan, E. Tlelo-Cuautle, Y. Cai, “Performance bound and yield analysis for analog  circuits under process variations”, Proc. Asia South Pacific Design Automation Conference (ASP-DAC’13), pp.761-766, Yokohama, Japan, Jan. 2013.

C25 T. Yu, S. X.-D. Tan, Y. Cai, and P. Tang, “Time-domain performance bound analysis for analog and interconnect circuits considering process variations”, Proc. Asia South Pacific Design Automation Conference (ASP-DAC’14), Singapore, Singapore, Jan. 2014.

C26 A. Zhang, G. Shi, S. X-.D. Tan, J. Cheng, “Simultaneous SNR and SNR-variation optimization for Sigma-Delta modulator design”, Int, Conf. Solid State and Integrated Circuit Technology (ICSICT’04), Guilin, China, Oct. 2014.

C27 Y. Zhu, S. X.-D. Tan, “GPU-accelerated parallel Monte Carlo analysis of analog circuits by hierarchical graph-based solver”, Proc. Asia South Pacific Design Automation Conference (ASP-DAC’15), Chiba, Japan, Jan. 2015.