PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Statistical parameter identification of analog integrated circuit reverse models

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We solve the manufacturing problem of identifying the model statistical parameters ensuring a satisfactory quality of analog circuits produced in a photolithographic process. We formalize it in a statistical framework as the problem of inverting the mapping from the population of the circuit model parameters to the population of the performances. Both parameters and performances are random. From a sample of the latter population we want to identify the statistical features of the former that produce a performance distribution complying with production samples. The key artifact of the solution method we propose consists of describing the above mapping in terms of a mixture of granular functions, where each is responsible for a fuzzy set within the input-output space, hence for a cluster therein. The way of synthesizing the whole space as a mixture of these clusters is learnt directly from the examples. As a result, we have an analytical form of the mapping that approximates complex Spice models in terms of polynomials in the model parameters, and an implicit expression of the distribution law of the induced performances that allows a relatively quick and easy management of the model distribution statistical parameters. This flows into a semiautomatic procedure managing an adaptive composition of different granular modules to cope with the circuit peculiarities. We check the method both on real world manufacturing problems and on ad hoc benchmarks.
Słowa kluczowe
Rocznik
Strony
115--134
Opis fizyczny
Bibliogr. 55 poz., rys.
Twórcy
autor
  • Dipartimento di Scienze dell’Informazione via Comelico 39/41, 20135 Milano, Italy
autor
  • Dipartimento di Scienze dell’Informazione via Comelico 39/41, 20135 Milano, Italy
autor
  • Dipartimento di Scienze dell’Informazione via Comelico 39/41, 20135 Milano, Italy
autor
  • STMicroelectronics Stradale Primo Sole 50, 95121 Catania, Italy
autor
  • STMicroelectronics Stradale Primo Sole 50, 95121 Catania, Italy
autor
  • STMicroelectronics Stradale Primo Sole 50, 95121 Catania, Italy
Bibliografia
  • [1] Bernstein K., Frank D.J., Gattiker A.E., Haensch W., Ji B.L., Nassif S.R., Nowak E.J., Pearson D.J., Rohrer N.J., High-performance CMOS variability in the 65-nm regime and beyond. IBM Journal of Research Development 50:433-449, 2006.
  • [2] Boning D.S., Nassif S., Models of process varia¬tions in device and interconnect. In Chandrakasan, A. ed., Design of High Performance Microprocessor Circuits, chapter 6, IEEE Press, 1999.
  • [3] Buhler M., Koehl J., Bickford, J. Hibbeler, J. Schlichtmann, U. Sommer, R. Pronath, M., Ripp A., DFM/DFY design for manufacturability and yield - influence of process variations in digital, analog and mixed-signal circuit design. In: DATE06. 387-392, 2006.
  • [4] McConaghy T, Palmers P., Gao P., Steyaert M., Gielen G.G.E., Variation-Aware Analog Structural Synthesis: A Computational Intelligence Approach. Springer, 2009.
  • [5] Qu M., Styblinski M., Parameter extraction for statistical IC modeling based on recursive inverse approximation. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on 16, 1250-1259, 1997.
  • [6] Koskinen T, Cheung P., Statistical and behavioural modelling of analogue integrated circuits. Circuits, Devices and Systems, IEE Proceed¬ings G 140, 171-176, 1993.
  • [7] Lee S.H., Choi C.H., Kong J.T., Lee W.S., Yoo J.H., An efficient statistical analysis methodology and its application to high-density DRAMs. In: Proceedings of the 1997 IEEE/ACM International Conference on Computer-Aided Design (ICCAD-97), Washington, DC, USA, IEEE Computer Society, 678-683, 1997.
  • [8] Cheng B„ Dideban D., Moezi N., Millar C, Gareth R., Xingsheng W., Scott R., Asen, A., Benchmarking statistical compact modeling strategies for capturing device intrinsic parameter fluctuations in BSIM4 and PSP. IEEE Design and Test of Computers 99, 2010.
  • [9] Quarles T, PedersonD., Newton R., Sangiovanni-Vincentelli A., Wayne C, Spice http://bwrc.eecs.berkeley.edu/Classes/icbook/SPICE/, 2009.
  • [10] Rohatgi V.K., An Introduction to Probablity Theory and Mathematical Statistics. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York, 1976.
  • [11] McConaghy T, Gielen G., Analysis of simulation-driven numerical performance modeling techniques for application to analog circuit optimization. In: Proceedings of IEEE International Symposium on Circuits and Systems, 2005.
  • [12] McConaghy T, Gielen G.G.E., Double-strength CAFFEINE: fast template-free symbolic modeling of analog circuits via implicit canonical form functions and explicit introns. Design Automation and Test in Europe, 269-274, 2006.
  • [13] Bolt M., Rocchi M., Engel J., Realistic statistical worst-case simulations of VLSI circuits. Semiconductor Manufacturing, IEEE Transactions on 4, 193-198, 1991.
  • [14] Kundert K.S., The Designers Guide to SPICE and SPECTRE. Kluwer Academic Publishers, Boston (1998)
  • [15] Apolloni B., Bassis S., Malchiodi D., Witold P., The Puzzle of Granular Computing. Volume 138 of Studies in Computational Intelligence. Springer Verlag, 2008.
  • [16] Eeckelaert T, Daems W., Gielen G., Sansen W., Generalized simulation-based posynomial model generation for analog integrated circuits. Analog Integr. Circuits Signal Process, 40:193—203, 2004.
  • [17] Hershenson M., Boyd S., Lee T, Optimal design of a CMOS OP-AMP via geometric programming. IEEE Trans, on Computer-Aided Design of Inte¬grated Circuits and Systems 20:1-21, 2001.
  • [18] Liu W., Jin X., Xi X., Chen J., Jeng M.C., Liu Z., Cheng Y, Chen K, Chan M., Hui, K. Huang J., Tu R., Ko P.K., Hu C, BSIM3v3.3MOSFETModel UsersManual. Department of Electrical Engineering and Computer Sciences, University of Califor¬nia, Berkeley, CA 94720, 2005.
  • [19] Bowman K.A., Duvall S.G., Meindl J.D., Impact of die-to-die and within-die parameter fluctuations on the maximum clock frequency distribution for gigascale integration. IEEE Journal of Solid-State Circuits 37:183-190, 2002.
  • [20] Rao R., Srivastava A., Blaauw D., Sylvester D., Statistical estimation of leakage current considering inter- and intra-die process variation. In: ISLPED 03: Proceedings of the 2003 international symposium on Low power electronics and design, New York, NY, USA, ACM.
  • [21] Eshbaugh K.S., Generation of correlated parameters for statistical circuit simulation. IEEE Trans¬actions on CAD of Integrated Circuits and Systems 11:1198-1206, 1992.
  • [22] Mood A.M., Graybill F.A., Boes DC, Introduction to the Theory of Statistics. McGraw-Hill, New York, 1974.
  • [23] Ning Q., On the momentum term in gradient descent learning algorithms. Neural Networks 12:145-151, 1999.
  • [24] Price K.V., Storn R.M., Lampinen J.A., Differential Evolution, A Practical Approach to Global Op¬timization. Volume 538 of Natural Computing Se¬ries. Springer, 2005.
  • [25] Moller M.F., A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks 6:525-533, 1993.
  • [26] More J.J., The Levenberg-Marquardt algorithm: Implementation and theory. Numerical Analysis 630/1978:105-116, 1978.
  • [27] Duch W., Kordos M., Multilayer perceptron trained with numerical gradient. In: Proceedings of the International Conference on Artificial Neural Networks (ICANN) and International Conference on Neural Information Processing (ICONIP), Istanbul, 106-109, 2003.
  • [28] Duch W., Kordos M., Variable Step Search algorithm for feedforward networks. Neurocomputing 71:2470-2480, 2008.
  • [29] Nelder J.A., Mean R., A simplex method for function minimization. Computer Journal 7:308-313, 1965.
  • [30] Wolfram Research Inc., Mathematica 7, 2008.
  • [31] Nocedal J., Wright S.J., Numerical Optimization. Series: Springer series in operations research. Springer, New York, 1999.
  • [32] Zhang R, The Schur Complement and Its Applica-tions. Volume 4 of Numerical Methods and Algorithms. Springer, Netherland, 2005.
  • [33] Jolliffe I.T., Principal Component Analysis. Springer Verlag, 1986.
  • [34] Hinton G.E., Sejnowski T.J., Learning andrelearn-ing in Boltzmann Machines. In Rumelhart, D.E., McClelland J.L., et al., eds., Parallel Distributed Processing: Volume 1: Foundations. MIT Press, Cambridge, 282-317, 1987.
  • [35] Cybenko G., Approximations by superpositions of sigmoidal functions. Mathematics of Control, Signals, and Systems 2:303-314, 1989.
  • [36] Leader J.J., Numerical Analysis and Scientific Computation. Addison Wesley, 2004.
  • [37] Aldenderfer M.S., Blashfield R.K., Cluster Analysis. Sage, Newbury Park (CA), 1984.
  • [38] Nikolaev N., de Menezes L.M., Iba H., Overfitting avoidance in genetic programming of polynomials. E-Commerce Technology, IEEE International Conference on 2:1209-1214, 2002.
  • [39] Cohn D., Ghahramani Z., Jordan M., Active learning with statistical models. Journal of Artificial Intelligence Research 4:129-145, 1996.
  • [40] Barnett V, The ordering of multivariate data. Jour¬nal of Royal Statistical Society Series A 139:319-354, 1976.
  • [41] Apolloni B., Bassis S., Gaito S., Malchiodi D., Ap-preciation of medical treatments by learning underlying functions with good confidence. Current Pharmaceutical Design 13:1545-1570, 2007.
  • [42] Liu R.Y, Parelius J.M., Singh K., Multivariate analysis by data depth: Descriptive statistics, graphics and. inference. The Annals of Statistics 27:783-858, 1999.
  • [43] McLachlan G.J., Krishnan T., The EM Algorithm and Extensions. 2nd edn. Wiley SeriesMn Probability and Statistics. Wiley-Interscience, 2008.
  • [44] Purviance J.E., Petzold M.C., Potratz C, A linear statistical FET model using principal component analysis. Microwave Theory and Techniques, IEEE Transactions on 37:1389-1394, 1989.
  • [45] Friedman J.H., Multivariate adaptive regression splines. Annals of Statistics 19:1-141, 1991.
  • [46] Daems S., Gielen G., Sansen,W., Simulation-based generation of posynomial performance models for the sizing of analog integrated circuits. IEEE Transactions on Computer-Aided Design of Inte¬grated Circuits and Systems 22:517-534, 2003.
  • [47] Taher H., Schreurs D., Nauwelaers B., Extraction of small signal equivalent circuit model parameters for statistical modeling of HBT using artificial neural networks. In: Gallium Arsenide Applications Symposium (GAAS 2005) 3—7 ottobre 2005.
  • [48] Hatami S., Azizi M.Y, Bahrami H.R., Motaval-izadeh D., Afzali-Kusha A., Accurate and efficient modeling of SOI MOSFET with technology independent neural networks. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 23:1580-1587, 2004.
  • [49] Vancorenland P., Van der Plas G., Steyaert M., Gielen G., Sansen W., A layout-aware synthesis methodology for RF circuits. In: ICCAD01: Proceedings of the 2001 IEEE/ACM International Conference on Computer-Aided Design, Piscataway, NJ, USA, IEEE Press.
  • [50] Ampazis N., Perantonis S.J., Two highly efficient second order algorithms for training feedforward networks. IEEE Transactions on Neural Networks 13:1064-1074, 2002.
  • [51] Ampazis N., Perantonis S.J., Olmam neural network toolbox for matlab, 2002.
  • [52] Elder IV J.F., Brown D.E., Induction and polyno¬mial networks, network models for control and pro¬cessing. In Fraser M., ed.: Intellect, Portland, OR, 143-198, 2000.
  • [53] Jekabsons G.,Varireg software,http://www.cs.rtu.lv/jekabsons/, 2010.
  • [54] Jekabsons G., Adaptive basis function construction: an approach for adaptive building of sparse polynomial regression models. Machine Learning, In-Tech 28 In Press, 2010.
  • [55] McConaghy T, Eeckelaert T, Gielen G., CAFFEINE: Template-free symbolic model generation of analog circuits via canonical form functions and genetic programming. Design Automation and Test in Europe, 1070-1075, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e0ff35db-4db4-4666-a821-693ae15b8940
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.