Automatic Thermal Network Extraction and Multiscale Electro-Thermal Simulation

  • Massimiliano CulpoEmail author
  • Carlo de Falco
  • Georg Denk
  • Steffen Voigtmann
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 14)


We present a new strategy to perform chip-level electro-thermal simulation. In our approach electrical behaviour of each circuit element is modeled by standard compact models with an added temperature node (1; 2). Mutual heating is accounted for by a 2-D or 3-D diffusion reaction PDE, which is coupled to the electrical network by enforcing instantaneous energy conservation. To cope with the multiscale nature of heat diffusion in VLSI circuit a suitable spatial discretization scheme is adopted which allows for efficient meshing of large domains with details at a much smaller scale. Preliminary numerical results on a realistic test case are included as a validation of the model and of the numerical method.


Circuit Element Temperature Node Preliminary Numerical Result Thermal Network Thermal Element 
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  1. 1.
    Osman, A., Osman, M., Dogan, N., Imam, M.: An extended tanh law mosfet model for high temperature circuit simulation. Solid-State Circuits, IEEE Journal of 30(2), 147–150 (1995)CrossRefGoogle Scholar
  2. 2.
    Ku, J.C., Ismail, Y.: On the scaling of temperature-dependent effects. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on 26(10), 1882–1888 (2007)CrossRefGoogle Scholar
  3. 3.
    Szekely, V., Poppe, A., Pahi, A., Csendes, A., Hajas, G., Rencz, M.: Electro-thermal and logi-thermal simulation of vlsi designs. VLSI Systems, IEEE Transactions on 5(3), 258–269 (1997)CrossRefGoogle Scholar
  4. 4.
    Igic, P., Mawby, P., Towers, M., Batcup, S.: Dynamic electro-thermal physically based compact models of the power devices for device and circuit simulations. Semiconductor Thermal Measurement and Management, 2001. XVII Annual IEEE Symposium pp. 35–42 (2001)Google Scholar
  5. 5.
    Ho, C., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. Circuits and Systems, IEEE Transactions on 22(6), 504–509 (1975)CrossRefGoogle Scholar
  6. 6.
    Günther, M., Feldmann, U.: CAD-based electric-circuit modeling in industry. I. Mathematical structure and index of network equations. Surveys Math. Indust. 8(2), 97–129 (1999)zbMATHGoogle Scholar
  7. 7.
    Bartel, A., Günther, M.: From SOI to abstract electric-thermal-1d multiscale modeling for first order thermal effects. Math. Comput. Model. Dyn. Syst. 9, 25–44 (2003)zbMATHGoogle Scholar
  8. 8.
    de Falco, C., Culpo, M.: A PDE thermal model for CHIP-level simulation including substrate heating effects. Tech. rep., DCU School of Math. Sciences (2008)Google Scholar
  9. 9.
    Rezzonico, V., Lozinski, A., Picasso, M., Rappaz, J., Wagner, J.: Multiscale algorithm with patches of finite elements. Math. Comput. Simulation 76(1-3), 181–187 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Alí, G., Bartel, A., Culpo, M., de Falco, C.: Analysis of a PDE thermal element model for electrothermal circuit simulation (2008). Submitted to SCEE08 prooceedingsGoogle Scholar
  11. 11.
    Biondi, T., Greco, G., Allia, M., Liotta, S., Bazzano, G., Rinaudo, S.: Distributed modeling of layout parasitics in large-area high-speed silicon power devices. Power Electronics, IEEE Transactions on 22(5), 1847–1856 (2007)CrossRefGoogle Scholar
  12. 12.
    Greco, G., Rallo, C.: Xa integration in custom power mosfet analysis flow. In: SNUG 2008 proceedings (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Massimiliano Culpo
    • 1
    Email author
  • Carlo de Falco
    • 2
  • Georg Denk
    • 3
  • Steffen Voigtmann
    • 3
  1. 1.Bergische Universität WuppertalWuppertalGermany
  2. 2.Dublin City UniversityDublin 9Ireland
  3. 3.Qimonda AG MunichMunichGermany

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