Abstract
In this work we address the well-posedness of the steady-state and transient problems stemming from the coupling of a network of lumped electric elements and a PDE model of heat diffusion in the chip substrate. In particular we consider the thermal element model presented in [1] and we prove that it can be controlled by any combination of voltage sources (imposing the average current in a region of the chip) and current sources (imposing the Joule power per unit area produced in a region) connected to its temperature nodes. This result justifies the implementation of the element as a linear n-port conductance as carried out in [2].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Culpo, M., de Falco, C.: A pde thermal model for chip-level simulation including substrate heating effects. Preprint MS-08-10, School of Mathematical Sciences (2008)
Culpo, M., de Falco, C., Denk, G., Voigtmann, S.: Automatic thermal network extraction and multiscale electro-thermal simulation. In: Proceedings of the SCEE 2008 Conference (Submitted) (2008)
roadmap commitee, I.: International tecnology roadmap for semiconductors 2007. Tech. rep., ITRS (2007)
Culpo, M., de Falco, C.: Dynamical iteration schemes for coupled simulation. In: Proceedings of the GAMM2008 meeting (Submitted) (2008)
Grasser, T., Selberherr, S.: Fully coupled electrothermal mixed-mode device simulation of sige hbt circuits. Electron Devices, IEEE Transactions on 48(7), 1421–1427 (Jul 2001). DOI 10.1109/16.930661
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. Seventeenth Annual IEEE Symposium pp. 35–42 (2001). DOI 10.1109/STHERM.2001.915142
Bartel, A.: Partial Differential-Algebraic Models in Chip Design Thermal and. Semiconductor Problems. VDI-Verlag (2004)
Quarteroni, A., Valli, A.: Numerical approximation of Partial Differential Equations. Computational Mathematics. Springer (1997)
Evans, L.: Partial Differential Equations. American Mathematichal Society (1998)
Deheuvels, R.: Formes quadratiques et groupes classiques. Presses Universitaires de France, Paris (1981)
Silvester, J.: Determinants of block matrices. The Mathematical Gazette 84(501), 460–467 (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alì, G., Bartel, A., Culpo, M., de Falco, C. (2010). Analysis of a PDE Thermal Element Model for Electrothermal Circuit Simulation. In: Roos, J., Costa, L. (eds) Scientific Computing in Electrical Engineering SCEE 2008. Mathematics in Industry(), vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12294-1_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-12294-1_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12293-4
Online ISBN: 978-3-642-12294-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)