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Scientific Computing in Electrical Engineering SCEE 2008 pp 261–272Cite as

Heating of Semiconductor Devices in Electric Circuits

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Part of the book series: Mathematics in Industry ((TECMI,volume 14))

Abstract

Thermal effects in a coupled circuit-device system are modeled and numerically simulated. The circuit equations arise from modified nodal analysis. The transport in the semiconductor devices is modeled by the energy-transport equations for the electrons and the drift-diffusion equations for the holes, coupled to the Poisson equation for the electric potential. The lattice temperature is described by a heat equation with a heat source including energy relaxation heat, recombination heat, hole Joule heating, and radiation. The circuit-device model is coupled to a thermal network. The resulting system of nonlinear partial differential-algebraic equations is discretized in time using backward difference formulas and in space using (mixed) finite elements. Heating effects from numerical simulations in a pn-junction diode and a clipper circuit are presented.

Invited speaker at the SCEE 2008 conference

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References

  1. Einwich, K., Schwarz, P., Trappe, P., Zojer, H.: Simulatorkopplung für den Entwurf komplexer Schaltkreise der Nachrichtentechnik. In: 7. ITG-Fachtagung “Mikroelektronik für die Informationstechnik”, Chemnitz, pp. 139–144 (1996)

    Google Scholar 

  2. Selva Soto, M., Tischendorf, C.: Numerical analysis of DAEs from coupled circuit and semiconductor simulation. Appl. Numer. Math., 53, 471–488 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Tischendorf, C.: Coupled Systems of Differential Algebraic and Partial Differential Equations in Circuit and Device Simulations. Habilitation thesis, Humboldt-Universität zu Berlin, Germany (2003)

    Google Scholar 

  4. Brunk, M., Jüngel, A.: Numerical coupling of electric circuit equations and energy-transport models for semiconductors. SIAM J. Sci. Comput., 30, 873–894 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Adler, M.: Accurate calculations of the forward drop and power dissipation in thyristors. IEEE Trans. Electr. Dev., 25, 16–22 (1978)

    Article  Google Scholar 

  6. Wachutka, G.: Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling. IEEE Trans. Comp. Aided Design, 9, 1141–1149 (1990)

    Article  Google Scholar 

  7. Albinus, G., Gajewski, H., Hünlich, R.: Thermodynamic design of energy models of semiconductor devices. Nonlinearity, 15, 367–383 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Alí, G., Carini, M.: Energy-transport models for semiconductor devices and their coupling with electric networks. In: V. Cutello, G. Fotia, L. Puccio (eds) Applied and industrial mathematics in Italy II, pp. 13–24, World Sci. Publ., NJ (2007)

    Google Scholar 

  9. Brunk, M., Jüngel, A.: Self-heating in a coupled thermo-electric circuit-device model. Preprint, Vienna University of Technology, Austria (2008)

    Google Scholar 

  10. Ben Abdallah, N., Degond, P.: On a hierarchy of macroscopic models for semiconductors. J. Math. Phys., 37, 3308–3333 (1996)

    MathSciNet  Google Scholar 

  11. Selberherr, S.: Analysis and Simulation of Semiconductor Devices. Springer, Berlin (1984)

    Google Scholar 

  12. Bandelow, U., Gajewski, H., Hünlich, H.: Fabry-Perot lasers: thermodynamic-based modeling. In: J. Piprek (ed.), Optoelectronic Devices. Advanced Simulation and Analysis, pp. 63–85, Springer, Berlin (2005)

    Google Scholar 

  13. Jüngel, A.: Transport Equations for Semiconductors. Lecture Notes in Physics, Vol. 773. Springer, Berlin (2009)

    Google Scholar 

  14. Anile, A., Romano, V., Russo, G.: Extendend hydrodynamic model of carrier transport in semiconductors. SIAM J. Appl. Math., 61, 74–101 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tischendorf, C.: Topological index calculation of differential-algebraic equations in circuit simulation. Surv. Math. Industr., 8, 187–199 (1999)

    MATH  MathSciNet  Google Scholar 

  16. Bartel, A.: Partial Differential-Algebraic Models in Chip Design – Thermal and Semiconductor Problems. Ph.D. thesis, Universität Karlsruhe, Germany (2003)

    Google Scholar 

  17. Marini, L. D., Pietra, P.: New mixed finite element schemes for current continuity equations. COMPEL, 9, 257–268 (1990)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Markus Brunk

  2. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040, Vienna, Austria

    Ansgar Jüngel

Authors
  1. Markus Brunk
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  2. Ansgar Jüngel
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Corresponding author

Correspondence to Markus Brunk .

Editor information

Editors and Affiliations

  1. , Faculty of Electronics, Communications a, Aalto University School of Science and T, AALTO, 00076, Finland

    Janne Roos

  2. , Faculty of Electronics, Communications a, Aalto University School of Science and T, AALTO, 00076, Finland

    Luis R.J. Costa

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Brunk, M., Jüngel, A. (2010). Heating of Semiconductor Devices in Electric Circuits. 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_34

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