Skip to main content

Advertisement

SpringerLink
Log in

Self-heating in a coupled thermo-electric circuit-device model

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

The self-heating of a coupled thermo-electric circuit-semiconductor system is modeled and numerically simulated. The system consists of semiconductor devices, an electric network with resistors, capacitors, inductors, and voltage sources, and a thermal network. The flow of the charge carriers is described by the energy-transport equations coupled to a heat equation for the lattice temperature. The electric circuit is modeled by the network equations from modified nodal analysis coupled to a thermal network describing the evolution of the temperatures in the lumped and distributed circuit elements. The three subsystems are coupled through thermo-electric, electric circuit-device, and thermal network-device interface conditions. The resulting system of nonlinear partial differential-algebraic equations is discretized in time by the 2-stage backward difference formula and in space by a mixed finite-element method. Numerical simulations of a one-dimensional ballistic diode and a frequency multiplier circuit containing a pn-junction diode illustrate the heating of the semiconductor device and circuit resistors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  2. Litsios, J., Schmithüsen, B., Krumbein, U., Schenk, A., Lyumkis, E., Polsky, B., Fichtner, W.: DESSIS 3.0 Manual. ISE Integrated Systems Engineering, Zürich (1996)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  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. Gaur, S., Navon, D.: Two-dimensional carrier flow in a transistor structure under nonisothermal conditions. IEEE Trans. Electr. Dev. 23, 50–57 (1976)

    Article  Google Scholar 

  7. Sharma, D., Ramanathan, K.: Modeling thermal effects on MOS I–V characteristics. IEEE Electr. Dev. Lett. 4, 362–364 (1983)

    Article  Google Scholar 

  8. Chryssafis, A., Love, W.: A computer-aided analysis of one-dimensional thermal transients in n-p-n power transistors. Solid-State Electron. 22, 249–256 (1979)

    Article  Google Scholar 

  9. Selberherr, S.: Analysis and Simulation of Semiconductor Devices. Springer, Wien (1984)

    Google Scholar 

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

    Article  Google Scholar 

  11. Albinus, G., Gajewski, H., Hünlich, R.: Thermodynamic design of energy models of semiconductor devices. Nonlinearity 15(2), 367–383 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bartel, A., Günther, M.: Multirate co-simulation of first order thermal models in electric circuit design. In: Schilders, W., et al. (eds.) Scientific Computing in Electrical Engineering. Proceedings SCEE 2002, pp. 23–28. Springer, Berlin (2002)

    Google Scholar 

  13. Bartel, A., Günther, M.: From SOI to abstract electric-thermal-1d multiscale modeling for first order thermal effects. Math. Comput. Modell. Dyn. Syst. 9, 25–44 (2003)

    Article  MATH  Google Scholar 

  14. Ali, G., Carini, M.: Energy-transport models for semiconductor devices and their coupling with electric networks. In: Applied and Industrial Mathematics in Italy II. Ser. Adv. Math. Appl. Sci., vol. 75, pp. 13–24. World Scientific, Singapore (2007)

    Google Scholar 

  15. Grasser, K.-T.: Mixed-Mode Device Simulation. PhD thesis, TU Wien (1999)

  16. Knaipp, M.: Modellierung von Temperatureinflüssen in Halbleiterbauelementen. PhD thesis, TU Wien (1998)

  17. Wachutka, G.: Consistent treatment of carrier emission and capture kinetics in electrothermal and energy transport models. Microelectr. J. 26, 307–315 (1995)

    Article  Google Scholar 

  18. Feldmann, U.: Numerical simulation of multiscale models for radio frequency circuits in the time domain. In: Jäger, W., Krebs, H.-J. (eds.) Mathematics—Key Technology for the Future. Springer, Berlin (2008)

    Google Scholar 

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

    MathSciNet  Google Scholar 

  20. Degond, P., Jüngel, A., Pietra, P.: Numerical discretization of energy-transport models for semiconductors with non-parabolic band structure. SIAM J. Sci. Comput. 22, 986–1007 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  23. Tischendorf, C.: Coupled systems of differential algebraic and partial differential equations in circuit and device simulation. Modeling and numerical analysis. Habilitation thesis at the Humboldt University of Berlin (2003)

  24. Bartel, A.: Partial differential-algebraic models in chip design—Thermal and semiconductor problems. PhD thesis, Universität Karlsruhe, Germany (2003)

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

    Google Scholar 

  26. Brunk, M., Jüngel, A.: Simulation of thermal effects in optoelectronic devices using coupled energy-transport and circuit models. M3AS 18(12), 2125–2150 (2009)

    Google Scholar 

  27. Chen, D., Kan, E., Ravaioli, U., Shu, C., Dutton, R.: An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects. IEEE Electr. Dev. Lett. 13, 26–28 (1992)

    Article  Google Scholar 

  28. Kosina, H., Grasser, T., Tang, T.-W., Selberherr, S.: A review of hydrodynamic and energy-transport models for semiconductor device simulation. Proc. IEEE 91, 251–274 (2003)

    Article  Google Scholar 

  29. Markowich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations. Springer, Wien (1990)

    MATH  Google Scholar 

  30. Anile, V. Romano A.M., Russo, G.: Extended hydrodynamical model of carrier transport in semiconductors. SIAM J. Appl. Math. 61, 74–101 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  31. Yamnahakki, A.: Second-order boundary conditions for the drift-diffusion equations for semiconductors. Math. Models Methods Appl. Sci. 5, 429–455 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  32. Hiqueras, I., März, R.: Differential algebraic systems with properly stated leading terms. Comput. Math. Appl. 48, 215–235 (2004)

    Article  MathSciNet  Google Scholar 

  33. März, R.: Differential algebraic systems anew. Appl. Numer. Math. 42, 315–335 (2004)

    Article  Google Scholar 

  34. Massobrio, G., Antognetti, P.: Semiconductor Device Modeling with SPICE, 2nd edn. McGraw-Hill, New York (1993)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  36. Levinshtein, M.: Handbook Series on Semiconductor Parameters. World Scientific, London (1996)

    Google Scholar 

  37. Medina, E., Pagani, M.: Multi-physics modeling and numerical simulation of electrothermal effects in semiconductor devices. Master’s thesis, Politecnico di Milano, Italy (2006)

  38. Romano, V., Anile, A.M., Marrocco, A., Sellier, J.M.: 2d numerical simulation of the mep energy-transport model with a mixed finite element scheme. J. Comutational Electron. 4, 231–259 (2005)

    Google Scholar 

  39. Jüngel, A., Tang, S.: A relaxation scheme for hydrodynamic equations for semconductors. Appl. Numer. Math. 43, 229–252 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  40. Holst, S., Jüngel, A., Pietra, P.: An adaptive mixed scheme for energy-transport simulations of field-effect transistors. SIAM J. Sci. Comput. 25, 1698–1716 (2004)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department C, Institute for Mathematics, Bergische Universität Wuppertal, Gaußstrasse 20, 42119, Wuppertal, Germany

    Markus Brunk

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

    Ansgar Jüngel

Authors
  1. Markus Brunk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ansgar Jüngel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ansgar Jüngel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brunk, M., Jüngel, A. Self-heating in a coupled thermo-electric circuit-device model. J Comput Electron 10, 163–178 (2011). https://doi.org/10.1007/s10825-010-0324-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-010-0324-9

Keywords

Search

Navigation