Skip to main content
SpringerLink
Log in

Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

At cryogenic temperatures the electron–hole plasma in semiconductors becomes strongly degenerate, leading to very sharp internal layers, extreme depletion in intrinsic domains and strong nonlinear diffusion. As a result, the numerical simulation of the drift–diffusion system suffers from serious convergence issues using standard methods. We consider a one-dimensional p-i-n diode to illustrate these problems and present a simple temperature-embedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forward-biased devices as they appear e.g. in optoelectronic applications. Moreover, the method can be applied to wide band gap semiconductors where similar numerical issues occur already at room temperature.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Akturk, A., Allnutt, J., Dilli, Z., Goldsman, N., Peckerar, M.: Device modeling at cryogenic temperatures: effects of incomplete ionization. IEEE Trans. Electron Device 54(11), 2984–2990 (2007)

    Article  ADS  Google Scholar 

  • Bessemoulin-Chatard, M.: A finite volume scheme for convection–diffusion equations with nonlinear diffusion derived from the Scharfetter–Gummel scheme. Numer. Math. 121, 637–670 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Cressler, J.D., Mantooth, H.A.: Extreme Environment Electronics. CRC Press, Boca Raton (2012)

    Book  Google Scholar 

  • Davis, T.A.: Algorithm 832: UMFPACK V4.3—an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30, 196–199 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Farrell, P., Rotundo, N., Doan, D.H., Kantner, M., Fuhrmann, J., Koprucki, T.: Numerical methods for drift–diffusion models. WIAS Preprint 2263 (2016). In: Piprek, J. (ed.) Handbook of Optoelectronic Device Modeling and Simulation. Taylor and Francis, London (2017) (To appear)

  • Hager, W.W.: Condition estimates. SIAM J. Sci. Stat. Comput. 5, 311–316 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  • Jüngel, A.: Qualitative behaviour of solutions of a degenerate nonlinear drift–diffusion model for semiconductors. Math. Model Methods Appl. Sci. 5(4), 497–518 (1995)

    Article  MATH  Google Scholar 

  • Koprucki, T., Rotundo, N., Farrell, P., Doan, D.H., Fuhrmann, J.: On thermodynamic consistency of a Scharfetter–Gummel scheme based on a modified thermal voltage for drift–diffusion equations with diffusion enhancement. Opt. Quantum Electron. 47(6), 1327–1332 (2014)

    Article  Google Scholar 

  • Mott, N.F.: Metal–Insulator Transitions. Taylor and Francis, London (1974)

    Google Scholar 

  • Patterson, R.L., Hammoud, A., Elbuluk, M.: Assessment of electronics for cryogenic space exploration missions. Cryogenics 46, 231–236 (2006)

    Article  ADS  Google Scholar 

  • Richey, D.M., Cressler, J.D., Jaeger, R.C.: Numerical simulation of SiGe HBT’s at cryogenic temperatures. J. Phys. IV France 04(C6), C6-127–C6-32 (1994)

    Article  Google Scholar 

  • Richter, H., Greiner-Bär, M., Pavlov, S.G., Semenov, A.D., Wienold, M., Schrottke, L., Giehler, M., Hey, R., Grahn, H.T., Hübers, H.-W.: A compact, continuous-wave terahertz source based on a quantum-cascade laser and a miniature cryocooler. Opt. Express 18(10), 10179 (2010)

    Article  Google Scholar 

  • Schlehahn, A., Thoma, A., Munnelly, P., Kamp, M., Höfling, S., Heindel, T., Schneider, C., Reitzenstein, S.: An electrically driven cavity-enhanced source of indistinguishable photons with 61% overall efficiency. APL Photonics 1, 011301 (2016)

    Article  ADS  Google Scholar 

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

    Book  Google Scholar 

  • Selberherr, S.: Low temperature MOS device modeling. In: Proceedings of the 172nd Meeting of the Electrochemical Society, vol. 88-9, pp. 70–86. Honolulu (1987)

  • Shah, P., Mitin, V., Grupen, M., Song, G.H., Hess, K.: Numerical simulation of wide band-gap AlGaN/InGaN light-emitting diodes for output power characteristics and emission spectra. J. Appl. Phys. 79, 2755 (1996)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) within the collaborative research center 787 Semiconductor Nanophotonics. The authors would like to thank Jürgen Fuhrmann for useful discussions and one of the reviewers for encouraging us to extend our considerations to wide band gap semiconductors.

Author information

Authors and Affiliations

  1. Weierstraß Institute (WIAS), Mohrenstr. 39, 10117, Berlin, Germany

    Markus Kantner & Thomas Koprucki

Authors
  1. Markus Kantner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Koprucki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markus Kantner.

Additional information

This article is part of the Topical Collection on Numerical Simulation of Optoelectronic Devices, NUSOD’ 15.

Guest edited by Julien Javaloyes, Weida Hu, Slawek Sujecki and Yuh-Renn Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kantner, M., Koprucki, T. Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures. Opt Quant Electron 48, 543 (2016). https://doi.org/10.1007/s11082-016-0817-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-016-0817-2

Keywords

Search

Navigation