Journal of Computational Electronics

, Volume 15, Issue 4, pp 1505–1510 | Cite as

Efficient numerical procedure for the determination of the wave function-independent terms in longitudinal optical phonon scattering rates formulated in the Fourier domain

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Abstract

A recently developed Fourier-transform-based formulation of the longitudinal optical phonon scattering rates in heterostructures allows us to separate the wave functions from multidimensional integrals, which depend on the intersubband transition energy, the chemical potential, and the electron temperature. Here, we discuss an efficient determination of these integrals and an automatic fitting procedure in order to provide a compact table of pre-calculated integrals. As a result, computation times on a scale of minutes for the scattering rates are achieved for any reasonable set of parameters.

Keywords

Longitudinal optical phonon Scattering rates Adaptive method Heterostructures 
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Notes

Acknowledgments

The authors would like to thank O. Marquardt for a careful reading of the manuscript and G. Rozas for helpful discussions.

References

  1. 1.
    Faist, J., Capasso, F., Sivco, D.L., Sirtori, C., Hutchinson, A.L., Cho, A.Y.: Quantum cascade laser. Science 264, 553–556 (1994). doi: 10.1126/science.264.5158.553 CrossRefGoogle Scholar
  2. 2.
    Köhler, R., Tredicucci, A., Beltram, F., Beere, H.E., Linfield, E.H., Davies, A.G., Ritchie, D.A., Iotti, R.C., Rossi, F.: Terahertz semiconductor-heterostructure laser. Nature 417, 156–159 (2002). doi: 10.1038/417156a CrossRefGoogle Scholar
  3. 3.
    Harrison, P.: Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures. Wiley, Chichester (2005)CrossRefGoogle Scholar
  4. 4.
    Williams, B.S.: Terahertz quantum-cascade lasers. Nat. Photon. 1, 517–525 (2007). doi: 10.1038/nphoton.2007.166 CrossRefGoogle Scholar
  5. 5.
    Jirauschek, C., Kubis, T.: Modeling techniques for quantum cascade lasers. Appl. Phys. Rev. 1, 011307 (2014). doi: 10.1063/1.4863665 CrossRefGoogle Scholar
  6. 6.
    Lü, X., Schrottke, L., Luna, E., Grahn, H.T.: Efficient simulation of the impact of interface grading on the transport and optical properties of semiconductor heterostructures. Appl. Phys. Lett. 104, 232106 (2014). doi: 10.1063/1.4882653 CrossRefGoogle Scholar
  7. 7.
    Schrottke, L., Lü, X., Grahn, H.T.: Fourier transform-based scattering-rate method for self-consistent simulations of carrier transport in semiconductor heterostructures. J. Appl. Phys. 117, 154309 (2015). doi: 10.1063/1.4918671 CrossRefGoogle Scholar
  8. 8.
    Lü, X., Schrottke, L., Grahn, H.T.: Fourier-transform-based model for carrier transport in semiconductor heterostructures: Longitudinal optical phonon scattering. J. Appl. Phys. 119, 214302 (2016). doi: 10.1063/1.4952741 CrossRefGoogle Scholar
  9. 9.
    Schrottke, L., Giehler, M., Wienold, M., Hey, R., Grahn, H.T.: Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers. Semicond. Sci. Technol. 25, 045025 (2010). doi: 10.1088/0268-1242/25/4/045025 CrossRefGoogle Scholar
  10. 10.
    Taj, D., Iotti, R.C., Rossi, F.: Microscopic modeling of energy relaxation and decoherence in quantum optoelectronic devices at the nanoscale. Eur. Phys. J. B 72, 305–322 (2009). doi: 10.1140/epjb/e2009-00363-4 CrossRefGoogle Scholar
  11. 11.
    Arumugam, K., Godunov, A., Ranjan, D., Terzić, B., Zubair, M.: A memory efficient algorithm for adaptive multidimensional integration with multiple GPUs. In: 20th Annual International Conference on High Performance Computing, pp. 169–175 (2013). doi: 10.1109/HiPC.2013.6799120
  12. 12.
    Berntsen, J., Espelid, T.O., Genz, A.: An adaptive algorithm for the approximate calculation of multiple integrals. ACM Trans. Math. Software 17, 437–451 (1991). doi: 10.1145/210232.210233 MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Hahn, T.: Cuba-a library for multidimensional numerical integration. Comput. Phys. Commun. 168, 78–95 (2005). doi: 10.1016/j.cpc.2005.01.010
  14. 14.
    Berntsen, J., Espelid, T.O., Genz, A.: Algorithm 698: Dcuhre: an adaptive multidimensional integration routine for a vector of integrals. ACM Trans. Math. Software 17, 452–456 (1991). doi: 10.1145/210232.210234
  15. 15.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran 90: The art of Parallel Scientific Computing. Press Syndicate of the University of Cambridge, Cambridge (2002)MATHGoogle Scholar
  16. 16.
    Vurgaftman, I., Meyer, J.R., Ram-Mohan, L.R.: Band parameters for iiiv compound semiconductors and their alloys. J. Appl. Phys. 89, 5815–5875 (2001). doi: 10.1063/1.1368156 CrossRefGoogle Scholar
  17. 17.
    Schrottke, L., Lü, X., Rozas, G., Biermann, K., Grahn, H.T.: Terahertz GaAs/AlAs quantum-cascade lasers. Appl. Phys. Lett. 108, 102102 (2016). doi: 10.1063/1.4943657 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Paul-Drude-Institut für FestkörperelektronikLeibniz-Institut im Forschungsverbund Berlin e. V.BerlinGermany

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