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Scattering matrix approach to direct solution of the Schrödinger equation

Abstract

We discuss a numerically stable method, the Usuki method, which is closely related to both the scattering matrix approach and recursive Green’s functions. This approach provides a viable approach to directly solving the Schrödinger equation in simulations of semiconductor devices. It has a major advantage over the Green’s function in that the electron density can be obtained far more efficiently for use in the self-consistent loop. Various applications of this approach have been studied, although here we focus upon the application of the method to study MOSFETS.

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References

  1. Moore, G.E.: Electronics 38 (1965)

  2. Marinescu, D.C., Marinescu, G.M.: Approaching Quantum Computation. Pearson Prentice Hall, Upper Saddle River (2005)

    Google Scholar 

  3. Zutic, I., Fabian, J., Das Sarma, S.: Rev. Mod. Phys. 76, 323 (2004)

    Article  Google Scholar 

  4. Usuki, T., et al.: Phys. Rev. B 52, 8244 (1995)

    Article  Google Scholar 

  5. Ferry, D.K., Goodnick, S.M., Bird, J.P.: Transport in Nanostructures, 2nd edn. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  6. Weinberg, S.: The Quantum Theory of Fields, vol. 1, Sect. 3.1. Cambridge University Press, Cambridge (2005)

    MATH  Google Scholar 

  7. Akis, R., et al.: In: Bird, J.P. (ed.) Electron Transport in Quantum Dots, pp. 209–276. Kluwer Academic, Boston (2003)

    Google Scholar 

  8. Ando, T.: Phys. Rev. B 44, 8017 (1991)

    Article  Google Scholar 

  9. Gilbert, M.J., Ferry, D.K.: J. Appl. Phys. 95, 7954 (2004)

    Article  Google Scholar 

  10. Gilbert, M.J., Ferry, D.K.: J. Comput. Electron. 3, 355 (2004)

    Article  Google Scholar 

  11. Neofotistos, G., Lake, R., Datta, S.: Phys. Rev. B 43, 2442 (1991)

    Article  Google Scholar 

  12. Akis, R., Bird, J.P., Ferry, D.K.: J. Phys. Condens. Matter 8, L667 (1996)

    Article  Google Scholar 

  13. Frensley, W.R.: Rev. Mod. Phys 62, 745 (1990)

    Article  Google Scholar 

  14. Gebauer, R., Car, R.: Phys. Rev. B 70, 125324 (2004)

    Article  Google Scholar 

  15. Büttiker, M.: Phys. Rev. Lett. 57, 1761 (1986)

    Article  Google Scholar 

  16. Venugopal, R., et al.: J. Appl. Phys. 93, 5613 (2003)

    Article  Google Scholar 

  17. Gilbert, M.J., Akis, R., Ferry, D.K.: J. Appl. Phys. 98, 094303 (2005)

    Article  Google Scholar 

  18. Ferry, D.K., Gilbert, M.J., Akis, R.: IEEE Trans. Electron Devices 55, 2820 (2008)

    Article  Google Scholar 

  19. Akis, R., Ferry, D.K., Bird, J.P.: Phys. Rev. B 54, 17705 (1996)

    Article  Google Scholar 

  20. Bird, J.P., et al.: Phys. Rev. Lett. 82, 4691 (1999)

    Article  Google Scholar 

  21. Bird, J.P., et al.: Rept. Prog. Phys. 66, 583 (2003)

    Article  Google Scholar 

  22. Ferry, D.K., Akis, R., Bird, J.P.: J. Phys. Condens. Matter 17, S1017 (2005)

    Article  Google Scholar 

  23. Zurek, W.H.: Rev. Mod. Phys. 75, 715 (2003)

    Article  MathSciNet  Google Scholar 

  24. Ferry, D.K., Akis, R., Bird, J.P.: Phys. Rev. Lett. 93, 026803 (2004)

    Article  Google Scholar 

  25. Zurek, W.H.: Nat. Phys. 5, 181 (2009)

    Article  Google Scholar 

  26. Brunner, R., et al.: Phys. Rev. Lett. 101, 024102 (2008)

    Article  MathSciNet  Google Scholar 

  27. Burke, A.M., et al.: Phys. Rev. Lett. 104, 176801 (2010)

    Article  Google Scholar 

Download references

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Akis, R., Ferry, D.K. Scattering matrix approach to direct solution of the Schrödinger equation. J Comput Electron 9, 232–236 (2010). https://doi.org/10.1007/s10825-010-0335-6

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  • DOI: https://doi.org/10.1007/s10825-010-0335-6

Keywords

  • Semiconductor
  • Quantum simulation
  • Devices