A Multi-Scale Approach to Wavefunction Engineering of Subdimensional Quantum Semiconductor Structures

Conference paper
Part of the Environmental Science and Engineering book series (ESE)

Abstract

With on going reduction in dimension of nano-devices it becomes imperative to include interface and structure boundaries accounting for complex, mixed boundary conditions. A Lagrangian approach to the physics provides the natural framework for such calculations, with computational work based on the finite element method. This variational approach has led to the design of mid-IR cascade lasers and the solution of the Schrödinger-Poisson self-consistency in arbitrary layered structures. Applications of this methodology lead to the solution for energy levels in a magnetic field in the Voigt geometry. The effect of surface proximity on binding energy for impurity states in nanowires and the beautiful physics of complex topological surfaces such as a Mobius ring are displayed as further examples of the issues addressable through multi-scale parallel computing within this variational framework.

Keywords

Lagrangians Finite elements Wavefunction engineering Design of semiconductor heterostructures 

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Notes

Acknowledgments

This report was written while on sabbatical leave at the Naval Research Laboratory, and I thank Dr. Fritz Kub for his hospitality. I wish to thank J. Albrecht, Z. Li, and K. H. Yoo for discussions. I also thank Quantum Semiconductor Algorithms, Inc., for the use of their finite element and sparse matrix analysis software.

References

  1. 1.
    E. O. Kane, J. Phys. Chem. Solids 6, 236 (1958); Semiconductors and Semimetals Vol 1, edited by R K Willardson and A C Beer (New York; Academic, 1966); Handbook on Semiconductors Vol 1, edited by W Paul (Amsterdam; North-Holland) p 193 (1982); J. M. Luttinger and W. Kohn Phys. Rev. 97 869 (1955).Google Scholar
  2. 2.
    B. A. Foreman Phys. Rev. B 48 4964(1993); M. G. Burt, Semicond. Sci. Technol. 2, 460 (1987); Erratum 2, 701 (1987); J. Phys. Condens. Matter 4, 6651 (1992).CrossRefGoogle Scholar
  3. 3.
    L. R. Ram-Mohan, A. M. Girgis, J. D. Albrecht, and C. W. Litton, Superlattices and Microstructures 39, 455–477 (2006). L. R. Ram-Mohan and K.-H. Yoo, J, Phys. Condens. Matter 18, R901-R917 (2006).CrossRefGoogle Scholar
  4. 4.
    P. O. Lowdin, J. Chem. Phys. 19 1396 (1951).Google Scholar
  5. 5.
    M. Gell-Mann and M. Levy Il Nuovo Cimento 16 53 (1960).CrossRefGoogle Scholar
  6. 6.
    L. R. Ram-Mohan, Finite Element and Boundary Element Applications to Quantum Mechanics (Oxford; Oxford UP, 2002).Google Scholar
  7. 7.
    L R Ram-Mohan and J R Meyer J. Nonlin. Opt. Phys. Mater. 4 191 (1995); L R, Ram-Mohan, D. Dossa. I. Vurgaftman and J. R. Meyer Handbook of Nanostructured Materials and Nanotechnology vol 2, ed. H S Nalwa (New York; Academic Press, 1999) chap 15.Google Scholar
  8. 8.
    L. R. Ram-Mohan, J. Moussa and K. H. Yoo, J. Appl. Phys. 95, 3081 (2004).Google Scholar
  9. 9.
    S. T. Jang, K. H. Yoo and L. R. Ram-Mohan, Proceedings of the 13th Int. Symp. Physics of Semiconductors and Applications, Korea; Journal of the Korean Phys.l Soc. 50, 834–838 (2007).Google Scholar
  10. 10.
    I. Vurgaftman, J. R. Meyer and L. R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).Google Scholar
  11. 11.
    L. R. Ram-Mohan and K. H. Yoo, Physical Review B 82, 1–8 (2010).Google Scholar
  12. 12.
    J. Yoon, I. Shalish, A. M. Girgis, L. R. Ram-Mohan, and V. Narayanamurti, Appl. Phys. Lett. 94, 142102 (1–3) (2009).CrossRefGoogle Scholar
  13. 13.
    Zehao Li and L. R. Ram-Mohan, Phys. Rev.B 85, 195438–1-9 (2012).Google Scholar
  14. 14.
    P. G. Kassebaum, C. Boucher and L. R. Ram-Mohan, J. Comput. Phys. 231 5747-5760 (2012).Google Scholar
  15. 15.
    J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton, New Jersey, 2008). (Fig. 6(a) is a superposition of our results with those of Joannopoulos, et al. Their figure was reproduced with permission from Princeton U.P.).Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Departments of Physics and ECEWorcester Polytechnic InstituteWorcesterUSA

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