Electronic States in Three Dimensional Quantum Dot/Wetting Layer Structures

  • Marta Markiewicz
  • Heinrich Voss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3980)


Although self-assembled quantum dots are grown on wetting layers, most simulations exclude the wetting layer. The neglected effects on the electronic structure of a pyramidal InAs quantum dot embedded in a GaAs matrix are investigated based on the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, and a finite height hard-wall 3D confinement potential. By comparing quantum dots with wetting layers and a dot without a wetting layer, we find that the presence of a wetting layer may effect the electronic structure essentially.


Nonlinear Eigenvalue Problem Arnoldi Method GaAs Matrix Krylov Space Iterative Projection Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bastard, G.: Wave Mechanics Applied to Semiconductor Heterostructures. Les editions de physique, Les Ulis Cedex (1988)Google Scholar
  2. 2.
    Betcke, T., Voss, H.: A Jacobi–Davidson–type projection method for nonlinear eigenvalue problems. Future Generation Computer Systems 20(3), 363–372 (2004)CrossRefGoogle Scholar
  3. 3.
    Chuang, S.L.: Physics of Optoelectronic Devices. John Wiley & Sons, New York (1995)Google Scholar
  4. 4.
    FEMLAB, Version 3.1. COMSOL, Inc., Burlington, MA, USA (2004)Google Scholar
  5. 5.
    Filikhin, I., Deyneka, E., Melikian, G., Vlahovic, B.: Electron states of semiconductor quantum ring with geometry and size variations. Molecular Simulation 31, 779–785 (2005)CrossRefGoogle Scholar
  6. 6.
    Filikhin, I., Deyneka, E., Vlahovic, B.: Energy dependent effective mass model of InAs/GaAs quantum ring. Model.Simul.Mater.Sci.Eng. 12, 1121–1130 (2004)CrossRefGoogle Scholar
  7. 7.
    Harrison, P.: Quantum Wells, Wires and Dots. Theoretical and Computational Physics. John Wiley & Sons, Chicester (2000)Google Scholar
  8. 8.
    Hwang, T.-M., Lin, W.-W., Liu, J.-L., Wang, W.: Jacobi–Davidson methods for cubic eigenvalue problems. Numer.Lin.Alg.Appl. 12, 605–624 (2005)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hwang, T.-M., Lin, W.-W., Wang, W.-C., Wang, W.: Numerical simulation of three dimensional quantum dot. J. Comput.Phys. 196, 208–232 (2004)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Li, Y.: Numerical calculation of electronic structure for three-dimensional nanoscale semiconductor quantum dots and rings. J. Comput. Electronics 2, 49–57 (2003)CrossRefGoogle Scholar
  11. 11.
    Li, Y., Voskoboynikov, O., Lee, C.P., Sze, S.M.: Computer simulation of electron energy level for different shape InAs/GaAs semiconductor quantum dots. Comput.Phys.Comm. 141, 66–72 (2001)MATHCrossRefGoogle Scholar
  12. 12.
    Melnik, R.V., Willatzen, M.: Modelling coupled motion of electrons in quantum dots with wetting layers. In: Proceedings of the 5th Internat.Conference on Modelling and Simulation of Microsystems, MSM 2002, Puerto Rico, USA, pp. 506–509 (2002)Google Scholar
  13. 13.
    Melnik, R.V., Willatzen, M.: Bandstructures of conical quantum dots with wetting layers. Nanotechnology 15, 1–8 (2004)CrossRefGoogle Scholar
  14. 14.
    Melnik, R.V., Zotsenko, K.N.: Computations of coupled electronic states in quantum dot/wetting layer cylindrical structures. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Dongarra, J.J., Zomaya, A.Y., Gorbatchev, Y.E. (eds.) Proceedings of Computational Science – ICCS 2002, 3rd International Conference, Part III. LNCS, vol. 2659, pp. 343–349. Springer, Heidelberg (2003)Google Scholar
  15. 15.
    Melnik, R.V., Zotsenko, K.N.: Finite element analysis of coupled electronic states in quantum dot nanostructures. Modelling Simul. Mater. Sci. Eng. 12, 465–477 (2004)CrossRefGoogle Scholar
  16. 16.
    Neumaier, A.: Residual inverse iteration for the nonlinear eigenvalue problem. SIAM J. Numer. Anal. 22, 914–923 (1985)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Voss, H.: Initializing iterative projection methods for rational symmetric eigenproblems. In: Online Proceedings of the Dagstuhl Seminar Theoretical and Computational Aspects of Matrix Algorithms, Schloss Dagstuhl (2003),
  18. 18.
    Voss, H.: An Arnoldi method for nonlinear eigenvalue problems. BIT Numerical Mathematics 44, 387–401 (2004)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Voss, H.: Electron energy level calculation for quantum dots. Technical Report 91, Institute of Numerical Simulation, Hamburg University of Technology (2005); To appear in Comput. Phys. CommGoogle Scholar
  20. 20.
    Voss, H.: A rational eigenvalue problem governing relevant energy states of a quantum dots. Technical Report 92, Institute of Numerical Simulation, Hamburg University of Technology, (2005); To appear in J. Comput. PhysGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marta Markiewicz
    • 1
  • Heinrich Voss
    • 1
  1. 1.Institute of Numerical SimulationHamburg University of TechnologyHamburgGermany

Personalised recommendations