Journal of Mathematical Chemistry

, Volume 46, Issue 3, pp 934–941 | Cite as

Optical gap and excitation energies of small Ge nanocrystals

  • C. S. Garoufalis
Original Paper


Using the density functional theory (DFT) with the hybrid nonlocal exchange correlation functional of Becke and Lee, Yang and Parr (B3LYP), we have calculated the optical gap and the oscillator strengths for several of the lowest, spin and symmetry allowed, electronic transitions of small Ge nanocrystals passivated by hydrogen. The largest nanoparticle has an approximate diameter of 2 nm. Our results show that the optical gap exhibits size dependence (due to quantum confinement) roughly similar to silicon nanoparticles. However, for this range of diameters, there is an indirect-to-direct transition in the spectra of Ge as the size of the nanocrystals decrease. The first allowed excitation (fundamental optical gap) of each germanium nanoparticle has relatively larger oscillator strengths compared to silicon. The diameter of the smallest Ge nanocrystal capable to emit in the visible region of the spectrum, is approximately 1.9 nm, compared to 2.2 nm for silicon nanocrystals.


Ge nanocrystals Optical properties Quantum dots 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Canham L.T.: Appl. Phys. Lett. 57, 1046 (1990)CrossRefGoogle Scholar
  2. 2.
    Vasiliev I., Öğüt S., Chelikowsky J.R.: Phys. Rev. Lett. 86, 1813 (2001)CrossRefGoogle Scholar
  3. 3.
    Garoufalis C.S., Zdetsis A.D., Grimme S.: Phys. Rev. Lett. 87, 276402 (2001)CrossRefGoogle Scholar
  4. 4.
    Wilcoxon J.P., Provencio P.P., Samara G.A.: Phys. Rev. B. 64, 035417 (2001)CrossRefGoogle Scholar
  5. 5.
    Heath J.R., Shiang J.J., Alivisatos A.P.: J. Chem. Phys. 101, 1607 (1994)CrossRefGoogle Scholar
  6. 6.
    Palummo M., Onida G., Del Sole R.: Phys. Stat. sol. 175, 23 (1999)CrossRefGoogle Scholar
  7. 7.
    Weissker H., Furthmüller J., Bechstedt F.: Phys. Rev. B. 65, 155328 (2002)CrossRefGoogle Scholar
  8. 8.
    Melnikov D.V., Chelikowsky J.R.: Solid State Commun. 127, 361 (2003)CrossRefGoogle Scholar
  9. 9.
    A.D. Zdetsis, C.S. Garoufalis, S. Grimme, in NATO Advanced Research Workshop on “Quantum Dots: Fundamentals, Applications, and Frontiers” (Crete 2003), ed. by B.A. Joyce et al. (Springer, Heidelberg, 2005), pp. 317–332Google Scholar
  10. 10.
    Zdetsis A.D.: Rev. Adv. Mater. Sci. (RAMS). 11, 56–78 (2006)Google Scholar
  11. 11.
    M.E. Casida in Recent Advances in Density Functional Methods, ed. by D.P. Chong (World Scientific, Singapore, 1995)Google Scholar
  12. 12.
    Stephens P.J., Devlin F.J., Chabalowski C.F., Frisch M.J.: J. Phys. Chem. 98, 11623 (1994)CrossRefGoogle Scholar
  13. 13.
    Muscat J., Wander A., Harrison N.M.: Chem. Phys. Lett. 342, 397 (2001)CrossRefGoogle Scholar
  14. 14.
    TURBOMOLE (Version 5.3) Universitat Karlsruhe (2000)Google Scholar
  15. 15.
    Schäfer A., Horn H., Ahlrichs R.: J. Chem. Phys. 97, 2571 (1992)CrossRefGoogle Scholar
  16. 16.
    Tsolakidis A., Martin R.M.: Phys. Rev. B. 71, 125319 (2005)CrossRefGoogle Scholar
  17. 17.
    C.S. Garoufalis, A.D. Zdetsis, Phys. Chem. Chem. Phys. 8(7), 808 (2006). doi: 10.1039/B513184G Google Scholar
  18. 18.
    Yu M., Jayanthi C.S., Drabold D.A., Wu S.Y.: Phys. Rev. B. 68, 035404 (2003)CrossRefGoogle Scholar
  19. 19.
    Garoufalis C.S., Zdetsis A.D.: J. Phys. Conf. Ser. 10, 69 (2005)CrossRefGoogle Scholar
  20. 20.
    Kanemitsu Y., Uto H., Masumoto Y., Maeda Y.: Appl. Phys. Lett. 61, 2187 (1992)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of PatrasPatrasGreece

Personalised recommendations