Phonons in a nanoparticle mechanically coupled to a substrate

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 15, 2003, Pages

  Patton, Kelly R ^a   Geller, Michael R ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; CRYSTAL; ELECTRON; ENERGY; MATHEMATICAL ANALYSIS; NANOPARTICLE; OSCILLATION; PHYSICS; VIBRATION;

EID: 0038179156     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.155418     Document Type: Article

References (17)

1. A. N. Cleland, Foundations of Nanomechanics (Springer-Verlag, Berlin, 2002).
2. H S. Yang, S P. Feofilov, D K. Williams, J C. Milora, B M. Tissue, R S. Meltzer, and W M. Dennis, Physica B263, 476 (1999).
3. The average nanoparticle size was stated incorrectly in Ref. 2. The correct value is 13 nm. See H S. Yang, K S. Hong, S P. Feofilov, B M. Tissue, R S. Meltzer, and W M. Dennis, J. Lumin.83, 139 (1999).
4. V A. Markel and M R. Geller, J. Phys.: Condens. Matter12, 7569 (2000).
5. The experiment of Ref. 2 did not directly probe the phonon spectrum of the nanoparticle. However, both the observed exponential decay of the excited electronic state and our estimates of the electron-phonon interaction strength suggest that the nanoparticle is in the relaxational regime where the electron’s lifetime is determined by the phonon DOS through Fermi’s golden rule. See M R. Geller, W M. Dennis, V A. Markel, K R. Patton, D T. Simon, and H S. Yang, Physica B316, 430 (2002) for a brief discussion of this question.
6. A. Zangwill, Physics at Surfaces (Cambridge University, New York, 1988).
7. V L. Gurevich and H R. Schober, Phys. Rev. B57, 11 295 (1998).
8. H. Lamb, Proc. London Math. Soc.13, 189 (1882).
9. Throughout this work we use I to label the vibrational modes of the substrate and J for the nanoparticle.
10. H. Ezawa, Ann. Phys. (N.Y.)67, 438 (1971).
11. K R. Patton and M R. Geller, Phys. Rev. B64, 155320 (2001).
12. K R. Patton and M R. Geller, J. Lumin.94, 747 (2001). The vibrational eigenmodes in this preliminary report have frequencies slightly different than the present work because of a numerical error brought to our attention by Dan Murray.
13. This agreement is fortuitous, however, because we did not account for the modified sound velocity of the bath. After this modification is made, the golden-rule estimate for the low-frequency DOS is too large (by a factor of 50 at 3 (formula presented) as expected.
14. Each such double-precision complex matrix requires about 9 GB of memory.
15. For Si we use the branch-averaged sound velocity (formula presented)
16. We note, however, that when the Lamb mode frequency becomes resonant with the electronic two-level system, the electronic relaxation rate is not simply related to the phonon DOS.
17. For example, the Lamb mode frequency for a 13-nm (formula presented) nanoparticle is about 9 (formula presented) and for one made of Si is 12 (formula presented) These estimates follow from Eq. (52) using the (formula presented) transverse sound speed of (formula presented) as measured by C. Proust, Y. Vaills, and L. E. Husson, Solid State Commun. 93, 729 (1995).