On the line widths of vibrational features in inelastic electron tunneling spectroscopy

Nano Letters

Volumn 4, Issue 9, 2004, Pages 1605-1611

  Galperin, Michael ^a   Ratner, Mark A ^a   Nitzan, Abraham ^b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; CHEMICAL BOND; ELECTRON; ELECTRONICS; INELASTIC ELECTRON TUNNELING SPECTROSCOPY; MOLECULAR BIOLOGY; MOLECULAR INTERACTION; MOLECULE; PHONON; SPECTROSCOPY; VIBRATION;

EID: 4644293963     PISSN: 15306984     EISSN: None     Source Type: Journal    
DOI: 10.1021/nl049319y     Document Type: Article

References (43)

1. Wolf, E. L. Principles of electron tunneling spectroscopy; Oxford University Press: New York, 1985; Vol. 71.
2. Hipps, K. W.; Mazur, U. J. Phys. Chem. 1993, 97, 7803.
3. Lee, H. J.; Ho, W. Science 1999, 286, 1719.
4. Lorente, N.; Persson, M.; Lauhon, L. J.; Ho, W. Phys. Rev. Lett. 2001, 86, 2593
5. Hahn, J. R.; Ho, W. Phys. Rev. Lett. 2001, 87, 196102.
6. Lauhon, L. J.; Ho, W. Phys. Rev. Lett. 2000, 85, 4566.
7. Hahn, J. R.; Lee, H. J.; Ho, W. Phys. Rev. Lett. 2000, 85, 1914.
8. Gaudioso, J.; Laudon, J. L.; Ho, W. Phys. Rev. Lett. 2000, 85, 1918.
9. Stipe, B. C.; Rezaei, M. A.; Ho, W. Phys. Rev. Lett. 1999, 82, 1724.
10. Lauhon, L. J.; Ho, W. Phys. Rev. B 1999, 60, R8525.
11. Zhitenev, N. B.; Meng, H.; Bao, Z. Phys. Rev. Lett. 2002, 88, 226801.
12. Park, H.; Park, J.; Lim, A. K. L.; Anderson, E. H.; Alivisatos, A. P.; McEuen, P. L. Nature 2000, 407, 57.
13. Wang, W.; Lee, T.; Kretzschmar, I.; Reed, M. A. Nano Lett. 2004, 4, 643.
14. Kushmerick, J. G.; Lazorcik, J.; Patterson, C. H.; Shashidhar, R.; Seferos, D. S.; Bazan, G. C. Nano Lett. 2004, 4, 639.
15. Lee, H. J.; Ho, W. Phys. Rev. B 2000, 61, R16347.
16. Smit, R. H. M.; Noat, Y.; Untiedt, C.; Lang, N. D.; Hemert, M. C. V.; Ruitenbeek, J. M. V. Nature 2002, 419, 906.
17. Persson, B. N. J. Phys. Scripta 1988, 38, 282.
18. Baratoff, A.; Persson, B. N. J. J. Vac. Sci. Technol. A 1988, 6, 331.
19. Persson, B. N. J.; Baratoff, A. Phys. Rev. Lett. 1987, 59, 339.
20. Troisi, A.; Ratner, M. A.; Nitzan, A. J. Chem. Phys. 2003, 118, 6072.
21. Keldysh, L. V. Sov. Phys. JETP 1965, 20, 1018.
22. Kadanoff, L. P.; Baym, G. Quantum Statistical Mechanics. Green's Function Methods in Equilibrium and Nonequilibrium Problems; Benjamin: Reading, MA, 1962.
23. Wagner, M. Phys. Rev. B 1991, 44, 6104.
24. Datta, S. Electric transport in Mesoscopic Systems; Cambridge University Press: Cambridge, 1995.
25. Mii, T.; Tikhodeev, S. G.; Ueba, H. Phys. Rev. B 2003, 68, 205406.
26. Mii, T.; Tikhodeev, S.; Ueba, H. Surf. Sci. 2002, 502-503, 26.
27. Tikhodeev, S.; Natario, M.; Makoshi, K.; Mii, T.; Ueba, H. Surf. Sci. 2001, 493, 63.
28. Davis, L. C. Phys. Rev. B 1970, 2, 1714.
29. Bayman, A.; Hansma, P.; Kaska, W. C. Phys. Rev. B 1981, 24, 2449.
30. Galperin, M.; Ratner, M. A.; Nitzan, A., to be published.
31. Mahan, G. D. Many-particle physics, 3rd ed.; Plenum Press: New York, 2000.
32. Haug, H.; Jauho, A.-P. Quantum Kinetics in Transport and Optics of Semiconductors; Springer: Berlin, 1996; Vol. 123.
33. 2/πLatin small letter h with stroke), we may encounter the situation where in the negatively biased bridge backscattered electrons of energies in the conduction window between the left and right Fermi energies are locally depleted near the junction. This causes increased reflection at the onset of inelastic scattering, which is presumably the dominant mechanism for observed negative peaks in point contact spectroscopy characterized by large transmission probabilities, see e.g., R. H. M. Smit, et al. Nature 2002, 479, 906; N. Agraït, et al. Phys. Rev. Lett. 2002, 88, 216803.
34. 2/πLatin small letter h with stroke), we may encounter the situation where in the negatively biased bridge backscattered electrons of energies in the conduction window between the left and right Fermi energies are locally depleted near the junction. This causes increased reflection at the onset of inelastic scattering, which is presumably the dominant mechanism for observed negative peaks in point contact spectroscopy characterized by large transmission probabilities, see e.g., R. H. M. Smit, et al. Nature 2002, 479, 906; N. Agraït, et al. Phys. Rev. Lett. 2002, 88, 216803.
35. Gauyacq, J. P.; Borisov, A. G.; Raseev, G. Surf. Sci. 2001, 490, 99.
36. Kinoshita, I.; Misu, A.; Munakata, T. J. Chem Phys. 1995, 102, 2970.
37. Wingreen, N. S.; Meir, Y. Phys. Rev. B 1994, 49, 11040.
38. This should provide a reasonable simplification provided that the molecular electronic level is far enough (relative to its width Γ) from the metal band edge. The same assumption used for the phonon bath in eq 16 is generally valid because of the smallness of the vibrational width γ.
39. Migdal, A. B. Sov. Phys. JETP 1958, 7, 996.
40. Other workers have used SCBA for similar applications, see, e.g., Hyldgaard, P.; Hershfield, S.; Davies, J. H.; Wilkins, J. W. Ann. Phys. 1994, 236, 1. Our calculation goes beyond that done by these authors in several ways: first, we do not limit it to zero temperature, second, we calculate the nonequilibrium behavior of both electron and primary phonon systems while these authors assume that the phonon remains in equilibrium; and finally, most important in the present context, we address the electronic contribution to the phonon self-energy as part of the self-consistent calculation-a step that was not done before.
41. Datta, S.; Tian, W. D.; Hong, S. H.; Reifenberger, R.; Henderson, J. I.; Kubiak, C. P. Phys. Rev. Lett. 1997, 79, 2530.
42. Tian, W. D.; Datta, S.; Hong, S. H.; Reifenberger, R.; Henderson, J. I.; Kubiak, C. P. J. Chem. Phys. 1998, 109, 2874.
43. ph up to values of tens of wavenumbers for the latter.