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Effect of a Metal Contact on Surface Phonons and on Electron Energy Losses in Dielectric Films
Phys. Rev. B 5, 4792 – Published 15 June, 1972
DOI: https://doi.org/10.1103/PhysRevB.5.4792
Abstract
We consider a dielectric film which is bounded on one side by a semi-infinite metal and by vacuum on the other side. We analyze the effect of the electronic screening, due to the free electrons in the metal, on the surface optical-phonon modes in the dielectric film and calculate the energy loss experienced by fast electrons in passing through such a film. The dielectric is represented by the usual continuum-model frequency-dependent dielectric constant including the bulk phonons, and the free electrons in the metal are treated within the Thomas-Fermi approximation. Whereas the high-frequency surface mode is not much affected by the presence of the metal, except at long wavelengths, the low-frequency mode experiences a drastic relaxation up to wavelengths of the order of the Thomas-Fermi screening length. These effects are accompanied by a strong enhancement of the interaction of electrons with the high-frequency surface mode, in most of its frequency range, and a similarly strong reduction of the interaction with the low-frequency mode. As a result, the energy loss of fast electrons due to the excitation of the high-frequency mode is redistributed over the frequency range covered by this mode, in such a way that the intensity is lowered very close to the LO-phonon frequency and strongly enhanced at lower frequencies down to the limiting surface-mode frequency of the unperturbed film. On the other hand, the energy loss associated with the excitation of the low-frequency surface mode is negligible in this case. Numerical results for typical cases indicate that the predicted effects should be experimentally observable.
References (17)
- E. A. Stern and R. A. Ferrell, Phys. Rev. 120, 130 (1960)
- P. Schmüser, Z. Physik 180, 105 (1964) H. Raether, in Springer Tracts in Modern Physics, Ergebnisse der Exakten Naturwissenschaften, edited by G. Höhler (Springer-Verlag, Berlin, 1965), Vol. 38, p. 84
- (a) C. J. Powell and J. B. Swan, Phys. Rev. 118, 640 (1960) (b) A. Otto, Z. Physik 185, 232 (1965) (c) C. Kunz, ibid. 196, 311 (1966) (d) T. Kloos, ibid. 208, 77 (1968) (e) J. Daniels, ibid. 213, 227 (1968)
- H. Boersch, J. Geiger, and W. Stickel, Z. Physik 212, 130 (1968)
- C. Kittel, Quantum Theory of Solids (Wiley, New York, 1964)
- J. Geiger and W. Stickel, Phys. Letters 28A, 629 (1969)
- J. Heinrichs, preceding paper, Phys. Rev. B 5, 4775 (1972)
- I. Giaever and H. R. Zeller, Phys. Rev. Letters 21, 1385 (1968)
- J. B. Chase and K. L. Kliewer, Phys. Rev. B 2, 4389 (1970)
- R. Fuchs and K. L. Kliewer, Phys. Rev. 140, 2076 (1965)
- K. L. Kliewer and R. Fuchs, Phys. Rev. 144, 495 (1966)
- Landolt-Börnstein Tabellen, Vol. II (Springer-Verlag, Berlin, 1955)
- T. E. Hartmann, J. Appl. Phys. 35, 3283 (1964)
- A. Lucas and E. Kartheuser, Phys. Rev. B 1, 3588 (1970)
- T. Fujiwara and K. Ohtaka, J. Phys. Soc. Japan 24, 1326 (1968)