Reflectance anisotropy spectra of Cu and Ag (110) surfaces from ab initio theory

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 11, 2001, Pages

  Monachesi, Patrizia ^a   Palummo, Maurizia ^a   Del Sole, Rodolfo ^a   Ahuja, Rajeev ^b   Eriksson, Olle ^b  

^a INFM   (Italy)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

COPPER; SILVER;

ANISOTROPY; ARTICLE; CALCULATION; DIELECTRIC CONSTANT; MATHEMATICAL ANALYSIS; PHASE TRANSITION; REFLECTOMETRY; SEMICONDUCTOR; THEORY;

EID: 0035884118     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.115421     Document Type: Article

References (33)

1. D E. Aspnes, J. Vac. Sci. Technol. B3, 1502 (1985).
2. Y. Borensztein, W I. Mochan, J. Tarriba, R G. Barrera, and A. Tadjeddine, Phys. Rev. Lett.71, 2334 (1993).
3. K. Stahrenberg, T. Hermann, N. Esser, J. Sahn, W. Richter, S V. Hoffmann, and Ph. Hofmann, Phys. Rev. B58, R10 207 (1998).
4. V. Fernandez, D. Pahlke, N. Esser, K. Stahrenberg, O. Hunderi, A M. Bradshaw, and W. Richter, Surf. Sci.377, 388 (1997).
5. W L. Mochan, R G. Barrera, Y. Borensztein, and A. Tajeddine, Physica A207, 334 (1994).
6. J K. Hansen, J. Bremer, and O. Hunderi, Phys. Status Solidi A170, 271 (1998).
7. J. Bremer, J.-K. Hansen, and O. Hunderi, Surf. Sci. Lett.436, L735 (1999).
8. K. Stahrenberg, Th. Hermann, N. Esser, and W. Richter, Phys. Rev. B61, 3043 (2000).
9. J. Bremer, J.-K. Hansen, and O. Hunderi, Appl. Surf. Sci.142, 286 (1999).
10. J. Bremer, J.-K. Hansen, O. Hunderi, K. Stahrenberg, and T. Worren, Surf. Sci.459, 39 (2000).
11. R J. Cole, B G. Frederick, and P. Weightman, J. Vac. Sci. Technol. A15, 3088 (1998).
12. P J. Feibelman, Prog. Surf. Sci.12, 287 (1982).
13. P. Monachesi, M. Palummo, R. Del Sole, R. Ahuja, and O. Eriksson, in Optical Properties of Materials, edited by J. R. Chelikowsky, S. G. Louie, G. Martinez, and E. L. Shirley, MRS Symposia Proceedings No. 579 (Materials Research Society, Pittsburgh, 2001), p. 59.
14. S. Bouarab, M. Mebarki, A. Ziane, and M A. Khan, Phys. Rev. B63, 195409 (2001).
15. W. Kohn and L J. Sham, Phys. Rev.140, A1133 (1965).
16. L. Hedin and B I. Lundquist, J. Phys. C5, 1629 (1972).
17. F. Manghi, R. Del Sole, A. Selloni, and E. Molinari, Phys. Rev. B41, 9935 (1990).
18. R. Del Sole, Solid State Commun.37, 537 (1981).
19. This formula is equivalent to that obtained from the three-layer model devised by J D E. McIntyre and D E. Aspnes, Surf. Sci.24, 417 (1971).
20. The presence of d in Eqs. (1) and (2), introduced to obtain an adimensional (formula presented), makes the calculated RAS independent of d.
21. R. Del Sole and E. Fiorino, Phys. Rev. B29, 4631 (1984).
22. S. Albrecht, L. Reining, R. Del Sole, and G. Onida, Phys. Rev. Lett.80, 4510 (1998), and references therein.
23. H. Ehrenreich and M L. Cohen, Phys. Rev.115, 786 (1959).
24. P B. Johnson and R W. Christy, Phys. Rev. B6, 4370 (1972).
25. A. Marini and G. Onida (private communication). Such (very time consuming)calculations would not give any further physical insight in our case.
26. J. Wills and B R. Cooper, Phys. Rev. B36, 3809 (1987).
27. O K. Andersen, Phys. Rev. B12, 3060 (1975).
28. O. Jepsen and O K. Andersen, Solid State Commun.9, 1763 (1971).
29. M. Guillopé and B. Legrand, Surf. Sci.215, 577 (1989).
30. A state is surface or bulk according to the criterion (Ref. 17) of considering it as surface if its localization on the two outermost layers of each surface is larger than a given threshold (formula presented) (4/11 being the surface localization of an equally distributed state).
31. The occurrence of (formula presented) at about 3.7 eV is related to the onset of interband transitions (Ref. 24). This occurs at 3.3 eV in our calculations, 0.5 eV lower than in the experiment (Ref. 24).
32. O. Pulci, G. Onida, R. Del Sole, and L. Reining, Phys. Rev. Lett.81, 5374 (1998).
33. M A. Cazalilla, J F. Dolado, A. Rubio, and P M. Echenique, Phys. Rev. B61, 8033 (2000).