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Superficies y vacío
Print version ISSN 1665-3521
Superf. vacío vol.18 n.4 Ciudad de México Dec. 2005
Articles
Electron-phonon interaction effects on the dielectric response of Si
* Instituto de Investigación en Comunicación Óptica, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000, San Luis Potosí SLP, México.
** Max-Planck-Institut für Festkörperforschung Heisenbergstrasse 1, 70569 Stuttgart, Germany.
The availability of isotopically pure semiconductors in the last fifteen years has triggered their scientific and technological interest. The effects of the electron-phonon interaction on the band structure can be experimentally investigated by measuring the temperature or the isotopic composition dependence of energy gaps. In this article, we discuss the effects of isotopic composition on the dielectric function of silicon by using spectroscopic ellipsometry in the energy range from 3.1 to 3.7 eV. The silicon crystals investigated are the isotopically pure 28Si and 30Si, and the natural Si ( nat Si, M nat = 28.14 amu). At low temperatures, the energies of the interband transitions become mass-dependent through the dependence of the electron-phonon interaction and the lattice parameter on the average isotopic mass. We determine the mass dependence of critical point energies and other optical parameters as accurately as possible by analyzing the ellipsometric data in reciprocal (Fourier-inverse) rather than direct (frequency) space.
Keywords: Optical constants; Semiconductors; Theory; Models; Numerical simulation
Acknowledgments
We would like to thank D.E. Aspnes for having introduced us to the reciprocal space method of analysis. Thanks are also due to D. Rönnow, T. Ruf, M. Konuma and S.D. Yoo for their collaboration in earlier versions of this work.
References
[1] M. Cardona, in Festkörperprobleme/ Advances in Solid State Physics, edited by R. Helbig, (Vieweg, Braunschweig, Wiesbaden 1994) p. 35. [ Links ]
[2] H. Holloway, K.C. Hass, M.A. Tamor, T. R. Anthony and W. F. Banholzer, Phys. Rev. B 44, 7123 (1991). [ Links ]
[3] R. C. Buschert, A. E. Merlini, S. Pace, S. Rodriguez, and M.H. Grimsditch, Phys. Rev. B 38, 5219 (1988). [ Links ]
[4] N. Garro, A. Cantarero, M. Cardona, A. Göbel, T. Ruf and K. Eberl, Phys. Rev. B 54, 4732 (1996). [ Links ]
[5] Kazimirov, J. Zegenhagen, and M. Cardona, Science, 282, 930 (1998). [ Links ]
[6] P. Pavone, and S. Baroni, Solid State Commun. 90 295 (1994). [ Links ]
[7] C. P. Herrero, Solid State Commun. 110, 243 (1999). [ Links ]
[8] ; Debernardi and M. Cardona, Phys. Rev. B 54, 11305 (1996). [ Links ]
[9] S. Zollner, M. Cardona and S. Gopalan, Phys. Rev. B 45, [ Links ]
[10] D. Rönnow, L.F. Lastras-Martínez and M. Cardona, Eur. Phys. J. B 5, 29 (1998). [ Links ]
[11] Göbel, T. Ruf, J. M. Zhang, R. Lauck, and M. Cardona, Phys. Rev. B 59, 2749 (1999). [ Links ]
[12] J. M. Zhang, T. Ruf , R. Lauck , and M. Cardona, Phys. Rev. B 57, 9716 (1998). [ Links ]
[13] Göbel, T. Ruf, C.T. Lin, M. Cardona, J.C. Merle, and M. Joucla, Phys. Rev. B 56, 210 (1997). [ Links ]
[14] L. F. Lastras-Martínez, T. Ruf, M. Konuma andM. Cardona, Phys. Rev. B 61, 12946 (2000). [ Links ]
[15] S. D. Yoo, D. E. Aspnes, L. F. Lastras-Martínez, T. Ruf, M. Konuma andM. Cardona, phys. stat. sol. (b) 220, 117 (2000). [ Links ]
[16] J. Bardeen, W. Schockley, Phys. Rev. 80, 72 (1950). [ Links ]
[17] M. Cardona, Solid State Commun. 133, 3 (2005). [ Links ]
[18] P. Lautenschlager, M. Garriga, L. Viña and M. Cardona , Phys. Rev. B 36, 4821 (1987). [ Links ]
[19] D. E. Aspnes, Surface Sci. 135, 284 (1983). [ Links ]
[20] D. E. Aspnes, and H. Arwin, J. Opt. Soc. Am. 73, 1759 (1983). [ Links ]
[21] D. E. Aspnes, Solar Energy Materials and Solar Cells 32, 413 (1994). [ Links ]
[22] R. N. Bracewell, The Fourier transform and its applications (McGraw-Hill, Singapore, 1986). [ Links ]
[23] J. Emsley, The Elements (Clarendon Press, Oxford, 991). [ Links ]
[24] D.E. Aspnes and A.A. Studna, Applied Optics 14, 220 (1975). [ Links ]
[25] R. M. A. Azzam and N.M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1997). [ Links ]
[26] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, New York, 1997), p. 650. [ Links ]
[27] P. Lautenschlager, P. B. Allen andM. Cardona, Phys. Rev. B 31, 2163 (1985). [ Links ]
[28] W. Kress in Landolt-Börnstein Tables, New Series, Vol. 17a, Physics of Group IV Elements and III-V Compounds, edited by O. Madelung, 64 (Springer-Verlag, Berlin-Heidelberg, 1982). [ Links ]
Received: July 26, 2005; Accepted: December 08, 2005
This is an open-access article distributed under the terms of the
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