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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry Van Driel
  • Vol. 26, Iss. 4 — Apr. 1, 2009
  • pp: 725–733

One electron and discrete excitonic contributions to the optical response of semiconductors around E 1 transition: analysis in the reciprocal space

L. F. Lastras-Martínez, R. E. Balderas-Navarro, J. Ortega-Gallegos, A. Lastras-Martínez, J. M. Flores-Camacho, and K. Hingerl  »View Author Affiliations

JOSA B, Vol. 26, Issue 4, pp. 725-733 (2009)

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Spectroscopic ellipsometry (SE) has been utilized during the past decades for the measurement of the dielectric function of semiconductors. By using SE, interband critical point parameters such as energy gaps and broadenings are routinely determined. In the direct-space analysis approach, these parameters are known by taking the numerical energy derivatives of the dielectric function and fitting the spectra by using a Lorenzian line shape. However, in many cases the noise of the spectra does not allow the determination of such parameters as precisely as they are needed. Additionally, the determination of the character of the transitions, which is uncorrelated (one electron) or correlated (discrete excitons), is necessary for the analysis of the dielectric function. For instance, different values for the broadening parameter are obtained by using uncorrelated or correlated line shapes. We use a reciprocal-space analysis instead of the most commonly used direct-space analysis for determining without any uncertainty the character and, consequently, a precise value of the broadening parameter of the E 1 transitions of GaP, GaAs, Si, CdTe, GaSb, HgTe, and an alloy semiconductor: Cd 0.18 Hg 0.82 Te .

© 2009 Optical Society of America

OCIS Codes
(160.4760) Materials : Optical properties
(260.2130) Physical optics : Ellipsometry and polarimetry
(240.2130) Optics at surfaces : Ellipsometry and polarimetry

ToC Category:
Physical Optics

Original Manuscript: October 30, 2008
Revised Manuscript: December 15, 2008
Manuscript Accepted: January 15, 2009
Published: March 18, 2009

L. F. Lastras-Martínez, R. E. Balderas-Navarro, J. Ortega-Gallegos, A. Lastras-Martínez, J. M. Flores-Camacho, and K. Hingerl, "One electron and discrete excitonic contributions to the optical response of semiconductors around E1 transition: analysis in the reciprocal space," J. Opt. Soc. Am. B 26, 725-733 (2009)

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  1. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5to6.0 eV,” Phys. Rev. B 27, 985-1009 (1983). [CrossRef]
  2. G. E. Jellison, Jr., “Optical functions of GaAs, GaP, Ge determined by two channel polarization ellipsometry,” Opt. Mater. 1, 151-160 (1992). [CrossRef]
  3. P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, “Interband critical points of GaAs and their temperature dependence,” Phys. Rev. B 35, 9174-9189 (1987). [CrossRef]
  4. P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, “Temperature dependence of the dielectric function and interband critical points in silicon,” Phys. Rev. B 36, 4821-4830 (1987). [CrossRef]
  5. S. Adachi, T. Kimura, and N. Suzuki, “Optical properties of CdTe: experiment and modeling,” J. Appl. Phys. 74, 3435-3441 (1993). [CrossRef]
  6. Y. W. Jung, T. H. Ghong, Y. D. Kim, and D. E. Aspnes, “Effect of overlayers on critical-point parameters in the analysis of ellipsometric spectra,” Appl. Phys. Lett. 91, 121903 (2007). [CrossRef]
  7. M. Muñoz, K. Wei, and F. H. Pollak, “Spectral ellipsometry of GaSb: Experiment and modeling,” Phys. Rev. B 60, 8105-8110 (1999). [CrossRef]
  8. P. Lautenschlager, M. Garriga, and M. Cardona, “Temperature dependence of the interband critical-point parameters of InP,” Phys. Rev. B 36, 4813-4820 (1987). [CrossRef]
  9. M. Cardona, Modulation Spectroscopy (Academic, 1969).
  10. D. E. Aspnes, “Modulation spectroscopy/electric field effects on the dielectric function of semiconductors,” Handbook on Semiconductors, M.Balkanski ed. (North-Holland, 1980), Vol. 2, pp. 109-179.
  11. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors (Springer, 1996).
  12. A. B. Djurisic, Y. Chan, E. H. Li, “Progress in the room-temperature optical functions of semiconductors,” Mater. Sci. Eng. R. 38, 237-293 (2002). [CrossRef]
  13. D. E. Aspnes and H. Arwin, “Analysis of optical-spectra by Fourier methods--filtering and least-square regression in reciprocal space,” J. Opt. Soc. Am. 73, 1759-1764 (1983). [CrossRef]
  14. S. D. Yoo and D. E. Aspnes, “Elimination of endpoint-discontinuity artifacts in the analysis of spectra in reciprocal space,” J. Appl. Phys. 89, 8183-8192 (2001). [CrossRef]
  15. D. E. Aspnes, “The analysis of optical-spectra by Fourier methods,” Surf. Sci. 135, 284-306 (1983). [CrossRef]
  16. D. E. Aspnes, “Fourier critical-point analysis-extension to Gaussian lineshapes,” Sol. Energy Mater. Sol. Cells 32, 413-419 (1994). [CrossRef]
  17. L. F. Lastras-Martínez, T. Ruf, M. Konuma, M. Cardona, and D. E. Aspnes, “Isotopic effects on the dielectric response of Si around the E1 gap,” Phys. Rev. B 61, 12946-12951 (2000). [CrossRef]
  18. S. D. Yoo, D. E. Aspnes, L. F. Lastras-Martínez, T. Ruf, M. Konuma, and M. Cardona, “High-resolution spectroscopy with reciprocal-space analysis: application to isotopically pure Si,” Phys. Status Solidi B 220, 117-125 (2000). [CrossRef]
  19. J. Price and A. C. Diebold, “Spectroscopic ellipsometry characterization of ultrathin silicon-on-insulator films,” J. Vac. Sci. Technol. B 24, 2156-2159 (2006). [CrossRef]
  20. A. C. Diebold and J. Price, “Observation of quantum confinement and quantum size effects,” Phys. Status Solidi A 205, 896-900 (2008). [CrossRef]
  21. P. H. Hahn, W. G. Schmidt, and F. Bechstedt, “Bulk excitonic effects in surface optical spectra,” Phys. Rev. Lett. 88, 016402 (2002). [CrossRef] [PubMed]
  22. W. G. Schmidt, F. Bechstedt, W. Lu, and J. Bernholc, “Interplay of surface reconstruction and surface electric fields in the optical anisotropy of GaAs(001),” Phys. Rev. B 66, 085334 (2002). [CrossRef]
  23. L. F. Lastras-Martínez, J. M. Flores-Camacho, R. E. Balderas-Navarro, M. Chavira-Rodríguez, A. Lastras-Martínez, and M. Cardona, “Effect of reconstruction-induced strain on the reflectance difference spectroscopy of GaAs (001) around E1 and E1+Δ1 transitions,” Phys. Rev. B 75, 235315 (2007). [CrossRef]
  24. L. D. Sun, M. Hohage, P. Zeppenfeld, and R. E. Balderas-Navarro, “Origin and temperature dependence of the surface optical anisotropy on Cu(110),” Surf. Sci. 589, 153-163 (2005). [CrossRef]
  25. J. M. Flores-Camacho, O. F. Núñez-Olvera, G. Rodríguez-Pedroza, A. Lastras-Martínez, and L. F. Lastras-Martínez, “Lock-in amplifier-based rotating-analyzer spectroscopic ellipsometer with micro-controlled angular frequency,” Rev. Mex. Fis. 51, 274-283 (2005).
  26. H. Arwin and D. E. Aspnes, “Nondestructive analysis of Hg1-XCdXTe(X=0.00,0.20,0.29,and1.00) by spectroscopic ellipsometry. 2. Substrate, oxide, and interface properties,” J. Vac. Sci. Technol. A 2, 1316-1323 (1984). [CrossRef]
  27. O. S. Heavens, Optical Properies of Thin Solid Films (Dover, 1991).
  28. D. E. Aspnes, B. Schwartz, A. A. Studna, L. Derick, and L. A. Koszi, “Optical properties of anodically grown native oxides on some Ga-V compounds from 1.5to6.0 eV,” J. Appl. Phys. 48, 3510-3513 (1977). [CrossRef]
  29. R. H. Philipp, “Silicon dioxide (SiO2) (Glass),” in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), pp. 749-763.
  30. J. E. Rowe and D. E. Aspnes, “Approximate treatment of exciton effects in electric field modulation via the Slater-Koster interaction,” Phys. Rev. Lett. 25, 162-165 (1970). [CrossRef]
  31. B. Velický and J. Sak, “Excitonic effects in the interband absorption of semiconductors,” Phys. Status Solidi B 16, 147-157 (1966). [CrossRef]
  32. S. Zollner, M. Garriga, J. Kircher, J. Humlicek, M. Cardona, and G. Neuhold, “Temperature dependence of the dielectric function and the interband critical-point parameters of GaP,” Phys. Rev. B 48, 7915-7929 (1993). [CrossRef]
  33. M. Rohlfing and S. G. Louie, “Electron-hole excitations and optical spectra from first principles,” Phys. Rev. B 62, 4927-4944 (2000). [CrossRef]
  34. S. Zollner, M. Garriga, J. Humlicek, S. Gopalan, and M. Cardona, “Temperature dependence of the dielectric function and the interband critical-point parameters of GaSb,” Phys. Rev. B 43, 4349-4360 (1991). [CrossRef]
  35. L. Viña, C. Umbach, M. Cardona, and L. Vodopyanov, “Ellipsometric studies of electronic interband transitions in CdxHg1−xTe,” Phys. Rev. B 29, 6752-6760 (1984). [CrossRef]

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