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Line shape of the optical dielectric function
1.D. E. Aspnes and J. E. Rowe, Phys. Rev. B 5, 4022 (1972);
1.D. K. Aspnes, Surf. Sci. 37, 418 (1973).
2.L. Vina, C. Umbach, M. Cardona, and L. Vodopyanov, Phys. Rev. B 29, 6752 (1984).
3.M. Erman, thesis, Paris, Orsay, 1987.
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9.J. W. Garland, P. M. Raccah, and M. Viccaro (unpublished).
10.This approximation is very accurate for third‐ and higher‐order derivatives and when fitting data taken at temperatures is very accurate even for first‐ and second‐order derivatives. This is because the line shape goes rapidly to zero as increases, showing that only k points very close to the critical k point, contribute significantly, and because the parabolic‐hand approximation becomes exact for k points sufficiently close to The accuracy of this approximation has been verified by numerical calculations.
11.O. J. Glembocki and B. V. Shanabrook, Superlatt. Microstruct. 3, 235 (1987).
12.P. M. Raccah, J. W. Garland, S. E. Buttrill, Jr., L. Francke, and J. Jackson, Appl. Phys. Lett. 52, 9 May (1988).
13.The fractional standard deviation of the analytic Lorentzian fit to the Lorentzian numerical‐third‐derivative line shape was only 0.015; the best fit to that line shape, obtained using a 94% Lorentzian and 6% Gaussian line shape, showed a fractional standard deviation of 0.008. The analytic Gaussian fit to the Gaussian numerical‐third‐derivative line shape was even better. The third derivatives were taken using the procedure of A. Savitsky and M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
14.D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983), quoted in more detail in Handbook of Optical Constants of Solids, edited by E. O. Palik (Academic, New York, 1985), pp. 429–432.
15.However, this fitting procedure introduces a systematic error into the linewidth Γ, for which one must correct.
16.B. V. Shanabrook, O. J. Glembocki, and W. T. Beard, Phys. Rev. B 35, 2540 (1987).
17.H. Shen, P. Parayanthal, F. H. Pollak, M. Tomkiewicz, T. J. Drummond, and J. N. Schulman, Appl. Phys. Lett. 48, 653 (1986).
18.Alloy clustering could lead to an approximately Lorentzian component in the inhomogencous broadening, but it would be far too small to explain our results for MCT alloys.
19.P. M. Raccah, J. W. Garland, Z. Zhang, F. A. Chambers, and D. J. Vezzetti, Phys. Rev. B 36, 4271 (1986).
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