Abstract

The effect of surface roughness on the ellipsometric response of semiconductor surfaces is investigated. CdTe(211)B layers were grown on Ge(211) by molecular beam epitaxy using less than optimal growth conditions to enhance the formation of surface roughness. Their optical properties, measured by rotating-compensator ellipsometry, showed small but significant sample-to-sample differences not explainable in terms of nanometer-scale roughness. A critical-point analysis established that the critical-point structure of the dielectric function was the same for all samples. This result suggested that the observed sample-to-sample variations were due to macroscopic roughness, which scatters off-specular light into the detector, thereby causing errors. We introduced tentative corrections for off-specular reflection that fitted the observed differences and thus supported the idea that off-specular reflection was responsible for the observed differences. These results were obtained using CdTe but are easily extensible to other rough opaque materials.

© 2006 Optical Society of America

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  1. A. Million, N. K. Dhar, and J. H. Dinan, "Heteroepitaxy of CdTe on {211}Si substrates by molecular beam epitaxy," J. Cryst. Growth 159, 76-80 (1996).
    [CrossRef]
  2. A. Rogalski, "Comparison of the performance of quantum well and conventional bulk infrared photodetectors," Infrared Phys. Technol. 38, 295 (1997).
    [CrossRef]
  3. M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
    [CrossRef]
  4. P. Ballet, X. Baudry, J.-P. Zanatta, and A. Million, "In situ real time analysis of the MBE growth of CdTe on Ge: a comparison of data analysis techniques," J. Cryst. Growth, submitted for publication.
  5. Wollam, Inc., 645 M St. Suite 102, Lincoln, Nebr. 68508.
  6. J. Lee, J. Koh, and R. W. Collins, "Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and thin films," Rev. Sci. Instrum. 72, 1742-1754 (2001), and references cited therein.
    [CrossRef]
  7. B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
    [CrossRef]
  8. C. C. Kim, P. M. Raccah, and J. W. Garland, "The improvement of phase modulated spectroscopic ellipsomerty," Rev. Sci. Instrum. 63, 2958-2966 (1992).
    [CrossRef]
  9. V. M. Bermudez and H. Ritz, "Wavelength-scanning polarization-modulation ellipsometry: some practical considerations," Appl. Opt. 17, 542-552 (1978).
    [CrossRef] [PubMed]
  10. W. M. Duncan and S. Henck, "In situ spectra ellipsometry for real-time measurement and control," Appl. Surf. Sci. 63, 1179-1185 (1993).
    [CrossRef]
  11. T. Mori and D. E. Aspnes, "Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system," Thin Solid Films 455-456, 33-38 (2004).
    [CrossRef]
  12. S. M. F. Nee, "The effects of incoherent scattering on ellipsometry," in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 119-127 (1992).
    [CrossRef]
  13. S. M. F. Nee, "Effects of near-specular scattering a polarimetry," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 304-313 (1994), and references contained therein.
    [CrossRef]
  14. J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).
  15. D. A. Aspnes, J. B. Theeten, and F. Hottier, "Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry," Phys. Rev. B 20, 3292-3302 (1979).
    [CrossRef]
  16. S. Adachi, T. Kimura, and N. Suzuki, "Optical properties of CdTe: experiment and modeling," J. Appl. Phys. 74, 3435-3541 (1993).
    [CrossRef]
  17. H. Ehrenreich and M. H. Cohen, "Self-consistent field approach to the many-electron problem," Phys. Rev. 115, 786-790 (1959).
    [CrossRef]
  18. O. Castaing, J. T. Benhlal, and R. Granger, "An attempt to model the dielectric function in II-VI ternary compounds Hg1−xZnxTe and Cd1−xZnxTe," Eur. Phys. J. B 7, 563-572 (1999). These authors give a different expression for the JDS in that they add up separately each contribution arising from any given pair of (c) and (v) bands. However, many contributions overlap: WE0—>E1(E) and WE0—>E2(E) overlap between E1 and E2. Hence, although this implementation is correct in principle, it causes substantial parameter correlation.
    [CrossRef]
  19. P. Barak, "Smoothing and differentiation by an adaptive-degree polynomial filter," Anal. Chem. 67, 2758-2762 (1995).
    [CrossRef]
  20. P. A. Gorry, "General least-squares smoothing and differentiation by the convolution by the convolution (Savitzky-Golay) method," Anal. Chem. 62, 570-573 (1990).
    [CrossRef]
  21. C. Kim, J. Garland, H. Abad, and P. M. Raccah. "Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation," Phys. Rev. B 45, 11749-11767 (1992).
    [CrossRef]
  22. C. Kim and S. Sivananthan, "Modeling the optical dielectric function of II-VI compound CdTe," J. Appl. Phys. 78, 4003-4010 (1995).
    [CrossRef]
  23. C. C. Kim, M. Daraselia, J. W. Garland, and S. Sivananthan, "Temperature dependence of the optical properties of CdTe," Phys. Rev. B 56, 4768-4797 (1997).
  24. G. Badano, A. Million, P. Ballet, and A. Etcheberry, "Fast detection of precipitates and oxides on CdZnTe surfaces by the spectroscopic ellipsometry," J. Electron. Mater., submitted for publication.
  25. J. T. Benhlal, K. Strauch, R. Granger, and R. Triboulet, "Temperature dependence of the dielectric function and of the parameters of critical point transitions of CdTe," Opt. Mater. 12, 143-156 (1999).
    [CrossRef]
  26. 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]
  27. H. Arwin and D. E. Aspnes, "Nondestructive analysis of HgCdTe (x=0.00, 0.20, 0.29, and 1.00) by spectroscopic ellipsometry. II. Substrate, oxide, and interface properties," J. Vac. Sci. Technol. A 2, 1316-1323 (1984).
    [CrossRef]
  28. S. M. F. Nee, "Polarization of specular reflection and near-specular scattering by a rough surface," Appl. Opt. 35, 3570-3582 (1996).
    [CrossRef]
  29. D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Many-body and correlation effects in surface and interface spectra of optically absorbing materials," Phys. Status Solidi A 170, 199-210 (1998).
    [CrossRef]
  30. D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Coherence effects and time dependences of the optical response of surface and interfaces of optically absorbing material," Phys. Status Solidi B 220, 709-715 (2000).
    [CrossRef]
  31. L. Mantese, K. A. Bell, D. E. Aspnes, and U. Rossow, "Photon-induced localization in optically absorbing materials," Phys. Lett. A 253, 93-97 (1999).
    [CrossRef]
  32. For the effect of strain on the critical points of CdTe, see K. Hingerl, R. E. Bladeras-Navarro, A. Bonnanni, and S. Stifter, "Influence of anisotropic in-plane strain on critical point resonances in reflectance difference date," J. Vac. Sci. Technol. B 19, 1650-1657 (2001).
    [CrossRef]

2004 (1)

T. Mori and D. E. Aspnes, "Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system," Thin Solid Films 455-456, 33-38 (2004).
[CrossRef]

2001 (2)

J. Lee, J. Koh, and R. W. Collins, "Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and thin films," Rev. Sci. Instrum. 72, 1742-1754 (2001), and references cited therein.
[CrossRef]

For the effect of strain on the critical points of CdTe, see K. Hingerl, R. E. Bladeras-Navarro, A. Bonnanni, and S. Stifter, "Influence of anisotropic in-plane strain on critical point resonances in reflectance difference date," J. Vac. Sci. Technol. B 19, 1650-1657 (2001).
[CrossRef]

2000 (1)

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Coherence effects and time dependences of the optical response of surface and interfaces of optically absorbing material," Phys. Status Solidi B 220, 709-715 (2000).
[CrossRef]

1999 (3)

L. Mantese, K. A. Bell, D. E. Aspnes, and U. Rossow, "Photon-induced localization in optically absorbing materials," Phys. Lett. A 253, 93-97 (1999).
[CrossRef]

O. Castaing, J. T. Benhlal, and R. Granger, "An attempt to model the dielectric function in II-VI ternary compounds Hg1−xZnxTe and Cd1−xZnxTe," Eur. Phys. J. B 7, 563-572 (1999). These authors give a different expression for the JDS in that they add up separately each contribution arising from any given pair of (c) and (v) bands. However, many contributions overlap: WE0—>E1(E) and WE0—>E2(E) overlap between E1 and E2. Hence, although this implementation is correct in principle, it causes substantial parameter correlation.
[CrossRef]

J. T. Benhlal, K. Strauch, R. Granger, and R. Triboulet, "Temperature dependence of the dielectric function and of the parameters of critical point transitions of CdTe," Opt. Mater. 12, 143-156 (1999).
[CrossRef]

1998 (2)

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Many-body and correlation effects in surface and interface spectra of optically absorbing materials," Phys. Status Solidi A 170, 199-210 (1998).
[CrossRef]

1997 (2)

A. Rogalski, "Comparison of the performance of quantum well and conventional bulk infrared photodetectors," Infrared Phys. Technol. 38, 295 (1997).
[CrossRef]

C. C. Kim, M. Daraselia, J. W. Garland, and S. Sivananthan, "Temperature dependence of the optical properties of CdTe," Phys. Rev. B 56, 4768-4797 (1997).

1996 (2)

A. Million, N. K. Dhar, and J. H. Dinan, "Heteroepitaxy of CdTe on {211}Si substrates by molecular beam epitaxy," J. Cryst. Growth 159, 76-80 (1996).
[CrossRef]

S. M. F. Nee, "Polarization of specular reflection and near-specular scattering by a rough surface," Appl. Opt. 35, 3570-3582 (1996).
[CrossRef]

1995 (2)

P. Barak, "Smoothing and differentiation by an adaptive-degree polynomial filter," Anal. Chem. 67, 2758-2762 (1995).
[CrossRef]

C. Kim and S. Sivananthan, "Modeling the optical dielectric function of II-VI compound CdTe," J. Appl. Phys. 78, 4003-4010 (1995).
[CrossRef]

1994 (2)

S. M. F. Nee, "Effects of near-specular scattering a polarimetry," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 304-313 (1994), and references contained therein.
[CrossRef]

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

1993 (2)

W. M. Duncan and S. Henck, "In situ spectra ellipsometry for real-time measurement and control," Appl. Surf. Sci. 63, 1179-1185 (1993).
[CrossRef]

S. Adachi, T. Kimura, and N. Suzuki, "Optical properties of CdTe: experiment and modeling," J. Appl. Phys. 74, 3435-3541 (1993).
[CrossRef]

1992 (3)

S. M. F. Nee, "The effects of incoherent scattering on ellipsometry," in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 119-127 (1992).
[CrossRef]

C. Kim, J. Garland, H. Abad, and P. M. Raccah. "Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation," Phys. Rev. B 45, 11749-11767 (1992).
[CrossRef]

C. C. Kim, P. M. Raccah, and J. W. Garland, "The improvement of phase modulated spectroscopic ellipsomerty," Rev. Sci. Instrum. 63, 2958-2966 (1992).
[CrossRef]

1990 (1)

P. A. Gorry, "General least-squares smoothing and differentiation by the convolution by the convolution (Savitzky-Golay) method," Anal. Chem. 62, 570-573 (1990).
[CrossRef]

1984 (2)

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]

H. Arwin and D. E. Aspnes, "Nondestructive analysis of HgCdTe (x=0.00, 0.20, 0.29, and 1.00) by spectroscopic ellipsometry. II. Substrate, oxide, and interface properties," J. Vac. Sci. Technol. A 2, 1316-1323 (1984).
[CrossRef]

1982 (1)

B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
[CrossRef]

1979 (1)

D. A. Aspnes, J. B. Theeten, and F. Hottier, "Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry," Phys. Rev. B 20, 3292-3302 (1979).
[CrossRef]

1978 (1)

1959 (1)

H. Ehrenreich and M. H. Cohen, "Self-consistent field approach to the many-electron problem," Phys. Rev. 115, 786-790 (1959).
[CrossRef]

Abad, H.

C. Kim, J. Garland, H. Abad, and P. M. Raccah. "Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation," Phys. Rev. B 45, 11749-11767 (1992).
[CrossRef]

Adachi, S.

S. Adachi, T. Kimura, and N. Suzuki, "Optical properties of CdTe: experiment and modeling," J. Appl. Phys. 74, 3435-3541 (1993).
[CrossRef]

Arias, M.

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

Arwin, H.

H. Arwin and D. E. Aspnes, "Nondestructive analysis of HgCdTe (x=0.00, 0.20, 0.29, and 1.00) by spectroscopic ellipsometry. II. Substrate, oxide, and interface properties," J. Vac. Sci. Technol. A 2, 1316-1323 (1984).
[CrossRef]

Aspnes, D. A.

D. A. Aspnes, J. B. Theeten, and F. Hottier, "Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry," Phys. Rev. B 20, 3292-3302 (1979).
[CrossRef]

Aspnes, D. E.

T. Mori and D. E. Aspnes, "Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system," Thin Solid Films 455-456, 33-38 (2004).
[CrossRef]

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Coherence effects and time dependences of the optical response of surface and interfaces of optically absorbing material," Phys. Status Solidi B 220, 709-715 (2000).
[CrossRef]

L. Mantese, K. A. Bell, D. E. Aspnes, and U. Rossow, "Photon-induced localization in optically absorbing materials," Phys. Lett. A 253, 93-97 (1999).
[CrossRef]

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Many-body and correlation effects in surface and interface spectra of optically absorbing materials," Phys. Status Solidi A 170, 199-210 (1998).
[CrossRef]

H. Arwin and D. E. Aspnes, "Nondestructive analysis of HgCdTe (x=0.00, 0.20, 0.29, and 1.00) by spectroscopic ellipsometry. II. Substrate, oxide, and interface properties," J. Vac. Sci. Technol. A 2, 1316-1323 (1984).
[CrossRef]

Badano, G.

G. Badano, A. Million, P. Ballet, and A. Etcheberry, "Fast detection of precipitates and oxides on CdZnTe surfaces by the spectroscopic ellipsometry," J. Electron. Mater., submitted for publication.

Bajaj, J.

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

Ballet, P.

G. Badano, A. Million, P. Ballet, and A. Etcheberry, "Fast detection of precipitates and oxides on CdZnTe surfaces by the spectroscopic ellipsometry," J. Electron. Mater., submitted for publication.

P. Ballet, X. Baudry, J.-P. Zanatta, and A. Million, "In situ real time analysis of the MBE growth of CdTe on Ge: a comparison of data analysis techniques," J. Cryst. Growth, submitted for publication.

Barak, P.

P. Barak, "Smoothing and differentiation by an adaptive-degree polynomial filter," Anal. Chem. 67, 2758-2762 (1995).
[CrossRef]

Baudry, X.

P. Ballet, X. Baudry, J.-P. Zanatta, and A. Million, "In situ real time analysis of the MBE growth of CdTe on Ge: a comparison of data analysis techniques," J. Cryst. Growth, submitted for publication.

Bell, K. A.

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Coherence effects and time dependences of the optical response of surface and interfaces of optically absorbing material," Phys. Status Solidi B 220, 709-715 (2000).
[CrossRef]

L. Mantese, K. A. Bell, D. E. Aspnes, and U. Rossow, "Photon-induced localization in optically absorbing materials," Phys. Lett. A 253, 93-97 (1999).
[CrossRef]

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Many-body and correlation effects in surface and interface spectra of optically absorbing materials," Phys. Status Solidi A 170, 199-210 (1998).
[CrossRef]

Benhlal, J. T.

O. Castaing, J. T. Benhlal, and R. Granger, "An attempt to model the dielectric function in II-VI ternary compounds Hg1−xZnxTe and Cd1−xZnxTe," Eur. Phys. J. B 7, 563-572 (1999). These authors give a different expression for the JDS in that they add up separately each contribution arising from any given pair of (c) and (v) bands. However, many contributions overlap: WE0—>E1(E) and WE0—>E2(E) overlap between E1 and E2. Hence, although this implementation is correct in principle, it causes substantial parameter correlation.
[CrossRef]

J. T. Benhlal, K. Strauch, R. Granger, and R. Triboulet, "Temperature dependence of the dielectric function and of the parameters of critical point transitions of CdTe," Opt. Mater. 12, 143-156 (1999).
[CrossRef]

Bermudez, V. M.

Bladeras-Navarro, R. E.

For the effect of strain on the critical points of CdTe, see K. Hingerl, R. E. Bladeras-Navarro, A. Bonnanni, and S. Stifter, "Influence of anisotropic in-plane strain on critical point resonances in reflectance difference date," J. Vac. Sci. Technol. B 19, 1650-1657 (2001).
[CrossRef]

Bonnanni, A.

For the effect of strain on the critical points of CdTe, see K. Hingerl, R. E. Bladeras-Navarro, A. Bonnanni, and S. Stifter, "Influence of anisotropic in-plane strain on critical point resonances in reflectance difference date," J. Vac. Sci. Technol. B 19, 1650-1657 (2001).
[CrossRef]

Cardona, M.

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]

Castaing, O.

O. Castaing, J. T. Benhlal, and R. Granger, "An attempt to model the dielectric function in II-VI ternary compounds Hg1−xZnxTe and Cd1−xZnxTe," Eur. Phys. J. B 7, 563-572 (1999). These authors give a different expression for the JDS in that they add up separately each contribution arising from any given pair of (c) and (v) bands. However, many contributions overlap: WE0—>E1(E) and WE0—>E2(E) overlap between E1 and E2. Hence, although this implementation is correct in principle, it causes substantial parameter correlation.
[CrossRef]

Cohen, M. H.

H. Ehrenreich and M. H. Cohen, "Self-consistent field approach to the many-electron problem," Phys. Rev. 115, 786-790 (1959).
[CrossRef]

Collins, R. W.

J. Lee, J. Koh, and R. W. Collins, "Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and thin films," Rev. Sci. Instrum. 72, 1742-1754 (2001), and references cited therein.
[CrossRef]

Dalby, J. L.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
[CrossRef]

Daraselia, M.

C. C. Kim, M. Daraselia, J. W. Garland, and S. Sivananthan, "Temperature dependence of the optical properties of CdTe," Phys. Rev. B 56, 4768-4797 (1997).

Dewames, R. E.

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

Dhar, N. K.

A. Million, N. K. Dhar, and J. H. Dinan, "Heteroepitaxy of CdTe on {211}Si substrates by molecular beam epitaxy," J. Cryst. Growth 159, 76-80 (1996).
[CrossRef]

Dinan, J. H.

A. Million, N. K. Dhar, and J. H. Dinan, "Heteroepitaxy of CdTe on {211}Si substrates by molecular beam epitaxy," J. Cryst. Growth 159, 76-80 (1996).
[CrossRef]

Drevillon, B.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
[CrossRef]

Duncan, W. M.

W. M. Duncan and S. Henck, "In situ spectra ellipsometry for real-time measurement and control," Appl. Surf. Sci. 63, 1179-1185 (1993).
[CrossRef]

Duvaut, P.

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

Ehrenreich, H.

H. Ehrenreich and M. H. Cohen, "Self-consistent field approach to the many-electron problem," Phys. Rev. 115, 786-790 (1959).
[CrossRef]

Etcheberry, A.

G. Badano, A. Million, P. Ballet, and A. Etcheberry, "Fast detection of precipitates and oxides on CdZnTe surfaces by the spectroscopic ellipsometry," J. Electron. Mater., submitted for publication.

Ferret, P.

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

Garland, J.

C. Kim, J. Garland, H. Abad, and P. M. Raccah. "Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation," Phys. Rev. B 45, 11749-11767 (1992).
[CrossRef]

Garland, J. W.

C. C. Kim, M. Daraselia, J. W. Garland, and S. Sivananthan, "Temperature dependence of the optical properties of CdTe," Phys. Rev. B 56, 4768-4797 (1997).

C. C. Kim, P. M. Raccah, and J. W. Garland, "The improvement of phase modulated spectroscopic ellipsomerty," Rev. Sci. Instrum. 63, 2958-2966 (1992).
[CrossRef]

Gorry, P. A.

P. A. Gorry, "General least-squares smoothing and differentiation by the convolution by the convolution (Savitzky-Golay) method," Anal. Chem. 62, 570-573 (1990).
[CrossRef]

Granger, R.

J. T. Benhlal, K. Strauch, R. Granger, and R. Triboulet, "Temperature dependence of the dielectric function and of the parameters of critical point transitions of CdTe," Opt. Mater. 12, 143-156 (1999).
[CrossRef]

O. Castaing, J. T. Benhlal, and R. Granger, "An attempt to model the dielectric function in II-VI ternary compounds Hg1−xZnxTe and Cd1−xZnxTe," Eur. Phys. J. B 7, 563-572 (1999). These authors give a different expression for the JDS in that they add up separately each contribution arising from any given pair of (c) and (v) bands. However, many contributions overlap: WE0—>E1(E) and WE0—>E2(E) overlap between E1 and E2. Hence, although this implementation is correct in principle, it causes substantial parameter correlation.
[CrossRef]

Henck, S.

W. M. Duncan and S. Henck, "In situ spectra ellipsometry for real-time measurement and control," Appl. Surf. Sci. 63, 1179-1185 (1993).
[CrossRef]

Hingerl, K.

For the effect of strain on the critical points of CdTe, see K. Hingerl, R. E. Bladeras-Navarro, A. Bonnanni, and S. Stifter, "Influence of anisotropic in-plane strain on critical point resonances in reflectance difference date," J. Vac. Sci. Technol. B 19, 1650-1657 (2001).
[CrossRef]

Hottier, F.

D. A. Aspnes, J. B. Theeten, and F. Hottier, "Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry," Phys. Rev. B 20, 3292-3302 (1979).
[CrossRef]

Isselin, S.

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

Kim, C.

C. Kim and S. Sivananthan, "Modeling the optical dielectric function of II-VI compound CdTe," J. Appl. Phys. 78, 4003-4010 (1995).
[CrossRef]

C. Kim, J. Garland, H. Abad, and P. M. Raccah. "Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation," Phys. Rev. B 45, 11749-11767 (1992).
[CrossRef]

Kim, C. C.

C. C. Kim, M. Daraselia, J. W. Garland, and S. Sivananthan, "Temperature dependence of the optical properties of CdTe," Phys. Rev. B 56, 4768-4797 (1997).

C. C. Kim, P. M. Raccah, and J. W. Garland, "The improvement of phase modulated spectroscopic ellipsomerty," Rev. Sci. Instrum. 63, 2958-2966 (1992).
[CrossRef]

Kimura, T.

S. Adachi, T. Kimura, and N. Suzuki, "Optical properties of CdTe: experiment and modeling," J. Appl. Phys. 74, 3435-3541 (1993).
[CrossRef]

Koh, J.

J. Lee, J. Koh, and R. W. Collins, "Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and thin films," Rev. Sci. Instrum. 72, 1742-1754 (2001), and references cited therein.
[CrossRef]

Kozlowski, L. J.

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

Lee, J.

J. Lee, J. Koh, and R. W. Collins, "Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and thin films," Rev. Sci. Instrum. 72, 1742-1754 (2001), and references cited therein.
[CrossRef]

Mantese, L.

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Coherence effects and time dependences of the optical response of surface and interfaces of optically absorbing material," Phys. Status Solidi B 220, 709-715 (2000).
[CrossRef]

L. Mantese, K. A. Bell, D. E. Aspnes, and U. Rossow, "Photon-induced localization in optically absorbing materials," Phys. Lett. A 253, 93-97 (1999).
[CrossRef]

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Many-body and correlation effects in surface and interface spectra of optically absorbing materials," Phys. Status Solidi A 170, 199-210 (1998).
[CrossRef]

Marbot, R.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
[CrossRef]

Million, A.

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

A. Million, N. K. Dhar, and J. H. Dinan, "Heteroepitaxy of CdTe on {211}Si substrates by molecular beam epitaxy," J. Cryst. Growth 159, 76-80 (1996).
[CrossRef]

G. Badano, A. Million, P. Ballet, and A. Etcheberry, "Fast detection of precipitates and oxides on CdZnTe surfaces by the spectroscopic ellipsometry," J. Electron. Mater., submitted for publication.

P. Ballet, X. Baudry, J.-P. Zanatta, and A. Million, "In situ real time analysis of the MBE growth of CdTe on Ge: a comparison of data analysis techniques," J. Cryst. Growth, submitted for publication.

Mori, T.

T. Mori and D. E. Aspnes, "Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system," Thin Solid Films 455-456, 33-38 (2004).
[CrossRef]

Nee, S. M. F.

S. M. F. Nee, "Polarization of specular reflection and near-specular scattering by a rough surface," Appl. Opt. 35, 3570-3582 (1996).
[CrossRef]

S. M. F. Nee, "Effects of near-specular scattering a polarimetry," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 304-313 (1994), and references contained therein.
[CrossRef]

S. M. F. Nee, "The effects of incoherent scattering on ellipsometry," in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 119-127 (1992).
[CrossRef]

Pasko, J. G.

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

Perrin, J.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
[CrossRef]

Raccah, P M.

C. Kim, J. Garland, H. Abad, and P. M. Raccah. "Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation," Phys. Rev. B 45, 11749-11767 (1992).
[CrossRef]

Raccah, P. M.

C. C. Kim, P. M. Raccah, and J. W. Garland, "The improvement of phase modulated spectroscopic ellipsomerty," Rev. Sci. Instrum. 63, 2958-2966 (1992).
[CrossRef]

Ritz, H.

Rogalski, A.

A. Rogalski, "Comparison of the performance of quantum well and conventional bulk infrared photodetectors," Infrared Phys. Technol. 38, 295 (1997).
[CrossRef]

Rolland, G.

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

Rossow, U.

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Coherence effects and time dependences of the optical response of surface and interfaces of optically absorbing material," Phys. Status Solidi B 220, 709-715 (2000).
[CrossRef]

L. Mantese, K. A. Bell, D. E. Aspnes, and U. Rossow, "Photon-induced localization in optically absorbing materials," Phys. Lett. A 253, 93-97 (1999).
[CrossRef]

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Many-body and correlation effects in surface and interface spectra of optically absorbing materials," Phys. Status Solidi A 170, 199-210 (1998).
[CrossRef]

Sivananthan, S.

C. C. Kim, M. Daraselia, J. W. Garland, and S. Sivananthan, "Temperature dependence of the optical properties of CdTe," Phys. Rev. B 56, 4768-4797 (1997).

C. Kim and S. Sivananthan, "Modeling the optical dielectric function of II-VI compound CdTe," J. Appl. Phys. 78, 4003-4010 (1995).
[CrossRef]

Stifter, S.

For the effect of strain on the critical points of CdTe, see K. Hingerl, R. E. Bladeras-Navarro, A. Bonnanni, and S. Stifter, "Influence of anisotropic in-plane strain on critical point resonances in reflectance difference date," J. Vac. Sci. Technol. B 19, 1650-1657 (2001).
[CrossRef]

Strauch, K.

J. T. Benhlal, K. Strauch, R. Granger, and R. Triboulet, "Temperature dependence of the dielectric function and of the parameters of critical point transitions of CdTe," Opt. Mater. 12, 143-156 (1999).
[CrossRef]

Suzuki, N.

S. Adachi, T. Kimura, and N. Suzuki, "Optical properties of CdTe: experiment and modeling," J. Appl. Phys. 74, 3435-3541 (1993).
[CrossRef]

Tennant, W. E.

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

Theeten, J. B.

D. A. Aspnes, J. B. Theeten, and F. Hottier, "Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry," Phys. Rev. B 20, 3292-3302 (1979).
[CrossRef]

Theret, G.

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

Triboulet, R.

J. T. Benhlal, K. Strauch, R. Granger, and R. Triboulet, "Temperature dependence of the dielectric function and of the parameters of critical point transitions of CdTe," Opt. Mater. 12, 143-156 (1999).
[CrossRef]

Umbach, C.

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]

Viña, L.

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]

Violet, A.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
[CrossRef]

Vodopyanov, L.

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]

Zanatta, J. P.

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

Zanatta, J.-P.

P. Ballet, X. Baudry, J.-P. Zanatta, and A. Million, "In situ real time analysis of the MBE growth of CdTe on Ge: a comparison of data analysis techniques," J. Cryst. Growth, submitted for publication.

Zandian, M.

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

Anal. Chem. (2)

P. Barak, "Smoothing and differentiation by an adaptive-degree polynomial filter," Anal. Chem. 67, 2758-2762 (1995).
[CrossRef]

P. A. Gorry, "General least-squares smoothing and differentiation by the convolution by the convolution (Savitzky-Golay) method," Anal. Chem. 62, 570-573 (1990).
[CrossRef]

Appl. Opt. (2)

Appl. Surf. Sci. (1)

W. M. Duncan and S. Henck, "In situ spectra ellipsometry for real-time measurement and control," Appl. Surf. Sci. 63, 1179-1185 (1993).
[CrossRef]

Eur. Phys. J. B (1)

O. Castaing, J. T. Benhlal, and R. Granger, "An attempt to model the dielectric function in II-VI ternary compounds Hg1−xZnxTe and Cd1−xZnxTe," Eur. Phys. J. B 7, 563-572 (1999). These authors give a different expression for the JDS in that they add up separately each contribution arising from any given pair of (c) and (v) bands. However, many contributions overlap: WE0—>E1(E) and WE0—>E2(E) overlap between E1 and E2. Hence, although this implementation is correct in principle, it causes substantial parameter correlation.
[CrossRef]

Infrared Phys. Technol. (1)

A. Rogalski, "Comparison of the performance of quantum well and conventional bulk infrared photodetectors," Infrared Phys. Technol. 38, 295 (1997).
[CrossRef]

J. Appl. Phys. (2)

C. Kim and S. Sivananthan, "Modeling the optical dielectric function of II-VI compound CdTe," J. Appl. Phys. 78, 4003-4010 (1995).
[CrossRef]

S. Adachi, T. Kimura, and N. Suzuki, "Optical properties of CdTe: experiment and modeling," J. Appl. Phys. 74, 3435-3541 (1993).
[CrossRef]

J. Cryst. Growth (2)

J. P. Zanatta, P. Ferret, P. Duvaut, S. Isselin, G. Theret, G. Rolland, and A. Million, "Heteroepitaxy of CdTe on Ge(211) substrates by molecular beam epitaxy," J. Cryst. Growth 185, 1297-1301 (1998).

A. Million, N. K. Dhar, and J. H. Dinan, "Heteroepitaxy of CdTe on {211}Si substrates by molecular beam epitaxy," J. Cryst. Growth 159, 76-80 (1996).
[CrossRef]

J. Vac. Sci. Technol. A (1)

H. Arwin and D. E. Aspnes, "Nondestructive analysis of HgCdTe (x=0.00, 0.20, 0.29, and 1.00) by spectroscopic ellipsometry. II. Substrate, oxide, and interface properties," J. Vac. Sci. Technol. A 2, 1316-1323 (1984).
[CrossRef]

J. Vac. Sci. Technol. B (1)

For the effect of strain on the critical points of CdTe, see K. Hingerl, R. E. Bladeras-Navarro, A. Bonnanni, and S. Stifter, "Influence of anisotropic in-plane strain on critical point resonances in reflectance difference date," J. Vac. Sci. Technol. B 19, 1650-1657 (2001).
[CrossRef]

Opt. Mater. (1)

J. T. Benhlal, K. Strauch, R. Granger, and R. Triboulet, "Temperature dependence of the dielectric function and of the parameters of critical point transitions of CdTe," Opt. Mater. 12, 143-156 (1999).
[CrossRef]

Phys. Lett. A (1)

L. Mantese, K. A. Bell, D. E. Aspnes, and U. Rossow, "Photon-induced localization in optically absorbing materials," Phys. Lett. A 253, 93-97 (1999).
[CrossRef]

Phys. Rev. (1)

H. Ehrenreich and M. H. Cohen, "Self-consistent field approach to the many-electron problem," Phys. Rev. 115, 786-790 (1959).
[CrossRef]

Phys. Rev. B (4)

D. A. Aspnes, J. B. Theeten, and F. Hottier, "Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry," Phys. Rev. B 20, 3292-3302 (1979).
[CrossRef]

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]

C. C. Kim, M. Daraselia, J. W. Garland, and S. Sivananthan, "Temperature dependence of the optical properties of CdTe," Phys. Rev. B 56, 4768-4797 (1997).

C. Kim, J. Garland, H. Abad, and P. M. Raccah. "Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation," Phys. Rev. B 45, 11749-11767 (1992).
[CrossRef]

Phys. Status Solidi A (1)

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Many-body and correlation effects in surface and interface spectra of optically absorbing materials," Phys. Status Solidi A 170, 199-210 (1998).
[CrossRef]

Phys. Status Solidi B (1)

D. E. Aspnes, L. Mantese, K. A. Bell, and U. Rossow, "Coherence effects and time dependences of the optical response of surface and interfaces of optically absorbing material," Phys. Status Solidi B 220, 709-715 (2000).
[CrossRef]

Proc. SPIE (3)

M. Arias, J. G. Pasko, M. Zandian, J. Bajaj, L. J. Kozlowski, R. E. Dewames, and W. E. Tennant, "Molecular beam epitaxy (MBE) HgCdTe flexible growth technology for the manufacturing of infrared photovoltaic detectors," in Producibility of II-VI Materials and Devices, H. K. Pollehn and R. S. Balcerak, eds., Proc. SPIE 2228, 210-224 (1994).
[CrossRef]

S. M. F. Nee, "The effects of incoherent scattering on ellipsometry," in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 119-127 (1992).
[CrossRef]

S. M. F. Nee, "Effects of near-specular scattering a polarimetry," in Polarization Analysis and Measurement II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 2265, 304-313 (1994), and references contained therein.
[CrossRef]

Rev. Sci. Instrum. (3)

J. Lee, J. Koh, and R. W. Collins, "Dual rotating-compensator multichannel ellipsometer: instrument development for high-speed Mueller matrix spectroscopy of surfaces and thin films," Rev. Sci. Instrum. 72, 1742-1754 (2001), and references cited therein.
[CrossRef]

B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, "Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis," Rev. Sci. Instrum. 53, 969-977 (1982).
[CrossRef]

C. C. Kim, P. M. Raccah, and J. W. Garland, "The improvement of phase modulated spectroscopic ellipsomerty," Rev. Sci. Instrum. 63, 2958-2966 (1992).
[CrossRef]

Thin Solid Films (1)

T. Mori and D. E. Aspnes, "Comparison of the capabilities of rotating-analyzer and rotating-compensator ellipsometers by measurements on a single system," Thin Solid Films 455-456, 33-38 (2004).
[CrossRef]

Other (3)

G. Badano, A. Million, P. Ballet, and A. Etcheberry, "Fast detection of precipitates and oxides on CdZnTe surfaces by the spectroscopic ellipsometry," J. Electron. Mater., submitted for publication.

P. Ballet, X. Baudry, J.-P. Zanatta, and A. Million, "In situ real time analysis of the MBE growth of CdTe on Ge: a comparison of data analysis techniques," J. Cryst. Growth, submitted for publication.

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of the JDS used for the CP model. It is divided into four zones, separated by discontinuities.

Fig. 2
Fig. 2

Simultaneous fit to ε ( ω ) and its second derivative. (a) Plot of the real part of ε ( ω ) (squares) and its imaginary part (empty circles). (b) The imaginary part of the numerically calculated second derivatives of ε ( ω ) and (c) the teal part. The solid curves are the fits obtained as explained in the text.

Fig. 3
Fig. 3

JDS multiplied by 8 π 2 e 2 m 2 as deduced from a fit to sample 24350. The dotted curve indicates the uncertainty (standard deviation) in the average JDS obtained from a simultaneous fit to all the samples analyzed in this paper. Both the shape of the JDS and the sign of the discontinuity at E 1 are similar to what was found in Ref. [21].

Fig. 4
Fig. 4

Results of a fit to Δ s ( ω ) = ε 2 ( ω ) ( N ) ε 2 ( ω ) M . The real part (squares) and imaginary part (dots) of Δ s are shown. The solid and the dashed curves represent the fits obtained, leaving a total of six parameters free to vary and imposing Ψ s = Ψ .

Fig. 5
Fig. 5

Values of the u cos ( Ψ s ) parameter of each sample obtained from the fits to Δ s ( ω ) = ε 2 ( ω ) ( N ) ε 2 ( ω ) M , obtained, leaving six parameters vary. In the fits, we took Ψ s Ψ .

Tables (5)

Tables Icon

Table 1 Thickness (in Micrometers) and FHM of the x-Ray Rocking Curve and its Spreading across the Wafer, for the Layers Used for This Study a

Tables Icon

Table 2 Values of the CP Energies E i (in Electron Volts), Linewidths Γ i (in Mega-Electron-Volts), and Thickness of the Oxide Layer t (in Angstroms) Determined by a Fit to ε 2 ( ω ) and Its Second Derivative a

Tables Icon

Table 3 Average Values of the p and q Polynomial Coefficients Obtained from a Simultaneous Fit of L 2 ( ω ) and Its Second Derivative to All the 15 Spectra Measured, Which Are Multiplied by 8 π 2 e 2 m 2

Tables Icon

Table 4 Values of the CP Energies E i and Linewidths Γ i (given in Electron Volts) Found in the Literature a

Tables Icon

Table 5 Results of the Fits to the Difference Spectra Δ s ( ω ) = ε 2 ( ω ) ( N ) ε 2 ( ω ) M , Showing the Thickness of the Oxide Layer t, the Shifts in the CP Energies, the Changes in Linewidths, and the Three Parameters That Describe the Presence of Near-Specular Scattering and Cross Polarization a

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ε ( ω ) = 1 + 8 π 2 e 2 m 2 c , v W c v ( E ) d E { [ Φ ( ω E ) Φ ( ω + E ) ] } .
J c v ( ω ) = BZ δ [ E c ( k ) E v ( k ) ω ] d k
L ( E ) = 1 8 π 2 e 2 m 2 n [ ( p n H n q n F n ) ] I + ( p n H n ) I + ( p n G n q n K n ) I I + ( p n G n q n K n ) I I I + ( p n G n q n H n ) I V + ε 1 ,
χ 2 , n 2 = 1 N j [ ε 2 ( n ) ( ω j ) L 2 ( n ) ( ω j ) σ 2 ( n ) ( ω j ) ] 2 .
R = exp ( g ) [ R e + B R 0 ξ ( g ) ] ,
tan ( Δ Δ ) = u ζ sin ( Δ s Δ ) [ sin 2 Ψ + u ζ cos ( Δ s Δ ) ] ,
sin 2 ( Ψ Ψ ) u ζ cos 2 Ψ [ sin 2 Ψ cos ( Δ s Δ ) + u ζ ] sin 2 Ψ + u ζ u sin 2 Ψ cos 2 Ψ s ,
χ 2 = 1 N j [ D s ( ω j ) Δ s ( ω j ) σ s ( ω j ) ] 2 ,

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