Abstract

Nonuniformity in the thickness of thin films can severely distort their transmission spectra as compared with those of flat, smooth films. Methods that extract properties such as refractive index, thickness, and extinction coefficient of such films can suffer inaccuracies when they are applied to wedged or nonuniformly thick films. To accurately extract optical properties of nonuniform films, we have developed a novel numerical method and efficient constitutive relations that can determine film properties from just the transmission spectrum for films that are locally smooth with negligible scattering loss. This optimum parameter extraction (OPE) method can accommodate films with two-dimensional thickness variation that would result in significant errors in the values of refractive index and film thickness if not considered. We show that for carefully chosen test cases and for actual pulsed-laser-deposition AlN thin films, properties such as refractive index, extinction coefficient, and film thickness were very accurately determined by using our OPE method. These results are compared with previous techniques to determine the properties of thin films, and the accuracy of and applicable conditions for all these methods are discussed.

© 2006 Optical Society of America

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  1. R. J. Swanepoel, 'Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,' Sci. Instrum. 17, 896-903 (1984).
    [CrossRef]
  2. R. J. Swanepoel, 'Determination of the thickness and optical constants of amorphous silicon,' Sci. Instrum. 16, 1214-1222 (1983).
    [CrossRef]
  3. D. E. Aspnes, 'The accurate determination of optical properties by ellipsometry,' in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 89.
  4. E. A. Irene, 'Applications of spectroscopic ellipsometry to microelectronics,' Thin Solid Films 233, 96-111 (1993).
    [CrossRef]
  5. R. Petrich and O. Stenzel, 'Modeling of transmittance, reflectance and scattering of rough polycrystalline CVD diamond layers in application to the determination of optical constants,' Opt. Mater. 3, 65-76 (1994).
    [CrossRef]
  6. E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
    [CrossRef]
  7. E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
    [CrossRef]
  8. In the literature cited on envelope methods for extracting thin-film parameters, this quantity is often referred to as absorbance. We do not use this terminology here in order to be consistent with more widely used optics terminology and to avoid possible confusion.
  9. J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
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  10. TFCalc, Software Spectra Inc., Portland, Oregon, www.sspectra.com.
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  13. B. Titan, 'Fitting refractive-index data with the Sellmeier dispersion formula,' Appl. Opt. 23, 4477-4485 (1984).
  14. A. R. Forouhi and I. Bloomer, 'Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,' Phys. Rev. B 34, 7018-7026 (1986).
    [CrossRef]
  15. N. W. Ashcroft and N. D. Mermin, 'The Drude theory of metals,' in Solid State Physics (Saunders, 1976), p. 16.
  16. S. Cabuk and A. Mamedov, 'Urbach rule and optical properties of LiNbO3 and LiTaO3,' J. Opt. A 1, 424-427 (1999).
  17. C. Rincon, S. M. Wasim, and G. Marin, 'Effect of donor-acceptor defect pairs on the electrical and optical properties of CuIn3Te5,' J. Phys. Condens. Matter 14, 997-1009 (2002).
    [CrossRef]
  18. D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
    [CrossRef]
  19. J. I. Pankove, Optical Process in Semiconductors (Prentice-Hall, 1971), Chap. 3.
  20. R. Fletcher and M. J. D. Powell, 'A rapidly convergent descent method for minimization,' Computer J. 6, 163-168 (1963).
  21. D. Goldfarb, 'A family of variable metric updates derived by variational means,' Math. Comput. 24, 23-26 (1970).
  22. E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
    [CrossRef]
  23. J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
    [CrossRef]
  24. E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
    [CrossRef]
  25. E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
    [CrossRef]
  26. M. McClain, A. Feldman, D. Kahaner, and X. Ying, 'An algorithm and computer program for the calculation of envelope curves,' Comput. Phys. 5, 45-48 (1991).
    [CrossRef]
  27. Filmetrics Inc., San Diego, California, www.filmetrics.com.
  28. R. D. Vispute, J. Narayan, H. Wu, and K. Jangannadham, 'Epitaxial growth of AlN thin films on silicon (111) substrates by pulsed laser deposition,' J. Appl. Phys. 77, 4724-4728 (1995).
    [CrossRef]

2004 (1)

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

2002 (1)

C. Rincon, S. M. Wasim, and G. Marin, 'Effect of donor-acceptor defect pairs on the electrical and optical properties of CuIn3Te5,' J. Phys. Condens. Matter 14, 997-1009 (2002).
[CrossRef]

1999 (2)

S. Cabuk and A. Mamedov, 'Urbach rule and optical properties of LiNbO3 and LiTaO3,' J. Opt. A 1, 424-427 (1999).

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

1997 (2)

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
[CrossRef]

1996 (1)

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

1995 (2)

E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
[CrossRef]

R. D. Vispute, J. Narayan, H. Wu, and K. Jangannadham, 'Epitaxial growth of AlN thin films on silicon (111) substrates by pulsed laser deposition,' J. Appl. Phys. 77, 4724-4728 (1995).
[CrossRef]

1994 (1)

R. Petrich and O. Stenzel, 'Modeling of transmittance, reflectance and scattering of rough polycrystalline CVD diamond layers in application to the determination of optical constants,' Opt. Mater. 3, 65-76 (1994).
[CrossRef]

1993 (3)

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

E. A. Irene, 'Applications of spectroscopic ellipsometry to microelectronics,' Thin Solid Films 233, 96-111 (1993).
[CrossRef]

1991 (1)

M. McClain, A. Feldman, D. Kahaner, and X. Ying, 'An algorithm and computer program for the calculation of envelope curves,' Comput. Phys. 5, 45-48 (1991).
[CrossRef]

1986 (1)

A. R. Forouhi and I. Bloomer, 'Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,' Phys. Rev. B 34, 7018-7026 (1986).
[CrossRef]

1984 (2)

B. Titan, 'Fitting refractive-index data with the Sellmeier dispersion formula,' Appl. Opt. 23, 4477-4485 (1984).

R. J. Swanepoel, 'Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,' Sci. Instrum. 17, 896-903 (1984).
[CrossRef]

1983 (1)

R. J. Swanepoel, 'Determination of the thickness and optical constants of amorphous silicon,' Sci. Instrum. 16, 1214-1222 (1983).
[CrossRef]

1970 (1)

D. Goldfarb, 'A family of variable metric updates derived by variational means,' Math. Comput. 24, 23-26 (1970).

1963 (1)

R. Fletcher and M. J. D. Powell, 'A rapidly convergent descent method for minimization,' Computer J. 6, 163-168 (1963).

Amvacher, O.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Angerer, H.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, 'The Drude theory of metals,' in Solid State Physics (Saunders, 1976), p. 16.

Aspnes, D. E.

D. E. Aspnes, 'The accurate determination of optical properties by ellipsometry,' in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 89.

Bernal-Oliva, A. M.

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

Bloomer, I.

A. R. Forouhi and I. Bloomer, 'Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,' Phys. Rev. B 34, 7018-7026 (1986).
[CrossRef]

Brunner, D.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Bustarret, E.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Cabuk, S.

S. Cabuk and A. Mamedov, 'Urbach rule and optical properties of LiNbO3 and LiTaO3,' J. Opt. A 1, 424-427 (1999).

Corrales, C.

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

Dimitrov, R.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Elliott, S. R.

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

Ewen, P. J. S.

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

Ewen, P. J.S.

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

Feldman, A.

M. McClain, A. Feldman, D. Kahaner, and X. Ying, 'An algorithm and computer program for the calculation of envelope curves,' Comput. Phys. 5, 45-48 (1991).
[CrossRef]

Fernandez-Pena, J.

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

Fletcher, R.

R. Fletcher and M. J. D. Powell, 'A rapidly convergent descent method for minimization,' Computer J. 6, 163-168 (1963).

Forouhi, A. R.

A. R. Forouhi and I. Bloomer, 'Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,' Phys. Rev. B 34, 7018-7026 (1986).
[CrossRef]

Freudenberg, F.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Goldfarb, D.

D. Goldfarb, 'A family of variable metric updates derived by variational means,' Math. Comput. 24, 23-26 (1970).

Gonzalez-Leal, J. M.

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
[CrossRef]

Hopler, R.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Irene, E. A.

E. A. Irene, 'Applications of spectroscopic ellipsometry to microelectronics,' Thin Solid Films 233, 96-111 (1993).
[CrossRef]

Jangannadham, K.

R. D. Vispute, J. Narayan, H. Wu, and K. Jangannadham, 'Epitaxial growth of AlN thin films on silicon (111) substrates by pulsed laser deposition,' J. Appl. Phys. 77, 4724-4728 (1995).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1981), pp. 482-486.

Jimenez-Garay, R.

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
[CrossRef]

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

Kahaner, D.

M. McClain, A. Feldman, D. Kahaner, and X. Ying, 'An algorithm and computer program for the calculation of envelope curves,' Comput. Phys. 5, 45-48 (1991).
[CrossRef]

Ledesma, A.

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

Lukic, S. R.

E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
[CrossRef]

Mamedov, A.

S. Cabuk and A. Mamedov, 'Urbach rule and optical properties of LiNbO3 and LiTaO3,' J. Opt. A 1, 424-427 (1999).

Marin, G.

C. Rincon, S. M. Wasim, and G. Marin, 'Effect of donor-acceptor defect pairs on the electrical and optical properties of CuIn3Te5,' J. Phys. Condens. Matter 14, 997-1009 (2002).
[CrossRef]

Marquez, E.

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
[CrossRef]

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

Martil, I.

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

McClain, M.

M. McClain, A. Feldman, D. Kahaner, and X. Ying, 'An algorithm and computer program for the calculation of envelope curves,' Comput. Phys. 5, 45-48 (1991).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, 'The Drude theory of metals,' in Solid State Physics (Saunders, 1976), p. 16.

Narayan, J.

R. D. Vispute, J. Narayan, H. Wu, and K. Jangannadham, 'Epitaxial growth of AlN thin films on silicon (111) substrates by pulsed laser deposition,' J. Appl. Phys. 77, 4724-4728 (1995).
[CrossRef]

Owen, A. E.

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

Pankove, J. I.

J. I. Pankove, Optical Process in Semiconductors (Prentice-Hall, 1971), Chap. 3.

Perovic, D. M.

E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
[CrossRef]

Petrich, R.

R. Petrich and O. Stenzel, 'Modeling of transmittance, reflectance and scattering of rough polycrystalline CVD diamond layers in application to the determination of optical constants,' Opt. Mater. 3, 65-76 (1994).
[CrossRef]

Powell, M. J. D.

R. Fletcher and M. J. D. Powell, 'A rapidly convergent descent method for minimization,' Computer J. 6, 163-168 (1963).

Prieto-Alcon, R.

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

Ramirez-Malo, J. B.

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

Reyes, J.

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

Rincon, C.

C. Rincon, S. M. Wasim, and G. Marin, 'Effect of donor-acceptor defect pairs on the electrical and optical properties of CuIn3Te5,' J. Phys. Condens. Matter 14, 997-1009 (2002).
[CrossRef]

Stenzel, O.

R. Petrich and O. Stenzel, 'Modeling of transmittance, reflectance and scattering of rough polycrystalline CVD diamond layers in application to the determination of optical constants,' Opt. Mater. 3, 65-76 (1994).
[CrossRef]

Stuchlik, M.

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

Stutzmann, M.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

Swanepoel, R.

E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
[CrossRef]

Swanepoel, R. J.

R. J. Swanepoel, 'Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,' Sci. Instrum. 17, 896-903 (1984).
[CrossRef]

R. J. Swanepoel, 'Determination of the thickness and optical constants of amorphous silicon,' Sci. Instrum. 16, 1214-1222 (1983).
[CrossRef]

Titan, B.

Villares, P.

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

Vispute, R. D.

R. D. Vispute, J. Narayan, H. Wu, and K. Jangannadham, 'Epitaxial growth of AlN thin films on silicon (111) substrates by pulsed laser deposition,' J. Appl. Phys. 77, 4724-4728 (1995).
[CrossRef]

Vlcek, M.

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

Wasim, S. M.

C. Rincon, S. M. Wasim, and G. Marin, 'Effect of donor-acceptor defect pairs on the electrical and optical properties of CuIn3Te5,' J. Phys. Condens. Matter 14, 997-1009 (2002).
[CrossRef]

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1981), pp. 482-486.

Wu, H.

R. D. Vispute, J. Narayan, H. Wu, and K. Jangannadham, 'Epitaxial growth of AlN thin films on silicon (111) substrates by pulsed laser deposition,' J. Appl. Phys. 77, 4724-4728 (1995).
[CrossRef]

Ying, X.

M. McClain, A. Feldman, D. Kahaner, and X. Ying, 'An algorithm and computer program for the calculation of envelope curves,' Comput. Phys. 5, 45-48 (1991).
[CrossRef]

Appl. Opt. (1)

Comput. Phys. (1)

M. McClain, A. Feldman, D. Kahaner, and X. Ying, 'An algorithm and computer program for the calculation of envelope curves,' Comput. Phys. 5, 45-48 (1991).
[CrossRef]

Computer J. (1)

R. Fletcher and M. J. D. Powell, 'A rapidly convergent descent method for minimization,' Computer J. 6, 163-168 (1963).

J. Appl. Phys. (2)

R. D. Vispute, J. Narayan, H. Wu, and K. Jangannadham, 'Epitaxial growth of AlN thin films on silicon (111) substrates by pulsed laser deposition,' J. Appl. Phys. 77, 4724-4728 (1995).
[CrossRef]

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Amvacher, and M. Stutzmann, 'Optical constants of epitaxial AlGaN films and their temperature dependence,' J. Appl. Phys. 82, 5090-5096 (1997).
[CrossRef]

J. Non-Cryst. Solids (1)

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J.S. Ewen, and A. E. Owen, 'On the influence of Ag-photodoping on the optical properties of As-S glass films,' J. Non-Cryst. Solids 164-166, 1223-1226 (1993).
[CrossRef]

J. Opt. A (1)

S. Cabuk and A. Mamedov, 'Urbach rule and optical properties of LiNbO3 and LiTaO3,' J. Opt. A 1, 424-427 (1999).

J. Phys. Condens. Matter (1)

C. Rincon, S. M. Wasim, and G. Marin, 'Effect of donor-acceptor defect pairs on the electrical and optical properties of CuIn3Te5,' J. Phys. Condens. Matter 14, 997-1009 (2002).
[CrossRef]

J. Phys. D (1)

E. Marquez, J. M. Gonzalez-Leal, R. Jimenez-Garay, S. R. Lukic, and D. M. Perovic, 'Refractive-index dispersion and the optical-absorption edge of wedge-shaped thin films of CuxAs50Se50-x metal-chalcogenide glasses,' J. Phys. D 30, 690-702 (1997).
[CrossRef]

Mater. Chem. Phys. (2)

E. Marquez, A. M. Bernal-Oliva, J. M. Gonzalez-Leal, R. Prieto-Alcon, A. Ledesma, R. Jimenez-Garay, and I. Martil, 'Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1-1.8 eV),' Mater. Chem. Phys. 60, 231-239 (1999).
[CrossRef]

J. B. Ramirez-Malo, E. Marquez, C. Corrales, J. Fernandez-Pena, J. Reyes, P. Villares, and R. Jimenez-Garay, 'A new study of the refractive-index dispersion of Ag-photodoped thin films of As30S70 chalcogenide glass,' Mater. Chem. Phys. 44, 186-189 (1996).
[CrossRef]

Math. Comput. (1)

D. Goldfarb, 'A family of variable metric updates derived by variational means,' Math. Comput. 24, 23-26 (1970).

Opt. Mater. (3)

E. Marquez, J. B. Ramirez-Malo, J. Fernandez-Pena, P. Villares, R. Jimenez-Garay, P. J. S. Ewen, and A. E. Owen, 'On the optical properties of wedge-shaped thin films of silver-photodoped arsenic-sulfur As30S70 glass,' Opt. Mater. 2, 143-150 (1993).
[CrossRef]

R. Petrich and O. Stenzel, 'Modeling of transmittance, reflectance and scattering of rough polycrystalline CVD diamond layers in application to the determination of optical constants,' Opt. Mater. 3, 65-76 (1994).
[CrossRef]

J. M. Gonzalez-Leal, R. Prieto-Alcon, M. Stuchlik, M. Vlcek, S. R. Elliott, and E. Marquez, 'Determination of the surface roughness and refractive index of amorphous As40S60 films deposited by spin coating,' Opt. Mater. 27, 147-154 (2004).
[CrossRef]

Phys. Rev. B (1)

A. R. Forouhi and I. Bloomer, 'Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,' Phys. Rev. B 34, 7018-7026 (1986).
[CrossRef]

Sci. Instrum. (2)

R. J. Swanepoel, 'Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,' Sci. Instrum. 17, 896-903 (1984).
[CrossRef]

R. J. Swanepoel, 'Determination of the thickness and optical constants of amorphous silicon,' Sci. Instrum. 16, 1214-1222 (1983).
[CrossRef]

Thin Solid Films (2)

E. A. Irene, 'Applications of spectroscopic ellipsometry to microelectronics,' Thin Solid Films 233, 96-111 (1993).
[CrossRef]

E. Marquez, J. B. Ramirez-Malo, P. Villares, R. Jimenez-Garay, and R. Swanepoel, 'Optical characterization of wedge-shaped thin films of amorphous arsenic tri-sulfide based only on their shrunk transmission spectra,' Thin Solid Films 254, 83-91 (1995).
[CrossRef]

Other (8)

Filmetrics Inc., San Diego, California, www.filmetrics.com.

D. E. Aspnes, 'The accurate determination of optical properties by ellipsometry,' in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), p. 89.

TFCalc, Software Spectra Inc., Portland, Oregon, www.sspectra.com.

Film Wizard, Scientific Computing Inc., Encinitas, California, www.sci-soft.com.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1981), pp. 482-486.

N. W. Ashcroft and N. D. Mermin, 'The Drude theory of metals,' in Solid State Physics (Saunders, 1976), p. 16.

In the literature cited on envelope methods for extracting thin-film parameters, this quantity is often referred to as absorbance. We do not use this terminology here in order to be consistent with more widely used optics terminology and to avoid possible confusion.

J. I. Pankove, Optical Process in Semiconductors (Prentice-Hall, 1971), Chap. 3.

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Figures (8)

Fig. 1
Fig. 1

(a) Absorbing thin film with a variation in thickness on a thick, finite transparent substrate; (b) triangular surface irregularities; (c) rectangular surface irregularities; (d) sinusoidal surface irregularities.

Fig. 2
Fig. 2

Plot of the error of thickness, , and nonuniformity, Δd, versus the film transmittance [χ = exp(−αd)] at 633 nm, using the wedge-shaped envelope method. The simulated film had a thickness of 2000 nm and Δd = 40 nm. The dotted lines are a guide for the eye.

Fig. 3
Fig. 3

(a) Simulated transmission spectra for an absorbing film with uniform thickness and perfect smoothness compared with films with Tdx = 40), Tdx = 40, Δdy = 20), and Tdx = 40, Δdy = 20, Δrx = 10). At this scale Tdx = 40), Tdx = 40, Δdy = 20), and Tdx = 40, Δdy = 20, Δrx = 10) are indistinguishable from one another. (b) Magnified section of (a) over the wavelength range 355–375 nm.

Fig. 4
Fig. 4

Diagram of the UHV system used for AlN film deposition with PLD.

Fig. 5
Fig. 5

Optical properties of an AlN film deposited at high fluence and at a 500 °C substrate temperature: (a) transmittance, (b) refractive index, (c) extinction coefficient. Notation in the legends: exp, experimental measurement; fitted, the OPE method; wedge, wedge-shaped envelope method; convention, conventional envelope method.

Fig. 6
Fig. 6

Optical properties of an AlN film deposited at low fluence and at a 300 °C substrate temperature: (a) transmittance, (b) refractive index, (c) extinction coefficient. Notation in the legends: exp, experimental measurement; fitted, the OPE method; wedge, wedge-shaped envelope method; convention, conventional envelope method.

Fig. 7
Fig. 7

Representative cross-section SEM micrograph of an AlN film deposited at high fluence and at a 100 °C substrate temperature.

Fig. 8
Fig. 8

Thickness profile along the optical spectrometer slit axis of a fractured AlN film deposited at high fluence and at a 100 °C substrate temperature. The inset shows the profile in the region of the 4 mm long spectrometer aperture centered at 40.4 mm as well as the linear regression fit to that data.

Tables (3)

Tables Icon

Table 1 Error (%) for the Index of Refraction, n, Thickness, d̄, and Nonuniformity, Δd, Due to the Nonzero Extinction Coefficient Determined for Simulated Spectra by Using the Wedge-Shaped Envelope Method a

Tables Icon

Table 2 Optical Parameters and Error Determined by Using the OPE Method for Simulated Spectra Considering only 1-D Thickness Nonuniformity a

Tables Icon

Table 3 Properties of AlN Films Analyzed by the OPE Method (and by the Wedge-Shaped Method and Conventional Method for Selected Cases) a

Equations (11)

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

T = A χ B C χ + D χ 2 ,
A = 16 s ( n 2 + k 2 ) , B = [ ( n + 1 ) 2 + k 2 ] [ ( n + 1 ) ( n + s 2 ) + k 2 ] , C = [ ( n 2 1 + k 2 ) ( n 2 s 2 + k 2 ) 2 k 2 ( s 2 + 1 ) ] 2   cos   ϕ k [ 2 ( n 2 s 2 + k 2 ) + ( s 2 + 1 ) ( n 2 1 + k 2 ) ] 2   sin   ϕ , D = [ ( n 1 ) 2 + k 2 ] [ ( n 1 ) ( n s 2 ) + k 2 ] , ϕ = 4 π n d / λ , χ = exp ( α d ) , α = 4 π k / λ .
d = d ¯ + β Δ d ,
β = 2 x / L ( 1 β 1 ) .
T Δ d = 1 ϕ 2 ϕ 1 ϕ 1 ϕ 2 A χ B C χ + D χ 2  d ϕ ,
T Δ d = 1 2 1 1 A χ B C χ + D χ 2  d β ,
d = d ¯ + β Δ d x + γ Δ d y + δ Δ r x + ε Δ r y ,
T Δ d = 1 2 1 2 1 2 1 2 × - 1 1 1 1 1 1 1 1 A χ B C χ + D χ 2  d β d γ d δ d ε .
n ( λ ) = p [ n r e f ( λ ) 1 ] + 1 ,
k ( λ ) = A exp ( B / λ ) ,
Cost = { 1 m j = 1 m [ ( T ex , j T fit, j ) W j ] 2 } 1 / 2 ,

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