Abstract

Optical and electron-energy-loss data for evaporated-aluminum films have been critically analyzed and used in an iterative, self-consistent algorithm that represents a combination of the Kramers–Kronig analysis and the semiquantum-model application. The novel values of the intrinsic optical functions of aluminum have been determined in a wide spectral range from 200 μm (6.2 meV) to 0.12 nm (10 keV). These functions are in accordance with recent calculations by Lee and Chang [Phys. Rev. B 49, 2362 (1994)], with dc conductivity measurements, and are in good agreement with both peak positions and line widths obtained from electron-energy-loss experiments. The results are examined for internal consistency by inertial and f-sum rules.

© 1995 Optical Society of America

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1994 (1)

K.-H. Lee, K. J. Chang, “First-principles study of the optical properties and the dielectric response of Al,” Phys. Rev. B 49, 2362–2367 (1994).
[CrossRef]

1993 (2)

H. V. Nguyen, I. An, R. W. Collins, “Evolution of the optical functions of thin-film aluminum: a real time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947–3965 (1993).
[CrossRef]

S. Tanuma, C. J. Powell, D. R. Penn, “Use of sum rules on the energy-loss function for the evaluation of experimental optical data,” J. Electron Spectrosc. Relat. Phenom. 62, 95–109 (1993).
[CrossRef]

1991 (1)

1990 (2)

M. I. Marković, A. D. Rakić, “Determination of the reflection coefficients of laser light of wavelengths λ ∊ (0.22 μm, 200 μm) from the surface of aluminum using the Lorentz-Drude model,” Appl. Opt. 29, 3479–3483 (1990).
[CrossRef]

M. I. Marković, A. D. Rakić, “Determination of optical properties of aluminium including electron reradiation in the Lorentz–Drude model,” Opt. Laser Technol. 22, 394–398 (1990).
[CrossRef]

1988 (4)

1987 (1)

1986 (1)

D. Y. Smith, B. Segal, “Intraband and interband processes in the infrared spectrum of metallic aluminum,” Phys. Rev. B 34, 5191–5198 (1986).
[CrossRef]

1985 (1)

1983 (1)

D. C. Jiles, M. P. Staines, “Piezo optic properties of aluminum,” Solid State Commun. 47, 37–41 (1983).
[CrossRef]

1981 (2)

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminum,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

G. R. Parkins, W. Lawrence, R. W. Christy, “Intraband optical conductivity σ(ω, T) of Cu, Ag, and Au: contribution from electron–electron scattering,” Phys. Rev. B 23, 6408–6415 (1981).
[CrossRef]

1980 (1)

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistency and sum-rule tests in the Kramers–Kronig analysis of optical data: application to aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[CrossRef]

1978 (1)

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B 17, 4689–4694 (1978).
[CrossRef]

1977 (2)

S. P. Singhal, J. Callaway, “Self-consistent energy bands in aluminum—improved calculation,” Phys. Rev. B 16, 1744–1746 (1977).
[CrossRef]

J. A. Nelson, P. J. Bunyan, “Calculation of bandstructure of aluminum using the model potential method,” J. Phys. F 7, 1467–1475 (1977).
[CrossRef]

1976 (1)

F. W. King, “Sum rules for the optical constants,” J. Math. Phys. 17, 1509–1514 (1976).
[CrossRef]

1975 (1)

1974 (3)

K. Sturm, N. W. Ashcroft, “Nonlocal effects in absorption edges: energy-dependent pseudopotentials,” Phys. Rev. B 10, 1343–1349 (1974).
[CrossRef]

A. Balzarotti, A. Bianconi, E. Burattini, “Role of the density of conduction states on the L2-3 absorption spectrum of aluminum,” Phys. Rev. B 9, 5003–5007 (1974).
[CrossRef]

M. Altarelli, D. Y. Smith, “Superconvergence and sum rules for the optical constants: physical meaning, comparison with experiment, and generalization,” Phys. Rev. B 9, 1290–1298 (1974).
[CrossRef]

1972 (1)

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

1971 (3)

J. G. Endriz, W. E. Spicer, “Study of aluminum films I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

N. W. Ashcroft, K. Sturm, “Interband absorption and the optical properties of polyvalent metals,” Phys. Rev. B 3, 1898–1910 (1971).
[CrossRef]

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

1970 (2)

C. J. Powell, “Analysis of optical and inelastic-electron-scattering data. II. Application to Al,” J. Opt. Soc. Am. 60, 78–93 (1970).
[CrossRef]

C. Gahwiller, F. C. Brown, “Photoabsorption near the LII-III edge of silicon and aluminum,” Phys. Rev. B 2, 1918–1925 (1970).
[CrossRef]

1969 (1)

R. Haensel, B. Sontag, C. Kunz, T. Sasaki, “Contribution of the L shell to the total absorption cross section of aluminum,” J. Appl. Phys. 40, 3046–3047 (1969).
[CrossRef]

1966 (3)

A. Daude, M. Priol, S. Robin, “Propriétés optiques dans l’ultraviolet lointain de couches d’aluminium évaporées en ultravide et non exposées à l’air,” C. R. Acad. Sci. Ser. B 263, 1178–1181 (1966).

R. W. Ditchburn, G. H. C. Freeman, “The optical constants of aluminium from 12 to 36 eV,” Proc. R. Soc. London Ser. A 294, 20–37 (1966).
[CrossRef]

W. A. Harrison, “Parallel-band effects in interband optical absorption,” Phys. Rev. 147, 467–469 (1966).
[CrossRef]

1965 (1)

R. N. Gurzhi, M. I. Kaganov, “Vliyanie mezhelektronih stolknovenii na opticheskie svoistva metallov” Zh. Eksp. Teor. Fiz. 49, 941–943, (1965).

1964 (2)

1963 (3)

H. Ehrenreich, H. R. Philipp, B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928 (1963).
[CrossRef]

W. A. Harrison, “Electronic structure and the properties of metals. II. Application to zinc,” Phys. Rev. 129, 2512–2524 (1963).
[CrossRef]

H. E. Bennett, M. Silver, E. J. Ashley, “Infrared reflectance of aluminum in ultrahigh vacuum,” J. Opt. Soc. Am. 53, 1089–1095 (1963).
[CrossRef]

1962 (1)

H. Ehrenreich, H. R. Philipp, “Optical properties of Ag and Cu,” Phys. Rev. 128, 1622–1629 (1962).
[CrossRef]

1961 (1)

1959 (1)

S. Roberts, “Optical properties of nickel and tungsten and their interpretation according to Drude’s formula,” Phys. Rev. 114, 104–115 (1959).
[CrossRef]

1957 (1)

F. C. Jahoda, “Fundamental absorption of barium oxide from its reflectivity spectrum,” Phys. Rev. 107, 1261–1265, 1957.
[CrossRef]

1954 (2)

Alexander, R. W.

Altarelli, M.

M. Altarelli, D. Y. Smith, “Superconvergence and sum rules for the optical constants: physical meaning, comparison with experiment, and generalization,” Phys. Rev. B 9, 1290–1298 (1974).
[CrossRef]

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

An, I.

H. V. Nguyen, I. An, R. W. Collins, “Evolution of the optical functions of thin-film aluminum: a real time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947–3965 (1993).
[CrossRef]

Arendt, P.

Arendt, P. N.

Ashcroft, N. W.

K. Sturm, N. W. Ashcroft, “Nonlocal effects in absorption edges: energy-dependent pseudopotentials,” Phys. Rev. B 10, 1343–1349 (1974).
[CrossRef]

N. W. Ashcroft, K. Sturm, “Interband absorption and the optical properties of polyvalent metals,” Phys. Rev. B 3, 1898–1910 (1971).
[CrossRef]

Ashley, E. J.

Balzarotti, A.

A. Balzarotti, A. Bianconi, E. Burattini, “Role of the density of conduction states on the L2-3 absorption spectrum of aluminum,” Phys. Rev. B 9, 5003–5007 (1974).
[CrossRef]

Beaglehole, D.

D. Beaglehole, “The ultraviolet absorption of the noble metals,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, ed. (North-Holland, Amsterdam, 1966), pp. 154–163.

Bell, R. J.

Bennett, H. E.

H. E. Bennett, M. Silver, E. J. Ashley, “Infrared reflectance of aluminum in ultrahigh vacuum,” J. Opt. Soc. Am. 53, 1089–1095 (1963).
[CrossRef]

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory for silver, gold and aluminum in the infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, ed. (North-Holland, Amsterdam, 1966), pp. 175–189.

Bennett, J. M.

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory for silver, gold and aluminum in the infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, ed. (North-Holland, Amsterdam, 1966), pp. 175–189.

Bianconi, A.

A. Balzarotti, A. Bianconi, E. Burattini, “Role of the density of conduction states on the L2-3 absorption spectrum of aluminum,” Phys. Rev. B 9, 5003–5007 (1974).
[CrossRef]

Blanco, J. R.

Bodó, Z.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Brown, F. C.

C. Gahwiller, F. C. Brown, “Photoabsorption near the LII-III edge of silicon and aluminum,” Phys. Rev. B 2, 1918–1925 (1970).
[CrossRef]

Bunyan, P. J.

J. A. Nelson, P. J. Bunyan, “Calculation of bandstructure of aluminum using the model potential method,” J. Phys. F 7, 1467–1475 (1977).
[CrossRef]

Burattini, E.

A. Balzarotti, A. Bianconi, E. Burattini, “Role of the density of conduction states on the L2-3 absorption spectrum of aluminum,” Phys. Rev. B 9, 5003–5007 (1974).
[CrossRef]

Callaway, J.

S. P. Singhal, J. Callaway, “Self-consistent energy bands in aluminum—improved calculation,” Phys. Rev. B 16, 1744–1746 (1977).
[CrossRef]

Cameron, B. J.

Cash, W. C.

Chang, K. J.

K.-H. Lee, K. J. Chang, “First-principles study of the optical properties and the dielectric response of Al,” Phys. Rev. B 49, 2362–2367 (1994).
[CrossRef]

Christy, R. W.

G. R. Parkins, W. Lawrence, R. W. Christy, “Intraband optical conductivity σ(ω, T) of Cu, Ag, and Au: contribution from electron–electron scattering,” Phys. Rev. B 23, 6408–6415 (1981).
[CrossRef]

Collins, R. W.

H. V. Nguyen, I. An, R. W. Collins, “Evolution of the optical functions of thin-film aluminum: a real time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947–3965 (1993).
[CrossRef]

Daude, A.

A. Daude, M. Priol, S. Robin, “Propriétés optiques dans l’ultraviolet lointain de couches d’aluminium évaporées en ultravide et non exposées à l’air,” C. R. Acad. Sci. Ser. B 263, 1178–1181 (1966).

de Boor, C.

C. de Boor, “cadre: an algorithm for numerical quadrature,” in Mathematical Software, J. R. Rice, ed. (Academic, New York, (1971), Chap. 7.

Dexter, D. L.

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

Ditchburn, R. W.

R. W. Ditchburn, G. H. C. Freeman, “The optical constants of aluminium from 12 to 36 eV,” Proc. R. Soc. London Ser. A 294, 20–37 (1966).
[CrossRef]

Ehrenreich, H.

H. R. Philipp, H. Ehrenreich, “Optical constants in the x-ray range,” J. Appl. Phys. 35, 1416–1419 (1964).
[CrossRef]

H. Ehrenreich, H. R. Philipp, B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928 (1963).
[CrossRef]

H. Ehrenreich, H. R. Philipp, “Optical properties of Ag and Cu,” Phys. Rev. 128, 1622–1629 (1962).
[CrossRef]

Endriz, J. G.

J. G. Endriz, W. E. Spicer, “Study of aluminum films I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

Fisher, R. F.

Freeman, G. H. C.

R. W. Ditchburn, G. H. C. Freeman, “The optical constants of aluminium from 12 to 36 eV,” Proc. R. Soc. London Ser. A 294, 20–37 (1966).
[CrossRef]

Gahwiller, C.

C. Gahwiller, F. C. Brown, “Photoabsorption near the LII-III edge of silicon and aluminum,” Phys. Rev. B 2, 1918–1925 (1970).
[CrossRef]

Gergely, G.

Gudat, W.

Gurzhi, R. N.

R. N. Gurzhi, M. I. Kaganov, “Vliyanie mezhelektronih stolknovenii na opticheskie svoistva metallov” Zh. Eksp. Teor. Fiz. 49, 941–943, (1965).

Haensel, R.

R. Haensel, B. Sontag, C. Kunz, T. Sasaki, “Contribution of the L shell to the total absorption cross section of aluminum,” J. Appl. Phys. 40, 3046–3047 (1969).
[CrossRef]

Hagemann, H. J.

Harrison, W. A.

W. A. Harrison, “Parallel-band effects in interband optical absorption,” Phys. Rev. 147, 467–469 (1966).
[CrossRef]

W. A. Harrison, “Electronic structure and the properties of metals. II. Application to zinc,” Phys. Rev. 129, 2512–2524 (1963).
[CrossRef]

Hass, G.

Hunter, W. R.

Inokuti, M.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistency and sum-rule tests in the Kramers–Kronig analysis of optical data: application to aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[CrossRef]

D. Y. Smith, E. Shiles, M. Inokuti, “The optial properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–408.

Jahoda, F. C.

F. C. Jahoda, “Fundamental absorption of barium oxide from its reflectivity spectrum,” Phys. Rev. 107, 1261–1265, 1957.
[CrossRef]

Jiles, D. C.

D. C. Jiles, M. P. Staines, “Piezo optic properties of aluminum,” Solid State Commun. 47, 37–41 (1983).
[CrossRef]

Kaganov, M. I.

R. N. Gurzhi, M. I. Kaganov, “Vliyanie mezhelektronih stolknovenii na opticheskie svoistva metallov” Zh. Eksp. Teor. Fiz. 49, 941–943, (1965).

King, F. W.

F. W. King, “Sum rules for the optical constants,” J. Math. Phys. 17, 1509–1514 (1976).
[CrossRef]

Kunz, C.

H. J. Hagemann, W. Gudat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” J. Opt. Soc. Am. 65, 742–744 (1975).
[CrossRef]

R. Haensel, B. Sontag, C. Kunz, T. Sasaki, “Contribution of the L shell to the total absorption cross section of aluminum,” J. Appl. Phys. 40, 3046–3047 (1969).
[CrossRef]

Lawrence, W.

G. R. Parkins, W. Lawrence, R. W. Christy, “Intraband optical conductivity σ(ω, T) of Cu, Ag, and Au: contribution from electron–electron scattering,” Phys. Rev. B 23, 6408–6415 (1981).
[CrossRef]

Lee, K.-H.

K.-H. Lee, K. J. Chang, “First-principles study of the optical properties and the dielectric response of Al,” Phys. Rev. B 49, 2362–2367 (1994).
[CrossRef]

Maksimov, E. G.

E. G. Maksimov, I. I. Mazin, S. N. Rashkeev, Y. A. Uspenski, “First principles calculations of the optical properties of metals,” J. Phys. F 18, 833–849 (1988).
[CrossRef]

Markovic, M. I.

M. I. Marković, A. D. Rakić, “Determination of optical properties of aluminium including electron reradiation in the Lorentz–Drude model,” Opt. Laser Technol. 22, 394–398 (1990).
[CrossRef]

M. I. Marković, A. D. Rakić, “Determination of the reflection coefficients of laser light of wavelengths λ ∊ (0.22 μm, 200 μm) from the surface of aluminum using the Lorentz-Drude model,” Appl. Opt. 29, 3479–3483 (1990).
[CrossRef]

Mathewson, A. G.

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

Mazin, I. I.

E. G. Maksimov, I. I. Mazin, S. N. Rashkeev, Y. A. Uspenski, “First principles calculations of the optical properties of metals,” J. Phys. F 18, 833–849 (1988).
[CrossRef]

McMarr, P. J.

Myers, H. P.

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

Nelson, J. A.

J. A. Nelson, P. J. Bunyan, “Calculation of bandstructure of aluminum using the model potential method,” J. Phys. F 7, 1467–1475 (1977).
[CrossRef]

Newnam, B.

Newnam, B. E.

Newquist, L. A.

Nguyen, H. V.

H. V. Nguyen, I. An, R. W. Collins, “Evolution of the optical functions of thin-film aluminum: a real time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947–3965 (1993).
[CrossRef]

Nussenzveig, H. M.

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

Ordal, M. A.

Parkins, G. R.

G. R. Parkins, W. Lawrence, R. W. Christy, “Intraband optical conductivity σ(ω, T) of Cu, Ag, and Au: contribution from electron–electron scattering,” Phys. Rev. B 23, 6408–6415 (1981).
[CrossRef]

Penn, D. R.

S. Tanuma, C. J. Powell, D. R. Penn, “Use of sum rules on the energy-loss function for the evaluation of experimental optical data,” J. Electron Spectrosc. Relat. Phenom. 62, 95–109 (1993).
[CrossRef]

Philipp, H. R.

H. R. Philipp, H. Ehrenreich, “Optical constants in the x-ray range,” J. Appl. Phys. 35, 1416–1419 (1964).
[CrossRef]

H. Ehrenreich, H. R. Philipp, B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928 (1963).
[CrossRef]

H. Ehrenreich, H. R. Philipp, “Optical properties of Ag and Cu,” Phys. Rev. 128, 1622–1629 (1962).
[CrossRef]

Pinneo, J. M.

Powell, C. J.

S. Tanuma, C. J. Powell, D. R. Penn, “Use of sum rules on the energy-loss function for the evaluation of experimental optical data,” J. Electron Spectrosc. Relat. Phenom. 62, 95–109 (1993).
[CrossRef]

C. J. Powell, “Analysis of optical and inelastic-electron-scattering data. II. Application to Al,” J. Opt. Soc. Am. 60, 78–93 (1970).
[CrossRef]

Priol, M.

A. Daude, M. Priol, S. Robin, “Propriétés optiques dans l’ultraviolet lointain de couches d’aluminium évaporées en ultravide et non exposées à l’air,” C. R. Acad. Sci. Ser. B 263, 1178–1181 (1966).

Querry, M. R.

Rakic, A. D.

M. I. Marković, A. D. Rakić, “Determination of the reflection coefficients of laser light of wavelengths λ ∊ (0.22 μm, 200 μm) from the surface of aluminum using the Lorentz-Drude model,” Appl. Opt. 29, 3479–3483 (1990).
[CrossRef]

M. I. Marković, A. D. Rakić, “Determination of optical properties of aluminium including electron reradiation in the Lorentz–Drude model,” Opt. Laser Technol. 22, 394–398 (1990).
[CrossRef]

Rashkeev, S. N.

E. G. Maksimov, I. I. Mazin, S. N. Rashkeev, Y. A. Uspenski, “First principles calculations of the optical properties of metals,” J. Phys. F 18, 833–849 (1988).
[CrossRef]

Roberts, S.

S. Roberts, “Optical properties of nickel and tungsten and their interpretation according to Drude’s formula,” Phys. Rev. 114, 104–115 (1959).
[CrossRef]

Robin, S.

A. Daude, M. Priol, S. Robin, “Propriétés optiques dans l’ultraviolet lointain de couches d’aluminium évaporées en ultravide et non exposées à l’air,” C. R. Acad. Sci. Ser. B 263, 1178–1181 (1966).

Saber, J. M.

Sasaki, T.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistency and sum-rule tests in the Kramers–Kronig analysis of optical data: application to aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[CrossRef]

R. Haensel, B. Sontag, C. Kunz, T. Sasaki, “Contribution of the L shell to the total absorption cross section of aluminum,” J. Appl. Phys. 40, 3046–3047 (1969).
[CrossRef]

Schulz, L. G.

Scott, M.

Scott, M. L.

Segal, B.

D. Y. Smith, B. Segal, “Intraband and interband processes in the infrared spectrum of metallic aluminum,” Phys. Rev. B 34, 5191–5198 (1986).
[CrossRef]

Segall, B.

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminum,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

H. Ehrenreich, H. R. Philipp, B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928 (1963).
[CrossRef]

Shiles, E.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistency and sum-rule tests in the Kramers–Kronig analysis of optical data: application to aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[CrossRef]

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B 17, 4689–4694 (1978).
[CrossRef]

D. Y. Smith, E. Shiles, M. Inokuti, “The optial properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–408.

Silver, M.

Singhal, S. P.

S. P. Singhal, J. Callaway, “Self-consistent energy bands in aluminum—improved calculation,” Phys. Rev. B 16, 1744–1746 (1977).
[CrossRef]

Smith, D. Y.

D. Y. Smith, B. Segal, “Intraband and interband processes in the infrared spectrum of metallic aluminum,” Phys. Rev. B 34, 5191–5198 (1986).
[CrossRef]

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistency and sum-rule tests in the Kramers–Kronig analysis of optical data: application to aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[CrossRef]

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B 17, 4689–4694 (1978).
[CrossRef]

M. Altarelli, D. Y. Smith, “Superconvergence and sum rules for the optical constants: physical meaning, comparison with experiment, and generalization,” Phys. Rev. B 9, 1290–1298 (1974).
[CrossRef]

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

D. Y. Smith, “Dispersion theory, sum rules, and their application to the analysis of optical data,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 35–68.

D. Y. Smith, E. Shiles, M. Inokuti, “The optial properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–408.

Sontag, B.

R. Haensel, B. Sontag, C. Kunz, T. Sasaki, “Contribution of the L shell to the total absorption cross section of aluminum,” J. Appl. Phys. 40, 3046–3047 (1969).
[CrossRef]

Spicer, W. E.

J. G. Endriz, W. E. Spicer, “Study of aluminum films I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

Staines, M. P.

D. C. Jiles, M. P. Staines, “Piezo optic properties of aluminum,” Solid State Commun. 47, 37–41 (1983).
[CrossRef]

Stern, F.

F. Stern, “Elementary theory of the optical properties of solids,” in Solid State Physics, F. Steitz, D. Turnbull, eds. (Academic, New York, 1963), Vol. 15, pp. 299–408.
[CrossRef]

Sturm, K.

K. Sturm, N. W. Ashcroft, “Nonlocal effects in absorption edges: energy-dependent pseudopotentials,” Phys. Rev. B 10, 1343–1349 (1974).
[CrossRef]

N. W. Ashcroft, K. Sturm, “Interband absorption and the optical properties of polyvalent metals,” Phys. Rev. B 3, 1898–1910 (1971).
[CrossRef]

Swartzlander, A. B.

Szmulowicz, F.

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminum,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

Takacs, P. Z.

Tangherlini, F. R.

Tanuma, S.

S. Tanuma, C. J. Powell, D. R. Penn, “Use of sum rules on the energy-loss function for the evaluation of experimental optical data,” J. Electron Spectrosc. Relat. Phenom. 62, 95–109 (1993).
[CrossRef]

Uspenski, Y. A.

E. G. Maksimov, I. I. Mazin, S. N. Rashkeev, Y. A. Uspenski, “First principles calculations of the optical properties of metals,” J. Phys. F 18, 833–849 (1988).
[CrossRef]

Vedam, K.

Waylonis, J. E.

Windt, D. L.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Wooten, F.

F. Wooten, Optical Properties of Solids (Academic, New York, 1972).

Appl. Opt. (7)

C. R. Acad. Sci. Ser. B (1)

A. Daude, M. Priol, S. Robin, “Propriétés optiques dans l’ultraviolet lointain de couches d’aluminium évaporées en ultravide et non exposées à l’air,” C. R. Acad. Sci. Ser. B 263, 1178–1181 (1966).

J. Appl. Phys. (2)

R. Haensel, B. Sontag, C. Kunz, T. Sasaki, “Contribution of the L shell to the total absorption cross section of aluminum,” J. Appl. Phys. 40, 3046–3047 (1969).
[CrossRef]

H. R. Philipp, H. Ehrenreich, “Optical constants in the x-ray range,” J. Appl. Phys. 35, 1416–1419 (1964).
[CrossRef]

J. Electron Spectrosc. Relat. Phenom. (1)

S. Tanuma, C. J. Powell, D. R. Penn, “Use of sum rules on the energy-loss function for the evaluation of experimental optical data,” J. Electron Spectrosc. Relat. Phenom. 62, 95–109 (1993).
[CrossRef]

J. Math. Phys. (1)

F. W. King, “Sum rules for the optical constants,” J. Math. Phys. 17, 1509–1514 (1976).
[CrossRef]

J. Opt. Soc. Am. (7)

J. Phys. F (2)

J. A. Nelson, P. J. Bunyan, “Calculation of bandstructure of aluminum using the model potential method,” J. Phys. F 7, 1467–1475 (1977).
[CrossRef]

E. G. Maksimov, I. I. Mazin, S. N. Rashkeev, Y. A. Uspenski, “First principles calculations of the optical properties of metals,” J. Phys. F 18, 833–849 (1988).
[CrossRef]

Opt. Laser Technol. (1)

M. I. Marković, A. D. Rakić, “Determination of optical properties of aluminium including electron reradiation in the Lorentz–Drude model,” Opt. Laser Technol. 22, 394–398 (1990).
[CrossRef]

Phys. Rev. (6)

F. C. Jahoda, “Fundamental absorption of barium oxide from its reflectivity spectrum,” Phys. Rev. 107, 1261–1265, 1957.
[CrossRef]

S. Roberts, “Optical properties of nickel and tungsten and their interpretation according to Drude’s formula,” Phys. Rev. 114, 104–115 (1959).
[CrossRef]

H. Ehrenreich, H. R. Philipp, “Optical properties of Ag and Cu,” Phys. Rev. 128, 1622–1629 (1962).
[CrossRef]

H. Ehrenreich, H. R. Philipp, B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928 (1963).
[CrossRef]

W. A. Harrison, “Electronic structure and the properties of metals. II. Application to zinc,” Phys. Rev. 129, 2512–2524 (1963).
[CrossRef]

W. A. Harrison, “Parallel-band effects in interband optical absorption,” Phys. Rev. 147, 467–469 (1966).
[CrossRef]

Phys. Rev. B (15)

N. W. Ashcroft, K. Sturm, “Interband absorption and the optical properties of polyvalent metals,” Phys. Rev. B 3, 1898–1910 (1971).
[CrossRef]

S. P. Singhal, J. Callaway, “Self-consistent energy bands in aluminum—improved calculation,” Phys. Rev. B 16, 1744–1746 (1977).
[CrossRef]

K.-H. Lee, K. J. Chang, “First-principles study of the optical properties and the dielectric response of Al,” Phys. Rev. B 49, 2362–2367 (1994).
[CrossRef]

F. Szmulowicz, B. Segall, “Calculation of optical spectra of aluminum,” Phys. Rev. B 24, 892–903 (1981).
[CrossRef]

J. G. Endriz, W. E. Spicer, “Study of aluminum films I. Optical studies of reflectance drops and surface oscillations on controlled-roughness films,” Phys. Rev. B 4, 4144–4159 (1971).
[CrossRef]

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistency and sum-rule tests in the Kramers–Kronig analysis of optical data: application to aluminum,” Phys. Rev. B 22, 1612–1628 (1980).
[CrossRef]

A. Balzarotti, A. Bianconi, E. Burattini, “Role of the density of conduction states on the L2-3 absorption spectrum of aluminum,” Phys. Rev. B 9, 5003–5007 (1974).
[CrossRef]

C. Gahwiller, F. C. Brown, “Photoabsorption near the LII-III edge of silicon and aluminum,” Phys. Rev. B 2, 1918–1925 (1970).
[CrossRef]

H. V. Nguyen, I. An, R. W. Collins, “Evolution of the optical functions of thin-film aluminum: a real time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947–3965 (1993).
[CrossRef]

D. Y. Smith, B. Segal, “Intraband and interband processes in the infrared spectrum of metallic aluminum,” Phys. Rev. B 34, 5191–5198 (1986).
[CrossRef]

K. Sturm, N. W. Ashcroft, “Nonlocal effects in absorption edges: energy-dependent pseudopotentials,” Phys. Rev. B 10, 1343–1349 (1974).
[CrossRef]

G. R. Parkins, W. Lawrence, R. W. Christy, “Intraband optical conductivity σ(ω, T) of Cu, Ag, and Au: contribution from electron–electron scattering,” Phys. Rev. B 23, 6408–6415 (1981).
[CrossRef]

M. Altarelli, D. Y. Smith, “Superconvergence and sum rules for the optical constants: physical meaning, comparison with experiment, and generalization,” Phys. Rev. B 9, 1290–1298 (1974).
[CrossRef]

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B 17, 4689–4694 (1978).
[CrossRef]

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

Phys. Scr. (1)

A. G. Mathewson, H. P. Myers, “Absolute values of the optical constants of some pure metals,” Phys. Scr. 4, 291–292 (1971).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

R. W. Ditchburn, G. H. C. Freeman, “The optical constants of aluminium from 12 to 36 eV,” Proc. R. Soc. London Ser. A 294, 20–37 (1966).
[CrossRef]

Solid State Commun. (1)

D. C. Jiles, M. P. Staines, “Piezo optic properties of aluminum,” Solid State Commun. 47, 37–41 (1983).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

R. N. Gurzhi, M. I. Kaganov, “Vliyanie mezhelektronih stolknovenii na opticheskie svoistva metallov” Zh. Eksp. Teor. Fiz. 49, 941–943, (1965).

Other (9)

F. Wooten, Optical Properties of Solids (Academic, New York, 1972).

F. Stern, “Elementary theory of the optical properties of solids,” in Solid State Physics, F. Steitz, D. Turnbull, eds. (Academic, New York, 1963), Vol. 15, pp. 299–408.
[CrossRef]

C. de Boor, “cadre: an algorithm for numerical quadrature,” in Mathematical Software, J. R. Rice, ed. (Academic, New York, (1971), Chap. 7.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory for silver, gold and aluminum in the infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, ed. (North-Holland, Amsterdam, 1966), pp. 175–189.

D. Y. Smith, “Dispersion theory, sum rules, and their application to the analysis of optical data,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 35–68.

R. C. Weast, ed., CRC Handbook of Chemistry and Physics70th ed. (CRC Press, Boca Raton, Fla., 1990).

D. Y. Smith, E. Shiles, M. Inokuti, “The optial properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–408.

D. Beaglehole, “The ultraviolet absorption of the noble metals,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, ed. (North-Holland, Amsterdam, 1966), pp. 154–163.

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Figures (8)

Fig. 1
Fig. 1

Comparison of the measured Al reflectance to R(ω) obtained with the self-consistent KK analysis plus selected experimental data.

Fig. 2
Fig. 2

Electon-energy-loss function calculated from values of the dielectric function determined with the KK analysis in this paper (denoted by the circled dots). The solid line represents the data from the Lorentz function with the center position at ωp = 14.94 eV and the full width at half-maximum ΔE1/2 = 0.48 eV.

Fig. 3
Fig. 3

Phase θ(ω) of the reflectivity of aluminum film as derived from the KK analysis in this study: le, low energy; exp, experimental; he, high energy.

Fig. 4
Fig. 4

R(ω) of a smooth Al film as calculated from optical constants obtained from the KK analysis plus selected experimental data points.

Fig. 5
Fig. 5

Plot of the intrinsic extinction coefficient k(ω) of Al film as derived from the KK analysis in this study plus selected experimental data points.

Fig. 6
Fig. 6

Plot of the intrinsic refractive index n(ω) of aluminum film as derived from the KK analysis in this study plus selected experimental data points.

Fig. 7
Fig. 7

Plot of the dielectric function of bulk Al film derived from the KK analysis in this study plus selected experimental data points.

Fig. 8
Fig. 8

Number density of electrons/Al atom Neff(ω) that contribute to absorption processes, as obtained by means of the finite-energy f-sum rules: el, electrons; at, atom.

Tables (3)

Tables Icon

Table 1 Semiquantum-Model (Oscillator-Model) Parameter Values Employed for the Calculation of Trial Values of k(ω) between ωl = 6.2 meV and ωp = 14.94 eV

Tables Icon

Table 2 Values of the Intrinsic Optical Constants n(ω) and k(ω) and Reflectance R(ω) of Aluminum Determined in this Study

Tables Icon

Table 3 Drude-Model Parameter Values Employed for the Low-Frequency-Region Extrapolations

Equations (28)

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

^ r ( ω ) = ^ r ( f ) ( ω ) + ^ r ( b ) ( ω ) .
^ r ( f ) ( ω ) = 1 - Ω p 2 ω ( ω + i Γ 0 ) .
^ r ( b ) ( ω ) = - j = 1 k f j ω p 2 ( ω 2 - ω j 2 ) + i ω Γ j ,
Ω p = ( N eff , f e e 2 m 0 ) 1 / 2 ,
n ( ω ) - 1 = 2 π P 0 + ω k ( ω ) ( ω ) 2 - ω 2 d ω .
2 π P 0 + ω k ( ω ) ( ω ) 2 - ω 2 d ω = 0 ,
n ( ω ) - 1 = 2 π 0 + ω k ( ω ) - ω k ( ω ) ( ω ) 2 - ω 2 d ω ,
lim ω ω ω k ( ω ) - ω k ( ω ) ( ω ) 2 - ω 2 = k ( ω ) 2 ω + 1 2 d k d ω .
n ( ω ) - 1 = I dm + I sqm + I exp + I ae .
k = k i exp + C i , 1 ( ω - ω i ) + C i , 2 ( ω - ω i ) 2 + C i , 3 ( ω - ω i ) 3 ,
d k d ω | ω = ω i = C i , 1 ,
r 1 = 1 - ω p , t 2 ω 2 ,
r 2 = C ω δ ,
δ = { 3.97778 + 0.22222 × 10 - 5 ω , ω < 10 5 eV 4.2 , ω > 10 5 eV ,
R ( ω ) = [ n ( ω ) - 1 ] 2 + k ( ω ) 2 [ n ( ω ) + 1 ] 2 + k ( ω ) 2 ,
R ae ( ω ) = ω p , t 4 16 ω 4 = ( 16.43 ω ) 4 ,
θ ( ω ) = ω π 0 + log R ( ω ) - log R ( ω ) ( ω 2 - ω 2 ) d ω .
lim ω ω log R ( ω ) - log R ( ω ) ( ω 2 - ω 2 ) = - 1 2 ω R ( ω ) dR d ω ,
n ( ω ) = 1 - R ( ω ) 1 + R ( ω ) - 2 R ( ω ) cos [ θ ( ω ) ] ,
k ( ω ) = 2 R ( ω ) sin [ θ ( ω ) ] 1 + R ( ω ) - 2 R ( ω ) cos [ θ ( ω ) ] ,
r 1 ( ω ) = n ( ω ) 2 - k ( ω ) 2 ,
r 2 ( ω ) = 2 n ( ω ) k ( ω ) .
ζ = 0 + [ n ( ω ) - 1 ] d ω 0 + n ( ω ) - 1 d ω .
n ( ω ) = 1 - ω p , t 2 2 ω 2 ,
0 + [ r 1 ( ω ) - 1 ] d ω = - π 2 0 σ 0 .
N eff r = 2 m 0 π e 2 0 ω ω r 2 ( ω ) d ω ,
N eff k = 4 m 0 π e 2 0 ω ω k ( ω ) d ω ,
N eff r - 1 = - 2 m 0 π e 2 0 ω ω Im [ r - 1 ( ω ) ] d ω .

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