Abstract

Using the National Institute of Standards and Technology high-accuracy cryogenic radiometer (HACR), we have realized a scale of absolute spectral response between 406 and 920 nm. The HACR, an electrical-substitution radiometer operating at cryogenic temperatures, achieves a combined relative standard uncertainty of 0.021%. Silicon photodiode light-trapping detectors were calibrated against the HACR with a typical relative standard uncertainty of 0.03% at nine laser wavelengths between 406 and 920 nm. Modeling of the quantum efficiency of these detectors yields their responsivity throughout this range with comparable accuracy.

© 1996 Optical Society of America

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  1. J. M. Houston, C. L. Cromer, J. E. Hardis, T. C. Larason, “Comparison of the NIST high accuracy cryogenic radiometer and the NIST scale of detector spectral response,” Metrologia 30, 285–290 (1993).
    [CrossRef]
  2. T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “The National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
    [CrossRef] [PubMed]
  3. C. L. Cromer, “A new spectral response calibration method using a silicon photodiode trap detector,” presented at the 1991 Measurement Science Conference, Anaheim, Calif., 31 January–1 February 1991.
  4. N. P. Fox, “Trap detectors and their properties,” Metrologia 28, 197–202 (1991).
    [CrossRef]
  5. M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 632–633.
  7. J. E. Martin, N. P. Fox, P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
    [CrossRef]
  8. F. Lei, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia, 30, 297–303 (1993).
    [CrossRef]
  9. R. Kohler, R. Goebel, R. Pello, “Report on the international comparison of spectral responsivity of silicon detectors,” Rapport BIPM-94/9, doc. CCPR/94-2 (Bureau International des Poids et Mesures, Pavillon de Breteuil, 93212 Sevres, Cedex, France).
  10. Model 1337-1010BQ, Hamamatsu Corporation, 360 Foothill Rd., P.O. Box 6910, Bridgewater, N.J. 08807-0910. Certain trade names and company products are mentioned in the text or identified in an illustration to specify adequately the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products are necessarily the best available for the purpose.
  11. R. Kohler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
    [CrossRef]
  12. B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, Gaithersburg, Md., 1994).
  13. J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795–3799 (1980).
    [CrossRef] [PubMed]
  14. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]
  15. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), Chaps. 10 and 11.
  16. J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1991).
    [CrossRef]
  17. J. Geist, H. Baltes, “High accuracy modeling of photodiode quantum efficiency,” Appl. Opt. 28, 3929–3939 (1989).
    [CrossRef] [PubMed]
  18. G. E. Jellison, “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41–47 (1992).
    [CrossRef]
  19. J. Geist, A. Migdall, H. P. Baltes, “Analytic representation of the silicon absorption coefficient in the indirect transition region,” Appl. Opt. 27, 3777–3779 (1988).
    [CrossRef] [PubMed]
  20. H. A. Weakliem, D. Redfield, “Temperature dependence of the optical properties of silicon,” J. Appl. Phys. 50, 1491–1493 (1979).
    [CrossRef]
  21. J. Geist, “Quantum efficiency of the p-n junction as an absolute radiometric scale,” Appl. Opt. 18, 760–762 (1979).
    [CrossRef] [PubMed]
  22. H. R. Phillip, “Influence of oxide layers on the determination of the optical properties of silicon,” J. Appl. Phys. 43, 2835–2839 (1972).
    [CrossRef]
  23. W. C. Dash, R. Newman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99, 1151–1155 (1955).
    [CrossRef]
  24. A. A. Vol’fson, V. K. Subashiev, “Fundamental absorption edge of silicon heavily doped with donor or acceptor impurities,” Sov. Phys. Semicond. 1, 327–332 (1967).
  25. D. E. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 547–569.
  26. D. E. Aspnes, J. B. Theeten, “Spectroscopic analysis of the interface between Si and its thermally grown oxide,” J. Electrochem. Soc. 127, 1359–1365 (1980).
    [CrossRef]
  27. R. Hulthen, “Optical constants of epitaxial silicon in the region 1–3.3 eV,” Phys. Scr. 12, 342–344 (1975).
    [CrossRef]
  28. R. Braunstein, A. R. Moore, F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109, 695–710 (1958).
    [CrossRef]
  29. J. Geist, A. R. Schaefer, J. F. Song, Y. H. Wang, E. F. Zalewski, “An accurate value for the absorption coefficient of silicon at 633 nm,” J. Res. Natl. Inst. Stand. Technol. 95, 549–558 (1990).
    [CrossRef]
  30. G. E. Jellison, F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
    [CrossRef]

1996

1993

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

F. Lei, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia, 30, 297–303 (1993).
[CrossRef]

J. M. Houston, C. L. Cromer, J. E. Hardis, T. C. Larason, “Comparison of the NIST high accuracy cryogenic radiometer and the NIST scale of detector spectral response,” Metrologia 30, 285–290 (1993).
[CrossRef]

1992

G. E. Jellison, “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41–47 (1992).
[CrossRef]

1991

N. P. Fox, “Trap detectors and their properties,” Metrologia 28, 197–202 (1991).
[CrossRef]

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1991).
[CrossRef]

R. Kohler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
[CrossRef]

1990

J. Geist, A. R. Schaefer, J. F. Song, Y. H. Wang, E. F. Zalewski, “An accurate value for the absorption coefficient of silicon at 633 nm,” J. Res. Natl. Inst. Stand. Technol. 95, 549–558 (1990).
[CrossRef]

1989

1988

1985

J. E. Martin, N. P. Fox, P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

1982

G. E. Jellison, F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

1980

D. E. Aspnes, J. B. Theeten, “Spectroscopic analysis of the interface between Si and its thermally grown oxide,” J. Electrochem. Soc. 127, 1359–1365 (1980).
[CrossRef]

J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795–3799 (1980).
[CrossRef] [PubMed]

1979

H. A. Weakliem, D. Redfield, “Temperature dependence of the optical properties of silicon,” J. Appl. Phys. 50, 1491–1493 (1979).
[CrossRef]

J. Geist, “Quantum efficiency of the p-n junction as an absolute radiometric scale,” Appl. Opt. 18, 760–762 (1979).
[CrossRef] [PubMed]

1975

R. Hulthen, “Optical constants of epitaxial silicon in the region 1–3.3 eV,” Phys. Scr. 12, 342–344 (1975).
[CrossRef]

1972

H. R. Phillip, “Influence of oxide layers on the determination of the optical properties of silicon,” J. Appl. Phys. 43, 2835–2839 (1972).
[CrossRef]

1967

A. A. Vol’fson, V. K. Subashiev, “Fundamental absorption edge of silicon heavily doped with donor or acceptor impurities,” Sov. Phys. Semicond. 1, 327–332 (1967).

1965

1958

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109, 695–710 (1958).
[CrossRef]

1955

W. C. Dash, R. Newman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99, 1151–1155 (1955).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, “Spectroscopic analysis of the interface between Si and its thermally grown oxide,” J. Electrochem. Soc. 127, 1359–1365 (1980).
[CrossRef]

Baltes, H.

Baltes, H. P.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), Chaps. 10 and 11.

Bonhoure, J.

R. Kohler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 632–633.

Braunstein, R.

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109, 695–710 (1958).
[CrossRef]

Chandler-Horowitz, D.

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1991).
[CrossRef]

Cromer, C. L.

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “The National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
[CrossRef] [PubMed]

J. M. Houston, C. L. Cromer, J. E. Hardis, T. C. Larason, “Comparison of the NIST high accuracy cryogenic radiometer and the NIST scale of detector spectral response,” Metrologia 30, 285–290 (1993).
[CrossRef]

C. L. Cromer, “A new spectral response calibration method using a silicon photodiode trap detector,” presented at the 1991 Measurement Science Conference, Anaheim, Calif., 31 January–1 February 1991.

Dash, W. C.

W. C. Dash, R. Newman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99, 1151–1155 (1955).
[CrossRef]

Edwards, D. E.

D. E. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 547–569.

Fischer, J.

F. Lei, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia, 30, 297–303 (1993).
[CrossRef]

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

Fox, N. P.

N. P. Fox, “Trap detectors and their properties,” Metrologia 28, 197–202 (1991).
[CrossRef]

J. E. Martin, N. P. Fox, P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

Friedrich, R.

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

Geist, J.

Gentile, T. R.

Goebel, R.

R. Kohler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
[CrossRef]

R. Kohler, R. Goebel, R. Pello, “Report on the international comparison of spectral responsivity of silicon detectors,” Rapport BIPM-94/9, doc. CCPR/94-2 (Bureau International des Poids et Mesures, Pavillon de Breteuil, 93212 Sevres, Cedex, France).

Hardis, J. E.

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “The National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
[CrossRef] [PubMed]

J. M. Houston, C. L. Cromer, J. E. Hardis, T. C. Larason, “Comparison of the NIST high accuracy cryogenic radiometer and the NIST scale of detector spectral response,” Metrologia 30, 285–290 (1993).
[CrossRef]

Herman, F.

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109, 695–710 (1958).
[CrossRef]

Houston, J. M.

T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, A. C. Parr, “The National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 1056–1068 (1996).
[CrossRef] [PubMed]

J. M. Houston, C. L. Cromer, J. E. Hardis, T. C. Larason, “Comparison of the NIST high accuracy cryogenic radiometer and the NIST scale of detector spectral response,” Metrologia 30, 285–290 (1993).
[CrossRef]

Hulthen, R.

R. Hulthen, “Optical constants of epitaxial silicon in the region 1–3.3 eV,” Phys. Scr. 12, 342–344 (1975).
[CrossRef]

James, C. R.

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1991).
[CrossRef]

Jellison, G. E.

G. E. Jellison, “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41–47 (1992).
[CrossRef]

G. E. Jellison, F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

Jung, H. J.

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

Key, P. J.

J. E. Martin, N. P. Fox, P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

Kohler, R.

R. Kohler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
[CrossRef]

R. Kohler, R. Goebel, R. Pello, “Report on the international comparison of spectral responsivity of silicon detectors,” Rapport BIPM-94/9, doc. CCPR/94-2 (Bureau International des Poids et Mesures, Pavillon de Breteuil, 93212 Sevres, Cedex, France).

Kuyatt, C. E.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, Gaithersburg, Md., 1994).

Larason, T. C.

J. M. Houston, C. L. Cromer, J. E. Hardis, T. C. Larason, “Comparison of the NIST high accuracy cryogenic radiometer and the NIST scale of detector spectral response,” Metrologia 30, 285–290 (1993).
[CrossRef]

Lei, F.

F. Lei, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia, 30, 297–303 (1993).
[CrossRef]

Malitson, I. H.

Martin, J. E.

J. E. Martin, N. P. Fox, P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

Migdall, A.

Modine, F. A.

G. E. Jellison, F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

Moore, A. R.

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109, 695–710 (1958).
[CrossRef]

Newman, R.

W. C. Dash, R. Newman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99, 1151–1155 (1955).
[CrossRef]

Parr, A. C.

Pello, R.

R. Kohler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
[CrossRef]

R. Kohler, R. Goebel, R. Pello, “Report on the international comparison of spectral responsivity of silicon detectors,” Rapport BIPM-94/9, doc. CCPR/94-2 (Bureau International des Poids et Mesures, Pavillon de Breteuil, 93212 Sevres, Cedex, France).

Phillip, H. R.

H. R. Phillip, “Influence of oxide layers on the determination of the optical properties of silicon,” J. Appl. Phys. 43, 2835–2839 (1972).
[CrossRef]

Redfield, D.

H. A. Weakliem, D. Redfield, “Temperature dependence of the optical properties of silicon,” J. Appl. Phys. 50, 1491–1493 (1979).
[CrossRef]

Robinson, A. M.

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1991).
[CrossRef]

Schaefer, A. R.

J. Geist, A. R. Schaefer, J. F. Song, Y. H. Wang, E. F. Zalewski, “An accurate value for the absorption coefficient of silicon at 633 nm,” J. Res. Natl. Inst. Stand. Technol. 95, 549–558 (1990).
[CrossRef]

J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795–3799 (1980).
[CrossRef] [PubMed]

Song, J. F.

J. Geist, A. R. Schaefer, J. F. Song, Y. H. Wang, E. F. Zalewski, “An accurate value for the absorption coefficient of silicon at 633 nm,” J. Res. Natl. Inst. Stand. Technol. 95, 549–558 (1990).
[CrossRef]

Stock, M.

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

Subashiev, V. K.

A. A. Vol’fson, V. K. Subashiev, “Fundamental absorption edge of silicon heavily doped with donor or acceptor impurities,” Sov. Phys. Semicond. 1, 327–332 (1967).

Taylor, B. N.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, Gaithersburg, Md., 1994).

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, “Spectroscopic analysis of the interface between Si and its thermally grown oxide,” J. Electrochem. Soc. 127, 1359–1365 (1980).
[CrossRef]

Thornagel, R.

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

Ulm, G.

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

Vol’fson, A. A.

A. A. Vol’fson, V. K. Subashiev, “Fundamental absorption edge of silicon heavily doped with donor or acceptor impurities,” Sov. Phys. Semicond. 1, 327–332 (1967).

Wang, Y. H.

J. Geist, A. R. Schaefer, J. F. Song, Y. H. Wang, E. F. Zalewski, “An accurate value for the absorption coefficient of silicon at 633 nm,” J. Res. Natl. Inst. Stand. Technol. 95, 549–558 (1990).
[CrossRef]

Weakliem, H. A.

H. A. Weakliem, D. Redfield, “Temperature dependence of the optical properties of silicon,” J. Appl. Phys. 50, 1491–1493 (1979).
[CrossRef]

Wende, B.

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 632–633.

Zalewski, E. F.

J. Geist, A. R. Schaefer, J. F. Song, Y. H. Wang, E. F. Zalewski, “An accurate value for the absorption coefficient of silicon at 633 nm,” J. Res. Natl. Inst. Stand. Technol. 95, 549–558 (1990).
[CrossRef]

J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795–3799 (1980).
[CrossRef] [PubMed]

Appl. Opt.

J. Appl. Phys.

G. E. Jellison, F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

H. A. Weakliem, D. Redfield, “Temperature dependence of the optical properties of silicon,” J. Appl. Phys. 50, 1491–1493 (1979).
[CrossRef]

H. R. Phillip, “Influence of oxide layers on the determination of the optical properties of silicon,” J. Appl. Phys. 43, 2835–2839 (1972).
[CrossRef]

J. Electrochem. Soc.

D. E. Aspnes, J. B. Theeten, “Spectroscopic analysis of the interface between Si and its thermally grown oxide,” J. Electrochem. Soc. 127, 1359–1365 (1980).
[CrossRef]

J. Opt. Soc. Am.

J. Res. Natl. Inst. Stand. Technol.

J. Geist, A. R. Schaefer, J. F. Song, Y. H. Wang, E. F. Zalewski, “An accurate value for the absorption coefficient of silicon at 633 nm,” J. Res. Natl. Inst. Stand. Technol. 95, 549–558 (1990).
[CrossRef]

J. Geist, D. Chandler-Horowitz, A. M. Robinson, C. R. James, “Numerical modeling of silicon photodiodes for high accuracy applications, Parts I, II, and III,” J. Res. Natl. Inst. Stand. Technol. 96, 463–492 (1991).
[CrossRef]

Metrologia

J. M. Houston, C. L. Cromer, J. E. Hardis, T. C. Larason, “Comparison of the NIST high accuracy cryogenic radiometer and the NIST scale of detector spectral response,” Metrologia 30, 285–290 (1993).
[CrossRef]

J. E. Martin, N. P. Fox, P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21, 147–155 (1985).
[CrossRef]

F. Lei, J. Fischer, “Characterization of photodiodes in the UV and visible spectral region based on cryogenic radiometry,” Metrologia, 30, 297–303 (1993).
[CrossRef]

N. P. Fox, “Trap detectors and their properties,” Metrologia 28, 197–202 (1991).
[CrossRef]

M. Stock, J. Fischer, R. Friedrich, H. J. Jung, R. Thornagel, G. Ulm, B. Wende, “Present state of the comparison between radiometric scales based on three primary standards,” Metrologia 30, 439–449 (1993).
[CrossRef]

R. Kohler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
[CrossRef]

Opt. Mater.

G. E. Jellison, “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41–47 (1992).
[CrossRef]

Phys. Rev.

W. C. Dash, R. Newman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99, 1151–1155 (1955).
[CrossRef]

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109, 695–710 (1958).
[CrossRef]

Phys. Scr.

R. Hulthen, “Optical constants of epitaxial silicon in the region 1–3.3 eV,” Phys. Scr. 12, 342–344 (1975).
[CrossRef]

Sov. Phys. Semicond.

A. A. Vol’fson, V. K. Subashiev, “Fundamental absorption edge of silicon heavily doped with donor or acceptor impurities,” Sov. Phys. Semicond. 1, 327–332 (1967).

Other

D. E. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 547–569.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), Chaps. 10 and 11.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, Gaithersburg, Md., 1994).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 632–633.

R. Kohler, R. Goebel, R. Pello, “Report on the international comparison of spectral responsivity of silicon detectors,” Rapport BIPM-94/9, doc. CCPR/94-2 (Bureau International des Poids et Mesures, Pavillon de Breteuil, 93212 Sevres, Cedex, France).

Model 1337-1010BQ, Hamamatsu Corporation, 360 Foothill Rd., P.O. Box 6910, Bridgewater, N.J. 08807-0910. Certain trade names and company products are mentioned in the text or identified in an illustration to specify adequately the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products are necessarily the best available for the purpose.

C. L. Cromer, “A new spectral response calibration method using a silicon photodiode trap detector,” presented at the 1991 Measurement Science Conference, Anaheim, Calif., 31 January–1 February 1991.

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Figures (11)

Fig. 1
Fig. 1

Design of the silicon photodiode light-trapping detectors.

Fig. 2
Fig. 2

Measured values of η e for trap detector 2 (filled circles), with error bars equal to the uncertainties listed in Table 1. The solid curve shows η e (λ), which is the result of modeling the variation of η e with wavelength in the range between 406 and 920 nm (see Section 4).

Fig. 3
Fig. 3

Effect of the power-dependent nonequivalence error on η m (at 633 nm). The open circles (filled squares) show data taken before (after) the nonequivalence error was eliminated. At low values of P m , where the type A uncertainty dominates, the error bars represent the standard deviation of the mean. The solid curve shows the result of fitting the data shown by open circles to Eq. (4).

Fig. 4
Fig. 4

Variation of reflectance R t of the trap detectors with wavelength. The data for the two trap detectors are shown by open squares (trap 1) and filled circles (trap 2), and the solid curve is R t (λ), which is the reflectance calculated from the analytical formula in Born and Wolf,6 using a oxide thickness of 28.05 nm.

Fig. 5
Fig. 5

Results of modeling η i versus α(λ), using the approach of Geist et al.13 The values of η i for trap detector 2 are shown by filled circles with error bars equal to the uncertainties. The error bars shown for α(λ) were estimated from a review of published data (see Appendix A). The solid curve is a fit to Eq. (7). The values of the fitting parameters are P = 0.9762 ± 0.0019, T = 0.300 ± 0.04 μm, and H = 2.72 ± 0.20 mm.

Fig. 6
Fig. 6

Results of modeling η i versus λ, using the approach of Geist et al.16 The values of η i for trap detector 2 are shown by filled circles with error bars equal to the uncertainties. The solid curve shows the results of using the model of Geist et al.16

Fig. 7
Fig. 7

Model for the variation of collection efficiency P(x) with depth x into the photodiode. Parameters P f , T, P r , D, and h are discussed in text.

Fig. 8
Fig. 8

Results of modeling η i versus λ, using the new model described in text. The values of η i for trap detector 2 are shown by filled circles with error bars equal to the uncertainties. The uncertainty shown for α(λ) was estimated from a review of published data (see Appendix A). The solid curve shows the results of a fit to Eq. (9) and is also the final result for η i (λ). The values of the fitting parameters are P f = 0.9757 ± 0.0018, T = 0.289 ± 0.04 μm, P r = 0.99776 ± 0.0008, and D = 29 ± 19 μm.

Fig. 9
Fig. 9

Results of modeling η i versus λ, including the data point at 951 nm, with the model described in text. The data for η i for trap detector 2 are shown by filled circles with error bars equal to the uncertainties. The solid curve is a fit to Eq. (9) with the last term modified as described in the text. The values of the fitting parameters are P f = 0.9756 ± 0.002, T = 0.287 ± 0.04 μm, P r = 0.99849 ± 0.0005, D = 16 ± 14 μm, and R = 0.29 ± 0.12.

Fig. 10
Fig. 10

Values of k(λ) for silicon that we have used to determine α(λ).

Fig. 11
Fig. 11

Relative deviations of several published data sets for k(λ) from the values we have chosen (shown in Fig. 10; designated by k o here).

Tables (3)

Tables Icon

Table 1 Measured Values of η e of Two Silicon Photodiode Light-Trapping Detectors

Tables Icon

Table 2 Components of the Combined Relative Standard Uncertainty in η e for Each Wavelength Listed in Table 1

Tables Icon

Table 3 Values of R t , R t k ), and η i

Equations (9)

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η e = h c e n λ S ,
η e = 1239 . 48 ( S λ )
P L = 1 T ( N P H A + P S ) ,
η m = B η P m C P m ,
N d = B P m C P m ;
η e = η i ( 1 R t ) ,
η i ( λ ) = P + 1 P α ( λ ) T { 1 exp [ α ( λ ) T ] } h α ( λ ) L 2 exp [ α ( λ ) H ] ,
η i ( λ ) = 0 h exp [ α ( λ ) x ] α ( λ ) P ( x ) d x ,
η i ( λ ) = P f + 1 P f α ( λ ) T { 1 exp [ α ( λ ) T ] } 1 P r α ( λ ) [ D T ] { exp [ α ( λ ) T ] exp [ α ( λ ) D ] } P r exp [ α ( λ ) h ] ,

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