Abstract

Both the integrated-charge and the peak-voltage responsivity of a 1-cm2 Si photodiode optimized for the extreme ultraviolet have been measured with 532-nm-wavelength pulsed radiation. The peak power of the optical pulse is varied from 35 mW to 24 kW with a pulse width of 8.25 ns. A decrease in responsivity is observed with increasing pulse energy, and a model is presented that accounts for the observed loss of responsivity. The integrated-charge responsivity decreases because the presence of photogenerated majority carriers increases the direct recombination rate. The peak-voltage responsivity is reduced because the electric susceptibility of the electrons and holes in the depletion region increases the capacitance of the device. The influence of an applied reverse bias on both responsivities is investigated. The integrated-charge responsivity is found to be identical, with a 1% uncertainty, to the cw responsivity of the device if the energy dependence is considered.

© 2003 Optical Society of America

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References

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    [CrossRef]
  3. R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
    [CrossRef]
  4. R. Thornagel, R. Klein, G. Ulm, “The electron storage ring BESSY II as a primary source standard from the visible to the x-ray range,” Metrologia 38, 385–389 (2001).
    [CrossRef]
  5. R. Stuik, F. Scholze, J. Tümmler, F. Bijkerk, “Absolute calibration of a multilayer-based XUV diagnostic,” Nucl. Instrum. Methods A 492, 305–316 (2002).
    [CrossRef]
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  7. R. Stuik, F. Bijkerk, “Linearity of p-n junction photodiodes under pulsed irradiation,” Nucl. Instrum. Methods A 489, 370–378 (2002).
    [CrossRef]
  8. D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  24. Technical Advisory Group 4, Metrology, International Vocabulary of Basic and General Terms in Metrology, 2nd ed. (International Organization for Standards, Geneva, Switzerland, 1993).
  25. M. Richter, U. Kroth, A. Gottwald, C. Gerth, K. Tiedtke, T. Saito, I. Tassy, K. Vogler, “Metrology of pulsed radiation for 157-nm lithography,” Appl. Opt. 41, 7167–7172 (2002).
    [CrossRef] [PubMed]

2003

R. Korde, C. Prince, D. Cunningham, R. E. Vest, E. Gullikson, “Present status of radiometric quality silicon photodiodes,” Metrologia 40, S145–S149 (2003).
[CrossRef]

2002

R. Stuik, F. Scholze, J. Tümmler, F. Bijkerk, “Absolute calibration of a multilayer-based XUV diagnostic,” Nucl. Instrum. Methods A 492, 305–316 (2002).
[CrossRef]

R. Stuik, F. Bijkerk, “Linearity of p-n junction photodiodes under pulsed irradiation,” Nucl. Instrum. Methods A 489, 370–378 (2002).
[CrossRef]

J. F. Seely, C. N. Boyer, G. E. Holland, J. L. Weaver, “X-ray absolute calibration of the time response of a silicon photodiode,” Appl. Opt. 41, 5209–5217 (2002).
[CrossRef] [PubMed]

M. Richter, U. Kroth, A. Gottwald, C. Gerth, K. Tiedtke, T. Saito, I. Tassy, K. Vogler, “Metrology of pulsed radiation for 157-nm lithography,” Appl. Opt. 41, 7167–7172 (2002).
[CrossRef] [PubMed]

2001

R. Thornagel, R. Klein, G. Ulm, “The electron storage ring BESSY II as a primary source standard from the visible to the x-ray range,” Metrologia 38, 385–389 (2001).
[CrossRef]

2000

S. W. Brown, G. P. Eppeldauer, K. R. Lykke, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–582 (2000).
[CrossRef]

1997

H. O. Funsten, D. M. Suszcynsky, S. M. Ritzau, R. Korde, “Response of 100% internal quantum efficiency silicon photodiodes to 200 eV-40 keV electrons,” IEEE Trans. Nucl. Sci. 44, 2561–2565 (1997).
[CrossRef]

R. Soufli, E. M. Gullikson, “Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet-soft-x-ray region,” Appl. Opt. 36, 5499–5507 (1997).
[CrossRef] [PubMed]

1996

1993

R. Korde, J. S. Cable, L. R. Canfield, “One gigarad passivating nitrided oxides for 100-percent internal quantum efficiency silicon photodiodes,” IEEE Trans. Nucl. Sci. 40, 1655–1659 (1993).
[CrossRef]

1989

1983

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

Banine, V.

V. Banine, “Update on EUVL source requirements,” presented at the Extreme Ultraviolet Lithography Source Workshop, Dallas, Tex., 14 October 2002.

Bijkerk, F.

R. Stuik, F. Scholze, J. Tümmler, F. Bijkerk, “Absolute calibration of a multilayer-based XUV diagnostic,” Nucl. Instrum. Methods A 492, 305–316 (2002).
[CrossRef]

R. Stuik, F. Bijkerk, “Linearity of p-n junction photodiodes under pulsed irradiation,” Nucl. Instrum. Methods A 489, 370–378 (2002).
[CrossRef]

Boyer, C. N.

Brown, S. W.

S. W. Brown, G. P. Eppeldauer, K. R. Lykke, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–582 (2000).
[CrossRef]

Cable, J. S.

R. Korde, J. S. Cable, L. R. Canfield, “One gigarad passivating nitrided oxides for 100-percent internal quantum efficiency silicon photodiodes,” IEEE Trans. Nucl. Sci. 40, 1655–1659 (1993).
[CrossRef]

Canfield, L. R.

R. Korde, J. S. Cable, L. R. Canfield, “One gigarad passivating nitrided oxides for 100-percent internal quantum efficiency silicon photodiodes,” IEEE Trans. Nucl. Sci. 40, 1655–1659 (1993).
[CrossRef]

L. R. Canfield, J. Kerner, R. Korde, “Stability and quantum efficiency performance of silicon photodiode detectors in the far ultraviolet,” Appl. Opt. 28, 3940–3943 (1989).
[CrossRef] [PubMed]

L. R. Canfield, “Photodiode detectors,” in Vacuum Ultraviolet Spectroscopy II, J. A. R. Samson, D. L. Ederer, eds. (Academic, San Diego, Calif., 1998), pp. 117–138.
[CrossRef]

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

Cromer, C. L.

Cunningham, D.

R. Korde, C. Prince, D. Cunningham, R. E. Vest, E. Gullikson, “Present status of radiometric quality silicon photodiodes,” Metrologia 40, S145–S149 (2003).
[CrossRef]

Dowell, M.

H. Laabs, M. Dowell, Optoelectronics Division National Institute of Standards and Technology, 325 Broadway, Boulder, Colo. 80305 (personal communication, 15May2002).

Eppeldauer, G. P.

S. W. Brown, G. P. Eppeldauer, K. R. Lykke, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–582 (2000).
[CrossRef]

Funsten, H. O.

H. O. Funsten, D. M. Suszcynsky, S. M. Ritzau, R. Korde, “Response of 100% internal quantum efficiency silicon photodiodes to 200 eV-40 keV electrons,” IEEE Trans. Nucl. Sci. 44, 2561–2565 (1997).
[CrossRef]

Furst, M. L.

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

Gentile, T. R.

Gerth, C.

Gottwald, A.

Grantham, S. E.

R. E. Vest, E. Wilcox, S. E. Grantham, C. Tarrio, “Calibration of detectors for extreme ultraviolet lithography in pulsed radiation,” presented at the NewRad Conference, Gaithersburg, Md., 20–24 May 2002.

C. Tarrio, R. E. Vest, S. E. Grantham, “Absolute extreme-ultraviolet metrology,” in Harnessing Light: Optical Science and Metrology at NIST, C. Londono, ed., Proc. SPIE4450, 94–107 (2001).
[CrossRef]

Graves, R. M.

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

Gullikson, E.

R. Korde, C. Prince, D. Cunningham, R. E. Vest, E. Gullikson, “Present status of radiometric quality silicon photodiodes,” Metrologia 40, S145–S149 (2003).
[CrossRef]

Gullikson, E. M.

Hamilton, A.

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

Herman, C.

B. Sapoval, C. Herman, Physics of Semiconductors (Springer-Verlag, New York, 1995).
[CrossRef]

Holland, G. E.

Houston, J. M.

Hughey, L. R.

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

Kerner, J.

Klein, R.

R. Thornagel, R. Klein, G. Ulm, “The electron storage ring BESSY II as a primary source standard from the visible to the x-ray range,” Metrologia 38, 385–389 (2001).
[CrossRef]

Korde, R.

R. Korde, C. Prince, D. Cunningham, R. E. Vest, E. Gullikson, “Present status of radiometric quality silicon photodiodes,” Metrologia 40, S145–S149 (2003).
[CrossRef]

H. O. Funsten, D. M. Suszcynsky, S. M. Ritzau, R. Korde, “Response of 100% internal quantum efficiency silicon photodiodes to 200 eV-40 keV electrons,” IEEE Trans. Nucl. Sci. 44, 2561–2565 (1997).
[CrossRef]

R. Korde, J. S. Cable, L. R. Canfield, “One gigarad passivating nitrided oxides for 100-percent internal quantum efficiency silicon photodiodes,” IEEE Trans. Nucl. Sci. 40, 1655–1659 (1993).
[CrossRef]

L. R. Canfield, J. Kerner, R. Korde, “Stability and quantum efficiency performance of silicon photodiode detectors in the far ultraviolet,” Appl. Opt. 28, 3940–3943 (1989).
[CrossRef] [PubMed]

Kroth, U.

Laabs, H.

H. Laabs, M. Dowell, Optoelectronics Division National Institute of Standards and Technology, 325 Broadway, Boulder, Colo. 80305 (personal communication, 15May2002).

Lucatorto, T. B.

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

Lykke, K. R.

S. W. Brown, G. P. Eppeldauer, K. R. Lykke, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–582 (2000).
[CrossRef]

Madden, R. P.

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

Prince, C.

R. Korde, C. Prince, D. Cunningham, R. E. Vest, E. Gullikson, “Present status of radiometric quality silicon photodiodes,” Metrologia 40, S145–S149 (2003).
[CrossRef]

Richter, M.

Ritzau, S. M.

H. O. Funsten, D. M. Suszcynsky, S. M. Ritzau, R. Korde, “Response of 100% internal quantum efficiency silicon photodiodes to 200 eV-40 keV electrons,” IEEE Trans. Nucl. Sci. 44, 2561–2565 (1997).
[CrossRef]

Saito, T.

Sapoval, B.

B. Sapoval, C. Herman, Physics of Semiconductors (Springer-Verlag, New York, 1995).
[CrossRef]

Scholze, F.

R. Stuik, F. Scholze, J. Tümmler, F. Bijkerk, “Absolute calibration of a multilayer-based XUV diagnostic,” Nucl. Instrum. Methods A 492, 305–316 (2002).
[CrossRef]

Seely, J. F.

J. F. Seely, C. N. Boyer, G. E. Holland, J. L. Weaver, “X-ray absolute calibration of the time response of a silicon photodiode,” Appl. Opt. 41, 5209–5217 (2002).
[CrossRef] [PubMed]

J. F. Seely, “Responsivity model for a silicon photodiode in the extreme ultraviolet,” in Instrumentation for UV/EUV Astronomy and Solar Missions, S. Fineschi, C. M. Korendyke, O. H. W. Siegmund, B. E. Woodgate, eds., Proc. SPIE4139, 1–7 (2000).
[CrossRef]

Soufli, R.

Studna, A. A.

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

Stuik, R.

R. Stuik, F. Scholze, J. Tümmler, F. Bijkerk, “Absolute calibration of a multilayer-based XUV diagnostic,” Nucl. Instrum. Methods A 492, 305–316 (2002).
[CrossRef]

R. Stuik, F. Bijkerk, “Linearity of p-n junction photodiodes under pulsed irradiation,” Nucl. Instrum. Methods A 489, 370–378 (2002).
[CrossRef]

Suszcynsky, D. M.

H. O. Funsten, D. M. Suszcynsky, S. M. Ritzau, R. Korde, “Response of 100% internal quantum efficiency silicon photodiodes to 200 eV-40 keV electrons,” IEEE Trans. Nucl. Sci. 44, 2561–2565 (1997).
[CrossRef]

Tarrio, C.

C. Tarrio, R. E. Vest, S. E. Grantham, “Absolute extreme-ultraviolet metrology,” in Harnessing Light: Optical Science and Metrology at NIST, C. Londono, ed., Proc. SPIE4450, 94–107 (2001).
[CrossRef]

R. E. Vest, E. Wilcox, S. E. Grantham, C. Tarrio, “Calibration of detectors for extreme ultraviolet lithography in pulsed radiation,” presented at the NewRad Conference, Gaithersburg, Md., 20–24 May 2002.

Tassy, I.

Thornagel, R.

R. Thornagel, R. Klein, G. Ulm, “The electron storage ring BESSY II as a primary source standard from the visible to the x-ray range,” Metrologia 38, 385–389 (2001).
[CrossRef]

Tiedtke, K.

Tümmler, J.

R. Stuik, F. Scholze, J. Tümmler, F. Bijkerk, “Absolute calibration of a multilayer-based XUV diagnostic,” Nucl. Instrum. Methods A 492, 305–316 (2002).
[CrossRef]

Ulm, G.

R. Thornagel, R. Klein, G. Ulm, “The electron storage ring BESSY II as a primary source standard from the visible to the x-ray range,” Metrologia 38, 385–389 (2001).
[CrossRef]

Vest, R. E.

R. Korde, C. Prince, D. Cunningham, R. E. Vest, E. Gullikson, “Present status of radiometric quality silicon photodiodes,” Metrologia 40, S145–S149 (2003).
[CrossRef]

C. Tarrio, R. E. Vest, S. E. Grantham, “Absolute extreme-ultraviolet metrology,” in Harnessing Light: Optical Science and Metrology at NIST, C. Londono, ed., Proc. SPIE4450, 94–107 (2001).
[CrossRef]

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

R. E. Vest, E. Wilcox, S. E. Grantham, C. Tarrio, “Calibration of detectors for extreme ultraviolet lithography in pulsed radiation,” presented at the NewRad Conference, Gaithersburg, Md., 20–24 May 2002.

Vogler, K.

Weaver, J. L.

Wilcox, E.

R. E. Vest, E. Wilcox, S. E. Grantham, C. Tarrio, “Calibration of detectors for extreme ultraviolet lithography in pulsed radiation,” presented at the NewRad Conference, Gaithersburg, Md., 20–24 May 2002.

Appl. Opt.

IEEE Trans. Nucl. Sci.

H. O. Funsten, D. M. Suszcynsky, S. M. Ritzau, R. Korde, “Response of 100% internal quantum efficiency silicon photodiodes to 200 eV-40 keV electrons,” IEEE Trans. Nucl. Sci. 44, 2561–2565 (1997).
[CrossRef]

R. Korde, J. S. Cable, L. R. Canfield, “One gigarad passivating nitrided oxides for 100-percent internal quantum efficiency silicon photodiodes,” IEEE Trans. Nucl. Sci. 40, 1655–1659 (1993).
[CrossRef]

Metrologia

R. Korde, C. Prince, D. Cunningham, R. E. Vest, E. Gullikson, “Present status of radiometric quality silicon photodiodes,” Metrologia 40, S145–S149 (2003).
[CrossRef]

S. W. Brown, G. P. Eppeldauer, K. R. Lykke, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–582 (2000).
[CrossRef]

R. Thornagel, R. Klein, G. Ulm, “The electron storage ring BESSY II as a primary source standard from the visible to the x-ray range,” Metrologia 38, 385–389 (2001).
[CrossRef]

Nucl. Instrum. Methods A

R. Stuik, F. Scholze, J. Tümmler, F. Bijkerk, “Absolute calibration of a multilayer-based XUV diagnostic,” Nucl. Instrum. Methods A 492, 305–316 (2002).
[CrossRef]

R. Stuik, F. Bijkerk, “Linearity of p-n junction photodiodes under pulsed irradiation,” Nucl. Instrum. Methods A 489, 370–378 (2002).
[CrossRef]

Phys. Rev. B

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

Other

L. R. Canfield, “Photodiode detectors,” in Vacuum Ultraviolet Spectroscopy II, J. A. R. Samson, D. L. Ederer, eds. (Academic, San Diego, Calif., 1998), pp. 117–138.
[CrossRef]

“NIST Optical Technology Division Home Page,” retrieved 19December2002, http://physics.nist.gov/Divisions/Div844/div844.html .

B. Sapoval, C. Herman, Physics of Semiconductors (Springer-Verlag, New York, 1995).
[CrossRef]

P. Singh, “Lecture 11 from ECE 3590 Semiconductor Materials and Devices” (Villanova University, 11June1997), retrieved Nov2002, http://www.ece.villanova.edu/~singh/lec11/sld027.html .

Technical Advisory Group 4, Metrology, International Vocabulary of Basic and General Terms in Metrology, 2nd ed. (International Organization for Standards, Geneva, Switzerland, 1993).

R. E. Vest, E. Wilcox, S. E. Grantham, C. Tarrio, “Calibration of detectors for extreme ultraviolet lithography in pulsed radiation,” presented at the NewRad Conference, Gaithersburg, Md., 20–24 May 2002.

V. Banine, “Update on EUVL source requirements,” presented at the Extreme Ultraviolet Lithography Source Workshop, Dallas, Tex., 14 October 2002.

C. Tarrio, R. E. Vest, S. E. Grantham, “Absolute extreme-ultraviolet metrology,” in Harnessing Light: Optical Science and Metrology at NIST, C. Londono, ed., Proc. SPIE4450, 94–107 (2001).
[CrossRef]

R. E. Vest, L. R. Canfield, M. L. Furst, R. M. Graves, A. Hamilton, L. R. Hughey, T. B. Lucatorto, R. P. Madden, “NIST programs for radiometry in the far ultraviolet spectral region,” in Ultraviolet Atmospheric and Space Remote Sensing: Methods and Instrumentation II, G. R. Carruthers, K. F. Dymond, eds., Proc. SPIE3818, 15–26 (1999).
[CrossRef]

J. F. Seely, “Responsivity model for a silicon photodiode in the extreme ultraviolet,” in Instrumentation for UV/EUV Astronomy and Solar Missions, S. Fineschi, C. M. Korendyke, O. H. W. Siegmund, B. E. Woodgate, eds., Proc. SPIE4139, 1–7 (2000).
[CrossRef]

“NIST Optoelectronics Division Home Page,” retrieved 19December2002, http://www.boulder.nist.gov/div815/ .

H. Laabs, M. Dowell, Optoelectronics Division National Institute of Standards and Technology, 325 Broadway, Boulder, Colo. 80305 (personal communication, 15May2002).

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Fig. 1
Fig. 1

Schematic diagram of the optical system. The half-wave plate and the polarizer form a variable attenuator that maintains a constant pulse energy on the pyroelectric detector. One controls the pulse energy incident upon the Si photodiode by removing and inserting combinations of neutral-density filters.

Fig. 2
Fig. 2

Schematic diagram of the bias tee. The resistor R 1 was originally 1 kΩ (low-Z tee) but was replaced with 100 kΩ (high-Z tee). For high-frequency components such as the Fourier components of a fast pulse, the capacitors in the dashed box are a low-impedance path to ground. The photodiode output pulse sees the resistance R 1 in parallel with the oscilloscope’s input impedance.

Fig. 3
Fig. 3

Total charge collected by an external circuit as a function of incident pulse energy. The points are data with reverse-bias values of 2 V (circles), 4 V (squares), 6 V (diamonds), 8 V (triangles), and 10 V (inverted triangles). Filled symbols with solid-curve fits were obtained with the low-Z bias tee; open symbols with dashed-curve fits were obtained with the high-Z bias tee. The curves are the expected signal based on the curve fits to the responsivity data shown in Fig. 4. At sufficiently low pulse energy, the signal is not a function of reverse bias. The onset of significant saturation is a function of reverse bias.

Fig. 4
Fig. 4

Integrated-charge responsivity as a function of incident pulse energy. The points are data with reverse-bias values of 2 V (circles), 4 V (squares), 6 V (diamonds), 8 V (triangles), and 10 V (inverted triangles). Filled symbols with solid-curve fits were obtained with the low-Z bias tee; open symbols with dashed-curve fits were obtained with the high-Z bias tee. The curves are the curve fitting results of the data to Eq. (2).

Fig. 5
Fig. 5

Maximum pulse energy that produces a linear response in the Si photodiode as a function of reverse-bias voltage when the integrated charge (filled circles) and peak voltage (open circles) are measured. Here the limit is taken as the pulse energy at which the responsivity is reduced by 2% from the value in the low-power limit.

Fig. 6
Fig. 6

Peak voltage detected by an external circuit as a function of incident pulse energy. The points are data with reverse-bias values of 2 V (circles), 4 V (squares), 6 V (diamonds), 8 V (triangles), and 10 V (inverted triangles). Filled symbols with solid-curve fits were obtained with the low-Z bias tee; open symbols with dashed-curve fits were obtained with the high-Z bias tee. The curves are the expected signal based on the curve fits to the responsivity data shown in Fig. 7. The signal is a function of reverse bias at all the pulse energies studied.

Fig. 7
Fig. 7

Peak-voltage responsivity as a function of incident pulse energy. The points are data with reverse-bias values of 2 V (circles), 4 V (squares), 6 V (diamonds), 8 V (triangles), and 10 V (inverted triangles). Filled symbols with solid-curve fits were obtained with the low-Z bias tee; open symbols with dashed-curve fits were obtained with the high-Z bias tee. The curves are the curve fitting results of the data to Eq. (2).

Fig. 8
Fig. 8

Schematic diagram of a photodiode. At the junction between the p-type and the n-type Si regions the free carriers from each side diffuse across the boundary and recombine, leaving a depletion region of width d with no free carriers and ionized dopants. The ionized dopants generate an electric field across the depletion region, oriented from the n-type to the p-type Si. An incident photon generates an electron-hole pair that is separated by the field: the holes drift to the anode, and the electrons drift to the cathode. The depletion region is modeled as a capacitive electrical element in the photodiode circuit.

Fig. 9
Fig. 9

Integrated-charge responsivity curve fitting parameters as a function of reverse bias. The parameters plotted here are from the curve fits to the data in Fig. 4. The parameter α Q (filled circles) is independent of reverse bias. The solid horizontal line is the mean value, and the dashed lines indicate the uncertainty of the mean. The parameter β Q (open circles) is fitted to Eq. (9) and varies as (ϕ + V)-1, where ϕ = 0.64 V is the barrier potential of the junction and V is the reverse bias.

Fig. 10
Fig. 10

Peak-voltage responsivity extrapolated to zero pulse energy to show the intrinsic dependence of the junction capacitance on reverse bias. The curve is a curve fit of the data to Eq. (13).

Fig. 11
Fig. 11

Peak-voltage responsivity curve fitting parameters as a function of reverse bias. The parameters plotted here are from the curve fits to the data in Fig. 7. The parameter α v (filled circles) is fitted to Eq. (14) and varies as (ϕ + V)-0.5, whereas the parameter β v (open circles) is fitted to Eq. (15) and varies as (ϕ + V)-1, where ϕ is the barrier potential of the junction and V is the reverse bias.

Tables (1)

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Table 1 Photodiode Parameters Determined from Curve Fits to Responsivity Data

Equations (15)

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Q=pulse Itdt=1/Rpulse Vtdt,
ηQEp=1αQ+βQEp,
C=εA/d.
d=kϕ+Vp,
1τn=Mp0dV+ncdVdV,
nc=ηQ0qEpγAzdV,
fQ=lτn=lMp0+MηQ0/qγAzEpdV,
ηQEp=ηQ011+ηQ0/qpγAzEp=1αQ+βQEp,
βQ=1m0.64+V2p,
ηvEp=ηQ0/C,
P=Pl+Pc=χl+χcE=χl+ncξcγAdE,
ηvEp=ηQ0Adε0+χl+ξcηQ0/γqd2Ep=ηQ0αv+βvEp,
ηv0=ηQ0dAε=nϕ+Vp,
αv=xd=1sϕ+Vp,
βv=yd2=1tϕ+V2p,

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