Abstract

Results are presented for modeling of the shape of the internal quantum efficiency (IQE) versus wave length for silicon photodiodes in the 400nm to 900nm wavelength range. The IQE data are based on measurements of the external quantum efficiencies of three transmission optical trap detectors using an extensive set of laser wavelengths, along with the transmittance of the traps. We find that a simplified version of a previously reported IQE model fits the data with an accuracy of better than 0.01%. These results provide an important validation of the National Institute of Standards and Technology (NIST) spectral radiant power responsivity scale disseminated through the NIST Spectral Comparator Facility, as well as those scales disseminated by other National Metrology Institutes who have employed the same model.

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References

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  1. E. F. Zalewski and C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22, 2867-2873(1983).
    [CrossRef] [PubMed]
  2. Hamamatsu Corporation, 360 Foothill Road, Bridgewater, New Jersey 08807, USA.
  3. T. R. Gentile, J. M. Houston, and C. L. Cromer, “Realization of a scale of absolute spectral response using the National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 4392-4402 (1996).
    [CrossRef] [PubMed]
  4. F. Sametoglu, “Establishment of illuminance scale at UME with and accurately calibrated radiometer,” Opt. Rev. 13, 326-337 (2006).
    [CrossRef]
  5. A. Ferrero, J. Campos, A. Pons, and A. Corrons, “New model for the internal quantum efficiency of photodiodes based on photocurrent analysis,” Appl. Opt. 44, 4392-4403 (2005).
    [CrossRef]
  6. J. Gran and A. S. Sudbo, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204-212 (2004).
    [CrossRef]
  7. J. Campos, A. Pons, and P. Corredera, “Spectral responsivity scale in the visible range based on single silicon photodiodes,” Metrologia 40, S181-S184 (2003).
    [CrossRef]
  8. C. Hicks, M. Kalatsky, R. A. Metzler, and A. O. Goushcha, “Quantum efficiency of silicon photodiodes in the near-infrared spectral range,” Appl. Opt. 42, 4415-4422 (2003).
    [CrossRef] [PubMed]
  9. J. Hartmann, J. Fischer, U. Johannsen, and L. Werner, “Analytical model for the temperature dependence of the spectral responsivity of silicon,” J. Opt. Soc. Am. B 18, 942-947(2001).
    [CrossRef]
  10. L. Werner, J. Fischer, U. Johannsen, and J. Hartmann, “Accurate determination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nm using a laser-based cryogenic radiometer,” Metrologia 37, 279-284 (2000).
    [CrossRef]
  11. T. Kübarsepp, P. Kärhä, and E. Ikonen, “Interpolation of the spectral responsivity of silicon photodetectors in the near ultraviolet,” Appl. Opt. 39, 9-15 (2000).
    [CrossRef]
  12. S.W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for spectral irradiance and radiance responsivity calibrations using uniform sources,” Appl. Opt. 45, 8218-8236 (2006).
    [CrossRef] [PubMed]
  13. T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements (U. S. Government Printing Office, 1998).
  14. L-1 Standards and Technology, New Windsor, Maryland, USA. Certain trade names and company products are mentioned in the text or identified in an illustration in order to adequately specify 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.
  15. G.P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic design of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stand. Technol. 105, 813-828 (2000).
  16. A. Haapalinna, P. Kärhä, and E. Ikonen, “Spectral reflectance of silicon photodiodes,” Appl. Optics 37, 729-732 (1998).
    [CrossRef]
  17. J. Geist, E. F. Zalewski, and A. R. Schaefer, “Spectral response self-calibration and interpolation of silicon photodiodes,” Appl. Opt. 19, 3795-3799 (1980).
    [CrossRef] [PubMed]
  18. G. E. Jellison, Jr., “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1, 41-47 (1992).
    [CrossRef]
  19. J. Geist, A. Migdall, and H. P. Baltes, “Analytic representation of the silicon absorption coefficient in the indirect transition region,” Appl. Opt. 27, 3777-3779 (1988).
    [CrossRef] [PubMed]
  20. T. Kubarsepp, P. Kärhä, and E. Ikonen, “Characterization of a polarization-independent transmission trap detector,” Appl. Opt. 36, 2807-2812 (1997).
    [CrossRef] [PubMed]
  21. B. N. Taylor and C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, 1994). This reference is available on line at http://physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf.

2006 (2)

2005 (1)

A. Ferrero, J. Campos, A. Pons, and A. Corrons, “New model for the internal quantum efficiency of photodiodes based on photocurrent analysis,” Appl. Opt. 44, 4392-4403 (2005).
[CrossRef]

2004 (1)

J. Gran and A. S. Sudbo, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204-212 (2004).
[CrossRef]

2003 (2)

J. Campos, A. Pons, and P. Corredera, “Spectral responsivity scale in the visible range based on single silicon photodiodes,” Metrologia 40, S181-S184 (2003).
[CrossRef]

C. Hicks, M. Kalatsky, R. A. Metzler, and A. O. Goushcha, “Quantum efficiency of silicon photodiodes in the near-infrared spectral range,” Appl. Opt. 42, 4415-4422 (2003).
[CrossRef] [PubMed]

2001 (1)

2000 (3)

L. Werner, J. Fischer, U. Johannsen, and J. Hartmann, “Accurate determination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nm using a laser-based cryogenic radiometer,” Metrologia 37, 279-284 (2000).
[CrossRef]

T. Kübarsepp, P. Kärhä, and E. Ikonen, “Interpolation of the spectral responsivity of silicon photodetectors in the near ultraviolet,” Appl. Opt. 39, 9-15 (2000).
[CrossRef]

G.P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic design of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stand. Technol. 105, 813-828 (2000).

1998 (1)

A. Haapalinna, P. Kärhä, and E. Ikonen, “Spectral reflectance of silicon photodiodes,” Appl. Optics 37, 729-732 (1998).
[CrossRef]

1997 (1)

1996 (1)

1992 (1)

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

1988 (1)

1983 (1)

1980 (1)

Baltes, H. P.

Brown, W.

Bruce, S. S.

T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements (U. S. Government Printing Office, 1998).

Campos, J.

A. Ferrero, J. Campos, A. Pons, and A. Corrons, “New model for the internal quantum efficiency of photodiodes based on photocurrent analysis,” Appl. Opt. 44, 4392-4403 (2005).
[CrossRef]

J. Campos, A. Pons, and P. Corredera, “Spectral responsivity scale in the visible range based on single silicon photodiodes,” Metrologia 40, S181-S184 (2003).
[CrossRef]

Corredera, P.

J. Campos, A. Pons, and P. Corredera, “Spectral responsivity scale in the visible range based on single silicon photodiodes,” Metrologia 40, S181-S184 (2003).
[CrossRef]

Corrons, A.

A. Ferrero, J. Campos, A. Pons, and A. Corrons, “New model for the internal quantum efficiency of photodiodes based on photocurrent analysis,” Appl. Opt. 44, 4392-4403 (2005).
[CrossRef]

Cromer, C. L.

Duda, C. R.

Eppeldauer, G. P.

Eppeldauer, P.

G.P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic design of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stand. Technol. 105, 813-828 (2000).

Ferrero, A.

A. Ferrero, J. Campos, A. Pons, and A. Corrons, “New model for the internal quantum efficiency of photodiodes based on photocurrent analysis,” Appl. Opt. 44, 4392-4403 (2005).
[CrossRef]

Fischer, J.

J. Hartmann, J. Fischer, U. Johannsen, and L. Werner, “Analytical model for the temperature dependence of the spectral responsivity of silicon,” J. Opt. Soc. Am. B 18, 942-947(2001).
[CrossRef]

L. Werner, J. Fischer, U. Johannsen, and J. Hartmann, “Accurate determination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nm using a laser-based cryogenic radiometer,” Metrologia 37, 279-284 (2000).
[CrossRef]

Geist, J.

Gentile, T. R.

Goushcha, A. O.

Gran, J.

J. Gran and A. S. Sudbo, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204-212 (2004).
[CrossRef]

Haapalinna, A.

A. Haapalinna, P. Kärhä, and E. Ikonen, “Spectral reflectance of silicon photodiodes,” Appl. Optics 37, 729-732 (1998).
[CrossRef]

Hartmann, J.

J. Hartmann, J. Fischer, U. Johannsen, and L. Werner, “Analytical model for the temperature dependence of the spectral responsivity of silicon,” J. Opt. Soc. Am. B 18, 942-947(2001).
[CrossRef]

L. Werner, J. Fischer, U. Johannsen, and J. Hartmann, “Accurate determination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nm using a laser-based cryogenic radiometer,” Metrologia 37, 279-284 (2000).
[CrossRef]

Hicks, C.

Houston, J. M.

Ikonen, E.

Jellison, G. E.

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

Johannsen, U.

J. Hartmann, J. Fischer, U. Johannsen, and L. Werner, “Analytical model for the temperature dependence of the spectral responsivity of silicon,” J. Opt. Soc. Am. B 18, 942-947(2001).
[CrossRef]

L. Werner, J. Fischer, U. Johannsen, and J. Hartmann, “Accurate determination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nm using a laser-based cryogenic radiometer,” Metrologia 37, 279-284 (2000).
[CrossRef]

Kalatsky, M.

Kärhä, P.

Kubarsepp, T.

Kübarsepp, T.

Kuyatt, C. E.

B. N. Taylor and C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, 1994). This reference is available on line at http://physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf.

Larason, T. C.

T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements (U. S. Government Printing Office, 1998).

Lykke, K. R.

Lynch, D. C.

G.P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic design of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stand. Technol. 105, 813-828 (2000).

Metzler, R. A.

Migdall, A.

Parr, A. C.

T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements (U. S. Government Printing Office, 1998).

Pons, A.

A. Ferrero, J. Campos, A. Pons, and A. Corrons, “New model for the internal quantum efficiency of photodiodes based on photocurrent analysis,” Appl. Opt. 44, 4392-4403 (2005).
[CrossRef]

J. Campos, A. Pons, and P. Corredera, “Spectral responsivity scale in the visible range based on single silicon photodiodes,” Metrologia 40, S181-S184 (2003).
[CrossRef]

Sametoglu, F.

F. Sametoglu, “Establishment of illuminance scale at UME with and accurately calibrated radiometer,” Opt. Rev. 13, 326-337 (2006).
[CrossRef]

Schaefer, A. R.

Sudbo, A. S.

J. Gran and A. S. Sudbo, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204-212 (2004).
[CrossRef]

Taylor, B. N.

B. N. Taylor and C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, 1994). This reference is available on line at http://physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf.

Werner, L.

J. Hartmann, J. Fischer, U. Johannsen, and L. Werner, “Analytical model for the temperature dependence of the spectral responsivity of silicon,” J. Opt. Soc. Am. B 18, 942-947(2001).
[CrossRef]

L. Werner, J. Fischer, U. Johannsen, and J. Hartmann, “Accurate determination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nm using a laser-based cryogenic radiometer,” Metrologia 37, 279-284 (2000).
[CrossRef]

Zalewski, E. F.

Appl. Opt. (9)

E. F. Zalewski and C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22, 2867-2873(1983).
[CrossRef] [PubMed]

T. R. Gentile, J. M. Houston, and C. L. Cromer, “Realization of a scale of absolute spectral response using the National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 4392-4402 (1996).
[CrossRef] [PubMed]

A. Ferrero, J. Campos, A. Pons, and A. Corrons, “New model for the internal quantum efficiency of photodiodes based on photocurrent analysis,” Appl. Opt. 44, 4392-4403 (2005).
[CrossRef]

C. Hicks, M. Kalatsky, R. A. Metzler, and A. O. Goushcha, “Quantum efficiency of silicon photodiodes in the near-infrared spectral range,” Appl. Opt. 42, 4415-4422 (2003).
[CrossRef] [PubMed]

T. Kübarsepp, P. Kärhä, and E. Ikonen, “Interpolation of the spectral responsivity of silicon photodetectors in the near ultraviolet,” Appl. Opt. 39, 9-15 (2000).
[CrossRef]

S.W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for spectral irradiance and radiance responsivity calibrations using uniform sources,” Appl. Opt. 45, 8218-8236 (2006).
[CrossRef] [PubMed]

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

J. Geist, A. Migdall, and H. P. Baltes, “Analytic representation of the silicon absorption coefficient in the indirect transition region,” Appl. Opt. 27, 3777-3779 (1988).
[CrossRef] [PubMed]

T. Kubarsepp, P. Kärhä, and E. Ikonen, “Characterization of a polarization-independent transmission trap detector,” Appl. Opt. 36, 2807-2812 (1997).
[CrossRef] [PubMed]

Appl. Optics (1)

A. Haapalinna, P. Kärhä, and E. Ikonen, “Spectral reflectance of silicon photodiodes,” Appl. Optics 37, 729-732 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Res. Natl. Inst. Stand. Technol. (1)

G.P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic design of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stand. Technol. 105, 813-828 (2000).

Metrologia (3)

L. Werner, J. Fischer, U. Johannsen, and J. Hartmann, “Accurate determination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nm using a laser-based cryogenic radiometer,” Metrologia 37, 279-284 (2000).
[CrossRef]

J. Gran and A. S. Sudbo, “Absolute calibration of silicon photodiodes by purely relative measurements,” Metrologia 41, 204-212 (2004).
[CrossRef]

J. Campos, A. Pons, and P. Corredera, “Spectral responsivity scale in the visible range based on single silicon photodiodes,” Metrologia 40, S181-S184 (2003).
[CrossRef]

Opt. Mater. (1)

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

Opt. Rev. (1)

F. Sametoglu, “Establishment of illuminance scale at UME with and accurately calibrated radiometer,” Opt. Rev. 13, 326-337 (2006).
[CrossRef]

Other (4)

Hamamatsu Corporation, 360 Foothill Road, Bridgewater, New Jersey 08807, USA.

T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements (U. S. Government Printing Office, 1998).

L-1 Standards and Technology, New Windsor, Maryland, USA. Certain trade names and company products are mentioned in the text or identified in an illustration in order to adequately specify 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.

B. N. Taylor and C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Tech. Note 1297 (National Institute of Standards and Technology, 1994). This reference is available on line at http://physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf.

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Figures (9)

Fig. 1
Fig. 1

Apparatus for trap calibration using the L-1 absolute cryogenic radiometer. The apparatus and measurements are discussed in the text.

Fig. 2
Fig. 2

External quantum efficiency (EQE) of the transmission traps: T-01 (red solid circles), T-02 (blue solid squares), and T-03 (green open diamonds). The smooth curve shows the EQE for T-02 determined from the three-parameter IQE model [Eq. (1)] discussed in Subsection 3B and the transmittance calculation discussed in Subsection  2B.

Fig. 3
Fig. 3

Schematic of the experimental apparatus used to determine the trap transmittance. The apparatus and measurements are discussed in the text.

Fig. 4
Fig. 4

Transmittance of trap T-01. The line is the calculated transmission for an oxide thickness of 30.0 nm . The error bars are smaller than the size of the points.

Fig. 5
Fig. 5

Model for the variation of the collection efficiency P ( x ) with distance into a photodiode of depth h. The dotted line shows the four-parameter model first employed in Ref. [3], and the solid line shows the three-parameter model employed in this paper. The parameters P f , P r , T, and D are discussed in the text.

Fig. 6
Fig. 6

Internal quantum efficiency (IQE) for trap T-02 versus the silicon absorption coefficient α ( λ ) in μm 1 , determined from the EQE measurements and the calculated transmittance for an oxide thickness of 30.0 nm . The solid line is a fit to the three-parameter model [Eq. (1)] with fitted parameters P f = 0.98316 ± 0.00026 , T = ( 0.31108 ± 0.0086 ) μm , and P r = 0.99921 ± 0.00002 . The error bars indicate the combined standard uncertainty, which was determined by adding the standard deviation of the trap and cryogenic radiometer signals, and an estimate of 0.01% for Type B uncertainties [21], in quadrature. The reduced χ 2 for the fit is 98 / 100 . For clarity, the estimated uncertainties of 20% in the absorption coefficient [3] are not shown.

Fig. 7
Fig. 7

Residuals (fractional difference between fit and data for IQE) for the three traps (top to bottom, T-01 to T-03). The fitted parameters for T-02 are listed in the caption for Fig. 6; the parameters for trap T-01 are P f = 0.97661 ± 0.00022 , T = ( 0.35102 ± 0.0065 ) μm , and P r = 0.99736 ± 0.00002 (reduced χ 2 = 178 / 100 ), and for trap T-03 are 0.98102 ± 0.00024 , T = ( 0.3258 ± 0.0076 ) μm , and P r = 0.99861 ± 0.00002 (reduced χ 2 = 119 / 100 ).

Fig. 8
Fig. 8

Difference between the EQE for trap T-02 determined from the IQE fit and from interpolation using Eq. (2).

Fig. 9
Fig. 9

Deviations of the fitted values for the IQE of trap T-02 for an increase of a given fitted parameter by its uncertainty, while refitting all other parameters. Key for shifts: increased P f (red, solid circles), increased T (blue, open squares), and increased P r (green, solid diamonds).

Tables (1)

Tables Icon

Table 1 Oxide Thicknesses Reported in the Literature as Determined from Reflectance of Individual Photodiodes, or Reflectance or Transmittance of Trap Detectors a

Equations (2)

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η i ( λ ) = P f + P r P f α ( λ ) T { 1 exp [ α ( λ ) T ] } .
EQE ( λ ) = a 1 1 + exp [ ( λ a 2 ) / a 3 ] b 1 1 + ( λ b 2 ) 2 / b 3 2 c 1 1 + ( λ c 2 ) 2 / c 3 2 .

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