Abstract

The quantum efficiency of silicon photodiodes and factors that might be responsible for the drop in quantum efficiency in the near-infrared spectral range were analyzed. It was shown that poor reflectivity from the rear surface of the die could account for a decrease in Si photodiode quantum efficiency in near-infrared spectral range by more than 20%. The photodiode quantum efficiency was modeled with an appropriate representation for the carrier-collection efficiency dependence on the die penetration depth. A corrected analytical expression for calculating the photodiode quantum efficiency is given. Some methods to improve the quantum efficiency of silicon photodiodes in near-infrared spectral range are discussed.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).
  2. O. Christensen, “Quantum efficiency of the internal photoelectric effect in silicon and germanium,” J. Appl. Phys. 47, 689–695 (1976).
    [CrossRef]
  3. A. Haapalinna, P. Kärhä, E. Ikonen, “Spectral reflectance of silicon photodiodes,” Appl. Opt. 37, 729–732 (1998).
    [CrossRef]
  4. M. J. Keevers, M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66, 174–176 (1995).
    [CrossRef]
  5. A. S. Grove, Physics and Technology of Semiconductor Devices (Wiley, New York, 1967).
  6. J. Geist, “Silicon photodiode front region collection efficiency models,” J. Appl. Phys. 51, 3993–3995 (1980).
    [CrossRef]
  7. T. S. Moss, Optical Properties of Semiconductors (Butterworth Scientific, London, 1959).
  8. L. Werner, J. Fischer, U. Johannsen, 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]
  9. J. Hartmann, J. Fischer, U. Johannsen, 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. J. Geist, E. F. Zalewski, “The quantum yield of silicon in the visible,” Appl. Phys. Lett. 35, 503–505 (1979).
    [CrossRef]
  11. E. Antončik, N. K. S. Gaur, “Theory of the quantum efficiency in silicon and germanium,” J. Phys. C 11, 735–744 (1978).
    [CrossRef]
  12. R. Korde, J. Geist, “Quantum efficiency stability of silicon photodiodes,” Appl. Opt. 26, 5284–5290 (1987).
    [CrossRef] [PubMed]
  13. S. E. Holland, N. W. Wang, W. W. Moses, “Development of low noise, back-side illuminated silicon photodiode arrays,” IEEE Trans. Nucl. Sci. 44, 443–447 (1997).
    [CrossRef]
  14. R. Köhler, R. Goebel, R. Pello, J. Bonhoure, “Effects of humidity and cleaning on the sensitivity of Si photodiodes,” Metrologia 28, 211–215 (1991).
    [CrossRef]
  15. T. N. Swe, K. S. Yeo, K. W. Chew, S. Chu, “Design and optimization of novel high responsivity, wideband silicon photodiode,” Jpn. J. Appl. Phys. 40, 2738–2740 (2001).
    [CrossRef]
  16. M. J. Keevers, M. A. Green, “Extended infrared response of silicon solar cells and the impurity photovoltaic effect,” Sol. Energy Mater. Sol. Cells 41/42, 195–204 (1996).
    [CrossRef]
  17. T. Trupke, M. A. Green, P. Würfel, “Improving solar cell efficiencies of subband-gap light,” J. Appl. Phys. 92, 4117–4122 (2002).
    [CrossRef]
  18. M. A. Green, D. Jordan, “Technology and economics of three advanced silicon solar cells,” Prog. Photovolt. Res. Appl. 6, 169–180 (1998).
    [CrossRef]
  19. M. A. Green, “Third generation photovoltaics: solar cells for 2020 and beyond,” Physica E 14, 65–70 (2002).
    [CrossRef]
  20. E. Daub, P. Würfel, “Ultra-low values of the absorption coefficient of Si obtained from luminescence,” Phys. Rev. Lett. 74, 1020–1023 (1995).
    [CrossRef] [PubMed]
  21. W. C. Dash, R. Neuman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99, 1151–1155 (1955).
    [CrossRef]
  22. 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]
  23. T. R. Gentile, J. M. Houston, 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, 4392–4403 (1996).
    [CrossRef] [PubMed]
  24. S. Adachi, Optical Constants of Crystalline and Amorphous Semiconductors. Numerical Data and Graphical Information (Kluwer Academic, Boston, 1999).
  25. J. Geist, “Quantum efficiency of the p-n junction in silicon as an absolute radiometric standard,” Appl. Opt. 18, 760–762 (1979).
    [CrossRef] [PubMed]

2002 (2)

T. Trupke, M. A. Green, P. Würfel, “Improving solar cell efficiencies of subband-gap light,” J. Appl. Phys. 92, 4117–4122 (2002).
[CrossRef]

M. A. Green, “Third generation photovoltaics: solar cells for 2020 and beyond,” Physica E 14, 65–70 (2002).
[CrossRef]

2001 (2)

T. N. Swe, K. S. Yeo, K. W. Chew, S. Chu, “Design and optimization of novel high responsivity, wideband silicon photodiode,” Jpn. J. Appl. Phys. 40, 2738–2740 (2001).
[CrossRef]

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

2000 (1)

L. Werner, J. Fischer, U. Johannsen, 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]

1998 (2)

M. A. Green, D. Jordan, “Technology and economics of three advanced silicon solar cells,” Prog. Photovolt. Res. Appl. 6, 169–180 (1998).
[CrossRef]

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

1997 (1)

S. E. Holland, N. W. Wang, W. W. Moses, “Development of low noise, back-side illuminated silicon photodiode arrays,” IEEE Trans. Nucl. Sci. 44, 443–447 (1997).
[CrossRef]

1996 (2)

M. J. Keevers, M. A. Green, “Extended infrared response of silicon solar cells and the impurity photovoltaic effect,” Sol. Energy Mater. Sol. Cells 41/42, 195–204 (1996).
[CrossRef]

T. R. Gentile, J. M. Houston, 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, 4392–4403 (1996).
[CrossRef] [PubMed]

1995 (2)

E. Daub, P. Würfel, “Ultra-low values of the absorption coefficient of Si obtained from luminescence,” Phys. Rev. Lett. 74, 1020–1023 (1995).
[CrossRef] [PubMed]

M. J. Keevers, M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66, 174–176 (1995).
[CrossRef]

1991 (1)

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

1987 (1)

1980 (2)

1979 (2)

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

J. Geist, E. F. Zalewski, “The quantum yield of silicon in the visible,” Appl. Phys. Lett. 35, 503–505 (1979).
[CrossRef]

1978 (1)

E. Antončik, N. K. S. Gaur, “Theory of the quantum efficiency in silicon and germanium,” J. Phys. C 11, 735–744 (1978).
[CrossRef]

1976 (1)

O. Christensen, “Quantum efficiency of the internal photoelectric effect in silicon and germanium,” J. Appl. Phys. 47, 689–695 (1976).
[CrossRef]

1955 (1)

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

Adachi, S.

S. Adachi, Optical Constants of Crystalline and Amorphous Semiconductors. Numerical Data and Graphical Information (Kluwer Academic, Boston, 1999).

Antoncik, E.

E. Antončik, N. K. S. Gaur, “Theory of the quantum efficiency in silicon and germanium,” J. Phys. C 11, 735–744 (1978).
[CrossRef]

Bonhoure, J.

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

Chew, K. W.

T. N. Swe, K. S. Yeo, K. W. Chew, S. Chu, “Design and optimization of novel high responsivity, wideband silicon photodiode,” Jpn. J. Appl. Phys. 40, 2738–2740 (2001).
[CrossRef]

Christensen, O.

O. Christensen, “Quantum efficiency of the internal photoelectric effect in silicon and germanium,” J. Appl. Phys. 47, 689–695 (1976).
[CrossRef]

Chu, S.

T. N. Swe, K. S. Yeo, K. W. Chew, S. Chu, “Design and optimization of novel high responsivity, wideband silicon photodiode,” Jpn. J. Appl. Phys. 40, 2738–2740 (2001).
[CrossRef]

Cromer, C. L.

Dash, W. C.

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

Daub, E.

E. Daub, P. Würfel, “Ultra-low values of the absorption coefficient of Si obtained from luminescence,” Phys. Rev. Lett. 74, 1020–1023 (1995).
[CrossRef] [PubMed]

Fischer, J.

J. Hartmann, J. Fischer, U. Johannsen, 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, 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]

Gaur, N. K. S.

E. Antončik, N. K. S. Gaur, “Theory of the quantum efficiency in silicon and germanium,” J. Phys. C 11, 735–744 (1978).
[CrossRef]

Geist, J.

Gentile, T. R.

Goebel, R.

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

Green, M. A.

M. A. Green, “Third generation photovoltaics: solar cells for 2020 and beyond,” Physica E 14, 65–70 (2002).
[CrossRef]

T. Trupke, M. A. Green, P. Würfel, “Improving solar cell efficiencies of subband-gap light,” J. Appl. Phys. 92, 4117–4122 (2002).
[CrossRef]

M. A. Green, D. Jordan, “Technology and economics of three advanced silicon solar cells,” Prog. Photovolt. Res. Appl. 6, 169–180 (1998).
[CrossRef]

M. J. Keevers, M. A. Green, “Extended infrared response of silicon solar cells and the impurity photovoltaic effect,” Sol. Energy Mater. Sol. Cells 41/42, 195–204 (1996).
[CrossRef]

M. J. Keevers, M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66, 174–176 (1995).
[CrossRef]

Grove, A. S.

A. S. Grove, Physics and Technology of Semiconductor Devices (Wiley, New York, 1967).

Haapalinna, A.

Hartmann, J.

J. Hartmann, J. Fischer, U. Johannsen, 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, 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]

Holland, S. E.

S. E. Holland, N. W. Wang, W. W. Moses, “Development of low noise, back-side illuminated silicon photodiode arrays,” IEEE Trans. Nucl. Sci. 44, 443–447 (1997).
[CrossRef]

Houston, J. M.

Ikonen, E.

Johannsen, U.

J. Hartmann, J. Fischer, U. Johannsen, 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, 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]

Jordan, D.

M. A. Green, D. Jordan, “Technology and economics of three advanced silicon solar cells,” Prog. Photovolt. Res. Appl. 6, 169–180 (1998).
[CrossRef]

Kärhä, P.

Keevers, M. J.

M. J. Keevers, M. A. Green, “Extended infrared response of silicon solar cells and the impurity photovoltaic effect,” Sol. Energy Mater. Sol. Cells 41/42, 195–204 (1996).
[CrossRef]

M. J. Keevers, M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66, 174–176 (1995).
[CrossRef]

Köhler, R.

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

Korde, R.

Moses, W. W.

S. E. Holland, N. W. Wang, W. W. Moses, “Development of low noise, back-side illuminated silicon photodiode arrays,” IEEE Trans. Nucl. Sci. 44, 443–447 (1997).
[CrossRef]

Moss, T. S.

T. S. Moss, Optical Properties of Semiconductors (Butterworth Scientific, London, 1959).

Neuman, R.

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

Pello, R.

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

Schaefer, A. R.

Swe, T. N.

T. N. Swe, K. S. Yeo, K. W. Chew, S. Chu, “Design and optimization of novel high responsivity, wideband silicon photodiode,” Jpn. J. Appl. Phys. 40, 2738–2740 (2001).
[CrossRef]

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).

Trupke, T.

T. Trupke, M. A. Green, P. Würfel, “Improving solar cell efficiencies of subband-gap light,” J. Appl. Phys. 92, 4117–4122 (2002).
[CrossRef]

Wang, N. W.

S. E. Holland, N. W. Wang, W. W. Moses, “Development of low noise, back-side illuminated silicon photodiode arrays,” IEEE Trans. Nucl. Sci. 44, 443–447 (1997).
[CrossRef]

Werner, L.

J. Hartmann, J. Fischer, U. Johannsen, 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, 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]

Würfel, P.

T. Trupke, M. A. Green, P. Würfel, “Improving solar cell efficiencies of subband-gap light,” J. Appl. Phys. 92, 4117–4122 (2002).
[CrossRef]

E. Daub, P. Würfel, “Ultra-low values of the absorption coefficient of Si obtained from luminescence,” Phys. Rev. Lett. 74, 1020–1023 (1995).
[CrossRef] [PubMed]

Yeo, K. S.

T. N. Swe, K. S. Yeo, K. W. Chew, S. Chu, “Design and optimization of novel high responsivity, wideband silicon photodiode,” Jpn. J. Appl. Phys. 40, 2738–2740 (2001).
[CrossRef]

Zalewski, E. F.

Appl. Opt. (5)

Appl. Phys. Lett. (2)

M. J. Keevers, M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66, 174–176 (1995).
[CrossRef]

J. Geist, E. F. Zalewski, “The quantum yield of silicon in the visible,” Appl. Phys. Lett. 35, 503–505 (1979).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

S. E. Holland, N. W. Wang, W. W. Moses, “Development of low noise, back-side illuminated silicon photodiode arrays,” IEEE Trans. Nucl. Sci. 44, 443–447 (1997).
[CrossRef]

J. Appl. Phys. (3)

T. Trupke, M. A. Green, P. Würfel, “Improving solar cell efficiencies of subband-gap light,” J. Appl. Phys. 92, 4117–4122 (2002).
[CrossRef]

O. Christensen, “Quantum efficiency of the internal photoelectric effect in silicon and germanium,” J. Appl. Phys. 47, 689–695 (1976).
[CrossRef]

J. Geist, “Silicon photodiode front region collection efficiency models,” J. Appl. Phys. 51, 3993–3995 (1980).
[CrossRef]

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

J. Phys. C (1)

E. Antončik, N. K. S. Gaur, “Theory of the quantum efficiency in silicon and germanium,” J. Phys. C 11, 735–744 (1978).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. N. Swe, K. S. Yeo, K. W. Chew, S. Chu, “Design and optimization of novel high responsivity, wideband silicon photodiode,” Jpn. J. Appl. Phys. 40, 2738–2740 (2001).
[CrossRef]

Metrologia (2)

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

L. Werner, J. Fischer, U. Johannsen, 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]

Phys. Rev. (1)

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

Phys. Rev. Lett. (1)

E. Daub, P. Würfel, “Ultra-low values of the absorption coefficient of Si obtained from luminescence,” Phys. Rev. Lett. 74, 1020–1023 (1995).
[CrossRef] [PubMed]

Physica E (1)

M. A. Green, “Third generation photovoltaics: solar cells for 2020 and beyond,” Physica E 14, 65–70 (2002).
[CrossRef]

Prog. Photovolt. Res. Appl. (1)

M. A. Green, D. Jordan, “Technology and economics of three advanced silicon solar cells,” Prog. Photovolt. Res. Appl. 6, 169–180 (1998).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

M. J. Keevers, M. A. Green, “Extended infrared response of silicon solar cells and the impurity photovoltaic effect,” Sol. Energy Mater. Sol. Cells 41/42, 195–204 (1996).
[CrossRef]

Other (4)

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).

T. S. Moss, Optical Properties of Semiconductors (Butterworth Scientific, London, 1959).

A. S. Grove, Physics and Technology of Semiconductor Devices (Wiley, New York, 1967).

S. Adachi, Optical Constants of Crystalline and Amorphous Semiconductors. Numerical Data and Graphical Information (Kluwer Academic, Boston, 1999).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Dependence of the responsivity at 1060 nm on the reverse bias for the three photodiodes discussed in the text. The resistivity of bulk Si used to build photodiodes 1, 2, and 3 were ca. 8 k Ω cm, 5–9 k Ω cm, and 8–15 k Ω cm, respectively.

Fig. 2
Fig. 2

(a) Optical transmittance of the p-type bulk Si wafers ground to the 75-μm thickness and polished. Curve 1, pure p-type bulk material (resistivity ρ = 8–16 k Ω cm); curve 2, 12-μm-thick n-type (Boron) diffusion on the top of the pure p-type bulk material (resistivity ρ ≈ 8 k Ω cm); curve 3, low-resistivity (ρ = 0.01–0.02 Ω cm) p-type bulk material. The wafers had the native thickness Si oxide on the surfaces. (b) Intrinsic optical transmittance of the dies with the junction depths of ∼3 μm (curve 1) and ∼12 μm (curve 2). The dies’ thickness was 75 μm, and the Si oxide layer was native. See the text for more details.

Fig. 3
Fig. 3

Schematic of an optical beam reflection from the surface of the wafer (die). I 0 is an incident beam, I R is the total reflection from the wafer (die) that accounts for the multiple reflections, I R1 is the beam reflected from the front surface. The dotted and dashed lines show schematically the beam propagation inside the sample and the transmitted beam, respectively.

Fig. 4
Fig. 4

Experimentally measured total reflectance R (λ) and retrieved reflectance R 1(λ) with Eq. (3) for the two dies. (a) Antireflection Si oxide layer on the front surface and gold-plated and sintered backside of the die. (b) Si oxide-Si nitride antireflection double layer on the front surface and gold-plated, not sintered backside of the die. Experimental graphs R (λ) were measured with an HP RSA-8453 integrating sphere reflectance spectrometer. The theoretical dependencies for the front side reflectance are shown with the dashed curves. See text for more details.

Fig. 5
Fig. 5

Experimentally measured internal QE ηin(λ) (solid curve). Wafer or die properties: high dc resistivity (8–16 k Ω cm) 381-μm-thick wafer, polished backside, gold-plated wafer backside with sintering, ∼3-μm junction depth. Curves 2 (solid squares), 3 (solid triangles), and 4 (open circles) are the theoretical internal QE’s calculated for the 381-μm-thick die by use of the literature data on Si absorption coefficient,4,24 with the assumption of no losses due to the carrier recombination on the surface and in the crystal bulk, and for the rear surface reflectance of 95%, 56%, and 35%, respectively.

Fig. 6
Fig. 6

Profiles of the carrier-collection efficiency P(x) used in fitting experimental results. Value l is the characteristic length close to the junction depth, d is the depletion width in the case of the graph shown in (a) or an independent characteristic depth in the case of the graph shown in (b), h is the die thickness. See text for more details.

Fig. 7
Fig. 7

Top, Fitting results for the internal QE ηin(λ) of the 381-μm-thick die with the back metal sintered. Solid curve is the experimentally measured internal QE described also in Fig. 5. The curve plotted in solid squares is the best-fit result for the model a [see Fig. 6(a) for the carrier-collection efficiency function] with all free-running parameters shown in Table 1. Bottom, Fitting residues showing deviation of the theoretical dependence from the experimentally measured curve in NIR spectral range.

Tables (1)

Tables Icon

Table 1 Best-Fit Parameters for the Two Profiles of the Carriers’-Collection Efficiency Function P(x) shown in Fig. 6 and for the Two Different Dies

Equations (8)

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

Sλ=IpPopt=ηexλqhνηexλλμm1.23948=1-R1ληinλλμm1.23948,
Tiλ=Tλ1-Rλ.
RλIRI0=R1λ+RB1-R1λ2 exp-2αλh +RB2R1λexp-2αλh1-R1λ2+RB3R12λ×1-R1λ2exp-2αλh3+,
ηinλ=1-exp-αλh0hdxαλexp-αλx.
ηinλ=0hdxPxαλexp-αλx.
ηinλ=0hdxPxαλexp-αλx +RB exp-αλh0hdxPh-x ×αλexp-αλx,
ηinλ=PS+1-PSαλl1-exp-αλl-1-PBαλd-lexp-αλl-exp-αλd-PB exp-αλh+RB exp-αλh×PB+1-PSαλlexp-αλh-exp-αλh-l-1-PBαλd-lexp-αλh-l-exp-αλh-d-PS exp-αλh,
ηinλ=PS+PB-PSαλl1-exp-αλl+PB-PRαλh-dexp-αλh-exp-αλd-PR exp-αλh+RB exp-αλhPR+PB-PRαλh-d×1-exp-αλh-d+PB-PSαλlexp-αλh-exp-αλh-l-PS exp-αλh,

Metrics