Abstract

A model of the quantum efficiency of a planar silicon photodiode that is useful in connection with high-accuracy optical-radiation measurements is developed. The model is based mostly on macroscopic (phenomenological) optical and electronic properties of the device that must be determined from experiments on the device, but the connection with the microscopic physical properties (band structure) of silicon is made. The predictions of this model differ significantly from recent experimental results for the variation of the internal quantum efficiency with angle for a silicon photodiode as reported by Durnin <i>et al.</i> [J. Opt. Soc. Am. 71, 115 (1981)]. A repetition of these measurements is described. The results do not agree with those reported by Durnin <i>et al.</i> but do agree well with the predictions of the quantum-efficiency model.

© 1982 Optical Society of America

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  1. J. Durnin, C. Reece, and L. Mandel, "Does a photodetector always measure the rate of arrival of photons?" J. Opt. Soc. Am. 71, 115–117 (1981).
  2. F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.
  3. E. F. Zalewski and J. Geist, "Silicon photodiode absolute spectral response self-calibration," Appl. Opt. 19, 1214–1216 (1980).
  4. Also, for reasons not mentioned in the text, such as the possible noncompatibility of the concept of radiance and electromagnetic theory, e.g., see A. T. Friberg, "On the existence of a radiance function for finite planar sources of arbitrary states of coherence," J. Opt. Soc. Am. 69, 192–202 (1979).
  5. J. Geist, "On the possibility of an absolute radiometric standard based on the quantum efficiency of a silicon photodiode," Proc. Soc. Photo-Opt. Instrum. Eng. 196, 75–83 (1979), presents an earlier version of the model to be derived here.
  6. Two-millimeter thicknesses of pure borosilicate glasses with comparable boron concentration show no absorption in the visible and near-uv spectral regions.
  7. The accumulation of a dirt film on the oxide could alter this conclusion. Under normal circumstances, this process takes a period of the order of years, and such films can be removed by cleaning; e.g., see A. R. Schaefer, "Reflectance and external quantum efficiency change of a silicon photodiode after surface cleaning," Appl. Opt. 18, 2531 (1979).
  8. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), p. 632.
  9. I. H. Malitson, "Interspecimen comparison of the refractive index of fused silica," J. Opt. Soc. Am. 55, 1205–1209 (1965).
  10. H. R. Philipp, "Influence of oxide layers on the determination of the optical properties of silicon," J. Appl. Phys. 43, 2835–2839 (1972); H. R. Philipp, General Electric Research and Development, Schenectady, New York (personal communication).
  11. D. E. Aspnes and J. B. Theeten, "Spectroscopic analysis of the interface between Si and its thermally grown oxide," J. Electrochem. Soc. 127, 1359–1365 (1980).
  12. F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.
  13. J. R. Chelikowsky and M. L. Cohen, "Electronic structure of silicon," Phys. Rev. B 10, 5095–5107 (1974).
  14. W. Hanke and L. J. Sham, "Many-particle effects in the optical excitations of a semiconductor," Phys. Rev. Lett. 43, 387–390 (1979).
  15. O. Christensen, "Quantum efficiency of the internal photoelectric effect in silicon and germanium," J. Appl. Phys. 47, 689–695 (1976).
  16. E. Antončík and N. K. S. Gaur, "Theory of the quantum efficiency in silicon and germanium," J. Phys. C. 11, 735–743 (1978).
  17. R. C. Alig, S. Bloom, and C. W. Struck, "Scattering by ionization and phonon emission in semiconductors," Phys. Rev. B 22, 5565–5582 (1980).
  18. J. Geist, E. F. Zalewski, and L. T. Bao, "The quantum yield of silicon in the near-ultraviolet" (National Bureau of Standards, Washington, D.C., 1981).
  19. W. Spitzer and H. Y. Fan, "Infrared absorption in n-type silicon," Phys. Rev. 108, 268–271 (1957).
  20. H. J. Hovel, Solar Cells, Vol. 11 of Semiconductors and Semi-metals, R. K. Willardson and A. C. Beer, eds. (Academic, New York, 1975), p. 16.
  21. J. Geist and J. R. Lowney, "Effect of band-gap narrowing on the built-in electric field in n-type silicon," J. Appl. Phys. 52, 1121–1123 (1981).
  22. G. D. Mahan, "Energy gap in Si and Ge: impurity dependence," J. Appl. Phys. 51, 2634–2646 (1980).
  23. Ref. 20, Chap. 2.
  24. S. S. Li, "The dopant density and temperature dependence of hole mobility and resistivity in boron doped silicon," Solid-State Electron. 21, 1109–1117 (1978), describes such an effort for holes.
  25. J. Geist, "Silicon photodiode front region collection efficiency models," J. Appl. Phys. 51, 3993–3995 (1980).
  26. J. Geist, E. F. Zalewski, and A. R. Schaefer, "Spectral response self-calibration and interpolation of silicon photodiodes," Appl. Opt. 19, 3795–3799 (1980).
  27. J. Geist, E. Liang, and A. R. Schaefer, "Complete collection of minority carriers from the inversion layer in induced junction diodes," J. Appl. Phys. 52, 4879–4881 (1981).
  28. J. Geist and E. F. Zalewski, "The quantum yield of silicon in the visible," Appl. Phys. Lett. 35, 503–506 (1979).
  29. J. Geist, A. J. D. Farmer, P. J. Martin, F. J. Wilkinson, and S. Collicott, "Elimination of interface recombination in oxide passivated silicon p+n photodiodes by storage of negative charge on the oxide surface," Appl. Opt. 21, 1130–1135 (1982).
  30. Identification of commercial devices is provided for completeness of the experimental procedure. It implies neither endorsement of the National Bureau of Standards nor that the device is the best available for the particular application.

1982 (1)

1981 (3)

J. Durnin, C. Reece, and L. Mandel, "Does a photodetector always measure the rate of arrival of photons?" J. Opt. Soc. Am. 71, 115–117 (1981).

J. Geist and J. R. Lowney, "Effect of band-gap narrowing on the built-in electric field in n-type silicon," J. Appl. Phys. 52, 1121–1123 (1981).

J. Geist, E. Liang, and A. R. Schaefer, "Complete collection of minority carriers from the inversion layer in induced junction diodes," J. Appl. Phys. 52, 4879–4881 (1981).

1980 (6)

J. Geist, "Silicon photodiode front region collection efficiency models," J. Appl. Phys. 51, 3993–3995 (1980).

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

G. D. Mahan, "Energy gap in Si and Ge: impurity dependence," J. Appl. Phys. 51, 2634–2646 (1980).

R. C. Alig, S. Bloom, and C. W. Struck, "Scattering by ionization and phonon emission in semiconductors," Phys. Rev. B 22, 5565–5582 (1980).

E. F. Zalewski and J. Geist, "Silicon photodiode absolute spectral response self-calibration," Appl. Opt. 19, 1214–1216 (1980).

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

1979 (5)

W. Hanke and L. J. Sham, "Many-particle effects in the optical excitations of a semiconductor," Phys. Rev. Lett. 43, 387–390 (1979).

Also, for reasons not mentioned in the text, such as the possible noncompatibility of the concept of radiance and electromagnetic theory, e.g., see A. T. Friberg, "On the existence of a radiance function for finite planar sources of arbitrary states of coherence," J. Opt. Soc. Am. 69, 192–202 (1979).

J. Geist, "On the possibility of an absolute radiometric standard based on the quantum efficiency of a silicon photodiode," Proc. Soc. Photo-Opt. Instrum. Eng. 196, 75–83 (1979), presents an earlier version of the model to be derived here.

The accumulation of a dirt film on the oxide could alter this conclusion. Under normal circumstances, this process takes a period of the order of years, and such films can be removed by cleaning; e.g., see A. R. Schaefer, "Reflectance and external quantum efficiency change of a silicon photodiode after surface cleaning," Appl. Opt. 18, 2531 (1979).

J. Geist and E. F. Zalewski, "The quantum yield of silicon in the visible," Appl. Phys. Lett. 35, 503–506 (1979).

1978 (2)

S. S. Li, "The dopant density and temperature dependence of hole mobility and resistivity in boron doped silicon," Solid-State Electron. 21, 1109–1117 (1978), describes such an effort for holes.

E. Antončík and N. K. S. Gaur, "Theory of the quantum efficiency in silicon and germanium," J. Phys. C. 11, 735–743 (1978).

1976 (1)

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

1974 (1)

J. R. Chelikowsky and M. L. Cohen, "Electronic structure of silicon," Phys. Rev. B 10, 5095–5107 (1974).

1965 (1)

1957 (1)

W. Spitzer and H. Y. Fan, "Infrared absorption in n-type silicon," Phys. Rev. 108, 268–271 (1957).

Alig, R. C.

R. C. Alig, S. Bloom, and C. W. Struck, "Scattering by ionization and phonon emission in semiconductors," Phys. Rev. B 22, 5565–5582 (1980).

Antoncík, E.

E. Antončík and N. K. S. Gaur, "Theory of the quantum efficiency in silicon and germanium," J. Phys. C. 11, 735–743 (1978).

Aspnes, D. E.

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

Bao, L. T.

J. Geist, E. F. Zalewski, and L. T. Bao, "The quantum yield of silicon in the near-ultraviolet" (National Bureau of Standards, Washington, D.C., 1981).

Bassani, F.

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.

Bloom, S.

R. C. Alig, S. Bloom, and C. W. Struck, "Scattering by ionization and phonon emission in semiconductors," Phys. Rev. B 22, 5565–5582 (1980).

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), p. 632.

Chelikowsky, J. R.

J. R. Chelikowsky and M. L. Cohen, "Electronic structure of silicon," Phys. Rev. B 10, 5095–5107 (1974).

Christensen, O.

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

Cohen, M. L.

J. R. Chelikowsky and M. L. Cohen, "Electronic structure of silicon," Phys. Rev. B 10, 5095–5107 (1974).

Collicott, S.

Durnin, J.

Fan, H. Y.

W. Spitzer and H. Y. Fan, "Infrared absorption in n-type silicon," Phys. Rev. 108, 268–271 (1957).

Farmer, A. J. D.

Friberg, A. T.

Gaur, N. K. S.

E. Antončík and N. K. S. Gaur, "Theory of the quantum efficiency in silicon and germanium," J. Phys. C. 11, 735–743 (1978).

Geist, J.

J. Geist, A. J. D. Farmer, P. J. Martin, F. J. Wilkinson, and S. Collicott, "Elimination of interface recombination in oxide passivated silicon p+n photodiodes by storage of negative charge on the oxide surface," Appl. Opt. 21, 1130–1135 (1982).

J. Geist, E. Liang, and A. R. Schaefer, "Complete collection of minority carriers from the inversion layer in induced junction diodes," J. Appl. Phys. 52, 4879–4881 (1981).

J. Geist and J. R. Lowney, "Effect of band-gap narrowing on the built-in electric field in n-type silicon," J. Appl. Phys. 52, 1121–1123 (1981).

E. F. Zalewski and J. Geist, "Silicon photodiode absolute spectral response self-calibration," Appl. Opt. 19, 1214–1216 (1980).

J. Geist, "Silicon photodiode front region collection efficiency models," J. Appl. Phys. 51, 3993–3995 (1980).

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

J. Geist and E. F. Zalewski, "The quantum yield of silicon in the visible," Appl. Phys. Lett. 35, 503–506 (1979).

J. Geist, "On the possibility of an absolute radiometric standard based on the quantum efficiency of a silicon photodiode," Proc. Soc. Photo-Opt. Instrum. Eng. 196, 75–83 (1979), presents an earlier version of the model to be derived here.

J. Geist, E. F. Zalewski, and L. T. Bao, "The quantum yield of silicon in the near-ultraviolet" (National Bureau of Standards, Washington, D.C., 1981).

Hanke, W.

W. Hanke and L. J. Sham, "Many-particle effects in the optical excitations of a semiconductor," Phys. Rev. Lett. 43, 387–390 (1979).

Hovel, H. J.

H. J. Hovel, Solar Cells, Vol. 11 of Semiconductors and Semi-metals, R. K. Willardson and A. C. Beer, eds. (Academic, New York, 1975), p. 16.

Li, S. S.

S. S. Li, "The dopant density and temperature dependence of hole mobility and resistivity in boron doped silicon," Solid-State Electron. 21, 1109–1117 (1978), describes such an effort for holes.

Liang, E.

J. Geist, E. Liang, and A. R. Schaefer, "Complete collection of minority carriers from the inversion layer in induced junction diodes," J. Appl. Phys. 52, 4879–4881 (1981).

Lowney, J. R.

J. Geist and J. R. Lowney, "Effect of band-gap narrowing on the built-in electric field in n-type silicon," J. Appl. Phys. 52, 1121–1123 (1981).

Mahan, G. D.

G. D. Mahan, "Energy gap in Si and Ge: impurity dependence," J. Appl. Phys. 51, 2634–2646 (1980).

Malitson, I. H.

Mandel, L.

Martin, P. J.

Parravicini, G. Pastori

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.

Philipp, H. R.

H. R. Philipp, "Influence of oxide layers on the determination of the optical properties of silicon," J. Appl. Phys. 43, 2835–2839 (1972); H. R. Philipp, General Electric Research and Development, Schenectady, New York (personal communication).

Reece, C.

Schaefer, A. R.

Sham, L. J.

W. Hanke and L. J. Sham, "Many-particle effects in the optical excitations of a semiconductor," Phys. Rev. Lett. 43, 387–390 (1979).

Spitzer, W.

W. Spitzer and H. Y. Fan, "Infrared absorption in n-type silicon," Phys. Rev. 108, 268–271 (1957).

Struck, C. W.

R. C. Alig, S. Bloom, and C. W. Struck, "Scattering by ionization and phonon emission in semiconductors," Phys. Rev. B 22, 5565–5582 (1980).

Theeten, J. B.

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

Wilkinson, F. J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), p. 632.

Zalewski, E. F.

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

E. F. Zalewski and J. Geist, "Silicon photodiode absolute spectral response self-calibration," Appl. Opt. 19, 1214–1216 (1980).

J. Geist and E. F. Zalewski, "The quantum yield of silicon in the visible," Appl. Phys. Lett. 35, 503–506 (1979).

J. Geist, E. F. Zalewski, and L. T. Bao, "The quantum yield of silicon in the near-ultraviolet" (National Bureau of Standards, Washington, D.C., 1981).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

J. Geist and E. F. Zalewski, "The quantum yield of silicon in the visible," Appl. Phys. Lett. 35, 503–506 (1979).

J. Appl. Phys. (5)

J. Geist, E. Liang, and A. R. Schaefer, "Complete collection of minority carriers from the inversion layer in induced junction diodes," J. Appl. Phys. 52, 4879–4881 (1981).

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

J. Geist and J. R. Lowney, "Effect of band-gap narrowing on the built-in electric field in n-type silicon," J. Appl. Phys. 52, 1121–1123 (1981).

G. D. Mahan, "Energy gap in Si and Ge: impurity dependence," J. Appl. Phys. 51, 2634–2646 (1980).

J. Geist, "Silicon photodiode front region collection efficiency models," J. Appl. Phys. 51, 3993–3995 (1980).

J. Electrochem. Soc. (1)

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

J. Opt. Soc. Am. (3)

J. Phys. C. (1)

E. Antončík and N. K. S. Gaur, "Theory of the quantum efficiency in silicon and germanium," J. Phys. C. 11, 735–743 (1978).

Phys. Rev. (1)

W. Spitzer and H. Y. Fan, "Infrared absorption in n-type silicon," Phys. Rev. 108, 268–271 (1957).

Phys. Rev. B (2)

R. C. Alig, S. Bloom, and C. W. Struck, "Scattering by ionization and phonon emission in semiconductors," Phys. Rev. B 22, 5565–5582 (1980).

J. R. Chelikowsky and M. L. Cohen, "Electronic structure of silicon," Phys. Rev. B 10, 5095–5107 (1974).

Phys. Rev. Lett. (1)

W. Hanke and L. J. Sham, "Many-particle effects in the optical excitations of a semiconductor," Phys. Rev. Lett. 43, 387–390 (1979).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. Geist, "On the possibility of an absolute radiometric standard based on the quantum efficiency of a silicon photodiode," Proc. Soc. Photo-Opt. Instrum. Eng. 196, 75–83 (1979), presents an earlier version of the model to be derived here.

Solid-State Electron. (1)

S. S. Li, "The dopant density and temperature dependence of hole mobility and resistivity in boron doped silicon," Solid-State Electron. 21, 1109–1117 (1978), describes such an effort for holes.

Other (9)

H. R. Philipp, "Influence of oxide layers on the determination of the optical properties of silicon," J. Appl. Phys. 43, 2835–2839 (1972); H. R. Philipp, General Electric Research and Development, Schenectady, New York (personal communication).

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.

H. J. Hovel, Solar Cells, Vol. 11 of Semiconductors and Semi-metals, R. K. Willardson and A. C. Beer, eds. (Academic, New York, 1975), p. 16.

Ref. 20, Chap. 2.

F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon, Oxford, 1975), Chap. 5.

J. Geist, E. F. Zalewski, and L. T. Bao, "The quantum yield of silicon in the near-ultraviolet" (National Bureau of Standards, Washington, D.C., 1981).

Two-millimeter thicknesses of pure borosilicate glasses with comparable boron concentration show no absorption in the visible and near-uv spectral regions.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), p. 632.

Identification of commercial devices is provided for completeness of the experimental procedure. It implies neither endorsement of the National Bureau of Standards nor that the device is the best available for the particular application.

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