Abstract

The spectral dependence of the infrared absorption cross section of As in Si near 0 K has been determined from infrared transmission measurements for three As concentrations (5.3, 8.4, and 15.9 × 1017 cm−3) in the impurity band regime. The results demonstrate some features of physical interest. With increasing As concentration, the lines associated with the intra-atomic transitions broaden asymmetrically, while the integral of the total absorption cross section over photon energy is conserved as required by the oscillator strength sum rule. It thus appears that the cross section for the intra-atomic transitions is conserved as the lines hybridize with the continuum. Comparison of our results with photoionization cross-sectional data suggests that the lines contribute to the cross section for photoionization through field and thermally assisted transitions when they are near the threshold for photoionization.

© 1989 Optical Society of America

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References

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  1. F. Szmulowicz, F. L. Madarasz, “Blocked Impurity Band Detectors—An Analytical Model: Figures of Merit,” J. Appl. Phys. 62, 2533 (1987) and references therein.
    [CrossRef]
  2. M. D. Petroff, M. G. Stapelbroek, W. A. Kleinhans, “Detection of Individual 0.4–28μm Wavelength Photons Via Impurity-Impact Ionization in a Solid-State Photomultiplier,” Appl. Phys. Lett. 51, 406 (1987).
    [CrossRef]
  3. J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral Response Self-Calibration and Interpolation of Silicon Photodiodes,” Appl. Opt. 19, 3795 (1980).
    [CrossRef] [PubMed]
  4. M. D. Petroff, M. G. Stapelbroek, “Spectral Response, Gain, and Noise Models for IBC Detectors,” IRIA-IRIS Proceedings, Specialty Group on Infrared Detectors (ERIM, Ann Arbor, MI, 1985).
  5. The author thanks R. A. Florence of Rockwell International, Anaheim, CA 92803-3105, for providing the samples used in this work.
  6. The author thanks J. R. Ehrstein of NIST (NBS) for these measurements.
  7. Solecon Laboratories, San Jose, CA 95131. This and other references to commercial products or services are included in this paper for the sole purpose of facilitating the complete description of the experimental procedure. Their inclusion constitutes neither an endorsement of the product or service, nor the implication that it is the best for the particular application.
  8. The author thanks W. Gallagher of NIST (NBS) for this measurement.
  9. G. Masetti, M. Severi, S. Solmi, “Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron-Doped Silicon,” IEEE Trans. Electron Devices ED-30, 764 (1983).
    [CrossRef]
  10. The author thanks P. H. Chi and D. S. Simons of NIST (NBS) for these measurements.
  11. W. R. Thurber, R. L. Mattis, Y. M. Liu, J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 1807 (1980).
    [CrossRef]
  12. J. W. Bichard, J. C. Giles, “Optical Absorption Spectra of Arsenic and Phosphorus in Silicon,” Can. J. Phys. 40, 1480 (1962).
    [CrossRef]
  13. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Properties of Solids, E. D. Palik, Ed. (Academic, New York, 1985), p. 547.
  14. MIDAC, Costa Mesa, CA 92627.
  15. D. D. Coon, R. P. G. Karunasiri, “Green’s-Function-Quantum-Defect Treatment of Impurity Photoionization in Semiconductors,” Phys. Rev. B 33, 8228 (1986).
    [CrossRef]
  16. F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 340 (1963).
  17. M. G. Stapelbroek, Rockwell International; private communication (1988).
  18. N. Sclar, “Properties of Doped Silicon and Germanium Infrared Detectors,” Prog. Quantum Electron. 9, 149 (1984).
    [CrossRef]
  19. J. R. Lowney, “Application of Multiscattering Theory to Impurity Bands in Si:As,” J. Appl. Phys. 69, 4544 (1988).
    [CrossRef]

1988

J. R. Lowney, “Application of Multiscattering Theory to Impurity Bands in Si:As,” J. Appl. Phys. 69, 4544 (1988).
[CrossRef]

1987

F. Szmulowicz, F. L. Madarasz, “Blocked Impurity Band Detectors—An Analytical Model: Figures of Merit,” J. Appl. Phys. 62, 2533 (1987) and references therein.
[CrossRef]

M. D. Petroff, M. G. Stapelbroek, W. A. Kleinhans, “Detection of Individual 0.4–28μm Wavelength Photons Via Impurity-Impact Ionization in a Solid-State Photomultiplier,” Appl. Phys. Lett. 51, 406 (1987).
[CrossRef]

1986

D. D. Coon, R. P. G. Karunasiri, “Green’s-Function-Quantum-Defect Treatment of Impurity Photoionization in Semiconductors,” Phys. Rev. B 33, 8228 (1986).
[CrossRef]

1984

N. Sclar, “Properties of Doped Silicon and Germanium Infrared Detectors,” Prog. Quantum Electron. 9, 149 (1984).
[CrossRef]

1983

G. Masetti, M. Severi, S. Solmi, “Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron-Doped Silicon,” IEEE Trans. Electron Devices ED-30, 764 (1983).
[CrossRef]

1980

W. R. Thurber, R. L. Mattis, Y. M. Liu, J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 1807 (1980).
[CrossRef]

J. Geist, E. F. Zalewski, A. R. Schaefer, “Spectral Response Self-Calibration and Interpolation of Silicon Photodiodes,” Appl. Opt. 19, 3795 (1980).
[CrossRef] [PubMed]

1963

F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 340 (1963).

1962

J. W. Bichard, J. C. Giles, “Optical Absorption Spectra of Arsenic and Phosphorus in Silicon,” Can. J. Phys. 40, 1480 (1962).
[CrossRef]

Bichard, J. W.

J. W. Bichard, J. C. Giles, “Optical Absorption Spectra of Arsenic and Phosphorus in Silicon,” Can. J. Phys. 40, 1480 (1962).
[CrossRef]

Coon, D. D.

D. D. Coon, R. P. G. Karunasiri, “Green’s-Function-Quantum-Defect Treatment of Impurity Photoionization in Semiconductors,” Phys. Rev. B 33, 8228 (1986).
[CrossRef]

Edwards, D. F.

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Properties of Solids, E. D. Palik, Ed. (Academic, New York, 1985), p. 547.

Filliben, J. J.

W. R. Thurber, R. L. Mattis, Y. M. Liu, J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 1807 (1980).
[CrossRef]

Geist, J.

Giles, J. C.

J. W. Bichard, J. C. Giles, “Optical Absorption Spectra of Arsenic and Phosphorus in Silicon,” Can. J. Phys. 40, 1480 (1962).
[CrossRef]

Karunasiri, R. P. G.

D. D. Coon, R. P. G. Karunasiri, “Green’s-Function-Quantum-Defect Treatment of Impurity Photoionization in Semiconductors,” Phys. Rev. B 33, 8228 (1986).
[CrossRef]

Kleinhans, W. A.

M. D. Petroff, M. G. Stapelbroek, W. A. Kleinhans, “Detection of Individual 0.4–28μm Wavelength Photons Via Impurity-Impact Ionization in a Solid-State Photomultiplier,” Appl. Phys. Lett. 51, 406 (1987).
[CrossRef]

Liu, Y. M.

W. R. Thurber, R. L. Mattis, Y. M. Liu, J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 1807 (1980).
[CrossRef]

Lowney, J. R.

J. R. Lowney, “Application of Multiscattering Theory to Impurity Bands in Si:As,” J. Appl. Phys. 69, 4544 (1988).
[CrossRef]

Madarasz, F. L.

F. Szmulowicz, F. L. Madarasz, “Blocked Impurity Band Detectors—An Analytical Model: Figures of Merit,” J. Appl. Phys. 62, 2533 (1987) and references therein.
[CrossRef]

Masetti, G.

G. Masetti, M. Severi, S. Solmi, “Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron-Doped Silicon,” IEEE Trans. Electron Devices ED-30, 764 (1983).
[CrossRef]

Mattis, R. L.

W. R. Thurber, R. L. Mattis, Y. M. Liu, J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 1807 (1980).
[CrossRef]

Petroff, M. D.

M. D. Petroff, M. G. Stapelbroek, W. A. Kleinhans, “Detection of Individual 0.4–28μm Wavelength Photons Via Impurity-Impact Ionization in a Solid-State Photomultiplier,” Appl. Phys. Lett. 51, 406 (1987).
[CrossRef]

M. D. Petroff, M. G. Stapelbroek, “Spectral Response, Gain, and Noise Models for IBC Detectors,” IRIA-IRIS Proceedings, Specialty Group on Infrared Detectors (ERIM, Ann Arbor, MI, 1985).

Schaefer, A. R.

Sclar, N.

N. Sclar, “Properties of Doped Silicon and Germanium Infrared Detectors,” Prog. Quantum Electron. 9, 149 (1984).
[CrossRef]

Severi, M.

G. Masetti, M. Severi, S. Solmi, “Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron-Doped Silicon,” IEEE Trans. Electron Devices ED-30, 764 (1983).
[CrossRef]

Solmi, S.

G. Masetti, M. Severi, S. Solmi, “Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron-Doped Silicon,” IEEE Trans. Electron Devices ED-30, 764 (1983).
[CrossRef]

Stapelbroek, M. G.

M. D. Petroff, M. G. Stapelbroek, W. A. Kleinhans, “Detection of Individual 0.4–28μm Wavelength Photons Via Impurity-Impact Ionization in a Solid-State Photomultiplier,” Appl. Phys. Lett. 51, 406 (1987).
[CrossRef]

M. D. Petroff, M. G. Stapelbroek, “Spectral Response, Gain, and Noise Models for IBC Detectors,” IRIA-IRIS Proceedings, Specialty Group on Infrared Detectors (ERIM, Ann Arbor, MI, 1985).

M. G. Stapelbroek, Rockwell International; private communication (1988).

Stern, F.

F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 340 (1963).

Szmulowicz, F.

F. Szmulowicz, F. L. Madarasz, “Blocked Impurity Band Detectors—An Analytical Model: Figures of Merit,” J. Appl. Phys. 62, 2533 (1987) and references therein.
[CrossRef]

Thurber, W. R.

W. R. Thurber, R. L. Mattis, Y. M. Liu, J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 1807 (1980).
[CrossRef]

Zalewski, E. F.

Appl. Opt.

Appl. Phys. Lett.

M. D. Petroff, M. G. Stapelbroek, W. A. Kleinhans, “Detection of Individual 0.4–28μm Wavelength Photons Via Impurity-Impact Ionization in a Solid-State Photomultiplier,” Appl. Phys. Lett. 51, 406 (1987).
[CrossRef]

Can. J. Phys.

J. W. Bichard, J. C. Giles, “Optical Absorption Spectra of Arsenic and Phosphorus in Silicon,” Can. J. Phys. 40, 1480 (1962).
[CrossRef]

IEEE Trans. Electron Devices

G. Masetti, M. Severi, S. Solmi, “Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron-Doped Silicon,” IEEE Trans. Electron Devices ED-30, 764 (1983).
[CrossRef]

J. Appl. Phys.

J. R. Lowney, “Application of Multiscattering Theory to Impurity Bands in Si:As,” J. Appl. Phys. 69, 4544 (1988).
[CrossRef]

F. Szmulowicz, F. L. Madarasz, “Blocked Impurity Band Detectors—An Analytical Model: Figures of Merit,” J. Appl. Phys. 62, 2533 (1987) and references therein.
[CrossRef]

J. Electrochem. Soc.

W. R. Thurber, R. L. Mattis, Y. M. Liu, J. J. Filliben, “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 1807 (1980).
[CrossRef]

Phys. Rev. B

D. D. Coon, R. P. G. Karunasiri, “Green’s-Function-Quantum-Defect Treatment of Impurity Photoionization in Semiconductors,” Phys. Rev. B 33, 8228 (1986).
[CrossRef]

Prog. Quantum Electron.

N. Sclar, “Properties of Doped Silicon and Germanium Infrared Detectors,” Prog. Quantum Electron. 9, 149 (1984).
[CrossRef]

Solid State Phys.

F. Stern, “Elementary Theory of the Optical Properties of Solids,” Solid State Phys. 15, 340 (1963).

Other

M. G. Stapelbroek, Rockwell International; private communication (1988).

The author thanks P. H. Chi and D. S. Simons of NIST (NBS) for these measurements.

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Properties of Solids, E. D. Palik, Ed. (Academic, New York, 1985), p. 547.

MIDAC, Costa Mesa, CA 92627.

M. D. Petroff, M. G. Stapelbroek, “Spectral Response, Gain, and Noise Models for IBC Detectors,” IRIA-IRIS Proceedings, Specialty Group on Infrared Detectors (ERIM, Ann Arbor, MI, 1985).

The author thanks R. A. Florence of Rockwell International, Anaheim, CA 92803-3105, for providing the samples used in this work.

The author thanks J. R. Ehrstein of NIST (NBS) for these measurements.

Solecon Laboratories, San Jose, CA 95131. This and other references to commercial products or services are included in this paper for the sole purpose of facilitating the complete description of the experimental procedure. Their inclusion constitutes neither an endorsement of the product or service, nor the implication that it is the best for the particular application.

The author thanks W. Gallagher of NIST (NBS) for this measurement.

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Figures (5)

Fig. 1
Fig. 1

Transmission spectra of Si:As samples containing different concentrations of As. Sample A, nominal 600-μm thick sample of pure Si; sample B, nominal 500-μm thick Si substrate with 6-μm thick epitaxial layer containing 5.3 × 1017 atomic As cm−3; sample D, 476-μm thick sample of Si containing 1.1 × 1016 atomic As cm3; sample E, nominal 500-μm thick Si substrate with 6.3-μm thick epitaxial layer containing 1.6 × 1018 atomic As cm−3. The spectrum of sample C, which had a 6-μm layer containing 8.4 × 1017 atomic As is not shown to simplify the figure.

Fig. 2
Fig. 2

Comparison of the measured cross section for 1.1 × 1016 As cm−3 in Si with the theoretical cross section for photoionization of dilute As in Si due to Coon and Karunasiri.15

Fig. 3
Fig. 3

Comparison of the measured absorption cross section for 5.3 × 1017 As cm−3 in Si (this work) with 0.7 times the photoionization cross section reported in Ref. 4 (0.7 × PS). The estimated uncertainty of the absorption cross section is shown at the bottom of the figure. It is known to be larger than indicated where the line isdashed.

Fig. 4
Fig. 4

Comparison of the measured absorption cross section for 8.4 × 1017 As cm−3 in Si (this work) with 0.7 times the photoionization cross section reported in Ref. 4 (0.7 × PS). The estimated uncertainty of the absorption cross section is shown at the bottom of the figure. It is known to be larger than indicated where the line is dashed.

Fig. 5
Fig. 5

Comparison of the measured absorption cross section for 1.6 × 1018 As cm−3 in Si (this work) with 0.7 times the photoionization cross section reported in Ref. 4 (0.7 × PS). The estimated uncertainty of the absorption cross section is shown at the bottom of the figure. It is known to be larger than indicated where the line is dashed.

Tables (2)

Tables Icon

Table I As Concentrations N, Widths of the As-Doped Layers W, and As Doses D in the Samples Used in this Investigation

Tables Icon

Table II Integral of the As Absorption Cross Sections from 250 to 740 cm−1 for Different As Concenterations

Equations (8)

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σ ( N , h ν ) = α A s   ( h ν ) / N ,
D = N W ,
R s W = 1 q μ A s ( N ) N
D = 1 / [ R s q μ As ( D / W ) ]   ,
τ S ( h ν ) = [ 1 ρ ( h ν ) ] 2 + [ 1 ρ ( h ν ) ] 4 + 4 ρ ( h ν ) 2 T S ( h ν ) 2 2 ρ ( h ν ) 2 T S ( h ν ) ,
τ S ( h ν ) = exp [ α S ( h ν ) W S ]  ,
T S ( h ν ) = [ 1 ρ ( h ν ) ] 2 τ S ( h ν ) 1 ρ ( h ν ) 2 τ S ( h ν ) 2
σ ( ν ) = σ ( ν 0 ) ( ν 0 / ν ) 2 ,

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