Abstract

Highly compensated Ge: Ga photoconductors have been fabricated and evaluated for high bandwidth heterodyne detection. Bandwidths up to 60 MHz have been obtained with corresponding current responsivity of 0.01 A/W.

© 1988 Optical Society of America

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References

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  1. E. E. Haller, “Physics and Design of Advanced IR Bolometers and Photoconductors,” Infrared Phys. 25, 257 (1985).
    [CrossRef]
  2. P. R. Bratt, “Impurity Germanium and Silicon Infrared Detectors,” in Semiconductors and Semimetals, Vol. 2, R. K. Willardson, C. A. Beer, Eds. (Academic, New York, 1977), Chap. 2.
    [CrossRef]
  3. A. L. Betz, J. Zmuidzinas, in presentation to L. Fisk on SOFIA (Stratospheric Observatory for Infrared Astronomy), Ames Research Center (1987).
  4. H. P. Roser, R. Wattenbach, E. J. Durwen, G. V. Schultz, “A High Resolution Heterodyne Spectrometer from 100μm to 1,000μm and the Detection of CO (J = 7–6), CO (J = 6–5), and CO (J = 3–2),” Astron. Astrophys. 165, 287 (1986).
  5. P. L. Richards, L. T. Greenberg, “Infrared Detectors for Low-Background Astronomy: Incoherent and Coherent Devices from One Micrometer to One Millimeter,” in Infrared and Millimeter Waves, Vol. 6 (Academic, New York, 1982), pp. 149–207.
  6. R. M. Westervelt, S. W. Teitsworth, “Nonlinear Transient Response of Extrinsic Ge Far-Infrared Photoconductors,” J. Appl. Phys. 57, 5457 (1985).
    [CrossRef]
  7. S. H. Koenig, R. D. Brown, W. Schillinger (KBS), “Electrical Conduction in n-Type Germanium at Low Temperatures,” Phys. Rev. 128, 1668 (1962).
    [CrossRef]
  8. F. Kohl, W. Muller, E. Gornik, “Speed Limitation of Ge Far-Infrared Photoconductive Detectors,” Infrared Phys. 18, 697 (1978).
    [CrossRef]
  9. G. Dodel, J. Heppner, E. Holzhauer, E. Gornik, “Wideband Heterodyne Detection in the Far-Infrared with Extrinsic Ge Photoconductors,” J. Appl. Phys. 54, 4254 (1983).
    [CrossRef]
  10. M. Lax, “Cascade Capture of Electrons in Solids,” Phys. Rev. 119, 1502 (1960).
    [CrossRef]
  11. G. Ascarelli, S. Rodriguez, “Recombination of Electrons and Donors in n-Type Germanium,” Phys. Rev. 124, 1321 (1961).
    [CrossRef]
  12. R. A. Brown, S. Rodriguez, “Low-Temperature Recombination of Electrons and Donors on n-Type Germanium and Silicon,” Phys. Rev. 153, 890 (1967).
    [CrossRef]
  13. V. N. Abakumov, V. I. Perel, I. N. Yassievitch, “Capture of Carriers by Attractive Centers in Semiconductors,” Sov. Phys. Semicond. 12, 1 (1978).
  14. E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen, E. Kreysa, “NTD Germanium: A Novel Material for Low Temperature Bolometers,” in Proceedings, Fourth International Conference on Neutron Transmutation Doping of Semiconductors, R. D. Larabee, Ed. (Plenum, New York, 1984), pp. 21–36.
    [CrossRef]
  15. N. P. Palaio, M.S. Thesis, U. California, Berkeley, Lawrence Berkeley Laboratory Report LBL-16695 (1983).
  16. N. M. Haegel, M.S. Thesis, U. California, Berkeley (1983).
  17. B. I. Shklovskii, A. L. Efros, 1984 Electronic Properties of Doped Semiconductors (Springer-Verlag, New York, 1984).
  18. E. N. Grossman, “A Far-Infrared Heterodyne Spectrometer for Airborne Astronomy,” Ph.D. Dissertation, California Institute of Technology (1987).
  19. D. M. Watson, E. N. Grossman, T. G. Phillips1988, in preparation.
  20. H. Krautle, E. Sauter, G. V. Schultz, “Antenna Characteristics of Whisker Diodes Used as Submillimeter Receivers,” Infrared Phys. 17, 477 (1977).
    [CrossRef]
  21. E. N. Grossman, “The Performance of Schottky Diodes as Far-Infrared Modulators,” Int. J. Infrared Millimeter Waves 8, 1293 (1987).
    [CrossRef]
  22. S. W. Teitsworth, R. M. Westervelt, “Chaos and Broadband Noise in Extrinsic Photoconductors,” Phys. Rev. Lett. 56, 516 (1984).
    [CrossRef]

1987 (1)

E. N. Grossman, “The Performance of Schottky Diodes as Far-Infrared Modulators,” Int. J. Infrared Millimeter Waves 8, 1293 (1987).
[CrossRef]

1986 (1)

H. P. Roser, R. Wattenbach, E. J. Durwen, G. V. Schultz, “A High Resolution Heterodyne Spectrometer from 100μm to 1,000μm and the Detection of CO (J = 7–6), CO (J = 6–5), and CO (J = 3–2),” Astron. Astrophys. 165, 287 (1986).

1985 (2)

R. M. Westervelt, S. W. Teitsworth, “Nonlinear Transient Response of Extrinsic Ge Far-Infrared Photoconductors,” J. Appl. Phys. 57, 5457 (1985).
[CrossRef]

E. E. Haller, “Physics and Design of Advanced IR Bolometers and Photoconductors,” Infrared Phys. 25, 257 (1985).
[CrossRef]

1984 (1)

S. W. Teitsworth, R. M. Westervelt, “Chaos and Broadband Noise in Extrinsic Photoconductors,” Phys. Rev. Lett. 56, 516 (1984).
[CrossRef]

1983 (1)

G. Dodel, J. Heppner, E. Holzhauer, E. Gornik, “Wideband Heterodyne Detection in the Far-Infrared with Extrinsic Ge Photoconductors,” J. Appl. Phys. 54, 4254 (1983).
[CrossRef]

1978 (2)

F. Kohl, W. Muller, E. Gornik, “Speed Limitation of Ge Far-Infrared Photoconductive Detectors,” Infrared Phys. 18, 697 (1978).
[CrossRef]

V. N. Abakumov, V. I. Perel, I. N. Yassievitch, “Capture of Carriers by Attractive Centers in Semiconductors,” Sov. Phys. Semicond. 12, 1 (1978).

1977 (1)

H. Krautle, E. Sauter, G. V. Schultz, “Antenna Characteristics of Whisker Diodes Used as Submillimeter Receivers,” Infrared Phys. 17, 477 (1977).
[CrossRef]

1967 (1)

R. A. Brown, S. Rodriguez, “Low-Temperature Recombination of Electrons and Donors on n-Type Germanium and Silicon,” Phys. Rev. 153, 890 (1967).
[CrossRef]

1962 (1)

S. H. Koenig, R. D. Brown, W. Schillinger (KBS), “Electrical Conduction in n-Type Germanium at Low Temperatures,” Phys. Rev. 128, 1668 (1962).
[CrossRef]

1961 (1)

G. Ascarelli, S. Rodriguez, “Recombination of Electrons and Donors in n-Type Germanium,” Phys. Rev. 124, 1321 (1961).
[CrossRef]

1960 (1)

M. Lax, “Cascade Capture of Electrons in Solids,” Phys. Rev. 119, 1502 (1960).
[CrossRef]

Abakumov, V. N.

V. N. Abakumov, V. I. Perel, I. N. Yassievitch, “Capture of Carriers by Attractive Centers in Semiconductors,” Sov. Phys. Semicond. 12, 1 (1978).

Ascarelli, G.

G. Ascarelli, S. Rodriguez, “Recombination of Electrons and Donors in n-Type Germanium,” Phys. Rev. 124, 1321 (1961).
[CrossRef]

Betz, A. L.

A. L. Betz, J. Zmuidzinas, in presentation to L. Fisk on SOFIA (Stratospheric Observatory for Infrared Astronomy), Ames Research Center (1987).

Bratt, P. R.

P. R. Bratt, “Impurity Germanium and Silicon Infrared Detectors,” in Semiconductors and Semimetals, Vol. 2, R. K. Willardson, C. A. Beer, Eds. (Academic, New York, 1977), Chap. 2.
[CrossRef]

Brown, R. A.

R. A. Brown, S. Rodriguez, “Low-Temperature Recombination of Electrons and Donors on n-Type Germanium and Silicon,” Phys. Rev. 153, 890 (1967).
[CrossRef]

Brown, R. D.

S. H. Koenig, R. D. Brown, W. Schillinger (KBS), “Electrical Conduction in n-Type Germanium at Low Temperatures,” Phys. Rev. 128, 1668 (1962).
[CrossRef]

Dodel, G.

G. Dodel, J. Heppner, E. Holzhauer, E. Gornik, “Wideband Heterodyne Detection in the Far-Infrared with Extrinsic Ge Photoconductors,” J. Appl. Phys. 54, 4254 (1983).
[CrossRef]

Durwen, E. J.

H. P. Roser, R. Wattenbach, E. J. Durwen, G. V. Schultz, “A High Resolution Heterodyne Spectrometer from 100μm to 1,000μm and the Detection of CO (J = 7–6), CO (J = 6–5), and CO (J = 3–2),” Astron. Astrophys. 165, 287 (1986).

Efros, A. L.

B. I. Shklovskii, A. L. Efros, 1984 Electronic Properties of Doped Semiconductors (Springer-Verlag, New York, 1984).

Gornik, E.

G. Dodel, J. Heppner, E. Holzhauer, E. Gornik, “Wideband Heterodyne Detection in the Far-Infrared with Extrinsic Ge Photoconductors,” J. Appl. Phys. 54, 4254 (1983).
[CrossRef]

F. Kohl, W. Muller, E. Gornik, “Speed Limitation of Ge Far-Infrared Photoconductive Detectors,” Infrared Phys. 18, 697 (1978).
[CrossRef]

Greenberg, L. T.

P. L. Richards, L. T. Greenberg, “Infrared Detectors for Low-Background Astronomy: Incoherent and Coherent Devices from One Micrometer to One Millimeter,” in Infrared and Millimeter Waves, Vol. 6 (Academic, New York, 1982), pp. 149–207.

Grossman, E. N.

E. N. Grossman, “The Performance of Schottky Diodes as Far-Infrared Modulators,” Int. J. Infrared Millimeter Waves 8, 1293 (1987).
[CrossRef]

E. N. Grossman, “A Far-Infrared Heterodyne Spectrometer for Airborne Astronomy,” Ph.D. Dissertation, California Institute of Technology (1987).

D. M. Watson, E. N. Grossman, T. G. Phillips1988, in preparation.

Haegel, N. M.

N. M. Haegel, M.S. Thesis, U. California, Berkeley (1983).

Haller, E. E.

E. E. Haller, “Physics and Design of Advanced IR Bolometers and Photoconductors,” Infrared Phys. 25, 257 (1985).
[CrossRef]

E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen, E. Kreysa, “NTD Germanium: A Novel Material for Low Temperature Bolometers,” in Proceedings, Fourth International Conference on Neutron Transmutation Doping of Semiconductors, R. D. Larabee, Ed. (Plenum, New York, 1984), pp. 21–36.
[CrossRef]

Hansen, W. L.

E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen, E. Kreysa, “NTD Germanium: A Novel Material for Low Temperature Bolometers,” in Proceedings, Fourth International Conference on Neutron Transmutation Doping of Semiconductors, R. D. Larabee, Ed. (Plenum, New York, 1984), pp. 21–36.
[CrossRef]

Heppner, J.

G. Dodel, J. Heppner, E. Holzhauer, E. Gornik, “Wideband Heterodyne Detection in the Far-Infrared with Extrinsic Ge Photoconductors,” J. Appl. Phys. 54, 4254 (1983).
[CrossRef]

Holzhauer, E.

G. Dodel, J. Heppner, E. Holzhauer, E. Gornik, “Wideband Heterodyne Detection in the Far-Infrared with Extrinsic Ge Photoconductors,” J. Appl. Phys. 54, 4254 (1983).
[CrossRef]

Koenig, S. H.

S. H. Koenig, R. D. Brown, W. Schillinger (KBS), “Electrical Conduction in n-Type Germanium at Low Temperatures,” Phys. Rev. 128, 1668 (1962).
[CrossRef]

Kohl, F.

F. Kohl, W. Muller, E. Gornik, “Speed Limitation of Ge Far-Infrared Photoconductive Detectors,” Infrared Phys. 18, 697 (1978).
[CrossRef]

Krautle, H.

H. Krautle, E. Sauter, G. V. Schultz, “Antenna Characteristics of Whisker Diodes Used as Submillimeter Receivers,” Infrared Phys. 17, 477 (1977).
[CrossRef]

Kreysa, E.

E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen, E. Kreysa, “NTD Germanium: A Novel Material for Low Temperature Bolometers,” in Proceedings, Fourth International Conference on Neutron Transmutation Doping of Semiconductors, R. D. Larabee, Ed. (Plenum, New York, 1984), pp. 21–36.
[CrossRef]

Lax, M.

M. Lax, “Cascade Capture of Electrons in Solids,” Phys. Rev. 119, 1502 (1960).
[CrossRef]

Muller, W.

F. Kohl, W. Muller, E. Gornik, “Speed Limitation of Ge Far-Infrared Photoconductive Detectors,” Infrared Phys. 18, 697 (1978).
[CrossRef]

Palaio, N. P.

E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen, E. Kreysa, “NTD Germanium: A Novel Material for Low Temperature Bolometers,” in Proceedings, Fourth International Conference on Neutron Transmutation Doping of Semiconductors, R. D. Larabee, Ed. (Plenum, New York, 1984), pp. 21–36.
[CrossRef]

N. P. Palaio, M.S. Thesis, U. California, Berkeley, Lawrence Berkeley Laboratory Report LBL-16695 (1983).

Perel, V. I.

V. N. Abakumov, V. I. Perel, I. N. Yassievitch, “Capture of Carriers by Attractive Centers in Semiconductors,” Sov. Phys. Semicond. 12, 1 (1978).

Phillips, T. G.

D. M. Watson, E. N. Grossman, T. G. Phillips1988, in preparation.

Richards, P. L.

P. L. Richards, L. T. Greenberg, “Infrared Detectors for Low-Background Astronomy: Incoherent and Coherent Devices from One Micrometer to One Millimeter,” in Infrared and Millimeter Waves, Vol. 6 (Academic, New York, 1982), pp. 149–207.

Rodder, M.

E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen, E. Kreysa, “NTD Germanium: A Novel Material for Low Temperature Bolometers,” in Proceedings, Fourth International Conference on Neutron Transmutation Doping of Semiconductors, R. D. Larabee, Ed. (Plenum, New York, 1984), pp. 21–36.
[CrossRef]

Rodriguez, S.

R. A. Brown, S. Rodriguez, “Low-Temperature Recombination of Electrons and Donors on n-Type Germanium and Silicon,” Phys. Rev. 153, 890 (1967).
[CrossRef]

G. Ascarelli, S. Rodriguez, “Recombination of Electrons and Donors in n-Type Germanium,” Phys. Rev. 124, 1321 (1961).
[CrossRef]

Roser, H. P.

H. P. Roser, R. Wattenbach, E. J. Durwen, G. V. Schultz, “A High Resolution Heterodyne Spectrometer from 100μm to 1,000μm and the Detection of CO (J = 7–6), CO (J = 6–5), and CO (J = 3–2),” Astron. Astrophys. 165, 287 (1986).

Sauter, E.

H. Krautle, E. Sauter, G. V. Schultz, “Antenna Characteristics of Whisker Diodes Used as Submillimeter Receivers,” Infrared Phys. 17, 477 (1977).
[CrossRef]

Schillinger (KBS), W.

S. H. Koenig, R. D. Brown, W. Schillinger (KBS), “Electrical Conduction in n-Type Germanium at Low Temperatures,” Phys. Rev. 128, 1668 (1962).
[CrossRef]

Schultz, G. V.

H. P. Roser, R. Wattenbach, E. J. Durwen, G. V. Schultz, “A High Resolution Heterodyne Spectrometer from 100μm to 1,000μm and the Detection of CO (J = 7–6), CO (J = 6–5), and CO (J = 3–2),” Astron. Astrophys. 165, 287 (1986).

H. Krautle, E. Sauter, G. V. Schultz, “Antenna Characteristics of Whisker Diodes Used as Submillimeter Receivers,” Infrared Phys. 17, 477 (1977).
[CrossRef]

Shklovskii, B. I.

B. I. Shklovskii, A. L. Efros, 1984 Electronic Properties of Doped Semiconductors (Springer-Verlag, New York, 1984).

Teitsworth, S. W.

R. M. Westervelt, S. W. Teitsworth, “Nonlinear Transient Response of Extrinsic Ge Far-Infrared Photoconductors,” J. Appl. Phys. 57, 5457 (1985).
[CrossRef]

S. W. Teitsworth, R. M. Westervelt, “Chaos and Broadband Noise in Extrinsic Photoconductors,” Phys. Rev. Lett. 56, 516 (1984).
[CrossRef]

Watson, D. M.

D. M. Watson, E. N. Grossman, T. G. Phillips1988, in preparation.

Wattenbach, R.

H. P. Roser, R. Wattenbach, E. J. Durwen, G. V. Schultz, “A High Resolution Heterodyne Spectrometer from 100μm to 1,000μm and the Detection of CO (J = 7–6), CO (J = 6–5), and CO (J = 3–2),” Astron. Astrophys. 165, 287 (1986).

Westervelt, R. M.

R. M. Westervelt, S. W. Teitsworth, “Nonlinear Transient Response of Extrinsic Ge Far-Infrared Photoconductors,” J. Appl. Phys. 57, 5457 (1985).
[CrossRef]

S. W. Teitsworth, R. M. Westervelt, “Chaos and Broadband Noise in Extrinsic Photoconductors,” Phys. Rev. Lett. 56, 516 (1984).
[CrossRef]

Yassievitch, I. N.

V. N. Abakumov, V. I. Perel, I. N. Yassievitch, “Capture of Carriers by Attractive Centers in Semiconductors,” Sov. Phys. Semicond. 12, 1 (1978).

Zmuidzinas, J.

A. L. Betz, J. Zmuidzinas, in presentation to L. Fisk on SOFIA (Stratospheric Observatory for Infrared Astronomy), Ames Research Center (1987).

Astron. Astrophys. (1)

H. P. Roser, R. Wattenbach, E. J. Durwen, G. V. Schultz, “A High Resolution Heterodyne Spectrometer from 100μm to 1,000μm and the Detection of CO (J = 7–6), CO (J = 6–5), and CO (J = 3–2),” Astron. Astrophys. 165, 287 (1986).

Infrared Phys. (3)

E. E. Haller, “Physics and Design of Advanced IR Bolometers and Photoconductors,” Infrared Phys. 25, 257 (1985).
[CrossRef]

H. Krautle, E. Sauter, G. V. Schultz, “Antenna Characteristics of Whisker Diodes Used as Submillimeter Receivers,” Infrared Phys. 17, 477 (1977).
[CrossRef]

F. Kohl, W. Muller, E. Gornik, “Speed Limitation of Ge Far-Infrared Photoconductive Detectors,” Infrared Phys. 18, 697 (1978).
[CrossRef]

Int. J. Infrared Millimeter Waves (1)

E. N. Grossman, “The Performance of Schottky Diodes as Far-Infrared Modulators,” Int. J. Infrared Millimeter Waves 8, 1293 (1987).
[CrossRef]

J. Appl. Phys. (2)

R. M. Westervelt, S. W. Teitsworth, “Nonlinear Transient Response of Extrinsic Ge Far-Infrared Photoconductors,” J. Appl. Phys. 57, 5457 (1985).
[CrossRef]

G. Dodel, J. Heppner, E. Holzhauer, E. Gornik, “Wideband Heterodyne Detection in the Far-Infrared with Extrinsic Ge Photoconductors,” J. Appl. Phys. 54, 4254 (1983).
[CrossRef]

Phys. Rev. (4)

M. Lax, “Cascade Capture of Electrons in Solids,” Phys. Rev. 119, 1502 (1960).
[CrossRef]

G. Ascarelli, S. Rodriguez, “Recombination of Electrons and Donors in n-Type Germanium,” Phys. Rev. 124, 1321 (1961).
[CrossRef]

R. A. Brown, S. Rodriguez, “Low-Temperature Recombination of Electrons and Donors on n-Type Germanium and Silicon,” Phys. Rev. 153, 890 (1967).
[CrossRef]

S. H. Koenig, R. D. Brown, W. Schillinger (KBS), “Electrical Conduction in n-Type Germanium at Low Temperatures,” Phys. Rev. 128, 1668 (1962).
[CrossRef]

Phys. Rev. Lett. (1)

S. W. Teitsworth, R. M. Westervelt, “Chaos and Broadband Noise in Extrinsic Photoconductors,” Phys. Rev. Lett. 56, 516 (1984).
[CrossRef]

Sov. Phys. Semicond. (1)

V. N. Abakumov, V. I. Perel, I. N. Yassievitch, “Capture of Carriers by Attractive Centers in Semiconductors,” Sov. Phys. Semicond. 12, 1 (1978).

Other (9)

E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen, E. Kreysa, “NTD Germanium: A Novel Material for Low Temperature Bolometers,” in Proceedings, Fourth International Conference on Neutron Transmutation Doping of Semiconductors, R. D. Larabee, Ed. (Plenum, New York, 1984), pp. 21–36.
[CrossRef]

N. P. Palaio, M.S. Thesis, U. California, Berkeley, Lawrence Berkeley Laboratory Report LBL-16695 (1983).

N. M. Haegel, M.S. Thesis, U. California, Berkeley (1983).

B. I. Shklovskii, A. L. Efros, 1984 Electronic Properties of Doped Semiconductors (Springer-Verlag, New York, 1984).

E. N. Grossman, “A Far-Infrared Heterodyne Spectrometer for Airborne Astronomy,” Ph.D. Dissertation, California Institute of Technology (1987).

D. M. Watson, E. N. Grossman, T. G. Phillips1988, in preparation.

P. R. Bratt, “Impurity Germanium and Silicon Infrared Detectors,” in Semiconductors and Semimetals, Vol. 2, R. K. Willardson, C. A. Beer, Eds. (Academic, New York, 1977), Chap. 2.
[CrossRef]

A. L. Betz, J. Zmuidzinas, in presentation to L. Fisk on SOFIA (Stratospheric Observatory for Infrared Astronomy), Ames Research Center (1987).

P. L. Richards, L. T. Greenberg, “Infrared Detectors for Low-Background Astronomy: Incoherent and Coherent Devices from One Micrometer to One Millimeter,” in Infrared and Millimeter Waves, Vol. 6 (Academic, New York, 1982), pp. 149–207.

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Figures (4)

Fig. 1
Fig. 1

Block diagram the FIR heterodyne receiver used, in modified form, to measure Ge:Ga bandwidth and photoconductive gain.19

Fig. 2
Fig. 2

Field dependence of the recombination bandwidth, measured on detector 496-5.5. The rolloff at high field is due to carrier heating.

Fig. 3
Fig. 3

Measured recombination bandwidth as a function of minority impurity concentration, for the NTD detectors. The dotted line corresponds to the linear dependence of Eq. (10) using a carrier temperature of T h = 4.2 K and a recombination cross section of σ r = 3.2 × 10−13 cm2.

Fig. 4
Fig. 4

Direct detection responsivity as a function of compensating impurity concentration.

Tables (2)

Tables Icon

Table 1 Doping Concentrations of Samples (cm−3)

Tables Icon

Table 2 Photoconductive gain derived from g-r noise

Equations (16)

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

i ph = e P h ν [ η G 1 + ( ω τ r ) 2 ] ,
G = τ r τ tr = τ r ( μ E b l ) ,
i gr 2 = 4 e i ph G 1 + ( ω τ r ) 2 ( A 2 / Hz ) ,
σ r = { π 9 [ ln ( γ 1.78 δ ) + δ γ ] } 1 l i ( e 2 k T ) 3 ( m * s 2 k T ) 2 ,
γ k T m * s 2 .
σ r = π r T 2 ( r T l 0 ) ,
r T = 2 k T
σ r = 4 π 3 1 l 0 ( e 2 k T ) 3 = 1.1 × 10 - 9 T K 3 cm 2 ,
( m * e 2 k T ) 2 .
0.3 K < m * s 2 k < 0.8 K .
P out / B = A ( R d R a R d + R a ) i 2 ( W / Hz ) ,
B = N D σ r v T N D T h - 3 / 2 ,
e E v d = ( 1 2 m * v T 2 ) ( v T l i ) ,
v d = e E m * ( l e v T ) .
σ r = B ( N D ) N D v T = B ( N D ) N D ( 3 k T h m * ) - 1 / 2 .
σ r = 3.2 × 10 - 13 ( 4.2 K T h ) 1 / 2 cm 2 .

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