Abstract

The first part of this paper deals with general concepts of noise and response in photodetectors. The noise in photodetectors is of a fivefold nature: (i) noise produced by the blackbody photon field, Jb; (ii) noise produced by the ambient photon field Ja; (iii) noise associated with the signal Js; (iv) spontaneous noise characteristic for the device and not associated with Ja; (v) noise associated with the circuitry or amplifiers. Concepts for the characterization of the noise are—the noise equivalent powers Peq,λ[λ,ff,A], Peq[λ,ff,A] Peq,T[T,ff,A], and Peq,T[T,ff,A]; the photon limited noise equivalent powers eq,λ[λ,ff,A], eq,T[T,ff,A]; various detectivities Dλ*[λ,f], DT*[T,f]; the photon limited detectivities DT*{Tss}, Dλ*{Tss}, Dλ*{Tee}, and Dλ† giving the ultimate limit attainable with a detector in radiative equilibrium; the noise figure F and the signal-to-noise ratio σ/N. The merits and limitations of photon limited behavior are discussed and the theoretical detectivities are calculated for various circumstances. If, in the absence of a signal, the noise stems mainly from the circuitry (class B), a characterization by Peq or D is largely arbitrary. Such is the case for photoemissive detectors and photoconductive insulators in the absence of bias light. In the event that the device operates and produces the main noise in the absence of a signal (class A), concepts like Peq, D, F, are meaningful (semiconductors, p-n junctions, bolometers, PEM cells, etc.). Special attention has been given to introducing a consistent notation. I the second part of this paper we discuss two topics: some aspects of the photodetective conversion processes and the fluctuations of the photon field. The photodetective processes in emission diodes, junction diodes, photovoltaic cells, and avalanche diodes are simple. The noise is mainly of (amplified) shot noise nature. In photoconductors and PEM cells we must consider the collective carrier processes (unless the electrodes are blocking as in detectors in the thirties). Such processes do not fit too well a gain mechanism as has often been suggested as is testified by ambipolar sweep out and by the non-Poisson nature of generation–recombination (g–r) and transport fluctuations. The noise in a blackbody field is stated and the effect of imperfect absorbers is considered, involving stimulated emission. The commonly applied variance theorem leads to a degrading of the Boson factor. The noise of nonthermal photon fields is discussed following Mandel–Wolf, Alkemade, and Enns. In a nonthermal equilibrium state the effects of coherence and wave-interaction noise are manifest in the detector-output noise. In the final part the detectivity is derived for various devices. We first consider briefly photoemission devices, junction photodiodes, both in short-circuited and photovoltaic operation, and avalanche diodes. Avalanche multiplication decreases the detectivity by a factor G½, where G is the gain. A new derivation of McIntyre’s formula—including the effect of a non-Poissonian Boson field is presented. The remainder is devoted to photoconductive detectors. Four classes are distinguished: intrinsic, minority trapping models (like PbS), two center models (like CdS), extrinsic semiconductors (like Ge: Au). The main theoretical results are stated and illustrative experimental results are discussed. Some remarks are made on hot electron photoconductivity and Landau level transitions in magnetically tuned InSb detectors.

© 1967 Optical Society of America

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1967 (1)

L. H. Anderson, K. M. van Vliet, Physica 33(1967).

1966 (4)

H. S. Sommers, E. K. Gatchel, Proc. IEEE 54, 1553 (1966).
[Crossref]

P. Handel, Z. Naturforsh. 21a, 562, 573, 579 (1966).

M. E. Hines, IEEE Trans. ED-13, 158 (1966).

R. J. McIntyre, IEEE Trans. ED-13, 164 (1966).

1965 (4)

L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[Crossref]

H. Levinstein, Appl. Opt. 4, 629 (1965).
[Crossref]

S. Okazaki, M. Hiramatsu, Solid-State Electron. 8, 401 (1965).
[Crossref]

E. H. Putley, Appl. Opt. 4, 649 (1965).
[Crossref]

1964 (5)

H. Shenker, W. J. Moore, E. M. Swiggard, J. Appl. Phys. 35, 2965 (1964).
[Crossref]

K. M. van Vliet, Physica 30, 1092 (1964).
[Crossref]

K. M. van Vliet, Phys. Letters 8, 22 (1964).
[Crossref]

K. M. van Vliet, Phys. Rev. 133, A1182 (1964); erratum 138, 3AB (1965).
[Crossref]

A. S. Tager, Fiz. Tverd. Tela 6, 2418 (1964); Soviet Phys.—Solid State 8, 1919 (1965).

1963 (2)

R. H. Haitz, A. Goetzberger, R. M. Scarlett, W. Shockley, J. Appl. Phys. 34, 1581 (1963).
[Crossref]

E. V. Buryak, S. A. Kaufman, K. M. Kulikov, Fiz. Tverd. Tela 5, 345 (1963); Soviet Phys.—Solid State 5, 249 (1963).

1962 (3)

F. M. Klaassen, K. M. van Vliet, J. It. Fassett, J. Phys. Chem. Solids 22, 391 (1962).
[Crossref]

S. Borrello, H. Levinstein, J. Appl. Phys. 33, 2947 (1962).
[Crossref]

S. M. Kogan, Fiz. Tverd. Tela. 4, 1891 (1962); Phys. Soviet–Solid State 4, 1396 (1962).

1961 (8)

M. Pilkuhn, Z. Naturforsch. 16a, 173 (1961).

P. Bratt, W. Engeler, H. Levinstein, A. MacRae, J. Pehek, Infrared Phys. 1, 27 (1961).
[Crossref]

R. E. Burgess, J. Phys. Chem. Solids 22, 371 (1961).
[Crossref]

J. Neuringer, W. Bernard, J. Phys. Chem. Solids 22, 385 (1961).
[Crossref]

W. Engeler, H. Levinstein, C. Stannard, J. Phys. Chem. Solids 22, 249 (1961).
[Crossref]

K. M. van Vliet, E. R. Chenette, Physica 31, 985 (1961).
[Crossref]

D. W. Goodwin, J. Phys. Chem. Solids 22, 401 (1961).
[Crossref]

F. M. Klaassen, J. Blok, H. C. Booy, Physica 27, 87 (1961).

1960 (8)

M. Lax, Rev. Mod. Phys. 32, 25 (1960).
[Crossref]

F. M. Klaassen, K. M. van Vliet, J. Blok, Physica 26, 605 (1960).
[Crossref]

K. S. Champlin, Physica 26, 751 (1960).
[Crossref]

M. Lax, P. Mengert, J. Phys. Chem. Solids 14, 248 (1960).
[Crossref]

L. Johnson, H. Levinstein, Phys. Rev. 117, 1191 (1960).
[Crossref]

R. Clark Jones, J. Opt. Soc. Am. 50, 1058 (1960).
[Crossref]

J. J. Brophy, R. J. Robinson, Phys. Rev. 117, 738 (1960).
[Crossref]

H. Shenker, Bull. Am. Phys. Soc. 5, 195 (1960); Bull. Am. Phys. Soc. 6, 137 (1961).

1959 (9)

R. L. Petritz, Proc. Inst. Radio Engrs. 47, 1458 (1959).

R. Clark Jones, Proc. Inst. Radio Engrs. 47, 1481 (1959).

R. E. Burgess, Disc. Faraday Soc. 28, 151 (1959).
[Crossref]

L. Mandel, Proc. Phys. Soc. (London) 74, 233 (1959).
[Crossref]

C. T. J. Alkemade, Physica 25, 1145 (1959).
[Crossref]

W. J. Beyen, P. Bratt, H. Davis, L. Johnson, H. Levinstein, A. MacRae, J. Opt. Soc. Am. 49, 686 (1959).
[Crossref]

H. Levinstein, Proc. Inst. Radio Engrs. 47, 1478 (1959).

G. Heiland, E. Mollwo, Solid State Phys. 8, 1911 (1959).

R. Newmann, W. W. Tyler, Solid State Phys. 8, 49 (1959).
[Crossref]

1958 (7)

H. A. Klasens, J. Phys. Chem. Solids 7, 175 (1958). See also, F. N. Hooge, D. Polder, J. Phys. Chem. Solids 25, 977 (1964).
[Crossref]

J. E. Hill, K. M. van Vliet, J. Appl. Phys. 29, 177 (1958).
[Crossref]

S. Teitler, J. Appl. Phys. 29, 1585 (1958).
[Crossref]

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).
[Crossref]

J. E. Hill, K. M. van Vliet, Physica 24, 709 (1958).
[Crossref]

K. M. van Vliet, Proc. Inst. Radio Engrs. 46, 1004 (1958).

F. M. Klaassen, J. Blok, Physica 24, 975 (1958).
[Crossref]

1957 (4)

R. Clark Jones, IRIS 2, No. 1, 12 (1957).

W. Shockley, J. T. Last, Phys. Rev. 107, 392 (1957).
[Crossref]

H. H. Woostbury, W. W. Tyler, Phys. Rev. 105, 84 (1957).
[Crossref]

C. B. Collins, R. O. Carlson, Phys. Rev. 108, 1409 (1957).
[Crossref]

1956 (5)

J. C. Slater, Phys. Rev. 103, 1631 (1956).
[Crossref]

R. L. Petritz, Phys. Rev. 104, 1508 (1956).
[Crossref]

R. H. Harada, H. T. Minden, Phys. Rev. 102, 1258 (1956).
[Crossref]

K. M. van Vliet, J. Blok, Physica 22, 525 (1956).
[Crossref]

K. M. van Vliet, J. Blok, C. Ris, J. Steketee, Physica 22, 723 (1956).
[Crossref]

1955 (4)

C. I. Shulman, Phys. Rev. 98, 384 (1955).
[Crossref]

J. Broser, R. Broser-Warminsky, Ann. Physik 16, 361 (1955).
[Crossref]

J. Lambe, C. C. Klick, Phys. Rev. 98, 909 (1955).
[Crossref]

M. L. Schultz, G. A. Morton, Proc. Inst. Radio Engrs. 43, 1819 (1955).

1954 (1)

F. Stöckmann, Z. Physik 138, 404 (1954).
[Crossref]

1953 (2)

R. W. Smith, A. Rose, Phys. Rev. 92, 857 (1953). See also, A. Rose, Phys. Rev. 97, 322 (1955); also R. Bube, J. Phys. Chem. Solids 1, 234 (1957).
[Crossref]

R. C. Schwantes, J. H. Hannam, A. van der Ziel, J. Appl. Phys. 27, 573 (1953).
[Crossref]

1952 (2)

F. L. Lummis, R. L. Petritz, Phys. Rev. 86, 660 (1952).

R. B. Dingle, Proc. Roy. Soc. (London) A211, 500 (1952).

1951 (2)

G. S. Herzog, A. van der Ziel, Phys. Rev. 84, 1249 (1951).
[Crossref]

A. Rose, RCA Rev. 12, 362 (1951).

1950 (2)

F. S. Goucher, Phys. Rev. 78, 816 (1950).
[Crossref]

J. Broser, R. Warminsky, Ann. Physik 7, 289 (1950).
[Crossref]

1949 (1)

1947 (1)

L. Sosnowski, Phys. Rev. 72, 641 (1947).
[Crossref]

1946 (1)

H. A. Klasens, Nature 158, 306 (1946); and M. Schon, Ann. Physik 3, 333 (1948).
[Crossref]

1937 (1)

R. Hilsch, R. W. Pohl, Z. Physik 108, 55 (1937); Z. Physik 112, 252 (1939).
[Crossref]

1932 (1)

K. Hecht, Z. Physik 77, 235 (1932).
[Crossref]

1920 (1)

B. Gudden, R. Pohl, Z. Physik 2, 181 (1920).
[Crossref]

Alkemade, C. T. J.

C. T. J. Alkemade, Physica 25, 1145 (1959).
[Crossref]

Anderson, L. H.

L. H. Anderson, K. M. van Vliet, Physica 33(1967).

Beran, M.

M. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, New York, 1964).

Bernard, W.

J. Neuringer, W. Bernard, J. Phys. Chem. Solids 22, 385 (1961).
[Crossref]

Beyen, W. J.

Blok, J.

F. M. Klaassen, J. Blok, H. C. Booy, Physica 27, 87 (1961).

F. M. Klaassen, K. M. van Vliet, J. Blok, Physica 26, 605 (1960).
[Crossref]

F. M. Klaassen, J. Blok, Physica 24, 975 (1958).
[Crossref]

K. M. van Vliet, J. Blok, C. Ris, J. Steketee, Physica 22, 723 (1956).
[Crossref]

K. M. van Vliet, J. Blok, Physica 22, 525 (1956).
[Crossref]

Booy, H. C.

F. M. Klaassen, J. Blok, H. C. Booy, Physica 27, 87 (1961).

Borrello, S.

S. Borrello, H. Levinstein, J. Appl. Phys. 33, 2947 (1962).
[Crossref]

Bratt, P.

P. Bratt, W. Engeler, H. Levinstein, A. MacRae, J. Pehek, Infrared Phys. 1, 27 (1961).
[Crossref]

W. J. Beyen, P. Bratt, H. Davis, L. Johnson, H. Levinstein, A. MacRae, J. Opt. Soc. Am. 49, 686 (1959).
[Crossref]

P. Bratt, “Germanium and InSb Infrared Detectors”, Syracuse University Res. Inst. Final Report (February1960).

Brophy, J. J.

J. J. Brophy, R. J. Robinson, Phys. Rev. 117, 738 (1960).
[Crossref]

Broser, J.

J. Broser, R. Broser-Warminsky, Ann. Physik 16, 361 (1955).
[Crossref]

J. Broser, R. Warminsky, Ann. Physik 7, 289 (1950).
[Crossref]

Broser-Warminsky, R.

J. Broser, R. Broser-Warminsky, Ann. Physik 16, 361 (1955).
[Crossref]

Burgess, R. E.

R. E. Burgess, J. Phys. Chem. Solids 22, 371 (1961).
[Crossref]

R. E. Burgess, Disc. Faraday Soc. 28, 151 (1959).
[Crossref]

Burstein, E.

E. Burstein, G. Picus, N. Sclar, in Photoconductivity Conference, R. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), p. 353.

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E. V. Buryak, S. A. Kaufman, K. M. Kulikov, Fiz. Tverd. Tela 5, 345 (1963); Soviet Phys.—Solid State 5, 249 (1963).

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C. B. Collins, R. O. Carlson, Phys. Rev. 108, 1409 (1957).
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K. S. Champlin, Physica 26, 751 (1960).
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R. Clark Jones, J. Opt. Soc. Am. 50, 1058 (1960).
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M. B. Colligan, M.Sc. thesis, University of Minnesota, 1963.

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F. M. Klaassen, K. M. van Vliet, J. It. Fassett, J. Phys. Chem. Solids 22, 391 (1962).
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J. R. Fassett, Contract No. DA 36–039 sc 78009 (1March1960), U. S. Signal Corps, pp. 26–44.

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W. Feller, An Introduction to Probability Theory and Its Applications (John Wiley & Sons, New York, 1957), Chap. 17.

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H. S. Sommers, E. K. Gatchel, Proc. IEEE 54, 1553 (1966).
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R. H. Haitz, A. Goetzberger, R. M. Scarlett, W. Shockley, J. Appl. Phys. 34, 1581 (1963).
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D. W. Goodwin, J. Phys. Chem. Solids 22, 401 (1961).
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G. Heiland, E. Mollwo, Solid State Phys. 8, 1911 (1959).

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J. E. Hill, K. M. van Vliet, J. Appl. Phys. 29, 177 (1958).
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R. Hilsch, R. W. Pohl, Z. Physik 108, 55 (1937); Z. Physik 112, 252 (1939).
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M. E. Hines, IEEE Trans. ED-13, 158 (1966).

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S. Okazaki, M. Hiramatsu, Solid-State Electron. 8, 401 (1965).
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F. J. Hyde, Rept. Conf. Phys. Soc. Semiconductors, Rugby, England, 1956 (The Institute of Physics and the Physical Society, London, 1956), p. 5.

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Kaufman, S. A.

E. V. Buryak, S. A. Kaufman, K. M. Kulikov, Fiz. Tverd. Tela 5, 345 (1963); Soviet Phys.—Solid State 5, 249 (1963).

Klaassen, F. M.

F. M. Klaassen, K. M. van Vliet, J. It. Fassett, J. Phys. Chem. Solids 22, 391 (1962).
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F. M. Klaassen, J. Blok, H. C. Booy, Physica 27, 87 (1961).

F. M. Klaassen, K. M. van Vliet, J. Blok, Physica 26, 605 (1960).
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F. M. Klaassen, J. Blok, Physica 24, 975 (1958).
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H. A. Klasens, J. Phys. Chem. Solids 7, 175 (1958). See also, F. N. Hooge, D. Polder, J. Phys. Chem. Solids 25, 977 (1964).
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H. A. Klasens, Nature 158, 306 (1946); and M. Schon, Ann. Physik 3, 333 (1948).
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J. Lambe, C. C. Klick, Phys. Rev. 98, 909 (1955).
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S. M. Kogan, Fiz. Tverd. Tela. 4, 1891 (1962); Phys. Soviet–Solid State 4, 1396 (1962).

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P. W. Kruse, R. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, New York, 1962).

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E. V. Buryak, S. A. Kaufman, K. M. Kulikov, Fiz. Tverd. Tela 5, 345 (1963); Soviet Phys.—Solid State 5, 249 (1963).

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J. Lambe, C. C. Klick, Phys. Rev. 98, 909 (1955).
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W. Shockley, J. T. Last, Phys. Rev. 107, 392 (1957).
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M. Lax, P. Mengert, J. Phys. Chem. Solids 14, 248 (1960).
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H. Levinstein, Appl. Opt. 4, 629 (1965).
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S. Borrello, H. Levinstein, J. Appl. Phys. 33, 2947 (1962).
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W. Engeler, H. Levinstein, C. Stannard, J. Phys. Chem. Solids 22, 249 (1961).
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P. Bratt, W. Engeler, H. Levinstein, A. MacRae, J. Pehek, Infrared Phys. 1, 27 (1961).
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L. Johnson, H. Levinstein, Phys. Rev. 117, 1191 (1960).
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H. Levinstein, Proc. Inst. Radio Engrs. 47, 1478 (1959).

W. J. Beyen, P. Bratt, H. Davis, L. Johnson, H. Levinstein, A. MacRae, J. Opt. Soc. Am. 49, 686 (1959).
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F. L. Lummis, R. L. Petritz, Phys. Rev. 86, 660 (1952).

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P. Bratt, W. Engeler, H. Levinstein, A. MacRae, J. Pehek, Infrared Phys. 1, 27 (1961).
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W. J. Beyen, P. Bratt, H. Davis, L. Johnson, H. Levinstein, A. MacRae, J. Opt. Soc. Am. 49, 686 (1959).
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L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
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L. Mandel, Proc. Phys. Soc. (London) 74, 233 (1959).
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L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).
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P. W. Kruse, R. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, New York, 1962).

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R. J. McIntyre, IEEE Trans. ED-13, 164 (1966).

R. J. McIntyre, Report at the Solid State Devices Conference, Princeton, June 1965.

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P. W. Kruse, R. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, New York, 1962).

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M. Lax, P. Mengert, J. Phys. Chem. Solids 14, 248 (1960).
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R. H. Harada, H. T. Minden, Phys. Rev. 102, 1258 (1956).
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G. Heiland, E. Mollwo, Solid State Phys. 8, 1911 (1959).

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H. Shenker, W. J. Moore, E. M. Swiggard, J. Appl. Phys. 35, 2965 (1964).
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M. L. Schultz, G. A. Morton, Proc. Inst. Radio Engrs. 43, 1819 (1955).

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T. S. Moss, Photoconductivity in the Elements (Academic Press, New York, 1952).

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J. Neuringer, W. Bernard, J. Phys. Chem. Solids 22, 385 (1961).
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R. Newmann, W. W. Tyler, Solid State Phys. 8, 49 (1959).
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S. Okazaki, M. Hiramatsu, Solid-State Electron. 8, 401 (1965).
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M. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, New York, 1964).

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P. Bratt, W. Engeler, H. Levinstein, A. MacRae, J. Pehek, Infrared Phys. 1, 27 (1961).
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R. L. Petritz, Proc. Inst. Radio Engrs. 47, 1458 (1959).

R. L. Petritz, Phys. Rev. 104, 1508 (1956).
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F. L. Lummis, R. L. Petritz, Phys. Rev. 86, 660 (1952).

R. L. Petritz, in Photoconductivity Conference, R. G. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), pp. 49–77.

Picus, G.

E. Burstein, G. Picus, N. Sclar, in Photoconductivity Conference, R. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), p. 353.

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M. Pilkuhn, Z. Naturforsch. 16a, 173 (1961).

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B. Gudden, R. Pohl, Z. Physik 2, 181 (1920).
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R. Hilsch, R. W. Pohl, Z. Physik 108, 55 (1937); Z. Physik 112, 252 (1939).
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P. J. Price, in Fluctuation Phenomena in Solids, R. E. Burgess, Ed. (Academic Press, New York, 1965), Chap. VIII.)

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E. H. Putley, Appl. Opt. 4, 649 (1965).
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E. H. Putley, Proceedings of the 7th International Conference on Semiconductors, Paris, 1964 (Dunod, Paris, 1964), p. 443.

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K. M. van Vliet, J. Blok, C. Ris, J. Steketee, Physica 22, 723 (1956).
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Rittner, E. S.

E. S. Rittner, in Photoconductivity Conference, R. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), p. 215.

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J. J. Brophy, R. J. Robinson, Phys. Rev. 117, 738 (1960).
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R. W. Smith, A. Rose, Phys. Rev. 92, 857 (1953). See also, A. Rose, Phys. Rev. 97, 322 (1955); also R. Bube, J. Phys. Chem. Solids 1, 234 (1957).
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A. Rose, RCA Rev. 12, 362 (1951).

A. Rose, in Photoconductivity Conference, R. G. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), pp. 3–48.

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R. H. Haitz, A. Goetzberger, R. M. Scarlett, W. Shockley, J. Appl. Phys. 34, 1581 (1963).
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E. Schrödinger, Statistical Thermodynamics (Cambridge University Press, New York, 1960).

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M. L. Schultz, G. A. Morton, Proc. Inst. Radio Engrs. 43, 1819 (1955).

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R. C. Schwantes, J. H. Hannam, A. van der Ziel, J. Appl. Phys. 27, 573 (1953).
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Sclar, N.

E. Burstein, G. Picus, N. Sclar, in Photoconductivity Conference, R. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), p. 353.

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H. Shenker, W. J. Moore, E. M. Swiggard, J. Appl. Phys. 35, 2965 (1964).
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H. Shenker, Bull. Am. Phys. Soc. 5, 195 (1960); Bull. Am. Phys. Soc. 6, 137 (1961).

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R. H. Haitz, A. Goetzberger, R. M. Scarlett, W. Shockley, J. Appl. Phys. 34, 1581 (1963).
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W. Shockley, J. T. Last, Phys. Rev. 107, 392 (1957).
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C. I. Shulman, Phys. Rev. 98, 384 (1955).
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J. C. Slater, Phys. Rev. 103, 1631 (1956).
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R. W. Smith, A. Rose, Phys. Rev. 92, 857 (1953). See also, A. Rose, Phys. Rev. 97, 322 (1955); also R. Bube, J. Phys. Chem. Solids 1, 234 (1957).
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H. S. Sommers, E. K. Gatchel, Proc. IEEE 54, 1553 (1966).
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L. Sosnowski, Phys. Rev. 72, 641 (1947).
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Stannard, C.

W. Engeler, H. Levinstein, C. Stannard, J. Phys. Chem. Solids 22, 249 (1961).
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K. M. van Vliet, J. Blok, C. Ris, J. Steketee, Physica 22, 723 (1956).
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F. Stöckmann, Z. Physik 138, 404 (1954).
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F. Stöckmann, in Photoconductivity Conference, R. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), pp. 269–286.

Swiggard, E. M.

H. Shenker, W. J. Moore, E. M. Swiggard, J. Appl. Phys. 35, 2965 (1964).
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Tager, A. S.

A. S. Tager, Fiz. Tverd. Tela 6, 2418 (1964); Soviet Phys.—Solid State 8, 1919 (1965).

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S. Teitler, J. Appl. Phys. 29, 1585 (1958).
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R. Newmann, W. W. Tyler, Solid State Phys. 8, 49 (1959).
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H. H. Woostbury, W. W. Tyler, Phys. Rev. 105, 84 (1957).
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van der Ziel, A.

R. C. Schwantes, J. H. Hannam, A. van der Ziel, J. Appl. Phys. 27, 573 (1953).
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G. S. Herzog, A. van der Ziel, Phys. Rev. 84, 1249 (1951).
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A. van der Ziel, Fluctuation Phenomena in Semiconductors (Butterworths, London, 1959).

A. van der Ziel, Noise (Prentice-Hall, New York, 1954).

van Vliet, K. M.

L. H. Anderson, K. M. van Vliet, Physica 33(1967).

K. M. van Vliet, Phys. Letters 8, 22 (1964).
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K. M. van Vliet, Physica 30, 1092 (1964).
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K. M. van Vliet, Phys. Rev. 133, A1182 (1964); erratum 138, 3AB (1965).
[Crossref]

F. M. Klaassen, K. M. van Vliet, J. It. Fassett, J. Phys. Chem. Solids 22, 391 (1962).
[Crossref]

K. M. van Vliet, E. R. Chenette, Physica 31, 985 (1961).
[Crossref]

F. M. Klaassen, K. M. van Vliet, J. Blok, Physica 26, 605 (1960).
[Crossref]

J. E. Hill, K. M. van Vliet, J. Appl. Phys. 29, 177 (1958).
[Crossref]

K. M. van Vliet, Proc. Inst. Radio Engrs. 46, 1004 (1958).

J. E. Hill, K. M. van Vliet, Physica 24, 709 (1958).
[Crossref]

K. M. van Vliet, J. Blok, C. Ris, J. Steketee, Physica 22, 723 (1956).
[Crossref]

K. M. van Vliet, J. Blok, Physica 22, 525 (1956).
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K. M. van Vliet, Proceedings of the 7th International Congress on Semiconductors, Paris, 1964 (Dunod, Paris, 1964), p. 831.

K. M. van Vliet, J. R. Fassett, in Fluctuation Phenomena in Solids, R. E. Burgess, Ed. (Academic Press, New York, 1965), Chap. VII.

Warminsky, R.

J. Broser, R. Warminsky, Ann. Physik 7, 289 (1950).
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Wolf, E.

L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
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Woostbury, H. H.

H. H. Woostbury, W. W. Tyler, Phys. Rev. 105, 84 (1957).
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Ann. Physik (2)

J. Broser, R. Warminsky, Ann. Physik 7, 289 (1950).
[Crossref]

J. Broser, R. Broser-Warminsky, Ann. Physik 16, 361 (1955).
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Appl. Opt. (2)

Bull. Am. Phys. Soc. (1)

H. Shenker, Bull. Am. Phys. Soc. 5, 195 (1960); Bull. Am. Phys. Soc. 6, 137 (1961).

Disc. Faraday Soc. (1)

R. E. Burgess, Disc. Faraday Soc. 28, 151 (1959).
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Fiz. Tverd. Tela (2)

A. S. Tager, Fiz. Tverd. Tela 6, 2418 (1964); Soviet Phys.—Solid State 8, 1919 (1965).

E. V. Buryak, S. A. Kaufman, K. M. Kulikov, Fiz. Tverd. Tela 5, 345 (1963); Soviet Phys.—Solid State 5, 249 (1963).

Fiz. Tverd. Tela. (1)

S. M. Kogan, Fiz. Tverd. Tela. 4, 1891 (1962); Phys. Soviet–Solid State 4, 1396 (1962).

IEEE Trans. (2)

M. E. Hines, IEEE Trans. ED-13, 158 (1966).

R. J. McIntyre, IEEE Trans. ED-13, 164 (1966).

Infrared Phys. (1)

P. Bratt, W. Engeler, H. Levinstein, A. MacRae, J. Pehek, Infrared Phys. 1, 27 (1961).
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IRIS (1)

R. Clark Jones, IRIS 2, No. 1, 12 (1957).

J. Appl. Phys. (6)

R. C. Schwantes, J. H. Hannam, A. van der Ziel, J. Appl. Phys. 27, 573 (1953).
[Crossref]

R. H. Haitz, A. Goetzberger, R. M. Scarlett, W. Shockley, J. Appl. Phys. 34, 1581 (1963).
[Crossref]

J. E. Hill, K. M. van Vliet, J. Appl. Phys. 29, 177 (1958).
[Crossref]

S. Borrello, H. Levinstein, J. Appl. Phys. 33, 2947 (1962).
[Crossref]

H. Shenker, W. J. Moore, E. M. Swiggard, J. Appl. Phys. 35, 2965 (1964).
[Crossref]

S. Teitler, J. Appl. Phys. 29, 1585 (1958).
[Crossref]

J. Opt. Soc. Am. (3)

J. Phys. Chem. Solids (7)

F. M. Klaassen, K. M. van Vliet, J. It. Fassett, J. Phys. Chem. Solids 22, 391 (1962).
[Crossref]

R. E. Burgess, J. Phys. Chem. Solids 22, 371 (1961).
[Crossref]

D. W. Goodwin, J. Phys. Chem. Solids 22, 401 (1961).
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M. Lax, P. Mengert, J. Phys. Chem. Solids 14, 248 (1960).
[Crossref]

H. A. Klasens, J. Phys. Chem. Solids 7, 175 (1958). See also, F. N. Hooge, D. Polder, J. Phys. Chem. Solids 25, 977 (1964).
[Crossref]

W. Engeler, H. Levinstein, C. Stannard, J. Phys. Chem. Solids 22, 249 (1961).
[Crossref]

J. Neuringer, W. Bernard, J. Phys. Chem. Solids 22, 385 (1961).
[Crossref]

Nature (1)

H. A. Klasens, Nature 158, 306 (1946); and M. Schon, Ann. Physik 3, 333 (1948).
[Crossref]

Phys. Letters (1)

K. M. van Vliet, Phys. Letters 8, 22 (1964).
[Crossref]

Phys. Rev. (16)

J. Lambe, C. C. Klick, Phys. Rev. 98, 909 (1955).
[Crossref]

R. W. Smith, A. Rose, Phys. Rev. 92, 857 (1953). See also, A. Rose, Phys. Rev. 97, 322 (1955); also R. Bube, J. Phys. Chem. Solids 1, 234 (1957).
[Crossref]

G. S. Herzog, A. van der Ziel, Phys. Rev. 84, 1249 (1951).
[Crossref]

K. M. van Vliet, Phys. Rev. 133, A1182 (1964); erratum 138, 3AB (1965).
[Crossref]

J. J. Brophy, R. J. Robinson, Phys. Rev. 117, 738 (1960).
[Crossref]

C. I. Shulman, Phys. Rev. 98, 384 (1955).
[Crossref]

F. S. Goucher, Phys. Rev. 78, 816 (1950).
[Crossref]

L. Johnson, H. Levinstein, Phys. Rev. 117, 1191 (1960).
[Crossref]

H. H. Woostbury, W. W. Tyler, Phys. Rev. 105, 84 (1957).
[Crossref]

C. B. Collins, R. O. Carlson, Phys. Rev. 108, 1409 (1957).
[Crossref]

W. Shockley, J. T. Last, Phys. Rev. 107, 392 (1957).
[Crossref]

F. L. Lummis, R. L. Petritz, Phys. Rev. 86, 660 (1952).

L. Sosnowski, Phys. Rev. 72, 641 (1947).
[Crossref]

J. C. Slater, Phys. Rev. 103, 1631 (1956).
[Crossref]

R. L. Petritz, Phys. Rev. 104, 1508 (1956).
[Crossref]

R. H. Harada, H. T. Minden, Phys. Rev. 102, 1258 (1956).
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Physica (11)

K. M. van Vliet, J. Blok, Physica 22, 525 (1956).
[Crossref]

K. S. Champlin, Physica 26, 751 (1960).
[Crossref]

K. M. van Vliet, J. Blok, C. Ris, J. Steketee, Physica 22, 723 (1956).
[Crossref]

F. M. Klaassen, J. Blok, Physica 24, 975 (1958).
[Crossref]

J. E. Hill, K. M. van Vliet, Physica 24, 709 (1958).
[Crossref]

C. T. J. Alkemade, Physica 25, 1145 (1959).
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L. H. Anderson, K. M. van Vliet, Physica 33(1967).

F. M. Klaassen, J. Blok, H. C. Booy, Physica 27, 87 (1961).

F. M. Klaassen, K. M. van Vliet, J. Blok, Physica 26, 605 (1960).
[Crossref]

K. M. van Vliet, Physica 30, 1092 (1964).
[Crossref]

K. M. van Vliet, E. R. Chenette, Physica 31, 985 (1961).
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Proc. IEEE (1)

H. S. Sommers, E. K. Gatchel, Proc. IEEE 54, 1553 (1966).
[Crossref]

Proc. Inst. Radio Engrs. (5)

M. L. Schultz, G. A. Morton, Proc. Inst. Radio Engrs. 43, 1819 (1955).

R. Clark Jones, Proc. Inst. Radio Engrs. 47, 1481 (1959).

R. L. Petritz, Proc. Inst. Radio Engrs. 47, 1458 (1959).

K. M. van Vliet, Proc. Inst. Radio Engrs. 46, 1004 (1958).

H. Levinstein, Proc. Inst. Radio Engrs. 47, 1478 (1959).

Proc. Phys. Soc. (London) (2)

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).
[Crossref]

L. Mandel, Proc. Phys. Soc. (London) 74, 233 (1959).
[Crossref]

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A. van der Ziel, Fluctuation Phenomena in Semiconductors (Butterworths, London, 1959).

P. W. Kruse, R. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, New York, 1962).

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P. Bratt, “Germanium and InSb Infrared Detectors”, Syracuse University Res. Inst. Final Report (February1960).

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (U. S. Government Printing Office, Washington, D. C., 1964), Chap. 27.

F. M. Klaassen, thesis, Free University of Amsterdam, 1961.

M. B. Colligan, M.Sc. thesis, University of Minnesota, 1963.

F. J. Hyde, Rept. Conf. Phys. Soc. Semiconductors, Rugby, England, 1956 (The Institute of Physics and the Physical Society, London, 1956), p. 5.

E. Burstein, G. Picus, N. Sclar, in Photoconductivity Conference, R. Breckenridge, B. R. Russell, E. E. Hahn, Eds. (John Wiley & Sons, New York, 1956), p. 353.

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Figures (10)

Fig. 1
Fig. 1

(a) Computed values of I(h/kT)3, Eq. (42), for sharp cutoff absorption spectra. From this figure one easily constructs curves for the detectivity. (b) Computation of I(h/kT)3 in the near ir.

Fig. 2
Fig. 2

(a) Computed values for D*/√ η ¯ for 300°K, 200°K, and 90°K between 0.6 μ and 4.0 μ. (b) Same as (a) but for the near ir. The dotted curve gives a comparison with the result at 300°K by Bratt et al.14

Fig. 3
Fig. 3

Noise of PbS Kodak cells (after Klaassen et al.17).

Fig. 4
Fig. 4

Response (curve II) and noise (curve I) for CdS with λ = 5580 Å, used for computation of the detective quantum efficiency (after van Vliet et al.21).

Fig. 5
Fig. 5

Equivalent circuit of setup.

Fig. 6
Fig. 6

Diagrams of noise and signal transmission. (a); Signal transmission for photoemitter. (b) Same as (a) but plus electron multiplication. (c) Signal transmission for photoconduetive cells (d) Noise transmission corresponding to (b). (e) Noise transmission corresponding to (c).

Fig. 7
Fig. 7

Primary photocurrents in AgCl, λ = 6000 Å; after Hecht.28

Fig. 8
Fig. 8

Two level excitation using Einstein’s terminology.

Fig. 9
Fig. 9

Computed spectra for S(P), S(PN), and S(N) in class II photoconductors (after Klaassen et al.15). These spectral densities are represented by the dotted lines. The full line represents S(i), assuming that b = 1.5.

Fig. 10
Fig. 10

Illustrative noise curves for counter-doped p-type gold-doped germanium. Curve (1) 77°K; I assumed 10 μA (after Johnson and Levinstein91 or Beyen et al.94). Curve (2) 90°K, I = 78 μA. Resistance assumed 200 kΩ (after Neuringer and Bernard92). Curve (3) 93°K, I = 3.8 μA, R = 21 MΩ (after Colligan, unpublished). Curve (4) 88°K, I = 19.2 μA, R = 12 MΩ (after Fassett97,16). Curve (5) 88°K, I = 9.7 μA, R = 12 MΩ (after Fassett97,16). Curve (6) 77°K?, I = 90 μA (after Buryak et al.95). The magnitude has been computed as good as possible from the authors’ data which often list S(v) (f) without details of circuitry.

Tables (3)

Tables Icon

Table I Some Computed and Observed Values for the Detectivity

Tables Icon

Table II Dectectivity Data According to Klaassen et al.15,17

Tables Icon

Table III Impurity Levels in Si, Ge, and InSb

Equations (157)

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S b i ( r ) ( B ν , f ) + S a i ( r ) ( a ν , f ) + S s p ( r ) ( f ) = S det ( r ) ( f ) .
S det ( r ) ( f ) = S t h ( r ) ( f ) + S g r ( r ) ( f ) + S t r ( r ) ( f ) + S e x ( r ) ( f ) .
S b i ( r ) ( ν , f ) = R 2 ( ν , f ) S J b ( ν , f ) ,
S a i ( r ) ( ν , f ) = R 2 ( ν , f ) S J a ( ν , f ) .
S b i ( r ) ( B ν , f ) = R 2 ( ν , f ) S J b ( ν , f ) d ν ,
S a i ( r ) ( a ν , f ) = R 2 ( ν , f ) S J a ( ν , f ) d ν .
S b i ( r ) ( B ν , f ) = R 2 ( ν 0 , f ) B ν S B b ( ν , f ) d ν = R 2 ( ν 0 , f ) S J b ( B ν , f )
σ / N = r ( f ) / [ S det ( r ) ( f ) + S e q ( r ) ( f ) ] ½ ( Δ f ) ½ .
( σ N ) 2 = j 2 ( ν , f ) R 2 ( ν , f ) [ S det ( r ) ( f ) + S e q ( r ) ( f ) ] Δ f .
P e q , λ [ λ , f , Δ f , A ] = h ν s J e q [ λ , f , Δ f , A ] = h ν s [ S det ( r ) ( f ) + S e q ( r ) ( f ) ] ½ ( Δ f ) ½ / R ( ν s , f ) .
P e q , λ [ λ , f , Δ f , A ] = h ν s J e q , λ [ λ , f , Δ f , A ] = h ν s [ S det ( r ) ( f ) Δ f ] ½ / R ( ν s , f ) .
P e q , λ [ λ , f , Δ f , A ] = P e q , λ [ λ , f , 1 , 1 ] ( A Δ f ) ½ .
D λ * = D λ [ λ , f , 1 , 1 ] = 1 / P e q , λ [ λ , f , 1 , 1 ] .
D T * [ T , f ] = 1 / P e q , T [ T , f , 1 , 1 ] .
F ( f ) = ( D λ * / D λ * ) 2 or ( D T * / D T * ) 2 .
D T * { T s , Ω s } [ T s , f ] or D λ * { T s , Ω s } [ λ , f ] .
D T * or λ { T s , Ω s } = ( π / Ω s ) ½ D T * or λ { T s , 2 π } ,
S J b ( ν , f ) = η i ( ν ) S J b ( ν , f ) .
R ( ν , f ) = R ( ν , f ) / η i ( ν ) .
S b i ( r ) ( ν , f ) = R 2 ( ν , f ) S J b ( ν , f ) = [ η i ( ν ) ] - 1 R 2 ( ν , f ) S J b ( ν , f )
S b i ( r ) ( B ν , f ) = R 2 ( ν 0 , f ) B ν [ S J b ( ν , f ) / η i ( ν ) ] d ν .
S ( r ) ( f ) = [ R 2 ( ν 0 , f ) / η d ] B ν S J b ( ν , f ) d ν ,
S J ( Δ ν , f ) = Δ ν 2 J ¯ ( ν ) [ 1 + B ( f , ν ) ] d ν ,
S J ( Δ ν , f ) = Δ ν 2 J ¯ ( ν ) η i ( ν ) [ 1 + η i ( ν ) B ( f , ν ) ] .
j s ( ν s , f ) / p s ( f ) = J s ( ν s ) / P s .
j s ( Δ ν s , f ) = p s ( f ) Δ ν s [ J s ( ν s ) / P s ] η i ( ν s ) d ν s .
D * = Δ ν s [ J s ( ν ) / P s ] η i ( ν ) d ν { Δ ν 2 J ¯ ( ν ) A - 1 η i ( ν ) [ 1 + η i ( ν ) B ( f , ν ) ] d ν } ½ .
J ¯ ( ν ) = c A q ( ν ) / 4 = 2 π A ( ν 2 / c 2 ) ( e h ν / k T - 1 ) - 1 ,
J s ( ν ) / P s = c A q ( ν ) / 4 σ T s 4 ,
B ( ν ) = ( e h ν / k T - 1 ) - 1
Δ ν = Δ ν s = ( ν 0 , ) .
G ( T , η ) = h ν s η ( ν s ) ν 0 2 π A ( ν 2 / c 2 ) η ( ν ) σ T 4 ( e h ν / k T - 1 ) d ν ;
I ( T , η ) = 1 η ( ν s ) ν 0 ν 2 [ e h ν / k T + η ( ν ) - 1 ] ( e h ν / k T - 1 ) 2 η ( ν ) d ν .
D T * { T s , 2 π } = G ( T s , η i ) c 2 h ν s [ η i ( ν s ) π ] ½ [ I ( T s , η i ) ] - ½ .
J ¯ ( ν ) as in Eq . ( 27 ) with T s T e ,
J s ( ν ) Δ ν s = P s / h ν s , Δ ν s ν s ,
D λ * { T e , 2 π } = c 2 h ν s [ η i ( ν s ) π ] ½ [ I ( T e , η i ) ] - ½ .
D T * { T s , Ω s } = G ( T s , η i ) D λ * { T s , Ω s } .
D λ * { T e , 2 π } = c 2 h ν s [ η i ( ν s ) 2 π ] ½ [ I ( T e , 1 ) ] - ½ .
B = J ¯ a π / Z 1 ( f 2 π 2 + a 2 )
D λ * { J ¯ , a ( ν L ) , Ω } = η i ( ν s ) h ν s ( A 2 η i ( ν L ) ) ½ × { J ¯ [ 1 + J ¯ a π Z 1 ( π 2 f 2 + a 2 ) ] } - ½ .
D λ * { J ¯ , line source } ( h ν s ) - 1 [ A η i ( ν s ) / 2 J ¯ ] ½
I ( T , 1 ) = ( k T h ) 3 { π 2 3 + y [ y e y - 1 - 2 1 y 0 y t d t e t - 1 ] } ,
I ( T , 1 ) ~ ( k T / h ) 3 ( y 2 + 2 y + 2 ) e - y .
G ( T , η ) = 2 π A ν s k 3 σ c 2 T h 2 ( 2.404 - 0 y t 2 d t e t - 1 ) .
G ( T , η ) ~ ( 2 π A ν s k 3 / σ c 2 T h 2 ) e - y ( y 2 + 2 y + 2 ) .
R ( ν , f ) = 5 × 10 - 18 A / quanta sec - 1 , f = 10 Hz ; J ¯ a = 2.45 × 10 15 quanta / sec tungsten , λ = 5580 Å , a ν 50 Å .
D λ * { J ¯ a , a ν } [ 5580 , 10 ] 2.9 × 10 9 ; D λ ( obs ) = 2.7 × 10 9 .
S ( i ) ( ω ) = S a i ( i ) ( ω ) + S b i ( i ) ( ω ) + S s p ( i ) ( ω ) + 4 k T g i + 4 k T R n | R x + Z R x × Z | 2 .
I ¯ = G I ¯ p r = q ( τ / τ d ) η J ¯ .
τ d = L / μ E = L 2 / μ V ,
I ¯ = q μ N ¯ ( V / L 2 ) ,
N ¯ = τ η J ¯ , or n ¯ = τ η J ¯ / A d
p / t + μ a E · p + g ( p ) - r ( p ) - D a 2 p = Δ Φ ( r , t ) ,
μ a = ( n - p ) μ n μ p μ n n + u p p ;     D a = ( n + p ) D n D p D n n + D p p .
δ p ¯ ( x ) = ( η J ¯ / A d ) τ [ 1 - exp ( - x / μ a E τ ) ] .
I = q ( A d / L ) δ p ( L ) ¯ E ( μ n + μ p ) = q L - 1 ( η J ¯ τ ) E × ( μ n + μ p ) [ 1 - exp ( - L / μ a E τ ) ] .
I ¯ sat = q ( η J ¯ ) ( μ n + μ p ) / μ a .
I ¯ sat = q ( μ n + μ p ) E ( η J ¯ τ ) L - 1 { 1 - μ a E τ L × [ 1 - exp ( - L μ a E τ ) ] } ,
var N Δ N 2 ¯ = N ¯ ( 1 + N ¯ / Z ) = N ¯ ( 1 + B ) .
B = N ¯ / Z = 1 / ( e h ν / k T - 1 ) .
m θ ( t ) = t t + θ J b ( t ) d t = θ J b ( θ , t ) ,
S J b = 2 θ [ Δ J b ( θ , t ) ] 2 ¯ = ( 2 / θ ) Δ m θ 2 ¯ = ( 2 / θ ) m θ ¯ ( 1 + B ) = 2 J ¯ b ( 1 + B ) .
S J b = 2 J ¯ b + 2 J ¯ b 2 B / J ¯ b ,
S J b = 2 J ¯ b + 2 J ¯ b 2 λ 2 / 2 π A ( Δ ν ) .
n = α = 1 m P α ,
n ¯ = m ¯ P ¯ , var n = ( P ¯ ) 2 var m + m ¯ var P .
Δ n θ 2 ¯ = η m θ ¯ ( 1 + η B ) = n ¯ θ ( 1 + η B ) = n ¯ θ ( 1 + B ) .
S η J = 2 J ¯ ( 1 + η B ) .
var n k = ( P ¯ ) 2 k ( var m ) + m ¯ ( var P ) ( P ¯ ) k [ 1 - ( P ¯ ) k ] P ¯ ( 1 - P ¯ ) .
S J α = 2 η J ¯ ( 1 + η B ) ,
S J ρ = 2 ( 1 - η ) J ¯ [ 1 + ( 1 - η ) B ] .
S J = 2 η J ¯ [ 1 + ( 2 - η ) B ] .
S J α + S J = 4 η J ¯ ( 1 + B ) .
Φ = ( m θ α - m θ , - m θ ) / θ ,
var Φ = ( 1 / θ 2 ) [ var m θ α + var m θ + var m θ - 2 covar ( m θ α , m θ ) ] = ( 1 / θ 2 ) [ var m θ α + var m θ - 2 covar ( m θ α , m θ ) ] .
S Φ = S J α + S J - 2 S ( J α J ) = 4 η i J ¯ ( 1 + B ) ,
d n / d t = n J B 12 - n J B 21 - n A 21 = J α - J - J = Φ .
η i = ( J ¯ α - J ¯ ) / J ¯ = n 0 B 12 - n 0 B 21 ,
n 0 / n 0 = ( B 12 / B 21 ) e - h ν / k T .
η i = 4 n 0 B 12 / ( 1 + B ) .
S Φ = 4 n 0 B 12 J ¯ 4 g 0
S Φ = 2 g 0 + 2 r 0 ,
S n = 4 g 0 τ * 2 / ( 1 + ω 2 τ * 2 ) ,
1 / τ * = J 0 [ ( d n B 21 / d n ) ] n 0 - ( d n B 12 / d n ) n 0 ] - ( d n A 21 / d n ) n 0 .
Φ E ( θ ) = 0 F ( f ) e - j ω θ d f ,
I ( t ) = Φ E ( 0 ) = 0 F ( ν ) d ν .
Φ Δ I ( θ ) = Φ E ( θ ) Φ E * ( θ ) .
S Δ I ( F ( ν ) , f ) = 2 0 F ( ν ) F ( ν + f ) d ν = 2 I 2 0 F ( ν ) F ( ν + f ) d ν ,
F ( ν ) = I ( 1 / σ 2 π ) exp [ - ( ν - ν 0 ) 2 / 2 σ 2 ] .
S Δ I ( Gaussian a , f ) = ( 2 I / a ) exp [ - π f 2 / a 2 ] .
F ( ν ) = 2 I a / [ 4 π 2 ( ν - ν 0 ) 2 + a 2 ] .
S Δ I ( Lor a f ) = 2 π I a / ( π 2 f 2 + a 2 ) .
S J a [ F ( ν ) , f ] = 2 J a + 2 J a 2 Z 1 - 1 0 F ( ν ) F ( ν + f ) d ν ,
S J a ( F ( ν ) f ) 2 J a + 2 J a 2 λ 0 2 τ c / Ω A ,     ( f ν 0 ) ,
B ( f , ν 0 ) = m τ λ 0 2 A Ω τ 0 F ( ν ) F ( ν + f ) d ν m τ Z ,
S J a [ F ( ν ) , f ] = 2 J a [ 1 + B ( f , ν 0 ) ] ,
S a i ( i ) [ F ( ν ) , f ] = 2 I ¯ [ 1 + η B ( f , ν 0 ) ] .
i ( ω ) = q η j s ( ω ) ,
R ( ω ) = q η
P e q , λ [ λ f , Δ f , A ] = h ν s [ 4 k T g i Δ f ] ½ q η .
P ¯ = δ ;     P 2 ¯ = κ δ ;     var P = ( κ - δ ) δ .
var n a = m ¯ δ 2 k [ 1 + κ - δ δ - 1 ( 1 - 1 δ k ) ] m ¯ δ 2 k ( κ - 1 δ - 1 ) .
S det ( i ) ( f ) = 2 q I p r δ 2 k κ - 1 δ - 1 = 2 q I a G κ - 1 δ - 1 .
P e q , λ [ λ , f , 1 , A ] = h ν s [ 2 q I a ( κ - 1 ) / ( δ - 1 ) ] ½ q η G ½ = h ν s [ ( 2 q I p r ) ½ / q η ] [ ( κ - 1 ) / ( δ - 1 ) ] ½ .
P ¯ = γ ;     var p = ξ 2 .
1 + γ + γ 2 + = 1 / ( 1 - γ ) = G .
S det ( i ) = 2 q I 0 G 2 [ 1 + ξ 2 / ( 1 - γ ) ] .
var n k = m ¯ ( 1 + η B ) γ 2 k + m ¯ ξ 2 γ k ( 1 - γ k ) / γ ( 1 - γ ) .
covar ( n k , n k ) = γ ( k - k ) var n k , k > k .
var N θ = k = 0 var n k + 2 k > k covar ( n k , n k ) = k = 0 [ 1 + 2 ( γ + γ 2 + γ 3 + ) ] var n k .
var N θ = m ¯ G 2 ( 1 + η B ) + m ¯ G 3 ξ 2 .
S det ( i ) = 2 q I p r G 2 [ 1 + η B + ξ 2 G ] .
S det ( i ) 2 q I p r G 3 ξ 2 = 2 q I aval G 2 ξ 2 .
D λ * = 1 h ν s { η 2 ( ν s ) q 2 J aval [ ( 1 + η B ) / G + ξ 2 ] } ½ ,
I = I J - I 0 ( e q V / k T - 1 ) = 0 ,
V = ( k T / q ) log ( 1 + I J / I 0 ) .
v ( ω ) = k T q i J ( ω ) I 0 = k T I 0 η j s ( ω ) .
R ( v ) ( ω ) = ( k T / I 0 ) η ( ν s ) .
P e q , λ [ λ , f , 1 , A ] = [ 4 k T R 0 Δ f ] ½ / ( k T η / I 0 ) .
D λ * = [ η ( ν s ) / 2 h ν s ] ( τ h / p 0 L h ) ½ .
S ( i ) ( ω ) = [ I / ( b N 0 + P 0 ) ] 2 [ b 2 S ( N ) ( ω ) + 2 b S ( N P ) ( ω ) + S ( P ) ( ω ) ] ;
i ( ω ) = [ I / ( b N 0 + P 0 ) ] [ b Δ N ( ω ) + Δ P ( ω ) ] ,
Δ N ( ω ) = R ( N ) ( ν , ω ) j ( ν , ω ) Δ P ( ω ) = R ( P ) ( ν , ω ) j ( ν , ω ) } .
R ( i ) ( ω ) = [ I / ( b N 0 + P 0 ) ] [ b R ( N ) ( ω ) + R ( P ) ( ω ) ] .
P e q , λ [ λ , f , 1 , A ] = { b 2 S ( N ) + 2 b S ( N P ) + S ( P ) b 2 ( R ( N ) ) 2 + 2 b R ( N ) R ( P ) + ( R ( P ) ) 2 } ½ .
P e q , λ [ λ , f , 1 , A ] = [ S ( N ) ] ½ / R ( N ) or [ S ( P ) ] ½ / R ( P ) .
S ( P ) ( f ) = S ( N ) ( f ) 4 n 0 p 0 A d n 0 + p 0 τ S R 1 + ω 2 τ S R 2 + 4 n 0 p 0 A d n 0 + p 0 τ 2 τ p 0 ( n 0 + n 1 ) τ S R τ n 0 ( p 0 + p 1 ) τ 2 1 + ω 2 τ 2 2 ,
τ S R = τ n 0 ( p 0 + p 1 ) + τ p 0 ( n 0 + n 1 ) n 0 + p 0 ,
τ 2 = τ n 0 τ p 0 N i / τ S R ( n 0 + p 0 ) ,
R ( P ) ( f ) = R ( N ) ( f ) = η τ S R / ( 1 + ω 2 τ S R 2 ) ½ .
D λ * = η ( ν s ) 2 h ν s [ n 0 + p 0 n 0 p 0 τ S R d ] ½ .
D λ = η ( ν s ) 2 h ν s [ n 0 + p 0 n 0 p 0 τ * d ] ½ .
F = τ * / τ .
S ( P ) ( f ) = S ( N ) ( f ) = 4 n 0 p 0 A d n 0 + p 0 × i j F i j 2 ( 1 / τ + D ξ 1 2 / B 2 + D η j 2 / C 2 ) ω 2 + ( 1 / τ + D ξ i 2 / B 2 + D η j 2 / C 2 ) 2 ,
F i j = 4 ( ξ i η j ) ½ sin ξ i sin η j ( 2 ξ i + sin 2 ξ i ) ½ ( 2 η j + sin 2 η j ) ½ ,
ξ tan ξ = s B / D , η tan η = s C / D ,
S ( P ) ( f ) = S ( N ) ( f ) = 4 n 0 p 0 A d n 0 + p 0 × Re τ 1 + j ω τ { 1 - [ ( τ s / τ ) ( 1 + j ω τ ) + γ C cosh γ C ] - 1 } ,
γ C = [ τ d / τ ( 1 + j ω τ ) ] ½ ,             τ s = C / s ,
R ( P ) = R ( N ) = η s { } τ / ( 1 + j ω τ ) ,
1 / τ = 1 / τ + 1 / ( τ s + τ d / 3 ) ,
τ 1 ( N t - n t ) / ( C n 1 ( p 0 + p 1 + n t ) ,
τ 2 [ B ( N t - n t ) ] - 1 ,
S ( P ) 4 p 0 τ 1 V 1 + ω 2 τ 1 2 n t p 0 + p 1 + n t + 4 n 0 τ 2 V 1 + ω 2 τ 2 2 [ C p 0 B ( N t - n t ) ] 2 ,
S ( N P ) 4 n 0 τ 1 V 1 + ω 2 τ 1 2 n 0 p 0 + p 1 + n t - 4 n 0 τ 2 V 1 + ω 2 τ 2 2 C p 0 B ( N t - n t ) ,
S ( N ) 4 n 0 τ 1 V 1 + ω 2 τ 1 2 n 0 2 ( p 0 + p 1 + n t ) p 0 + 4 n 0 τ 2 V 1 + ω 2 τ 2 2 .
S ( i ) 4 I 2 τ 1 p 0 ( 1 + ω 2 τ 1 2 ) V n t p 0 + p 1 + n t + 4 b 2 I 2 n 0 τ 2 p 0 2 V ( 1 + ω 2 τ 2 2 ) .
R ( i ) ( ν s , f ) η ( ν s ) I V p 0 1 ( 1 + ω 2 τ 1 2 ) 1 / 2 + b τ 2 ( 1 + ω 2 τ 2 2 ) ½ .
D λ * [ λ , ω τ 2 1 ] = η ( ν s ) 2 h ν s ( τ 1 p 0 d ) ½ ( p 0 + p 1 + n t n t ) ½ .
S ( P ) ( f ) = K 1 V / ( 1 + ω 2 τ 1 2 ) + K 2 V / ( 1 + ω 2 τ 2 2 )
K 1 = 4 τ 1 N 0 - [ δ 2 ( 2 p 0 + p 2 ) - δ 1 p 0 δ 2 ( N 0 - + p 0 + p 2 ) - δ 1 p 0 ] ,
K 2 = 4 τ 2 p 0 [ N 0 - / ( N 0 - + p 0 + p 2 ) ] ,
1 / τ 1 = δ 1 p 0 , 1 / τ 2 = δ 2 ( N 0 - + p 0 + p 2 ) .
S ( P ) ( f ) = 4 var P τ 2 / ( 1 + ω 2 τ 2 2 )
var P = P 0 ( p 0 + q 0 ) ( N a - p 0 - q 0 ) V p 0 N a + ( p 0 + q 0 ) ( N a - p 0 - q 0 ) = γ p 0 A d ,
D λ * = [ η ( ν s ) / 2 h ν s ] ( τ 2 / γ p 0 d ) ½ .
η i 2 ( 2 J ¯ b ) + 2 η i ( 1 - η i ) J ¯ b = 2 η i J ¯ b .

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