Abstract

A model is developed for junction detectors based on the antisymmetric electromagnetic-structure mode for two high-free-carrier-density regions separated by a slightly conductive barrier. The complex propagation constant is shown to increase as the 3/4 power of the frequency in a range defined by the ratio of the barrier conductivity to dielectric coefficient and by the free-carrier relaxation frequency and as the 1/4 power below this frequency range. This is shown to result in a decrease in the visible frequency heterodyne mixing response proportional to the 3/4 power of the intermediate frequency (2.3 dB per decade) from 100 GHz to a few terahertz. A linear inverse-frequency decrease in internal-junction quantum efficiency results for the same frequency range with a constant internal quantum efficiency below this.

© 1985 Optical Society of America

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References

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  1. H.-U. Daniel, M. Steiner, and H. Walther, “Response of metal-insulator-metal point contact diode to visible laser light,” Appl. Phys. 25, 7–12 (1981).
    [Crossref]
  2. R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
    [Crossref]
  3. H.-U. Daniel, B. Maurer, M. Steiner, and H. Walther, “Schottky diode mixer for visible laser light and microwave harmonics up to 0.43 THz,” Appl. Phys. Lett 41, 313–315 (1982).
    [Crossref]
  4. D. P. Siu and T. K. Gustafson, “Coherent coupling of radiation to metal–barrier–metal structures via surface plasmons,” Appl. Phys. Lett. 31, 71–73 (1977).
    [Crossref]
  5. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
    [Crossref]
  6. J. Tucker, “Quantum limited detection in tunnel junction mixers,” IEEE J. Quantum Electron. QE-15, 1234–1258 (1979).
    [Crossref]
  7. Stephen R. Whiteley, “Stationary state theory of tunneling with applications to stimulated inelastic tunneling through structure mode interaction,” Ph.D. dissertation (University of California, Berkeley, Calif., 1982).
  8. We note that by substituting expressions (8a) and (8b) into Eq. (5), Eq. (7) can be obtained directly.
  9. J. G. Simmons, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 1793–1803 (1963).
    [Crossref]
  10. T. K. Gustafson, “Coherent conversion of the sunlight spectrum,” , June1983.
  11. G. I. Stegeman and J. J. Burke, “Long-range surface plasmons in electrode structures,” Appl. Phys. Lett. 43, 221–223 (1983).
    [Crossref]
  12. B. N. Kurdi and D. G. Hall, “Electromagnetic modes of the asymmetric metal–oxide–metal tunnel junction,” Opt. Commun. 51, 303–307 (1984).
    [Crossref]

1984 (1)

B. N. Kurdi and D. G. Hall, “Electromagnetic modes of the asymmetric metal–oxide–metal tunnel junction,” Opt. Commun. 51, 303–307 (1984).
[Crossref]

1983 (2)

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

G. I. Stegeman and J. J. Burke, “Long-range surface plasmons in electrode structures,” Appl. Phys. Lett. 43, 221–223 (1983).
[Crossref]

1982 (1)

H.-U. Daniel, B. Maurer, M. Steiner, and H. Walther, “Schottky diode mixer for visible laser light and microwave harmonics up to 0.43 THz,” Appl. Phys. Lett 41, 313–315 (1982).
[Crossref]

1981 (1)

H.-U. Daniel, M. Steiner, and H. Walther, “Response of metal-insulator-metal point contact diode to visible laser light,” Appl. Phys. 25, 7–12 (1981).
[Crossref]

1979 (1)

J. Tucker, “Quantum limited detection in tunnel junction mixers,” IEEE J. Quantum Electron. QE-15, 1234–1258 (1979).
[Crossref]

1977 (1)

D. P. Siu and T. K. Gustafson, “Coherent coupling of radiation to metal–barrier–metal structures via surface plasmons,” Appl. Phys. Lett. 31, 71–73 (1977).
[Crossref]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

1963 (1)

J. G. Simmons, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 1793–1803 (1963).
[Crossref]

Bergquist, J. C.

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

Burke, J. J.

G. I. Stegeman and J. J. Burke, “Long-range surface plasmons in electrode structures,” Appl. Phys. Lett. 43, 221–223 (1983).
[Crossref]

Burkins, L.

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

Daniel, H.-U.

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

H.-U. Daniel, B. Maurer, M. Steiner, and H. Walther, “Schottky diode mixer for visible laser light and microwave harmonics up to 0.43 THz,” Appl. Phys. Lett 41, 313–315 (1982).
[Crossref]

H.-U. Daniel, M. Steiner, and H. Walther, “Response of metal-insulator-metal point contact diode to visible laser light,” Appl. Phys. 25, 7–12 (1981).
[Crossref]

Drullinger, R. E.

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Evenson, K. M.

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

Gustafson, T. K.

D. P. Siu and T. K. Gustafson, “Coherent coupling of radiation to metal–barrier–metal structures via surface plasmons,” Appl. Phys. Lett. 31, 71–73 (1977).
[Crossref]

T. K. Gustafson, “Coherent conversion of the sunlight spectrum,” , June1983.

Hall, D. G.

B. N. Kurdi and D. G. Hall, “Electromagnetic modes of the asymmetric metal–oxide–metal tunnel junction,” Opt. Commun. 51, 303–307 (1984).
[Crossref]

Jennings, D. A.

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

Kurdi, B. N.

B. N. Kurdi and D. G. Hall, “Electromagnetic modes of the asymmetric metal–oxide–metal tunnel junction,” Opt. Commun. 51, 303–307 (1984).
[Crossref]

Maurer, B.

H.-U. Daniel, B. Maurer, M. Steiner, and H. Walther, “Schottky diode mixer for visible laser light and microwave harmonics up to 0.43 THz,” Appl. Phys. Lett 41, 313–315 (1982).
[Crossref]

Petersen, F. R.

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

Simmons, J. G.

J. G. Simmons, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 1793–1803 (1963).
[Crossref]

Siu, D. P.

D. P. Siu and T. K. Gustafson, “Coherent coupling of radiation to metal–barrier–metal structures via surface plasmons,” Appl. Phys. Lett. 31, 71–73 (1977).
[Crossref]

Stegeman, G. I.

G. I. Stegeman and J. J. Burke, “Long-range surface plasmons in electrode structures,” Appl. Phys. Lett. 43, 221–223 (1983).
[Crossref]

Steiner, M.

H.-U. Daniel, B. Maurer, M. Steiner, and H. Walther, “Schottky diode mixer for visible laser light and microwave harmonics up to 0.43 THz,” Appl. Phys. Lett 41, 313–315 (1982).
[Crossref]

H.-U. Daniel, M. Steiner, and H. Walther, “Response of metal-insulator-metal point contact diode to visible laser light,” Appl. Phys. 25, 7–12 (1981).
[Crossref]

Tucker, J.

J. Tucker, “Quantum limited detection in tunnel junction mixers,” IEEE J. Quantum Electron. QE-15, 1234–1258 (1979).
[Crossref]

Walther, H.

H.-U. Daniel, B. Maurer, M. Steiner, and H. Walther, “Schottky diode mixer for visible laser light and microwave harmonics up to 0.43 THz,” Appl. Phys. Lett 41, 313–315 (1982).
[Crossref]

H.-U. Daniel, M. Steiner, and H. Walther, “Response of metal-insulator-metal point contact diode to visible laser light,” Appl. Phys. 25, 7–12 (1981).
[Crossref]

Whiteley, Stephen R.

Stephen R. Whiteley, “Stationary state theory of tunneling with applications to stimulated inelastic tunneling through structure mode interaction,” Ph.D. dissertation (University of California, Berkeley, Calif., 1982).

Appl. Phys. (1)

H.-U. Daniel, M. Steiner, and H. Walther, “Response of metal-insulator-metal point contact diode to visible laser light,” Appl. Phys. 25, 7–12 (1981).
[Crossref]

Appl. Phys. Lett (1)

H.-U. Daniel, B. Maurer, M. Steiner, and H. Walther, “Schottky diode mixer for visible laser light and microwave harmonics up to 0.43 THz,” Appl. Phys. Lett 41, 313–315 (1982).
[Crossref]

Appl. Phys. Lett. (3)

D. P. Siu and T. K. Gustafson, “Coherent coupling of radiation to metal–barrier–metal structures via surface plasmons,” Appl. Phys. Lett. 31, 71–73 (1977).
[Crossref]

R. E. Drullinger, K. M. Evenson, D. A. Jennings, F. R. Petersen, J. C. Bergquist, L. Burkins, and H.-U. Daniel, “2.5-THz frequency difference measurements in the visible using metal–insulator–metal diodes,” Appl. Phys. Lett. 42, 137–138 (1983).
[Crossref]

G. I. Stegeman and J. J. Burke, “Long-range surface plasmons in electrode structures,” Appl. Phys. Lett. 43, 221–223 (1983).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Tucker, “Quantum limited detection in tunnel junction mixers,” IEEE J. Quantum Electron. QE-15, 1234–1258 (1979).
[Crossref]

J. Appl. Phys. (1)

J. G. Simmons, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 1793–1803 (1963).
[Crossref]

Opt. Commun. (1)

B. N. Kurdi and D. G. Hall, “Electromagnetic modes of the asymmetric metal–oxide–metal tunnel junction,” Opt. Commun. 51, 303–307 (1984).
[Crossref]

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Other (3)

T. K. Gustafson, “Coherent conversion of the sunlight spectrum,” , June1983.

Stephen R. Whiteley, “Stationary state theory of tunneling with applications to stimulated inelastic tunneling through structure mode interaction,” Ph.D. dissertation (University of California, Berkeley, Calif., 1982).

We note that by substituting expressions (8a) and (8b) into Eq. (5), Eq. (7) can be obtained directly.

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Figures (5)

Fig. 1
Fig. 1

Assumed geometry of junction detector for visible frequency-mixing experiments. ωvis1 and ωvis2 are the visible dye-laser frequencies. The i. f. is ωmm = ωvis1ωvis2.

Fig. 2
Fig. 2

Junction mode dispersion curves and the internal quantum efficiency from Eqs. (6) and (17) with parameters estimated for nickel–nickel oxide–nickel junctions. The parameters are ωp = 1.3 × 1016 rad/sec, τ = 9.2 × 1015 sec, τd = 1 S/m, 2d = 20 Å, = 0, f = 0.

Fig. 3
Fig. 3

The factor R = |1 + ρA exp(−i2)/1 − ρA2 exp(−2iLβ)| for various values of ρA2 as a function of angular frequency, ω: (a) junction length of 500 Å, (b) junction length of 5000 Å, (c) junction length of 10 000 Å. Junction parameters are ωp 1.3 × 1016 rad/sec, τ = 9.2 × 10−15 sec, σd = 1 S/m, 2d=20 Å, = 0, =0. For each set of curves, ρA2 varies from 0.9 to 0.99, the uppermost curve in each case corresponding to ρA2 = 0 99 A typical value of L(b/2)(d2J/dV2)VloVmm/IN, where IN is the shot-noise current that is bias, is unity for a bandwidth of a megahertz. For this case, R is numerically equal to |S/N|.

Fig. 4
Fig. 4

The factor R = |1 + ρA exp(−2iLβ)/1 − ρA2 exp(−2iLβ)| as a function of junction length L with ρA2 = 0.998. The junction parameters are the same as those given in Fig. 2. L = 10 μm shows the highly damped response for L > (β″)−1.

Fig. 5
Fig. 5

Junction quantum efficiency η as a function of the relaxation time τ. One observes that η → 100% in the relaxation region when σd/f ≫ 1/τ.

Equations (22)

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( γ f f ) tanh ( γ f d ) + ( γ e c ) = 0.
σ d = 2 d R d A = 2 d d J d V .
γ f = [ β 2 f f 1 - ω 2 μ 0 f ] 1 / 2 ,
c 0 = 1 - ω p 2 ω 2 ( 1 1 - i ω τ ) - ω p 2 τ ω i = - σ M ω 0 i ,
γ f 2 - γ c f c 1 d .
β ( ω ) = ± e f 1 1 / 2 { e f 1 ± [ f 1 2 - 4 μ 0 ω 2 d 2 c 2 ( c - f 1 ) ] 1 / 2 2 c 2 d 2 + ω 2 μ 0 } 1 / 2 .
β = ( - ω f 1 / d ) 1 / 2 ( - μ 0 / c ) 1 / 4 .
γ f β ( f f 1 ) 1 / 2 .
γ c ( - ω 2 μ c ) 1 / 2 .
β ( ( f - i σ d / ω ) d ω p ) 1 / 2 ( μ 0 0 τ ) 1 / 4 ω 3 / 4 ( 0.92 - 0.38 i ) ,
β ω ( μ 0 0 ) 1 / 4 ( f d ω p ) 1 / 2 [ 1 - i 4 1 ω τ - i 2 ( σ d f ω ) ]
β = ( ω μ 0 σ m ) 1 / 2 ( 1 - i ) / 2 = ( 1 - i ) / δ c .
E x = ( V p 2 d ) exp ( - i β z + i ω t ) ,
V mm = V p exp ( i ω mm t ) [ 1 + ρ A exp ( - i 2 β L ) ] [ 1 - ρ A 2 exp ( - i 2 β L ) ] .
I = ½ d 2 I d V 2 V lo * exp ( - i ω lo t ) V mm = L b 2 d 2 J d V 2 V lo * V p exp ( i ω s t ) [ i β L + ( 1 - ρ A 2 ) / 2 ] .
T t = b 2 ω 0 d z d J d V V p V p * exp ( - 2 β z ) .
P ω Re ( 1 2 V p I p * ) ω = 1 2 ω Re V p 2 z g *
η = b 2 d J d V 1 β Re ( 1 Z g * ) = σ d 2 β ( β ) 2 + ( β ) 2 ( β ω f + σ d β ) .
β 2 = ω μ 0 ( ω f - i σ d ) = ( β ) 2 - ( β ) 2 + 2 i β β ,
P L = Re ( d j ω f β 2 2 β f 1 ) H y 2 .
P = Re ( β d ω f 1 ) H y 2 .
η = 1 + ( 1 4 ω τ + σ d 2 f ω ) 2 ( 1 + f 2 σ d τ ) 1 + σ d ω f ( 1 4 ω τ + σ d 2 f ω ) .

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