Abstract

The effect of the non-steady-state photoelectromotive force (PEMF) in photoconductive crystals is considered for excitation frequencies equal to or higher than the inverse photocarrier lifetime. The theoretical analysis, based on a widely used model of an impurity photoconductor with one partially compensated donor level, is performed for the case of an external dc electric field applied to the sample. The average lifetimes of photoelectrons and their mobilities are estimated from experiments on the PEMF in cubic BSO and BTO crystals.

© 1993 Optical Society of America

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  1. M. P. Petrov, S. I. Stepanov, and G. S. Trofimov, “Time-varying EMF in a nonuniformly illuminated photoconductor,” Sov. Tech. Phys. Lett. 12, 379–381 (1986); G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1559–1562 (1986).
  2. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216–2225 (1990).
    [Crossref]
  3. I. A. Sokolov and S. I. Stepanov, “Non-steady-state photovoltage in crystals with long relaxation time of photoconductivity,” Electron. Lett. 26, 1275 (1990).
    [Crossref]
  4. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive crystals,” Phys. Rep. 93, 199–299 (1982).
    [Crossref]
  5. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).
    [Crossref]
  6. R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “Trap-recharging waves and thermocurrent instabilities in compensated semiconductors,” Sov. Phys. Semicond. 7, 102–107 (1973).
  7. S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
    [Crossref]
  8. J. P. Partanen, J. M. C. Jonathan, and R. W. Hellwarth, “Direct determination of electron mobility in photorefractive Bi12SiO20by a holographic time-of-flight technique,” Appl. Phys. Lett. 57, 2404–2406 (1990).
    [Crossref]

1990 (3)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216–2225 (1990).
[Crossref]

I. A. Sokolov and S. I. Stepanov, “Non-steady-state photovoltage in crystals with long relaxation time of photoconductivity,” Electron. Lett. 26, 1275 (1990).
[Crossref]

J. P. Partanen, J. M. C. Jonathan, and R. W. Hellwarth, “Direct determination of electron mobility in photorefractive Bi12SiO20by a holographic time-of-flight technique,” Appl. Phys. Lett. 57, 2404–2406 (1990).
[Crossref]

1986 (1)

M. P. Petrov, S. I. Stepanov, and G. S. Trofimov, “Time-varying EMF in a nonuniformly illuminated photoconductor,” Sov. Tech. Phys. Lett. 12, 379–381 (1986); G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1559–1562 (1986).

1982 (2)

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive crystals,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

1973 (1)

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “Trap-recharging waves and thermocurrent instabilities in compensated semiconductors,” Sov. Phys. Semicond. 7, 102–107 (1973).

Fuks, B. I.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “Trap-recharging waves and thermocurrent instabilities in compensated semiconductors,” Sov. Phys. Semicond. 7, 102–107 (1973).

Günter, P.

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive crystals,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Hellwarth, R. W.

J. P. Partanen, J. M. C. Jonathan, and R. W. Hellwarth, “Direct determination of electron mobility in photorefractive Bi12SiO20by a holographic time-of-flight technique,” Appl. Phys. Lett. 57, 2404–2406 (1990).
[Crossref]

Jonathan, J. M. C.

J. P. Partanen, J. M. C. Jonathan, and R. W. Hellwarth, “Direct determination of electron mobility in photorefractive Bi12SiO20by a holographic time-of-flight technique,” Appl. Phys. Lett. 57, 2404–2406 (1990).
[Crossref]

Kazarinov, R. F.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “Trap-recharging waves and thermocurrent instabilities in compensated semiconductors,” Sov. Phys. Semicond. 7, 102–107 (1973).

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).
[Crossref]

Kulikov, V. V.

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

Partanen, J. P.

J. P. Partanen, J. M. C. Jonathan, and R. W. Hellwarth, “Direct determination of electron mobility in photorefractive Bi12SiO20by a holographic time-of-flight technique,” Appl. Phys. Lett. 57, 2404–2406 (1990).
[Crossref]

Petrov, M. P.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216–2225 (1990).
[Crossref]

M. P. Petrov, S. I. Stepanov, and G. S. Trofimov, “Time-varying EMF in a nonuniformly illuminated photoconductor,” Sov. Tech. Phys. Lett. 12, 379–381 (1986); G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1559–1562 (1986).

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).
[Crossref]

Sokolov, I. A.

I. A. Sokolov and S. I. Stepanov, “Non-steady-state photovoltage in crystals with long relaxation time of photoconductivity,” Electron. Lett. 26, 1275 (1990).
[Crossref]

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216–2225 (1990).
[Crossref]

Stepanov, S. I.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216–2225 (1990).
[Crossref]

I. A. Sokolov and S. I. Stepanov, “Non-steady-state photovoltage in crystals with long relaxation time of photoconductivity,” Electron. Lett. 26, 1275 (1990).
[Crossref]

M. P. Petrov, S. I. Stepanov, and G. S. Trofimov, “Time-varying EMF in a nonuniformly illuminated photoconductor,” Sov. Tech. Phys. Lett. 12, 379–381 (1986); G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1559–1562 (1986).

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).
[Crossref]

Suris, R. A.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “Trap-recharging waves and thermocurrent instabilities in compensated semiconductors,” Sov. Phys. Semicond. 7, 102–107 (1973).

Trofimov, G. S.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216–2225 (1990).
[Crossref]

M. P. Petrov, S. I. Stepanov, and G. S. Trofimov, “Time-varying EMF in a nonuniformly illuminated photoconductor,” Sov. Tech. Phys. Lett. 12, 379–381 (1986); G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1559–1562 (1986).

Appl. Phys. Lett. (1)

J. P. Partanen, J. M. C. Jonathan, and R. W. Hellwarth, “Direct determination of electron mobility in photorefractive Bi12SiO20by a holographic time-of-flight technique,” Appl. Phys. Lett. 57, 2404–2406 (1990).
[Crossref]

Electron. Lett. (1)

I. A. Sokolov and S. I. Stepanov, “Non-steady-state photovoltage in crystals with long relaxation time of photoconductivity,” Electron. Lett. 26, 1275 (1990).
[Crossref]

J. Appl. Phys. (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216–2225 (1990).
[Crossref]

Opt. Commun. (1)

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

Phys. Rep. (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive crystals,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Sov. Phys. Semicond. (1)

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “Trap-recharging waves and thermocurrent instabilities in compensated semiconductors,” Sov. Phys. Semicond. 7, 102–107 (1973).

Sov. Tech. Phys. Lett. (1)

M. P. Petrov, S. I. Stepanov, and G. S. Trofimov, “Time-varying EMF in a nonuniformly illuminated photoconductor,” Sov. Tech. Phys. Lett. 12, 379–381 (1986); G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1559–1562 (1986).

Other (1)

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Experimental arrangement for observation of the non-steady-state PEMF.

Fig. 2
Fig. 2

Theoretical curves Jω(ω) calculated in accordance with Eq. (15) for τ = 19 μs and KLD ≪ 1. 1, τM = τ/4; 2, τM = τ; 3, τM = 4τ. The curves were calculated for a fixed σ0τM product, which is typical for standard experimental conditions, for which τM can be changed only by a change in the average light intensity.

Fig. 3
Fig. 3

a, Frequency transfer function of the PEMF in BTO crystal, λ = 633 nm, I1 ≃ 6 mW/mm2, I2 ≃ 3 mW/mm2, K ≃ 370 mm−1, Δ ≃ 0.3 rad, ω0 ≃ 4 kHz. b, Frequency transfer function of the PEMF in BSO crystal. λ = 514 nm, I3 ≃ 0.3 mW/mm2, Δ ≃ 0.3 rad, ω0 ≃ 1.5 kHz.

Fig. 4
Fig. 4

a, Spatial frequency dependence of the PEMF in BTO crystal. λ = 633 nm, I1 ≃ 6 mW/mm2, Δ ≃ 0.3 rad. b, Spatial frequency dependence of the PEMF in BSO crystal. λ = 514 nm, I2 ≃ 0.3 mW/mm2, Δ ≃ 0.3 rad.

Fig. 5
Fig. 5

Spatial frequency dependence of the second cutoff frequency ω0 in BSO. λ ≃ 458 nm, I ≃ 0.5 mW/mm2, m ≃ 0.3, Δ ≃ 0.3 rad.

Fig. 6
Fig. 6

a, Frequency transfer function Jω(ω) of the PEMF obtained in BSO for various amplitudes of the external field E0: 1–4, 2–8, 3–10, and 4–12 kV/cm. λ ≃ 458 nm, Λ ≃ 90 μm, I ≃ 0.5 nW/mm2, m ≃ 0.3, Δ ≃ 0.3 rad. b, Theoretical dependences Jω(ω) calculated for τ ≃ 85 μs and μ ≃ 0.016 cm2/Vs for the same amplitudes of the external field E0: 1–4, 2–8, 3–10, and 4–12 kV/cm; Λ = 90 μm.

Fig. 7
Fig. 7

Experimental dependence of the second resonance frequency ωr as a function of the applied dc voltage E0. BSO; λ ≃ 458 nm, Λ ≃ 90 μm, I ≃ 0.5 mW/mm2, m ≃ 0.3, Δ ≃ 0.3 rad.

Equations (21)

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τ sc = τ M ( 1 + K 2 L D 2 ) .
I ( x , t ) = I 0 { 1 + m cos [ K x + Δ cos ( ω t ) ] } .
n ( x , t ) / t = g ( x , t ) n ( x , t ) / τ ( j ( x , t ) / x ) / e .
j ( x , t ) = e μ n ( x , t ) E sc ( x , t ) + e D [ n ( x , t ) / x ]
( 0 E sc ) / x = ρ ,
ρ / t = j / x .
0 2 E sc / x t = j / x .
j ( t ) = L 1 0 L e μ n ( x , t ) E sc ( x , t ) d x .
n ( x , t ) = n 0 + n + 0 exp ( i K x ) + n 0 exp ( i K x ) + n + + exp [ i ( K x + ω t ) ] + n + exp [ i ( K x + ω t ) ] + n + exp [ i ( K x ω t ) ] + n exp [ i ( K x + ω t ) ] ,
E sc ( x , t ) = E 0 + E sc + 0 exp ( i K x ) + E sc 0 exp ( i K x ) + E sc + + exp [ i ( K x + ω t ) ] + E sc + exp [ i ( K x + ω t ) ] + E sc + exp [ i ( K x ω t ) ] + E sc exp [ i ( K x + ω t ) ] .
n ± + = g ± + τ ( 1 + i ω τ M ) / { 1 ω 2 τ τ M + i ω [ τ + τ M ( 1 + K 2 L D 2 i K L 0 ) ] } , E sc ± + = g ± + τ ( E 0 + i E D ) / { 1 ω 2 τ τ M + i ω [ τ + τ M ( 1 + K 2 L D 2 i K L 0 ) ] } .
j ω ( E sc + + n 0 + E sc + 0 n + + E sc + n + 0 + E sc 0 n + + ) .
j ω = m 2 Δ σ 0 4 { 2 i E 0 ω τ M ( E 0 + i E D ) 1 ω 2 τ τ M + i ω [ τ + τ M ( 1 + K 2 L D 2 + i K L 0 ) ] 2 i E 0 ω τ M ( E 0 i E D ) 1 ω 2 τ τ M + i ω [ τ + τ M ( 1 + K 2 L D 2 i K L 0 ) ] } .
j ω = ( m 2 Δ σ 0 / 4 ) [ 2 i E 0 ω τ M ( E 0 + i E D ) 1 + i ω τ M ( 1 + K 2 L D 2 + i K L 0 ) 2 i E 0 ω τ M ( E 0 i E D ) 1 + i ω τ M ( 1 + K 2 L D 2 i K L 0 ) ] ,
J ω = S ( m 2 Δ σ 0 / 2 ) × i ω τ M E D 1 ω 2 τ τ M + i ω [ τ + τ M ( 1 + K 2 L D 2 ) ] .
ω r 1 / τ M K L 0 , ω r K L 0 / τ + 1 / τ M K L 0 .
J ω r S m 2 Δ σ 0 E 0 K L 0 2 ( 1 + K 2 L D 2 )
Δ ω = 2 ( 1 + K 2 L D 2 ) / τ M ( K L 0 ) 2 = ω r [ 2 ( 1 + K 2 L D 2 ) / K L 0 ] ,
ω r K μ E 0 ,
J ω r S m 2 Δ σ 0 E 0 8 ( 1 + K 2 L D 2 ) ,
Δ ω = 2 ( 1 + K 2 L D 2 ) / τ ,

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