Abstract

A photorefractive phase shift can be generated under dc applied fields if the dominant photocarriers have a nonlinear velocity-field dependence with a vanishing differential mobility. Phase shifts as large as π/2 are possible when velocity saturation disables dielectric relaxation while still permitting large drift rates. The inability of the space-charge field to relax leads to a saturated trap density that mimics trap-limited behavior. All direct-gap photorefractive semiconductors have strong velocity saturation from hot-electron transport effects, most widely known for the origin of the Gunn effect. Previous photorefractive trap-limited-field studies may have to be reevaluated in the context of transport nonlinearity.

© 1994 Optical Society of America

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References

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  1. P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
    [CrossRef]
  2. Q. Wang, R. M. Brubaker, D. D. Nolte, J. Opt. Soc. Am. B 9, 1626 (1992).
    [CrossRef]
  3. Q. Wang, R. M. Brubaker, D. D. Nolte, “Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures, ” J. Opt. Soc. Am. B (to be published).
  4. B. K. Ridley, T. B. Watkins, Proc. Phys. Soc. London 78, 293 (1961).
    [CrossRef]
  5. K. Hess, H. Morkoc, H. Schichijo, B. G. Streetman, Appl. Phys. Lett. 55, 1421 (1989).
    [CrossRef]
  6. B. K. Ridley, P. H. Wisbey, Br. J. Phys. 18, 761 (1967).
    [CrossRef]
  7. D. D. Nolte, D. H. Olson, A. M. Glass, J. Appl. Phys. 68, 4111 (1990).
    [CrossRef]
  8. J. B. Gunn, Solid State Commun. 1, 88 (1963).
    [CrossRef]
  9. H. K. Sacks, A. G. Milnes, Int. J. Electron. 28, 565 (1970).
    [CrossRef]

1992 (1)

1990 (1)

D. D. Nolte, D. H. Olson, A. M. Glass, J. Appl. Phys. 68, 4111 (1990).
[CrossRef]

1989 (1)

K. Hess, H. Morkoc, H. Schichijo, B. G. Streetman, Appl. Phys. Lett. 55, 1421 (1989).
[CrossRef]

1970 (1)

H. K. Sacks, A. G. Milnes, Int. J. Electron. 28, 565 (1970).
[CrossRef]

1967 (1)

B. K. Ridley, P. H. Wisbey, Br. J. Phys. 18, 761 (1967).
[CrossRef]

1963 (1)

J. B. Gunn, Solid State Commun. 1, 88 (1963).
[CrossRef]

1961 (1)

B. K. Ridley, T. B. Watkins, Proc. Phys. Soc. London 78, 293 (1961).
[CrossRef]

Brubaker, R. M.

Q. Wang, R. M. Brubaker, D. D. Nolte, J. Opt. Soc. Am. B 9, 1626 (1992).
[CrossRef]

Q. Wang, R. M. Brubaker, D. D. Nolte, “Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures, ” J. Opt. Soc. Am. B (to be published).

Glass, A. M.

D. D. Nolte, D. H. Olson, A. M. Glass, J. Appl. Phys. 68, 4111 (1990).
[CrossRef]

Gunn, J. B.

J. B. Gunn, Solid State Commun. 1, 88 (1963).
[CrossRef]

Günter, P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
[CrossRef]

Hess, K.

K. Hess, H. Morkoc, H. Schichijo, B. G. Streetman, Appl. Phys. Lett. 55, 1421 (1989).
[CrossRef]

Huignard, J.-P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
[CrossRef]

Milnes, A. G.

H. K. Sacks, A. G. Milnes, Int. J. Electron. 28, 565 (1970).
[CrossRef]

Morkoc, H.

K. Hess, H. Morkoc, H. Schichijo, B. G. Streetman, Appl. Phys. Lett. 55, 1421 (1989).
[CrossRef]

Nolte, D. D.

Q. Wang, R. M. Brubaker, D. D. Nolte, J. Opt. Soc. Am. B 9, 1626 (1992).
[CrossRef]

D. D. Nolte, D. H. Olson, A. M. Glass, J. Appl. Phys. 68, 4111 (1990).
[CrossRef]

Q. Wang, R. M. Brubaker, D. D. Nolte, “Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures, ” J. Opt. Soc. Am. B (to be published).

Olson, D. H.

D. D. Nolte, D. H. Olson, A. M. Glass, J. Appl. Phys. 68, 4111 (1990).
[CrossRef]

Ridley, B. K.

B. K. Ridley, P. H. Wisbey, Br. J. Phys. 18, 761 (1967).
[CrossRef]

B. K. Ridley, T. B. Watkins, Proc. Phys. Soc. London 78, 293 (1961).
[CrossRef]

Sacks, H. K.

H. K. Sacks, A. G. Milnes, Int. J. Electron. 28, 565 (1970).
[CrossRef]

Schichijo, H.

K. Hess, H. Morkoc, H. Schichijo, B. G. Streetman, Appl. Phys. Lett. 55, 1421 (1989).
[CrossRef]

Streetman, B. G.

K. Hess, H. Morkoc, H. Schichijo, B. G. Streetman, Appl. Phys. Lett. 55, 1421 (1989).
[CrossRef]

Wang, Q.

Q. Wang, R. M. Brubaker, D. D. Nolte, J. Opt. Soc. Am. B 9, 1626 (1992).
[CrossRef]

Q. Wang, R. M. Brubaker, D. D. Nolte, “Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures, ” J. Opt. Soc. Am. B (to be published).

Watkins, T. B.

B. K. Ridley, T. B. Watkins, Proc. Phys. Soc. London 78, 293 (1961).
[CrossRef]

Wisbey, P. H.

B. K. Ridley, P. H. Wisbey, Br. J. Phys. 18, 761 (1967).
[CrossRef]

Appl. Phys. Lett. (1)

K. Hess, H. Morkoc, H. Schichijo, B. G. Streetman, Appl. Phys. Lett. 55, 1421 (1989).
[CrossRef]

Br. J. Phys. (1)

B. K. Ridley, P. H. Wisbey, Br. J. Phys. 18, 761 (1967).
[CrossRef]

Int. J. Electron. (1)

H. K. Sacks, A. G. Milnes, Int. J. Electron. 28, 565 (1970).
[CrossRef]

J. Appl. Phys. (1)

D. D. Nolte, D. H. Olson, A. M. Glass, J. Appl. Phys. 68, 4111 (1990).
[CrossRef]

J. Opt. Soc. Am. B (1)

Proc. Phys. Soc. London (1)

B. K. Ridley, T. B. Watkins, Proc. Phys. Soc. London 78, 293 (1961).
[CrossRef]

Solid State Commun. (1)

J. B. Gunn, Solid State Commun. 1, 88 (1963).
[CrossRef]

Other (2)

Q. Wang, R. M. Brubaker, D. D. Nolte, “Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures, ” J. Opt. Soc. Am. B (to be published).

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Phase shift of the space-charge field versus the applied field for a fringe spacing of 5 μm, n0/p0 = 100, ND = 5 × 1017 cm−3, and NA = 1.0 × 1016 cm−3. The saturation velocities of the three curves are 1.0 × 107, 2.0 × 107, and 3.0 × 107 cm/s. The phase shift for linear transport is shown for comparison.

Fig. 2
Fig. 2

Amplitude to the space-charge field versus the applied field for conditions identical to Fig. 1.

Fig. 3
Fig. 3

Amplitude of the space-charge field for a fringe spacing of 5 μm, ND = 5 × 1017 cm−3, and NA = 1.0 × 1016 cm−3. The electron-hole density ratios of the three curves are 104, 103, and 102, respectively. The field for linear transport is shown for comparison.

Fig. 4
Fig. 4

Phase shift of the space-charge field versus the fringe spacing for E = 5 kV/cm, ND = 5 × 1017 cm−3, and NA = 1.0 × 1016 cm−3. The field for linear transport is shown for comparison.

Tables (2)

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Table 1 Transport Lengths

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Table 2 Parameters for Space-Charge-Field Calculations

Equations (9)

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j e = e n v ( E ) + k B T ( μ n ) ,
Γ die = e n 0 0 μ nonlin ,
μ nonlin = d v ( E ) d E + i K k B T e E [ d v ( E ) d E - v ( E ) E ] ,
E 1 = - i m { ( i K L E h + K 2 L D h 2 + 1 ) ( - i K L E e + K 2 L D e 2 ) - p 0 τ e n 0 τ h ( i K L E h + K 2 L D h 2 ) ( - i K L E e + K 2 L D e 2 + 1 ) K τ e [ ( i K L E h + K 2 L D h 2 + 1 ) ( μ nonlin + μ - i E + E D E q ) + ( - i L E e K + K 2 L D e 2 + 1 ) p 0 n 0 μ h ] } ,
E 1 = - m 1 + i K L E h ( μ nonlin μ + p 0 μ h μ n 0 ) E q E 0 - i ( 1 + p 0 L μ h E q τ e n 0 ) E q ,
E 1 = - m E 0 + i E D μ nonlin μ E q + i E 0 - E D E q ,
E 1 = i m E q ,
E 0 E q μ nonlin μ + p 0 μ h n 0 μ 1 + p 0 K μ h E q τ e n 0 ,
v ( E ) = v 0 [ 1 - exp ( - μ 1 E v 0 ) ] ,

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