Abstract

Pumping n-type GaAs and InSb with ultrafast THz pulses having intensities higher than 150MWcm2 shows strong free-carrier absorption saturation at temperatures of 300K and 200K, respectively. If the energy imparted to the carriers exceeds the bandgap, impact ionization processes can occur. The dynamics of carrier cooling in GaAs and impact ionization in InSb were monitored using THz-pump/THz probe spectroscopy, which provides both sub-bandgap excitation and probing, eliminating any direct optical electron-hole generation that complicates the evaluation of results in optical pump/THz probe experiments.

© 2009 Optical Society of America

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  1. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductors Nanostructures, 2nd ed. (Springer, 1999).
  2. M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41, 12140-12149 (1990).
    [CrossRef]
  3. S. E. Ralph, Y. Chen, J. Woodall, and D. McInturff, “Subpicosecond photoconductivity of In0.53Ga0.47As: Intervalley scattering rates observed via THz spectroscopy,” Phys. Rev. B 54, 5568-5573 (1996).
    [CrossRef]
  4. M. C. Nuss, D. H. Auston, and F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355-2358 (1987).
    [CrossRef] [PubMed]
  5. A. Mayer and F. Keilmann, “Far-infrared nonlinear optics. II. χ(3) contributions from the dynamics of free carriers in semiconductors,” Phys. Rev. B 33, 6962-6968 (1986).
    [CrossRef]
  6. J. Hebling, G. Almasi, I. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10, 1161-1166 (2002).
    [PubMed]
  7. T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
    [CrossRef]
  8. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
    [CrossRef]
  9. M. C. Hoffmann, K.-L. Yeh, J. J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15, 11706-11713 (2007).
    [CrossRef] [PubMed]
  10. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523-3526 (1995).
    [CrossRef]
  11. D. Turchinovich and J. I. Dijkhuis, “Performance of combined <100>-<110> ZnTe crystals in an amplified THz time-domain spectrometer,” Opt. Commun. 270, 96-99 (2007).
    [CrossRef]
  12. P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
    [CrossRef]
  13. H. Shichijo and K. Hess, “Band-structure-dependent transport and impact ionization in GaAs,” Phys. Rev. B 23, 4197-4207 (1981).
    [CrossRef]
  14. C. J. Stanton and D. W. Bailey, “Rate equations for the study of femtosecond intervalley scattering in compound semiconductors,” Phys. Rev. B 45, 8369-8377 (1992).
    [CrossRef]
  15. T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.
  16. C. L. Littler and D. G. Seller, “Temperature dependence of the energy gap of InSb using nonlinear optical techniques,” Appl. Phys. Lett. 46, 986-988 (1985).
    [CrossRef]
  17. D. G. Avery, D. W. Goodwin, and M. A. E. Rennie, “New infra-red detectors using indium antimonide,” J. Sci. Instrum. 34, 394-395 (1957).
    [CrossRef]
  18. C. L. Dick and B. Ancker-Johnson, “Nonequilibrium carrier phenomena in n-type InSb,” Phys. Rev. B 5, 526-544 (1972).
    [CrossRef]
  19. H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
    [CrossRef]
  20. X. M. Weng and X. L. Lei, “Hot-electron high-frequency mobility in wide-and narrow-gap semiconductors,” Phys. Status Solidi B 187, 579-588 (1995).
    [CrossRef]
  21. J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Nonlinear optical effects in germanium in the THz range: THz-pump THz-probe measurement of carrier dynamics,” in Ultrafast Phenomena XVI (Springer, 2008).
  22. R. Asauskas, Z. Dobrovolskis, and A. Krotkus, “Maximum drift velocity of electrons in indium antimonide at 77 K,” Sov. Phys. Semicond. 14, 1377-1380 (1980).
  23. M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
    [CrossRef]
  24. S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).
  25. E. M. Conwell, High Field Transport in Semiconductors (Academic, 1967).
  26. D. K. Ferry, “Decay of polar-optical phonons in semiconductors,” Phys. Rev. B 9, 4277-4280 (1974).
    [CrossRef]
  27. E. S. Koteles, W. R. Datars, and G. Dolling, “Far-infrared phonon absorption in InSb,” Phys. Rev. B 9, 572-582 (1974).
    [CrossRef]
  28. R. Brazis and R. Raguotis, “Electron and phonon dynamics in indium antimonide crystals,” Opt. Quantum Electron. 40, 249-252 (2008).
    [CrossRef]

2009 (1)

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
[CrossRef]

2008 (2)

R. Brazis and R. Raguotis, “Electron and phonon dynamics in indium antimonide crystals,” Opt. Quantum Electron. 40, 249-252 (2008).
[CrossRef]

H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[CrossRef]

2007 (4)

D. Turchinovich and J. I. Dijkhuis, “Performance of combined <100>-<110> ZnTe crystals in an amplified THz time-domain spectrometer,” Opt. Commun. 270, 96-99 (2007).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

M. C. Hoffmann, K.-L. Yeh, J. J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15, 11706-11713 (2007).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

1996 (1)

S. E. Ralph, Y. Chen, J. Woodall, and D. McInturff, “Subpicosecond photoconductivity of In0.53Ga0.47As: Intervalley scattering rates observed via THz spectroscopy,” Phys. Rev. B 54, 5568-5573 (1996).
[CrossRef]

1995 (2)

X. M. Weng and X. L. Lei, “Hot-electron high-frequency mobility in wide-and narrow-gap semiconductors,” Phys. Status Solidi B 187, 579-588 (1995).
[CrossRef]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523-3526 (1995).
[CrossRef]

1992 (1)

C. J. Stanton and D. W. Bailey, “Rate equations for the study of femtosecond intervalley scattering in compound semiconductors,” Phys. Rev. B 45, 8369-8377 (1992).
[CrossRef]

1990 (1)

M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41, 12140-12149 (1990).
[CrossRef]

1987 (1)

M. C. Nuss, D. H. Auston, and F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355-2358 (1987).
[CrossRef] [PubMed]

1986 (2)

A. Mayer and F. Keilmann, “Far-infrared nonlinear optics. II. χ(3) contributions from the dynamics of free carriers in semiconductors,” Phys. Rev. B 33, 6962-6968 (1986).
[CrossRef]

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

1985 (1)

C. L. Littler and D. G. Seller, “Temperature dependence of the energy gap of InSb using nonlinear optical techniques,” Appl. Phys. Lett. 46, 986-988 (1985).
[CrossRef]

1981 (1)

H. Shichijo and K. Hess, “Band-structure-dependent transport and impact ionization in GaAs,” Phys. Rev. B 23, 4197-4207 (1981).
[CrossRef]

1980 (1)

R. Asauskas, Z. Dobrovolskis, and A. Krotkus, “Maximum drift velocity of electrons in indium antimonide at 77 K,” Sov. Phys. Semicond. 14, 1377-1380 (1980).

1974 (2)

D. K. Ferry, “Decay of polar-optical phonons in semiconductors,” Phys. Rev. B 9, 4277-4280 (1974).
[CrossRef]

E. S. Koteles, W. R. Datars, and G. Dolling, “Far-infrared phonon absorption in InSb,” Phys. Rev. B 9, 572-582 (1974).
[CrossRef]

1972 (1)

C. L. Dick and B. Ancker-Johnson, “Nonequilibrium carrier phenomena in n-type InSb,” Phys. Rev. B 5, 526-544 (1972).
[CrossRef]

1957 (1)

D. G. Avery, D. W. Goodwin, and M. A. E. Rennie, “New infra-red detectors using indium antimonide,” J. Sci. Instrum. 34, 394-395 (1957).
[CrossRef]

Almasi, G.

Ancker-Johnson, B.

C. L. Dick and B. Ancker-Johnson, “Nonequilibrium carrier phenomena in n-type InSb,” Phys. Rev. B 5, 526-544 (1972).
[CrossRef]

Andrews, S. R.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Asauskas, R.

R. Asauskas, Z. Dobrovolskis, and A. Krotkus, “Maximum drift velocity of electrons in indium antimonide at 77 K,” Sov. Phys. Semicond. 14, 1377-1380 (1980).

Ashley, T.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Auston, D. H.

M. C. Nuss, D. H. Auston, and F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355-2358 (1987).
[CrossRef] [PubMed]

Avery, D. G.

D. G. Avery, D. W. Goodwin, and M. A. E. Rennie, “New infra-red detectors using indium antimonide,” J. Sci. Instrum. 34, 394-395 (1957).
[CrossRef]

Bailey, D. W.

C. J. Stanton and D. W. Bailey, “Rate equations for the study of femtosecond intervalley scattering in compound semiconductors,” Phys. Rev. B 45, 8369-8377 (1992).
[CrossRef]

Barnes, A. R.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Brazis, R.

R. Brazis and R. Raguotis, “Electron and phonon dynamics in indium antimonide crystals,” Opt. Quantum Electron. 40, 249-252 (2008).
[CrossRef]

Buckle, L.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Capasso, F.

M. C. Nuss, D. H. Auston, and F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355-2358 (1987).
[CrossRef] [PubMed]

Chau, R.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Chen, Y.

S. E. Ralph, Y. Chen, J. Woodall, and D. McInturff, “Subpicosecond photoconductivity of In0.53Ga0.47As: Intervalley scattering rates observed via THz spectroscopy,” Phys. Rev. B 54, 5568-5573 (1996).
[CrossRef]

Cluff, J. A.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Conwell, E. M.

E. M. Conwell, High Field Transport in Semiconductors (Academic, 1967).

Datars, W. R.

E. S. Koteles, W. R. Datars, and G. Dolling, “Far-infrared phonon absorption in InSb,” Phys. Rev. B 9, 572-582 (1974).
[CrossRef]

Datta, S.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Dean, A. B.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Dick, C. L.

C. L. Dick and B. Ancker-Johnson, “Nonequilibrium carrier phenomena in n-type InSb,” Phys. Rev. B 5, 526-544 (1972).
[CrossRef]

Dijkhuis, J. I.

D. Turchinovich and J. I. Dijkhuis, “Performance of combined <100>-<110> ZnTe crystals in an amplified THz time-domain spectrometer,” Opt. Commun. 270, 96-99 (2007).
[CrossRef]

Dmitriev, A. P.

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

Dobrovolskis, Z.

R. Asauskas, Z. Dobrovolskis, and A. Krotkus, “Maximum drift velocity of electrons in indium antimonide at 77 K,” Sov. Phys. Semicond. 14, 1377-1380 (1980).

Dolling, G.

E. S. Koteles, W. R. Datars, and G. Dolling, “Far-infrared phonon absorption in InSb,” Phys. Rev. B 9, 572-582 (1974).
[CrossRef]

Emel'yanov, S. A.

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

Emery, M. T.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Fearn, M.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Ferry, D. K.

D. K. Ferry, “Decay of polar-optical phonons in semiconductors,” Phys. Rev. B 9, 4277-4280 (1974).
[CrossRef]

Feurer, T.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Ganichev, S. D.

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

Goodwin, D. W.

D. G. Avery, D. W. Goodwin, and M. A. E. Rennie, “New infra-red detectors using indium antimonide,” J. Sci. Instrum. 34, 394-395 (1957).
[CrossRef]

Grischkowsky, D.

M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41, 12140-12149 (1990).
[CrossRef]

Hayes, D. G.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Hebling, J.

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
[CrossRef]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

J. Hebling, G. Almasi, I. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10, 1161-1166 (2002).
[PubMed]

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Nonlinear optical effects in germanium in the THz range: THz-pump THz-probe measurement of carrier dynamics,” in Ultrafast Phenomena XVI (Springer, 2008).

Hebling, J. J.

Hess, K.

H. Shichijo and K. Hess, “Band-structure-dependent transport and impact ionization in GaAs,” Phys. Rev. B 23, 4197-4207 (1981).
[CrossRef]

Hilton, K. P.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Hoffmann, M. C.

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
[CrossRef]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

M. C. Hoffmann, K.-L. Yeh, J. J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15, 11706-11713 (2007).
[CrossRef] [PubMed]

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Nonlinear optical effects in germanium in the THz range: THz-pump THz-probe measurement of carrier dynamics,” in Ultrafast Phenomena XVI (Springer, 2008).

Huggard, P. G.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Hwang, H. Y.

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
[CrossRef]

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Nonlinear optical effects in germanium in the THz range: THz-pump THz-probe measurement of carrier dynamics,” in Ultrafast Phenomena XVI (Springer, 2008).

Jefferies, R.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Keiding, S. R.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Keilmann, F.

A. Mayer and F. Keilmann, “Far-infrared nonlinear optics. II. χ(3) contributions from the dynamics of free carriers in semiconductors,” Phys. Rev. B 33, 6962-6968 (1986).
[CrossRef]

Koteles, E. S.

E. S. Koteles, W. R. Datars, and G. Dolling, “Far-infrared phonon absorption in InSb,” Phys. Rev. B 9, 572-582 (1974).
[CrossRef]

Kozma, I.

Krotkus, A.

R. Asauskas, Z. Dobrovolskis, and A. Krotkus, “Maximum drift velocity of electrons in indium antimonide at 77 K,” Sov. Phys. Semicond. 14, 1377-1380 (1980).

Kuhl, J.

Lei, X. L.

X. M. Weng and X. L. Lei, “Hot-electron high-frequency mobility in wide-and narrow-gap semiconductors,” Phys. Status Solidi B 187, 579-588 (1995).
[CrossRef]

Lindenberg, A. M.

H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[CrossRef]

Linfield, E. H.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Littler, C. L.

C. L. Littler and D. G. Seller, “Temperature dependence of the energy gap of InSb using nonlinear optical techniques,” Appl. Phys. Lett. 46, 986-988 (1985).
[CrossRef]

Martin, T.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Mayer, A.

A. Mayer and F. Keilmann, “Far-infrared nonlinear optics. II. χ(3) contributions from the dynamics of free carriers in semiconductors,” Phys. Rev. B 33, 6962-6968 (1986).
[CrossRef]

McInturff, D.

S. E. Ralph, Y. Chen, J. Woodall, and D. McInturff, “Subpicosecond photoconductivity of In0.53Ga0.47As: Intervalley scattering rates observed via THz spectroscopy,” Phys. Rev. B 54, 5568-5573 (1996).
[CrossRef]

Moore, G. P.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Nash, K. J.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Nelson, K. A.

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
[CrossRef]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

M. C. Hoffmann, K.-L. Yeh, J. J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15, 11706-11713 (2007).
[CrossRef] [PubMed]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Nonlinear optical effects in germanium in the THz range: THz-pump THz-probe measurement of carrier dynamics,” in Ultrafast Phenomena XVI (Springer, 2008).

Nuss, M. C.

M. C. Nuss, D. H. Auston, and F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355-2358 (1987).
[CrossRef] [PubMed]

Phillips, T. J.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Raguotis, R.

R. Brazis and R. Raguotis, “Electron and phonon dynamics in indium antimonide crystals,” Opt. Quantum Electron. 40, 249-252 (2008).
[CrossRef]

Ralph, S. E.

S. E. Ralph, Y. Chen, J. Woodall, and D. McInturff, “Subpicosecond photoconductivity of In0.53Ga0.47As: Intervalley scattering rates observed via THz spectroscopy,” Phys. Rev. B 54, 5568-5573 (1996).
[CrossRef]

Rennie, M. A. E.

D. G. Avery, D. W. Goodwin, and M. A. E. Rennie, “New infra-red detectors using indium antimonide,” J. Sci. Instrum. 34, 394-395 (1957).
[CrossRef]

Ritchie, D. A.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Seller, D. G.

C. L. Littler and D. G. Seller, “Temperature dependence of the energy gap of InSb using nonlinear optical techniques,” Appl. Phys. Lett. 46, 986-988 (1985).
[CrossRef]

Shah, J.

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductors Nanostructures, 2nd ed. (Springer, 1999).

Shaw, C. J.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

Shichijo, H.

H. Shichijo and K. Hess, “Band-structure-dependent transport and impact ionization in GaAs,” Phys. Rev. B 23, 4197-4207 (1981).
[CrossRef]

Stanton, C. J.

C. J. Stanton and D. W. Bailey, “Rate equations for the study of femtosecond intervalley scattering in compound semiconductors,” Phys. Rev. B 45, 8369-8377 (1992).
[CrossRef]

Statz, E. R.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Stoyanov, N. S.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Tang, W. A.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Terent'ev, Ya. V.

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

Turchinovich, D.

D. Turchinovich and J. I. Dijkhuis, “Performance of combined <100>-<110> ZnTe crystals in an amplified THz time-domain spectrometer,” Opt. Commun. 270, 96-99 (2007).
[CrossRef]

van Exter, M.

M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41, 12140-12149 (1990).
[CrossRef]

Vaughan, J. C.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Ward, D. W.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Wen, H.

H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[CrossRef]

Weng, X. M.

X. M. Weng and X. L. Lei, “Hot-electron high-frequency mobility in wide-and narrow-gap semiconductors,” Phys. Status Solidi B 187, 579-588 (1995).
[CrossRef]

Wiczer, M.

H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[CrossRef]

Wilding, P. J.

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

Woodall, J.

S. E. Ralph, Y. Chen, J. Woodall, and D. McInturff, “Subpicosecond photoconductivity of In0.53Ga0.47As: Intervalley scattering rates observed via THz spectroscopy,” Phys. Rev. B 54, 5568-5573 (1996).
[CrossRef]

Wu, Q.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523-3526 (1995).
[CrossRef]

Yaroshetskii, I. D.

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

Yassievich, I. N.

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

Yeh, K. L.

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
[CrossRef]

Yeh, K.-L.

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

M. C. Hoffmann, K.-L. Yeh, J. J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15, 11706-11713 (2007).
[CrossRef] [PubMed]

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Nonlinear optical effects in germanium in the THz range: THz-pump THz-probe measurement of carrier dynamics,” in Ultrafast Phenomena XVI (Springer, 2008).

Zhang, X.-C.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523-3526 (1995).
[CrossRef]

Annu. Rev. Mater. Res. (1)

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz polaritonics,” Annu. Rev. Mater. Res. 37, 317-350 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[CrossRef]

C. L. Littler and D. G. Seller, “Temperature dependence of the energy gap of InSb using nonlinear optical techniques,” Appl. Phys. Lett. 46, 986-988 (1985).
[CrossRef]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523-3526 (1995).
[CrossRef]

J. Appl. Phys. (1)

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382-2385 (2000).
[CrossRef]

J. Sci. Instrum. (1)

D. G. Avery, D. W. Goodwin, and M. A. E. Rennie, “New infra-red detectors using indium antimonide,” J. Sci. Instrum. 34, 394-395 (1957).
[CrossRef]

Opt. Commun. (1)

D. Turchinovich and J. I. Dijkhuis, “Performance of combined <100>-<110> ZnTe crystals in an amplified THz time-domain spectrometer,” Opt. Commun. 270, 96-99 (2007).
[CrossRef]

Opt. Express (2)

Opt. Quantum Electron. (1)

R. Brazis and R. Raguotis, “Electron and phonon dynamics in indium antimonide crystals,” Opt. Quantum Electron. 40, 249-252 (2008).
[CrossRef]

Phys. Rev. B (10)

D. K. Ferry, “Decay of polar-optical phonons in semiconductors,” Phys. Rev. B 9, 4277-4280 (1974).
[CrossRef]

E. S. Koteles, W. R. Datars, and G. Dolling, “Far-infrared phonon absorption in InSb,” Phys. Rev. B 9, 572-582 (1974).
[CrossRef]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by THz-pump THz-probe spectroscopy,” Phys. Rev. B 79, 161201(R) (2009).
[CrossRef]

C. L. Dick and B. Ancker-Johnson, “Nonequilibrium carrier phenomena in n-type InSb,” Phys. Rev. B 5, 526-544 (1972).
[CrossRef]

H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[CrossRef]

H. Shichijo and K. Hess, “Band-structure-dependent transport and impact ionization in GaAs,” Phys. Rev. B 23, 4197-4207 (1981).
[CrossRef]

C. J. Stanton and D. W. Bailey, “Rate equations for the study of femtosecond intervalley scattering in compound semiconductors,” Phys. Rev. B 45, 8369-8377 (1992).
[CrossRef]

M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41, 12140-12149 (1990).
[CrossRef]

S. E. Ralph, Y. Chen, J. Woodall, and D. McInturff, “Subpicosecond photoconductivity of In0.53Ga0.47As: Intervalley scattering rates observed via THz spectroscopy,” Phys. Rev. B 54, 5568-5573 (1996).
[CrossRef]

A. Mayer and F. Keilmann, “Far-infrared nonlinear optics. II. χ(3) contributions from the dynamics of free carriers in semiconductors,” Phys. Rev. B 33, 6962-6968 (1986).
[CrossRef]

Phys. Rev. Lett. (1)

M. C. Nuss, D. H. Auston, and F. Capasso, “Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide,” Phys. Rev. Lett. 58, 2355-2358 (1987).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

X. M. Weng and X. L. Lei, “Hot-electron high-frequency mobility in wide-and narrow-gap semiconductors,” Phys. Status Solidi B 187, 579-588 (1995).
[CrossRef]

Sov. Phys. JETP (1)

S. D. Ganichev, A. P. Dmitriev, S. A. Emel'yanov, Ya. V. Terent'ev, I. D. Yaroshetskii, and I. N. Yassievich, “Impact ionization in semiconductors under the influence of the electric field of an optical wave,” Sov. Phys. JETP 63, 256-263 (1986).

Sov. Phys. Semicond. (1)

R. Asauskas, Z. Dobrovolskis, and A. Krotkus, “Maximum drift velocity of electrons in indium antimonide at 77 K,” Sov. Phys. Semicond. 14, 1377-1380 (1980).

Other (4)

E. M. Conwell, High Field Transport in Semiconductors (Academic, 1967).

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductors Nanostructures, 2nd ed. (Springer, 1999).

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Nonlinear optical effects in germanium in the THz range: THz-pump THz-probe measurement of carrier dynamics,” in Ultrafast Phenomena XVI (Springer, 2008).

T. Ashley, A. R. Barnes, L. Buckle, S. Datta, A. B. Dean, M. T. Emery, M. Fearn, D. G. Hayes, K. P. Hilton, R. Jefferies, T. Martin, K. J. Nash, T. J. Phillips, W. A. Tang, P. J. Wilding, and R. Chau, “Novel InSb-based quantum well transistors for ultra-high speed, low power logic applications,” in Proceedings of IEEE Seventh International Conference on Solid-State and Integrated Circuits Technology (IEEE, 2004), pp. 2253-2256.

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Figures (7)

Fig. 1
Fig. 1

Schematic illustration of the experimental setup. Collinear THz pulses are generated by tilted pulse front excitation in LiNbO3 (LN) and detected electro-optically. See text for details.

Fig. 2
Fig. 2

(a) Average THz absorption in n-type GaAs for peak fields between 1 and 150 kV cm . The inset shows the simplified band structure of GaAs. (b) Frequency-resolved absorption spectra at selected field strengths.

Fig. 3
Fig. 3

(a) Recovery of the frequency-integrated absorption as a function of THz probe delay after the arrival of a strong THz pump pulse at t = 0 . (b) Frequency dependent absorption coefficient ( cm 1 ) as a function of probe delay times, revealing the relaxation of the excited carriers back to their equilibrium Drude-like behavior 5 ps after the arrival of the pump pulse.

Fig. 4
Fig. 4

Average effective mass, relative to the electron mass, obtained from Drude fits to the absorption spectra for different pump field strengths.

Fig. 5
Fig. 5

Time-resolved THz absorption of doped InSb at 200 K and 80 K after excitation by a 2 μ J THz pulse.

Fig. 6
Fig. 6

(a) time-resolved averaged absorption ( 0.2 1.6 THz ) in undoped InSb at 80 K for various fields (b) intensity dependent average absorption for the doped sample 35 ps after the THz excitation, the solid line is a fit to Eq. (2).

Fig. 7
Fig. 7

Frequency dependent absorption coefficient of doped InSb for probe delays up to 7 ps at a temperature of 200 K .

Equations (2)

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

α eff = 1 d ln ( T 2 0 t max E sam 2 ( t ) d t 0 t max E ref 2 ( t ) d t ) ,
Δ n n 0 = A exp ( E 0 2 E 2 ) ,

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