Abstract

We report on the development of a terahertz time-domain technique for measuring the momentum relaxation time of charge carriers in ultrathin semiconductor layers. Making use of the Drude model, our phase sensitive modulation technique directly provides the relaxation time. Time-resolved THz experiments were performed on n-doped GaAs and show precise agreement with data obtained by electrical characterization. The technique is well suited for studying novel materials where parameters such as the charge carriers’ effective mass or the carrier density are not known a priori.

© 2009 OSA

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  1. M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. 56(17), 1694–1696 (1990).
    [CrossRef]
  2. M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41(17), 12140–12149 (1990).
    [CrossRef]
  3. T.-I. Jeon, D. Grischkowsky, A. K. Mukherjee, and R. Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77(16), 2452–2454 (2000).
    [CrossRef]
  4. O. Ostroverkhova, D. G. Cooke, S. Shcherbyna, R. F. Egerton, F. A. Hegmann, and J. E. Anthony, “Bandlike transport in pentacene and functionalized pentacene thin films revealed by subpicosecond transient photoconductivity measurements,” Phys. Rev. B 71(3), 035204 (2005).
    [CrossRef]
  5. P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
    [CrossRef]
  6. X. Ai, M. C. Beard, K. P. Knutsen, S. E. Shaheen, G. Rumbles, and R. J. Ellingson, “Photoinduced charge carrier generation in a poly(3-hexylthiophene) and methanofullerene bulk heterojunction investigated by time-resolved terahertz spectroscopy,” J. Phys. Chem. B 110(50), 25462–25471 (2006).
    [CrossRef] [PubMed]
  7. T.-I. Jeon and D. Grischkowsky, “Observation of a Cole-Davidson type complex conductivity in the limit of very low carrier densities in doped silicon,” Appl. Phys. Lett. 72(18), 2259–2261 (1998).
    [CrossRef]
  8. E. Hendry, M. Koeberg, B. O’Regan, and M. Bonn, “Local field effects on electron transport in nanostructured TiO2 revealed by terahertz spectroscopy,” Nano Lett. 6(4), 755–759 (2006).
    [CrossRef] [PubMed]
  9. N. V. Smith, “Classical generalization of the Drude formula for the optical conductivity,” Phys. Rev. B 64(15), 155106 (2001).
    [CrossRef]
  10. D. W. Davidson and R. H. Cole, “Dielectric relaxation in glycerol, propylene glycol, and n-propanol,” J. Chem. Phys. 19(12), 1484–1490 (1951).
    [CrossRef]
  11. J. C. M. Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Sect. A 203(1), 385–420 (1904).
    [CrossRef]
  12. M. Schall and P. U. Jepsen, “Photoexcited GaAs surfaces studied by transient terahertz time-domain spectroscopy,” Opt. Lett. 25(1), 13–15 (2000).
    [CrossRef]
  13. In fact, the THz response scales with the sample's plasma frequency given by carrier density, effective mass, and background permittivity.
  14. L. Duvillaret, F. Garet, and J.-L. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38(2), 409–415 (1999).
    [CrossRef]
  15. T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18(7), 1562–1570 (2001).
    [CrossRef]
  16. M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
    [CrossRef]
  17. M. Fischer, M. Dressel, B. Gompf, A. K. Tripathi, and J. Pflaum, “Infrared spectroscopy on the charge accumulation layer in rubrene single crystals,” Appl. Phys. Lett. 89(18), 182103 (2006).
    [CrossRef]
  18. M. P. de Haas, R. J. O. M. Hoofman, L. D. A. Siebbeles, and J. M. Warman, “Highly mobile electrons and holes on isolated chains of the semiconducting polymer poly (phenylene vinylene),” Nature 392(6671), 54–56 (1998).
    [CrossRef]
  19. S. J. Allen, D. C. Tsui, and F. DeRosa, “Frequency dependence of the electron conductivity in the silicon inversion layer in the metallic and localized regimes,” Phys. Rev. Lett. 35(20), 1359–1362 (1975).
    [CrossRef]
  20. H. Scher and E. W. Montroll, “Anomalous transit-time dispersion in amorphous solids,” Phys. Rev. B 12(6), 2455–2477 (1975).
    [CrossRef]
  21. M. Pollak, “On dispersive transport by hopping and by trapping,” Philos. Mag. 36(5), 1157–1169 (1977).
    [CrossRef]
  22. P. Drude, “Zur Elektronentheorie der Metalle,” Annalen der Physik 306(3), 566–613 (1900).
    [CrossRef]
  23. N. Ashcroft and D. Mermin, Solid State Physics (Harcourt, 1976).
  24. M. Dressel and G. Grüner, Electrodynamics of Solids - Optical Properties of Electrons in Matter (Cambridge University press, 2002).
  25. S. Sze, Semiconductor Devices (John Wiley & Sons, 1985).
  26. A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86(12), 121114 (2005).
    [CrossRef]
  27. G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
    [CrossRef]
  28. Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
    [CrossRef]
  29. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18(3), 313–317 (2001).
    [CrossRef]
  30. To be more specific, E0y and E1y were measured after passage through the GaAs-wafer and the optical detection system. This does not affect differential quantities.
  31. F. M. Smits, “Measurement of sheet resistivities with the four-point probe,” Bell Syst. Tech. J. 37, 711–718 (1958).

2009 (1)

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[CrossRef]

2008 (1)

G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
[CrossRef]

2007 (1)

P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
[CrossRef]

2006 (3)

X. Ai, M. C. Beard, K. P. Knutsen, S. E. Shaheen, G. Rumbles, and R. J. Ellingson, “Photoinduced charge carrier generation in a poly(3-hexylthiophene) and methanofullerene bulk heterojunction investigated by time-resolved terahertz spectroscopy,” J. Phys. Chem. B 110(50), 25462–25471 (2006).
[CrossRef] [PubMed]

M. Fischer, M. Dressel, B. Gompf, A. K. Tripathi, and J. Pflaum, “Infrared spectroscopy on the charge accumulation layer in rubrene single crystals,” Appl. Phys. Lett. 89(18), 182103 (2006).
[CrossRef]

E. Hendry, M. Koeberg, B. O’Regan, and M. Bonn, “Local field effects on electron transport in nanostructured TiO2 revealed by terahertz spectroscopy,” Nano Lett. 6(4), 755–759 (2006).
[CrossRef] [PubMed]

2005 (2)

O. Ostroverkhova, D. G. Cooke, S. Shcherbyna, R. F. Egerton, F. A. Hegmann, and J. E. Anthony, “Bandlike transport in pentacene and functionalized pentacene thin films revealed by subpicosecond transient photoconductivity measurements,” Phys. Rev. B 71(3), 035204 (2005).
[CrossRef]

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86(12), 121114 (2005).
[CrossRef]

2001 (3)

2000 (2)

T.-I. Jeon, D. Grischkowsky, A. K. Mukherjee, and R. Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77(16), 2452–2454 (2000).
[CrossRef]

M. Schall and P. U. Jepsen, “Photoexcited GaAs surfaces studied by transient terahertz time-domain spectroscopy,” Opt. Lett. 25(1), 13–15 (2000).
[CrossRef]

1999 (1)

1998 (2)

M. P. de Haas, R. J. O. M. Hoofman, L. D. A. Siebbeles, and J. M. Warman, “Highly mobile electrons and holes on isolated chains of the semiconducting polymer poly (phenylene vinylene),” Nature 392(6671), 54–56 (1998).
[CrossRef]

T.-I. Jeon and D. Grischkowsky, “Observation of a Cole-Davidson type complex conductivity in the limit of very low carrier densities in doped silicon,” Appl. Phys. Lett. 72(18), 2259–2261 (1998).
[CrossRef]

1996 (1)

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[CrossRef]

1990 (2)

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. 56(17), 1694–1696 (1990).
[CrossRef]

M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41(17), 12140–12149 (1990).
[CrossRef]

1977 (1)

M. Pollak, “On dispersive transport by hopping and by trapping,” Philos. Mag. 36(5), 1157–1169 (1977).
[CrossRef]

1975 (2)

S. J. Allen, D. C. Tsui, and F. DeRosa, “Frequency dependence of the electron conductivity in the silicon inversion layer in the metallic and localized regimes,” Phys. Rev. Lett. 35(20), 1359–1362 (1975).
[CrossRef]

H. Scher and E. W. Montroll, “Anomalous transit-time dispersion in amorphous solids,” Phys. Rev. B 12(6), 2455–2477 (1975).
[CrossRef]

1958 (1)

F. M. Smits, “Measurement of sheet resistivities with the four-point probe,” Bell Syst. Tech. J. 37, 711–718 (1958).

1951 (1)

D. W. Davidson and R. H. Cole, “Dielectric relaxation in glycerol, propylene glycol, and n-propanol,” J. Chem. Phys. 19(12), 1484–1490 (1951).
[CrossRef]

1904 (1)

J. C. M. Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Sect. A 203(1), 385–420 (1904).
[CrossRef]

1900 (1)

P. Drude, “Zur Elektronentheorie der Metalle,” Annalen der Physik 306(3), 566–613 (1900).
[CrossRef]

Acuna, G.

G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
[CrossRef]

Ai, X.

X. Ai, M. C. Beard, K. P. Knutsen, S. E. Shaheen, G. Rumbles, and R. J. Ellingson, “Photoinduced charge carrier generation in a poly(3-hexylthiophene) and methanofullerene bulk heterojunction investigated by time-resolved terahertz spectroscopy,” J. Phys. Chem. B 110(50), 25462–25471 (2006).
[CrossRef] [PubMed]

Allen, S. J.

S. J. Allen, D. C. Tsui, and F. DeRosa, “Frequency dependence of the electron conductivity in the silicon inversion layer in the metallic and localized regimes,” Phys. Rev. Lett. 35(20), 1359–1362 (1975).
[CrossRef]

Anthony, J. E.

O. Ostroverkhova, D. G. Cooke, S. Shcherbyna, R. F. Egerton, F. A. Hegmann, and J. E. Anthony, “Bandlike transport in pentacene and functionalized pentacene thin films revealed by subpicosecond transient photoconductivity measurements,” Phys. Rev. B 71(3), 035204 (2005).
[CrossRef]

Bakker, H. J.

Baraniuk, R. G.

Beard, M. C.

X. Ai, M. C. Beard, K. P. Knutsen, S. E. Shaheen, G. Rumbles, and R. J. Ellingson, “Photoinduced charge carrier generation in a poly(3-hexylthiophene) and methanofullerene bulk heterojunction investigated by time-resolved terahertz spectroscopy,” J. Phys. Chem. B 110(50), 25462–25471 (2006).
[CrossRef] [PubMed]

Bonn, M.

E. Hendry, M. Koeberg, B. O’Regan, and M. Bonn, “Local field effects on electron transport in nanostructured TiO2 revealed by terahertz spectroscopy,” Nano Lett. 6(4), 755–759 (2006).
[CrossRef] [PubMed]

Buersgens, F.

G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
[CrossRef]

Cole, R. H.

D. W. Davidson and R. H. Cole, “Dielectric relaxation in glycerol, propylene glycol, and n-propanol,” J. Chem. Phys. 19(12), 1484–1490 (1951).
[CrossRef]

Cooke, D. G.

O. Ostroverkhova, D. G. Cooke, S. Shcherbyna, R. F. Egerton, F. A. Hegmann, and J. E. Anthony, “Bandlike transport in pentacene and functionalized pentacene thin films revealed by subpicosecond transient photoconductivity measurements,” Phys. Rev. B 71(3), 035204 (2005).
[CrossRef]

Coutaz, J.-L.

Davidson, D. W.

D. W. Davidson and R. H. Cole, “Dielectric relaxation in glycerol, propylene glycol, and n-propanol,” J. Chem. Phys. 19(12), 1484–1490 (1951).
[CrossRef]

de Haas, M. P.

M. P. de Haas, R. J. O. M. Hoofman, L. D. A. Siebbeles, and J. M. Warman, “Highly mobile electrons and holes on isolated chains of the semiconducting polymer poly (phenylene vinylene),” Nature 392(6671), 54–56 (1998).
[CrossRef]

Dekorsy, T.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86(12), 121114 (2005).
[CrossRef]

DeRosa, F.

S. J. Allen, D. C. Tsui, and F. DeRosa, “Frequency dependence of the electron conductivity in the silicon inversion layer in the metallic and localized regimes,” Phys. Rev. Lett. 35(20), 1359–1362 (1975).
[CrossRef]

Dorney, T. D.

Dressel, M.

M. Fischer, M. Dressel, B. Gompf, A. K. Tripathi, and J. Pflaum, “Infrared spectroscopy on the charge accumulation layer in rubrene single crystals,” Appl. Phys. Lett. 89(18), 182103 (2006).
[CrossRef]

Dreyhaupt, A.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86(12), 121114 (2005).
[CrossRef]

Drude, P.

P. Drude, “Zur Elektronentheorie der Metalle,” Annalen der Physik 306(3), 566–613 (1900).
[CrossRef]

Duvillaret, L.

Egerton, R. F.

O. Ostroverkhova, D. G. Cooke, S. Shcherbyna, R. F. Egerton, F. A. Hegmann, and J. E. Anthony, “Bandlike transport in pentacene and functionalized pentacene thin films revealed by subpicosecond transient photoconductivity measurements,” Phys. Rev. B 71(3), 035204 (2005).
[CrossRef]

Ellingson, R. J.

X. Ai, M. C. Beard, K. P. Knutsen, S. E. Shaheen, G. Rumbles, and R. J. Ellingson, “Photoinduced charge carrier generation in a poly(3-hexylthiophene) and methanofullerene bulk heterojunction investigated by time-resolved terahertz spectroscopy,” J. Phys. Chem. B 110(50), 25462–25471 (2006).
[CrossRef] [PubMed]

Fischer, M.

M. Fischer, M. Dressel, B. Gompf, A. K. Tripathi, and J. Pflaum, “Infrared spectroscopy on the charge accumulation layer in rubrene single crystals,” Appl. Phys. Lett. 89(18), 182103 (2006).
[CrossRef]

Gao, Q.

P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
[CrossRef]

Garet, F.

Garnett, J. C. M.

J. C. M. Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Sect. A 203(1), 385–420 (1904).
[CrossRef]

Gompf, B.

M. Fischer, M. Dressel, B. Gompf, A. K. Tripathi, and J. Pflaum, “Infrared spectroscopy on the charge accumulation layer in rubrene single crystals,” Appl. Phys. Lett. 89(18), 182103 (2006).
[CrossRef]

Grischkowsky, D.

T.-I. Jeon, D. Grischkowsky, A. K. Mukherjee, and R. Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77(16), 2452–2454 (2000).
[CrossRef]

T.-I. Jeon and D. Grischkowsky, “Observation of a Cole-Davidson type complex conductivity in the limit of very low carrier densities in doped silicon,” Appl. Phys. Lett. 72(18), 2259–2261 (1998).
[CrossRef]

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. 56(17), 1694–1696 (1990).
[CrossRef]

M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes in moderately doped silicon,” Phys. Rev. B 41(17), 12140–12149 (1990).
[CrossRef]

Guggenmos, A.

G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
[CrossRef]

Handloser, M.

G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
[CrossRef]

Hegmann, F. A.

O. Ostroverkhova, D. G. Cooke, S. Shcherbyna, R. F. Egerton, F. A. Hegmann, and J. E. Anthony, “Bandlike transport in pentacene and functionalized pentacene thin films revealed by subpicosecond transient photoconductivity measurements,” Phys. Rev. B 71(3), 035204 (2005).
[CrossRef]

Helm, M.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86(12), 121114 (2005).
[CrossRef]

Hendry, E.

E. Hendry, M. Koeberg, B. O’Regan, and M. Bonn, “Local field effects on electron transport in nanostructured TiO2 revealed by terahertz spectroscopy,” Nano Lett. 6(4), 755–759 (2006).
[CrossRef] [PubMed]

Herz, L. M.

P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
[CrossRef]

Hoofman, R. J. O. M.

M. P. de Haas, R. J. O. M. Hoofman, L. D. A. Siebbeles, and J. M. Warman, “Highly mobile electrons and holes on isolated chains of the semiconducting polymer poly (phenylene vinylene),” Nature 392(6671), 54–56 (1998).
[CrossRef]

Jagadish, C.

P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
[CrossRef]

Jansen, C.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[CrossRef]

Jeon, T.-I.

T.-I. Jeon, D. Grischkowsky, A. K. Mukherjee, and R. Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77(16), 2452–2454 (2000).
[CrossRef]

T.-I. Jeon and D. Grischkowsky, “Observation of a Cole-Davidson type complex conductivity in the limit of very low carrier densities in doped silicon,” Appl. Phys. Lett. 72(18), 2259–2261 (1998).
[CrossRef]

Jepsen, P. U.

Johnston, M. B.

P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
[CrossRef]

Kersting, R.

G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
[CrossRef]

Knutsen, K. P.

X. Ai, M. C. Beard, K. P. Knutsen, S. E. Shaheen, G. Rumbles, and R. J. Ellingson, “Photoinduced charge carrier generation in a poly(3-hexylthiophene) and methanofullerene bulk heterojunction investigated by time-resolved terahertz spectroscopy,” J. Phys. Chem. B 110(50), 25462–25471 (2006).
[CrossRef] [PubMed]

Koch, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[CrossRef]

Koeberg, M.

E. Hendry, M. Koeberg, B. O’Regan, and M. Bonn, “Local field effects on electron transport in nanostructured TiO2 revealed by terahertz spectroscopy,” Nano Lett. 6(4), 755–759 (2006).
[CrossRef] [PubMed]

Lang, C.

G. Acuna, F. Buersgens, C. Lang, M. Handloser, A. Guggenmos, and R. Kersting, “Interdigitated Terahertz Emitters,” Electron. Lett. 44(3), 229–231 (2008).
[CrossRef]

Lloyd-Hughes, J.

P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
[CrossRef]

Menon, R.

T.-I. Jeon, D. Grischkowsky, A. K. Mukherjee, and R. Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77(16), 2452–2454 (2000).
[CrossRef]

Mittleman, D. M.

Montroll, E. W.

H. Scher and E. W. Montroll, “Anomalous transit-time dispersion in amorphous solids,” Phys. Rev. B 12(6), 2455–2477 (1975).
[CrossRef]

Mukherjee, A. K.

T.-I. Jeon, D. Grischkowsky, A. K. Mukherjee, and R. Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77(16), 2452–2454 (2000).
[CrossRef]

Nienhuys, H.-K.

O’Regan, B.

E. Hendry, M. Koeberg, B. O’Regan, and M. Bonn, “Local field effects on electron transport in nanostructured TiO2 revealed by terahertz spectroscopy,” Nano Lett. 6(4), 755–759 (2006).
[CrossRef] [PubMed]

Ostroverkhova, O.

O. Ostroverkhova, D. G. Cooke, S. Shcherbyna, R. F. Egerton, F. A. Hegmann, and J. E. Anthony, “Bandlike transport in pentacene and functionalized pentacene thin films revealed by subpicosecond transient photoconductivity measurements,” Phys. Rev. B 71(3), 035204 (2005).
[CrossRef]

Parkinson, P.

P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient THz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007).
[CrossRef]

Pflaum, J.

M. Fischer, M. Dressel, B. Gompf, A. K. Tripathi, and J. Pflaum, “Infrared spectroscopy on the charge accumulation layer in rubrene single crystals,” Appl. Phys. Lett. 89(18), 182103 (2006).
[CrossRef]

Planken, P. C. M.

Pollak, M.

M. Pollak, “On dispersive transport by hopping and by trapping,” Philos. Mag. 36(5), 1157–1169 (1977).
[CrossRef]

Rumbles, G.

X. Ai, M. C. Beard, K. P. Knutsen, S. E. Shaheen, G. Rumbles, and R. J. Ellingson, “Photoinduced charge carrier generation in a poly(3-hexylthiophene) and methanofullerene bulk heterojunction investigated by time-resolved terahertz spectroscopy,” J. Phys. Chem. B 110(50), 25462–25471 (2006).
[CrossRef] [PubMed]

Schall, M.

Scheller, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[CrossRef]

Scher, H.

H. Scher and E. W. Montroll, “Anomalous transit-time dispersion in amorphous solids,” Phys. Rev. B 12(6), 2455–2477 (1975).
[CrossRef]

Shaheen, S. E.

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Other (5)

N. Ashcroft and D. Mermin, Solid State Physics (Harcourt, 1976).

M. Dressel and G. Grüner, Electrodynamics of Solids - Optical Properties of Electrons in Matter (Cambridge University press, 2002).

S. Sze, Semiconductor Devices (John Wiley & Sons, 1985).

In fact, the THz response scales with the sample's plasma frequency given by carrier density, effective mass, and background permittivity.

To be more specific, E0y and E1y were measured after passage through the GaAs-wafer and the optical detection system. This does not affect differential quantities.

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Figures (5)

Fig. 1
Fig. 1

a) Schematic diagram of a thin metallic layer of thickness d embedded in a dielectric with a refractive index n. The differential current Δ j driven by the incident field E inc causes a differential magnetic field Δ H which in turn causes the differential field Δ E measured by THz-TDS. b) Complex diagram illustrating the relation of the phase angle φ with the measured complex fields E 1y, E 0y, and ΔE y.

Fig. 2
Fig. 2

a) Time-resolved few-cycle THz pulse after transmission through the metal-semiconductor structure. b) Differential signal obtained by switching the GaAs between equilibrium and partial depletion. The modulation bias of −5 V increased the depletion zone by 400 nm.

Fig. 3
Fig. 3

Frequency dependence of the tangent of the phase angle φ obtained on the GaAs structure at room temperature (symbols). The solid line shows a calculation for τ = 198 fs. The dashed line indicates ωτ = 1.

Fig. 4
Fig. 4

a) Dependence of the phase angle φ on the modulation bias for room temperature. The data show the phase for frequencies of 1 and 2 THz, respectively. b) Dependence of the amplitude of the electromodulation signal on the modulation bias at 1 and at 2 THz, respectively. The solid lines depict calculations that take into account the depletion underneath the Schottky contacts with increasing bias.

Fig. 5
Fig. 5

Temperature dependence of the momentum relaxation time τ as extracted from THz phase measurements (symbols). The solid line shows the result of the electrical four-point characterization.

Equations (5)

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ΔjσE1Δdd,
ΔH·dr=Δj·dA.
S=ΔEyE1yΔdZ02nσ.
σ=Ne2τm*1iωτ1+ω2τ2,
tanϕ=ωτ.

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