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 Optical Society of America

1. Introduction

Terahertz (THz) time-domain spectroscopy (TDS) has developed towards an alternative technique for characterizing electrical transport in condensed matter. Many studies on semiconductors demonstrate excellent agreement with the Drude model and characteristic properties such as the complex conductivity have been deduced [15]. Recent reports on organic semiconductors [6], low doped inorganic semiconductors [7], and nanoparticles [8] reported deviations from a pure Drude behavior. Experimental data were reproduced with excellent precision using modified Drude models such as the Drude-Smith model [9], the Cole-Davidson model [10], or by incorporating the Maxwell Garnett theory [11].

All Drude models have in common that scattering is described by the momentum relaxation time τ which makes this time constant one of the most fundamental quantities that control charge transport. Deducing τ from optical data, however, demands knowledge of further parameters, such as of the carriers' density N, the effective mass m*, the background permittivity ε , and the thickness d of the sample [1,12,13]. The thickness d can be deduced in time-resolved experiments when the optical thickness exceeds the wavelength of the radiation [1416]. However, the progress in material science provides many novel materials, which are extremely thin and have unknown charge carrier densities and effective masses. Besides THz TDS, far-infrared as well as microwave techniques are used for characterizing such modern materials [17,18]. But these approaches require precise knowledge of material parameters or use fitting procedures.

In this work, we present an optical method for probing the Drude relaxation time without using any further parameters. In our technique we modulate the optical properties of the sample and record the differential response signal at THz frequencies. We will show that the phase of this signal directly provides the relaxation time. It is worth pointing out, that our method is not restricted to the THz band. The method can be adapted to any spectroscopic technique, which provides the optical phase of transmitted or reflected radiation.

Small modulations of the sample's optical properties can be achieved most conveniently by electromodulation techniques similar to the method described by Allen et al. [19]. The fact that the modulation of the charge carrier density resembles the operation of a field-effect transistor illustrates the application potential of the technique. Currently, numerous novel materials such as nanostructures or organic semiconductors have been developed for similar devices. Many of these materials, however, are inhomogeneous, include a high density of traps and grain boundaries, or have a broadened density of electronic states. Dispersive transport and hopping dominate electrical properties and mask the fundamental carrier dynamics on microscopic scales [20,21]. In such cases THz modulation spectroscopy may provide further insight into the fundamental carrier relaxation dynamics.

2. Method

The concept of our method is illustrated in Fig. 1a ). We study a thin sheet of a semiconductor, which has the thickness d and contains mobile carriers. Within the part Δd the charge carrier density can be modulated, e.g. the density can be reduced to zero. A fraction of an incident THz electric field E inc is transmitted through the doped layer, and generates a current density j which is proportional to the complex conductivity σ . In the following, it is convenient to discuss differential quantities such as the differential field ΔE = E 1 -E 0 where E 1 and E 0 are the transmitted electric fields in the case of an interaction across the entire layer and in the case the layer thickness is reduced by Δd, respectively.

 

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 Δj driven by the incident field E inc causes a differential magnetic field ΔH which in turn causes the differential field ΔE 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.

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The differential current density Δj can be described by a change of the thickness

ΔjσE1Δdd,
where we assumed the electric field to be virtually constant across the layer, which is a reasonable approximation for optically thin films. In order to deduce the impact of Δj on the reflection and transmission of radiation, we consider that Δj causes a differential magnetic field ΔH, which can be calculated by Ampere's law:

ΔH·dr=Δj·dA.

In layers which are thin compared with the wavelength (dλ), the x-components of ΔH dominate the above equation whereas the z-components can be neglected. We also consider that Δd is smaller than the skin depth. In consequence, the modulated current density Δj does not change significantly across the depleted layer. The magnetic field ΔH causes a differential electrical field given by ΔE = Z 0ΔH/ n, where Z 0 is the impedance of vacuum and n is the refractive index of the surrounding medium. Figure 1b) displays the fields in the complex plane. Using E 1y as reference provides:

S=ΔEyE1yΔdZ02nσ.

At this point we assume the conductivity of the original Drude model:

σ=Ne2τm*1iωτ1+ω2τ2,
where N is the carrier density and m* is the carriers’ effective mass [22,23]. Relating the imaginary part of S to the real part yields the optical phase of the signal:

tanϕ=ωτ.

Thus, the momentum relaxation time can be directly deduced from φ without the use of further parameters. This includes the change of the layer thickness Δd. Alternatively, the amplitude or intensity of the signal S can be analyzed in case that ωτ ≈1 [24]. In the Hagen-Rubens range (ωτ1), however, the spectra become structureless because the amplitude is proportional to 1/(1 + ω 2 τ 2)1/2. In contrast, the tangent of the phase angle is proportional to τ, which illustrates the strength of our technique when characterizing materials in which ultrafast scattering occurs.

3. Experimental

We tested the method on a GaAs structure grown by molecular beam epitaxy (MBE). It comprises an n-doped layer grown on a semi-insulating GaAs substrate. The layer is doped at 2·1016 cm−3 and has a thickness of 2 µm. For electronic control we fabricated a Schottky contact on top of the structure by depositing a 10 nm thick film of Cr. The second terminal is an ohmic AuGe contact. The doped layer in the GaAs can be partially depleted from electrons by the application of a negative bias V to the Schottky contact. The width of the depletion region follows a square root dependence on V [25], from which the modulated depth Δd can be calculated. In our experiments Δd is of the order of 100 nm. This is much smaller than the skin depth of the electron gas, which is about 20 μm at THz frequencies. Thus, the assumptions made in section 2 are justified. They can be applied to many other devices where conductive sheets are modulated, as for instance, in field-effect transistors.

In our experiments we apply time-resolved THz transmission spectroscopy. The sample is mounted in a cryostat, which allows for low-temperature measurements. A titanium-sapphire laser delivers pulses of 80 fs duration at 780 nm center wavelength and at a repetition rate of 80 MHz. About 700 mW of the laser power is used for the photoexcitation of an interdigitated THz emitter [26,27]. Parabolic mirror optics with NA = 0.3 focus the THz radiation onto the GaAs structure. The transmitted radiation is time-resolved by standard electro-optic sampling in a [110] ZnTe crystal of 1 mm thickness [28]. The setup has a bandwidth of 2.8 THz and the signal to noise ratio is about 105 Hz1/2. We measured the field strength of the THz pulses using the procedure described in Ref [29]. and deduced a peak field of 70 V/cm. The curve in Fig. 2a ) shows a THz pulse transmitted through the GaAs structure, whereas Fig. 2b) displays the differential signal, which we obtained by modulating the structure with a bias of −5 V. This corresponds to a change of the depletion width of about 400 nm.

 

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.

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4. Results and discussion

In order to prove the concept of our technique we measured the differential transmission through the GaAs structure at room temperature. The electron gas was modulated by switching the bias to the Schottky contact between 0 V and −1 V. This corresponds to a modulated layer thickness of 120 nm or to a modulated sheet density of n2 D = 2.4· 1011 cm−2. We recorded the THz signals E 1y and E 0y [30]. After Fourier transform of the differential THz signal ΔEy = E 1y-E 0y, the optical phase was obtained as described above. The data depicted in Fig. 3 show the expected dependence of the phase on the frequency. Using a relaxation time of 198 ± 2 fs provides an excellent agreement with Eq. (5). The linear behavior of tan φ confirms the validity of the original Drude model in our case. We do not observe deviations from the Drude model as reported for poly(3-hexylthiophene) [6], low doped silicon [7], and nanoparticles [8].

 

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.

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In section 2 we assumed that only the lateral components of ΔH contribute to Ampere's law whereas the perpendicular components can be neglected. We also assumed that the exciting THz field is virtually constant across the modulated layer. We validate these assumptions by measuring the THz signals in dependence on the modulation depth Δd by increasing the modulation bias V. As displayed in Fig. 4a ) the measured phase shows no dependence on V, which proves the validity of the assumptions. In contrast, the amplitude plotted in Fig. 4b) follows a square root dependence as expected for the increase of the depletion width. The calculation, however, shows deviations for higher voltages. We attribute these differences to imperfections of the Schottky contact and to inhomogeneities of the doping profile. This illustrates the difficulties that arise in deducing transport properties from amplitude data and highlights the reliability of phase measurements.

 

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.

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In the case of our well-defined MBE grown structure, parameters such as the doping density and the effective carrier mass are well known. Thus in this particular case, the momentum relaxation time can be extracted from four-point measurements [31]. Figure 5 shows temperature resolved data. Electrical and phase measurement differ by about 3%, which illustrates that our technique provides precise data. At low temperatures, however, freeze-out of the donors may lead to a reduced electrical conductivity, which explains the differences at about 100 K.

 

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.

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We emphasize that our approach is not advantageous in the case of homogeneous semiconductors with well known properties. In this case electrical characterization certainly is less elaborate. But many modern materials exhibit unknown charge carrier densities and effective masses. Additionally, many new materials are inhomogeneous. In such systems the mesoscopic morphology may limit electrical transport and in consequence extremely low mobilities are observed by electrical characterization. Examples are polycrystalline semiconductors, percolated networks of carbon nanotubes, and many organic substances where hopping transport is the most limiting factor. As mentioned in the introduction, such systems can be well described by modified Drude models. For the technique described in this work, we so far assumed the original Drude conductivity. It is worth pointing out that similar results as Eq. (5) can be achieved for the Drude-Smith approach [9] and the Cole-Davidson model [10]. This indicates that the presented method of phase analysis can be applied in a much broader framework and may open up new opportunities for characterizing charge transport in modern materials.

5. Conclusions

We developed a technique for directly measuring the Drude momentum relaxation time τ of charge carriers using the optical phase of a differential THz signal. The modulation of the structure under investigation provides a phase signal, which is proportional to τ. In contrast to other spectroscopic approaches, our technique is advantageous particularly in the Hagen-Rubens range. Thus, we are confident that our technique will provide new insights into many modern materials where scattering occurs on ultrafast time scales and electronic properties are not directly accessible by electronic means.

Acknowledgments

This work is partially supported by the Deutsche Forschungsgemeinschaft (DFG) through the Nanosystems Initiative Munich (NIM), and by the Deutsche Forschungsgemeinschaft (DFG), contract Ke 516/1-1. The authors acknowledge technical support by A. Guggenmos and S. Niedermaier.

References and links

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 Jr, 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).

References

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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)

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. 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]

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.

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]

Shcherbyna, S.

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]

Siebbeles, L. D. A.

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]

Smith, N. V.

N. V. Smith, “Classical generalization of the Drude formula for the optical conductivity,” Phys. Rev. B 64(15), 155106 (2001).
[Crossref]

Smits, F. M.

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

Tan, H. H.

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]

Tripathi, A. K.

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]

Tsui, D. C.

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]

van Exter, M.

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]

Warman, J. 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]

Wenckebach, T.

Winnerl, S.

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]

Wu, Q.

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

Zhang, X.-C.

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

Annalen der Physik (1)

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

Appl. Opt. (1)

Appl. Phys. Lett. (6)

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]

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]

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]

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]

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

Bell Syst. Tech. J. (1)

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

Electron. Lett. (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]

J. Chem. Phys. (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]

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

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

J. Phys. Chem. B (1)

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]

Nano Lett. (2)

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]

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]

Nature (1)

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]

Opt. Commun. (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]

Opt. Lett. (1)

Philos. Mag. (1)

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

Philos. Trans. R. Soc. London Sect. A (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]

Phys. Rev. B (4)

N. V. Smith, “Classical generalization of the Drude formula for the optical conductivity,” Phys. Rev. B 64(15), 155106 (2001).
[Crossref]

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]

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]

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

Phys. Rev. Lett. (1)

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]

Other (5)

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

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).

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)

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

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

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