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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 18016–18024
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Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, and T. Ozaki  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 18016-18024 (2012)
http://dx.doi.org/10.1364/OE.20.018016


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Abstract

We study the carrier density dependence of nonlinear terahertz (THz) absorption due to field-induced intervalley scattering in photoexcited GaAs using the optical-pump/THz-probe technique. The intervalley scattering in GaAs is strongly dependent on the photo-carrier density. As the carrier density is increased from 1 × 1017 to 4.7 × 1017 cm−3, the nonlinear absorption bleaching increases. However, if the carrier density is increased further above 4.7 × 1017 cm−3, the trend reverses and the bleaching is reduced. The initial increase in absorption bleaching is because, unlike low THz field, high THz field experiences intervalley scattering and nonparabolicity of the conduction band. On the other hand, a simple electron transport model shows that the reduction in intervalley scattering is mainly due to the increase in the electron-hole scattering rate with the increase in the carrier density. This increase in the electron-hole scattering rate limits the maximum kinetic energy attainable by the electrons and thus reduces the observed nonlinear absorption.

© 2012 OSA

1. Introduction

Investigations of high-field charge transport in semiconductors using far-infrared radiation have been of significant interest for more than two decades, primarily because of the relevance to device physics [1

1. A. G. Markelz, N. G. Asmar, B. Brar, and E. G. Gwinn, “Interband impact ionization by terahertz illumination of InAs heterostructures,” Appl. Phys. Lett. 69(26), 3975–3977 (1996). [CrossRef]

6

6. B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410(6824), 60–63 (2001). [CrossRef] [PubMed]

]. With the recent development of laser-based intense, few-cycle terahertz (THz) sources and coherent detection techniques [7

7. P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96(18), 187402 (2006). [CrossRef] [PubMed]

13

13. A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J.-P. Wolf, “Generation of 30 μJ single-cycle terahertz pulses at 100 Hz repetition rate by optical rectification,” Opt. Lett. 33(21), 2497–2499 (2008). [CrossRef] [PubMed]

], it is now possible to study the nonlinear optical response of semiconductors at THz frequencies on picosecond (and even sub-picosecond) timescales. For example, long-lived coherent THz emission centered around 2 THz and carrier-wave Rabi oscillations [14

14. P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, J. S. Lee, and U. Schade, “Carrier-wave Rabi flopping on radiatively coupled shallow donor transitions in n - type GaAs,” Phys. Rev. B 77(23), 235204 (2008). [CrossRef]

] have been excited using intense THz radiation [7

7. P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96(18), 187402 (2006). [CrossRef] [PubMed]

], due to the strong THz coupling to the impurity levels of n-type GaAs [7

7. P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96(18), 187402 (2006). [CrossRef] [PubMed]

, 14

14. P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, J. S. Lee, and U. Schade, “Carrier-wave Rabi flopping on radiatively coupled shallow donor transitions in n - type GaAs,” Phys. Rev. B 77(23), 235204 (2008). [CrossRef]

]. THz electric-field-induced impact ionization in InSb [15

15. H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78(12), 125203 (2008). [CrossRef]

, 16

16. M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by terahertz pump-terahertz probe spectroscopy,” Phys. Rev. B 79(16), 161201 (2009). [CrossRef]

], and mapping of the effective mass anisotropy in the non-parabolic conduction band of an InGaAs thin film [17

17. F. Blanchard, D. Golde, F. H. Su, L. Razzari, G. Sharma, R. Morandotti, T. Ozaki, M. Reid, M. Kira, S. W. Koch, and F. A. Hegmann, “Effective mass anisotropy of hot electrons in nonparabolic conduction bands of n-doped InGaAs films using ultrafast terahertz pump-probe techniques,” Phys. Rev. Lett. 107(10), 107401 (2011). [CrossRef] [PubMed]

] have been reported using an intense THz pulse. Moreover, these sources have allowed the observation of nonlinear THz absorption bleaching due to intervalley scattering in InGaAs, GaAs, Si, and Ge using THz-pump/THz-probe (TPTP) or optical-pump/THz-probe (OPTP) based experiments [18

18. L. Razzari, F. H. Su, G. Sharma, F. Blanchard, A. Ayesheshim, H. C. Bandulet, R. Morandotti, J. C. Kieffer, T. Ozaki, M. Reid, and F. A. Hegmann, “Nonlinear ultrafast modulation of the optical absorption of intense few-cycle terahertz pulses in n - doped semiconductors,” Phys. Rev. B 79(19), 193204 (2009). [CrossRef]

21

21. M. C. Hoffmann and D. Turchinovich, “Semiconductor saturable absorbers for ultrafast terahertz signals,” Appl. Phys. Lett. 96(15), 151110 (2010). [CrossRef]

].

Carrier dynamics in semiconductors can be monitored in the THz regime by either the OPTP or TPTP techniques. In the TPTP technique, one typically uses samples with fixed doping levels, and hence the free carrier density is also fixed. In OPTP, one can vary the free carrier density of the semiconductor sample by changing the fluence of the optical pump. This allows one to study the influence of carrier density on charge carrier dynamics, which is important for understanding and improving various optoelectronic devices.

2. Experimental set-up

The THz source used in this study is described in Ref [10

10. F. Blanchard, L. Razzari, H. C. Bandulet, G. Sharma, R. Morandotti, J. C. Kieffer, T. Ozaki, M. Reid, H. F. Tiedje, H. K. Haugen, and F. A. Hegmann, “Generation of 1.5 µJ single-cycle terahertz pulses by optical rectification from a large aperture ZnTe crystal,” Opt. Express 15(20), 13212–13220 (2007). [CrossRef] [PubMed]

]. Briefly, a 75 mm diameter large-aperture <110> ZnTe crystal is used as the nonlinear medium to generate high-power, few-cycle intense THz pulses via optical rectification, with a bandwidth extending from 0.1 to 2.8 THz. The temporal shape of the THz pulse is shown in Fig. 1
Fig. 1 Temporal shape of a THz pulse measured using electro-optic sampling, with the inset showing the corresponding Fourier amplitude spectrum.
, with the corresponding spectrum presented in the inset.

In the current work, a standard OPTP technique [23

23. M. C. Nuss and J. Orenstein, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer-Verlag, Berlin, 1998).

] based on the use of the above intense THz pulse is employed to study the effect of carrier density on the THz-induced nonlinearities in GaAs. A 0.5 mm thick, undoped GaAs wafer is placed at the focus of the THz beam, and is photoexcited by an 800 nm, 50 fs pump beam with a diameter of 8 mm FWHM. Free-space electro-optic (EO) sampling in a second 0.5 mm thick <110> ZnTe crystal is used to detect the THz pulse transmitted through the GaAs sample. Detection linearity is maintained by keeping the maximum probe beam modulation measured at the two photodiodes well below polarization over-rotation, i.e. by placing two silicon wafers after the sample to reduce the THz electric field impinging onto the detection crystal. Wire-grid polarizers are used to vary the intensity of the THz pulse at the sample position. To evaluate the THz electric field, we have used the same method reported in Ref [24

24. H. G. Roskos, M. D. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1(4), 349–368 (2007). [CrossRef]

], based on the following relation:
E0=η0WπωI2g2(t)dt
(1)
Here, E0 is the THz peak electric field, η0 is the free-space impedance (377 Ω), W is the THz energy, ωI is the intensity beam waist, and g(t) is the temporal shape of the THz electric field (with a peak value normalized to 1), which can be easily retrieved from the EO sampling measurements. The THz intensity beam waist was measured to be 0.6 mm by imaging the THz beam at the focus using a pyroelectric IR camera (ElectroPhysics, model PV320). The peak THz energy (W) is measured to be 0.53 μJ, using a Microtech Instrument pyroelectric detector. Substituting all the parameters into Eq. (1), the maximum THz electric field is evaluated to be 133 kV/cm. In our OPTP experiments, we have used two conditions for the THz probe beam, one with “high” THz fields at 133 kV/cm, and the other with “low” THz fields at 9 kV/cm.

A half-wave plate and a polarizer were used to vary the 800 nm optical pump fluence, ranging from ~2 μJ.cm−2 to 40 μJ.cm−2. From this parameter, the carrier density is estimated to range between 1 × 1017 and 10.6 × 1017 cm−3 [25

25. F. A. Hegmann and K. P. Lui, “Optical pump-terahertz probe investigation of carrier relaxation in radiation-damaged silicon-on-sapphire,” Proc. SPIE 4643, 31–41 (2002). [CrossRef]

], assuming an absorption depth of 1 μm. In order to investigate the effect of carrier density on the THz-induced nonlinearity, we measured the nonlinear THz absorption bleaching of the optically pumped GaAs at both “high” and “low” THz field strengths.

3. Results and discussions

3.1 Effect of carrier density on nonlinear THz absorption bleaching

The 800 nm optical pump beam excites the electrons from the valence band to the central Γ valley in the conduction band in the normally insulating GaAs sample. Figure 2
Fig. 2 Normalized transmission of the peak of the THz pulse as a function of the pump-probe delay for low and high THz peak field strengths. The full THz pulse transients are shown, including the reference (blue) and pumped transients at a pump-probe delay time of 8 ps for the low (red) and high (black) field strengths.
shows the normalized transmission of the main peak of the THz probe pulse through optically pumped GaAs as a function of the pump-probe delay time. The nonlinear response is then determined by monitoring the peak THz electric field of the pulse. When the optical pump and the THz probe overlap in time (at a pump-probe delay of 0 ps in Fig. 2), the THz transmission through the photoexcited GaAs sample is reduced, since the sample becomes more conductive due to the increased carrier density. However, even for large pump-probe delay times (a few hundreds of picoseconds), the normalized transmission at 133 kV/cm (Ehigh) is greater than that of the 9 kV/cm peak field THz pulse (Elow). This phenomenon has been shown to be due to the intervalley scattering between the central Γ and the L valley of the conduction band [18

18. L. Razzari, F. H. Su, G. Sharma, F. Blanchard, A. Ayesheshim, H. C. Bandulet, R. Morandotti, J. C. Kieffer, T. Ozaki, M. Reid, and F. A. Hegmann, “Nonlinear ultrafast modulation of the optical absorption of intense few-cycle terahertz pulses in n - doped semiconductors,” Phys. Rev. B 79(19), 193204 (2009). [CrossRef]

20

20. J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz-pump terahertz probe measurements,” Phys. Rev. B 81(3), 035201 (2010). [CrossRef]

], which increases the effective mass of a significant population of carriers in the L valley compared to the Γ valley, and thus reduces the mobility and conductivity of these carriers. The result is a bleaching of the pump-induced absorption at high THz probe field strengths, observed previously by F. Su et al. [19

19. F. H. Su, F. Blanchard, G. Sharma, L. Razzari, A. Ayesheshim, T. L. Cocker, L. V. Titova, T. Ozaki, J. C. Kieffer, R. Morandotti, M. Reid, and F. A. Hegmann, “Terahertz pulse induced intervalley scattering in photoexcited GaAs,” Opt. Express 17(12), 9620–9629 (2009). [CrossRef] [PubMed]

]

However, the effect of the carrier density on intervalley scattering has not been studied yet. Such effect can be quantified by defining the “THz induced absorption bleaching”, given as:
Absorptionbleaching=ThighTlow1,whereT=|Epump(t)|2dt|Eref(t)|2dt
(2)
Here, Epump and Eref are the transmitted THz electric field through the photoexcited (pump) and unexcited (ref) sample, and Thigh and Tlow are the normalized transmission at high (133 kV/cm) and low (9 kV/cm) THz fields, respectively. Figure 3
Fig. 3 The carrier density dependence of the experimental (black squares with error bar) and simulated (red line) THz absorption bleaching for 800 nm photoexcited GaAs. The effect of e-h scattering is incorporated by varying the intravalley scattering time in the simulation.
shows the THz induced nonlinearity for a carrier density ranging from 1.0 × 1017 to 10.6 × 1017 cm−3. It can be clearly seen from Fig. 3 that the absorption bleaching varies significantly with carrier density.

The absorption bleaching data in Fig. 3 can be divided into two carrier-density regions: (i) at relatively low carrier densities (< 4.7 × 1017 cm−3), the THz-induced nonlinearity increases with increasing carrier density from 1 × 1017 cm−3 onward. For the range of carrier densities we have investigated, absorption bleaching reaches a maximum at a carrier density of 4.7 × 1017 cm−3; (ii) for carrier densities from 4.7 × 1017 cm−3 to 10.6 × 1017 cm−3 (the maximum carrier density under investigation), absorption bleaching decreases monotonically. For the maximum value of the carrier density (10.6 × 1017 cm−3), absorption bleaching almost vanishes completely.

3.2 Theoretical interpretation

A simple Drude-based model [19

19. F. H. Su, F. Blanchard, G. Sharma, L. Razzari, A. Ayesheshim, T. L. Cocker, L. V. Titova, T. Ozaki, J. C. Kieffer, R. Morandotti, M. Reid, and F. A. Hegmann, “Terahertz pulse induced intervalley scattering in photoexcited GaAs,” Opt. Express 17(12), 9620–9629 (2009). [CrossRef] [PubMed]

], incorporating Γ− L intervalley scattering is used to describe the effect of carrier density on absorption bleaching in GaAs. THz transmission through the sample can be idealized as a thin conducting sheet with thickness d on an insulating substrate with index N, and can be expressed as follows [23

23. M. C. Nuss and J. Orenstein, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer-Verlag, Berlin, 1998).

]:
Etrans(t)=1Y0+Ys(2Y0Einc(t)Jd)
(3)
Here, Etrans and Einc are the transmitted and incident THz fields, Y0 = 1/377Ω−1 and Ys = NY0 are the free-space and substrate admittances, respectively, and J = (nΓΓ) is the current density in the film. Furthermore, e is the electronic charge, n is the electron density and ν is the electron drift velocity. The electron drift velocity (νΓ) in the Γ valley driven by the transmitted THz field Etrans can be described by the dynamic equation:
dνΓdt=eEtransmΓ*νΓτΓ
(4)
In the above equation, the Drude scattering time, τΓ , is dependent on the carrier density in the Γ valley. As the carrier density increases, e-h scattering reduces τΓ for the low field case. This in turn limits the maximum drift velocity achieved by electrons at higher carrier densities. In our simulation, τΓ is a fit parameter and is obtained from the fits to the nonlinear experimental data.

We also note that the change in electron populations in the Γ and L valleys is determined by the intervalley scattering rates. The L−Γ transfer rate (τ)−1 is kept constant [29

29. K. Blotekjaer, “Transport equations for electrons in two-valley semiconductors,” IEEE Trans. Electron. Dev. 17(1), 38–47 (1970). [CrossRef]

], while the Γ− L scattering rate (τΓ L)−1 is a function of the average kinetic energy (εΓ) [30

30. A. M. Anile and S. D. Hern, “Two-valley hydrodynamical models for electron transport in gallium arsenide: Simulation of Gunn oscillations,” VLSI Des. 15(4), 681–693 (2002). [CrossRef]

], where εΓ = [mΓ*(νΓ)2 + 3kBTL]/2 is the average kinetic energy of the electrons in the Γ valley. The scattering time τΓ L is zero at low energies but starts to increase rapidly at a threshold value εth to a maximum value τΓ L0 at high energies. The nonparabolicity of the conduction band is taken into account by changing the effective mass for high THz fields, given by the following equation:
mΓ*(εΓ)=mΓ0*(1+αΓεΓ)
(5)
Here, αΓ = 0.61 is the nonparabolicity factor for the Γ valley in GaAs and mΓ0* = 0.067me is the effective mass at the bottom of the conduction band [27

27. M. Lundstrom, Fundamentals of carrier transport (Cambridge University Press, Cambridge, 2000).

, 31

31. M. Grundmann, The Physics of Semiconductors (Springer-Verlag, 2006).

]. For the simulations, the “high” and “low” THz fields used are again 133 kV/cm and 9 kV/cm, respectively. We have used this model to simulate the experimental observation, as shown in Fig. 3 (red solid line). The simulated results match well with the experimental finding. The parameters used in these simulations are shown in Table 1

Table 1. Parameters used for simulation

table-icon
View This Table
.

During the absorption bleaching process, the incident field accelerates the electrons in the conducting layer of the sample and induces a population transfer between the different valleys of the conduction band. This in turn affects the current density J in Eq. (3), and hence modifies the transmitted field Etrans. Now the current density depends on the drift velocity, and the drift velocity depends not only on the transmitted THz electric field but also on the electron and hole population. As the population increases, the momentum component parallel to the THz E-field vector is randomized due to e-h scattering, limiting the maximum achievable velocity and hence the kinetic energy of the electrons. As the carrier density increases further, the e-h scattering rate increases approximately linearly with a logarithmic correction [32

32. D. G. Cooke, “Time-resolved terahertz spectroscopy of bulk and nanoscale semiconductors,” PhD dissertation, (Department of Physics, University of Alberta, 2007).

, 33

33. J. F. Young, P. J. Kelly, N. L. Henry, and M. W. C. Dharma-Wardana, “Carrier density dependence of hot-electron scattering rates in quasi-equilibrium electron-hole plasmas,” Solid State Commun. 78(5), 343–346 (1991). [CrossRef]

]. This has been taken into account in our model by decreasing the intravalley scattering rate in Eq. (4). The intervalley scattering rate depends on the energy of the electrons. If the kinetic energy of the electrons is reduced due to an increase in the e-h scattering, the intervalley scattering rate will also be reduced. This discussion suggests that absorption bleaching strongly depends on the charge carrier density.

4. Conclusions

In conclusion, we have investigated the effect of carrier density on the nonlinear absorption bleaching of intense THz pulses transmitted through photoexcited GaAs. The increase in absorption bleaching with the increase in carrier density follows from the initial increase in conductivity of the GaAs sample. For high THz fields, however, the transmission is affected less by an increase in carrier density, as compared to the low field case. The main reason for the relatively lower decrease in transmission for high fields is a reduction in electron mobility, due to two reasons: nonparabolicity of the conduction band and intervalley scattering from the high mobility Γ valley to the low mobility L valley. The intervalley scattering rate depends on the electron energy, which is limited by e-h scattering via the reduction of the electron mobility. Even if the intervalley scattering rate is lower (thus promoting population of the Γ valley), the electron will still experience a reduction in mobility due to the nonparabolicity of the conduction band. Therefore, the THz transmission through the photoexcited GaAs layer is less attenuated for high fields as compared to low fields. This initially increases the THz induced absorption bleaching (when the carrier density rises from 1 × 1017 to 4.7 × 1017 cm−3). However, a further increase in the carrier density beyond 4.7 × 1017 cm−3 leads to a monotonically decreasing absorption bleaching as a function of density. This can be explained instead by the increased e-h scattering rate as a function of density, which in turn reduces the mobility significantly to the point where intervalley scattering becomes less likely and nonparabolicity effects (happening at the edge of the conduction band) can be ignored. Thus the high field transmission approaches the low field transmission and the absorption bleaching is reduced. Despite the simplicity of our model, we find that it explains the carrier density dependence of the nonlinear THz absorption rather well.

Acknowledgment

We would like to acknowledge the financial support from Fonds de recherche du Québec - Nature et technology (FQRNT) and Natural Science and Engineering Research Council of Canada (NSERC).

References and links

1.

A. G. Markelz, N. G. Asmar, B. Brar, and E. G. Gwinn, “Interband impact ionization by terahertz illumination of InAs heterostructures,” Appl. Phys. Lett. 69(26), 3975–3977 (1996). [CrossRef]

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K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic dynamical Franz-Keldysh effect,” Phys. Rev. Lett. 81(2), 457–460 (1998). [CrossRef]

6.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410(6824), 60–63 (2001). [CrossRef] [PubMed]

7.

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96(18), 187402 (2006). [CrossRef] [PubMed]

8.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99(4), 043901 (2007). [CrossRef] [PubMed]

9.

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(17), 171121 (2007). [CrossRef]

10.

F. Blanchard, L. Razzari, H. C. Bandulet, G. Sharma, R. Morandotti, J. C. Kieffer, T. Ozaki, M. Reid, H. F. Tiedje, H. K. Haugen, and F. A. Hegmann, “Generation of 1.5 µJ single-cycle terahertz pulses by optical rectification from a large aperture ZnTe crystal,” Opt. Express 15(20), 13212–13220 (2007). [CrossRef] [PubMed]

11.

K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15(8), 4577–4584 (2007). [CrossRef] [PubMed]

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J. Á. Hebling, K.-L. Yeh, M. C. Hoffmann, and K. A. Nelson, “High-power THz generation, THz nonlinear optics and THz nonlinear spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 14(2), 345–353 (2008). [CrossRef]

13.

A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J.-P. Wolf, “Generation of 30 μJ single-cycle terahertz pulses at 100 Hz repetition rate by optical rectification,” Opt. Lett. 33(21), 2497–2499 (2008). [CrossRef] [PubMed]

14.

P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, J. S. Lee, and U. Schade, “Carrier-wave Rabi flopping on radiatively coupled shallow donor transitions in n - type GaAs,” Phys. Rev. B 77(23), 235204 (2008). [CrossRef]

15.

H. Wen, M. Wiczer, and A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78(12), 125203 (2008). [CrossRef]

16.

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by terahertz pump-terahertz probe spectroscopy,” Phys. Rev. B 79(16), 161201 (2009). [CrossRef]

17.

F. Blanchard, D. Golde, F. H. Su, L. Razzari, G. Sharma, R. Morandotti, T. Ozaki, M. Reid, M. Kira, S. W. Koch, and F. A. Hegmann, “Effective mass anisotropy of hot electrons in nonparabolic conduction bands of n-doped InGaAs films using ultrafast terahertz pump-probe techniques,” Phys. Rev. Lett. 107(10), 107401 (2011). [CrossRef] [PubMed]

18.

L. Razzari, F. H. Su, G. Sharma, F. Blanchard, A. Ayesheshim, H. C. Bandulet, R. Morandotti, J. C. Kieffer, T. Ozaki, M. Reid, and F. A. Hegmann, “Nonlinear ultrafast modulation of the optical absorption of intense few-cycle terahertz pulses in n - doped semiconductors,” Phys. Rev. B 79(19), 193204 (2009). [CrossRef]

19.

F. H. Su, F. Blanchard, G. Sharma, L. Razzari, A. Ayesheshim, T. L. Cocker, L. V. Titova, T. Ozaki, J. C. Kieffer, R. Morandotti, M. Reid, and F. A. Hegmann, “Terahertz pulse induced intervalley scattering in photoexcited GaAs,” Opt. Express 17(12), 9620–9629 (2009). [CrossRef] [PubMed]

20.

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz-pump terahertz probe measurements,” Phys. Rev. B 81(3), 035201 (2010). [CrossRef]

21.

M. C. Hoffmann and D. Turchinovich, “Semiconductor saturable absorbers for ultrafast terahertz signals,” Appl. Phys. Lett. 96(15), 151110 (2010). [CrossRef]

22.

G. Sharma, L. Razzari, F. H. Su, F. Blanchard, A. Ayesheshim, T. L. Cocker, L. V. Titova, H. C. Bandulet, T. Ozaki, J. C. Kieffer, R. Morandotti, M. Reid, and F. A. Hegmann, “Time-resolved terahertz spectroscopy of free carrier nonlinear dynamics in semiconductors,” IEEE Photon. J. 2(4), 578–592 (2010). [CrossRef]

23.

M. C. Nuss and J. Orenstein, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer-Verlag, Berlin, 1998).

24.

H. G. Roskos, M. D. Thomson, M. Kreß, and T. Löffler, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1(4), 349–368 (2007). [CrossRef]

25.

F. A. Hegmann and K. P. Lui, “Optical pump-terahertz probe investigation of carrier relaxation in radiation-damaged silicon-on-sapphire,” Proc. SPIE 4643, 31–41 (2002). [CrossRef]

26.

P. N. Saeta, J. F. Federici, B. I. Greene, and D. R. Dykaar, “Intervalley scattering in GaAs and InP probed by pulsed far-infrared transmission spectroscopy,” Appl. Phys. Lett. 60(12), 1477–1479 (1992). [CrossRef]

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M. Lundstrom, Fundamentals of carrier transport (Cambridge University Press, Cambridge, 2000).

28.

W. Walukiewicz, L. Lagowski, L. Jastrzebski, M. Lichtensteiger, and H. C. Gatos, “Electron mobility and free-carrier absorption in GaAs: Determination of the compensation ratio,” J. Appl. Phys. 50(2), 899–908 (1979). [CrossRef]

29.

K. Blotekjaer, “Transport equations for electrons in two-valley semiconductors,” IEEE Trans. Electron. Dev. 17(1), 38–47 (1970). [CrossRef]

30.

A. M. Anile and S. D. Hern, “Two-valley hydrodynamical models for electron transport in gallium arsenide: Simulation of Gunn oscillations,” VLSI Des. 15(4), 681–693 (2002). [CrossRef]

31.

M. Grundmann, The Physics of Semiconductors (Springer-Verlag, 2006).

32.

D. G. Cooke, “Time-resolved terahertz spectroscopy of bulk and nanoscale semiconductors,” PhD dissertation, (Department of Physics, University of Alberta, 2007).

33.

J. F. Young, P. J. Kelly, N. L. Henry, and M. W. C. Dharma-Wardana, “Carrier density dependence of hot-electron scattering rates in quasi-equilibrium electron-hole plasmas,” Solid State Commun. 78(5), 343–346 (1991). [CrossRef]

34.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B 62(23), 15764–15777 (2000). [CrossRef]

35.

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967). [CrossRef]

36.

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(22), 2355–2358 (1987). [CrossRef] [PubMed]

37.

D. G. Cooke, F. A. Hegmann, E. C. Young, and T. Tiedje, “Electron mobility in dilute GaAs bismide and nitride alloys measured by time-resolved terahertz spectroscopy,” Appl. Phys. Lett. 89(12), 122103 (2006). [CrossRef]

OCIS Codes
(300.6500) Spectroscopy : Spectroscopy, time-resolved
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Ultrafast Optics

History
Original Manuscript: April 27, 2012
Revised Manuscript: July 5, 2012
Manuscript Accepted: July 6, 2012
Published: July 23, 2012

Citation
G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, and T. Ozaki, "Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs," Opt. Express 20, 18016-18024 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-18016


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References

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  29. K. Blotekjaer, “Transport equations for electrons in two-valley semiconductors,” IEEE Trans. Electron. Dev.17(1), 38–47 (1970). [CrossRef]
  30. A. M. Anile and S. D. Hern, “Two-valley hydrodynamical models for electron transport in gallium arsenide: Simulation of Gunn oscillations,” VLSI Des.15(4), 681–693 (2002). [CrossRef]
  31. M. Grundmann, The Physics of Semiconductors (Springer-Verlag, 2006).
  32. D. G. Cooke, “Time-resolved terahertz spectroscopy of bulk and nanoscale semiconductors,” PhD dissertation, (Department of Physics, University of Alberta, 2007).
  33. J. F. Young, P. J. Kelly, N. L. Henry, and M. W. C. Dharma-Wardana, “Carrier density dependence of hot-electron scattering rates in quasi-equilibrium electron-hole plasmas,” Solid State Commun.78(5), 343–346 (1991). [CrossRef]
  34. M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B62(23), 15764–15777 (2000). [CrossRef]
  35. D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE55(12), 2192–2193 (1967). [CrossRef]
  36. 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(22), 2355–2358 (1987). [CrossRef] [PubMed]
  37. D. G. Cooke, F. A. Hegmann, E. C. Young, and T. Tiedje, “Electron mobility in dilute GaAs bismide and nitride alloys measured by time-resolved terahertz spectroscopy,” Appl. Phys. Lett.89(12), 122103 (2006). [CrossRef]

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