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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 15077–15089
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Single-walled carbon nanotubes as base material for THz photoconductive switching: a theoretical study from input power to output THz emission

Barmak Heshmat, Hamid Pahlevaninezhad, Matthew Craig Beard, Chris Papadopoulos, and Thomas Edward Darcie  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 15077-15089 (2011)
http://dx.doi.org/10.1364/OE.19.015077


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Abstract

This paper studies the relation between photoexcitation of a single-walled carbon nanotube (SWNT) based device, and its THz output power in the context of THz photoconductive (PC) switching and THz photomixing. A detailed approach of calculating output THz power for such a device describes the effect of each parameter on the performance of the THz PC switch and highlights the design dependent achievable limits. A numerical assessment, with typical values for each parameter, shows that–subject to thermal stability of the device–SWNT based PC switch can improve the output power by almost two orders of magnitudes compared to conventional materials such as LT-GaAs.

© 2011 OSA

1. Introduction

Nanomaterials —especially carbon nanotubes (CNT) and graphene— offer a set of exceptional properties that are potentially suitable for more efficient THz PC switches and photomixers [8

8. M. J. Hagmann, “Possibility of generating terahertz radiation by photomixing with clusters of carbon nanotubes,” J. Vac. Sci. Technol. B 26(2), 794 (2008). [CrossRef]

10

10. B. Heshmat, H. Pahlevaninezhad, T. E. Darcie, and C. Papadopoulos, “Evaluation of carbon nanotubes for THz photomixing,” IEEE Radar Conference (IEEE, 2010), pp. 1176–1179.

]. This includes both using these materials as high impedance waveguides in the antenna structure and as a high mobility, high absorption, base material in the antenna gap (Fig. 1(b)) [8

8. M. J. Hagmann, “Possibility of generating terahertz radiation by photomixing with clusters of carbon nanotubes,” J. Vac. Sci. Technol. B 26(2), 794 (2008). [CrossRef]

10

10. B. Heshmat, H. Pahlevaninezhad, T. E. Darcie, and C. Papadopoulos, “Evaluation of carbon nanotubes for THz photomixing,” IEEE Radar Conference (IEEE, 2010), pp. 1176–1179.

].

In both cases, increase in output power is anticipated, based on primary estimations [8

8. M. J. Hagmann, “Possibility of generating terahertz radiation by photomixing with clusters of carbon nanotubes,” J. Vac. Sci. Technol. B 26(2), 794 (2008). [CrossRef]

,10

10. B. Heshmat, H. Pahlevaninezhad, T. E. Darcie, and C. Papadopoulos, “Evaluation of carbon nanotubes for THz photomixing,” IEEE Radar Conference (IEEE, 2010), pp. 1176–1179.

]. However, there has been no design guidance for fabrication of such devices. So the effect of different parameters, such as tube alignment, carrier lifetime, exciton-exciton annihilation rate and contact resistance on the performance of such devices remains questionable. In order to choose a design path, the dynamics of a PC switch based on CNT material should be addressed thoroughly and that is the main focus of this paper.

2. Conversion of input power to free photocarriers in SWNT film

The connection between input power and free photocarriers in the SWNT film is found in two steps. First, the initial absorbed photon density is calculated and then, the dynamics of the excitons and photocarriers are considered in the film. The initial absorbed photon density is expressed by:
nabsη(ν)0Tpi(t)dthνV,
(1)
where pi(t)is the illuminating pulsed-laser power with repetition rate of 1/T. In the denominator, hνis the energy of each photon with frequency ν, and V is the volume of the material in which the photons are absorbed. The function η(ν) takes values between 0 and 1, depending on the optical density and quantum efficiency of SWNT film [11

11. M. E. Itkis, F. Borondics, A. Yu, and R. C. Haddon, “Bolometric infrared photoresponse of suspended single-walled carbon nanotube films,” Science 312(5772), 413–416 (2006). [CrossRef] [PubMed]

,12

12. D. A. Stewart and F. Léonard, “Energy conversion efficiency in nanotube optoelectronics,” Nano Lett. 5(2), 219–222 (2005). [CrossRef] [PubMed]

]. These parameters depend on CNT types present in the film, alignment of the tubes with the direction of the input light polarization, and filling factor of the CNT bundles. In the case of continuous wave illumination, the integration in Eq. (1) can be reduced to average power per second that will result in average absorbed photon density. Equation (1) is essentially the ratio of number of incident photons to the volume of the sample times the quantum efficiency. This equation assumes a linear relation between input power amplitude and absorbed photon density at a given frequency, thus slight variations of quantum efficiency with input power amplitude is neglected for simplicity [12

12. D. A. Stewart and F. Léonard, “Energy conversion efficiency in nanotube optoelectronics,” Nano Lett. 5(2), 219–222 (2005). [CrossRef] [PubMed]

,13

13. M. Freitag, Y. Martin, J. A. Misewich, R. Martel, and P. Avouris, “Photoconductivity of single carbon nanotubes,” Nano Lett. 3(8), 1067–1071 (2003). [CrossRef]

]. If a wide, non-uniform frequency spectrum is assumed for input power (pi(t)pi(t,ν)), the right hand side of Eq. (1) can be integrated over the total frequency range.

dne(t)dt=γEEne2(t)γCCne(t),ne(0)=nabs;dn(t)dt=γCCne(t)γdn(t),n(0)=0.
(2)

As it will be seen in sections 3 and 4, two key parameters of the carrier density function are its peak value and its pulse width (bandwidth). Both of these parameters are strongly influenced by excitation profile and the other rate parameters involved in Eq. (3). A typical set of experimental values, for randomly deposited SWNT films, is mentioned in Table 1

Table 1. A Typical Set of Experimental Values for Rate Parameters in Eq. (2)

table-icon
View This Table
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[19

19. M. C. Beard, J. L. Blackburn, and M. J. Heben, “Photogenerated free carrier dynamics in metal and semiconductor single-walled carbon nanotube films,” Nano Lett. 8(12), 4238–4242 (2008). [CrossRef] [PubMed]

21

21. Y. Z. Ma, L. Valkunas, S. L. Dexheimer, S. M. Bachilo, and G. R. Fleming, “Femtosecond spectroscopy of optical excitations in single-walled carbon nanotubes: evidence for exciton-exciton annihilation,” Phys. Rev. Lett. 94(15), 157402 (2005). [CrossRef] [PubMed]

].

Figure 2 shows the influence of nabs and excitation pulse width on the peak total number of photocarriers.

As it can be seen in Fig. 2(a), the peak photocarrier density curve has a knee after which the peak n(t) falls with exponential behavior. The location of the knee is directly influenced by carrier lifetime. For example, if a reduction to 90% of the maximum n(t) is allowed in a design, based on Fig. 2(a), the maximum of allowable input pulse width is increased from 0.26 ps to 4.42 ps with a decrease of carrier decay rate from 3.19 ps−1 to 0.03 ps−1. Care must be taken when using this graph in its lower limits, as the physics of the material excitation can change for pulse width less than 20fs range. The curves in Fig. 2(a) are likely to roll off on the left hand side as well [22

22. E. Castro-Camus, J. Lloyd-Hughes, and M. Johnston, “Three-dimensional carrier-dynamics simulation of terahertz emission from photoconductive switches,” Phys. Rev. B 71(19), 195301 (2005). [CrossRef]

,23

23. A. Gambetta, G. Galzerano, A. G. Rozhin, A. C. Ferrari, R. Ramponi, P. Laporta, and M. Marangoni, “Sub-100 fs pump-probe spectroscopy of single wall carbon nanotubes with a 100 MHz Er-fiber laser system,” Opt. Express 16(16), 11727–11734 (2008). [CrossRef] [PubMed]

]. Also, the saturation of peak n(t) in higher absorbed carrier densities is captured with Eqs. (3) and (4), as shown in Fig. 2(b). This is consistent with the experimental measurement of photocarriers reported in [19

19. M. C. Beard, J. L. Blackburn, and M. J. Heben, “Photogenerated free carrier dynamics in metal and semiconductor single-walled carbon nanotube films,” Nano Lett. 8(12), 4238–4242 (2008). [CrossRef] [PubMed]

]. The inset graph in Fig. 2(b) reveals that the variation of carrier lifetime has an exponential dependence for values less than 3 ps. The peak photocarrier density, however, enters a saturation region immediately after this value, and thus further increase of carrier lifetime will no longer have a significant contribution.

It should be further emphasized that unlike the case of CW THz photomixing where a short carrier lifetime (less than 2ps) is vital to deepen the THz photoconductivity modulation of the material in the gap, short carrier lifetime is not a necessity for THz PC switching. This is due to the pulsed nature of THz PC switching and the fact that the pulses are well distanced in time relative to carrier lifetime. In THz PC switching the THz components of the microantenna feed current are generated mainly by the initial sharp rise in the photocarrier density as seen in the inset graph of Fig. 2(a). Consequently, the smoother roll-off of photocarrier density that is affected by the carrier lifetime does not induce THz components in the current. In THz PC switching the carrier lifetime affects the peak photocarrier density as seen in the inset graph of Fig. 2(b) and the peak photocarrier density can affect the output THz power as it will be explained in the rest of this study.

3. Photocarriers conversion to photoconductivity in SWCNT film

For the case of a perfectly aligned, perfectly purified CNT film, values of mobility, localization constant, and percentage of free photocarriers are chosen within the range from Table 2 so that the conductivity is maximized. In a real case, however, parameters such as carrier lifetime, carrier mobility, electrical coupling and alignment with the applied field, etc., can be different for each CNT in the film. Therefore, a Monte Carlo (MC) integration method should be used for a more realistic result [32

32. A. Behnam and A. Ural, “Computational study of geometry-dependent resistivity scaling in single-walled carbon nanotube films,” Phys. Rev. B 75(12), 125432 (2007). [CrossRef]

]. This integration is based on Eq. (5) and is presented in Eq. (6) for qth iteration of calculation.
σphotoq(ω)=j=1Jk=1Kμjknfjke(1imωμjk/e)(1ξ1imωμjk/e).
(6)
In Eq. (6) m is the average effective mass of electrons.

The MC integration is performed by iteratively generating the initial distribution of the photocarriers. This distribution is based on a 3D probability density function with a 2D Gaussian (normal) distribution cross section and an exponential distribution along the radiation axis. This represents an illumination with Gaussian beam, and a material with Beer-Lambert absorption behavior [33

33. S. Haque, C. Marinelli, F. Udrea, and W. I. Milne, “Absorption characteristics of single wall carbon nanotubes,” NSTI Nanotech. Conference (NSTI, 2006), pp. 134–137.

]. In each iteration, the simulation bins the carriers into J × K cells along the gap (Fig. 3(a)
Fig. 3 (a) An illustration of binning process in MC calculation of conductivity in a partially aligned SWNT film. Each cell is a rectangular cuboid extending along the gap. (b) SEM image of a typical dip and slip deposition method results for s-SWNTs on a SiO2 substrate.
), applies randomly generated parameters to each cell, and does an overall summation. The outcomes of Q iterations are then averaged to give the final result.

There have been many different reports on mobility of CNTs in semiconducting SWNT samples [24

24. T. Hertel, R. Fasel, and G. Moos, “Charge-carrier dynamics in single-wall carbon nanotube bundles: a time-domain study,” Appl. Phys., A Mater. Sci. Process. 75(4), 449–465 (2002). [CrossRef]

,30

30. V. Perebeinos, J. Tersoff, and P. Avouris, “Mobility in semiconducting carbon nanotubes at finite carrier density,” Nano Lett. 6(2), 205–208 (2006). [CrossRef] [PubMed]

,31

31. T. Dürkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Lett. 4(1), 35–39 (2004). [CrossRef]

]. Based on Eq. (5), it is found that the conductivity is approximately linearly affected by the mobility at lower frequencies (f<1MHz). Here the mobility itself is assumed to be affected by alignment of CNTs with the applied field and the local carrier density of the bin ρjk as below [30

30. V. Perebeinos, J. Tersoff, and P. Avouris, “Mobility in semiconducting carbon nanotubes at finite carrier density,” Nano Lett. 6(2), 205–208 (2006). [CrossRef] [PubMed]

]:

μjk=(0.1+0.9u1)(10.99ρjkρmax)cos(15°×u2).
(7)

In Eq. (7), u1 and u2 are two independent random variables, sampled from a uniform distribution between zero and one, and mobility has units of m2/Vs. ρmax is the maximum local carrier density in the total volume. Also, the average effective mass is affected by local carrier density (mjk1(185ρjk)me1) as reported in [30

30. V. Perebeinos, J. Tersoff, and P. Avouris, “Mobility in semiconducting carbon nanotubes at finite carrier density,” Nano Lett. 6(2), 205–208 (2006). [CrossRef] [PubMed]

]. An angular deviation of almost 15° is consistent with our observation under scanning electron microscope (SEM) (Fig. 3(b)). This alignment is realizable via the slip-stick method [34

34. M. Engel, J. P. Small, M. Steiner, M. Freitag, A. A. Green, M. C. Hersam, and P. Avouris, “Thin film nanotube transistors based on self-assembled, aligned, semiconducting carbon nanotube arrays,” ACS Nano 2(12), 2445–2452 (2008). [CrossRef] [PubMed]

]. Alignment is assumed to affect the mobility so that the conductance can be approximated with simple classical formulation without concerns of CNTs directional conductance [35

35. J. Hone, M. C. Llaguno, N. M. Nemes, A. T. Johnson, J. E. Fischer, D. A. Walters, M. J. Casavant, J. Schmidt, and R. E. Smalley, “Electrical and thermal transport properties of magnetically aligned single wall carbon nanotube films,” Appl. Phys. Lett. 77(5), 666–669 (2000). [CrossRef]

] (section 4).

Figure 4
Fig. 4 Photoconductivity for three cases of: perfectly aligned and purified, partially aligned and purified, and randomly deposited and partially purified s-SWNT.
depicts the peak photoconductance, so each point is the peak of a time varying photoconductance that has the same temporal profile as n(t) in the inset graph of Fig. 2(a).

The lower limit (blue dotted line) is based on the random alignment and experimental verification in [19

19. M. C. Beard, J. L. Blackburn, and M. J. Heben, “Photogenerated free carrier dynamics in metal and semiconductor single-walled carbon nanotube films,” Nano Lett. 8(12), 4238–4242 (2008). [CrossRef] [PubMed]

]. The higher limit shown with dotted red line is based on the experimental semiconductor SWNT mobility measurement of 10 m2/Vs reported in [30

30. V. Perebeinos, J. Tersoff, and P. Avouris, “Mobility in semiconducting carbon nanotubes at finite carrier density,” Nano Lett. 6(2), 205–208 (2006). [CrossRef] [PubMed]

,31

31. T. Dürkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Lett. 4(1), 35–39 (2004). [CrossRef]

]. The MC integration result agrees closely with the DS model with mobility of 0.55 m2/Vs for lower carrier concentrations. The inset graph in Fig. 4 shows a close-up of the extra photoconductivity saturation effect due to mobility reduction with carrier density increase. This saturation is only due to phonon scattering effects, although further defects can also cause such behavior [30

30. V. Perebeinos, J. Tersoff, and P. Avouris, “Mobility in semiconducting carbon nanotubes at finite carrier density,” Nano Lett. 6(2), 205–208 (2006). [CrossRef] [PubMed]

].

4. Modeling the photoconductance effect on output power

For both PC switches and THz photomixers the last step of the analysis that connects the input power to the output THz power is the photoconductance, which appears in the equivalent circuit model (Fig. 5
Fig. 5 Schematic of the circuit model for the PC switch with s-SWNT in the gap. VB is the DC bias voltage, RL is the antenna resistance,Vc is the contact voltage, Rc and cʹ are contact resistance and capacitance, and C is the capacitance of the gap.
).

Based on the equivalent circuit model in Fig. 5, the voltage V across both the time varying conductance G(t) and the contacts is given by the solution to the following set of coupled, first-order inhomogeneous linear differential equations;
dVdt+(1+RLG(t))RLCVVB+2RLG(t)VCRLC=0,    with          V(0)=(2RC+G1(0))VB2RC+G1(0)+RL,dVCdt+(1+2RCG(t)cRC)VCG(t)cV=0,  with     VC(0)=RCVB2RC+G1(0)+RL.
(8)
The parameters in this formula are explained in Fig. 5. Unlike THz photomixers, where two lasers are beating together and the circuit model can be simplified into steady state sinusoidal form [6

6. J. Y. Suen, W. Li, Z. D. Taylor, and E. R. Brown, “Characterization and modeling of a terahertz photoconductive switch,” Appl. Phys. Lett. 96(14), 141103 (2010). [CrossRef]

,7

7. E. R. Brown, F. W. Smith, and K. A. McIntosh, “Coherent millimeter-wave generation by heterodyne conversion in low-temperature-grown GaAs photoconductors,” J. Appl. Phys. 73(3), 1480 (1993). [CrossRef]

], for a PC switch such simplification is not possible. Contact resistances cannot be ignored as in LT-GaAs model [7

7. E. R. Brown, F. W. Smith, and K. A. McIntosh, “Coherent millimeter-wave generation by heterodyne conversion in low-temperature-grown GaAs photoconductors,” J. Appl. Phys. 73(3), 1480 (1993). [CrossRef]

]. Contact resistance values can vary significantly, depending on the electrode material and fabrication method; this is a widely studied topic for CNTs in a gap [38

38. Y.-C. Tseng and J. Bokor, “Characterization of the junction capacitance of metal-semiconductor carbon nanotube Schottky contacts,” Appl. Phys. Lett. 96(1), 013103 (2010). [CrossRef]

,39

39. S. H. Han, S. H. Lee, J. H. Hur, J. Jang, Y.-B. Park, G. Irvin, and P. Drzaic, “Contact resistance between Au and solution-processed CNT,” Solid-State Electron. 54(5), 586–589 (2010). [CrossRef]

]. It is very likely that in higher frequencies a shunt capacitance dominates the contact behavior. This capacitance models the portion of CNTs that do not reach the contact and thus couple capacitively [38

38. Y.-C. Tseng and J. Bokor, “Characterization of the junction capacitance of metal-semiconductor carbon nanotube Schottky contacts,” Appl. Phys. Lett. 96(1), 013103 (2010). [CrossRef]

40

40. M. G. Kang, J. H. Lim, S. H. Hong, D. J. Lee, S. W. Hwang, D. Whang, J. S. Hwang, and D. Ahn, “Microwave characterization of a single wall carbon nanotube bundle,” Jpn. J. Appl. Phys. 47(6), 4965–4968 (2008). [CrossRef]

]. Considering the hypergeometric behavior embedded in conductivity and thus conductance, the value of V(t) cannot be expressed explicitly. Here, we have used the numerical Euler method with 10 fs step sizes to estimate V(t).

The output THz power can be calculated directly from the voltage V(t) and the Kirchoff voltage law in the main loop of the circuit as:

PTHz(t)=(VBV(t))2(VBV(0))2RL.
(9)

Figure 6 reveals that GaBiAs and LT-GaAs PC switches perform better than randomly aligned and partially purified CNTs; the case that we have chosen as lower limit condition (blue dotted line in Fig. 6). Improvement in alignment and purification boosts the CNT THz power to around 103µW, calculated based on MC results for photoconductivity; the output power is then limited by the saturation effect induced by high carrier density and circuit dynamics at around 561µW in 36.6mW of input power. Figure 6 shows that curves for higher conductivity are distorted by circuit dynamics, and as a result the power reaches saturation for lower carrier densities compared to the conductivity in Fig. 4. This is the direct result of the nonlinear relation between these two parameters. Although SWNT films are well known for high thermal conductance [45

45. K. Kordás, G. Tóth, P. Moilanen, M. Kumpumäki, J. Vähäkangas, A. Uusimäki, R. Vajtai, and P. M. Ajayan, “Chip cooling with integrated carbon nanotube microfin architectures,” Appl. Phys. Lett. 90(12), 123105 (2007). [CrossRef]

], it must be considered that the experimental validation of this increase in THz power is also subject to the thermal stability of the device.

Based on Fig. 7(a), PTHz has a maximum in certain value of RL. Increasing RL widens the pulse and thus reduces the bandwidth. This suggests that increase of RL might be desired up to a certain limit (here 500Ω) with trade off for bandwidth of the emitted THz pulse. Figure 7(b) shows the exponential decrease of power with increase in contact resistance. This exponential decrease is the result of voltage drop on the contacts, and also, it depends on the relative value of contact capacitance and G0. The dependence of PTHz on contact capacitance can be of interest for cases in which a capacitive coupling mechanism is unavoidable due to difficulties in fabrication of low resistance contacts [38

38. Y.-C. Tseng and J. Bokor, “Characterization of the junction capacitance of metal-semiconductor carbon nanotube Schottky contacts,” Appl. Phys. Lett. 96(1), 013103 (2010). [CrossRef]

41

41. Z. Yao, C. L. Kane, and C. Dekker, “High-field electrical transport in single-wall carbon nanotubes,” Phys. Rev. Lett. 84(13), 2941–2944 (2000). [CrossRef] [PubMed]

]. This can be the case when the gap is wider than the average length of CNTs in the film. It is found that with variation of contact capacitance, the power changes between two constant values with an exponential transition (Fig. 7(c)). These two lower level and higher level powers are reached when cʹ impedance is considered a short circuit or open circuit compared to Rc. Additionally, it is seen that the higher value of cʹ decreases the bandwidth; this is highlighted with dashed orange line in Fig. 7(c). Such increase of the pulse bandwidth is expected based on circuit theory, and the low-pass behavior of a capacitive contact. The gap capacitance C can also play a similar role. It is seen that by increasing the gap capacitance, the bandwidth and amplitude of the output THz power is dramatically reduced (Fig. 7(d)). This can be a significant factor in the design of the PC switch structure, sinceC=εfilmyz/x, whereεfilm is the average permittivity of the CNT film placed in the gap.

The photoconductance (Gphoto) and dark conductance (G0) are also affected by the geometry of the gap. The variation of these two parameters also affects the terahertz power. As can be seen in Figs. 7(e) and 7(f), the power has a non-monotonic behavior with variations of G0, while it increases exponentially with initial increase in Gphoto and then saturates at higher values. The variation of Gphoto in its typical µΩ−1 range is too small to have a significant effect on the output pulse bandwidth.

Finally, it is worthwhile to mention that the circuit dynamics presented here can also be applied to the photomixing case in which G(t) is changed in Eq. (8) with a sinusoidal function of time.

6. Conclusion

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7.

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11.

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13.

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19.

M. C. Beard, J. L. Blackburn, and M. J. Heben, “Photogenerated free carrier dynamics in metal and semiconductor single-walled carbon nanotube films,” Nano Lett. 8(12), 4238–4242 (2008). [CrossRef] [PubMed]

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21.

Y. Z. Ma, L. Valkunas, S. L. Dexheimer, S. M. Bachilo, and G. R. Fleming, “Femtosecond spectroscopy of optical excitations in single-walled carbon nanotubes: evidence for exciton-exciton annihilation,” Phys. Rev. Lett. 94(15), 157402 (2005). [CrossRef] [PubMed]

22.

E. Castro-Camus, J. Lloyd-Hughes, and M. Johnston, “Three-dimensional carrier-dynamics simulation of terahertz emission from photoconductive switches,” Phys. Rev. B 71(19), 195301 (2005). [CrossRef]

23.

A. Gambetta, G. Galzerano, A. G. Rozhin, A. C. Ferrari, R. Ramponi, P. Laporta, and M. Marangoni, “Sub-100 fs pump-probe spectroscopy of single wall carbon nanotubes with a 100 MHz Er-fiber laser system,” Opt. Express 16(16), 11727–11734 (2008). [CrossRef] [PubMed]

24.

T. Hertel, R. Fasel, and G. Moos, “Charge-carrier dynamics in single-wall carbon nanotube bundles: a time-domain study,” Appl. Phys., A Mater. Sci. Process. 75(4), 449–465 (2002). [CrossRef]

25.

P. L. McEuen, M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, and L. Balents, “Luttinger-liquid behavior in carbon nanotubes,” Nature 397(6720), 598–601 (1999). [CrossRef]

26.

T. Dürkop, B. M. Kim, and M. S. Fuhrer, “Properties and applications of high-mobility semiconducting nanotubes,” J. Phys. Condens. Matter 16(18), R553–R580 (2004). [CrossRef]

27.

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

28.

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

29.

M. Tsai, C. Yu, C. Yang, N. Tai, T. Perng, C. Tu, Z. Khan, Y. Liao, and C. Chi, “Electrical transport properties of individual disordered multiwalled carbon nanotubes,” Appl. Phys. Lett. 89(19), 192115 (2006). [CrossRef]

30.

V. Perebeinos, J. Tersoff, and P. Avouris, “Mobility in semiconducting carbon nanotubes at finite carrier density,” Nano Lett. 6(2), 205–208 (2006). [CrossRef] [PubMed]

31.

T. Dürkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Lett. 4(1), 35–39 (2004). [CrossRef]

32.

A. Behnam and A. Ural, “Computational study of geometry-dependent resistivity scaling in single-walled carbon nanotube films,” Phys. Rev. B 75(12), 125432 (2007). [CrossRef]

33.

S. Haque, C. Marinelli, F. Udrea, and W. I. Milne, “Absorption characteristics of single wall carbon nanotubes,” NSTI Nanotech. Conference (NSTI, 2006), pp. 134–137.

34.

M. Engel, J. P. Small, M. Steiner, M. Freitag, A. A. Green, M. C. Hersam, and P. Avouris, “Thin film nanotube transistors based on self-assembled, aligned, semiconducting carbon nanotube arrays,” ACS Nano 2(12), 2445–2452 (2008). [CrossRef] [PubMed]

35.

J. Hone, M. C. Llaguno, N. M. Nemes, A. T. Johnson, J. E. Fischer, D. A. Walters, M. J. Casavant, J. Schmidt, and R. E. Smalley, “Electrical and thermal transport properties of magnetically aligned single wall carbon nanotube films,” Appl. Phys. Lett. 77(5), 666–669 (2000). [CrossRef]

36.

S. Verghese, K. A. McIntosh, and E. R. Brown, “Highly tunable fiber-coupled photomixers with coherent terahertz output power,” IEEE Trans. Microw. Theory Tech. 45(8), 1301–1309 (1997). [CrossRef]

37.

S. Duffy, S. Verghese, K. A. McIntosh, A. Jackson, A. C. Gossard, and S. Matsuura, “Accurate modeling of dual dipole and slot elements used with photomixers for coherent terahertz output power,” IEEE Trans. Microw. Theory Tech. 49(6), 1032–1038 (2001). [CrossRef]

38.

Y.-C. Tseng and J. Bokor, “Characterization of the junction capacitance of metal-semiconductor carbon nanotube Schottky contacts,” Appl. Phys. Lett. 96(1), 013103 (2010). [CrossRef]

39.

S. H. Han, S. H. Lee, J. H. Hur, J. Jang, Y.-B. Park, G. Irvin, and P. Drzaic, “Contact resistance between Au and solution-processed CNT,” Solid-State Electron. 54(5), 586–589 (2010). [CrossRef]

40.

M. G. Kang, J. H. Lim, S. H. Hong, D. J. Lee, S. W. Hwang, D. Whang, J. S. Hwang, and D. Ahn, “Microwave characterization of a single wall carbon nanotube bundle,” Jpn. J. Appl. Phys. 47(6), 4965–4968 (2008). [CrossRef]

41.

Z. Yao, C. L. Kane, and C. Dekker, “High-field electrical transport in single-wall carbon nanotubes,” Phys. Rev. Lett. 84(13), 2941–2944 (2000). [CrossRef] [PubMed]

42.

V. Pačebutas, A. Biciūnas, S. Balakauskas, A. Krotkus, G. Andriukaitis, D. Lorenc, A. Pugzlys, and A. Baltuska, “Terahertz time-domain-spectroscopy system based on femtosecond Yb:fiber laser and GaBiAs photoconducting components,” Appl. Phys. Lett. 97(3), 031111 (2010). [CrossRef]

43.

M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, “Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs,” Appl. Opt. 36(30), 7853–7859 (1997). [CrossRef] [PubMed]

44.

P. Kordoš, M. Marso, and M. Mikulics, “Performance optimization of GaAs-based photomixers as sources of THz radiation,” Appl. Phys., A Mater. Sci. Process. 87(3), 563–567 (2007). [CrossRef]

45.

K. Kordás, G. Tóth, P. Moilanen, M. Kumpumäki, J. Vähäkangas, A. Uusimäki, R. Vajtai, and P. M. Ajayan, “Chip cooling with integrated carbon nanotube microfin architectures,” Appl. Phys. Lett. 90(12), 123105 (2007). [CrossRef]

46.

H. Pahlevaninezhad, B. Heshmat, and T. E. Darcie, “Advances in THz technology,” IEEE Photonics J. 3, 307–310 (2011).

OCIS Codes
(230.6080) Optical devices : Sources
(040.2235) Detectors : Far infrared or terahertz
(160.4236) Materials : Nanomaterials

ToC Category:
Materials

History
Original Manuscript: April 8, 2011
Revised Manuscript: June 23, 2011
Manuscript Accepted: July 9, 2011
Published: July 21, 2011

Citation
Barmak Heshmat, Hamid Pahlevaninezhad, Matthew Craig Beard, Chris Papadopoulos, and Thomas Edward Darcie, "Single-walled carbon nanotubes as base material for THz photoconductive switching: a theoretical study from input power to output THz emission," Opt. Express 19, 15077-15089 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15077


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  23. A. Gambetta, G. Galzerano, A. G. Rozhin, A. C. Ferrari, R. Ramponi, P. Laporta, and M. Marangoni, “Sub-100 fs pump-probe spectroscopy of single wall carbon nanotubes with a 100 MHz Er-fiber laser system,” Opt. Express 16(16), 11727–11734 (2008). [CrossRef] [PubMed]
  24. T. Hertel, R. Fasel, and G. Moos, “Charge-carrier dynamics in single-wall carbon nanotube bundles: a time-domain study,” Appl. Phys., A Mater. Sci. Process. 75(4), 449–465 (2002). [CrossRef]
  25. P. L. McEuen, M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, and L. Balents, “Luttinger-liquid behavior in carbon nanotubes,” Nature 397(6720), 598–601 (1999). [CrossRef]
  26. T. Dürkop, B. M. Kim, and M. S. Fuhrer, “Properties and applications of high-mobility semiconducting nanotubes,” J. Phys. Condens. Matter 16(18), R553–R580 (2004). [CrossRef]
  27. N. V. Smith, “Classical generalization of the drude formula for the optical conductivity,” Phys. Rev. B 64(15), 155106 (2001). [CrossRef]
  28. P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston, and L. M. Herz, “Transient terahertz conductivity of GaAs nanowires,” Nano Lett. 7(7), 2162–2165 (2007). [CrossRef]
  29. M. Tsai, C. Yu, C. Yang, N. Tai, T. Perng, C. Tu, Z. Khan, Y. Liao, and C. Chi, “Electrical transport properties of individual disordered multiwalled carbon nanotubes,” Appl. Phys. Lett. 89(19), 192115 (2006). [CrossRef]
  30. V. Perebeinos, J. Tersoff, and P. Avouris, “Mobility in semiconducting carbon nanotubes at finite carrier density,” Nano Lett. 6(2), 205–208 (2006). [CrossRef] [PubMed]
  31. T. Dürkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Lett. 4(1), 35–39 (2004). [CrossRef]
  32. A. Behnam and A. Ural, “Computational study of geometry-dependent resistivity scaling in single-walled carbon nanotube films,” Phys. Rev. B 75(12), 125432 (2007). [CrossRef]
  33. S. Haque, C. Marinelli, F. Udrea, and W. I. Milne, “Absorption characteristics of single wall carbon nanotubes,” NSTI Nanotech. Conference (NSTI, 2006), pp. 134–137.
  34. M. Engel, J. P. Small, M. Steiner, M. Freitag, A. A. Green, M. C. Hersam, and P. Avouris, “Thin film nanotube transistors based on self-assembled, aligned, semiconducting carbon nanotube arrays,” ACS Nano 2(12), 2445–2452 (2008). [CrossRef] [PubMed]
  35. J. Hone, M. C. Llaguno, N. M. Nemes, A. T. Johnson, J. E. Fischer, D. A. Walters, M. J. Casavant, J. Schmidt, and R. E. Smalley, “Electrical and thermal transport properties of magnetically aligned single wall carbon nanotube films,” Appl. Phys. Lett. 77(5), 666–669 (2000). [CrossRef]
  36. S. Verghese, K. A. McIntosh, and E. R. Brown, “Highly tunable fiber-coupled photomixers with coherent terahertz output power,” IEEE Trans. Microw. Theory Tech. 45(8), 1301–1309 (1997). [CrossRef]
  37. S. Duffy, S. Verghese, K. A. McIntosh, A. Jackson, A. C. Gossard, and S. Matsuura, “Accurate modeling of dual dipole and slot elements used with photomixers for coherent terahertz output power,” IEEE Trans. Microw. Theory Tech. 49(6), 1032–1038 (2001). [CrossRef]
  38. Y.-C. Tseng and J. Bokor, “Characterization of the junction capacitance of metal-semiconductor carbon nanotube Schottky contacts,” Appl. Phys. Lett. 96(1), 013103 (2010). [CrossRef]
  39. S. H. Han, S. H. Lee, J. H. Hur, J. Jang, Y.-B. Park, G. Irvin, and P. Drzaic, “Contact resistance between Au and solution-processed CNT,” Solid-State Electron. 54(5), 586–589 (2010). [CrossRef]
  40. M. G. Kang, J. H. Lim, S. H. Hong, D. J. Lee, S. W. Hwang, D. Whang, J. S. Hwang, and D. Ahn, “Microwave characterization of a single wall carbon nanotube bundle,” Jpn. J. Appl. Phys. 47(6), 4965–4968 (2008). [CrossRef]
  41. Z. Yao, C. L. Kane, and C. Dekker, “High-field electrical transport in single-wall carbon nanotubes,” Phys. Rev. Lett. 84(13), 2941–2944 (2000). [CrossRef] [PubMed]
  42. V. Pačebutas, A. Biciūnas, S. Balakauskas, A. Krotkus, G. Andriukaitis, D. Lorenc, A. Pugzlys, and A. Baltuska, “Terahertz time-domain-spectroscopy system based on femtosecond Yb:fiber laser and GaBiAs photoconducting components,” Appl. Phys. Lett. 97(3), 031111 (2010). [CrossRef]
  43. M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, “Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs,” Appl. Opt. 36(30), 7853–7859 (1997). [CrossRef] [PubMed]
  44. P. Kordoš, M. Marso, and M. Mikulics, “Performance optimization of GaAs-based photomixers as sources of THz radiation,” Appl. Phys., A Mater. Sci. Process. 87(3), 563–567 (2007). [CrossRef]
  45. K. Kordás, G. Tóth, P. Moilanen, M. Kumpumäki, J. Vähäkangas, A. Uusimäki, R. Vajtai, and P. M. Ajayan, “Chip cooling with integrated carbon nanotube microfin architectures,” Appl. Phys. Lett. 90(12), 123105 (2007). [CrossRef]
  46. H. Pahlevaninezhad, B. Heshmat, and T. E. Darcie, “Advances in THz technology,” IEEE Photonics J. 3, 307–310 (2011).

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