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

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  4. V. Pačebutas, A. Bičiūnas, S. Balakauskas, A. Krotkus, G. Andriukaitis, D. Lorenc, A. Pugžlys, and A. Baltuška, “Terahertz time-domain-spectroscopy system based on femtosecond Yb:fiber laser and GaBiAs photoconducting components,” Appl. Phys. Lett. 97(3), 031111 (2010).
    [CrossRef]
  5. J. F. O’Hara, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Enhanced terahertz detection via ErAs:GaAs nanoisland superlattices,” Appl. Phys. Lett. 88(25), 251119 (2006).
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    [CrossRef]
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    [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]
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  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]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2011 (1)

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

2010 (6)

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]

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

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]

V. Ryzhii, A. A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107(5), 054505 (2010).
[CrossRef]

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]

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]

2008 (6)

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]

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]

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]

A. Serra, D. Manno, E. Filippo, A. Tepore, M. Letizia Terranova, S. Orlanducci, and M. Rossi, “Photoconductivity of packed homotype bundles formed by aligned single-walled carbon nanotubes,” Nano Lett. 8(3), 968–971 (2008).
[CrossRef] [PubMed]

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]

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]

2007 (4)

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]

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]

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]

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]

2006 (5)

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]

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]

J. F. O’Hara, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Enhanced terahertz detection via ErAs:GaAs nanoisland superlattices,” Appl. Phys. Lett. 88(25), 251119 (2006).
[CrossRef]

S. Lu and B. Panchapakesan, “Photoconductivity in single wall carbon nanotube sheets,” Nanotechnology 17(8), 1843–1850 (2006).
[CrossRef]

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]

2005 (6)

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

X. Qiu, M. Freitag, V. Perebeinos, and P. Avouris, “Photoconductivity spectra of single-carbon nanotubes: implications on the nature of their excited States,” Nano Lett. 5(4), 749–752 (2005).
[CrossRef] [PubMed]

S. Ono, H. Murakami, A. Quema, G. Diwa, N. Sarukura, R. Nagasaka, Y. Ichikawa, H. Ogino, E. Ohshima, A. Yoshikawa, and T. Fukuda, “Generation of terahertz radiation using zinc oxide as photoconductive material excited by ultraviolet pulses,” Appl. Phys. Lett. 87(26), 261112 (2005).
[CrossRef]

S. Reich, M. Dworzak, A. Hoffmann, C. Thomsen, and M. S. Strano, “Excited-state carrier lifetime in single-walled carbon nanotubes,” Phys. Rev. B 71(3), 033402 (2005).
[CrossRef]

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]

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]

2004 (4)

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]

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]

T. D. Dragoman and M. Dragoman, “Terahertz fields and applications,” Prog. Quantum Electron. 28(1), 1–66 (2004).
[CrossRef]

A. Fujiwara, Y. Matsuoka, Y. Matsuoka, H. Suematsu, N. Ogawa, K. Miyano, H. Kataura, Y. Maniwa, S. Suzuki, and Y. Achiba, “Photoconductivity of single-wall carbon nanotube films,” Carbon 42(5-6), 919–922 (2004).
[CrossRef]

2003 (1)

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]

2002 (1)

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]

2001 (2)

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

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]

2000 (2)

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]

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]

1999 (1)

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]

1997 (2)

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]

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]

1993 (1)

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]

1983 (1)

D. Auston and P. Smith, “Generation and detection of millimeter waves by picosecond photoconductivity,” Appl. Phys. Lett. 43(7), 631 (1983).
[CrossRef]

Achiba, Y.

A. Fujiwara, Y. Matsuoka, Y. Matsuoka, H. Suematsu, N. Ogawa, K. Miyano, H. Kataura, Y. Maniwa, S. Suzuki, and Y. Achiba, “Photoconductivity of single-wall carbon nanotube films,” Carbon 42(5-6), 919–922 (2004).
[CrossRef]

Ahn, D.

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]

Ajayan, P. M.

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]

Andriukaitis, G.

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

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]

Auston, D.

D. Auston and P. Smith, “Generation and detection of millimeter waves by picosecond photoconductivity,” Appl. Phys. Lett. 43(7), 631 (1983).
[CrossRef]

Averitt, R. D.

J. F. O’Hara, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Enhanced terahertz detection via ErAs:GaAs nanoisland superlattices,” Appl. Phys. Lett. 88(25), 251119 (2006).
[CrossRef]

Avouris, P.

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]

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]

X. Qiu, M. Freitag, V. Perebeinos, and P. Avouris, “Photoconductivity spectra of single-carbon nanotubes: implications on the nature of their excited States,” Nano Lett. 5(4), 749–752 (2005).
[CrossRef] [PubMed]

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]

Bachilo, S. M.

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]

Balakauskas, S.

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]

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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).
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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).
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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).
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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).
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Yu, C.

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).
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J. F. O’Hara, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Enhanced terahertz detection via ErAs:GaAs nanoisland superlattices,” Appl. Phys. Lett. 88(25), 251119 (2006).
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ACS Nano (1)

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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).
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S. Ono, H. Murakami, A. Quema, G. Diwa, N. Sarukura, R. Nagasaka, Y. Ichikawa, H. Ogino, E. Ohshima, A. Yoshikawa, and T. Fukuda, “Generation of terahertz radiation using zinc oxide as photoconductive material excited by ultraviolet pulses,” Appl. Phys. Lett. 87(26), 261112 (2005).
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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).
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Carbon (1)

A. Fujiwara, Y. Matsuoka, Y. Matsuoka, H. Suematsu, N. Ogawa, K. Miyano, H. Kataura, Y. Maniwa, S. Suzuki, and Y. Achiba, “Photoconductivity of single-wall carbon nanotube films,” Carbon 42(5-6), 919–922 (2004).
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IEEE Photonics J. (1)

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S. Chuang, Physics of Optoelectronic Devices (J. Wiley, 1995), Chap. 2.

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Figures (7)

Fig. 1
Fig. 1

(a) Illustration of optical excitation of a THz photoconductive switch that has a center fed dipole antenna structure. (b) A PC switch made on a thin SiO2 oxide layer grown on a Si wafer. The gap is filled with aligned SWNTs and the antenna pattern is fabricated similar to conventional PC switches through common lithography processes (c) Block diagram of different steps of the analysis that links input laser excitation power and output THz emitted power.

Fig. 2
Fig. 2

(a) Peak total photocarrier density as a function of excitation pulse duration and carrier decay rate, γ d (carrier life time, τ = 1 / γ d ). The inset graph depicts the carrier density as a function of time (optical excitation pulse duration = 100fs, nabs = 1019 cm−3 and decay rate = 1.23 ps−1). (b) Peak total photocarrier density as a function of nabs. The inset graph shows the behavior of the same function within allowable carrier life time of SWNT.

Fig. 3
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.

Fig. 4
Fig. 4

Photoconductivity for three cases of: perfectly aligned and purified, partially aligned and purified, and randomly deposited and partially purified s-SWNT.

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.

Fig. 6
Fig. 6

Emitted average THz power vs average input excitation power. CNT curves are based on the conductivity values in Fig. 4. The GaBiAs PC switch and GaAs based photomixer output powers are inserted in 10, 20 and 30 mW of excitation power for comparison [4244].

Fig. 7
Fig. 7

The dynamics of output THz power with: (a) antenna resistance, RL (b) CNT to metal plate contance resistance, Rc (c) contance capacitace, cʹ (d) gap capacitance, C (e) photoconductance, Gphoto (f) dark conductance, G0 .

Tables (2)

Tables Icon

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

Tables Icon

Table 2 Previously Reported Values for Drude Smith Modeling of CNT Films

Equations (9)

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n a b s η ( ν ) 0 T p i ( t ) d t h ν V ,
d n e ( t ) d t = γ E E n e 2 ( t ) γ C C n e ( t ) , n e ( 0 ) = n a b s ; d n ( t ) d t = γ C C n e ( t ) γ d n ( t ) , n ( 0 ) = 0.
n ( t ) = γ C C 2 [ k 2 γ C C 2 F 2 1 ( 1 , γ d γ C C , 1 + γ d γ C C , e γ C C ( t + k 1 ) γ E E ) γ E E γ d ] ,
        k 1 = ln ( γ E E + γ C C / n a b s ) γ C C ,             and       k 2 = γ C C 2 F 2 1 ( 1 , γ d γ C C , 1 + γ d γ C C , e γ C C × k 1 γ E E ) γ E E γ d .
σ p h o t o ( ω ) = μ n f e ( 1 i ω τ s ) ( 1 ξ 1 i ω τ s ) + i μ ( n n f ) e ω τ s ( ω 2 ω l 2 i ω γ l ) .
σ p h o t o q ( ω ) = j = 1 J k = 1 K μ j k n f j k e ( 1 i m ω μ j k / e ) ( 1 ξ 1 i m ω μ j k / e ) .
μ j k = ( 0.1 + 0.9 u 1 ) ( 1 0.99 ρ j k ρ max ) cos ( 15 ° × u 2 ) .
d V d t + ( 1 + R L G ( t ) ) R L C V V B + 2 R L G ( t ) V C R L C = 0 ,     with           V ( 0 ) = ( 2 R C + G 1 ( 0 ) ) V B 2 R C + G 1 ( 0 ) + R L , d V C d t + ( 1 + 2 R C G ( t ) c R C ) V C G ( t ) c V = 0 ,   with       V C ( 0 ) = R C V B 2 R C + G 1 ( 0 ) + R L .
P T H z ( t ) = ( V B V ( t ) ) 2 ( V B V ( 0 ) ) 2 R L .

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