Despite an evermore complete plethora of complex domain-specific semiempirical models, no succinct recipe for large-scale carbon nanotube electromechanical systems design has been formulated. To combine the benefits of these highly sensitive miniaturized mechanical sensors with the vast functionalities available in electronics, we identify a reduced key parameter set of carbon nanotube properties, nanoelectromechanical system design, and operation that steers the sensor’s performance towards system applications, based on open- and closed-loop topologies. Suspended single-walled carbon nanotubes are reviewed in terms of their electromechanical properties with the objective of evaluating orders of magnitude of the electrical actuation and detection mechanisms. Open-loop time-averaging and 1ω or 2ω mixing methods are completed by a new 4ω actuation and detection technique. A discussion on their extension to closed-loop topologies and system applications concludes the analysis, covering signal-to-noise ratio, and the capability to spectrally isolate the motional information from parasitical feedthrough by contemporary electronic read-out techniques. 1. Introduction Since their discovery [1] and tremendous boost in popularity two decades ago [2], carbon nanotubes (CNTs) incited researchers from various domains to investigate, among others, their electrical and mechanical properties. Their high integrity, quality factor, and small dimensions are white hope for the single-walled carbon nanotubes’ (SWNTs) advance to applications, such as electromechanical resonators for RF transmission and reception, voltage-controlled oscillators, or single molecule weighing [3]. First models emerged and kept refining up to reach an impressive complexity, sometimes beyond the scope of circuit design, that generally prefers to trade model complexity for simplicity and clarity. To date, the library of models that describe in detail partial CNT behaviour under specific conditions has reached a critical volume. Focusing on strictly relevant parameters is not a trivial task for nanoelectromechanical system (NEMS) designers anymore. This is an unfortunate fact, when one considers that the relatively low device yield and rare occasions to observe the desired phenomena, already protract the CNT-NEMS’ advancement to system-level industrial applications. In this scope, our work reviews the state-of-the-art CNT-NEMS devices from a system-level point of view and draws clear guidelines on CNT parameter selection and device biasing to foster the CNT’s operation as a mechanical component
References
[1]
L. Radushkevich and V. Lukyanovich, “About the structure of carbon formed by thermal decomposition of carbon monoxide on iron substrate,” Zhurnal Fizicheskoi Khimii, vol. 26, pp. 88–95, 1952.
[2]
S. Iijima, “Helical microtubules of graphitic carbon,” Nature, vol. 354, no. 6348, pp. 56–58, 1991.
[3]
C. Kauth, M. Pastre, and M. Kayal, “On-chip mass sensing at the physical limits of nanoelectromechanical systems,” in Proceedings of the Advances in Sensors and Interfaces, pp. 131–135, Bari, Italy, June 2013.
[4]
H. Chandrahalim, C. I. Roman, and C. Hierold, “Analytic modeling and piezoresistive detection theory of acoustic resonances in carbon nanotubes,” in Proceedings of the 10th IEEE Conference on Nanotechnology, (NANO '10), pp. 778–781, Seoul, Republic of Korea, August 2010.
[5]
V. Sazonova, Y. Yalsh, I. üstünel, D. Roundy, T. A. Arlas, and P. L. McEuen, “A tunable carbon nanotube electrochemical oscillator,” Nature, vol. 431, no. 7006, pp. 284–287, 2004.
[6]
H. B. Peng, C. W. Chang, S. Aloni, T. D. Yuzvinsky, and A. Zettl, “Ultrahigh frequency nanotube resonators,” Physical Review Letters, vol. 97, no. 8, Article ID 087203, 2006.
[7]
B. Peng, L. Ding, and Z. Guo, “Resonant modelling of two types of tunable carbon nanotube electromechanical oscillators,” Micro and Nano Letters, vol. 5, no. 6, pp. 365–369, 2010.
[8]
M. Muoth, S. W. Lee, and C. Hierold, “Platform for strainable, TEM-compatible, MEMS-embedded carbon nanotube transistors,” in Proceedings of the 24th IEEE International Conference on Micro Electromechanical Systems (MEMS '11), pp. 83–86, Cancún, Mexico, January 2011.
[9]
S. J. Tans, A. R. M. Verschueren, and C. Dekker, “Room-temperature transistor based on a single carbon nanotube,” Nature, vol. 393, no. 6680, pp. 49–52, 1998.
[10]
P. L. McEuen, M. S. Fuhrer, and H. Park, “Single-walled carbon nanotube electronics,” IEEE Transactions on Nanotechnology, vol. 1, no. 1, pp. 78–84, 2002.
[11]
A. Javey, J. Guo, Q. Wang, M. Lundstrom, and H. Dai, “Ballistic carbon nanotube field-effect transistors,” Nature, vol. 424, no. 6949, pp. 654–657, 2003.
[12]
J. Chaste, L. Lechner, P. Morfin et al., “Single carbon nanotube transistor at GHz frequency,” Nano Letters, vol. 8, no. 2, pp. 525–528, 2008.
[13]
P. Burke, “An rf circuit model for carbon nanotubes,” in Proceedings of the 2nd IEEE-NANO Conference, pp. 393–396, 2002.
[14]
K. Koziol, C. Ducati, and A. H. Windle, “Carbon nanotubes with catalyst controlled chiral angle,” Chemistry of Materials, vol. 22, no. 17, pp. 4904–4911, 2010.
[15]
H. Guo, Z. Bo, P. Banghua et al., “Direct growth of semiconducting single-walled carbon nanotube array,” Journal of the American Chemical Society, vol. 131, no. 41, pp. 14642–14643, 2009.
[16]
S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejón, “Tight-binding description of graphene,” Physical Review B, vol. 66, no. 3, 2002.
[17]
A. Kleiner and S. Eggert, “Band gaps of primary metallic carbon nanotubes,” Physical Review B, vol. 63, no. 7, Article ID 073408, 4 pages, 2001.
[18]
W. Song, C. Jeon, Y. S. Kim et al., “Synthesis of bandgap-controlled semiconducting single-walled carbon nanotubes,” ACS Nano, vol. 4, no. 2, pp. 1012–1018, 2010.
[19]
C. L. Kane and E. J. Mele, “Size, shape, and low energy electronic structure of carbon nanotubes,” Physical Review Letters, vol. 78, no. 10, pp. 1932–1935, 1997.
[20]
S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, Cambridge, UK, May 1997.
[21]
J.-C. Charlier, X. Blase, and S. Roche, “Electronic and transport properties of nanotubes,” Reviews of Modern Physics, vol. 79, no. 2, pp. 677–732, 2007.
[22]
X. Zhou, J.-Y. Park, S. Huang, J. Liu, and P. L. McEuen, “Band structure, phonon scattering, and the performance limit of single-walled carbon nanotube transistors,” Physical Review Letters, vol. 95, no. 14, Article ID 146805, 2005.
[23]
T. Dürkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Letters, vol. 4, no. 1, pp. 35–39, 2004.
[24]
J. Tersoff, “Contact resistance of carbon nanotubes,” Applied Physics Letters, vol. 74, no. 15, pp. 2122–2124, 1999.
[25]
M. J. O’Connell, Carbon Nanotubes: Properties and Applications, Taylor & Francis, Oxford, UK, 2006.
[26]
Z. Yao, C. L. Kane, and C. Dekker, “High-field electrical transport in single-wall carbon nanotubes,” Physical Review Letters, vol. 84, no. 13, pp. 2941–2944, 2000.
[27]
A. Javey, J. Guo, D. B. Farmer et al., “Self-aligned ballistic molecular transistors and electrically parallel nanotube arrays,” Nano Letters, vol. 4, no. 7, pp. 1319–1322, 2004.
[28]
A. Javey, J. Guo, M. Paulsson et al., “High-field quasiballistic transport in short carbon nanotubes,” Physical Review Letters, vol. 92, no. 10, Article ID 106804, 2004.
[29]
F. Léonard and J. Tersoff, “Role of fermi-level pinning in nanotube schottky diodes,” Physical Review Letters, vol. 84, no. 20, pp. 4693–4696, 2000.
[30]
Z. Chen, J. Appenzeller, J. Knoch, Y.-M. Lin, and P. Avouris, “The role of metal-nanotube contact in the performance of carbon nanotube field-effect transistors,” Nano Letters, vol. 5, no. 7, pp. 1497–1502, 2005.
[31]
P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nature Nanotechnology, vol. 2, no. 10, pp. 605–615, 2007.
[32]
J. Guo, M. Lundstrom, and S. Datta, “Performance projections for ballistic carbon nanotube field-effect transistors,” Applied Physics Letters, vol. 80, no. 17, pp. 3192–3194, 2002.
[33]
M. Krüger, M. R. Buitelaar, T. Nussbaumer, C. Sch？nenberger, and L. Forró, “Electrochemical carbon nanotube field-effect transistor,” Applied Physics Letters, vol. 78, no. 9, pp. 1291–1293, 2001.
[34]
Z. Chen, D. Farmer, S. Xu, R. Gordon, P. Avouris, and J. Appenzeller, “Externally assembled gate-all-around carbon nanotube field-effect transistor,” IEEE Electron Device Letters, vol. 29, no. 2, pp. 183–185, 2008.
[35]
J. Appenzeller, J. Knoch, V. Derycke, R. Martel, S. Wind, and P. Avouris, “Field-modulated carrier transport in carbon nanotube transistors,” Physical Review Letters, vol. 89, no. 12, Article ID 126801, 4 pages, 2002.
[36]
M. Radosavljevi？, S. Heinze, J. Tersoff, and P. Avouris, “Drain voltage scaling in carbon nanotube transistors,” Applied Physics Letters, vol. 83, no. 12, pp. 2435–2437, 2003.
[37]
J. Appenzeller, M. Radosavljevi？, J. Knoch, and P. Avouris, “Tunneling versus thermionic emission in one-dimensional semiconductors,” Physical Review Letters, vol. 92, no. 4, 4 pages, 2004.
[38]
J. Nyg？rd, D. H. Cobden, M. Bockrath, P. L. McEuen, and P. E. Lindelof, “Electrical transport measurements on single-walled carbon nanotubes,” Applied Physics A, vol. 69, no. 3, pp. 297–304, 1999.
[39]
Y.-M. Lin, J. Appenzeller, and P. Avouris, “Ambipolar-to-unipolar conversion of carbon nanotube transistors by gate structure engineering,” Nano Letters, vol. 4, no. 5, pp. 947–950, 2004.
[40]
S. Rosenblatt, H. Lin, V. Sazonova, S. Tiwari, and P. L. McEuen, “Mixing at 50？GHz using a single-walled carbon nanotube transistor,” Applied Physics Letters, vol. 87, no. 15, Article ID 153111, 3 pages, 2005.
[41]
P. J. Burke, “AC performance of nanoelectronics: towards a ballistic THz nanotube transistor,” Solid-State Electronics, vol. 48, no. 10-11, pp. 1981–1986, 2004.
[42]
M. Dequesnes, Z. Tang, and N. R. Aluru, “Static and dynamic analysis of carbon nanotube-based switches,” Journal of Engineering Materials and Technology, Transactions of the ASME, vol. 126, no. 3, pp. 230–237, 2004.
[43]
D. A. Walters, L. M. Ericson, M. J. Casavant et al., “Elastic strain of freely suspended single-wall carbon nanotube ropes,” Applied Physics Letters, vol. 74, no. 25, pp. 3803–3805, 1999.
[44]
C. Stampfer, S. Rotter, and J. Burgdorfer, “Comment on dynamic range of nanotube- and nanowire-based electromechanical systems,” Applied Physics Letters, vol. 88, no. 3, Article ID 036101, 2006.
[45]
A. N. Cleland and M. L. Roukes, “Noise processes in nanomechanical resonators,” Journal of Applied Physics, vol. 92, no. 5, pp. 2758–2769, 2002.
[46]
H. W. C. Postma, I. Kozinsky, A. Husain, and M. L. Roukes, “Dynamic range of nanotube- and nanowire-based electromechanical systems,” Applied Physics Letters, vol. 86, no. 22, Article ID 223105, 3 pages, 2005.
[47]
A. K. Hüttel, G. A. Steele, B. Witkamp, M. Poot, L. P. Kouwenhoven, and H. S. J. Van Der Zant, “Carbon nanotubes as ultrahigh quality factor mechanical resonators,” Nano Letters, vol. 9, no. 7, pp. 2547–2552, 2009.
[48]
H. M. Ouakad and M. I. Younis, “Nonlinear dynamics of electrically actuated carbon nanotube resonators,” Journal of Computational and Nonlinear Dynamics, vol. 5, no. 1, Article ID 011009, 13 pages, 2010.
[49]
C. Zhou, J. Kong, and H. Dai, “Intrinsic electrical properties of individual single-walled carbon nanotubes with small band gaps,” Physical Review Letters, vol. 84, no. 24, pp. 5604–5607, 2000.
[50]
L. Yang and J. Han, “Electronic structure of deformed carbon nanotubes,” Physical Review Letter, vol. 85, no. 1, pp. 154–157, 2000.
[51]
M. Huang, Y. Wu, B. Chandra et al., “Direct measurement of strain-induced changes in the band structure of carbon nanotubes,” Physical Review Letters, vol. 100, no. 13, Article ID 136803, 2008.
[52]
G. Y. Guo, L. Liu, K. C. Chu, C. S. Jayanthi, and S. Y. Wu, “Electromechanical responses of single-walled carbon nanotubes: Interplay between the strain-induced energy-gap opening and the pinning of the Fermi level,” Journal of Applied Physics, vol. 98, no. 4, Article ID 044311, 4 pages, 2005.
[53]
Y. Yoon and J. Guo, “Analysis of strain effects in ballistic carbon nanotube FETs,” IEEE Transactions on Electron Devices, vol. 54, no. 6, pp. 1280–1287, 2007.
[54]
C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nano-electromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Letters, vol. 6, no. 7, pp. 1449–1453, 2006.
[55]
T. Helbling, Carbon Nanotube Field Effect Transistors As Electromechanical Transducers, vol. 8 of Scientific Reports on Micro and Nanosystems, Der Andere, T？nning, Germany, 2010.
[56]
X. M. H. Huang, C. A. Zormant, M. Mehreganyt, and M. L. Roukes, “Nanoelectromehanical systems: nanodevice motion at microwave frequencies,” Nature, vol. 421, no. 6922, article 496, 2003.
[57]
D. W. Carr, L. Sekaric, and H. G. Craighead, “Measurement of nanomechanical resonant structures in single-crystal silicon,” Journal of Vacuum Science and Technology B, vol. 16, no. 6, pp. 3821–3824, 1998.
[58]
P. G. Collins, M. S. Fuhrer, and A. Zettl, “1/f noise in carbon nanotubes,” Applied Physics Letters, vol. 76, no. 7, pp. 894–896, 2000.
[59]
C. Kauth, M. Pastre, and M. Kayal, “Wideband low-noise rf front-end for cnt-nems sensors,” in Proceedings of the Mixed Design of Integrated Circuits and Systems Conference, pp. 289–293, IEEE, Warsaw, Poland, May 2012.
[60]
C. Kauth, M. Pastre, and M. Kayal, “A self-regulating oscillator for sensor operation of nanoelectromechanical systems,” in Proceedings of the New Circuits and Systems Conference, pp. 1–4, IEEE, Paris, France, June 2013.
