NANO LETTERS
Coiled Carbon Nanotubes as Self-Sensing Mechanical Resonators
2004 Vol. 4, No. 9 1775-1779
Alexander Volodin,*,† Dieter Buntinx,† Markus Ahlskog,‡ Antonio Fonseca,§ Janosh B. Nagy,§ and Chris Van Haesendonck† Laboratorium Voor Vaste-Stoffysica en Magnetisme, Katholieke UniVersiteit LeuVen, B-3001 LeuVen, Belgium, Low-Temperature Laboratory, Helsinki UniVersity of Technology, 02015 Espoo, Finland, and Laboratoire de Re´ sonance Magne´ tique Nucle´ aire, Faculte´ s UniVersitaires Notre-Dame de la Paix, B-5000 Namur, Belgium Received June 3, 2004; Revised Manuscript Received July 14, 2004
ABSTRACT After adsorption on a silicon substrate, coiled multiwalled nanotubes retain a 3D structure with sections of freely suspended windings. Electrical gold contacts attached to the nanotubes turn out to be sensitive to vibrations (i.e., the contacts reveal a piezoresistive-like response). When exciting the nanotube windings either electrically or acoustically, the fundamental resonances (ranging from 100 to 400 MHz) can be detected. The resonators are sensitive to mass changes as small as a few tens of attograms.
The application of carbon nanotubes (CNTs) as mechanical resonant sensors involves a complicated sample preparation technique with CNTs bridging a slit or a trench in a substrate.1,2 Moreover, to observe mechanical vibrations of CNTs sophisticated measurements in an electron microscope are needed.1,3 As indicated in ref 1, integrating a sensitive measuring transducer with a CNT nanomechanical oscillator is a challenging task. The use of intrinsically coiled multiwalled CNTs, which demonstrate remarkable mechanical properties,4,5 enables us to avoid the above-mentioned complications. After adsorption on a piece of an oxidized wafer, the CNTs retain a 3D structure with sections of freestanding windings.4 These sections reveal characteristic mechanical resonances that are determined by their shape and dimensions. Here, we propose the application of the coiled CNTs, which are attached to electrical gold contacts and reveal a piezoresistive-like response, as convenient mechanical resonant sensors that do not require a complicated detection of the nanotube resonant oscillations. When attaching nanoparticles to the free-standing windings, the resulting shift of the resonance frequency can be reliably detected for masses as small as a few tens of attograms. The nanotube material containing the coiled multiwalled CNTs (along with a majority of straight nanotubes) is produced by the catalytic decomposition of acetylene, carried out at 700 °C in a flow reactor at atmospheric pressure.6 The CNTs typically have a diameter of 15-30 nm, and the windings of the coiled nanotubes typically have a diameter * Corresponding author. E-mail:
[email protected]. † Katholieke Universiteit Leuven. ‡ Helsinki University of Technology. § Faculte ´ s Universitaires Notre-Dame de la Paix. 10.1021/nl0491576 CCC: $27.50 Published on Web 07/31/2004
© 2004 American Chemical Society
of 200 nm. The purified carbon nanotube material is sonicated at low power in 2-propanol and is deposited onto a piece of an oxidized silicon wafer. The position of the coiled CNTs is determined with respect to the position of predefined gold markers in a scanning electron microscope (SEM). Knowing the exact position of the coiled CNTs allows us to use standard electron beam lithography and liftoff techniques to deposit narrow (around 150 nm) gold electrodes on top of the CNTs. The electrodes are 80 nm thick with an additional 2-5-nm-thick titanium sticking layer. In many cases, we succeeded in positioning the electrodes between the free-standing windings, where the thickness of the evaporated gold is sufficiently large to completely cover a coiled CNT near a section that touches the substrate. However, when the electrode is deposited on a free-standing winding, which at its highest point considerably exceeds the thickness of the electrode, the electrode can obviously be broken, resulting in no or an unreliable electrical contact. Figure 1a shows a noncontact atomic force microscopy (AFM) image of a contacted CNT coil. The electrical resistance of such CNT devices is typically about 1 MΩ. The high value of the resistance of the CNT devices can be attributed to poor electrical contact between the thin electrodes and the strongly curved nanotube. These contacts turn out to be sensitive to mechanical oscillations of the CNTs (i.e., they exhibit a piezoresistive-like effect, which we consider in more detail below). Extensive transport measurements on moderately curved but noncoiled tubes from the same batch7 indeed confirm that for such CNTs the contact resistance can be reduced to a few kΩ. However, consider-
Figure 1. (a) Atomic force microscopy (AFM) image of the coiled carbon nanotube CNT1. After adsorption on an oxidized silicon substrate, the coiled nanotubes form 3D structures with sections of free-standing, helix-shaped windings. The CNTs are electrically connected to the measuring circuit. The electrical contacts turn out to be sensitive to mechanical vibrations of the CNTs. (b) The measuring circuit contains two broad-band rf transformers and allows us to apply an ac current to the CNTs with a frequency of 40 kHz. The circuit enables us to detect high-frequency rf signals over a wide frequency range from 50 to 400 MHz. The mechanical excitation of the CNTs is induced either by applying a radio frequency (rf) electrical field between the CNT and a conductive AFM tip or by an ultrasonic transducer attached to the substrate. (c) Resonant response of the CNT2 device to electromechanical excitation when the AFM tip is positioned at a distance of about 1 µm above the windings of the CNT1.
ably wider contacts to the coiled CNTs often have a contact resistance of only a few tens of kΩ and do not reveal any piezoresistive-like response. The CNT devices are connected to a compact radio frequency (rf) circuit (Figure 1b) that contains two adjustable broad-band rf transformers and allows us to feed an alternating current (ac) into the CNTs at a frequency of 40 kHz and to detect rf signals over a wide frequency range between 50 and 400 MHz. The transformers also effectively decouple the CNT devices from the external circuits to protect them from destruction by parasitic currents. The mechanical excitation of a CNT is produced either by applying an rf electrical field to the CNT or by direct acoustical excitation with an ultrasonic transducer attached to the oxidized silicon substrate (Figure 1b). For the electrical field-induced excitation, an rf voltage with an amplitude between 20 and 200 mV and a frequency ranging from 25 to 200 MHz is applied between the CNT and a conductive AFM tip that is located in close proximity to the CNT. (The tip-to-sample separation is about 1 µm.) For direct excitation, 1776
an ultrasonic thin-film piezoelectrical transducer attached to the substrate provides a sinusoidal out-of-plane excitation of the sample. This broad-band transducer operates over a wide range of frequencies extending from 100 to 300 MHz. It emits longitudinal acoustical waves into the oxidized silicon substrate, causing vibrations of the surface. These surface vibrations are transmitted to the CNTs deposited on the surface. A controllable rf oscillator, an ac-coupled preamplifier with an rf rectifier, a lock-in amplifier. and a digital oscilloscope form the spectrum analyzer that drives our CNT devices and measures their response at the same frequency as the driving signal (for acoustical excitation) or at the double frequency (for electrical excitation). The frequency doubling is necessary because the force on the CNT depends on the square of the applied rf voltage. The fabricated CNT devices are mounted in an AFM operating in a vacuum chamber at a pressure below 1 mTorr. All measurements are performed at room temperature. From the SEM imaging of the CNTs, we already know some of their geometrical parameters. In contrast to the SEM imaging, noncontact AFM imaging also offers excellent depth resolution, providing complementary information about the 3D structure of the CNTs.4 We concentrate on two typical CNT devices: (1) CNT1, where the regular pitch8 is preserved after deposition (Figure 1a), and (2) CNT2, where the intrinsic regular pitch of the grown CNT is not preserved after deposition. AFM images of the latter CNT device are shown in Figure 2a. CNT1 consists of three free-standing windings, where the pitch B and radius R are the same within 10%. CNT2 (Figure 2a) also has three free-standing windings, but in this case the pitches and diameters differ by 20 to 30%. In Figure 1c, the solid curve gives the response of sample CNT1 upon excitation of the windings with an rf electrical field applied between the tip of the AFM and the coiled CNT. The resonance spectrum contains one single-resonance peak. Upon excitation with the tip of the AFM, sample CNT2 exhibits three resonance peaks at 93, 179, and 236 MHz (see the full curve in Figure 2a, where the three peaks are labeled 1, 3, and 2, respectively) with different amplitudes but approximately the same width. The amplitude of resonance 3 is about 1 order of magnitude smaller than the amplitude of resonances 1 and 2. Here, we do not focus on the difference in amplitude of the resonance peaks, which is influenced by frequency-dependent losses in the rf circuits. The observed rf response demonstrates that the resistance of the CNT devices is indeed affected by the electrical excitation of the windings. The relative resistance oscillation of the CNT devices, which can be inferred from the amplitude of the rf response, is less than 1%. We do not observe any shift of the resonance frequencies for larger vibrational amplitudes. We find that the rf response remains linear for the used rf voltage range (i.e., between 20 and 400 mV). Because we were unable to reach the nonlinear regime, we conclude that, according to the results reported in ref 9, the maximum amplitude of the excited oscillations in our CNT devices is less than 20 nm. Nano Lett., Vol. 4, No. 9, 2004
Figure 2. Response of the suspended windings of the coiled carbon nanotube CNT2, where the regular pitch is not preserved after deposition upon mechanical resonant excitation. (a) Scanning electron microscopy (SEM) image of the coiled CNT with electrical contacts. (c) SEM image of the same CNT loaded with carbon particles that were synthesized by the electron beam of the SEM. The observed resonances correspond to the fundamental oscillation modes of the free-standing windings (b) and of the windings loaded with carbon particles (d). The solid curves in parts b and d correspond to the resonances observed in case of excitation by applying an electrical field with the tip of the AFM, and the dotted curves correspond to the resonances observed in case of acoustical excitation of the substrate. The significant background signal in the case of acoustical excitation is due to acoustical resonances of the silicon substrate. From the shifts of the resonance frequencies (peaks labeled 2 and 3 in parts b and d), the masses of the attached carbon nanoparticles are determined to be 1.0 and 0.3 fg.
We observe similar resonances in the case of acoustical excitation of the coiled CNTs, although a significant background signal appears in this case. This is illustrated by the dotted curve in Figure 2b. The parasitic background signal is caused by acoustical resonances of the silicon substrate. We interpret the observed CNT resonances as stationary mechanical vibrational modes of the free-standing windings of the CNT. Indeed, these helix-shaped windings are expected to reveal characteristic mechanical resonances. Taking into account the limited precision (around 10%) with which we can infer the geometric parameters of a CNT winding from the SEM and AFM measurements, we rely on a simple analytical model where a winding is approximated by a circular arch clamped at both ends.10 Within this approximation, the resonance frequency of a winding with radius R and pitch B is given by fres )
πr g(R) 4π2R2 + B2
xEF
(1)
where r is the radius of the nanotube, E is the elastic modulus (Young modulus), and F is the density. The numerical factor g(R) depends on the opening angle of the arch,10 which is determined by the ratio of the length of the attached segment of the winding to its free-standing part. For our windings, this ratio is relatively small, and g(R) ≈ 0.6. Equation 1 Nano Lett., Vol. 4, No. 9, 2004
results from a Rayleigh analysis of the fundamental vibrational mode of the winding of the CNT that is treated as a thin elastic beam. The length of the arch corresponds to the length of the winding of the helix (i.e., (4π2R2 + B2)1/2). Sample CNT2 shown in Figure 2a has a radius r of about 18 nm. Considering the elastic modulus E of the CNT to be a free parameter and taking F ) 1.3 × 103 kg m-3,11 the best fit (based on eq 1) that reproduces the measured resonance frequencies within 10% is achieved for E ) 0.13 TPa. According to our earlier AFM measurements of the mechanical properties around 5 MHz of similar coiled CNTs,12 the Young modulus of the coiled CNTs is E ) 0.17 ( 0.05 TPa. The good agreement between measured and calculated resonance frequencies confirms that the freestanding windings behave as unstretched, curved elastic beams, where the intrinsic curvature of the catalytically grown nanotubes is likely to occur without a large elastic strain being involved. From the fit of the measured resonance frequencies, we surprisingly find that the weaker resonance peak in Figure 2b corresponds to winding 3 that does not carry any measuring current because it is located outside of the electrical contacts attached to the CNT. This reveals that an acousto-electrical effect in the CNT cannot be responsible for the detected resonance signal. We note that acoustoelectrical effects were also absent for straight CNTs at room temperature, where the resistance is temperature-independent.2 We therefore directly link the observed response of our CNT devices to the influence of the mechanical excitations on the electrical contacts of the CNT devices. Despite intensive studies of the transport properties of CNTs during recent years, an improved understanding of the contact resistance between metal electrodes and CNTs only very recently started to emerge.13 Our experimental results suggest that the resonant mechanical oscillations are causing oscillating mechanical stresses in the contact areas, giving rise to oscillations of the contact resistance. Assuming that some kind of tunneling barrier exists, the exponential dependence of the tunneling conductance on the barrier thickness provides an effective mechanism for sensing vibrations.14 Small-area tunneling junctions can be formed in the contact region because of the presence of thin layers of dielectric contamination. Despite the differences in the conductance mechanism, the piezoresistive response of our CNT devices is similar to that of a carbon microphone containing loosely packed carbon grains. When sound waves compress the carbon grains, the contact resistance between the grains changes. Although at this point we do not have any convincing proof that the contact resistance of our CNT devices is governed by electron tunneling, we note that the high value of the contact resistance (∼1 MΩ) is indicative of the existence of barriers with a transmission probability that is likely to be affected by local pressure waves. We note that most of the contacts with geometrical parameters similar to that of CTN1 or CNT2 reveal a piezoresistive-like response, although the amplitude of the response varies by about 2 orders of magnitude from one CNT device to the other. The high resistance can be linked 1777
to the curvature of the CNTs and the grains of the polycrystalline gold electrodes, which are expected to give rise to the formation of small-area tunneling junctions. As mentioned before, considerably wider contacts do not show any measurable piezoresistive-like effect. We are able to confirm the mechanical origin of the observed resonances by attaching carbon nanoparticles to windings 2 and 3 of CNT2 (SEM image in Figure 2c). The two carbon particles were synthesized in the SEM by focusing the electron beam on the upper part of windings 2 and 3. The electron beam ionizes hydrocarbon molecules that then form a contamination particle.15 The hydrocarbons are either present on the CNT surface or are introduced into the SEM vacuum chamber by the backstreaming of the oil of the vacuum pump. The upper part of winding 3 was exposed to the electron beam for a duration that is 10 times longer than for the upper part of winding 2. The resulting spectrum of sample CNT2 after loading with the carbon particles is shown in Figure 2d. Similar to Figure 2b, the solid curve corresponds to the case of excitation with an rf electrical field, and the dotted curve corresponds to the case of acoustical excitation. When comparing these spectra to the spectra of the original sample shown in Figure 2b, it is clear that resonance peaks 2 and 3 have shifted to lower frequencies and resonance peak 1, which corresponds to the unloaded winding, remains unaffected. From the shift of the resonance frequencies, the masses of the deposited particles are determined to be m2 ) 0.3 fg and m3 ) 1.0 fg, respectively. The observed difference in mass of the particles is about 3 times smaller than expected from the exposure time. This discrepancy can be accounted for by the drift of the focused electron beam during the exposure or by fluctuations of the available amount of hydrocarbons. We now move to a more detailed discussion of the sensitivity of our CNT devices to detect small forces or to measure small masses. There are three main parameters that determine the sensitivity of the coiled CNT sensors: (1) the mechanical quality factor Q, (2) the effective (motional) mass meff, and (3) the resonance frequency f0. The ultimate sensitivity is limited by the thermally induced vibrational noise that results in fluctuations of the resonance frequency:16 〈(δf )2〉 )
kBTb 1 1 f0kBTb ) 2 3 2 2πk Q 〈A0 〉 〈A0〉 8π meff f0Q c
(2)
where 〈A20〉 is the mean square amplitude of the vibration, b is the bandwidth of the measuring system (typically about 1 kHz), 4π2meff f 20 is the dynamic spring constant, kB is the Boltzmann constant, and T is the temperature. The minimum detectable mass can then be expressed as mmin ) 2meff
x
δf0 1 ) f0 A0
8πmeffkBTb f 30Q
(3)
From eq 3, it is clear that smaller sensors with a lower mass and a higher resonance frequency are more sensitive. 1778
The sensitivity also improves when increasing the quality factor of the resonator. The mechanical quality factor Q can be calculated from the width of the resonance peaks. The shape of the resonance peaks is approximately Lorentzian, as expected for damped harmonic vibrations. The full width at half-maximum corresponds to a value of Q ranging from 100 to 200 for CNT1 (Figure 2b and d). There are several damping mechanisms limiting the value of Q in vacuum: acoustical damping, damping due to frictional losses in the contact areas between the CNTs and the oxidized silicon substrate, and damping resulting from internal losses in the CNTs. The losses resulting in the lower values of Q are probably surfacerelated.9 The surface losses may be caused by surface contamination (amorphous carbon layer and graphitic particles17) or by defects in the catalytically produced CNTs. The response of our CNTs upon electrical excitation with an AFM tip reveals a good signal-to-noise ratio around 30 (solid curves in Figure 2b and d for resonance 2). However, the acoustically excited CNT devices reveal a superposition of resonance peaks originating from the CNT as well as from acoustical resonances of the silicon substrate (dotted curves in Figure 2b and d). The ratio between the CNT resonance signal and the parasitic background is around 5, reducing the CNT sensor performance in the case of acoustical excitation. Taking into account the observed signal-to-noise ratios from the experiments with the attached nanoparticles (Figure 2d), we estimate the minimum detectable mass to be a few tens of attograms. We note that according to eq 3 the thermodynamic limit for attached mass detection is about 0.1 ag. Provided the internal losses in the CNTs can be reduced, it may be possible to achieve very high values of Q around 10000, similar to the very high values of Q obtained for cantilevers fabricated from ultrathin singlecrystal silicon.18 Obviously, operating our CNT devices at low temperature enables us to achieve an additional decrease of mmin (eq 3). Moreover, at low temperature reduced thermal drifts provide the possibility of performing considerably slower measurements with a very narrow bandwidth b. For a sufficiently high value of Q and a sufficiently small bandwidth b, our CNT devices may allow (eq 3) the detection of single organic molecules with masses of only a few hundred atomic mass units (amu). In conclusion, we have demonstrated that it is possible to use coiled CNTs with attached electrodes as self-sensing mechanical resonators. Additional studies are required to obtain a better understanding of the piezoresistive response of the electrical contacts and to enhance their reproducibility. To achieve better control of piezoresistive behavior, one may envision including an artificial tunneling barrier between the nanotube and the contacts, which enhances the piezoresistive effect. Organic molecules, which self-assemble around the tube, may be used for this purpose. In fact, the functionalization of carbon nanotubes with chemically active side groups is presently an intensively investigated topic of research. We expect nanometer-sized devices based on coiled Nano Lett., Vol. 4, No. 9, 2004
CNTs to play a major role in future nanoelectromechanical components. Some of the coiled CNTs produced by the catalytic decomposition of acetylene have radii and pitches smaller than a few tens of nanometers.8 The resonance frequency of these tiny mechanical structures are well into the microwave GHz regime, making mechanics as fast as electronics.19 The self-sensing coiled nanotube sensors are well suited for measuring small forces and masses in the femtogram range. Acknowledgment. The work at the K.U. Leuven has been supported by the Fund for Scientific ResearchsFlanders (FWO) and by the Flemish Concerted Action (GOA) program. The collaboration between the FUNDP Namur and the K.U. Leuven has been funded by the Belgian InterUniversity Attraction Poles (IAP) program on Quantum Size Effects in Nanostructured Materials (P5/01/01). The work at the Helsinki University of Technology has been supported by the Academy of Finland and by the Large Scale Installation Program ULTI-3 of the European Commission. References (1) Babic, B.; Furer, J.; Sahoo, S.; Farhangfar, Sh.; Scho¨nenberger, C. Nano Lett. 2003, 3, 1577. (2) Reulet, B.; Kasumov, A. Yu.; Kociak, M.; Deblock, R.; Khodos, I. I.; Gorbatov, Yu. B.; Volkov, V. T.; Journet, C.; Bouchiat, H. Phys. ReV. Lett. 2000, 85, 2829. (3) Poncharal, P.; Wang, Z. L.; Ugarte, D.; de Heer, W. A. Science 1999, 283, 1513.
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(4) Volodin, A.; Ahlskog, M.; Seynaeve, E.; Van Haesendonck, C.; Fonseca, A.; Nagy, B. J. Phys. ReV. Lett. 2000, 84, 3342. (5) Chen, X.; Zhang, S.; Dikin, D.; Ding, W.; Ruoff, R.; Pan, L.; Nakayama, Y. Nano Lett. 2003, 3, 1299. (6) Hernadi, K.; Fonseca, A.; Nagy, B. J.; Bernaerts, D.; Fudala, A.; Lucas, A. A. Zeolites 1996, 17, 416. (7) Tarkiainen, R.; Ahlskog, M.; Zyuzin, A.; Hakonen, P.; Paalanen, M. Phys. ReV. B 2004, 69, 033402. (8) Bernaerts, D.; Zhang, X. B.; Zhang, X. F.; Amelinckx, S.; Van Tendeloo, G.; Van Landuyt, J.; Yvanov, V.; Nagy, B. J. Philos. Mag. A 1995, 71, 605. (9) Carr, D. W.; Evoy, S.; Sekaric, L.; Craighead, H. G.; Parpia, J. M. Appl. Phys. Lett. 1999, 75, 920. (10) Den Hartog, J. P. Mechanical Vibrations; McGraw-Hill: New York, 1934. (11) Lu, J. P. Phys. ReV. Lett. 1997, 79, 1297. (12) Volodin, A.; Van Haesendonck, C.; Tarkiainen, R.; Ahlskog, M.; Fonseca, A.; Nagy, B. J. Appl. Phys. A 2001, 72, S75. (13) Javey, A.; Guo, J.; Wang, Q.; Lundstrom, M.; Dai, H. Nature 2003, 424, 654. (14) Kenny, T. W.; Kaiser, W. J.; Podosek, J. A.; Rockstad, H. K.; Reynolds, J. K.; Vote, E. C. J. Vac. Sci. Technol., A 1993, 11, 797. (15) Molzen, W. W.; Broers, A. N.; Cuomo, J. J.; Harper, J. M. E.; Laibowitz, R. B. J. Vac. Sci. Technol. 1979, 16, 269. (16) Albrecht, T. R.; Gru¨tter, P.; Horne, D.; Rugar, D. J. Appl. Phys. 1991, 69, 668. (17) Frank, S.; Poncharal, P.; Wang, Z. L.; de Heer, W. A. Science 1998, 280, 1744. (18) Stowe, T. D.; Yasumura, K.; Kenny, T. W.; Botkin, D.; Wago, K.; Rugar, D. Appl. Phys. Lett. 1997, 71, 288. (19) Huang, X.-M. H.; Zorman, C. A.; Mehregany, M.; Roukes, M. L. Nature 2003, 421, 496.
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