Axially Tunable Carbon Nanotube Resonators Using Co-integrated

Letter pubs.acs.org/NanoLett

Axially Tunable Carbon Nanotube Resonators Using Co-integrated Microactuators Stuart Truax, Shih-Wei Lee, Matthias Muoth, and Christofer Hierold* Micro and Nanosystems, Department of Mechanical and Process Engineering, , ETH Zurich, Tannenstrasse 3, 8092, Zurich, Switzerland S Supporting Information *

ABSTRACT: Tuning of the mechanical resonance frequency of single-walled carbon nanotubes (SWCNTs) is achieved by application of uniaxial strain by purely mechanical means, utilizing both directly grown and dry-transferred SWCNTs. The induction of a beam-to-string transition is achieved, resulting in an axial tension sensitivity of 9.4 × 1010 Hz/ε in the vibrating string regime. Increases in the resonant Q-factor, removal of residual slack, and resonance frequency changes from 10 to 60 MHz are affected.

KEYWORDS: Carbon nanotube resonator, string regime, axial strain

S

integrated SWCNT resonator consists of a three-port suspended SWCNT field-effect transistor (FET) device with a drain electrode that can be horizontally displaced through contact with a collocated electrothermal actuator. The electrothermal actuator displaces the drain structure through thermal expansion caused by Joule heating due to an applied actuator voltage Va, with effective displacement responses of approximately 2 nm/mV. SWCNT resonances are measured using a 2ω-mixing scheme to acquire the down-mixed SWCNT drain current Idmix with DC biases on to the applied AC source−drain voltage vsd and AC gate voltage vg.5,10,11 In this technique, the AC source−drain signal vsd is applied at frequency 2ω+Δω, while the AC gate voltage vg is applied at frequency ω. The capacitive actuation between the gate electrode and SWCNT causes the SWCNT to mechanically resonate. Using a 2ω-mixing scheme, the drain current id caused by higher-order conductance modulation within the SWCNT is measured. The higher-order conductance modulation occurring at frequency 2ω has been shown in previous work to give higher signal-to-noise ratios5 and is thus used here in this work. The drain current components occurring at 2ω can be attributed to nonlinear signal mixing and strain-related effects. The drain current components at 2ω, when mixed with vsd, will produce a drain current Idmix at frequency Δω. The current Idmix is subsequently measured with a lock-in amplifier. For the directly grown SWCNT-based device, signal magnitudes of |νg| = 400 mV rms, |νsd| = 7 mV rms, and DC biases of Vg = 1 V and Vsd = 10 mV were applied on the gate and source ports, respectively (see also Supporting Information).

ingle-walled carbon nanotube (SWCNT) resonators show promise as ultrasensitive force sensors. Using the electric field from a gate electrode to induce axial tension in a suspended SWCNT, axial tension has been detected with resolutions of less than 10−18 Newtons at ultralow temperatures and low pressure.1 Another approach for inducing axial tension is moving the clamping points of a suspended SWCNT. With this method, changes in mechanical resonance frequency over orders of magnitude can be affected, with linearized axial tension sensitivities from 1.1 × 109 Hz/ε2 to 1 × 1011 Hz/ε3 in the initial part of the string regime. In previous work, the systems used to demonstrate this frequency tuning used either SWCNTs suspended between AFM tips or suspended between two substrates: one movable, the other stationary.2,3 Here we show two implementations of axial-tension tunable SWCNT mechanical resonators with cointegrated microactuators to affect the tuning. These devices represent another step toward chip-level SWCNT resonant force sensors and SWCNT resonators with a highly adjustable Q-factor. In this research, the removal of slack in an SWCNT mechanical resonator and application of axial tension to affect a beam-to-string transition is accomplished through the use of an electrothermal actuator collocated with the SWCNT resonator. Two types of devices were fabricated for this research: (1) an SWCNT resonator−actuator system using a directly grown SWCNT on a silicon-on-insulator (SOI) material stack4−7 and (2) an SWCNT resonator−actuator system using a pristine, dry-transferred SWCNT on a material stack using polycrystalline silicon based on the polyMUMPs process.8,9 All resonant measurements were performed under vacuum (1 × 10−3 Pa) and at 298 K. The respective SWCNTs broke during the respective measurement cycles. As a first case, the on-chip system comprised of the directly grown SWCNT resonator is presented. The presented © XXXX American Chemical Society

Received: May 25, 2014 Revised: August 30, 2014

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The device scheme for the directly grown SWCNT device and the respective actuation and readout signals for the device are shown in Figure 1. The illustrated scheme shows a

Figure 2. Surface plot of the mixed-down SWCNT drain current Idmix as a function of slack (left) and extracted resonance frequencies from same data compared to the model of eq 2 (right). Data are taken from the directly grown SWCNT SOI-based device of Figure 1. FEM simulations predict that Mode 1 corresponds to the slacked “jumprope” mode shape (left inset), and Mode 2 corresponds to the “longitudinal swinging” mode shape shown in the right inset. Mode 2 undergoes coupling to another slacked mode for s < 15%.

Figure 1. Scheme of the directly grown SWCNT resonator (center), showing the electrothermal actuator structure, side gate (G), source (S), and drain (D) electrodes. The electrodes carry the signals vsd, vg, and id, respectively. SEM images of the electrodes (left) and SWCNT used in the experiments (right) are shown. The unstrained length of the directly grown SWCNT was estimated to be 1.89 μm. False colors are used for clarity.

two resonance modes. The lower frequency mode (Mode 1) corresponds in frequency to the expected “jumprope” mode for a SWCNT of this length in the slacked regime. The upper frequency mode (Mode 2) couples with another, lower amplitude mode, which is expected as slacked-modes converge in frequency due to the reduction in slack. The mode shapes were inferred from eigenfrequency finite-element (FEM) simulations, which simulated a SWCNT with the catenary (i.e., “hanging chain”) profile expected in slacked SWCNTs. The “jumprope” mode shape for Mode 1 and the “longitudinal swinging” mode shape for Mode 2 as displayed in Figure 2 insets are both qualitatively predicted from FEM simulations and are generally expected to be the two lowest frequency modes. The FEM model did not take into account the force on the SWCNT from electric fields. Using eq 2 and the change in frequency of the two resonance modes shown, the initial slack is estimated to be 22% on the SWCNT with a total suspended length L of 1.89 μm. The force-per-unit length acting on the SWCNT is assumed to be from the DC electric field from the gate electrode, and is fitted to be f l = 0.3 μN/m. The agreement between the analytical model and the measurement data is shown in Figure 2 (right). For the measurements of Figure 2, the drain electrode is estimated to have a total travel distance of 400 nm. When the drain electrode is not displaced, Mode 1 has an average Q-factor of 48, and the Mode 2 has an average Q-factor of 20, both consistent with the typical Q-factors of SWCNTs observed under vacuum at 300 K.13,14 The resonant peaks of both modes have an antiresonance shape, caused by a phase difference between the resonant motion of the SWCNT and the AC electric current on the SWCNT. The arbitrary phase difference is attributed to parasitic capacitances and resistances specific to the device and measurement setup.15 The Q-factor is extracted by inverting the antiresonance peaks and measuring the −3dB bandwidth of the peaks.16 The line width of the measured peaks fluctuated during the measurement due to the finite frequency resolution of the measurement sweeps, causing a ±15% uncertainty in the measured Q-factor. However, the Qfactors are observed to increase on average with decrease in slack. The Q-factor of the Mode 1 in particular undergoes a 2× increase from approximately 50 to above 100. Figure 3 shows two resonant response curves for the first mode for two

decoupling structure at the connection between the drain electrode and the electrothermal actuator. This structure allows the displacement of the drain electrode only beyond a certain applied actuator voltage. An SiO2 layer around the electrothermal actuator structure also prevents the drain current id from flowing into the actuator structure, thus electrically decoupling the SWCNT from the actuator. An SEM image of the SWCNT used in the reported experiments is also shown in Figure 1. The SEM images were used to determine the SWCNT length L = 1.89 μm. For directly grown suspended SWCNTs, excess length in the suspended SWCNT is often encountered after SWCNT release. To quantify the effect of excess length on the mechanical resonance frequency, the slack parameter s is defined as s = (L − W)/L, where W is the initial distance between the clamping points (see also Supporting Information). In a slacked regime, the first few mechanical resonance frequencies of a suspended SWCNT are expressed by using a pendulum analogy:12

fn =

n 2

fl μL 24s

(1)

where f l is the assumed uniform external force per unit length on the SWCNT, n is the mode number, μ is mass per unit length, and L is the total suspended length. With a movable drain electrode, the slack parameter becomes adjustable, allowing the resonance frequency of the slacked, suspended SWCNT to be adjusted according to the drain displacement Δxd: fn =

n 2

⎛ L − W − Δxd ⎞−1/4 ⎜ ⎟ ⎠ L μL 24 ⎝ fl

(2)

For the directly grown SWCNT device featured in this work, the removal of slack and the resultant change in the resonance frequency is shown in Figure 2. The mixed-down drain current Idmix is displayed in the surface plot in Figure 2 (left), showing B

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dry-transferred device features a decoupling structure to prevent the drain current from flowing in to the actuator structure. As with the directly grown SWCNT device, the 2ωmixing scheme was used to measure the mixed-down drain current Idmix. Signal magnitudes of |νg| = 400 mV rms and |νsd| = 7 mV rms and DC biases of Vg = 5 V and Vsd = 200 mV were applied on the gate and source ports, respectively. The electrothermal actuator for this device had an estimated effective linearized displacement response of 0.05 nm/mV, resulting in a total travel distance of approximately 5 nm over the measurement range, although only 2 nm of this corresponds to straining of the SWCNT due to the decoupling structure. The SWCNT length was estimated to be 2.72 μm from the SEM measurement shown in Figure 4. Bundling of the SWCNT in this device was observed, resulting in multiple spurious frequency peaks and altered SWCNT mechanical properties (discussed below). When slack in the suspended SWCNT is negligible, the application of axial strain through a movable drain electrode allows the SWCNT to undergo a transition from the beam-like to the string-like vibrational regime (i.e., a beam-to-string transition), allowing frequency tunability not found in other micro- or nanoresonators due to the SWCNT’s small length and high Young’s modulus. In the beam regime, the mechanical resonance frequencies of the lowest-order modes are given by Euler−Bernoulli beam theory as

Figure 3. Two down-mixed frequency characteristics from the “jumprope” mode (Mode 1) of Figure 2. The Q factor roughly doubles as slack is removed from 22% to 9%. The antiresonance peak is due to an intrinsic phase difference between the resonant motion and the source−drain AC current.

different slacks and drain displacements: (1) Δxd = 0 nm, s = 22.2%, and (2) Δxd = 236 nm, s = 9.4%. For these two points of observation, the first mode Q-factor is observed to increase from 48 for Point 1 at 3.7 MHz to 100 for Point 2 at 4.6 MHz. Assuming the effective mass and damping parameters of the SWCNT remain constant, the effective stiffness k of the SWCNT should increase to effect the increase in resonant frequency, leading also to a proportional increase in Q-factor by the theory of harmonic oscillators. A tunable SWCNT resonator system based on drytransferred tubes effectively negates the issue of residual slack. The process step in which the tube is placed on the target substrate has the tendency to eliminate slack and induce a small amount of initial tension in the placed tube. The presented SWCNT resonator system based on dry-transferred SWCNTs is illustrated in Figure 4. For this device, a back-gate electrode was employed to achieve better coupling to the suspended SWCNT. As in the device with the directly grown tube, the

fn =

2 1 ⎛ λn ⎞ EI ⎜ ⎟ 2π ⎝ L ⎠ ρA

(3)

where I is the second area moment of inertia for the tube, ρ is the SWCNT density, A is the SWCNT cross-sectional area, and λn is 4.73 for the first mode and 7.85 for the second mode. In the beam regime, the bending rigidity EI is significant relative to inertial effects. With the application of axial tension beyond a critical value Tcrit, the SWCNT mechanical resonance frequencies become dependent on axial tension T and inertia according to17,18 fn =

n 2L

T ρA

(4)

In eq 4, the small length and high Young’s modulus of a SWCNT can allow frequency tunability over orders of magnitude for relatively small drain displacements. In this research, a dry-transferred SWCNT is placed and contacted onto a poly-silicon source−drain structure. The drain structure is actuated to apply axial tension to the tube, affecting a beamto-string transition. Figure 5 shows a surface plot of the amplitude of Idmix (left) and the extracted resonance frequencies from the surface plot data (right), both as a function of applied axial strain. The spurious modes around the shown first and second modes are attributed to bundling of the SWCNT near the source and drain contacts. The data for ε < 0 correspond to applied tension below the critical strain necessary for the beam-to-string transition. The quadratic displacement response of the actuator means only very small displacements occur initially, and strains ε > 0 represent full actuator−drain coupling and therefore large displacement. The initial portion of data corresponds to a beam regime with an estimated initial tension of 0.07 pN for the 2.72 μm tube bundle. Mode 1 is measured to be 3.4 MHz, and Mode 2 is measured to be 10 MHz. The SWCNT is modeled as having a diameter of 1 nm, a density ρ = 1400 kg/m3, a Young’s

Figure 4. Scheme of the dry-transferred SWCNT resonator (center), showing the electrothermal actuator structure, back-gate (G), source (S), and drain (D) electrodes. The electrodes carry the signals vsd, vg, and id, respectively. The device has a decoupling structure between the actuator and drain (not shown). SEM images of the electrodes (left) and SWCNT used in the experiment (right) are shown. The unstrained length of the dry-transferred SWCNT was estimated to be 2.72 μm. False colors are used for clarity. C

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Figure 5. Surface plot of the amplitude of the down-mixed drain current Idmix of the dry-transferred tube (left) and the associated extracted resonance frequencies plotted with models for the resonance frequencies of the tube in the string and beam regimes (right). The indices of the mode names from the experimental data denotes the index of the primary mode and the index of the associated spurious mode. Data for ε > 0 correspond to the beam-to-string transition.

modulus of E = 0.1 TPa, and a SWCNT wall thickness of 0.08 nm.17 The initial tension is estimated by backsolving the tension from the measured resonance frequencies using the above material parameters as inputs to the Euler−Bernoulli beam equation. The relatively low Young’s modulus is fitted to the data based on the estimated actuator displacement of approximately 5 nm over the measurement range and accounts for the fact that the bundled configuration of the SWCNTs may cause slipping between the constituent SWCNTs and therefore a reduced Young’s modulus. Typical Young’s modulus values for SWCNTs are in the 1 TPa range.19 The initial built-in tension in the tube is hypothesized to be due to the transfer and placement step of the dry-transfer process. At the point of zero applied strain, the SWCNT quickly transitions into the string regime after exceeding the critical tension. The string model is applied with same SWCNT parameters as the applied Euler− Bernoulli beam model and closely predicts the increase in frequency with increasing strain. In the initial part of the string regime, the tube demonstrates a linearized strain sensitivity of approximately 9.4 × 1010 Hz/ε, comparable to values reported in the literature in other SWCNT straining experiments.2,3 With increasing the applied strain in the string regime, the amplitude of the resonance peak decreases as a consequence of the increasing effective stiffness of SWCNT, posing a challenge for measuring the resonance at high applied strains. The second mode peak can be traced from its beam regime frequency of 10 MHz up to approximately 60 MHz during straining, as is shown in the surface plot of Figure 5. For the dry-transferred device, analysis of the Q-factors of the first mode during straining reveal the magnitude of the SWCNT damping parameter. Due to the decreasing amplitude of the resonance peaks with increasing strain, peak data from the initial portion of the straining measurement cycle are used to extract the Q-factors of the first mode, as shown in Figure 6. Using the relation Q = 2πfom/d, and estimating the SWCNT mass m at 3 × 10−21 kg, the extracted damping factor d has a value of approximately 4.7 × 10−15 kg/s. The extracted

Figure 6. Q-factor of the first mode of the dry-transfer-based SWCNT resonator as a function of resonance frequency during actuator straining. A linear fit allows the extraction of a damping parameter of approximately 4.7 × 10−15 kg/s. Data points correspond to first mode peaks with the highest signal-to-noise ratio.

damping parameter corresponds to internal damping mechanisms, as the experimental conditions of high vacuum and room temperature apply. The increase of the Q-factor for the first mode in the initial part of the string regime is on the order of 2×. For high strain regimes, however, the increase in Q-factor can be theoretically expected to be far greater.20 Two platforms for the axial tuning of SWCNT mechanical resonances are presented, utilizing the high sensitivity of SWCNTs in the string regime to axial tension to affect large frequency changes. Slack is removed in an SWCNT resonator using a directly grown SWCNT, demonstrating an increase in Q-factor from 48 to 100 for the first resonance mode with mode coupling between slacked modes observed. A drytransferred SWCNT is tuned into the string regime, causing a resonance frequency increase of over 6× for the second mode and attaining an axial strain sensitivity of 9.4 × 1010 Hz/ε. The force sensitivity of resonating carbon nanotubes portend their application in ultrasensitive force sensing. With further work, D

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(16) Petersan, P. J.; Anlage, S. M. J. Appl. Phys. 1998, DOI: 10.1063/ 1.368498. (17) Cao, G.; Chen, X.; Kysar, J. W. Phys. Rev. B 2005, DOI: 10.1103/PhysRevB.72.195412. (18) Bokaian, A. J. Sound Vib. 1990, DOI: 10.1016/0022-460X(90) 90663-K. (19) Wu, Y.; Huang, M.; Wang, F.; Huang, X. M. H.; Rosenblatt, S.; Huang, L.; Yan, H.; O’Brien, S. P.; Hone, J.; Heinz, T. F. Nano Lett. 2008, DOI: 10.1021/nl801563q. (20) Verbridge, S. S.; Parpia, J. M.; Reichenbach, R. B.; Bellan, L. M.; Craighead, H. G. J. Appl. Phys. 2006, DOI: 10.1063/1.2204829.

SWCNTs can someday be utilized as practical sensors by coupling them with external measurands and applied forces.

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ASSOCIATED CONTENT

S Supporting Information *

(1) Estimation of the SWCNT length and amount of slack, (2) mixing measurement of the SWCNT drain current, and (3) device fabrication. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

S.T., S.-W.L., and M.M. contributed equally. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support from the Swiss National Science Foundation (SNSF: Equip Program 206021 139153/1), ETH Zurich (Scientific Equipment Program), and Nano-Tera.ch (a program of the Swiss Confederation) and general support by the ETH FIRST laboratory team (in particular E. Gini and E. Ebnoether) and the EPFL Nanoelectronic Device Laboratory. The authors especially thank A. Eichler and A. Bachtold for sharing expertise. The authors also thank C. Roman, H. Chandrahalim, M. Haluska, J. Cao, and K. Chikkadi for helpful discussions.

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REFERENCES

(1) Moser, J.; Guttinger, J.; Eichler, A.; Esplandiu, M. J.; Liu, D. E.; Dykman, M. I.; Bachtold, A. Nat. Nanotechnol. 2013, DOI: 10.1038/ nnano.2013.97. (2) Wei, X.; Chen, Q.; Xu, S.; Peng, L.; Zuo, J. Adv. Funct. Mater. 2009, DOI: 10.1002/adfm.200900105. (3) Ning, Z. Y.; Shi, T. W.; Fu, M. Q.; Guo, Y.; Wei, X. L.; Gao, S.; Chen, Q. Nano Lett. 2014, DOI: 10.1021/nl4040913. (4) Lee, S.-W.; Muoth, M.; Hierold, C. Nanotechnology 2013, DOI: 10.1088/0957-4484/25/21/215301. (5) Lee, S.-W.; Truax, S.; Yu, L.; Roman, C.; Hierold, C. Appl. Phys. Lett. 2013, DOI: 10.1063/1.4815988. (6) Lee, S.-W.; Durrer, L.; Roman, C.; Hierold, C. Proc. 6th IEEE NEMS 2011, DOI: 10.1109/NEMS.2011.6017289. (7) Durrer, L.; Helbling, T.; Zenger, C.; Jungen, A.; Stampfer, C.; Hierold, C. Sens. Actuators, B 2008, DOI: 10.1016/j.snb.2007.11.007. (8) Muoth, M.; Chikkadi, K.; Yu, L.; Hierold, C. Proc. 26th IEEE Conf. Micro Electro Mech. Syst. (MEMS) 2013, DOI: 10.1109/ MEMSYS.2013.6474287. (9) Muoth, M.; Hierold, C. Proc. 25th IEEE Conf. Micro Electro Mech. Syst. (MEMS) 2012, DOI: 10.1109/MEMSYS.2012.6170417. (10) Bargatin, I.; Myers, E. B.; Arlett, J.; Gudlewski, B.; Roukes, M. L. Appl. Phys. Lett. 2005, DOI: 10.1063/1.1896103. (11) Mile, E.; Jourdan, G.; Bargatin, I.; Labarthe, S.; Marcoux, C.; Andreucci, P.; Hentz, S.; Kharrat, C.; Colinet, E.; Duraffourg, L. Nanotechnology 2010, DOI: 10.1088/0957-4484/21/16/165504. (12) Ü stünel, H.; Roundy, D.; Arias, T. A. Nano Lett. 2005, DOI: 10.1021/nl0481371. (13) Wu, C. C.; Zhong, Z. Nano Lett. 2011, DOI: 10.1021/ nl1039549. (14) Barnard, A. W.; Sazonova, V.; van der Zande, A. M.; McEuen, P. L. Proc. Natl. Acad. Sci. U.S.A. 2012, DOI: 10.1073/pnas.1216407109. (15) Knobel, R. G.; Cleland, A. N. Nature 2003, DOI: 10.1038/ nature01773. E

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