Transversally and Axially Tunable Carbon Nanotube Resonators In

Feb 14, 2014 - trench located between the metal source (S) and drain (D). Received: November ... electrodes, a narrow slit in the trench, and a highly...
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Transversally and Axially Tunable Carbon Nanotube Resonators In Situ Fabricated and Studied Inside a Scanning Electron Microscope Z. Y. Ning, T. W. Shi, M. Q. Fu, Y. Guo, X. L. Wei, S. Gao, and Q. Chen* Key Laboratory for the Physics and Chemistry of Nanodevices, Department of Electronics, Peking University, Beijing 100871, P. R. China S Supporting Information *

ABSTRACT: We report a new design of carbon nanotube (CNT) resonator, whose resonance frequency can be tuned not only transversally by a gate voltage, but also by the axial strain applied through directly pulling the CNT. The resonators are fabricated from individual suspended singlewalled CNT (SWCNT) in situ inside a scanning electron microscope. The resonance frequency of a SWCNT resonator can be tuned by more than 20 times with an increase of quality factor when the axial strain of the SWCNT is only increased from nearly zero to 2% at room temperature. The transversal gate-tuning ability is found to be weaker than the axial-tuning ability and decrease with increasing the axial strain. The gate voltage can hardly tune the resonance frequency when the initial axial strain is larger than 0.35% and the CNT acts like a tied string. The relationship among resonance frequency, gate voltage, and initial axial strain of the CNT obtained presently will allow for the designs of CNT resonators with high frequency and large tuning range. The present resonator also shows ultrahigh sensitivity in displacement and force detection, with a resolution being better than 2.4 pm and 0.55 pN, respectively. KEYWORDS: NEMS, SWCNT, nanotube resonator, in situ SEM, frequency tuning, sensor

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Here, we report a new design of CNT resonator, whose resonance frequency can be tuned not only transversally by a gate voltage, but also by the axial strain applied through directly pulling the CNT. The resonators are fabricated from individual suspended SWCNT in situ inside a scanning electron microscope (SEM). The frequency of a resonator increases from 21.04 to 430.62 MHz, and the quality factor (Q-factor) changes from 64.3 to 312.3 when the axial strain is only increased from nearly zero to 2% using a CNT with the length of 1.59 μm. The transversal gate-tuning ability is found to be weaker than the axial-tuning ability and decrease with increasing the axial strain. The relationship among resonance frequency, gate voltage, and initial axial strain is obtained and will allow for the designs of CNT resonators with high frequency and large tuning range. The present resonators also show ultrahigh sensitivity for displacement and force sensing. The CNT resonators were first fabricated in situ inside a SEM equipped with four nanomanipulators16 and a piezoelectric ceramics (PC). A PC-driven movable plate was installed in the SEM with its top surface at the same height as the top surface of a fixed block which had already been installed in the SEM (shown in Figure 1a). A three-terminal structure with a trench located between the metal source (S) and drain (D)

n the recent years, nanoelectromechanical (NEM) resonators based on single-walled carbon nanotubes (SWCNTs) have been demonstrated to have great potential in ultrasensitive mass sensors,1−4 force sensors,5,6 high-frequency sources and detectors,2,7−10 and exploring quantum phenomena in macroscopic systems,11,12 mainly due to the ultralow mass density and high Young’s modulus of SWCNTs.1−15 In most of these resonators, the mechanical motion of the nanotubes was actuated and detected simultaneously through electrostatic gate coupling with the suspended carbon nanotubes (CNTs) themselves served as frequency mixers.3−5,11,15 Usually, the frequency of the CNT resonators is tuned by changing the gate voltage in order to change the static force imposed to the nanotube, which changed the tension within the nanotube.2−6,11−15 However, so far, most of the reported CNT resonators have a frequency tuning range being only a couple of times of the fundamental frequency f 0, including the dual-gate configuration where the tuning range is about 3 times of f 0.13 Contracting Au electrodes upon cooling has also been demonstrated to increase the tensile stress within the CNT and tune the resonance frequency in a configuration,8 but the relative frequency raise is still less than 100% due to the inadequate strain in the CNT introduced by cooling. Thus, the effective way reported so far to fabricate high frequency resonator with high sensitivity is mainly to shorten the length of the suspended CNT.2,7−9 © 2014 American Chemical Society

Received: November 4, 2013 Revised: January 25, 2014 Published: February 14, 2014 1221

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Figure 1. (a) Schematic side-view of a resonator installed on a SEM sample stage. (b) Schematic top-view of a resonator. (c) 3D schematic diagram showing the resonator and the experimental setup. The dc gate voltage Vgdc is added via a bias T (not shown in the diagram) to couple with the ac voltage Vgac. (d) SEM image of a SWCNT resonator. (e) High-resolution TEM image of the same individual SWCNT as shown in (d). (f) The relation between the elongation of the SWCNT (ΔL) and the displacement of the PC (Δx) of the resonator shown in (d) measured experimentally (the dots) and the linear fitting result (the solid line). (g) The elongation (ΔL) and the axial strain (ε) of the SWCNT as a function of the displacement of the PC (Δx) during the experiments of measuring the resonator properties. The solid line is copied from (f). The dots are the setting points during the experiments.

(shown in Figure 1a). Finally, an individual SWCNT was placed across the S and D electrodes through nanomanipulation.16 The details of the manipulation method are given in Supporting Information 1. Figure 1d shows a SEM image of a resonator. Driven by the PC, the distance between the S and D electrodes can be changed in a range up to several

electrodes, a narrow slit in the trench, and a highly doped Si gate beneath a 500 nm thick SiO2 layer was prefabricated by micro- and nanolithography processes, as shown in Figure 1b and c. The three-terminal structure was then installed in the SEM with the D side (or the S side) fixed on the fixed block and the S side (or the D side) fixed to the movable plate 1222

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Figure 2. (a) A 3D plot showing the mixing currents as a function of driving frequency and axial strain (from nearly zero to 1.1%) measured with the gate voltage Vgdc = 0 V and the amplitude of Vgac and Vsac being 10 mV. Inset: The mixing currents measured when f was changed from 14 to 28 MHz under the axial strain of 0.004%. The dots are the experimental data, and the solid line is the Lorentzian fitting which yields f = 21.04 MHz and Q-factor being 64.3. (b) The resonance frequency ( f) and Q-factor of the resonator as a function of the axial strain. All resonance measurements were done inside the SEM vacuum chamber at pressure below 10−5 Torr. (c) The response of the resonance frequency (f) to the tension in the nanotube (T). The dots are experimental data. The solid line is the fitting result using a continuum model.

measuring the frequency-dependent mixing current Imix as described in previous reports.5,7,15 In the device shown in Figure 1d, the S and D electrodes are separated by 1.58 μm, the depth of the trench is 300 nm, and the length of the suspended part of the CNT is 1.59 μm. The diameter and chirality of this semiconducting CNT were determined to be 2.2 nm and (20, 12) using a high-resolution transmission electron microscopy (TEM) image (Figure 1e) and electron diffraction by transferring the neighboring part of the same individual CNT onto a TEM grid.16−18 In this way, we know the atomic structure of the same individual CNT in the resonator, which has not been realized in previous works to the best of our knowledge. The inset of Figure 2a shows a typical plot of mixing currents as a function of driving frequency during resonance measured when Vgdc = 0 V and the amplitude of Vgac and Vsac being 10 mV. The resonance frequency of a resonator was determined by fitting the plot using a continuum model.15 The SWCNT is in tension in the as-prepared resonator because we pulled it to stride over the trench to avoid it touching the bottom of the trench in the final nanomanipulation process. To release the pretension in the CNT, we decreased the distance between the S and D electrodes step by step using the PC and observed the decrease of the resonance frequency until there is no observable decrease after a rapid decrease of the resonance frequency with the

micrometers with the smallest step down to 0.016 nm (when the PC moves at its smallest step of 1 nm), which enables largerange and accurately controlled strain in the CNT. The repeatability of setting a position by the PC was confirmed to be within 4.8 pm (corresponding to the repeatability of the PC movement being 0.3 nm) by moving back to the same position for at least three times and measuring the resonant frequency of the CNT, which can detect a displacement in pm level as shown later. The relation between the elongation of the CNT (ΔL) and the displacement of the PC (Δx) were examined by measuring ΔL at each Δx by high magnification SEM images. Thirty experimental points were measured, and a linear relation was obtained with a deviation of 0.355% (standard error/value) in the linear fit, as shown in Figure 1f. The linear fitting result (the solid line in Figure 1f) is then used to determine the displacement and strain of the CNT in the following experiments (the dots in Figure 1g). As indicated in Figure 1c, an ac voltage Vgac at frequency ω is applied to the gate to actuate the CNT resonance. A dc voltage Vgdc which is coupled with the ac voltage Vgac via a bias-T can also be applied to the gate to tune the strain within the CNT. Another ac voltage Vsac at frequency ω+Δω with Δω = 10 kHz is applied to the S electrode. The current in the CNT is detected by a lock-in amplifier through the D electrode, at Δω, with a time constant of 100 ms. Thus, the resonance frequency can be detected by 1223

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Figure 3. (a and b) The response of the resonance frequency ( f) to the gate voltage (Vgdc) when the initial axial strain εi is changed from 0.004% to 0.35%. Parts of the data in (a) can be fitted by the relation of f ∝ Vg2 (the solid line in black), f ∝ Vg (the solid line in blue), or f ∝ Vg2/3 (the solid line in red). The transition points are pointed by the arrows. (c) The change of the resonance frequency (f) as a function of Vgdc and the initial axial strain εi introduced by pulling the CNT. (d) The relationship between f and εi when Vgdc is 0 and 6 V.

distance decrease, which indicates that the strain in the CNT reaches nearly zero. The lowest resonance frequency we measured from the SWCNT resonator shown in Figure 1d is f = 21.04 MHz with the Q-factor being 64.3. The axial strain in the SWCNT corresponding to f = 21.04 MHz is estimated to be 0.004% as will be discussed in the following paragraph. The SWCNT resonator only exhibits one vibration mode because in-plane and out-of-plane modes are degenerate for the nanotube without slack.15,19 We first tuned the frequency only by the axial strain by setting Vgdc = 0. We increased the distance between the S and D electrodes step by step using the PC and measured the resonance frequency of the resonator at each position. Knowing the displacement of the PC (Δx), we can obtain the elongation of the CNT (ΔL) from the solid line in Figure 1g (as indicated by the dots in Figure 1g) and calculate the strain in the CNT using ε = ΔL/L with L = 1.59 μm. Using this method, we do not need to examine the CNT by high magnification SEM and can avoid the electron beam induced damage during the measurements of the resonance property. Figure 2a shows the measured mixing currents as a function of driving frequency and axial strain (from nearly zero to 1.1%) with the gate voltage Vgdc = 0 V and the amplitude of Vgac and Vsac being 10 mV. The resonance curves measured under axial strain of 1.2−2% with the gate voltage Vgdc = 0 V and the amplitude of Vgac and Vsac being 15 mV are shown in Figure S1 in Supporting Information 2. An enormous increase of the resonance frequency from 21.04 to 430.62 MHz along with Q-factor changing from 64.3 to 312.3 was observed when the strain was only increased from nearly zero to 2% (as shown in Figure 2b). According to the beam theory, the resonance frequency f of a doubly clamped beam under tension T can be expressed as:20

fT = f0 1 + T /Tcr

(1)

where f 0 is the fundamental frequency of the beam without prestrain and Tcr is the critical buckling load for the beam.

f0 =

4.732 2πL2

EI ρA

Tcr = 4π 2EI /L2

(2) (3)

where E is the Young modulus, I is the moment of inertia, L is the length of the suspended nanotube, and ρ and A are the density and the cross-sectional area of the nanotube. As shown in Figure 2c, the experimental strain-frequency relation can be fitted well using eq 1, and the Young’s modulus E = 154 GPa and the fundamental frequency f 0 = 9.44 MHz of the SWCNT were obtained from the fitting. The detail about fitting the experimental data is given in Supporting Information 3. Accordingly, the strain in the CNT corresponding to the lowest resonance frequency we measured (21.04 MHz) is 0.004%, corresponding to an elongation about 0.064 nm for a 1.59 μm long CNT. Such a small strain might be due to the residual tension in the CNT which cannot be recovered by just releasing the nanotube. The resonance frequency goes up from 9.44 to 21.04 MHz with only 0.004% strain or 0.064 nm displacement, indicating the super sensitivity of the present resonator to strain and displacement. The presently obtained Young’s modulus is lower than that reported in the literature due to the following possibilities. The present CNTs were ultralong CNTs grown by chemical vapor deposition and may contain defects and have relatively low Young’s modulus. A small amount of amorphous carbon may adsorb on the CNT surface during the manipulation process to place the CNT onto 1224

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from Figure 2c and obtained 0.038 nN for f = 32.52 MHz. Therefore, at the transition point Vgdc = 2 V, the total tension inside the CNT is about 432 times of EI/L2. The theoretical prediction saying that when T0 is zero, the transition happens when Tt is about the same as EI/L2.21 However, the transition point for the case T0 is not zero has not been given clearly by the theoretical work. The present results imply the transition point move to larger Tt when T0 is not zero. When εi = 0.02%, the frequency depends weakly on Vgdc at low gate bias and can be fitted by f ∝ (Vgdc)2/3 when Vgdc is large, indicating the nanotube acts like a tied string.5,21 The transition happens when Vgdc is about 4.4 V, corresponding to f = 71.33 MHz. While, the residual tension in the CNT with εi = 0.02% is about 0.08 nN, which is more than 900 times of EI/L2. Therefore, the CNT always acts like a tied string when εi ≥ 0.02%.21 At the transition point when Vgdc = 4.4 V, f = 71.33 MHz, the total tension in the CNT is about 0.195 nN, which is about twice of the residual tension T0 (0.08 nN), this agrees with the theoretical prediction saying the resonance frequency of a tied string (when T0 ≫ EI/L2) depends weakly on Vgdc for low voltages, and above Tt ∼ 2T0, grows with an envelope ∝(Vgdc)2/3.21 In the case when εi > 0.02%, we only observed the regime where the resonance frequency depends weakly on Vgdc and did not observe the regime with f ∝ (Vgdc)2/3, because we could not reach the transition point by applying Vgdc up to 6 V. For example, when εi = 0.05%, the residual tension introduced by pulling the CNT is 0.190 nN, so that Vgdc should be 7.6 V to reach the point when the tension induced by the gate voltage equals the residual tension. Besides increasing the tuning range, the present work also provides a new way to obtain high frequency using a relatively long CNT. Using eq 1, we can estimate that if a CNT having a diameter of 2.2 nm (which is the same as that shown in Figure 1d) and a length of 150 nm is used to construct a resonator, the resonance frequency will increase from 1.07 to 4.98 GHz when its axial strain is increased from 0 to 2%. The present resonator also has ultrahigh sensitivity for displacement sensing and force sensing. The highest sensitivity could be obtained when the axial strain is nearly zero. From Figure 2b, the slope of the f−ε relation is 2.17 GHz per 1% when strain is 0.004%; therefore, for the 1.59 μm long CNT, the displacement sensitivity is calculated to be 135.87 MHz/ nm. As the resonance peak has the full width at half-maximum (FWHM) of 0.327 MHz, a displacement about 2.4 pm can be resolved. An axial force sensitivity of 0.60 MHz/pN and a sensing resolution of 0.55 pN are also obtained from Figure 2c. Note that higher resolution can be obtained if a longer CNT is used. Previously, we have obtained a force resolution of 0.12 pN using a 6.4 μm long CNT through in situ experiments.22 For comparison, the best commercial atomic force microscope can provide a vertical distance resolution about 50 pm and a force resolution about 50 pN. High displacement sensitivity5,23,24 and force sensitivity5,6,14,23,25 have been reported from CNT resonators by previous works. However, all of those works have been done at low temperature except in ref 5 which has been done at room temperature as in the present case. Besides, the displacement detected in all of the previous resonators is the transverse oscillating displacement of the CNTs or other mechanical resonators, while what we detected here is the elongation of the CNT along its axis or the static displacement of the electrodes connecting the CNT. Static displacement of a nanoscale cantilever has been detected via the electromechanically induced conductance change of a strained

the device, so that the resonance frequency we measured may be lower than that without amorphous carbon. As the CNT with 2% strain is still in elastic range, the axial tension in the CNT can be calculated by T = εEA, and the tension-frequency relation is obtained as shown in Figure 2c. In particular, the tension in the tube increases to 7.24 nN when the strain reaches 2%, while the gate-induced tension is usually less than 0.5 nN in the literature.5,15 This explains why the resonance frequency of the present CNT resonator can increase by more than 20 times, while the frequency can only be tuned in a much smaller range in gate-tuned nanotube resonators in the literature.2−6,11−15 When the strain is 0.004%, the tension is about 0.014 nN, indicating the super sensitivity of the present resonator to force. We then study the tuning ability of dc gate voltage Vgdc. The CNT was first released until its strain is 0.004%, corresponding to an elongation of 0.064 nm (this is the position nearest to zero strain point we can get). Then Vgdc was swept from 0 to 6 V with a step of 0.2 V, and the resonance frequency was observed to change from 21.04 to 76.76 MHz, as shown in Figure 3a. The initial axial strain in the CNT at Vgdc = 0 V (denoted as εi) is then gradually increased up to 2% by moving the S electrode using the PC, and the resonance frequency was measured at each Vgdc. The gate-induced frequency tuning was only observed when εi is smaller than 0.35%, as shown in Figure 3b, and also, the gate-tuning ability decreases as εi increases. When εi is larger than 0.35%, the resonance frequency can hardly be tuned by the gate voltage. Through measuring the Id−Vd and Id−Vg curves of the device, we examined the electronic properties of the same individual CNT under stress.18 The results show that the CNT is still semiconducting when the strain is 2%.18 Therefore, the decrease of the gate-tuning ability with the increasing strain is not due to the change of the electronic property of the CNT, but probably because it is harder to increase tension in the CNT by increasing the transversal electrostatic force when the CNT has a larger axial strain. Figure 3c is a 3D diagram showing how the resonance frequency changes with Vgdc and εi, where the cross points are the experimental data. Figure 3d shows how the frequency changes with initial axial strain εi applied by directly pulling when Vgdc is 0 and 6 V. Obviously, axial strain applied by directly pulling the CNT is more effective to tune the frequency than the gate voltage. Gate voltage can tune the resonance frequency in a small range when the initial strain εi is very small. The tuning ability of gate voltage decreases when εi increases. When εi is larger than 0.35%, gate voltage cannot tune the resonance frequency. The present resonator configuration, which uses pulling to apply axial strain to the CNT, is easy and safe comparing with applying large dc gate voltage and will allow for the designs of resonators with a high frequency and large tuning range. Furthermore, we observed that the data obtained at εi = 0.004% can be fitted by f ∝ (Vgdc)2 when Vgdc is smaller than 2 V and by f ∝ Vgdc when Vgdc is larger than 2 V (as shown in Figure 3a), indicating the CNT changed from a weak bending beam to a hanging chain.5,21 Theoretical work predicted when the residual tension T0 ≫ EI/L2, the tube always acts like a tied string.21 For the present CNT, EI/L2 = 0.088 pN. The residual tension T0 is about 160EI/L2 when the strain is 0.004%. The present results indicate that a SWCNT is still a weak bending beam at low tension when T0 is about 160EI/L2. The transition point, Vgdc=2 V, corresponding to f = 32.52 MHz. Knowing the frequency, we can estimate the total tension Tt inside the CNT 1225

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Figure 1d, and fitting the experimental data using equation 1 and finding the accurate strain in the CNT. This material is available free of charge via the Internet at http://pubs.acs.org.

SWCNT and a relative differential resistance sensitivity of 27.5%/nm has been demonstrated.26 The displacement sensitivity of the present device is much higher than this piezoresistive sensor. We also note that the force we measured from the present resonators is the static force applied to the CNT along its axis, which is equal to the force the CNT applied to the electrode connecting it. However, the force detected in all the previous resonators is the dynamic electrostatic force applied to the CNTs or other mechanical resonators by the gate voltage. The present force resolution is better than the existing static force sensors.27,28 CNT resonators have been extensively studied using mixing current measurement technique in the literature. However, we fabricated and measured CNT resonators in situ inside a SEM on a platform with a PC, so that a controllable stress can be applied along the CNT’s axis and tune the resonance frequency in a large range for the first time. Besides of that, fabricating and study the CNT resonators in situ in SEM also have many other advantages, such as those listed below. Through nanomanipulation in SEM, the same CNT can be transferred into TEM, and the diameter and chirality of the CNT can be characterized. The channel length of the resonator can be measured accurately through SEM observation. Knowing the atomic-level structure of the CNT used in the resonators in situ fabricated inside SEM, one can compare the experimental results with theoretical prediction quantitatively. The Young’s modulus and the tension of the CNT can be obtained through fitting the experimental data using a theoretical model. Also, CNTs with specific structure characterized by TEM beforehand can be selected and used to fabricate specific resonators. In conclusion, for the first time, we have fabricated and studied a new design of SWCNT resonator whose frequency can be tuned not only by the gate voltage, but also by the axial strain applied by directly pulling the CNT. The resonators are fabricated and studied in situ inside a SEM. Through nanomanipulation and TEM study, the atomic structure of the same individual CNT in the resonator has been characterized, which has not been realized before to the best of our knowledge. The frequency of a resonator based on a 1.59 μm long, (20, 12) SWCNT was tuned to more than 20 times when the strain was only increased from zero to 2% at room temperature, and its quality factor was also improved significantly. Such a tuning range is much larger than that in the literature. Through fitting the frequency-strain relation to a continuum model, the fundamental resonance frequency f 0, Young modulus, and the tension of the SWCNT were obtained. We observed that the gate-tuning ability is weaker than the tuning ability of axial strain applied by directly pulling the CNT. The gate-induced electrostatic force gradually loses the ability to tune the resonance frequency when the strain is increased from 0 to 0.35%, and the CNT becomes a tied string. The relationship among the resonance frequency, the gate voltage and the axial strain we obtained will allow for the design of CNT resonators with high frequency and large tuning range. The present resonators also have great potential in ultrahigh sensitivity for displacement sensing and force sensing. A displacement resolution of 2.4 pm and a force resolution of 0.55 pN were realized in the axis direction of the CNT.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Fei Wei and Mr. Rufan Zhang for supplying the CNTs used in the present work. We thank Dr. Xuedong Bai and Mr. Jiake Wei for characterizing the structure of the CNTs using TEM. We thank Professor Jianye Zhao for useful discussions. This work was supported by the MOST (2012CB932702, 2010CB934203) and the NSF of China (60925003, 11374022, 61321001).

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ASSOCIATED CONTENT

S Supporting Information *

In situ manipulation method to place a nanotube onto the device, resonance curves measured from the device shown in 1226

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(26) Stampfer, C.; Jungen, A.; Linderman, R.; Obergfell, D.; Roth, S.; Hierold, C. Nano Lett. 2006, 06, 1449−1453. (27) Yum, K.; Yu, M.-F. Nano Lett. 2006, 06, 329−333. (28) Nesterov, V. Meas. Sci. Technol. 2007, 18, 360−366.

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