NANO LETTERS
Nano-Electromechanical Displacement Sensing Based on Single-Walled Carbon Nanotubes
2006 Vol. 6, No. 7 1449-1453
C. Stampfer,*,† A. Jungen,† R. Linderman,†,‡ D. Obergfell,§ S. Roth,§ and C. Hierold† Micro and Nanosystems, ETH Zurich, 8092 Zurich, Switzerland, and Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany Received March 23, 2006
ABSTRACT We present a nano-electromechanical system based on an individual single-walled carbon nanotube (SWNT) demonstrating their potential use for future displacement sensing at the nanoscale. The fabrication and characterization of the proposed nanoscaled transducer, consisting of a suspended metal cantilever mounted on top of the center of a suspended SWNT, is presented and discussed. The displacement of the nanoscale cantilever is detected via the electromechanically induced change in conductance of the strained SWNT. A relative differential resistance sensitivity (for a metallic SWNT) of up to 27.5%/nm was measured and a piezoresistive gauge factor of a SWNT of up to 2900 was extracted.
The field of micro-electromechanical systems (MEMS)1 has constantly grown in the last 25 years, and the ongoing miniaturization has recently reached the nanoscale. A variety of nano-electromechanical systems (NEMS) like nanoscaled switches2 and nanotube-based pressure3 and mass sensors4 with novel transducer concepts have been presented and the huge potential for future ultrafast, highly sensitive, and low power devices has been shown.5-8 However, fundamental transducer concepts at the microscale (like capacitive, piezoresistive, and optical sensing) did not prove to be optimal for functional NEMS devices.8-10 Here we report on a novel concept of displacement sensing at the nanoscale based on single-walled carbon nanotubes (SWNTs)11,12 as active sensing elements. SWNTs, discovered in 1993,13 are today one of the most intensively studied nanostructures showing exceptional electrical, mechanical, and electromechanical properties14-20 (e.g., high elasticity and very high effective piezoresistive gauge factors of up to 1000).14 Moreover, the small dimensions of a SWNT (diameter of ≈1 nm and a length of up to several micrometers) enable a measurement area of approximately down to 1 nm × 1 nm (mainly limited by the nanotube diameter), where deflection could be measured. These small dimensions are difficult to reach by most conventional methods, since the size on which deflection can be measured is (intrinsically) limited by the * Corresponding author. E-mail:
[email protected]. † Micro and Nanosystems, ETH Zurich. ‡ Present address: IBM Research GmbH, Zurich Research Laboratory, 8803 Ru¨schlikon, Switzerland. § Max Planck Institute for Solid State Research. 10.1021/nl0606527 CCC: $33.50 Published on Web 06/17/2006
© 2006 American Chemical Society
measurement method: (i) optical methods are limited by the wavelength; (ii) capacitive sensing is limited by area and suffers from signal loss;9 (iii) scaling down classical diffusive piezoresistors leads to a strongly increased resistance and resistance noise at nanoscale.21 From this point of view, new materials (like nanowires and nanotubes) and new transducer concepts for sensing at the nanoscale become very interesting and promising. The displacement sensing is based on a suspended SWNT which is physically connected to the nanomechanical (or nano-electromechanical) structure (e.g., cantilever or bridge). If the nanomechanical structure, of which displacement is to be measured, undergoes a mechanical deflection, the SWNT is mechanically deformed (mainly axially stretched) which leads to a significant change in the electronic band gap and thus in the conductance of the SWNT. The conductance change can then be detected electrically. The basic concept of the displacement-sensing mechanism is illustrated in Figure 1. A double-clamped suspended SWNT of length LNT is electrically connected to two electrodes, source (S) and drain (D). Also, the SWNT is mechanically connected to the object which is measured. By deflecting the structure, e.g., a cantilever (C) by z, the SWNT is deformed and stretched (see Figure 1b) leading to a significant change in conductance, which is directly correlated to the deflection z. The maximum measurement range (-zmax, zmax) is limited by the length, LNTB, of the suspended SWNT branches and their limit of elasticity, max ≈ 6%. For example, this leads to a maximum measurement range of
Figure 1. Schematic illustration of the proposed single-walled carbon nanotube (SWNT) based displacement sensing mechanism. (a) A double clamped suspended SWNT of length LNT and branch lengths LNTB is electrically connected to source (S) and drain (D) electrodes, and the SWNT is mechanically connected to the object (C) which is measured. (b) Deflecting the structure (C) by z, including a force F leads to stretched SWNT and a nanotubeinduced back-coupling force FNT.
zmax ≈ 60 nm for LNTB ) 200 nm. This measurement range could be sufficient for a variety of possible NEMS applications.5,6,8 An important point to note is that this displacement sensing method shows a rather strong mechanical back coupling of the SWNT, FNT, to the nanomechanical structure on which the deflection is measured due to the high stiffness of the SWNT. SWNTs are reported to have a Young’s modulus of E ≈ 1 TPa.12 However, assuming that the forces, F, involved to deflect the specimen with the integrated SWNT are significantly larger than FNT ) EA(z/LNTB)3, where A is the cross-sectional area of the nanotube, the mechanical stiffness of the integrated SWNT can be neglected. (The cross-sectional area A is given by A ) πdt, where d ) 1.4 nm is the diameter of the SWNT and t ) 0.34 nm is the interlayer spacing of graphite.) Otherwise the back coupling force FNT has to be taken into account. E.g., we see below that the active force back coupling of the nanotube for deflections z e 30 nm can be neglected when the applied force significantly exceeds FNT ≈ 5 nN. To demonstrate the introduced concept, we fabricated a number of cantilever-based test devices22-26 as shown in Figure 2c. The fabrication technique involves prepatterned reference alignment markers that are used to align the device to randomly adsorbed SWNTs (arc-discharge SWNTs dispersed in sodium dodecyl sulfate). The starting material was highly doped silicon (Si) wafer substrates with 200 nm of deposited SiO2. Reference alignment markers were patterned by electron beam lithography (EBL) and the deposition of 2 nm Cr and 30 nm Au followed by lift off. Before the SWNTs were adsorbed, the surface was functionalized with a DAS, N-[3-(trimethoxysilyl)propyl]ethylenediamine (97%). Next atomic force microscope (AFM) images were recorded to determine the spatial orientation and the location of each discrete SWNT (see Figure 2a) to be integrated in the nanoscaled test device. EBL is subsequently used to pattern the metallic structures (1 nm Cr and 40 nm Au) for the nanoscaled device (Figure 2b). Finally diluted HF (4% for 5 min) etching followed by critical point drying completes the nanosized device fabrication (Figure 2c and Figure 3). For a more detailed process description please refer to ref 22. In Figure 3 we show the final device, where a suspended SWNT is placed underneath a released 200 nm wide and 1450
Figure 2. A schematic illustration of the fabrication process: (a) Dispersed SWNTs on SiO2 (200 nm)/highly doped Si substrate. (b) After e-beam lithography, Cr/Au (1 nm/40 nm) was evaporated followed by a lift-off process to form electrodes. The devices at this stage are operating as SWNT-based transistors. (c) Schematic of the final structure which was released by HF etching followed by critical point drying.
Figure 3. (a) SEM image of the final cantilever-SWNT-based sensing device. The white arrows indicate the location of the suspended SWNT. (b) Tapping mode AFM image of the device. Note that the resolution of the AFM image is limited by the envelope of the AFM tip dimensions.
1.5 µm long Au cantilever. The 600 nm long suspended SWNT with a diameter of approximately 1.2 nm, which can clearly be seen (white arrows in Figure 3a), is clamped by the two electrodes. Although the SEM image of Figure 3a shows controlled electrode patterns, the electrical connections of each SWNT were measured before the final release to characterize the SWNT as to be metallic or semiconducting. In this stage of the device process, the back gate electrode (highly doped Si underneath the 200 nm SiO2) can be used to examine the electrical properties of the individual SWNTs in a transistor configuration (see Figure 2b). In Figure 4a we show the I-V characteristic (at Vg ) 0 V) of a metallic SWNT before (white circles) and after (black circles) the HF release. The resistance of the nanotube (at Vds ) 50 mV) is slightly Nano Lett., Vol. 6, No. 7, 2006
Figure 4. Electromechanical measurements of an electromechanical sensor device based on a metallic SWNT. (a) I-V characteristic of the SWNT before (white circles) and after (black circles) the HF release process is shown. (b) The gate voltage independence of same SWNT before the final release is shown. (c) The resistance, R, is plotted as a function of the cantilever deflection, z, for three different up and down cycles (see lower insert). The dashed line is determined by the model described in the text.
increased from Rbefore ≈ 280 kΩ to Rafter ≈ 315 kΩ due to the HF release process. This small resistance change might be due to some physical changes at the contacts or/and due to some HF damaging of the SWNT. However, these issues are still in focus of further investigations. In Figure 4b the gate voltage dependence of the current Ids of the same metallic SWNT before the final release process is plotted for different Vds. The gate voltage independence of Ids proves the metallic or quasi-metallic character of the investigated SWNT. For the electromechanical displacement sensing, an AFM in contact mode is used to apply a force F onto the suspended Au cantilever (at the point P; see Figure 3b), which consequently deflects the SWNT by z (see Figure 1b). In Figures 4c and 5 we present the sensor performance of two different devices based on metallic SWNTs. As depicted in Figure 3b, the AFM tip pushes the Au cantilever at the point where the clamped, suspended nanotube is mechanically connected to the cantilever. For these experiments we used a precalibrated AFM tip with a force constant of kAFM ) 0.28 nN/nm. We electrically connected the cantilever structure with one of the outer electrodes in order to avoid electrical interference which could be caused by the floating potential on the Au cantilever and the AFM tip. In Figures 4c and 5, the resistance, R, of the metallic SWNTs is plotted as a function of the deflection, z, for several cycles: up (white symbols) and down (black symbols) movements. The remarkable resistance change is in both cases reproducible, which leads to the conclusion that the presented nanoelectromechanical device operates in the linear-elastic regime. The insert at the bottom in Figure 4c shows the nanotube Nano Lett., Vol. 6, No. 7, 2006
resistance as a function of time t, where each peak corresponds to a single AFM-based force vs displacement measurement. Note the high reproducibility of the peak series which is essential for any sensing application. The force, F, versus displacement, D, characteristic is plotted in the bottom insert of Figure 5. Note that forces of F ≈ 50 nN are necessary to deflect the test structures by approximately 30-40 nm. This sufficiently exceeds the critical back-coupling force, FNT ) 5 nN, such that in this case we can neglect the effect of the carbon nanotube within the mechanical model. This also explains the linear characteristic of the shown force vs displacement measurements. Moreover, the force vs deflection relation agrees well with the Euler-Bernoulli theory of beams,27,28 which we have shown elsewhere.23,24 The large nonlinear resistance change is attributed to changes in the band gap of the nanotube due to the strong reproducibility of the resistance change, rather than to changes in the metal-electrodes contacts.17,19 However, an elastic deformation at the contacts with a direct influence on the resistance change and kinking effects (local transitions from sp2 to sp3 hybridization) on the edges of the structure cannot be excluded. Nevertheless, we find good agreement in the limit of thermal activated transport17 by modeling the nanotube resistance R[z()] by R[z()] ) Rs +
(
[
)]
Eg[z()] 1 h 1 + exp , 2 2 kBT |t| 8e
(1)
where Rs is a series resistance with the metal-nanotube junction, |t|2 is the transmission through the carbon nanotube, and Eg ) (dEg/d) is the strain-dependent band gap of a metallic nanotube (torsion contributions are neglected). The strain in the suspended nanotube branches as a function of z is given by (z) )
x ( ) 1+
z
LNTB
2
-1
(2)
where LNTB ) 200 ( 20 nm is the length of one nanotube branch (see Figure 1a). Fitting a curve of the form of eq 1 to the measurement data (see solid line in the upper insert in Figure 5) leads to an estimation of Rs, |t|2, and dEg/d. For the two different metallic SWNTs presented in Figure 5 (and Figure 4), this gives the following parameters: Rs ) 316 ( 76 kΩ (Rs ) 93 ( 31 kΩ), |t|2 ) 0.2 ( 0.09 (|t|2 ) 0.04 ( 0.01), and dEg/d ) 90 ( 8 meV/% (dEg/d ) 177 ( 4 meV/%). It is noteworthy that these values agree well with earlier independent measurements on strained SWNTs.3,14-17 The model given by eqs 1 and 2 with the parameters fit to the measurement data provides good trendlines as shown by the dashed lines in Figures 4c and 5. Equation 2, moreover, allows extraction of the nonlinear piezoresistive gauge factors, βGF() ) (∆R()/R0)-1, of the integrated SWNTs. In Figure 6 the extracted piezoresistive gauge factors, βGF(), for the two different samples (#1 and #2) are plotted as a function of strain . The solid lines are 1451
Figure 5. Electromechanical measurements of a second electromechanical sensor device based on a metallic SWNT. The upper insert shows the resistance plotted as a function of the strain (see eq 2) in the nanotube branch. Note that all three cycles have been used for fitting (solid line). The lower insert shows a typical force versus deflection measurement performed on the cantilever-SWNT contact point (P).
by ∆Ids,JN ) (4kBTB/R)1/2, where B is the bandwidth. Hence, from a purely electrical point of view the theoretical resolution ∆zmin follows as ∆zmin ) |σR-1VdsIds-2| B-1/2∆Ids,JN ≈ 20 fm/Hz1/2. This is in the range of state-of-the-art MEMS devices.33 Note that the value of ∆zmin has in the end been extracted from the model (eqs 1 and 2; dashed line in Figure 5) and has not yet been validated by the experiment. Further improvements of the experimental setup and investigations on the electromechanical response of metallic and semiconducting SWNTs are needed to fully characterize the proposed sensing mechanism. To validate the model used in eq 1 of the strain-dependent resistance R(), variable-temperature experiments are needed. Moreover, additional electrical, mechanical, and electromechanical noise sources have to be investigated to fully describe the sensor performance of the proposed device. In conclusion, we have presented a nano-electromechanical-sensing device based on an individual single-walled carbon nanotube to measure small deflections at the nanoscale. The fabrication process has been briefly discussed, and electrical and electromechanical measurements on the SWNTbased transducer have been performed. The investigated suspended SWNTs showed piezoresistive gauge factors of up to 2900. Finally, the feasibility of the proposed sensing scheme has been shown and a relative differential resistance sensitivity of up to σR,rel ) 27.5%/nm has been extracted. Acknowledgment. The authors wish to thank Thomas Helbling, Ronald Grundbacher, Otte Homan, Franck Robin, Sybille Vuillmers, and Bernhard Boser for helpful discussions. Support by the ETH FIRST Lab and financial support by the TH-18/03-1 Grant and Swiss National Science Foundation (20021-108059/1) are gratefully acknowledged. References
Figure 6. The piezoresistive gauge factor βGF() of the two different single-walled carbon nanotubes from Figures 4 and 5 (sample #1 and #2) as a function of strain . The solid lines are computed from the theoretical model with the fitting parameters given in the text. The dashed line represents the gauge factor which can be accessed with state-of-the-art silicon-based strain gauges.
computed by making use of the model introduced above. Note, that the piezoresistive gauge factors, found in the range of up to βGF ) 2900, are clearly exceeding the gauge factors of state-of-the-art silicon strain gauges, βGF ≈ 200 (see dashed line in Figure 6).29 Finally, the model allows the extraction of an effective differential sensor sensitivity σR ) [dR/dz]|z0 at a certain working point z0; e.g., we find σR ) 1016 kΩ/nm at z0 ) 35 nm for the metallic SWNT from Figure 5 (see also dotted line in Figure 5). This corresponds to a relative differential resistance sensitivity σR,rel ) Rz0-1‚[dR/dz]|z0 of σR,rel ) 27.5%/nm. To estimate a (potential) theoretical limit of the accessible resolution ∆zmin of the presented displacement sensor, we restricted ourselves to the electrical thermal noise30 as the dominant noise source in the SWNT-based system for small Ids.31,32 Thus, flicker noise, electromechanical, mechanical and quantum mechanical noise sources are neglected. The Johnson-Nyquist thermal noise of the current Ids is given 1452
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