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Multimodal Electrothermal Silicon Microgrippers for Nanotube Manipulation
Nordström Andersen, Karin; Petersen, Dirch Hjorth; Carlson, Kenneth; Mølhave, Kristian; Sardan Sukas, Özlem; Horsewell, Andy; Eichhorn, Volkmar; Fatikow, S.; Bøggild, Peter
Published in: IEEE Transactions on Nanotechnology
Link to article, DOI: 10.1109/TNANO.2008.2006558
Publication date: 2009
Document Version Publisher's PDF, also known as Version of record
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Citation (APA): Nordström Andersen, K., Petersen, D. H., Carlson, K., Mølhave, K., Sardan Sukas, Ö., Horsewell, A., Eichhorn, V., Fatikow, S., & Bøggild, P. (2009). Multimodal Electrothermal Silicon Microgrippers for Nanotube Manipulation. IEEE Transactions on Nanotechnology, 8(1), 76-85. https://doi.org/10.1109/TNANO.2008.2006558
Multimodal Electrothermal Silicon Microgrippers for Nanotube Manipulation
Karin Nordstrom Andersen, D. H. Petersen, K. Carlson, K. Mølhave, Ozlem Sardan, A. Horsewell, Volkmar Eichhorn, Sergej Fatikow, Member, IEEE, and Peter Bøggild
Abstract—Microgrippers that are able to manipulate nanoob- jects reproducibly are key components in 3-D nanomanipulation systems. We present here a monolithic electrothermal microgrip- per prepared by silicon microfabrication, and demonstrate pick- and-place of an as-grown carbon nanotube from a 2-D array onto a transmission electron microscopy grid, as a first step toward a reliable and precise pick-and-place process for carbon nanotubes.
Index Terms—Carbon nanotubes, microgrippers, nanomanipu- lation, pick-and-place.
I. INTRODUCTION
S EVERAL groups have previously used microfabrication to make microgrippers for manipulation [1], and commer-
cial vendors exist today, such as Nascatec [2], Zyvex [3], and FemtoTools [4] . The concept of nanotweezers was first demon- strated by Kim and Lieber [5], who gripped nanowires and nanoparticles between two electrostatically biased carbon nan- otubes attached to a glass capillary. Based on a simple five- electrode microcantilever layout similar to that of Kim et al. [1], submicron grippers were fabricated. These microgrippers were capable of both opening and closing without applying a volt- age directly between the arms [6] and were used to manipulate silicon nanowires [7]. Here, we describe a more mechanically stable, electrothermal three-beam microgripper with a high grip- ping force, which can be fabricated in single-crystalline silicon (SCS) as well as polycrystalline silicon.
Manipulation of a carbon nanotube (CNT) from one place to another can be done inside a scanning electron microscope (SEM), in which a suitable combination of visual resolution and sample space allows macroscale manipulators with micro- or nanoscale precision to be incorporated, yet monitored with nanometer-scale precision [8]–[11]. Complex multiprobe sys- tems, allowing two or more scanning probe tips to be moved
Manuscript received December 8, 2007; revised March 13, 2008. First published September 30, 2008; current version published January 16, 2009. This work was supported by the European Union under Grant NANOHAND (IP 034274) and Grant NANORAC (STREP 013680). The review of this paper was arranged by Associate Editor L. Dong.
K. N. Andersen, D. H. Petersen, K. Carlson, K. Mølhave, O. Sardan, and P. Bøggild are with MIC—Department of Micro and Nanotechnology, NanoDTU, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark (e-mail: [email protected]; [email protected]; [email protected] dtu.dk; [email protected]; [email protected]; [email protected]).
A. Horsewell is with IPL—Department of Manufacturing Engineering and Management, NanoDTU, Kemitorvet, DTU, DK-2800 Lyngby, Denmark (e-mail: [email protected]).
V. Eichhorn and S. Fatikow are with the Division of Microrobotics and Con- trol Engineering, University of Oldenburg, 26111 Oldenburg, Germany.
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TNANO.2008.2006558
independently inside a SEM, have been used to characterize the mechanical properties of nanotubes and nanowires [3]. In these experiments, a combination of surface forces acting between the tip and the nanotube, a local soldering or gluing induced by electron beam deposition of carbonaceous material, and me- chanical force applied to the nanotube by two individual tips, was used for pick-and-place of the nanotube.
An array of vertically ordered CNTs [12] is an excellent exam- ple of a highly suited starting point for nanorobotic prototyping or even manufacturing of CNT-based devices.
One advantage of such a “component bank,” with well- defined positions for all the CNTs is that, once calibrated, the manipulation system can locate the CNT automatically. Another advantage is that the CNTs can be grown with a high degree of uniformity across a large area. A single CNT can then be picked up without risking sticking of other CNTs sticking to the ma- nipulation tool [12]. In this context, a key problem is to provide a manipulation tool that is small and delicate enough to align to a sub-100-nm-diameter CNT, mechanically strong enough to detach the as-grown CNT from the surface, and able to release the CNT again at the desired target position.
Electrothermal actuators generally allow a relatively high gripping force to be combined with a compact design [13], while the design presented earlier [14] is capable of both open- ing and closing. This feature expands the deflection range and turns out to be convenient in actual experiments. For instance, in the event that the microgripper jaws remain closed due to ad- hesive material between the jaws—the “open” reaction is then often enough to force the gap open. In this paper, we show that by fabricating the microgripper in SCS 1 1 1 (see Fig. 1) as well as polycrystalline silicon, we obtain a similar actuation and gripping force as with Au [14], but with the added benefits of an easier fabrication process, less adhesion, and less out-of-plane bending. Finally, we demonstrate its use in manipulating carbon nanotubes.
II. DESIGN CONSIDERATIONS
A. Actuation Modes
The 3-beam microgripper design allows several configura- tions for actuation of the microgrippers depending on how the bias voltage is applied over the six beams (see Fig. 2). To close the microgripper, the bias voltage V can be applied to the outer two beams with the inner four beams grounded, mode 3, (V, 0, 0, 0, 0, V ), or while letting the inner beams float [14], mode 2, (V, 0, F, F, 0, V ), where F refers to a floating potential, i.e. not connected. Biasing the left three beams with V and the
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ANDERSEN et al.: MULTIMODAL ELECTROTHERMAL SILICON MICROGRIPPERS FOR NANOTUBE MANIPULATION 77
Fig. 1. SEM image of electrothermal three-beam microgrippers fabricated in SCS. The inset shows a magnified top view.
Fig. 2. Six different actuation modes of the three-beam microgripper. The connection configuration is shown below each illustration, i.e. with 0, V , and −V signifying zero or finite potential, while F signifies “floating,” not con- nected. (1) Electrostatic. (2) Electrothermal two hot beams. (3) Electrothermal three hot beams. (4) Combination (ET + ES). (5) Electrothermal two hot beams. (6) Electrothermal three hot beams.
right three with 0, mode 1, (V, V, V , 0, 0, 0), results in purely electrostatic actuation. Finally, the electrothermal and electro- static actuation can be combined by using (V, 0, F, F, 0,−V ), where the different signs of the voltage on the left and right arms adds electrostatic to the electrothermal actuation.
Electrothermal actuation leads to high temperatures, ulti- mately reaching the melting point of silicon (∼1700 K), as the maximum deflection is approached—this is a common problem for all electrothermal actuators. In addition, the three-beam ac- tuator has its maximum temperature at the end-effector, which
Fig. 3. (Left) geometry of the three-beam microgripper is depicted. (Right) illustration of a single arm with the actuation A, and an arm which is blocked by the other arm, and an object of radius R.
implies that heat-induced damage of the object must be consid- ered as well.
The layout, however, enables the microgrippers to operate also by electrostatic actuation, i.e., by applying a voltage across the two three-beam arms. With electrostatic actuation, the mi- crogripper does not heat up; but the gripping force and deflection range are lower. Even though electrostatic actuation does not cause a short between the arms due to the native oxide present on the gripper arms, care has to be taken when gripping con- ducting samples. The tradeoff between a high gripping force and a low temperature implies that careful consideration has to be given to both the microgripper design and the mode of operation.
B. Actuation and Gripping Force Required to Break off a Carbon Nanotube
In order to align to and break off a vertically aligned, multi- walled carbon nanotube, such as presented by Carlson et al. [15], the gap g between the gripper arms must be large enough to con- veniently align the end-effectors to the carbon nanotube. Based on practical experience, this requires at least g = 1–2 µm, which is also a gap size that can be manufactured reliably with pho- tolithography.
In addition, each arm should be capable of not only closing to half the gap, g/2 (see Fig. 3), but also, further to increase the gripping force. If the gap can only barely be closed, no gripping force is available for manipulation. A large actuation combined with a large rigidity of the actuator is needed to eventually apply a large gripping force to a seized object.
When the microgripper is holding a carbon nanotube of radius R with zero gripping force, the free actuation of each arm is exactly g/2 − R (see Fig. 3). The gripping force is defined here as the spring constant, k, multiplied by the overhead actuation A = A − (g/2 − R) (see Fig. 3) still available when the gap is holding a nanotube
Fgrip = k ( A − g
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78 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 8, NO. 1, JANUARY 2009
Fig. 4. (A) Illustration of tensile and shear pulling. (B) SEM images of electrothermal microgripper picking carbon nanotubes with tensile and shear pulling, respectively. (C) Available (full lines) and required (dotted lines) grip- ping force versus CNT radius for breaking off CNTs (weak and strong) by shear pulling at Tm ax = 600 K for different microgripper geometries. (D) T = 1000 K (curves for tensile pulling not shown).
By bending a cylindrical CNT as a cantilever (one end fixed, one end free), it is possible to break it at the base where the stress and also the maximal bending moment Mmax will be located. The bending moment M (x) is related to the radius of curva- ture Rcurv and the deflection u(x) through the beam equation, R−1
curv = u′′(x) = −M(x)/EI , where E is the Young’s modu- lus of the nanotube and I = πR4/4 is the cylindrical plane mo- ment of inertia. For small curvatures, we get Rcurv = RE/σ, which then allows us to the express the maximum bending moment as
Mmax = πR3σmax
4 . (2)
A vertically aligned CNT can be detached using a microgrip- per either vertically (tensile pulling) or laterally (shear pulling). These two modes are illustrated in Fig. 4(A), and shown as SEM images of a microgripper picking up a carbon nanotube in Fig. 4(B). As discussed in a previous study [13], [15], shear pulling is much more effective than tensile pulling for nan- otubes/nanowires. If the microgripper is holding the CNT firmly, the CNT will be clamped at one end and guided at the other, which according to [16] gives the relationship: M = FLfree/2, where Lfree is the free length of the rod. With Fbend as the force required to bend the CNT to the breaking point, we get: Fbend = 2Mmax/Lfree .
To bend the CNT into a vertical position, as shown in Fig. 4, the left and right end-effector surfaces with length Lgrip must generate a moment equal to the bending moment of the nanotube Mmax , preventing the CNT from forcing the jaws open. This requires a force, Ftwist = Mmax/Lgrip . An estimate of the total required force can be done by adding the two contributions, Fbend and Ftwist
Fshear = πR3σmax
) (3)
which can be evaluated without knowing the Young’s mod- ulus. The spring constant of the three-beam microgripper is given by k = 11Egripperhw3/(4L3) [14], where Egripper is the Young’s modulus of the microgripper, and h,w, and L the height, width, and length of the gripper arms, respectively. The actuation as a function of the maximum allowed temperature Tmax = Tmax − 300 K in actuation mode 3 (see Fig. 2), can be written as [14]
A3 = αL2Tmax
18w (4)
where α is the thermal expansion coefficient. The expression for mode 2 can be found to be A2 = (4/3)A3 . There will al- most always be a maximum allowed temperature in a given manipulation experiment to avoid damage to the object or the microgripper. Clearly, this means that the melting point of sil- icon, around 1700 K, must not be exceeded. Both SCS and polycrystalline silicon, however, undergo plastic (irreversible) deformation at lower temperatures than the melting tempera- ture. At the stress levels applied during actuation, the transition from the elastic to the inelastic regime for polycrystalline sili- con occurs at around 1050 K [17], while plastic transformations start to occur at around 1200–1300 K for SCS [18].
Furthermore, few nanostructures can sustain temperatures above 1000 K without damage. Although structurally perfect single-walled CNTs have a melting point exceeding 4800 K [19] and a premelting point of 2600 K for CNTs with Stones–Wales defects [19], previous experiments have shown that operating temperatures much larger than the temperature reached during the PECVD growth (around 1100–1200 K) can lead to changes in the CNT structures [19]. Here, we take 1000 K to be the maximum temperature for CNT manipulation, as long as the experiments are done in vacuum; in air, the CNTs may oxidize at much lower temperatures.
In Fig. 4 the required gripping force Fshear (dotted lines) is plotted for carbon nanotubes/ nanowires with yield strengths of 7 GPa and 50 GPa, representing medium-strength CNTs and high-strength CNTs, respectively [20]–[22]. A yield stress of 7 GPa is also roughly representative of plasma-enhanced chem- ical vapor deposition (PECVD) grown CNTs with structural de- fects [20]–[22]. In Fig. 4(C), curves both for short (L∗ = 1 µm) and long (L∗ = 3 µm) CNTs are shown, where L∗ = Lfree = Lgrip .
The available force (full lines) calculated from (3) is plotted for Tmax = 600 K in Fig. 4(C) and Tmax = 1000 K in Fig. 4(D). Each curve is labeled with the geometric parameters, (length, width, height, and gap) of the microgripper. Microgrippers with
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ANDERSEN et al.: MULTIMODAL ELECTROTHERMAL SILICON MICROGRIPPERS FOR NANOTUBE MANIPULATION 79
lengths L = 100 and 200 µm, width 2 µm, heights 2 and 5 µm, and gap size 1 and 2 µm are plotted.
As an example, Fig. 4(C) predicts that weak (σmax = 7 GPa) CNTs with radii of up to 90 nm can be picked up by shear pulling, using a microgripper with dimensions: L = 200 µm, w = 2 µm, h = 5 µm, and g = 2 µm (heavy line).
From the curves, several observations can be made. 1) The shorter microgrippers with a gap size of 1 µm provide the largest force at 1000 K, but cannot close at 600 K, hereby not producing a gripping force. With a gap of 2 µm, the shorter microgrippers cannot close at all, and hence do not appear in any of the graphs; 2) At low temperature, T = 600 K, short, strong CNTs (50 GPa, 1 µm) with radii above 40 nm are not possible to break off even with the strongest microgrippers; 3) Increasing the height of the microgripper arms from 2 to 5 µm significantly improves the gripping force at both temperatures.
In a previous study by Molhave and Hansen [14], three- beam microgrippers made of gold had a width of 2 µm and a height of 1 µm. Gold has a thermal expansion coefficient of 14.2 × 10−6 K−1 , which is three to four times larger than silicon 2.5 × 10−6 K−1 [23], while the melting point of gold (∼1340 K) is not far from that of silicon (∼1700 K). As a re- sult, the actuation at maximum and intermediate temperatures is considerably smaller for Si, which must then be compensated by increasing the height of the microgripper.
This also reduces the out-of-plane bending, which was a se- rious problem for the small-aspect ratio microgrippers [14].
Thus, by keeping the beam width and gap size at the pho- tolithographic limit, w = 2 µm, a change of the height to 5 µm increases the out-of-plane spring constant kop by a factor of 125 according to kop ∝ wh3/L3 , while providing a reasonable gripping force. With a length of 200 µm, the microgripper can operate over a large temperature range.
C. Finite-Element Simulations of Shear Pulling: How to Break off a Nanotube
It is crucial that the nanotube breaks near the base and not near the microgripper, since retaining the free end is necessary for further handling. In the aforesaid calculations of a cylindrical nanorod, the maximum moment is obtained both at the base and at the microgripper simultaneously; hence, there is equal probability of the nanotube breaking at either point.
So far, we have assumed that the carbon nanotube is cylin- drical, and that the microgripper is completely closed. In prac- tice, carbon nanotubes and nanowires are often tapered [15]. The shear pulling method was analyzed using the finite-element analysis program COMSOL. Tapered and cylindrical nanorods with a diameter of 250 nm near the lower edge of the end- effector were modeled with 6000–10000 mesh elements. The Young’s modulus of the PECVD-grown multiwalled CNTs is expected to be within 0.1 and 1.0 TPa [20]–[22], [24] depend- ing on the precise internal structure, while the yield strength is roughly 1–10 GPa [20]–[22]. In the calculations, the Young’s modulus was set to 0.75 TPa. In Fig. 5(A), shear pulling of a cylindrical nanorod is shown, where a lateral deflection of 250 nm results in a stress of 18 GPa both at the base and at
Fig. 5. (A) Cylindrical nanorod held in a firm grip. (B) Tapered nanorod held in a firm grip. (C) Tapered nanorod pushed by single end-effector. (D) Tapered nanorod held in a loose grip.
the lower edge of the end-effector, as expected. In the case of a tapered nanorod, Fig. 5(B), the stress is much lower at the base, which inevitably leads to breaking near the end-effector. Fig. 5(C) indicates how this situation can be avoided; a sin- gle end-effector applies a point force of 15 µN laterally, i.e., Lfree = 3 µm above the surface, at the lower edge of the end- effector. This generates a stress of 8 GPa at the base with almost no stress at the end-effector contact point. However, using a sin- gle end-effector, the nanotube is likely to be lost after breaking. With an increase of the applied force from 15 to…