Fig. 1 Millimeter-sized MEMS nanomanipulator with a motion range of micrometers and resolution of sub-nanometers for precisely manipulating nanometer-sized objects.

This project was supported by Natural Sciences and Engineering Research Council of Canada (NSERC).

*Corresponding author: 5 King's College Road, Toronto, M5S 3G8. Tel: 1-416-946-0549; E-mail: sun@mie.utoronto.ca.

Millimeter-Sized Nanomanipulator with Sub-Nanometer Positioning Resolution and Large Force Output

Xinyu Liu, Student Member, IEEE, Jianhua Tong, Member, IEEE, Yu Sun*, Senior Member, IEEE

Advanced Micro and Nanosystems Laboratory, University of Toronto, Canada

Abstract — Nanomanipulation in space-limited environments (e.g., inside SEM, and particularly in TEM) requires small-sized nanomanipulators that are capable of producing sub-nanometer positioning resolutions and large output forces. This paper reports on a millimeter-sized MEMS (microelectromechanical systems) based nanomanipulator with a positioning resolution of 0.15nm and a motion range of ±2.55�m. An amplification mechanism is employed to convert input displacements, generated by conventional electrostatic comb-drive microactuator, to achieve a high positioning resolution on the output side. The device has a high load driving capability, driving a load as high as 98�N without sacrificing positioning performance. Testing results demonstrate that the mechanism has a high linearity (±2.4%). A capacitive displacement sensor is integrated for detecting input displacements that are converted into output displacements via a minification ratio, allowing closed-loop controlled nanomanipulation. The MEMS-based nano-manipulators are applicable to the characterization/manipulation of nano-materials and construction of nano devices.

Keywords — Nanomanipualtor, sub-nanometer resolution, amplification mechnism, MEMS

I. INTRODUCTION

Recent advances in nanoscience and nanotechnology, including the manipulation and characterization of nano-materials (e.g., carbon nanotubes, silicon nanowires, and zinc oxide nanorods) and NEMS (nanoeletromechanical systems) development, require millimeter-sized manipulators with sub-nanometer positioning resolutions, micrometer motion ranges, high repeatability, and large output forces.

Compared to commercially available nanomanipulators with electron-discharge-machined stages and piezoelectric actuators, MEMS microactuators have such advantages as low cost, small size, fast response, and flexibility for system integration, and therefore have been employed in various nanopositioning applications. Particularly, electrostatic microactuators have been widely used for nanopositioning. Electrostatic microactuators are capable of providing typical resolutions on the order of 10nm [1]-[3]. Compared to other microactuation mechanisms (e.g., electrothermal and electromagnetic), electrostatic microactuation offers the fastest response, and more importantly, the best repeatability that is critical for applications at the nano scale. However, the small output force capability of electrostatic microactuators limits their practical applications in the manipulation of nano-objects.

Electrothermal microactuators were also employed in the development of nanopositioners [4]. Although electrothermal microactuation provides much larger output forces, hysteresis and thermal drift make the positioning accuracy relatively low (hundreds of nanometers). Furthermore, the difficulty of well

controlled temperatures at the probe tip prevents its use in temperature sensitive applications.

This paper presents the design, fabrication, and testing of a millimeter-sized nanomanipulator that leverages the high repeatability and fast response of MEMS electrostatic microactuators while overcoming the limitation of low output forces. The device integrates a highly linear amplification mechanism, a lateral comb-drive microactuator, and a capacitive displacement sensor. The amplification mechanism is used to minify input displacements for achieving a high positioning resolution at the output probe tip and to amplify output forces for manipulating nano-objects. Fig. 1 shows a conceptual schematic where the MEMS-based millimeter-sized nanomanipulator is used to manipulate nanospheres.

II. WORKING PRINCIPLE

The nanomanipulator shown in Fig. 2 consists of a linear amplification mechanism, a lateral comb-drive microactuator, and a capacitive displacement sensor. The linear amplification mechanism, which operates in the reverse (minifying) mode, is used to convert large input motion (�m) into small output motion, significantly enhancing the positioning resolution. The comb-drive actuator consisting of groups of interdigitated comb fingers produces bi-directional motion that is resolved by the capacitive displacement sensor. The measurement of input displacements enables closed-loop position control of the comb-drive actuator.

The linear amplification mechanism, employed for minifying input displacements and amplifying output forces, integrates two typical amplification mechanisms: toggle mechanism and lever mechanism (Fig. 3(a)), which are connected in series by single-axis flexure hinges. In order to eliminate lateral displacements at the output end caused by lever rotation, two pairs of toggle mechanisms and lever

1-4244-0608-0/07/$20.00 © 2007 IEEE. 454

Proceedings of the 7th IEEEInternational Conference on Nanotechnology

August 2 - 5, 2007, Hong Kong

Fig. 2 Solid model of the MEMS nanomanipulator with capacitive displacement sensor.

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Fig. 3 (a) Schematics of inverse-mode linear amplification mechanism. (b) Displacement and stiffness analysis.

mechanisms are symmetrically configured. Compared to the two-stage lever amplification mechanism [5], the toggle-lever amplification mechanism provides a higher displacement amplification ratio and more compact structure [6][7]. As the testing results show, the amplification mechanism is highly linear. Thus, the capacitive displacement feedback on the input side can be used to reliably predict displacements on the output side, enabling precise closed-loop control of nanopositioning during nanomanipulation.

III. DEVICE STRUCTURE DESIGN

A. Analytical Model

In order to provide a systematic design approach for determining structural parameters of the amplification mechanism, an analytical model based on the pseudo-rigid-body approach was developed [8]. Fig. 3(b) illustrates half of the mechanism with equivalent boundary conditions. The minification ratio as a function of beam lengths (l0, l1, and l2) and angles (�1 and �2) is

)cotsin(cos 2111

0

θθθα

−−==

l

l

y

y

in

out (1)

where the minus sign represents opposite directions of yin and yout. The total input stiffness of the device is

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where E is the Young's modulus of silicon; w, h, and l are width, height, and length of the thin flexible beams (Fig. 3(a)); W1, H1, and L1 are width, height, and length of supporting beam 1; W2, H2, and L2 are width, height, and length of supporting beam 2; and Khinge is the rotational stiffness of the single-axis flexure hinge

2/1

2/5

9

2

R

EbtKhinge

π= (3)

where b, t, and R are specified in Fig. 3(b). In this design, all hinges have the same dimensional parameters.

B. Finite Element Simulation The dimensional parameters of the nanomanipulator are

summarized in Table I. Based on these parameters, finite element analysis (FEA) was conducted using ANSYS® to verify the validity of the developed theoretical models of the amplification mechanism. Table II shows the material properties of silicon used in simulation.

Electrostatic actuation forces were first calculated according to following equation

2

2

1V

g

hNF fa

e

ε= (4)

where )/(1085.8 2212 NmC−×=ε is the permittivity of air, V

the actuation voltage, hf the finger thickness, g the gap between adjacent comb fingers, and Na is the number of actuation comb finger pairs. These actuation forces were then applied as input to the finite element model. The FEA results are summarized in Table III. The theoretical calculation results based on the derived closed-form models (1) and (2) are in agreement with the FEA simulation results with errors within 5% in the complete output motion range (±2.55�m at actuation voltage of 60V), proving the validity of the derived minification ratio and stiffness models.

455

TABLE I DIMENSIONAL PARAMETERS OF AMPLIFICATION MECHANISM.

Structural parameters

Base 2.0mm×4.0mm Amplification

mechanism l0=75�m, l1=300�m, l2=300�m, �1=20°, �2=165°

Flexure hinge b=10�m, t=2�m, R=8�m

Support beam 1 W1=8�m, H1=10�m, L1=780�m

Support beam 2 W2=8�m, H2=10�m, L2=820�m

Thin flexible beams w=2�m, h=10�m, l=80�m

TABLE II SILICON MATERIAL PROPERTIES USED IN FEA.

Density 2.329 g/cm3

Young’s modulus 129.5 GPa

Poission’s ratio 0.28

TABLE III THEORETICAL AND FEA RESULTS OF DEVICE SPECIFICATIONS.

Theoretical FEA Difference

Input stiffness (�N/�m) 16.82 16.84 0.24%

Minification ratio -0.1128 -0.1187 5.0%

Fig. 4 Microfabrication process.

Fig. 5 SEM picture of a released device.

Due to bending, maximum stress occurs at two flexure hinges connecting toggle mechanisms with lever mechanisms. The maximum stress in the complete motion range (±2.55�m) was determined in FEA to be within 2.1GPa, which is within the yield strength of silicon (7GPa) [9].

As out-of-plane motion of the nanomanipulator probe tip is undesired, it was also investigated using FEA. The results show that out-of-plane displacements are within ±1nm in the complete motion range (±2.55�m), confirming that the nanomanipulator has a satisfactory stability in the out-of-plane direction.

IV. DEVICE FABRICATION The MEMS-based nanomanipulators were fabricated with a

glass wafer and a silicon-on-insulator (SOI) wafer, using wet glass etching, wet silicon etching, and silicon deep reactive ion etching (DRIE). The fabrication process, as illustrated in Fig. 4, is summarized as follows: (A) The fabrication process begins with a 500�m thick glass

wafer, on which 12�m deep cavities are etched using BOE etching.

(B) An SOI wafer is anodically bonded to the patterned glass wafer with the device layer (10�m thick) facing down.

(C) The silicon handle layer and buried SiO2 box layer are etched away, leaving only the single crystal silicon device layer on top of the patterned glass substrate.

(D) Metal layers of 500Å thick Ti-W and 2000Å Au are evaporated onto the device layer to form ohmic contacts, and are patterned using wet etching.

(E) The device layer is finally etched through using DRIE to form comb fingers, amplification mechanism, and other features.

V. TESTING RESULTS AND DISCUSSION Fig. 5 shows a released MEMS nanomanipulator. For

device testing, it was wire-bonded to a custom-made printed circuit board that contains a capacitance readout circuit. The

displacements at input and output ends of the amplification mechanism were measured under optical microscope (100× objective, NA 0.42; digital camera with 3.5× lens) using the auto-correlation method [10], and the measurement resolution is 2.58nm.

Fig. 6(a) shows the testing results of output displacements as a function of input displacements, proving a linearity of ±2.4% and a minification ratio of -0.1151 for the amplification mechanism. At 60V, the nanomanipulator is capable of generating ±2.55�m output displacements. A 30V voltage produces an output displacement of ±650nm (Fig. 6(b)). Compared to experimental data, the derived theoretical model of the amplification mechanism satisfactorily predicts output displacements with an error ≤ 6.2%.

Two fixed-guided thin beams (Fig. 5) are attached to the output probe for quantifying output forces of the nanomanipulator. The total stiffness of the force sensing beams is 40.5�N/�m. The measured output displacements with force sensing beams are shown in Fig. 6(c). The maximum output displacement is ±2.42�m, corresponding to a maximum output force of 98�N. Compared to the zero-load case (±2.55�m), the maximum displacement is only reduced by 5.1%, demonstrating a strong load driving capability of the nanomanipulator. Additionally, accelerated reliability testing shows that after 50 million actuation cycles, no signs of degradation/failure were observed.

Capacitance changes of the displacement sensor were measured by a readout circuit based on an ASIC from Analog Devices (AD7746). Fig. 7(a) shows the calibration results of the capacitive displacement sensor, proving a linear relationship between voltage changes and input displacements. The resolution of the readout circuit was determined to be 30aF/Hz1/2 that corresponds to an input displacement resolution

456

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2

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input displacement (μm)

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(a)

-1000 -500 0 500 1000

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voltage square (V2)

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(μm

) testing resultsregressiontheoretical results

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1

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3

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(μm

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(c)

Fig. 6 (a) Experimental data of output vs. input displacements. (b) Experimental and theoretical results of output displacements vs. actuation voltage squared. (c) Testing results of output displacements with force sensing beams.

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time (sec)

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t di

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(�m

)

desired positionclose-loop tracking position

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-1

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(b)

(b)

(a)

Fig. 7 (a) Calibration data of capacitive displacement sensor. (b) Experimental results of close-loop sinusoidal tracking.

of 1.31nm in a 10Hz bandwidth. The integrated capacitive displacement sensor permits the execution of closed-loop controlled nanopositioning/nanomanipulation. Fig. 7(b) shows the experimental results of close-loop sinusoidal tracking using a PID (proportional-integral-derivative) controller.

Considering the high input-output linearity from the amplification mechanism (±2.4%), capacitive displacement feedback on the input side can be used to reliably predict minified output displacements. Thus, the output positioning resolution was determined by scaling the input resolution (1.31nm) with the minification ratio (0.1151), which results in an output positioning resolution of 0.15±0.0036nm with the uncertainty arising from the ±2.4% linearity. Thermal-mechanical noise induced vibration was determined via the Nyquist’s Relation [11] to be 0.0031nm, indicating that the output positioning resolution is not limited by thermal-mechanical noise.

The millimeter-sized MEMS nanomanipulators provide many design flexibilities, such as extension to two axes and adjustment of motion range and resolution, and allow one to mount nanometer-sized end effectors on the probe for nanomanipulation (Fig. 1). The MEMS nanomanipulators

provide a small-sized, high-precision, low-cost platform for closed-loop manipulation of nanometer-sized objects and tensile/compression characterization of nano-materials.

VI. CONCLUSION

This paper presented the design, fabrication, and testing of a millimeter-sized MEMS nanomanipulator. The device has a positioning resolution of 0.15nm, an output motion range of ±2.55�m, and a high load driving capability (i.e., outputting a force of 98�N reduces motion range only by 5.1%). An amplification mechanism operating in the minification mode with a high linearity (±2.4%) was employed to minify input displacements and enhance the output displacement resolution. The integrated on-chip capacitive displacement sensor and the high linearity of the amplification mechanism are capable of providing precise position feedback, and closed-loop nanopositioning was experimentally demonstrated. The MEMS nanomanipulators are applicable to precisely manipulate and characterize nano-materials.

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