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Flexure-based dynamic-tunable five-axis nanopositioner for parallel nanomanufacturing
Accepted Manuscript Title: Flexure-based Dynamic-Tunable Five-Axis Nanopositioner for Parallel Nanomanufacturing Author: Chenglin Li Ji Wang Shih-Chi Chen PII: DOI: Reference:
S0141-6359(16)30021-6 http://dx.doi.org/doi:10.1016/j.precisioneng.2016.04.002 PRE 6383
To appear in:
Precision Engineering
Received date: Revised date: Accepted date:
4-9-2015 7-2-2016 1-4-2016
Please cite this article as: Li Chenglin, Wang Ji, Chen Shih-Chi.Flexure-based Dynamic-Tunable Five-Axis Nanopositioner for Parallel Nanomanufacturing.Precision Engineering http://dx.doi.org/10.1016/j.precisioneng.2016.04.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Flexure-based Dynamic-Tunable Five-Axis Nanopositioner for Parallel Nanomanufacturing Chenglin Li, Ji Wang, and Shih-Chi Chen* Department of Mechanical and Automation Engineering The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR, China *
Corresponding author: [email protected]
Highlights
We present a flexure-based dynamic-tunable five-axis nanopositioner for tip-based nanofabrication application.
The experimental characterization shows the nanopositioner achieves ±100 nm, ±100 nm, ±10 nm, ±1 µrad and ±1 μrad precision in the X, Y, Z, θX, and θY axis with a work volume of 10 mm × 10 mm × 80 μm with closed-loop control.
The dynamic-tuning concept enables trade-offs between the range and speed of the flexural nanopositioner so as to increase the throughput of the nanomanufacturing system.
Static dynamic-tuning results show the natural frequency of the X-Y stage can be increased by 2-3 times. Active dynamic tuning experiments show active vibration cancellation techniques can be implemented to the nanopositioner to further improves the dynamic performance, i.e. reducing the overshoot and settling time from 487 nm / 1.5 seconds to 256 nm / 0.5 second.
Nano-scratching experiments were performed to fabricate optical grating patterns on gold coated silicon substrates over a 5 × 1 mm2 area within ~15 min to demonstrate the practicality of the new method.
Abstract With the increasing demand for devices and systems with nanometer precision in the modern manufacturing industry, tip-based nanofabrication (TBN) has become an indispensable part of manufacturing process. However, a common issue that needs to be addressed is to increase the throughput of TBN, which is sequential and inherently slow. To overcome the difficulty, in this paper we present the design and control of a flexure-based five-axis nanopositioner with dynamic-tuning capability for parallel nanomanufacturing applications. The dynamic-tuning method enables trade-offs between the range and speed of the nanopositioner so as to increase the throughput of the nanomanufacturing system. The experimental results indicate that the nanopositioner conforms with the in-plane range and resolution requirements, i.e., ±5 mm/ 100 nm in X/Y axis, while its natural frequencies in X/Y axis can be increased by two to three times at the expense of decreased stroke, i.e., elastic range. In addition, real-time dynamictuning experiments show active vibration cancellation techniques can be implemented on the nanopositioner and effectively eliminate the unwanted dynamics and improve the overall dynamic performance. Lastly, we performed nano-scratching experiments using an 18 tip AFM array to fabricate optical grating patterns on gold coated silicon substrates of 5 × 1 mm2 to demonstrate the practicality of the new method. The experiment confirmed good parallelism had been achieved during the experiments, where the scratched gold lines have a consistent depth of ~160 nm. Keywords: Compliant mechanism; dynamic-tuning; multi-axis nanopositioner; parallel nanomanufacturing
1. Introduction Nanomanufacturing is a process to create nanoscale structures, devices and systems [1] that encompasses
various
technologies,
including
focused
ion
beam
lithography
(FIBL)
[2],
electrohydrodynamic (EHD) jet printing [3], and two-photon polymerization (TPP) [4]. Tip-based nanofabrication (TBN) is an important and versatile nanomanufacturing technology that utilizes microscale cantilevers with attached nanoscale tips to realize nanofabrication [5]; TBN enables a wide range of manufacturing applications, e.g., material removal, modification, deposition, manipulation etc. [5], and therein lies its potential to provide pattern flexibility for fast prototyping [6]. However, comparing with mask- or template-based nanomanufacturing methods such as photolithography, nanoimprint lithography (NIL) and microcontact printing (MCP), which provide large-area modification and high throughput [7], all TBN techniques share a low throughput issue inherited from the serial nature of tip movement [7]. To circumvent such restriction, two methods are generally applied to improve the TBN throughput [8]: operating multiple tips in parallel [9], [10], and increasing the tip operation speed/frequency [11], [12]. In other words, multi-axis nanopositioners with enhanced speed and precision is the key to ensure successful industrial application of TBN [13]. Nanopositioners can move objects of different sizes with nanometer level precision. They are important as they set the limits on our ability to measure, manipulate, and manufacture physical systems. As traditional mechanical linkages are susceptible to backlash and wear between joint members, compliant mechanisms, i.e., flexures, are often used to fulfill the strict repeatability and precision requirements [14]. However, compliant mechanisms demand a larger device envelope in comparison to the motion they can generate, causing inevitable trade-offs between the natural frequency and range. To realize large-area parallel nanomanufacturing, e.g., generating nano-patterns on a 1 × 1 cm2 substrate, the nanopositioner must meet the following requirements: (1) five degrees of freedom (DOF), i.e., X, Y, θX, θY, and Z, where X and Y axes are for in-plane nanomanufacturing, θX, θY ,and Z axes are for aligning and positioning the tip array with the substrate; (2) nanometer level repeatability and submicron level precision for position control in all five axes; (3) a range of ±5 mm/ ±5 mm in the X/Y axis for largearea nanomanufacturing and a range of ±40 μm/ ±2 mrad/ ±1.5 mrad in the Z/θX/θY axis respectively; and
(4) dynamic-tuning capability that allows the nanopositioner to travel a long distance to locate and manufacture locally at high speed. Among these requirements, the dynamic-tuning capability is of particular importance as it alleviates the side-effect of low natural frequency induced by a large-stroke flexure-based nanopositioner. 2. Dynamic-tuning for flexure-based nanopositioners Although the dynamic performance of a flexural mechanism is determined by its natural frequency, it is often compromised by the required stroke of the mechanism. In other words, high natural frequency can only be achieved at the expense of reduced stroke. To be more specific, a high-bandwidth flexure-guided nanopositioner is limited to a relatively small travel range [15], while a large-displacement flexure-based nanopositioner has low natural frequencies. For example, a millimeter-ranged flexure-based nanopositioner typically has a resonant frequency less than 100 Hz [16]. In this paper, we aim to develop a dynamictunable flexure-based nanopositioner that allows trade-offs between speed (natural frequency) and range (stroke)—a concept inspired by compliant actuators used in humanoid robots [17]. The dynamic-tuning effect is achieved by exploiting the ―stress-stiffening effect‖, i.e., the increased stiffness of a beam when experiencing tensile loads in the axial direction [18]. The natural frequency of a simply supported beam with an axial force N can be described by Equation (1), where ω is the natural frequency; l, A, I, E, ρ are the length, cross-sectional area, area moment of inertia, Young’s modulus and density of the beam, respectively [18]. For example, the natural frequency of a simply-supported rectangular-section titanium beam (E = 1.048×1011 Pa, ρ = 4428.78 kg/m3, 70 mm long, 10 mm wide, and 1 mm thick) can be shifted from 450 Hz to 1164 Hz when a 1000 N uniform axial tensile force is applied to one end of the beam. Note that compression load is not used as it may cause buckling and instability.
2
l
EI Nl 2 1 2 A EI
(1)
To extend the frequency tuning concept from a beam to a flexural mechanism, Fig. 1 presents the simulated results of a symmetric double parallelogram (DP) mechanism where its yield stress is reached by increasing the axial loads. Fig. 1A shows the computer-aided design (CAD) model. The material used in
the finite element analysis (FEA) simulation is titanium. Fig. 1B shows that dynamic-tuning enables tradeoffs between the natural frequency and the elastic range of the DP mechanism. Ground Elastic range [mm]
60 40
20 0
Axial load
Axial load Ground
A
0
50 100 150 Natural frequency [Hz]
200
B
Fig. 1. Simulated results of a symmetric DP flexure using Abaqus 6.12. A: CAD model with load and boundary conditions; B: The relationship between the range and frequency of the DP flexure
3. Nanopositioner assembly and experimental setup 3.1 Nanopositioner design Fig. 2A shows the layout of the nanopositioner, where an in-plane X-Y stage and an out-of-plane Z-θXθY stage are connected in series to achieve five DOF. The X-Y stage, designed based on the principle of constraint-based design, achieves decoupled X and Y motion by using multiple folded-beam mechanisms [19]; the extended range in the X and Y directions are achieved by the symmetric DP mechanism [20], [21]. High-resolution linear actuators (PI M-230.10S) are chosen for in-plane actuation because of the large strokes (10 mm) and high resolution (37 nm). In order to perform dynamic-tuning, two piezoelectric actuators (the green arrows in Fig. 2A; PI P-845.20) are used in each DP mechanism to generate axial loads/stresses. Since the increase of axial force leads to higher natural frequency, P-845.20 are chosen to generate high forces (3000 N). The dynamic-tuning design is implemented on the X-Y stage to enable tradeoffs between its range and speed in both axes. Fig. 2B shows the installation of the piezoelectric actuator for stiffness-tuning. The bottom of the actuator is affixed to the X-Y stage; a screw cap with a ball top is mounted on the head of the actuator to prevent torques and lateral forces. The preload and axial load can be applied with ease by turning the screw cap.
Screw cap In-plane stage
Out-of-plane stage
PA-X
PA-X
PA-Y LA-X
LA-Y
Y X
A
B
Fig. 2. A: Layout of the nanopositioner: the green arrows, i.e., PA-X and PA-Y, indicate the piezoelectric actuators (PI P-845.20) for stiffness-tuning and the white arrows, i.e., LA-X and LA-Y, indicate the linear actuators (PI M-230.10S) for in-plane actuation. B: Mechanical installation of the actuator for stiffnesstuning
Fig. 3 shows the layout of the out-of-plane compliant stage which generates independent motions in the Z, θX, and θY directions. The central stage is supported by six flexural arms. Three piezoelectric actuators (Newport NPA100) are installed below the motion tabs extending from the central stage, as indicated by the blue circles in Fig. 3B. Three capacitance probes (Lion Precision C8/CPL290) are used to measure the out-of-plane displacements for closed-loop position control, as indicated by the red circles in Fig. 3B. Piezoelectric actuators are used for high-speed parallelism control and nano-patterning application. Fig. 3C shows an interchangeable Z-θX-θY stage with a lower natural frequency and larger range.
Z - θX - θY stage
1
Actuators & sensors holder Cap probes
3
2
Y X
Piezo-actuators
A
B
C
Fig. 3. Z-θX-θY stage with integrated actuators (Newport NPA100) and sensors (Lion Precision C8). A: Side view; B: Top view; C: Interchangeable Z-θX-θY stage
3.2 Assembly and characterization Fig. 4 shows the prototype five-axis nanopositioner with integrated actuators and sensors. To characterize the dynamic properties, an impulse response experiment is conducted to obtain the resonant frequencies of the nanopositioner in different axes. Resonant frequencies are calculated from the displacement data by performing the fast Fourier transform (FFT). Table. 1 summarizes the measured and simulated resonant frequencies. These parameters are to be used in the dynamic-tuning experiments as well as the closed-loop control implementation. Z-θX-θY stage
Controllers
Manual Z-positioner
In-plane actuators
Actuators for stiffness-tuning
Cap probes
X-Y stage
Fig. 4. Prototype of the five-axis nanopositioner
Table. 1. Natural frequencies of the five-axis nanopositioner Frequency [Hz]
X
Y
Z
θX
θY
Simulated
15.5
20.1
2236
3499
3558
Measured
14.5
20.3
1936
3223
3182
To characterize the cross-axis motion coupling and to implement the open-loop control, static displacement experiments are performed to identify the matrix, SX, that maps actuator displacements/input voltages, XA, to mechanism displacements, XC. Six capacitance probes are fixed on a vibration isolation table to monitor the motions of the nanopositioner. One probe monitors the translation in X axis, two parallel probes monitor the translation in Y axis and the rotation in θZ axis (as shown in Fig. 5A), and three parallel probes monitor the out-of-plane motion (as shown in Fig. 3). For long range in-plane motion, a
custom-built Michaelson laser interferometer (resolution: ~80 nm) is used to monitor the translation in X and Y axis. Assuming small displacements, Equations (2) and (3) [22] can be used to obtain the matrix SX. The analytical solution of SX is shown in Equation (4), where a, b, and c are constant parameters related to the layout of the three piezoelectric actuators and the characteristic of the out-of-plane flexural stage. The analytical SX indicates that the motions in X axis, Y axis and out-of-plane axes are decoupled. Nevertheless, due to manufacturing errors and misaligned actuators and sensors, the measured SX has deviations, and the motions in different axes are coupled to a certain extent. The measured results are shown in Equation (5). The units used in Equation (2) – (5) are microns, milliradians and voltages.
XC SX X A x y z x y SX x y Vz1 Vz 2 Vz3
(2)
X A SX1 X C
(3)
1 0 SX 0 0 0
(4)
T
0 0 0 0 1 0 0 0 0 a a a 0 0 b b 0 2c c c
0 0 0 0.9646 0.0067 0.0039 0.9946 0 0 0 SX 0 0 0.1587 0.2119 0.2123 0 0 0.0002 0.0135 0.0136 0 0 0.0116 0.0078 0.0077
T
(5)
3.3 Nanomanufacturing station Fig. 5A presents the design of a nanomanufacturing station that integrates the five-axis nanopositioner with a custom-built atomic force microscopy (AFM) tip/stage assembly. An AFM tip array is affixed to the manual Z-positioner with a side imaging camera (Canon EOS 5D with 180 mm F/3.5L macro lens) that provides coarse distance control between the AFM tips and the sample. During a nano-patterning process, the Z-θX-θY stage controls the tip array in the Z position and the parallelism between the array and the sample, while the X-Y stage performs the actual X-Y scanning and patterning. When the area to be patterned is smaller than the default range of the X-Y stage, the stiffness-tuning commences. According to the FEA results in Fig. 1B, the natural frequency of the X-Y stage can be increased by a factor of two or higher to
achieve higher patterning speed and better dynamic characteristics. The nanomanufacturing station in Fig. 5 can be modified with ease for various applications. For example, multi-axis nano-scale wire electrical discharge machining (wire-EDM), on-chip nanomanipulation, nano-lithography, equipment for characterizing irregular nano-surfaces etc. In this work, we perform the nanoscale scratching experiments to demonstrate the precision and the uniqueness of the nanopositioner. Nanoscale scratching, a simple but versatile material removing technique, fabricates nanostructures by using micro-cantilevers with nanoscale tips [6]. As the nano-scratching technique is mostly AFM-based, AFM tips are directly installed on the manual Z-positioner (Fig. 5). The associated motion detection optics in the custom-built AFM are presented in Fig. 6, where a laser beam is first guided to an optical lever, i.e., AFM tip array, and subsequently directed to a charge-coupled device (CCD) camera (Allied Vision Prosilica GC 1350), achieving a 3 nm minimum detectable tip motion. This allows fine distance and parallelism control between the AFM tips and the substrate.
Z-θX-θY stage
Manual Z-positioner
Actuators for stiffness-tuning
Side view camera
Z Y
X In-plane actuators
X-Y stage
Out-of-plane actuators A
Cap probes
Z-θX-θY stage
AFM tip array
Substrate B Fig. 5. CAD model of the nanomanufacturing station designed for nano-scratching experiments. A: Global view. B: Zoom-in view of the red circle in A, showing the locations of the AFM tip array and the substrate
Mirror CCD
Laser AFM tips tip array
Attenuator
A
CCD Camera
Attenuators
AFM tip array
Mirrors
Nanopositioner
Laser 635C-60mW
Controllers
B Fig. 6. A: Schematic of the optical configuration for detecting the motion of the AFM tip array; the laser spot is resized to illuminate three AFM tips to enable simultaneous motion detection in the Z and θ Y direction; B: Side view of the actual setup for nano-scratching experiments
4. Experiments and discussion 4.1 Positioning experiments Static positioning experiments in selected axes (Y, Z, and θX) are performed to demonstrate the range and precision of the nanopositioner. In these experiments, the matrix, S X1 , was used as an open-loop controller. Fig. 7 shows the measured displacements and rotation in the Y, Z and θX axis respectively. The displacements and rotation are plotted versus open-loop displacement commands in the left three charts, and the off-axis errors are plotted versus displacement commands in the right three charts. Overall, we found the off-axis parasitic motions under open-loop control to be reasonably small, i.e., 0.05% of the device’s range.
4000
Translation [μm]
y position Linear model
3000 2000 1000
0
10
80
5
40
0
0
-5
-40 x
-10
0
1000
2000
3000
4000
0
5000
40
1000
2000
θx
3000
θy
4000
-80 5000
Y command [μm]
Y command [μm]
Translation [μm]
z position Linear model
20 0 -20 -40
2
150
1
75
0
0
-1
-75
x
y
θx
θy
-2
-40
-20
0
Z command [μm]
20
40
-150
-40
-20
0
20
Z command [μm]
40
Rotation [μradian]
Z measured [μm]
z
Rotation [μradian]
Y measured [μm]
5000
Translation [μm]
θx position Linear model
1000 0 -1000 -2000 -2000
-1000
0
1000
6
200
3
100
0
0
-3
-100
x -6 -2000
2000
-1000
y
0
θy
z
Rotation [μradian]
θx measured [μradian]
2000
-200 2000
1000
θx command [μradian]
θx command [μradian]
Fig. 7. Y, Z, and θX positioning results under open-loop control
In the second experiment, the nanopositioner is commanded to generate precise X and Z motions with the open-loop controller in a local work volume to demonstrate the nanoscale positioning capability. Fig. 8 plots the measured displacements (left column) and off-axis errors (right column) versus open-loop displacement commands. The results demonstrate that the nanopositioner can perform multi-axis nanopatterning tasks with 10s nanometer precision with open-loop control within a local work volume. The positioning results under open-loop control show that the errors increase with increasing displacements. The trend is also observed in the off-axis parasitic errors. Accordingly, the precision of the nanopositioner can be improved by implementing the closed-loop control.
Translation [nm]
x position Linear model
1000 0 -1000 -2000 -2000
-1000
0
1000
X command [nm]
2000
210
3
140
2
70
1
0
0
-70
-1
-140 -210 -2000
y -1000
0
z
θx 1000
X command [nm]
θy
-2
-3 2000
Rotation [μradian]
X measured [nm]
2000
Translation [nm]
z position Linear model
1000 0 -1000 -2000 -2000
-1000
0
1000
60
30
30
15
0
0
-30
-15
x -60 -2000
2000
-1000
Z command [nm]
θx
y
0
1000
θy
Rotation [μradian]
Z measured [nm]
2000
-30 2000
Z command [nm]
Fig. 8. X and Z positioning results under open-loop control within a local work volume In the third experiment, the nanopositioner is commanded to move in all five axes, i.e., X, Y, Z, θX, and θY, with a closed-loop PID controller to demonstrate the precision and stability. Fig. 9 plots the measured displacements (left column) and off-axis errors (right column) versus closed-loop displacement commands. The results show that the off-axis translational and rotational errors are controlled within ±100 nm, ±100 nm, ±10 nm, ±1 µrad and ±1 µrad in the X, Y, Z, θX and θY axis respectively, which substantially improves the positioning accuracy compared to the cases of open-loop control; the errors are comparable to the resolution of the capacitance probes (Lion Precision C8/CPL190, resolution: 20 nm, for the X and Y axis; Lion Precision C8/CPL290, resolution: 2.5 nm, for the Z, θX and θY axis).
Translation [nm]
x position Linear model
10 5 0 -5 -10 -15
20
1
10
0.5
0
0
-10
-0.5 y
-20 -15
-10
-5
0
5
X command [μm]
10
15
-15
z
-10
θx
-5
θy
-1
0
5
X command [μm]
10
15
Rotation [µradian]
X measured [μm]
15
100
10
Translation [nm]
y position Linear model
5 0 -5 -10 -15
1
50
0.5
0
0
-50
-0.5 x
-100 -15
-10
-5
0
5
10
15
-15
z
θx
-10
-5
Y command [μm]
0 -50 -100 -100
-50
0
50
100
150
50
0.5
0
0
-50
-0.5
x y θx θy -100 -150 -100 -50 0
150
Translation [nm]
0 -5 -10 -15
1
50
0.5
0
0
-50
-0.5
x
y
z
θy
-100 -10
-5
0
5
10
15
-1
-15
-10
θx command [μradian] 15
-5
0
5
10
15
θx command [μradian] 100
Translation [nm]
5 0 -5 -10 -15
1
50
0.5
0
0
-50
-0.5 x
y
z
θx
-100 -15
-10
-5
0
5
θy command [μradian]
10
15
Rotation [µradian]
θy position Linear model
10
Rotation [µradian]
θx measured [μradian]
100
100
5
-15
θy measured [μradian]
-1
50
Z command [nm]
θx position Linear model
10
15
1
Z command [nm] 15
10
100
z position Linear model
50
-150 -150
5
Y command [μm]
Translation [nm]
100
-1
0
Rotation [µradian]
Z measured [nm]
150
θy
Rotation [µradian]
Y measured [μm]
15
-1
-15
-10
-5
0
5
10
15
θy command [μradian]
Fig. 9. X, Y, Z, θX, and θY positioning results under closed-loop control
Fig. 10 shows the positioning results in all five axes under the PID control. In this experiment, the nanopositioner is commanded to perform three 10-μm and 100-μrad steps in the X, Y, Z, θX and θY axis in a
sequential fashion, with each step held for 30 seconds. As Fig. 10 shows, the motion in one axis does not affect motions in other five axes. It is found that, under closed-loop control, the X and Y axes have a resolution of ±100 nm, limited by the 100 nm minimum incremental motion of the linear actuators; likewise, the Z, θX, and θY axes have a resolution of ±10 nm, ±1 μrad, and ±1 μrad respectively. Note that error motions in θZ axis are mainly caused by manufacturing errors, which are relatively small, i.e., within ±5 μrad in this experiment.
30 29
310
[µradian]
30.1
[µm]
[µm]
31
30
29.9 4.7
[min]
7.4
290 10.4
7.7
[min]
10.7
[min]
40
400
30
300
20
200
10
100
0 x
-10 0
3
6
9
y
θx
z 12
θy
0
θz
Rotation [μradian]
Translation [μm]
4.4
300
-100 15
Time [min]
Fig. 10. Positioning results in all five axes, i.e., X, Y, Z, θX, and θY axis, with PID control
4.2 Stiffness-tuning and vibration cancellation To validate the in-plane dynamic-tuning capability, axial loads (displacements) are applied to the X-Y stage via the stiffness-tuning actuators (PA-X and PA-Y) shown in Fig. 2A. The results are presented in Fig. 11, indicating that resonant frequencies in X and Y directions can increase by two to three times by increasing the axial loads. (Note that at maximum actuator displacement, the elastic range of the X-Y stage is reduced to ~5 mm.) The errors between measured resonant frequencies and simulated results are within 5%, which are mainly attributed to (1) misalignments between the piezoelectric actuator and the loading axis, and (2) imperfect actuator constraints. From the corresponding Bode plots in Fig. 11, we confirm again that the natural frequencies increase with increasing actuator displacement; in addition, we find the
amplitudes of the higher modes increase with stiffness-tuning. This negative effect may be avoided by
40
40 30 20
10
Simulated Measured
Amplitude [dB]
Freq. (X direction) [Hz]
vibration cancellation techniques.
200
400
600
-40
PA-X, 0 μm PA-X, 200 μm PA-X, 500 μm
-80 -120
0
0
0
1
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10
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40
60 45 30
15
Simulated Measured
0
0
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400
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Amplitude [dB]
Freq. (Y direction) [Hz]
100
Frequency [Hz]
Disp. (PA-X, Figure 2A) [µm]
0 -40 PA-Y, 0 μm PA-Y, 200 μm PA-Y, 500 μm
-80 -120 1
Disp. (PA-Y, Figure 2A) [µm]
10
100
1000
Frequency [Hz]
Fig. 11. The relationship between resonant frequency/frequency spectrum and applied axial displacement; top row: X-direction with PA-X actuator; bottom row: Y-direction with PA-Y actuator
Besides tuning the resonant frequencies, the stiffness-tuning actuators, i.e., PA-X and PA-Y, can be used to further improve the system precision in transient situations via active vibration cancellation techniques [23]-[25]. Our method is inspired by the input shaping method [23]. Since PA-X and PA-Y actuators will induce small X and Y displacements to the nanopositioner due to the stage asymmetry, ―active tuning‖ (or active vibration cancellation) can be achieved by driving the related stiffness-tuning actuator, e.g., PA-X (PI P-845.20, resonant frequency: 12 kHz), with impulse signals when the linear actuator, e.g., LA-X (PI M-230.10S, maximum velocity: 1.2 mm/s), moves the stage. Fig. 12A and Fig. 12B present the operation principle and experimental results of the active tuning using a single pulse, where the step input induced vibration can be completely eliminated by the impulse response via the superposition principle, resulting in a vibration-free output. The step response and impulse response of an underdamped second-order system can be mathematically described in Equations (6) and (7) respectively:
e0 t t0 y t A A sin 0 1 2 t t0 ; 1 2
arccos
(6)
e0 t t0 y t B0 sin 0 1 2 t t0 2 1
(7)
where A is the amplitude of the step input; B is the amplitude of the impulse; ω0 is the underdamped natural frequency of the plant; ζ is the damping ratio of the plant; t is time; and t0 is the time of the input. Next, we consider a more general case, where the vibration may be more effectively reduced by using N pulses (generated by the stiffness-tuning actuator) [23]. To eliminate the vibration after all inputs have ended, the vibration amplitude which consists of a step response and a set of impulse responses should equal to zero. By using trigonometric relations, the following constraints are derived:
N
A0e ii tN t0 sin t0i 1 i2 i Bji e
ii tN t j
j 1
N
A0e ii tN t0 cos t0i 1 i2 i Bji e j 1
sin t ji 1 i2 0 ; Bj k Bj
ii tN t j
cos t ji 1 i2 0
(8)
where A0 is the amplitude of the step input; Bj is the amplitude of the jth impulse; ωi and ζi is the modal frequency and damping ratio of the ith mode of vibration; k is the proportional coefficient between the displacements of the stage and the stiffness-tuning actuator (the value of k varies with the position of the nanopositioner); t0 is the time of the step input; tj is the time of the jth impulse; and tN is the time of the last input. From Equation (8), the time and amplitude of the impulse in Fig. 12A and Fig. 12B can be found as t1
A 1 , and B1 0 e 1 1 1 12
1 112
1
by setting N = 1 and t0 = 0. For N > 1, tj and Bj (j = 1 to N) can
be obtained by solving Equation (8), where modal frequencies ωi and damping ratios ζi (i = 1 to N), are measured experimentally. Note that the modal frequencies ωi change with the stage displacement. Fig. 12C presents the control block diagram of the following active tuning experiments, where r1 is the position set point sent to the LA-X, and r2 is a set of pulse inputs sent to the PA-X. Fig. 12D presents the results of the active tuning experiments using one and two pulses, compared with open-loop and PID control. In the experiment, the linear actuator commands the stage to first generate a 10 μm step under open-loop control; the resulting system response has an overshoot of 487 nm and a settling time of 1.5
seconds. Using PID control alone, we find the overshoot and settling time are reduced to 370 nm and 1.30 seconds respectively. When combining the PID control and active tuning with one impulse, we find the overshoot and settling time are further reduced to 240 nm and 1.28 seconds respectively; with two pulses, we find slightly increased overshoot, i.e., 256 nm and substantially reduced settling time, i.e., 0.5 second. These results validate the effectiveness of active tuning. The Bode plot, shown in Fig. 12E, reconfirms the results, where the first and second modal frequencies at 40 Hz and 60 Hz are effectively suppressed, reducing the overshoot and ringing, as well as shortening the settling time. Overall, more robust and effective vibration cancellation can be achieved via using multiple pulses at the expense of increased overshoot and prolonged actuation time.
X measured [μm]
Position
11
Step Input
Response to Step Input Response to Impulse Input
Impulse Input
10
9
Open-loop Response to Pulse Input 8 0
0.05
0.1
Time
Time [s]
A
B
Command
Output
+
Plant of Nanopositioner
+ -
+
Pulse Generator
Feedback
C
0.15
30
10 9.5 Open-loop Control Closed-loop Control Active Tuning (1 Pulse) Active Tuning (2 Pulses)
9 8.5 0
0.5
1
Amplitude [dB]
X measured [μm]
10.5
1.5
Time [s] D
0
-30 -60
Open-loop Control Closed-loop Control Active Tuning (1 Pulse) Active Tuning (2 Pulses)
-90
-120 1
10
100
1000
Frequency [Hz] E
Fig. 12. Active vibration cancellation method. A: Illustration of vibration cancellation using a single impulse, where the impulse response is anti-phase in relation to the step response, resulting in a vibrationfree output. B: Measured step and impulse responses of the nanopositioner generated by the LA-X and PAX respectively under open-loop control. C: Control block diagram of the active tuning experiment. D, E: Displacement and frequency response measurements of the nanopositioner in the X axis using open-loop control, PID, active tuning with one pulse, and two pulses
4.3 Nano-scratching experiments Based on the nanomanufacturing station, we have performed nano-scratching experiments with stiffness-tuning as well as active tuning with PID control to produce grating patterns on different substrates with an AFM tip array. Fig. 13 shows the scanning electron microscope (SEM) images of the AFM tip array used in the nano-scratching experiments. As shown in Fig. 13, the AFM tip array is a 1-D array of 18 cantilevers with a pitch of 70 μm. Fig. 14 shows the SEM images of the nano-scratching results; Fig. 14A and Fig. 14B show nano-scratched patterns on soft materials, i.e., photoresist, where each line is 3 mm long and the periods are 1 μm and 1.2 μm respectively. Fig. 14C shows nano-scratched patterns on a gold coated silicon substrate, over a 5 × 1 mm2 area, where each line is ~300 nm wide and the period is 1 μm. In our experiments, the scratching speed is set to be 1 mm/s; the time required for patterning a 5 × 1 mm2 area is ~15 min.
80 nm 160 µm
70 µm 70 µm
Fig. 13. SEM images of the AFM tip arrays used in nano-scratching experiments.(NANOSENSORSTM SDPNP-Array2 AFM probe arrays, resonance frequency: 30 kHz)
200 nm
280 nm
1 µm
1.2 µm
A
1 µm
B
C
Fig. 14. SEM images of large-area nano-scratching results. A, B: Nano-scratching on photoresist; C: Nano-scratching on gold-coated silicon wafer
To characterize the parallelism control during the operation, we further characterized the width and depth profiles of the scratched lines on the gold substrate in two separate regions that are 1.2 mm apart, corresponding to lines scratched by the first and the last (18 th) AFM tip. In other words, if the tip array is controlled in perfect parallelism to the substrate, the scratched lines should have equal width and depth. The results are shown in Fig. 15. Fig. 15A presents the AFM tip array schematic as well as the two selected regions: A and B. Fig. 15B and Fig. 15C present the measured line profiles of region A and B respectively, where it can be observed that lines at region A and B have consistent depth ~160 nm and slightly different linewidth (~300 nm vs. ~500 nm), showing good parallelism had been achieved during the nano-scratching process. The straightness tolerance of the scratched lines are calculated to be ~35 nm.
A
70 μm
B
1.2 mm Substrate: gold coated silicon wafer A
B
C
Fig. 15. Characterization of line profiles at two different regions on the gold substrate. A: Schematic of AFM tip array and region A and region B; B: Cross-sectional profile of scratched lines in region A; C: Cross-sectional profile of scratched lines in region B
5. Conclusion In this paper, we present the design, modeling, assembly, and characterization of a dynamic-tunable flexure-based five-axis nanopositioner. Our experiments indicate that the nanopositioner achieves ±100 nm, ±100 nm, ±10 nm, ±1 µrad and ±1 μrad precision in the X, Y, Z, θX, and θY axis with a work volume of 10 mm × 10 mm × 80 μm, suitable for performing parallel probe-based nanofabrication as well as other nanomanufacturing
processes,
such
as
nanoscale
electro-machining
(nano-EM),
and
dip-pen
nanolithography (DPN). The dynamic tuning experiments show the nanopositioner can tune its natural frequency with between 15 Hz and 40 Hz, allowing effective trade-offs between the natural frequency and elastic range. The active tuning experiments show vibration cancellation techniques can be implemented to the flexure-based nanopositioner to further improve the system precision in transient situations. Lastly, the nanopositioner is integrated with a custom-designed AFM to perform nano-scratching experiments, creating grating patterns over a 5 × 1 mm2 area with sub-100 nm precision within a short time frame, i.e. ~15 min. Acknowledgment This work was supported by the HKSAR Innovation and Technology Commission under the Innovation and Technology Fund ITS/262/12: Design and Control of Flexure-Based Multi-Axis Nanopositioners for Ultra Precision Applications.
References [1] Chryssolouris G, Stavropoulos P, Tsoukantas G, Salonitis K, Stournaras A. Nanomanufacturing processes: a critical review. Int J Mater Prod Tec 2004;21(4):331-48. [2] Melngailis J. Focused ion beam technology and applications. J Vac Sci Technol B 1987;5(2):469-95. [3] Park JU, Hardy M, Kang SJ, Barton K, Adair K, kishore Mukhopadhyay D, et al. High-resolution electrohydrodynamic jet printing. Nat Mater 2007;6(10):782-9. [4] Cumpston BH, Ananthavel SP, Barlow S, Dyer DL, Ehrlich JE, Erskine LL, et al. Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication. Nature 1999;398(6722):51-4. [5] Tseng AA. Tip-based nanofabrication: fundamentals and applications. New York: Springer; 2011. [6] Malshe AP, Rajurkar KP, Virwani KR, Taylor CR, Bourell DL, Levy G, et al. Tip-based nanomanufacturing by electrical, chemical, mechanical and thermal processes. CIRP Ann-Manuf Techn 2010;59(2):628-51. [7] Huo F, Zheng Z, Zheng G, Giam LR, Zhang H, Mirkin CA. Polymer pen lithography. Science 2008;321(5896):1658-60. [8] Tseng AA, Jou S, Notargiacomo A, Chen TP. Recent developments in tip-based nanofabrication and its roadmap. J Nanosci Nanotechno 2008;8(5):2167-86. [9] Vettiger P, Cross G, Despont M, Drechsler U, Dürig U, Gotsmann B, et al. The "millipede"nanotechnology entering data storage. IEEE T Nanotechnol 2002;1(1):39-55. [10] Salaita K, Wang Y, Fragala J, Vega RA, Liu C, Mirkin CA. Massively parallel dip-pen nanolithography with 55 000-pen two-dimensional arrays. Angew Chem 2006;118(43):7378-81. [11] Clayton GM, Tien S, Leang KK, Zou Q, Devasia S. A review of feedforward control approaches in nanopositioning for high-speed SPM. J Dyn Syst 2009;131(6):061101. [12] Kodera N, Sakashita M, Ando T. Dynamic proportional-integral-differential controller for high-speed atomic force microscopy. Rev Sci Instrum 2006;77(8):083704. [13] Bloschock KP, Schofield AR, Kenny TW. Tip-based nanofabrication: an approach to true nanotechnology. In: Proc. of SPIE, vol. 8031. 2011. p. 803102. [14] Howell LL. Compliant mechanisms. New York: Wiley; 2001.
[15] Yong YK, Moheimani SOR, Kenton BJ, Leang KK. Invited review article: High-speed flexure-guided nanopositioning: Mechanical design and control issues. Rev Sci Instrum 2012;83(12):121101. [16] Kim JJ, Choi YM, Ahn D, Hwang B, Gweon DG, Jeong J. A millimeter-range flexure-based nanopositioning stage using a self-guided displacement amplification mechanism. Mech Mach Theory 2012;50:109-20. [17] Vanderborght B, Albu-Schäffer A, Bicchi A, Burdet E, Caldwell DG, Carloni R, et al. Variable impedance actuators: A review. Robot Auton Syst 2013;61(12):1601-14. [18] Timoshenko S. Strength of materials. Part 2: Advanced theory and problems. Van Nostrand; 1947. [19] Blanding DL. Exact constraint: machine design using kinematic principles. New York: ASME Press; 1999. [20] Jones RV. Parallel and rectilinear spring movements. J Sci Instrum 1951;28(2):38. [21] Awtar S, Slocum AH. Constraint-based design of parallel kinematic XY flexure mechanisms. J Mech Design 2007;129(8):816-30. [22] Culpepper ML, Anderson G. Design of a low-cost nano-manipulator which utilizes a monolithic, spatial compliant mechanism. Precis Eng 2004;28(4):469-82. [23] Singer NC, Seering WP. Preshaping command inputs to reduce system vibration. J Dyn Syst 1990;112(1):76-82. [24] Fuller CC, Elliott S, Nelson PA. Active control of vibration. Academic Press; 1996. [25] Li Y, Bechhoefer J. Feedforward control of a closed-loop piezoelectric translation stage for atomic force microscope. Rev Sci Instrum 2007;78(1):013702.
S0141-6359(16)30021-6 http://dx.doi.org/doi:10.1016/j.precisioneng.2016.04.002 PRE 6383
To appear in:
Precision Engineering
Received date: Revised date: Accepted date:
4-9-2015 7-2-2016 1-4-2016
Please cite this article as: Li Chenglin, Wang Ji, Chen Shih-Chi.Flexure-based Dynamic-Tunable Five-Axis Nanopositioner for Parallel Nanomanufacturing.Precision Engineering http://dx.doi.org/10.1016/j.precisioneng.2016.04.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Flexure-based Dynamic-Tunable Five-Axis Nanopositioner for Parallel Nanomanufacturing Chenglin Li, Ji Wang, and Shih-Chi Chen* Department of Mechanical and Automation Engineering The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR, China *
Corresponding author: [email protected]
Highlights
We present a flexure-based dynamic-tunable five-axis nanopositioner for tip-based nanofabrication application.
The experimental characterization shows the nanopositioner achieves ±100 nm, ±100 nm, ±10 nm, ±1 µrad and ±1 μrad precision in the X, Y, Z, θX, and θY axis with a work volume of 10 mm × 10 mm × 80 μm with closed-loop control.
The dynamic-tuning concept enables trade-offs between the range and speed of the flexural nanopositioner so as to increase the throughput of the nanomanufacturing system.
Static dynamic-tuning results show the natural frequency of the X-Y stage can be increased by 2-3 times. Active dynamic tuning experiments show active vibration cancellation techniques can be implemented to the nanopositioner to further improves the dynamic performance, i.e. reducing the overshoot and settling time from 487 nm / 1.5 seconds to 256 nm / 0.5 second.
Nano-scratching experiments were performed to fabricate optical grating patterns on gold coated silicon substrates over a 5 × 1 mm2 area within ~15 min to demonstrate the practicality of the new method.
Abstract With the increasing demand for devices and systems with nanometer precision in the modern manufacturing industry, tip-based nanofabrication (TBN) has become an indispensable part of manufacturing process. However, a common issue that needs to be addressed is to increase the throughput of TBN, which is sequential and inherently slow. To overcome the difficulty, in this paper we present the design and control of a flexure-based five-axis nanopositioner with dynamic-tuning capability for parallel nanomanufacturing applications. The dynamic-tuning method enables trade-offs between the range and speed of the nanopositioner so as to increase the throughput of the nanomanufacturing system. The experimental results indicate that the nanopositioner conforms with the in-plane range and resolution requirements, i.e., ±5 mm/ 100 nm in X/Y axis, while its natural frequencies in X/Y axis can be increased by two to three times at the expense of decreased stroke, i.e., elastic range. In addition, real-time dynamictuning experiments show active vibration cancellation techniques can be implemented on the nanopositioner and effectively eliminate the unwanted dynamics and improve the overall dynamic performance. Lastly, we performed nano-scratching experiments using an 18 tip AFM array to fabricate optical grating patterns on gold coated silicon substrates of 5 × 1 mm2 to demonstrate the practicality of the new method. The experiment confirmed good parallelism had been achieved during the experiments, where the scratched gold lines have a consistent depth of ~160 nm. Keywords: Compliant mechanism; dynamic-tuning; multi-axis nanopositioner; parallel nanomanufacturing
1. Introduction Nanomanufacturing is a process to create nanoscale structures, devices and systems [1] that encompasses
various
technologies,
including
focused
ion
beam
lithography
(FIBL)
[2],
electrohydrodynamic (EHD) jet printing [3], and two-photon polymerization (TPP) [4]. Tip-based nanofabrication (TBN) is an important and versatile nanomanufacturing technology that utilizes microscale cantilevers with attached nanoscale tips to realize nanofabrication [5]; TBN enables a wide range of manufacturing applications, e.g., material removal, modification, deposition, manipulation etc. [5], and therein lies its potential to provide pattern flexibility for fast prototyping [6]. However, comparing with mask- or template-based nanomanufacturing methods such as photolithography, nanoimprint lithography (NIL) and microcontact printing (MCP), which provide large-area modification and high throughput [7], all TBN techniques share a low throughput issue inherited from the serial nature of tip movement [7]. To circumvent such restriction, two methods are generally applied to improve the TBN throughput [8]: operating multiple tips in parallel [9], [10], and increasing the tip operation speed/frequency [11], [12]. In other words, multi-axis nanopositioners with enhanced speed and precision is the key to ensure successful industrial application of TBN [13]. Nanopositioners can move objects of different sizes with nanometer level precision. They are important as they set the limits on our ability to measure, manipulate, and manufacture physical systems. As traditional mechanical linkages are susceptible to backlash and wear between joint members, compliant mechanisms, i.e., flexures, are often used to fulfill the strict repeatability and precision requirements [14]. However, compliant mechanisms demand a larger device envelope in comparison to the motion they can generate, causing inevitable trade-offs between the natural frequency and range. To realize large-area parallel nanomanufacturing, e.g., generating nano-patterns on a 1 × 1 cm2 substrate, the nanopositioner must meet the following requirements: (1) five degrees of freedom (DOF), i.e., X, Y, θX, θY, and Z, where X and Y axes are for in-plane nanomanufacturing, θX, θY ,and Z axes are for aligning and positioning the tip array with the substrate; (2) nanometer level repeatability and submicron level precision for position control in all five axes; (3) a range of ±5 mm/ ±5 mm in the X/Y axis for largearea nanomanufacturing and a range of ±40 μm/ ±2 mrad/ ±1.5 mrad in the Z/θX/θY axis respectively; and
(4) dynamic-tuning capability that allows the nanopositioner to travel a long distance to locate and manufacture locally at high speed. Among these requirements, the dynamic-tuning capability is of particular importance as it alleviates the side-effect of low natural frequency induced by a large-stroke flexure-based nanopositioner. 2. Dynamic-tuning for flexure-based nanopositioners Although the dynamic performance of a flexural mechanism is determined by its natural frequency, it is often compromised by the required stroke of the mechanism. In other words, high natural frequency can only be achieved at the expense of reduced stroke. To be more specific, a high-bandwidth flexure-guided nanopositioner is limited to a relatively small travel range [15], while a large-displacement flexure-based nanopositioner has low natural frequencies. For example, a millimeter-ranged flexure-based nanopositioner typically has a resonant frequency less than 100 Hz [16]. In this paper, we aim to develop a dynamictunable flexure-based nanopositioner that allows trade-offs between speed (natural frequency) and range (stroke)—a concept inspired by compliant actuators used in humanoid robots [17]. The dynamic-tuning effect is achieved by exploiting the ―stress-stiffening effect‖, i.e., the increased stiffness of a beam when experiencing tensile loads in the axial direction [18]. The natural frequency of a simply supported beam with an axial force N can be described by Equation (1), where ω is the natural frequency; l, A, I, E, ρ are the length, cross-sectional area, area moment of inertia, Young’s modulus and density of the beam, respectively [18]. For example, the natural frequency of a simply-supported rectangular-section titanium beam (E = 1.048×1011 Pa, ρ = 4428.78 kg/m3, 70 mm long, 10 mm wide, and 1 mm thick) can be shifted from 450 Hz to 1164 Hz when a 1000 N uniform axial tensile force is applied to one end of the beam. Note that compression load is not used as it may cause buckling and instability.
2
l
EI Nl 2 1 2 A EI
(1)
To extend the frequency tuning concept from a beam to a flexural mechanism, Fig. 1 presents the simulated results of a symmetric double parallelogram (DP) mechanism where its yield stress is reached by increasing the axial loads. Fig. 1A shows the computer-aided design (CAD) model. The material used in
the finite element analysis (FEA) simulation is titanium. Fig. 1B shows that dynamic-tuning enables tradeoffs between the natural frequency and the elastic range of the DP mechanism. Ground Elastic range [mm]
60 40
20 0
Axial load
Axial load Ground
A
0
50 100 150 Natural frequency [Hz]
200
B
Fig. 1. Simulated results of a symmetric DP flexure using Abaqus 6.12. A: CAD model with load and boundary conditions; B: The relationship between the range and frequency of the DP flexure
3. Nanopositioner assembly and experimental setup 3.1 Nanopositioner design Fig. 2A shows the layout of the nanopositioner, where an in-plane X-Y stage and an out-of-plane Z-θXθY stage are connected in series to achieve five DOF. The X-Y stage, designed based on the principle of constraint-based design, achieves decoupled X and Y motion by using multiple folded-beam mechanisms [19]; the extended range in the X and Y directions are achieved by the symmetric DP mechanism [20], [21]. High-resolution linear actuators (PI M-230.10S) are chosen for in-plane actuation because of the large strokes (10 mm) and high resolution (37 nm). In order to perform dynamic-tuning, two piezoelectric actuators (the green arrows in Fig. 2A; PI P-845.20) are used in each DP mechanism to generate axial loads/stresses. Since the increase of axial force leads to higher natural frequency, P-845.20 are chosen to generate high forces (3000 N). The dynamic-tuning design is implemented on the X-Y stage to enable tradeoffs between its range and speed in both axes. Fig. 2B shows the installation of the piezoelectric actuator for stiffness-tuning. The bottom of the actuator is affixed to the X-Y stage; a screw cap with a ball top is mounted on the head of the actuator to prevent torques and lateral forces. The preload and axial load can be applied with ease by turning the screw cap.
Screw cap In-plane stage
Out-of-plane stage
PA-X
PA-X
PA-Y LA-X
LA-Y
Y X
A
B
Fig. 2. A: Layout of the nanopositioner: the green arrows, i.e., PA-X and PA-Y, indicate the piezoelectric actuators (PI P-845.20) for stiffness-tuning and the white arrows, i.e., LA-X and LA-Y, indicate the linear actuators (PI M-230.10S) for in-plane actuation. B: Mechanical installation of the actuator for stiffnesstuning
Fig. 3 shows the layout of the out-of-plane compliant stage which generates independent motions in the Z, θX, and θY directions. The central stage is supported by six flexural arms. Three piezoelectric actuators (Newport NPA100) are installed below the motion tabs extending from the central stage, as indicated by the blue circles in Fig. 3B. Three capacitance probes (Lion Precision C8/CPL290) are used to measure the out-of-plane displacements for closed-loop position control, as indicated by the red circles in Fig. 3B. Piezoelectric actuators are used for high-speed parallelism control and nano-patterning application. Fig. 3C shows an interchangeable Z-θX-θY stage with a lower natural frequency and larger range.
Z - θX - θY stage
1
Actuators & sensors holder Cap probes
3
2
Y X
Piezo-actuators
A
B
C
Fig. 3. Z-θX-θY stage with integrated actuators (Newport NPA100) and sensors (Lion Precision C8). A: Side view; B: Top view; C: Interchangeable Z-θX-θY stage
3.2 Assembly and characterization Fig. 4 shows the prototype five-axis nanopositioner with integrated actuators and sensors. To characterize the dynamic properties, an impulse response experiment is conducted to obtain the resonant frequencies of the nanopositioner in different axes. Resonant frequencies are calculated from the displacement data by performing the fast Fourier transform (FFT). Table. 1 summarizes the measured and simulated resonant frequencies. These parameters are to be used in the dynamic-tuning experiments as well as the closed-loop control implementation. Z-θX-θY stage
Controllers
Manual Z-positioner
In-plane actuators
Actuators for stiffness-tuning
Cap probes
X-Y stage
Fig. 4. Prototype of the five-axis nanopositioner
Table. 1. Natural frequencies of the five-axis nanopositioner Frequency [Hz]
X
Y
Z
θX
θY
Simulated
15.5
20.1
2236
3499
3558
Measured
14.5
20.3
1936
3223
3182
To characterize the cross-axis motion coupling and to implement the open-loop control, static displacement experiments are performed to identify the matrix, SX, that maps actuator displacements/input voltages, XA, to mechanism displacements, XC. Six capacitance probes are fixed on a vibration isolation table to monitor the motions of the nanopositioner. One probe monitors the translation in X axis, two parallel probes monitor the translation in Y axis and the rotation in θZ axis (as shown in Fig. 5A), and three parallel probes monitor the out-of-plane motion (as shown in Fig. 3). For long range in-plane motion, a
custom-built Michaelson laser interferometer (resolution: ~80 nm) is used to monitor the translation in X and Y axis. Assuming small displacements, Equations (2) and (3) [22] can be used to obtain the matrix SX. The analytical solution of SX is shown in Equation (4), where a, b, and c are constant parameters related to the layout of the three piezoelectric actuators and the characteristic of the out-of-plane flexural stage. The analytical SX indicates that the motions in X axis, Y axis and out-of-plane axes are decoupled. Nevertheless, due to manufacturing errors and misaligned actuators and sensors, the measured SX has deviations, and the motions in different axes are coupled to a certain extent. The measured results are shown in Equation (5). The units used in Equation (2) – (5) are microns, milliradians and voltages.
XC SX X A x y z x y SX x y Vz1 Vz 2 Vz3
(2)
X A SX1 X C
(3)
1 0 SX 0 0 0
(4)
T
0 0 0 0 1 0 0 0 0 a a a 0 0 b b 0 2c c c
0 0 0 0.9646 0.0067 0.0039 0.9946 0 0 0 SX 0 0 0.1587 0.2119 0.2123 0 0 0.0002 0.0135 0.0136 0 0 0.0116 0.0078 0.0077
T
(5)
3.3 Nanomanufacturing station Fig. 5A presents the design of a nanomanufacturing station that integrates the five-axis nanopositioner with a custom-built atomic force microscopy (AFM) tip/stage assembly. An AFM tip array is affixed to the manual Z-positioner with a side imaging camera (Canon EOS 5D with 180 mm F/3.5L macro lens) that provides coarse distance control between the AFM tips and the sample. During a nano-patterning process, the Z-θX-θY stage controls the tip array in the Z position and the parallelism between the array and the sample, while the X-Y stage performs the actual X-Y scanning and patterning. When the area to be patterned is smaller than the default range of the X-Y stage, the stiffness-tuning commences. According to the FEA results in Fig. 1B, the natural frequency of the X-Y stage can be increased by a factor of two or higher to
achieve higher patterning speed and better dynamic characteristics. The nanomanufacturing station in Fig. 5 can be modified with ease for various applications. For example, multi-axis nano-scale wire electrical discharge machining (wire-EDM), on-chip nanomanipulation, nano-lithography, equipment for characterizing irregular nano-surfaces etc. In this work, we perform the nanoscale scratching experiments to demonstrate the precision and the uniqueness of the nanopositioner. Nanoscale scratching, a simple but versatile material removing technique, fabricates nanostructures by using micro-cantilevers with nanoscale tips [6]. As the nano-scratching technique is mostly AFM-based, AFM tips are directly installed on the manual Z-positioner (Fig. 5). The associated motion detection optics in the custom-built AFM are presented in Fig. 6, where a laser beam is first guided to an optical lever, i.e., AFM tip array, and subsequently directed to a charge-coupled device (CCD) camera (Allied Vision Prosilica GC 1350), achieving a 3 nm minimum detectable tip motion. This allows fine distance and parallelism control between the AFM tips and the substrate.
Z-θX-θY stage
Manual Z-positioner
Actuators for stiffness-tuning
Side view camera
Z Y
X In-plane actuators
X-Y stage
Out-of-plane actuators A
Cap probes
Z-θX-θY stage
AFM tip array
Substrate B Fig. 5. CAD model of the nanomanufacturing station designed for nano-scratching experiments. A: Global view. B: Zoom-in view of the red circle in A, showing the locations of the AFM tip array and the substrate
Mirror CCD
Laser AFM tips tip array
Attenuator
A
CCD Camera
Attenuators
AFM tip array
Mirrors
Nanopositioner
Laser 635C-60mW
Controllers
B Fig. 6. A: Schematic of the optical configuration for detecting the motion of the AFM tip array; the laser spot is resized to illuminate three AFM tips to enable simultaneous motion detection in the Z and θ Y direction; B: Side view of the actual setup for nano-scratching experiments
4. Experiments and discussion 4.1 Positioning experiments Static positioning experiments in selected axes (Y, Z, and θX) are performed to demonstrate the range and precision of the nanopositioner. In these experiments, the matrix, S X1 , was used as an open-loop controller. Fig. 7 shows the measured displacements and rotation in the Y, Z and θX axis respectively. The displacements and rotation are plotted versus open-loop displacement commands in the left three charts, and the off-axis errors are plotted versus displacement commands in the right three charts. Overall, we found the off-axis parasitic motions under open-loop control to be reasonably small, i.e., 0.05% of the device’s range.
4000
Translation [μm]
y position Linear model
3000 2000 1000
0
10
80
5
40
0
0
-5
-40 x
-10
0
1000
2000
3000
4000
0
5000
40
1000
2000
θx
3000
θy
4000
-80 5000
Y command [μm]
Y command [μm]
Translation [μm]
z position Linear model
20 0 -20 -40
2
150
1
75
0
0
-1
-75
x
y
θx
θy
-2
-40
-20
0
Z command [μm]
20
40
-150
-40
-20
0
20
Z command [μm]
40
Rotation [μradian]
Z measured [μm]
z
Rotation [μradian]
Y measured [μm]
5000
Translation [μm]
θx position Linear model
1000 0 -1000 -2000 -2000
-1000
0
1000
6
200
3
100
0
0
-3
-100
x -6 -2000
2000
-1000
y
0
θy
z
Rotation [μradian]
θx measured [μradian]
2000
-200 2000
1000
θx command [μradian]
θx command [μradian]
Fig. 7. Y, Z, and θX positioning results under open-loop control
In the second experiment, the nanopositioner is commanded to generate precise X and Z motions with the open-loop controller in a local work volume to demonstrate the nanoscale positioning capability. Fig. 8 plots the measured displacements (left column) and off-axis errors (right column) versus open-loop displacement commands. The results demonstrate that the nanopositioner can perform multi-axis nanopatterning tasks with 10s nanometer precision with open-loop control within a local work volume. The positioning results under open-loop control show that the errors increase with increasing displacements. The trend is also observed in the off-axis parasitic errors. Accordingly, the precision of the nanopositioner can be improved by implementing the closed-loop control.
Translation [nm]
x position Linear model
1000 0 -1000 -2000 -2000
-1000
0
1000
X command [nm]
2000
210
3
140
2
70
1
0
0
-70
-1
-140 -210 -2000
y -1000
0
z
θx 1000
X command [nm]
θy
-2
-3 2000
Rotation [μradian]
X measured [nm]
2000
Translation [nm]
z position Linear model
1000 0 -1000 -2000 -2000
-1000
0
1000
60
30
30
15
0
0
-30
-15
x -60 -2000
2000
-1000
Z command [nm]
θx
y
0
1000
θy
Rotation [μradian]
Z measured [nm]
2000
-30 2000
Z command [nm]
Fig. 8. X and Z positioning results under open-loop control within a local work volume In the third experiment, the nanopositioner is commanded to move in all five axes, i.e., X, Y, Z, θX, and θY, with a closed-loop PID controller to demonstrate the precision and stability. Fig. 9 plots the measured displacements (left column) and off-axis errors (right column) versus closed-loop displacement commands. The results show that the off-axis translational and rotational errors are controlled within ±100 nm, ±100 nm, ±10 nm, ±1 µrad and ±1 µrad in the X, Y, Z, θX and θY axis respectively, which substantially improves the positioning accuracy compared to the cases of open-loop control; the errors are comparable to the resolution of the capacitance probes (Lion Precision C8/CPL190, resolution: 20 nm, for the X and Y axis; Lion Precision C8/CPL290, resolution: 2.5 nm, for the Z, θX and θY axis).
Translation [nm]
x position Linear model
10 5 0 -5 -10 -15
20
1
10
0.5
0
0
-10
-0.5 y
-20 -15
-10
-5
0
5
X command [μm]
10
15
-15
z
-10
θx
-5
θy
-1
0
5
X command [μm]
10
15
Rotation [µradian]
X measured [μm]
15
100
10
Translation [nm]
y position Linear model
5 0 -5 -10 -15
1
50
0.5
0
0
-50
-0.5 x
-100 -15
-10
-5
0
5
10
15
-15
z
θx
-10
-5
Y command [μm]
0 -50 -100 -100
-50
0
50
100
150
50
0.5
0
0
-50
-0.5
x y θx θy -100 -150 -100 -50 0
150
Translation [nm]
0 -5 -10 -15
1
50
0.5
0
0
-50
-0.5
x
y
z
θy
-100 -10
-5
0
5
10
15
-1
-15
-10
θx command [μradian] 15
-5
0
5
10
15
θx command [μradian] 100
Translation [nm]
5 0 -5 -10 -15
1
50
0.5
0
0
-50
-0.5 x
y
z
θx
-100 -15
-10
-5
0
5
θy command [μradian]
10
15
Rotation [µradian]
θy position Linear model
10
Rotation [µradian]
θx measured [μradian]
100
100
5
-15
θy measured [μradian]
-1
50
Z command [nm]
θx position Linear model
10
15
1
Z command [nm] 15
10
100
z position Linear model
50
-150 -150
5
Y command [μm]
Translation [nm]
100
-1
0
Rotation [µradian]
Z measured [nm]
150
θy
Rotation [µradian]
Y measured [μm]
15
-1
-15
-10
-5
0
5
10
15
θy command [μradian]
Fig. 9. X, Y, Z, θX, and θY positioning results under closed-loop control
Fig. 10 shows the positioning results in all five axes under the PID control. In this experiment, the nanopositioner is commanded to perform three 10-μm and 100-μrad steps in the X, Y, Z, θX and θY axis in a
sequential fashion, with each step held for 30 seconds. As Fig. 10 shows, the motion in one axis does not affect motions in other five axes. It is found that, under closed-loop control, the X and Y axes have a resolution of ±100 nm, limited by the 100 nm minimum incremental motion of the linear actuators; likewise, the Z, θX, and θY axes have a resolution of ±10 nm, ±1 μrad, and ±1 μrad respectively. Note that error motions in θZ axis are mainly caused by manufacturing errors, which are relatively small, i.e., within ±5 μrad in this experiment.
30 29
310
[µradian]
30.1
[µm]
[µm]
31
30
29.9 4.7
[min]
7.4
290 10.4
7.7
[min]
10.7
[min]
40
400
30
300
20
200
10
100
0 x
-10 0
3
6
9
y
θx
z 12
θy
0
θz
Rotation [μradian]
Translation [μm]
4.4
300
-100 15
Time [min]
Fig. 10. Positioning results in all five axes, i.e., X, Y, Z, θX, and θY axis, with PID control
4.2 Stiffness-tuning and vibration cancellation To validate the in-plane dynamic-tuning capability, axial loads (displacements) are applied to the X-Y stage via the stiffness-tuning actuators (PA-X and PA-Y) shown in Fig. 2A. The results are presented in Fig. 11, indicating that resonant frequencies in X and Y directions can increase by two to three times by increasing the axial loads. (Note that at maximum actuator displacement, the elastic range of the X-Y stage is reduced to ~5 mm.) The errors between measured resonant frequencies and simulated results are within 5%, which are mainly attributed to (1) misalignments between the piezoelectric actuator and the loading axis, and (2) imperfect actuator constraints. From the corresponding Bode plots in Fig. 11, we confirm again that the natural frequencies increase with increasing actuator displacement; in addition, we find the
amplitudes of the higher modes increase with stiffness-tuning. This negative effect may be avoided by
40
40 30 20
10
Simulated Measured
Amplitude [dB]
Freq. (X direction) [Hz]
vibration cancellation techniques.
200
400
600
-40
PA-X, 0 μm PA-X, 200 μm PA-X, 500 μm
-80 -120
0
0
0
1
800
10
1000
40
60 45 30
15
Simulated Measured
0
0
200
400
600
800
Amplitude [dB]
Freq. (Y direction) [Hz]
100
Frequency [Hz]
Disp. (PA-X, Figure 2A) [µm]
0 -40 PA-Y, 0 μm PA-Y, 200 μm PA-Y, 500 μm
-80 -120 1
Disp. (PA-Y, Figure 2A) [µm]
10
100
1000
Frequency [Hz]
Fig. 11. The relationship between resonant frequency/frequency spectrum and applied axial displacement; top row: X-direction with PA-X actuator; bottom row: Y-direction with PA-Y actuator
Besides tuning the resonant frequencies, the stiffness-tuning actuators, i.e., PA-X and PA-Y, can be used to further improve the system precision in transient situations via active vibration cancellation techniques [23]-[25]. Our method is inspired by the input shaping method [23]. Since PA-X and PA-Y actuators will induce small X and Y displacements to the nanopositioner due to the stage asymmetry, ―active tuning‖ (or active vibration cancellation) can be achieved by driving the related stiffness-tuning actuator, e.g., PA-X (PI P-845.20, resonant frequency: 12 kHz), with impulse signals when the linear actuator, e.g., LA-X (PI M-230.10S, maximum velocity: 1.2 mm/s), moves the stage. Fig. 12A and Fig. 12B present the operation principle and experimental results of the active tuning using a single pulse, where the step input induced vibration can be completely eliminated by the impulse response via the superposition principle, resulting in a vibration-free output. The step response and impulse response of an underdamped second-order system can be mathematically described in Equations (6) and (7) respectively:
e0 t t0 y t A A sin 0 1 2 t t0 ; 1 2
arccos
(6)
e0 t t0 y t B0 sin 0 1 2 t t0 2 1
(7)
where A is the amplitude of the step input; B is the amplitude of the impulse; ω0 is the underdamped natural frequency of the plant; ζ is the damping ratio of the plant; t is time; and t0 is the time of the input. Next, we consider a more general case, where the vibration may be more effectively reduced by using N pulses (generated by the stiffness-tuning actuator) [23]. To eliminate the vibration after all inputs have ended, the vibration amplitude which consists of a step response and a set of impulse responses should equal to zero. By using trigonometric relations, the following constraints are derived:
N
A0e ii tN t0 sin t0i 1 i2 i Bji e
ii tN t j
j 1
N
A0e ii tN t0 cos t0i 1 i2 i Bji e j 1
sin t ji 1 i2 0 ; Bj k Bj
ii tN t j
cos t ji 1 i2 0
(8)
where A0 is the amplitude of the step input; Bj is the amplitude of the jth impulse; ωi and ζi is the modal frequency and damping ratio of the ith mode of vibration; k is the proportional coefficient between the displacements of the stage and the stiffness-tuning actuator (the value of k varies with the position of the nanopositioner); t0 is the time of the step input; tj is the time of the jth impulse; and tN is the time of the last input. From Equation (8), the time and amplitude of the impulse in Fig. 12A and Fig. 12B can be found as t1
A 1 , and B1 0 e 1 1 1 12
1 112
1
by setting N = 1 and t0 = 0. For N > 1, tj and Bj (j = 1 to N) can
be obtained by solving Equation (8), where modal frequencies ωi and damping ratios ζi (i = 1 to N), are measured experimentally. Note that the modal frequencies ωi change with the stage displacement. Fig. 12C presents the control block diagram of the following active tuning experiments, where r1 is the position set point sent to the LA-X, and r2 is a set of pulse inputs sent to the PA-X. Fig. 12D presents the results of the active tuning experiments using one and two pulses, compared with open-loop and PID control. In the experiment, the linear actuator commands the stage to first generate a 10 μm step under open-loop control; the resulting system response has an overshoot of 487 nm and a settling time of 1.5
seconds. Using PID control alone, we find the overshoot and settling time are reduced to 370 nm and 1.30 seconds respectively. When combining the PID control and active tuning with one impulse, we find the overshoot and settling time are further reduced to 240 nm and 1.28 seconds respectively; with two pulses, we find slightly increased overshoot, i.e., 256 nm and substantially reduced settling time, i.e., 0.5 second. These results validate the effectiveness of active tuning. The Bode plot, shown in Fig. 12E, reconfirms the results, where the first and second modal frequencies at 40 Hz and 60 Hz are effectively suppressed, reducing the overshoot and ringing, as well as shortening the settling time. Overall, more robust and effective vibration cancellation can be achieved via using multiple pulses at the expense of increased overshoot and prolonged actuation time.
X measured [μm]
Position
11
Step Input
Response to Step Input Response to Impulse Input
Impulse Input
10
9
Open-loop Response to Pulse Input 8 0
0.05
0.1
Time
Time [s]
A
B
Command
Output
+
Plant of Nanopositioner
+ -
+
Pulse Generator
Feedback
C
0.15
30
10 9.5 Open-loop Control Closed-loop Control Active Tuning (1 Pulse) Active Tuning (2 Pulses)
9 8.5 0
0.5
1
Amplitude [dB]
X measured [μm]
10.5
1.5
Time [s] D
0
-30 -60
Open-loop Control Closed-loop Control Active Tuning (1 Pulse) Active Tuning (2 Pulses)
-90
-120 1
10
100
1000
Frequency [Hz] E
Fig. 12. Active vibration cancellation method. A: Illustration of vibration cancellation using a single impulse, where the impulse response is anti-phase in relation to the step response, resulting in a vibrationfree output. B: Measured step and impulse responses of the nanopositioner generated by the LA-X and PAX respectively under open-loop control. C: Control block diagram of the active tuning experiment. D, E: Displacement and frequency response measurements of the nanopositioner in the X axis using open-loop control, PID, active tuning with one pulse, and two pulses
4.3 Nano-scratching experiments Based on the nanomanufacturing station, we have performed nano-scratching experiments with stiffness-tuning as well as active tuning with PID control to produce grating patterns on different substrates with an AFM tip array. Fig. 13 shows the scanning electron microscope (SEM) images of the AFM tip array used in the nano-scratching experiments. As shown in Fig. 13, the AFM tip array is a 1-D array of 18 cantilevers with a pitch of 70 μm. Fig. 14 shows the SEM images of the nano-scratching results; Fig. 14A and Fig. 14B show nano-scratched patterns on soft materials, i.e., photoresist, where each line is 3 mm long and the periods are 1 μm and 1.2 μm respectively. Fig. 14C shows nano-scratched patterns on a gold coated silicon substrate, over a 5 × 1 mm2 area, where each line is ~300 nm wide and the period is 1 μm. In our experiments, the scratching speed is set to be 1 mm/s; the time required for patterning a 5 × 1 mm2 area is ~15 min.
80 nm 160 µm
70 µm 70 µm
Fig. 13. SEM images of the AFM tip arrays used in nano-scratching experiments.(NANOSENSORSTM SDPNP-Array2 AFM probe arrays, resonance frequency: 30 kHz)
200 nm
280 nm
1 µm
1.2 µm
A
1 µm
B
C
Fig. 14. SEM images of large-area nano-scratching results. A, B: Nano-scratching on photoresist; C: Nano-scratching on gold-coated silicon wafer
To characterize the parallelism control during the operation, we further characterized the width and depth profiles of the scratched lines on the gold substrate in two separate regions that are 1.2 mm apart, corresponding to lines scratched by the first and the last (18 th) AFM tip. In other words, if the tip array is controlled in perfect parallelism to the substrate, the scratched lines should have equal width and depth. The results are shown in Fig. 15. Fig. 15A presents the AFM tip array schematic as well as the two selected regions: A and B. Fig. 15B and Fig. 15C present the measured line profiles of region A and B respectively, where it can be observed that lines at region A and B have consistent depth ~160 nm and slightly different linewidth (~300 nm vs. ~500 nm), showing good parallelism had been achieved during the nano-scratching process. The straightness tolerance of the scratched lines are calculated to be ~35 nm.
A
70 μm
B
1.2 mm Substrate: gold coated silicon wafer A
B
C
Fig. 15. Characterization of line profiles at two different regions on the gold substrate. A: Schematic of AFM tip array and region A and region B; B: Cross-sectional profile of scratched lines in region A; C: Cross-sectional profile of scratched lines in region B
5. Conclusion In this paper, we present the design, modeling, assembly, and characterization of a dynamic-tunable flexure-based five-axis nanopositioner. Our experiments indicate that the nanopositioner achieves ±100 nm, ±100 nm, ±10 nm, ±1 µrad and ±1 μrad precision in the X, Y, Z, θX, and θY axis with a work volume of 10 mm × 10 mm × 80 μm, suitable for performing parallel probe-based nanofabrication as well as other nanomanufacturing
processes,
such
as
nanoscale
electro-machining
(nano-EM),
and
dip-pen
nanolithography (DPN). The dynamic tuning experiments show the nanopositioner can tune its natural frequency with between 15 Hz and 40 Hz, allowing effective trade-offs between the natural frequency and elastic range. The active tuning experiments show vibration cancellation techniques can be implemented to the flexure-based nanopositioner to further improve the system precision in transient situations. Lastly, the nanopositioner is integrated with a custom-designed AFM to perform nano-scratching experiments, creating grating patterns over a 5 × 1 mm2 area with sub-100 nm precision within a short time frame, i.e. ~15 min. Acknowledgment This work was supported by the HKSAR Innovation and Technology Commission under the Innovation and Technology Fund ITS/262/12: Design and Control of Flexure-Based Multi-Axis Nanopositioners for Ultra Precision Applications.
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