A force-decoupled compound parallel alignment stage for nanoimprint lithography Xiantao Sun, Weihai Chen, Rui Zhou, Wenjie Chen, and Jianbin Zhang Citation: Review of Scientific Instruments 84, 125002 (2013); doi: 10.1063/1.4838595 View online: http://dx.doi.org/10.1063/1.4838595 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/84/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effects of exposure time on defects and demolding force in soft ultraviolet nanoimprint lithography J. Vac. Sci. Technol. B 27, 2091 (2009); 10.1116/1.3186611 Soft photocurable nanoimprint lithography for compound semiconductor nanostructures J. Vac. Sci. Technol. B 26, 156 (2008); 10.1116/1.2823035 Ultrastiff stage for imprint lithography J. Vac. Sci. Technol. B 25, 2317 (2007); 10.1116/1.2798722 Advanced nanoimprint lithography using a graded functional imprinting material tailored for liquid crystal alignment J. Appl. Phys. 102, 063501 (2007); 10.1063/1.2778742 Nanoimprinting-lithography-induced self-aligned liquid crystals for novel multifunctional optical films Appl. Phys. Lett. 88, 073509 (2006); 10.1063/1.2173222
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
REVIEW OF SCIENTIFIC INSTRUMENTS 84, 125002 (2013)
A force-decoupled compound parallel alignment stage for nanoimprint lithography Xiantao Sun,1 Weihai Chen,1,a) Rui Zhou,1 Wenjie Chen,2 and Jianbin Zhang3 1
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China Mechatronics Group, Singapore Institute of Manufacturing Technology, Singapore 638075, Singapore 3 School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China 2
(Received 28 September 2013; accepted 16 November 2013; published online 6 December 2013) This paper presents the development of a force-decoupled compound parallel alignment stage for nanoimprint lithography. Parallel alignment stage is a critical component of nanoimprint machine to implement the uniform surface contact between the template with predefined micro/nano patterns and the substrate that accepts the patterns. A combination of a high-stiffness spherical air bearing and a multi degree-of-freedom flexure-based mechanism is adopted in the parallel alignment stage. Apart from the parallel alignment function, the proposed stage can also endure a large imprinting force (more than 1000 N) but does not cause any damage to the delicate flexure-based mechanism. The stage performance is evaluated to satisfy the alignment requirement through the theoretical modeling and finite element analysis. Experiments are conducted on the parallel alignment stage to verify its performance on the transferred grating patterns with linewidth of 2.5 μm. This result demonstrates that the proposed approach can enhance the load capacity of the parallel alignment stage without degrading its alignment accuracy for nanoimprint lithography. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4838595] I. INTRODUCTION
Nanoimprint lithography (NIL) is considered as a promising technology for the next generation lithography (NGL) owing to its merits of simplicity, high replication fidelity, low cost, and high throughput.1, 2 Compared with the conventional photolithography and other NGL techniques, such as the extreme ultraviolet, electron-beam, ion-beam, and X-ray lithography, NIL has a unique competitive advantage and extensive application prospects in the fabrication of micro/nano structures.3–7 The key difference between them is that NIL is a contact patterning process based on the deformation of polymer materials and can reach a very high resolution that is not limited by the light diffraction or scattering.8 Parallel surface contact between the template with predefined micro/nano patterns and the substrate that accepts the patterns is very critical for pattern fidelity in NIL, whereas the nonparallel surface contact will lead to the uneven patterns on the substrate.9, 10 Nowadays, there are three common methods to compensate for this parallel error, namely, hard parallel plate press, gas press, and soft-template based press. Most of the parallel alignment stages for NIL belong to the first one, i.e., the parallel error is eliminated by the alignment function of parallel alignment stages. Recently, many researchers have focused more attention on the parallel alignment stages for hard plate-to-plate based NIL. According to their working principles, the parallel alignment stages can be divided into three categories, namely, the passive, active, and compound alignment stages. The passive alignment stage is to utilize the elastic deformation of flexible elements to passively eliminate the parallel error between the a) Author to whom correspondence should be addressed. Electronic mail:
[email protected]. 0034-6748/2013/84(12)/125002/9/$30.00
template and the substrate, whereas the active one is to utilize the high-resolution sensors for error detection and then to actively eliminate it by the motion of precision mechanisms. The compound alignment stage is the combination of the above two stages. For example, Johnson presented a threeDOF (degree-of-freedom) passive substrate orientation stage for the single-imprint machine, which utilized a flexible ring with three fixed-fixed beams.11 Lee et al. developed a sixDOF passive compliant stage for the complete surface contact between the template and the substrate. It consisted of an inner mechanism and an outer mechanism arranged in series for the in-plane and out-of-plane motions, respectively.12, 13 Jia et al. described a three-DOF actively controlled compliant parallel stage utilizing flexure hinges for NIL. The system stiffness was analyzed using the matrix method.14 Choi et al. designed a compound parallel alignment stage for step and flash imprint lithography.15 The orientation of the template with respect to the substrate was first manually adjusted using three differential micrometers, and then a two-DOF passive flexure-based stage was utilized to eliminate the residual parallel error. However, the existing techniques in the design of parallel alignment stages for hard plate-to-plate based NIL do not consider the issue of delicate components within the imprinting force transmission path. Thus, this will result in a serious problem that the alignment accuracy cannot be guaranteed especially under a large imprinting force (typically more than 1000 N) for the hot embossing process. To address this problem, this paper presents a novel design approach to the parallel alignment stage with the function of decoupling the imprinting force, which combines a spherical air bearing (SAB) with a multi-DOF flexure-based mechanism. The large imprinting force is supported by the high-stiffness SAB, whereas only the small bending moment due to the
84, 125002-1
© 2013 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-2
Sun et al.
nonuniform imprinting force can reach the delicate flexurebased mechanism. Thus, the alignment accuracy of hard plate-to-plate based NIL machine can be also guaranteed even under a large imprinting force. This approach will make the proposed alignment stage able to be used not only for the ultraviolet imprinting process but also for the hot embossing process. The rest of this paper is organized as follows. The design considerations and mechanical structure of the forceddecoupled compound parallel alignment stage are first presented in Sec. II. Then, the stage performance is evaluated to satisfy the alignment requirement through the theoretical modeling and finite element analysis (FEA) in Secs. III and IV, respectively. NIL machine is constructed as shown in Sec. V, where the grating patterns with linewidth of 2.5 μm are successfully transferred from the silicon template to the polymethyl methacrylate (PMMA) substrate. Finally, this paper is concluded in Sec. VI. II. PARALLEL ALIGNMENT STAGE FOR NIL MACHINE A. Design considerations
Two critical challenges for NIL machine are pattern fidelity and overlay accuracy, which mainly depend on the performance of the parallel alignment stage. Parallel surface contact between the template and the substrate is very important for pattern fidelity, while a relative lateral motion between them will destroy the overlay accuracy. Fig. 1 shows the required DOF for the parallel surface contact between the template and the substrate. Such a surface contact can be accomplished through a translation along the z-axis and two tilting motions (θ x and θ y ) about the x- and y-axes. The translation can be controlled by a z-axis actuator attached to the template stage, while the two tilting motions can be performed by the parallel alignment stage. Parallel alignment stage can be integrated into the template or substrate stage. However, for the latter, not all parallel errors can be effectively compensated in view of the different template poses and initial contact positions.16 Moreover, in the alignment process, a tilt of the substrate stage will destroy the orthogonality between the substrate and the imprinting force, thus generating a horizontal force component to introduce a lateral motion of the substrate. Consequently, the parallel alignment stage should be placed on the template side instead of the substrate side. Even so, a tilt of the template will bring about a new issue to be solved in the alignment process,
FIG. 1. Required DOF for the parallel surface contact between the template and the substrate.
Rev. Sci. Instrum. 84, 125002 (2013)
FIG. 2. Lateral motion of the template induced by its tilt.
i.e., the coupled lateral motion d of the template induced by its tilt α, as shown in Fig. 2, which satisfies d = l sin α,
(1)
where l is the distance from the tilting center to the surface of the template. It can be seen that a large distance l will cause an obvious lateral motion of the template, which will seriously destroy the overlay accuracy of NIL. Thus, in order to avoid this coupled effect, the tilting center of the template should be located at its surface center O. Furthermore, for different NIL processes such as the ultraviolet imprinting process and the hot embossing process, the parallel alignment stage is required to endure the different imprinting force ranging from a few to thousands of Newton.17, 18 In other words, the alignment stage should have a large stiffness along the imprinting axis. On the other hand, it is also required to possess more flexibility to eliminate a large parallel error between the template and the substrate. It is obvious that the above two NIL processes are difficult to be accomplished with a hard plate-to-plate based NIL machine. The key to solve this issue is to design such a parallel alignment stage that can decouple the delicate flexure-based components from the imprinting force, i.e., enabling the imprinting force to bypass the flexure-based components and only allowing the small bending moment due to the nonuniform imprinting force to reach them. B. Mechanical structure
According to the above design considerations, a forcedecoupled compound parallel alignment stage is proposed as shown in Fig. 3. It can be seen that the alignment stage mainly consists of a SAB with a bowl-shaped stator and a hemispherical rotor with a radius of 80 mm, a preload mechanism and a multi-DOF flexure-based mechanism. The stator and the rotor have a carefully polished spherical surface to guarantee that they have a smooth interface. In addition, in order to guarantee the geometrical dimensions of flexure hinges, the multiDOF flexure-based mechanism is fabricated using the wire electrical discharge machining (WEDM) from the AL7075T651 material. The pressurized air from the air inlet is transmitted to the stator-rotor interface to form an air film through 12 uniformly distributed tiny orifices, thus the SAB can provide a frictionless two-DOF rotation around its spherical center about the x- and y-axes. The template center O coincides with the
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-3
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
FIG. 3. Force-decoupled compound parallel alignment stage: (a) cross-sectional view, (b) outer stage, and (c) inner stage.
spherical center of the SAB stator or rotor to avoid the coupled lateral motion of the template due to its tilt. Two sets of annular permanent magnets made of Nd-Fe-B alloy are mounted in the stator and the rotor, respectively, to balance the gravity of the rotor and meanwhile provide a preload to the air film for maximizing its stiffness and maintaining a constant thickness. Moreover, the material of the stator and the rotor is magnetic stainless steel with high permeability to avoid the magnetic flux leakage. The multi-DOF flexure-based mechanism includes two kinds of flexure-based stages for decoupled motions: an outer stage and an inner stage. The outer stage is a decoupled parallel XY stage with a two-layer stacked structure for a compact size. Its translations in x and y directions can be accurately controlled by two high-precision actuators. The inner stage, which is attached to the output end of the outer stage, is a serial combination of a serial XY stage and a three-DOF outof-plane stage. Moreover, the inner stage is connected to the SAB rotor through a connecting link. The five-DOF structure design of the inner stage is to satisfy the motion requirement of the two-DOF rotation (θ x and θ y ) of the SAB rotor and meanwhile restrict its undesired self-rotation (θ z ). Three uniformly distributed force sensors are utilized to measure the imprinting force distribution over the template. During the initial surface contact between the template and the substrate, they can also detect the parallel error. The working principle of the force-decoupled compound parallel alignment stage is illustrated in Fig. 4. When a large imprinting force is applied to the template, the SAB can transmit it to the rigid bracket through the high-stiffness air film, thus bypassing the delicate flexure-based mechanism, as shown in Fig. 4(a). The new force-decoupled characteristic makes the parallel alignment stage suitable not only for the ultraviolet imprinting process but also for the hot embossing process.
For the parallel alignment stage, the initial parallel error θ 0 between the template and the substrate is inevitable due to the manufacturing and assembly errors. During the imprinting process, the z-axis actuator first brings the template in contact with the substrate until a small imprinting force (typically a few Newton) is measured. However, the parallel error will cause the different results of three force sensors. These force signals will be sent to the control system to further drive the outer stage and then actively adjust the tilt of the template as shown in Fig. 4(b). The active alignment is needed only when the new template is installed. After the active alignment, most of the parallel error has been eliminated, but there still
FIG. 4. Working principle of the force-decoupled compound parallel stage: (a) and (b) active alignment and (c) and (d) passive alignment.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-4
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
remains a small parallel error θ due to the limited precision of the actuators and force sensors. Subsequently, as the imprinting force continues to increase, assuming that the contact position between the template and the substrate is the point A as shown in Fig. 4(c), the corresponding imprinting force F can be transformed into a vertical force F acting on the template center and a bending moment M. The vertical force F is supported by the high-stiffness air film, whereas the bending moment M drives the inner stage to passively adjust the tilt of the template until eliminating the residual parallel error θ and eventually resulting in the parallel surface contact, as shown in Fig. 4(d). III. MODELING AND ANALYSIS A. Alignment capacity analysis
According to the analysis in Sec. II, the multi-DOF flexure-based mechanism can function for both the active and passive alignments. Its mechanical performance, in terms of stiffness, motion range, and so on, directly determines the alignment capacity of the parallel alignment stage. In the section, this issue will be discussed in detail. Based on the pseudo-rigid-body model (PRBM) approach, each flexure hinge can be simplified as an ideal rigid joint with a linear spring. Thus, the parallel XY stage (i.e., the outer stage) and the serial XY stage as shown in Figs. 3(b) and 3(c) can be equivalent to an active prismatic joint 1 and a passive prismatic joint 2 along the x- or y-axis, respectively. Similarly, the three-DOF out-of-plane stage as shown in Fig. 3(c) can be also equivalent to a passive universal joint and a passive prismatic joint 3 along the z-axis, and their motion axes intersect at one point P. It should be noticed that the “active” joint means that it is directly driven by the actuator and conversely it is a “passive” joint. Due to the symmetric structure, the parallel alignment stage has the identical performance along the x- and y-axes. Further, its simplified model along the x-axis is obtained as shown in Fig. 5, where Ki represents the stiffness of the corresponding equivalent joint. For the active alignment as shown in Fig. 5(a), the template actively generates a tilting angle θ around its center O in the y direction under the input force/displacement (Fin , δ in ) from the x-actuator. Considering the distance d of the point P deviating from the template center O, for a small tilting angle θ , its displacements along the x- and z-axes can be obtained, respectively, as follows: δPx = d sin θ ∼ = dθ,
(2)
δPz = d · (1 − cos θ ) ∼ = (1/2)dθ 2 .
(3)
Under the equilibrium status for the parallel XY stage, the input force can be derived as Fin = Kx1 · δin + Kx2 · (δin − δPx ),
(4)
where δ in − δ Px represents the relative displacement of the passive prismatic joint 2, i.e., the deformation of the serial XY stage in the x direction. Moreover, during the initial surface contact between the template and the substrate, the small imprinting force as the
FIG. 5. Simplified model of the parallel alignment stage for (a) the active alignment and (b) the passive alignment stage.
feedback signal has a small influence on the deformation of the flexure-based components. Thus, according to the conservation of energy, the following equation is obtained as 1 1 1 2 Fin δin = Kx1 δin + Kx2 (δin − δPx )2 2 2 2 1 1 2 + Kθ θ 2 + Kz δPz . 2 2
(5)
Then, substituting Eqs. (2)–(4) into Eq. (5) yields a relation of the tilting angle of the template and the input displacement, which further gives δin =
d 2 Kx2 + Kθ dKz ·θ + · θ 3. dKx2 4Kx2
(6)
To achieve such a tilting angle, the required input force is obtained as Fin =
d 2 Kx1 Kx2 + Kx1 Kθ + Kx2 Kθ ·θ dKx2 +
dKz (Kx1 + Kx2 ) 3 ·θ . 4Kx2
(7)
For the passive alignment, the actively controlled actuators do not generate any outputs, thus the output end of the parallel XY stage is fixed as shown in Fig. 5(b). The large imprinting force F can be transformed into a vertical force F acting on the template center O and a bending moment M given by M = (1/2)Fl0 , where l0 is the length of the template. The former almost does not bring about any motions due to the high stiffness of the air film with respect to the flexure-based components, whereas the latter drives the inner stage to passively adjust the tilt of the template to eliminate the residual parallel error θ . Similarly with Eq. (5), the work done by the bending
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-5
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
moment is given as 1 1 Mθ = Kx2 [(δin − dθ + dθ )2 − (δin − dθ )2 ] 2 2 1 + Kθ [(θ + θ )2 − θ 2 ] 2 4 d2 θ + θ d 2θ 4 1 − + Kz . 2 4 4
FIG. 7. Deformation and parameters of a flexure beam.
(8) lowing equations can be obtained as
Thus, after the active and the passive alignments, the total adjusting angle of the parallel alignment stage is obtained as θ0 = θ + θ .
(9)
B. Stiffness modeling
As shown in Fig. 3(b), the parallel XY stage consists of four flexure modules A for the bottom layer and four flexure modules B for the top layer. After the assembly of the bottom and top layers, it forms four identical kinematic chains that connect the output end to the fixed base, each of which has two serially connected modules A and B. Moreover, any two adjacent chains are orthogonal to each other to decouple the output motions. Similarly, the serial XY stage as shown in Fig. 3(c) includes two flexure modules C connected in parallel in the x or y direction. The deformed shapes of the modules A, B, and C under an external force applied at the primary stage are shown in Fig. 6, respectively. It can be seen that each module utilizes the secondary stage to increase the motion of the primary stage, where the former only moves half of the latter. Although each module has different numbers of flexure beams, each flexure beam suffers from the identical deformation behavior as shown in Fig. 7. Considering the boundary condition of the zero rotation angle at the free end, the fol-
M=
Fl , 2
(10)
F l3 , (11) 12EI where δ is the transverse displacement at the free end, E represents the elastic modulus of the material, and I = bt3 /12 denotes the moment of inertia of the cross section. Then, the stiffness of the flexure modules A, B, and C seen at the output direction can be derived, respectively, as follows: δ=
KA =
Fy 2EbA tA3 4F = = , y 2δ lA3
(12)
KB =
2F EbB tB3 Fx = = , x 2δ lB3
(13)
KC =
EbC tC3 Fy 2F = = . y 2δ lC3
(14)
Further, the stiffness of the parallel XY stage and the serial XY stage can be obtained, respectively, as follows: Kx1 = 2KA + 2KB =
4EbA tA3 2EbB tB3 + , lA3 lB3
Kx2 = 2KC =
2EbC tC3 . lC3
(15)
(16)
As shown in Fig. 3(c), the three-DOF out-of-plane stage is composed of a tapered split flexure clamp and an annular flexure plate. The former is utilized to firmly hold the connecting link that is mounted in the SAB rotor, and the latter to implement the three-DOF out-of-plane motions (θ x , θ y , and z). It can be seen from Fig. 8 that the annular flexure plate includes four portions (I, II, III, and IV) connected in parallel that are separated by two fixed ends (A and C) and two free ends (B and D). Due to the symmetric structure, only one quarter model as shown in Fig. 8(b) is selected for the purpose of analysis. Moreover, for the annular flexure plate, the in-plane forces (Fx , Fy , and Mz ) have no impact on the outof-plane motions. As shown in Fig. 8(c), the bending moment and torque for any position are given, respectively, as follows:
FIG. 6. Basic flexure modules: (a) module A for the bottom layer, (b) module B for the top layer of the parallel XY stage, and (c) module C for the serial XY stage.
M(θ ) = Fz R cos θ + Mx sin θ − My cos θ,
(17)
T (θ ) = Fz R (1 − sin θ) + Mx cos θ + My sin θ,
(18)
where Fz , Mx , and My represent the out-of-plane forces at the free end D. R is the average radius of the annular flexure plate
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
Sun et al.
125002-6
Rev. Sci. Instrum. 84, 125002 (2013)
The rotation angle about the y-axis is given as θy = 0
π 2
M(θ )M(θ )y · Rdθ + EI
π 2
0
T (θ )T (θ )y · Rdθ GIp
π R2 (4 − π )R 2 · Fz = − + 4EI 4GIp
R πR R πR · Mx + · My + + + − 2EI 2GIp 4EI 4GIp = c31 Fz + c32 Mx + c33 My ,
FIG. 8. Three-DOF out-of-plane stage: (a) annular flexure plate, (b) force analysis for one quarter model, and (c) its schematic diagram.
and satisfies
The displacements of the point D in its local coordinate Dxyz can be obtained based on the unit-load method. Thus, the translation along the z-axis is given as
π 2
δz = 0
M(θ )M(θ )z · Rdθ + EI
π 2
0
= c11 Fz + c12 Mx + c13 My ,
(19)
where M(θ )z and T (θ )z are the corresponding unit loads and given by M(θ )z = R cos θ and T (θ )z = R(1 − cos θ ), respectively, G = E/(2(1 + γ )) is the shear modulus of the material, and Ip = bt3 [(1/3) − 0.21(t/b)(1 − (t4 /12b4 ))] is the torsional moment of inertia of the cross section.19 The rotation angle about the x-axis is given as
0
π 2
M(θ )M(θ )x · Rdθ + EI
0
π 2
T (θ )T (θ )x · Rdθ GIp
R2 πR R2 πR · Fz + · Mx + + 2EI 2GIp 4EI 4GIp
R R + · My + − 2EI 2GIp
=
c32
= c21 Fz + c22 Mx + c23 My , where M(θ )x = sin θ and T (θ )x = cos θ .
c33
My
(20)
My
where C0 is the compliance matrix of the flexure plate I and satisfies cij = cji , and its inverse is defined as the stiffness matrix as follows: ⎞ ⎛ k11 k12 k13 ⎟ ⎜ (23) K0 = C0−1 = ⎝ k21 k22 k23 ⎠ . k31
(4 − π )R 2 π R2 · My + + − 4EI 4GIp
c31
T (θ )T (θ )z · Rdθ GIp
2 3
R πR (3π − 8)R 3 R2 + + = · Fz + · Mx 4EI 4GIp 2EI 2GIp
θx =
where M(θ )y = − cos θ and T (θ )y = sin θ . Then, according to Eqs. (19)–(21), for the flexure plate I, the force-deformation relationship at the free end can be written in the matrix form as ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ c11 c12 c13 Fz δz Fz ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ θx ⎠ = ⎝ c21 c22 c23 ⎠ ⎝Mx ⎠ = C0 ⎝ Mx ⎠ , (22) θy
R1 + R2 R= . 2
(21)
k32
k33
Further, due to the parallel connections of four portions (I, II, III, and IV), the stiffness matrix of the entire three-DOF out-of-plane stage in the coordinate P-xyz, based on the matrix method,20, 21 can be derived as K = diag 4k11 4k22 4R 2 k11 − 4Rk31 − 4Rk13 + 4k33 (24) = diag Kz Kθx Kθy .
C. Design parameters
In order to guarantee that the parallel error between the template and the substrate due to the manufacturing and assembly errors can be fully eliminated through the active and passive alignments, the parallel alignment stage should possess a large angle adjustment capacity for different cases. It can be seen from the above analysis that the outer stage only functions for the active alignment, whereas the inner stage for the entire alignment process. Moreover, the bending moment from the nonuniform imprinting force in Eq. (8) is usually unknown for the passive alignment. This requires that the inner stage can endure a large deformation to implement the entire alignment process and meanwhile the maximum stress is still kept within the yield stress of the material. If the input force Fin , the distance d, and the adjusting angles θ and θ 0 are chosen as 150 N, 139 mm, π /720 rad and π /480 rad, respectively, the final geometrical and material parameters are determined as listed in Table I.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-7
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
TABLE I. Geometrical and material parameters. Description
Value (mm3 )
Dimensions of flexure module A Dimensions of flexure module B Dimensions of flexure module C Dimensions of annular flexure plate
21 × 16 × 0.6 21 × 16 × 0.6 12 × 10 × 0.5 10 × 6 × 0.6
Parameter lA × bA × tA lB × bB × tB lC × bC × tC R×b×t Density 2810
kg/m3
Poisson’s ratio
Young’s modular
Yield strength
0.33
71.7 GPa
503 MPa
IV. FINITE ELEMENT ANALYSIS
In order to further evaluate the performance of the parallel alignment stage and examine the accuracy of the established models, the FEA is performed with commercial software ANSYS. Based on the geometrical model as shown in Fig. 3, the finite element model is established and then meshed using a three-dimensional 20-node solid element named SOLID 95. The meshes are refined at the flexure elements with respect to the remaining parts to guarantee the simulation accuracy. The alignment capacity of the proposed parallel alignment stage is mainly determined by the stiffness of the multiDOF flexure-based mechanism along the motion directions. The actuation source is the force or bending moment applied at the output end of the three critical components, namely, the parallel XY stage, serial XY stage, and three-DOF out-ofplane stage, respectively. Fig. 9 illustrates their deformation simulations along the different directions, where they strictly follow the expected motion trajectory. After obtaining the input force or bending moment and corresponding displacement, their stiffness can be calculated as listed in Table II. It can be seen that there is a small discrepancy between the analytical models and the FEA results. This difference is mainly due to the nonlinear characteristics of the flexure elements.
Moreover, in order to achieve an adjusting angle of π /480 rad for the entire alignment process, the three-DOF stage is required to undergo a rotational deformation of π /480 rad and a translational deformation that satisfies Eq. (3), while the serial XY stage only for a translational deformation that satisfies Eq. (2). Their experienced maximum stresses are 106 MPa and 354.4 MPa, respectively, which indicate that the material at least has a safety factor of 1.42. On the other hand, in order to evaluate the alignment capacity of the entire parallel alignment stage, in the case of the single-axis drive, an input force Fin of 150 N is applied at the input end of the parallel XY stage to further adjust the template orientation. The simulation result indicates that the template can generate a tilting angle of about 5.3 mrad, which meets the design requirement for the active alignment. Nevertheless, in the case of the double-axis drive, the tilting angles of the template about the x- and y-axes are 4.9 mrad and 5.1 mrad, respectively. The deviation from the single-axis drive is attributed to the coupling effect between the two drive axes. The resulting maximum stress within the flexure elements is 152.5 MPa and far less than the yield strength of the material. Moreover, the template strictly rotates about its surface center, thus avoiding the lateral motion of the template in the alignment process and further guaranteeing the overlay accuracy for NIL. It mainly benefits from the coincidence between the template center and the spherical center of the SAB rotor or stator.
V. EXPERIMENTS
FIG. 9. Deformation simulations of the parallel XY stage, serial XY stage, and three-DOF out-of-plane stage: (a) x or y direction, (b) x or y direction, (c) z direction, and (d) θ x or θ y direction.
The imprint experiment is performed to verify the performance of the developed force-decoupled compound parallel alignment stage. The experimental setup is shown in Fig. 10. In order to reduce the external vibration disturbances on the micro/nano pattern transfer between the template and the substrate, the NIL machine is mounted on a heavy marble base with a thin rubber cushion attached to the bottom of the marble base. A z-axis actuator and a preloaded ball screw are employed to realize the vertical imprint motion, where four precision cylinders are to guide this motion, while the two actuators in the xy plane are utilized to implement the active alignment between the template and the substrate. The substrate temperature can be accurately controlled by the thermal control unit that consists of several cartridge heaters and thermocouples embedded within the substrate stage. In order to achieve the high thermal conductivity, aluminum alloy is selected as the material of the substrate stage. Three
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-8
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
TABLE II. Stiffness performance of parallel alignment stage. Parameter Kx1 Kx2 Kz Kθ
Description
Unit
Model
FEA
Translational stiffness of parallel XY stage Translational stiffness of serial XY stage Translational stiffness of three-DOF stage Rotational stiffness of three-DOF stage
N/μm N/μm N/μm N · μm/rad
0.161 0.104 0.113 6.31 × 106
0.182 0.107 0.153 5.75 × 106
high-precision force sensors are utilized to measure the imprinting force distribution over the template for the closedloop feedback during the active alignment. Moreover, an air compressor is required to provide the pressurized air for the SAB. It is known that the minimum feature size on the substrate is mainly determined by that on the template. Considering the manufacturing cost, a series of 2.5 μm wide grating patterns with a 3.5 μm period are fabricated on the silicon template with sufficient mechanical strength and durability using the electron-beam process. Polymethyl methacrylate (PMMA) is used as the substrate material. It has a small thermal expansion coefficient and a glass transition temperature (Tg ) of about 105 ◦ C. The imprint process is performed as follows. First, the PMMA substrate is heated above the Tg to increase its liquidity. Second, the z-axis actuator brings the template in contact with the substrate. After the active and passive alignments, a large imprinting force is applied to the viscous PMMA that is thus squeezed into the cavities of the template. Then, when the temperature drops to the room temperature and the PMMA is solidified, the template is carefully separated from the substrate leaving the micro/nano
FIG. 11. SEM images of (a) the template and (b) the substrate.
patterns on the substrate surface by releasing the imprinting force. To examine the grating patterns on the silicon template and PMMA substrate using the scanning electron microscope (SEM) for comparison, a thin Au film with thickness of a few nanometers is first uniformly deposited onto their entire surfaces. Fig. 11 shows the final SEM images of the template and substrate surfaces. The substrate temperature and imprinting force used in this experiment are about 145 ◦ C and 1200 N, respectively. It can be seen that the grating patterns on the substrate coincide with that on the template. This result further verifies that the proposed parallel alignment stage can be used in the hot embossing NIL. VI. CONCLUSIONS
FIG. 10. Manufactured prototype: (a) NIL machine and (b) parallel alignment stage.
Two critical challenges for NIL machine are pattern fidelity and overlay accuracy, which mainly depend on the performance of the parallel alignment stage. In this paper, a force-decoupled compound parallel alignment stage is proposed to guarantee the alignment accuracy especially
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-9
Sun et al.
under a large imprinting force for the hard plate-to-plate based hot embossing NIL. It consists of a high-stiffness SAB and a delicate multi-DOF flexure-based mechanism. The template center coincides with the spherical center of the SAB stator or rotor to avoid the coupled lateral motion of the template due to its tilt. The large imprinting force is supported by the highstiffness SAB, whereas only the small bending moment due to the nonuniform imprinting force can reach the flexure-based mechanism. The alignment capacity of the parallel alignment stage is mainly determined by the stiffness of the multi-DOF flexure-based mechanism along the different motion directions. Finite element analysis has been utilized to investigate the performance of the parallel alignment stage and examine the accuracy of the established models. The NIL machine is constructed and tested for the hot embossing NIL. The 2.5 μm wide grating patterns with a 3.5 μm period are successfully transferred from the silicon template to the PMMA substrate under the temperature of 145 ◦ C and imprinting force of 1200 N. ACKNOWLEDGMENTS
This research is supported by National Natural Science Foundation of China (NSFC) under Grant Nos. 91023036 and 51275018, and Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20131102110010.
Rev. Sci. Instrum. 84, 125002 (2013) 1 S.
Y. Chou, P. R. Krauss, and P. J. Renstrom, J. Vac. Sci. Technol. B 14, 4129–4133 (1996). 2 S. Y. Chou and P. R. Krauss, Microelectron. Eng. 35, 237–240 (1997). 3 D. Nilsson, T. Nielsen, and A. Kristensen, Rev. Sci. Instrum. 75, 4481– 4486 (2004). 4 S. Grego, A. Huffman, M. Lueck, B. R. Stoner, and J. Lannon, Microelectron. Eng. 87, 1846–1851 (2010). 5 U. Plachetka, A. Kristensen, S. Scheerlinck, J. Huskens, N. Koo, and H. Kurz, Microelectron. Eng. 85, 886–889 (2008). 6 Y. Wang, S. H. Goh, X. Bi, and K.-L. Yang, J. Colloid Interface Sci. 333, 188–194 (2009). 7 L. Lei, H. Li, J. Shi, and Y. Chen, Rev. Sci. Instrum. 81, 023103 (2010). 8 L. J. Guo, J. Phys. D: Appl. Phys. 37, R123 (2004). 9 W. Zhang and S. Y. Chou, Appl. Phys. Lett. 79, 845–847 (2001). 10 H. Lan, Y. Ding, H. Liu, and B. Lu, Microelectron. Eng. 84, 684–688 (2007). 11 S. C. Johnson, MS thesis, University of Texas, 1999. 12 J. J. Lee, K. B. Choi, and G. H. Kim, Curr. Appl. Phys. 6, 1007–1011 (2006). 13 K. B. Choi and J. J. Lee, Rev. Sci. Instrum. 76, 075106 (2005). 14 X. Jia, J. Liu, Y. Tian, and D. Zhang, Robotica 30, 925–939 (2011). 15 B. J. Choi, S. V. Sreenivasan, S. Johnson, M. Colburn, and C. G. Wilson, Precis. Eng. 25, 192–199 (2001). 16 J. Y. Shao, Y. C. Ding, H. Z. Liu, X. M. Li, H. M. Tian, and B. H. Xiao, Proc. Inst. Mech. Eng., Part B 226, 221–228 (2011). 17 P. Datta and J. Geoetter, Microsyst. Technol. 13, 265–270 (2007). 18 W. Lin, W. Chen, C. M. Kiew, C. L. Ng, H. Luo, C. S. Teo, and G. Yang, Key Eng. Mater. 447–448, 483–487 (2010). 19 W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain (McGraw-Hill, New York, 2002). 20 H. H. Pham and I. M. Chen, Precis. Eng. 29, 467–478 (2005). 21 Y. Li and Q. Xu, IEEE Trans. Robot. 25, 645–657 (2009).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
REVIEW OF SCIENTIFIC INSTRUMENTS 84, 125002 (2013)
A force-decoupled compound parallel alignment stage for nanoimprint lithography Xiantao Sun,1 Weihai Chen,1,a) Rui Zhou,1 Wenjie Chen,2 and Jianbin Zhang3 1
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China Mechatronics Group, Singapore Institute of Manufacturing Technology, Singapore 638075, Singapore 3 School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China 2
(Received 28 September 2013; accepted 16 November 2013; published online 6 December 2013) This paper presents the development of a force-decoupled compound parallel alignment stage for nanoimprint lithography. Parallel alignment stage is a critical component of nanoimprint machine to implement the uniform surface contact between the template with predefined micro/nano patterns and the substrate that accepts the patterns. A combination of a high-stiffness spherical air bearing and a multi degree-of-freedom flexure-based mechanism is adopted in the parallel alignment stage. Apart from the parallel alignment function, the proposed stage can also endure a large imprinting force (more than 1000 N) but does not cause any damage to the delicate flexure-based mechanism. The stage performance is evaluated to satisfy the alignment requirement through the theoretical modeling and finite element analysis. Experiments are conducted on the parallel alignment stage to verify its performance on the transferred grating patterns with linewidth of 2.5 μm. This result demonstrates that the proposed approach can enhance the load capacity of the parallel alignment stage without degrading its alignment accuracy for nanoimprint lithography. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4838595] I. INTRODUCTION
Nanoimprint lithography (NIL) is considered as a promising technology for the next generation lithography (NGL) owing to its merits of simplicity, high replication fidelity, low cost, and high throughput.1, 2 Compared with the conventional photolithography and other NGL techniques, such as the extreme ultraviolet, electron-beam, ion-beam, and X-ray lithography, NIL has a unique competitive advantage and extensive application prospects in the fabrication of micro/nano structures.3–7 The key difference between them is that NIL is a contact patterning process based on the deformation of polymer materials and can reach a very high resolution that is not limited by the light diffraction or scattering.8 Parallel surface contact between the template with predefined micro/nano patterns and the substrate that accepts the patterns is very critical for pattern fidelity in NIL, whereas the nonparallel surface contact will lead to the uneven patterns on the substrate.9, 10 Nowadays, there are three common methods to compensate for this parallel error, namely, hard parallel plate press, gas press, and soft-template based press. Most of the parallel alignment stages for NIL belong to the first one, i.e., the parallel error is eliminated by the alignment function of parallel alignment stages. Recently, many researchers have focused more attention on the parallel alignment stages for hard plate-to-plate based NIL. According to their working principles, the parallel alignment stages can be divided into three categories, namely, the passive, active, and compound alignment stages. The passive alignment stage is to utilize the elastic deformation of flexible elements to passively eliminate the parallel error between the a) Author to whom correspondence should be addressed. Electronic mail:
[email protected]. 0034-6748/2013/84(12)/125002/9/$30.00
template and the substrate, whereas the active one is to utilize the high-resolution sensors for error detection and then to actively eliminate it by the motion of precision mechanisms. The compound alignment stage is the combination of the above two stages. For example, Johnson presented a threeDOF (degree-of-freedom) passive substrate orientation stage for the single-imprint machine, which utilized a flexible ring with three fixed-fixed beams.11 Lee et al. developed a sixDOF passive compliant stage for the complete surface contact between the template and the substrate. It consisted of an inner mechanism and an outer mechanism arranged in series for the in-plane and out-of-plane motions, respectively.12, 13 Jia et al. described a three-DOF actively controlled compliant parallel stage utilizing flexure hinges for NIL. The system stiffness was analyzed using the matrix method.14 Choi et al. designed a compound parallel alignment stage for step and flash imprint lithography.15 The orientation of the template with respect to the substrate was first manually adjusted using three differential micrometers, and then a two-DOF passive flexure-based stage was utilized to eliminate the residual parallel error. However, the existing techniques in the design of parallel alignment stages for hard plate-to-plate based NIL do not consider the issue of delicate components within the imprinting force transmission path. Thus, this will result in a serious problem that the alignment accuracy cannot be guaranteed especially under a large imprinting force (typically more than 1000 N) for the hot embossing process. To address this problem, this paper presents a novel design approach to the parallel alignment stage with the function of decoupling the imprinting force, which combines a spherical air bearing (SAB) with a multi-DOF flexure-based mechanism. The large imprinting force is supported by the high-stiffness SAB, whereas only the small bending moment due to the
84, 125002-1
© 2013 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-2
Sun et al.
nonuniform imprinting force can reach the delicate flexurebased mechanism. Thus, the alignment accuracy of hard plate-to-plate based NIL machine can be also guaranteed even under a large imprinting force. This approach will make the proposed alignment stage able to be used not only for the ultraviolet imprinting process but also for the hot embossing process. The rest of this paper is organized as follows. The design considerations and mechanical structure of the forceddecoupled compound parallel alignment stage are first presented in Sec. II. Then, the stage performance is evaluated to satisfy the alignment requirement through the theoretical modeling and finite element analysis (FEA) in Secs. III and IV, respectively. NIL machine is constructed as shown in Sec. V, where the grating patterns with linewidth of 2.5 μm are successfully transferred from the silicon template to the polymethyl methacrylate (PMMA) substrate. Finally, this paper is concluded in Sec. VI. II. PARALLEL ALIGNMENT STAGE FOR NIL MACHINE A. Design considerations
Two critical challenges for NIL machine are pattern fidelity and overlay accuracy, which mainly depend on the performance of the parallel alignment stage. Parallel surface contact between the template and the substrate is very important for pattern fidelity, while a relative lateral motion between them will destroy the overlay accuracy. Fig. 1 shows the required DOF for the parallel surface contact between the template and the substrate. Such a surface contact can be accomplished through a translation along the z-axis and two tilting motions (θ x and θ y ) about the x- and y-axes. The translation can be controlled by a z-axis actuator attached to the template stage, while the two tilting motions can be performed by the parallel alignment stage. Parallel alignment stage can be integrated into the template or substrate stage. However, for the latter, not all parallel errors can be effectively compensated in view of the different template poses and initial contact positions.16 Moreover, in the alignment process, a tilt of the substrate stage will destroy the orthogonality between the substrate and the imprinting force, thus generating a horizontal force component to introduce a lateral motion of the substrate. Consequently, the parallel alignment stage should be placed on the template side instead of the substrate side. Even so, a tilt of the template will bring about a new issue to be solved in the alignment process,
FIG. 1. Required DOF for the parallel surface contact between the template and the substrate.
Rev. Sci. Instrum. 84, 125002 (2013)
FIG. 2. Lateral motion of the template induced by its tilt.
i.e., the coupled lateral motion d of the template induced by its tilt α, as shown in Fig. 2, which satisfies d = l sin α,
(1)
where l is the distance from the tilting center to the surface of the template. It can be seen that a large distance l will cause an obvious lateral motion of the template, which will seriously destroy the overlay accuracy of NIL. Thus, in order to avoid this coupled effect, the tilting center of the template should be located at its surface center O. Furthermore, for different NIL processes such as the ultraviolet imprinting process and the hot embossing process, the parallel alignment stage is required to endure the different imprinting force ranging from a few to thousands of Newton.17, 18 In other words, the alignment stage should have a large stiffness along the imprinting axis. On the other hand, it is also required to possess more flexibility to eliminate a large parallel error between the template and the substrate. It is obvious that the above two NIL processes are difficult to be accomplished with a hard plate-to-plate based NIL machine. The key to solve this issue is to design such a parallel alignment stage that can decouple the delicate flexure-based components from the imprinting force, i.e., enabling the imprinting force to bypass the flexure-based components and only allowing the small bending moment due to the nonuniform imprinting force to reach them. B. Mechanical structure
According to the above design considerations, a forcedecoupled compound parallel alignment stage is proposed as shown in Fig. 3. It can be seen that the alignment stage mainly consists of a SAB with a bowl-shaped stator and a hemispherical rotor with a radius of 80 mm, a preload mechanism and a multi-DOF flexure-based mechanism. The stator and the rotor have a carefully polished spherical surface to guarantee that they have a smooth interface. In addition, in order to guarantee the geometrical dimensions of flexure hinges, the multiDOF flexure-based mechanism is fabricated using the wire electrical discharge machining (WEDM) from the AL7075T651 material. The pressurized air from the air inlet is transmitted to the stator-rotor interface to form an air film through 12 uniformly distributed tiny orifices, thus the SAB can provide a frictionless two-DOF rotation around its spherical center about the x- and y-axes. The template center O coincides with the
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-3
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
FIG. 3. Force-decoupled compound parallel alignment stage: (a) cross-sectional view, (b) outer stage, and (c) inner stage.
spherical center of the SAB stator or rotor to avoid the coupled lateral motion of the template due to its tilt. Two sets of annular permanent magnets made of Nd-Fe-B alloy are mounted in the stator and the rotor, respectively, to balance the gravity of the rotor and meanwhile provide a preload to the air film for maximizing its stiffness and maintaining a constant thickness. Moreover, the material of the stator and the rotor is magnetic stainless steel with high permeability to avoid the magnetic flux leakage. The multi-DOF flexure-based mechanism includes two kinds of flexure-based stages for decoupled motions: an outer stage and an inner stage. The outer stage is a decoupled parallel XY stage with a two-layer stacked structure for a compact size. Its translations in x and y directions can be accurately controlled by two high-precision actuators. The inner stage, which is attached to the output end of the outer stage, is a serial combination of a serial XY stage and a three-DOF outof-plane stage. Moreover, the inner stage is connected to the SAB rotor through a connecting link. The five-DOF structure design of the inner stage is to satisfy the motion requirement of the two-DOF rotation (θ x and θ y ) of the SAB rotor and meanwhile restrict its undesired self-rotation (θ z ). Three uniformly distributed force sensors are utilized to measure the imprinting force distribution over the template. During the initial surface contact between the template and the substrate, they can also detect the parallel error. The working principle of the force-decoupled compound parallel alignment stage is illustrated in Fig. 4. When a large imprinting force is applied to the template, the SAB can transmit it to the rigid bracket through the high-stiffness air film, thus bypassing the delicate flexure-based mechanism, as shown in Fig. 4(a). The new force-decoupled characteristic makes the parallel alignment stage suitable not only for the ultraviolet imprinting process but also for the hot embossing process.
For the parallel alignment stage, the initial parallel error θ 0 between the template and the substrate is inevitable due to the manufacturing and assembly errors. During the imprinting process, the z-axis actuator first brings the template in contact with the substrate until a small imprinting force (typically a few Newton) is measured. However, the parallel error will cause the different results of three force sensors. These force signals will be sent to the control system to further drive the outer stage and then actively adjust the tilt of the template as shown in Fig. 4(b). The active alignment is needed only when the new template is installed. After the active alignment, most of the parallel error has been eliminated, but there still
FIG. 4. Working principle of the force-decoupled compound parallel stage: (a) and (b) active alignment and (c) and (d) passive alignment.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-4
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
remains a small parallel error θ due to the limited precision of the actuators and force sensors. Subsequently, as the imprinting force continues to increase, assuming that the contact position between the template and the substrate is the point A as shown in Fig. 4(c), the corresponding imprinting force F can be transformed into a vertical force F acting on the template center and a bending moment M. The vertical force F is supported by the high-stiffness air film, whereas the bending moment M drives the inner stage to passively adjust the tilt of the template until eliminating the residual parallel error θ and eventually resulting in the parallel surface contact, as shown in Fig. 4(d). III. MODELING AND ANALYSIS A. Alignment capacity analysis
According to the analysis in Sec. II, the multi-DOF flexure-based mechanism can function for both the active and passive alignments. Its mechanical performance, in terms of stiffness, motion range, and so on, directly determines the alignment capacity of the parallel alignment stage. In the section, this issue will be discussed in detail. Based on the pseudo-rigid-body model (PRBM) approach, each flexure hinge can be simplified as an ideal rigid joint with a linear spring. Thus, the parallel XY stage (i.e., the outer stage) and the serial XY stage as shown in Figs. 3(b) and 3(c) can be equivalent to an active prismatic joint 1 and a passive prismatic joint 2 along the x- or y-axis, respectively. Similarly, the three-DOF out-of-plane stage as shown in Fig. 3(c) can be also equivalent to a passive universal joint and a passive prismatic joint 3 along the z-axis, and their motion axes intersect at one point P. It should be noticed that the “active” joint means that it is directly driven by the actuator and conversely it is a “passive” joint. Due to the symmetric structure, the parallel alignment stage has the identical performance along the x- and y-axes. Further, its simplified model along the x-axis is obtained as shown in Fig. 5, where Ki represents the stiffness of the corresponding equivalent joint. For the active alignment as shown in Fig. 5(a), the template actively generates a tilting angle θ around its center O in the y direction under the input force/displacement (Fin , δ in ) from the x-actuator. Considering the distance d of the point P deviating from the template center O, for a small tilting angle θ , its displacements along the x- and z-axes can be obtained, respectively, as follows: δPx = d sin θ ∼ = dθ,
(2)
δPz = d · (1 − cos θ ) ∼ = (1/2)dθ 2 .
(3)
Under the equilibrium status for the parallel XY stage, the input force can be derived as Fin = Kx1 · δin + Kx2 · (δin − δPx ),
(4)
where δ in − δ Px represents the relative displacement of the passive prismatic joint 2, i.e., the deformation of the serial XY stage in the x direction. Moreover, during the initial surface contact between the template and the substrate, the small imprinting force as the
FIG. 5. Simplified model of the parallel alignment stage for (a) the active alignment and (b) the passive alignment stage.
feedback signal has a small influence on the deformation of the flexure-based components. Thus, according to the conservation of energy, the following equation is obtained as 1 1 1 2 Fin δin = Kx1 δin + Kx2 (δin − δPx )2 2 2 2 1 1 2 + Kθ θ 2 + Kz δPz . 2 2
(5)
Then, substituting Eqs. (2)–(4) into Eq. (5) yields a relation of the tilting angle of the template and the input displacement, which further gives δin =
d 2 Kx2 + Kθ dKz ·θ + · θ 3. dKx2 4Kx2
(6)
To achieve such a tilting angle, the required input force is obtained as Fin =
d 2 Kx1 Kx2 + Kx1 Kθ + Kx2 Kθ ·θ dKx2 +
dKz (Kx1 + Kx2 ) 3 ·θ . 4Kx2
(7)
For the passive alignment, the actively controlled actuators do not generate any outputs, thus the output end of the parallel XY stage is fixed as shown in Fig. 5(b). The large imprinting force F can be transformed into a vertical force F acting on the template center O and a bending moment M given by M = (1/2)Fl0 , where l0 is the length of the template. The former almost does not bring about any motions due to the high stiffness of the air film with respect to the flexure-based components, whereas the latter drives the inner stage to passively adjust the tilt of the template to eliminate the residual parallel error θ . Similarly with Eq. (5), the work done by the bending
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-5
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
moment is given as 1 1 Mθ = Kx2 [(δin − dθ + dθ )2 − (δin − dθ )2 ] 2 2 1 + Kθ [(θ + θ )2 − θ 2 ] 2 4 d2 θ + θ d 2θ 4 1 − + Kz . 2 4 4
FIG. 7. Deformation and parameters of a flexure beam.
(8) lowing equations can be obtained as
Thus, after the active and the passive alignments, the total adjusting angle of the parallel alignment stage is obtained as θ0 = θ + θ .
(9)
B. Stiffness modeling
As shown in Fig. 3(b), the parallel XY stage consists of four flexure modules A for the bottom layer and four flexure modules B for the top layer. After the assembly of the bottom and top layers, it forms four identical kinematic chains that connect the output end to the fixed base, each of which has two serially connected modules A and B. Moreover, any two adjacent chains are orthogonal to each other to decouple the output motions. Similarly, the serial XY stage as shown in Fig. 3(c) includes two flexure modules C connected in parallel in the x or y direction. The deformed shapes of the modules A, B, and C under an external force applied at the primary stage are shown in Fig. 6, respectively. It can be seen that each module utilizes the secondary stage to increase the motion of the primary stage, where the former only moves half of the latter. Although each module has different numbers of flexure beams, each flexure beam suffers from the identical deformation behavior as shown in Fig. 7. Considering the boundary condition of the zero rotation angle at the free end, the fol-
M=
Fl , 2
(10)
F l3 , (11) 12EI where δ is the transverse displacement at the free end, E represents the elastic modulus of the material, and I = bt3 /12 denotes the moment of inertia of the cross section. Then, the stiffness of the flexure modules A, B, and C seen at the output direction can be derived, respectively, as follows: δ=
KA =
Fy 2EbA tA3 4F = = , y 2δ lA3
(12)
KB =
2F EbB tB3 Fx = = , x 2δ lB3
(13)
KC =
EbC tC3 Fy 2F = = . y 2δ lC3
(14)
Further, the stiffness of the parallel XY stage and the serial XY stage can be obtained, respectively, as follows: Kx1 = 2KA + 2KB =
4EbA tA3 2EbB tB3 + , lA3 lB3
Kx2 = 2KC =
2EbC tC3 . lC3
(15)
(16)
As shown in Fig. 3(c), the three-DOF out-of-plane stage is composed of a tapered split flexure clamp and an annular flexure plate. The former is utilized to firmly hold the connecting link that is mounted in the SAB rotor, and the latter to implement the three-DOF out-of-plane motions (θ x , θ y , and z). It can be seen from Fig. 8 that the annular flexure plate includes four portions (I, II, III, and IV) connected in parallel that are separated by two fixed ends (A and C) and two free ends (B and D). Due to the symmetric structure, only one quarter model as shown in Fig. 8(b) is selected for the purpose of analysis. Moreover, for the annular flexure plate, the in-plane forces (Fx , Fy , and Mz ) have no impact on the outof-plane motions. As shown in Fig. 8(c), the bending moment and torque for any position are given, respectively, as follows:
FIG. 6. Basic flexure modules: (a) module A for the bottom layer, (b) module B for the top layer of the parallel XY stage, and (c) module C for the serial XY stage.
M(θ ) = Fz R cos θ + Mx sin θ − My cos θ,
(17)
T (θ ) = Fz R (1 − sin θ) + Mx cos θ + My sin θ,
(18)
where Fz , Mx , and My represent the out-of-plane forces at the free end D. R is the average radius of the annular flexure plate
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
Sun et al.
125002-6
Rev. Sci. Instrum. 84, 125002 (2013)
The rotation angle about the y-axis is given as θy = 0
π 2
M(θ )M(θ )y · Rdθ + EI
π 2
0
T (θ )T (θ )y · Rdθ GIp
π R2 (4 − π )R 2 · Fz = − + 4EI 4GIp
R πR R πR · Mx + · My + + + − 2EI 2GIp 4EI 4GIp = c31 Fz + c32 Mx + c33 My ,
FIG. 8. Three-DOF out-of-plane stage: (a) annular flexure plate, (b) force analysis for one quarter model, and (c) its schematic diagram.
and satisfies
The displacements of the point D in its local coordinate Dxyz can be obtained based on the unit-load method. Thus, the translation along the z-axis is given as
π 2
δz = 0
M(θ )M(θ )z · Rdθ + EI
π 2
0
= c11 Fz + c12 Mx + c13 My ,
(19)
where M(θ )z and T (θ )z are the corresponding unit loads and given by M(θ )z = R cos θ and T (θ )z = R(1 − cos θ ), respectively, G = E/(2(1 + γ )) is the shear modulus of the material, and Ip = bt3 [(1/3) − 0.21(t/b)(1 − (t4 /12b4 ))] is the torsional moment of inertia of the cross section.19 The rotation angle about the x-axis is given as
0
π 2
M(θ )M(θ )x · Rdθ + EI
0
π 2
T (θ )T (θ )x · Rdθ GIp
R2 πR R2 πR · Fz + · Mx + + 2EI 2GIp 4EI 4GIp
R R + · My + − 2EI 2GIp
=
c32
= c21 Fz + c22 Mx + c23 My , where M(θ )x = sin θ and T (θ )x = cos θ .
c33
My
(20)
My
where C0 is the compliance matrix of the flexure plate I and satisfies cij = cji , and its inverse is defined as the stiffness matrix as follows: ⎞ ⎛ k11 k12 k13 ⎟ ⎜ (23) K0 = C0−1 = ⎝ k21 k22 k23 ⎠ . k31
(4 − π )R 2 π R2 · My + + − 4EI 4GIp
c31
T (θ )T (θ )z · Rdθ GIp
2 3
R πR (3π − 8)R 3 R2 + + = · Fz + · Mx 4EI 4GIp 2EI 2GIp
θx =
where M(θ )y = − cos θ and T (θ )y = sin θ . Then, according to Eqs. (19)–(21), for the flexure plate I, the force-deformation relationship at the free end can be written in the matrix form as ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ c11 c12 c13 Fz δz Fz ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ θx ⎠ = ⎝ c21 c22 c23 ⎠ ⎝Mx ⎠ = C0 ⎝ Mx ⎠ , (22) θy
R1 + R2 R= . 2
(21)
k32
k33
Further, due to the parallel connections of four portions (I, II, III, and IV), the stiffness matrix of the entire three-DOF out-of-plane stage in the coordinate P-xyz, based on the matrix method,20, 21 can be derived as K = diag 4k11 4k22 4R 2 k11 − 4Rk31 − 4Rk13 + 4k33 (24) = diag Kz Kθx Kθy .
C. Design parameters
In order to guarantee that the parallel error between the template and the substrate due to the manufacturing and assembly errors can be fully eliminated through the active and passive alignments, the parallel alignment stage should possess a large angle adjustment capacity for different cases. It can be seen from the above analysis that the outer stage only functions for the active alignment, whereas the inner stage for the entire alignment process. Moreover, the bending moment from the nonuniform imprinting force in Eq. (8) is usually unknown for the passive alignment. This requires that the inner stage can endure a large deformation to implement the entire alignment process and meanwhile the maximum stress is still kept within the yield stress of the material. If the input force Fin , the distance d, and the adjusting angles θ and θ 0 are chosen as 150 N, 139 mm, π /720 rad and π /480 rad, respectively, the final geometrical and material parameters are determined as listed in Table I.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-7
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
TABLE I. Geometrical and material parameters. Description
Value (mm3 )
Dimensions of flexure module A Dimensions of flexure module B Dimensions of flexure module C Dimensions of annular flexure plate
21 × 16 × 0.6 21 × 16 × 0.6 12 × 10 × 0.5 10 × 6 × 0.6
Parameter lA × bA × tA lB × bB × tB lC × bC × tC R×b×t Density 2810
kg/m3
Poisson’s ratio
Young’s modular
Yield strength
0.33
71.7 GPa
503 MPa
IV. FINITE ELEMENT ANALYSIS
In order to further evaluate the performance of the parallel alignment stage and examine the accuracy of the established models, the FEA is performed with commercial software ANSYS. Based on the geometrical model as shown in Fig. 3, the finite element model is established and then meshed using a three-dimensional 20-node solid element named SOLID 95. The meshes are refined at the flexure elements with respect to the remaining parts to guarantee the simulation accuracy. The alignment capacity of the proposed parallel alignment stage is mainly determined by the stiffness of the multiDOF flexure-based mechanism along the motion directions. The actuation source is the force or bending moment applied at the output end of the three critical components, namely, the parallel XY stage, serial XY stage, and three-DOF out-ofplane stage, respectively. Fig. 9 illustrates their deformation simulations along the different directions, where they strictly follow the expected motion trajectory. After obtaining the input force or bending moment and corresponding displacement, their stiffness can be calculated as listed in Table II. It can be seen that there is a small discrepancy between the analytical models and the FEA results. This difference is mainly due to the nonlinear characteristics of the flexure elements.
Moreover, in order to achieve an adjusting angle of π /480 rad for the entire alignment process, the three-DOF stage is required to undergo a rotational deformation of π /480 rad and a translational deformation that satisfies Eq. (3), while the serial XY stage only for a translational deformation that satisfies Eq. (2). Their experienced maximum stresses are 106 MPa and 354.4 MPa, respectively, which indicate that the material at least has a safety factor of 1.42. On the other hand, in order to evaluate the alignment capacity of the entire parallel alignment stage, in the case of the single-axis drive, an input force Fin of 150 N is applied at the input end of the parallel XY stage to further adjust the template orientation. The simulation result indicates that the template can generate a tilting angle of about 5.3 mrad, which meets the design requirement for the active alignment. Nevertheless, in the case of the double-axis drive, the tilting angles of the template about the x- and y-axes are 4.9 mrad and 5.1 mrad, respectively. The deviation from the single-axis drive is attributed to the coupling effect between the two drive axes. The resulting maximum stress within the flexure elements is 152.5 MPa and far less than the yield strength of the material. Moreover, the template strictly rotates about its surface center, thus avoiding the lateral motion of the template in the alignment process and further guaranteeing the overlay accuracy for NIL. It mainly benefits from the coincidence between the template center and the spherical center of the SAB rotor or stator.
V. EXPERIMENTS
FIG. 9. Deformation simulations of the parallel XY stage, serial XY stage, and three-DOF out-of-plane stage: (a) x or y direction, (b) x or y direction, (c) z direction, and (d) θ x or θ y direction.
The imprint experiment is performed to verify the performance of the developed force-decoupled compound parallel alignment stage. The experimental setup is shown in Fig. 10. In order to reduce the external vibration disturbances on the micro/nano pattern transfer between the template and the substrate, the NIL machine is mounted on a heavy marble base with a thin rubber cushion attached to the bottom of the marble base. A z-axis actuator and a preloaded ball screw are employed to realize the vertical imprint motion, where four precision cylinders are to guide this motion, while the two actuators in the xy plane are utilized to implement the active alignment between the template and the substrate. The substrate temperature can be accurately controlled by the thermal control unit that consists of several cartridge heaters and thermocouples embedded within the substrate stage. In order to achieve the high thermal conductivity, aluminum alloy is selected as the material of the substrate stage. Three
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-8
Sun et al.
Rev. Sci. Instrum. 84, 125002 (2013)
TABLE II. Stiffness performance of parallel alignment stage. Parameter Kx1 Kx2 Kz Kθ
Description
Unit
Model
FEA
Translational stiffness of parallel XY stage Translational stiffness of serial XY stage Translational stiffness of three-DOF stage Rotational stiffness of three-DOF stage
N/μm N/μm N/μm N · μm/rad
0.161 0.104 0.113 6.31 × 106
0.182 0.107 0.153 5.75 × 106
high-precision force sensors are utilized to measure the imprinting force distribution over the template for the closedloop feedback during the active alignment. Moreover, an air compressor is required to provide the pressurized air for the SAB. It is known that the minimum feature size on the substrate is mainly determined by that on the template. Considering the manufacturing cost, a series of 2.5 μm wide grating patterns with a 3.5 μm period are fabricated on the silicon template with sufficient mechanical strength and durability using the electron-beam process. Polymethyl methacrylate (PMMA) is used as the substrate material. It has a small thermal expansion coefficient and a glass transition temperature (Tg ) of about 105 ◦ C. The imprint process is performed as follows. First, the PMMA substrate is heated above the Tg to increase its liquidity. Second, the z-axis actuator brings the template in contact with the substrate. After the active and passive alignments, a large imprinting force is applied to the viscous PMMA that is thus squeezed into the cavities of the template. Then, when the temperature drops to the room temperature and the PMMA is solidified, the template is carefully separated from the substrate leaving the micro/nano
FIG. 11. SEM images of (a) the template and (b) the substrate.
patterns on the substrate surface by releasing the imprinting force. To examine the grating patterns on the silicon template and PMMA substrate using the scanning electron microscope (SEM) for comparison, a thin Au film with thickness of a few nanometers is first uniformly deposited onto their entire surfaces. Fig. 11 shows the final SEM images of the template and substrate surfaces. The substrate temperature and imprinting force used in this experiment are about 145 ◦ C and 1200 N, respectively. It can be seen that the grating patterns on the substrate coincide with that on the template. This result further verifies that the proposed parallel alignment stage can be used in the hot embossing NIL. VI. CONCLUSIONS
FIG. 10. Manufactured prototype: (a) NIL machine and (b) parallel alignment stage.
Two critical challenges for NIL machine are pattern fidelity and overlay accuracy, which mainly depend on the performance of the parallel alignment stage. In this paper, a force-decoupled compound parallel alignment stage is proposed to guarantee the alignment accuracy especially
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
125002-9
Sun et al.
under a large imprinting force for the hard plate-to-plate based hot embossing NIL. It consists of a high-stiffness SAB and a delicate multi-DOF flexure-based mechanism. The template center coincides with the spherical center of the SAB stator or rotor to avoid the coupled lateral motion of the template due to its tilt. The large imprinting force is supported by the highstiffness SAB, whereas only the small bending moment due to the nonuniform imprinting force can reach the flexure-based mechanism. The alignment capacity of the parallel alignment stage is mainly determined by the stiffness of the multi-DOF flexure-based mechanism along the different motion directions. Finite element analysis has been utilized to investigate the performance of the parallel alignment stage and examine the accuracy of the established models. The NIL machine is constructed and tested for the hot embossing NIL. The 2.5 μm wide grating patterns with a 3.5 μm period are successfully transferred from the silicon template to the PMMA substrate under the temperature of 145 ◦ C and imprinting force of 1200 N. ACKNOWLEDGMENTS
This research is supported by National Natural Science Foundation of China (NSFC) under Grant Nos. 91023036 and 51275018, and Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20131102110010.
Rev. Sci. Instrum. 84, 125002 (2013) 1 S.
Y. Chou, P. R. Krauss, and P. J. Renstrom, J. Vac. Sci. Technol. B 14, 4129–4133 (1996). 2 S. Y. Chou and P. R. Krauss, Microelectron. Eng. 35, 237–240 (1997). 3 D. Nilsson, T. Nielsen, and A. Kristensen, Rev. Sci. Instrum. 75, 4481– 4486 (2004). 4 S. Grego, A. Huffman, M. Lueck, B. R. Stoner, and J. Lannon, Microelectron. Eng. 87, 1846–1851 (2010). 5 U. Plachetka, A. Kristensen, S. Scheerlinck, J. Huskens, N. Koo, and H. Kurz, Microelectron. Eng. 85, 886–889 (2008). 6 Y. Wang, S. H. Goh, X. Bi, and K.-L. Yang, J. Colloid Interface Sci. 333, 188–194 (2009). 7 L. Lei, H. Li, J. Shi, and Y. Chen, Rev. Sci. Instrum. 81, 023103 (2010). 8 L. J. Guo, J. Phys. D: Appl. Phys. 37, R123 (2004). 9 W. Zhang and S. Y. Chou, Appl. Phys. Lett. 79, 845–847 (2001). 10 H. Lan, Y. Ding, H. Liu, and B. Lu, Microelectron. Eng. 84, 684–688 (2007). 11 S. C. Johnson, MS thesis, University of Texas, 1999. 12 J. J. Lee, K. B. Choi, and G. H. Kim, Curr. Appl. Phys. 6, 1007–1011 (2006). 13 K. B. Choi and J. J. Lee, Rev. Sci. Instrum. 76, 075106 (2005). 14 X. Jia, J. Liu, Y. Tian, and D. Zhang, Robotica 30, 925–939 (2011). 15 B. J. Choi, S. V. Sreenivasan, S. Johnson, M. Colburn, and C. G. Wilson, Precis. Eng. 25, 192–199 (2001). 16 J. Y. Shao, Y. C. Ding, H. Z. Liu, X. M. Li, H. M. Tian, and B. H. Xiao, Proc. Inst. Mech. Eng., Part B 226, 221–228 (2011). 17 P. Datta and J. Geoetter, Microsyst. Technol. 13, 265–270 (2007). 18 W. Lin, W. Chen, C. M. Kiew, C. L. Ng, H. Luo, C. S. Teo, and G. Yang, Key Eng. Mater. 447–448, 483–487 (2010). 19 W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain (McGraw-Hill, New York, 2002). 20 H. H. Pham and I. M. Chen, Precis. Eng. 29, 467–478 (2005). 21 Y. Li and Q. Xu, IEEE Trans. Robot. 25, 645–657 (2009).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 15:59:53
