- Email: [email protected]
Dynamic modelling and experimental study of asymmetric optothermal microactuator
Optics Communications 383 (2017) 566–570
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Dynamic modelling and experimental study of asymmetric optothermal microactuator Shuying Wang, Qin Chun, Qingyang You, Yingda Wang, Haijun Zhang
crossmark
⁎
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Optothermal microactuator Dynamic modelling Deflection
This paper reports the dynamic modelling and experimental study of an asymmetric optothermal microactuator (OTMA). According to the principle of thermal flux, a theoretical model for instantaneous temperature distribution of an expansion arm is established and the expression of expansion increment is derived. Dynamic expansion properties of the arm under laser pulse irradiation are theoretically analyzed indicating that both of the maximum expansion and expansion amplitude decrease with the pulse frequency increasing. Experiments have been further carried out on an OTMA fabricated by using an excimer laser micromachining system. It is shown that the OTMA deflects periodically with the same frequency of laser pulse irradiation. Experimental results also prove that both OTMA’s maximum deflection and deflection amplitude (related to maximum expansion and expansion amplitude of the arm) decrease as frequency increases, matching with the theoretical model quite well. Even though the OTMA's deflection decrease at higher frequency, it is still capable of generating 8.2 μm maximum deflection and 4.2 μm deflection amplitude under 17 Hz/2 mW laser pulse irradiation. This work improves the potential applications of optothermal microactuators in micro-opto-electromechanical system (MOEMS) and micro/nano-technology fields.
1. Introduction With the development of micro-opto-electro-mechanical systems (MOEMS), high-performance microactuators have been increasingly required, which are considered as the key part for MOEMS devices to perform physical function. Many microactuators based on electrostatic [1], magnetic [2], piezoelectric [3,4], magnetostrictive [5], and thermal actuation [6,7] principles have been reported, among which, thermal actuation-based actuators [8,9] have been widely used in MOEMS where slow motions and large displacements are required. Electrothermal actuators [10] are capable of gaining bigger deflection angles and generating larger actuating forces, while photothermal micro-cantilevers and actuators are able to realize actuation directly by laser beam [11–13]. In our previous work [14], a kind of optothermal microactuator (OTMA) with hot/cold arms was proposed, and its static properties of expansion and deflection under continuous laser beams have been discussed. While in most of the practical applications, the MOEMS devices and OTMAs are required to work under dynamic conditions. Therefore, further efforts are needed to investigate dynamic properties of OTMA. In this paper, dynamic modelling and experimental study of an asymmetric OTMA is presented. Instantaneous temperature distribu-
⁎
tion and dynamic expansion properties the OTMA’s expansion arm are theoretically analyzed. Experiments are then conducted on such OTMA to check its dynamic properties, as well as to prove the validity of dynamic model. 2. Dynamic modelling of an OTMA The scheme of an asymmetric OTMA is shown in Fig. 1. The OTMA consists of two asymmetric arms which are joined at the free end and connected to the base through two narrow bridges at the fixed end. Heating is generated when a focused laser beam irradiates the OTMA's expansion arm (length L, width W, thickness D), causing temperature rise and volume expansion. The arm then elongates for ΔL and acquires an enlarged lateral deflection of ΔD due to connected free end.. Set the left end of the expansion arm as the coordinate origin (x=0), and the center of spot as x=L1, the free right end as x=L. A theoretical model describing the dynamic mechanism of optothermal temperature distribution and expansion is established. As shown in Fig. 2, an arbitrary element with dx length at the position x is chosen to analyze the heat transmission of the expansion arm. Within the dt period, the element gains a heat flux QLaser (QLaser is zero when the element is out of the spot) from laser irradiation, and Qx
Corresponding author. E-mail address: [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.optcom.2016.09.063 Received 29 April 2016; Received in revised form 29 August 2016; Accepted 29 September 2016 Available online 12 October 2016 0030-4018/ © 2016 Elsevier B.V. All rights reserved.
Optics Communications 383 (2017) 566–570
S. Wang et al.
partial differential equations with fixed solution: 2 ⎧ ∂T 2∂ T ⎪ ∂t = a ∂x 2 − b⋅ΔT + f (x, t ) ⎪ ⎪ K ⋅ ∂T x =0 − h1⋅ΔT (0, t ) = 0 ⎨ ∂x ⎪ ∂T ⎪ K ⋅ ∂x x = L − h2⋅ΔT (L , t ) = 0 ⎪ ΔT (x, 0) = 0 ⎩
(6)
Where a,b and f(x,t) are defined as:
a=
Fig. 1. Scheme of an asymmetric optothermal microactuator (OTMA) with its expansion arm irradiated by a laser spot.
K , ρC
b=
2(Wh w + DhD ) , ρWDC
f (x , t ) =
q (x , t ) ρDC
(7)
Solving Eq. (6) using eigen function method [15], the distribution of temperature rise can be given as follows: ∞
∑
ΔT (x, t ) =
n =1
exp(−bt − a2λ n t ) Vn (x ) νn
∫0
t
Un (ξ )exp(bξ + a2λ n ξ ) dξ
(8)
According to the relation between thermal expansion and temperature rise, the thermal expansion increment ΔL along the X direction can be expressed as:
ΔL (t ) = α
∫0
(1)
x=0
− h1⋅ΔT (0, t ) = 0
K⋅
∂T ∂x
x=L
− h2⋅ΔT (L , t ) = 0
(9)
Eqs. (8) and (9) are the general formulas of temperature rise and dynamic optothermal expansion. For an expansion arm made of certain material irradiated by a certain kind of laser, the distribution of temperature rise and the optothermal expansion can be obtained as long as all parameters are substituted into the equations. Laser pulse with a duty cycle of 0.5 and alterable frequencies is employed to analyze the dynamic properties of the expansion arm. For simplicity, the power-density distribution of laser spot is approximately assumed to be uniform. Therefore, the power-density distribution q(x,t) can be described as:
(2)
q (x , ⎧ρ q , t) = ⎨ A 0 ⎩ 0,
L1 − R ≤ x ≤ L1 + Rand 2mt0 ≤ t < (2m + 1) t0 x < L1 − Rorx > L1 + Ror (2m + 1) t0 ≤ t < 2(m + 1) t0
(m = 0, 1, 2, …)
(3)
(11)
Where q0 is the incident laser power density, ρA is the laser absorption ratio of the expansion arm, t0 the single pulse duration and 2t0 the pulse period. Within a certain laser pulse, 2mt0≤t < (2m+1)t0 stands for the “pulse-on” duration, and (2m+1)t0≤t < 2(m+1)t0 the “pulse-off” duration, set tr=t-2mt0 and εn=b+a2λn, Eq. (8) can be rewritten as:
(4)
Set the original temperature rise when t=0 is zero, that is
ΔT (x, 0) = 0
⎤ Un (ξ )exp(bξ + a2λ n ξ ) dξ ⎥ ⎥⎦
(10)
Where K, C and ρ are the thermal conductivity, heat capacity and density of the expansion arm, q is the power-density distribution of laser spot, ΔT and T=T0+ΔT are respectively the temperature rise and the real-time temperature of the element when the arm is irradiated (T0, the initial temperature), hD and hW are the coefficients of the convective heat transfer with air on the side and up/down surfaces. As the heat environment at the fixed end is different from the free end, the coefficients of the convective heat transfer are different, named h1, h2 respectively. h2 is the same with hD. The thermal boundary conditions can be expressed as:
∂T ∂x
t
2 ⎧ −1 K λ − h1h2 ⎪ λ L = nπ + ctg ( K λ (h1 + h2) ) ⎪ ⎪Vn (x ) = K λ n cos( λ n x ) + h1 sin( λ n x ) ⎨ (n = 1, 2, ⋯) L ⎪Un (t ) = ∫ Vn (x ) f (x, t ) dx 0 ⎪ ⎪ νn = ∫ L Vn (x )2dx = 1 (K2λ n + h12 )(L + h2 K ) + 1 h1 K 2 2 0 K2λn + h22 ⎩
Replace the terms of Eq. (1) by the fluxes shown in Fig. 2, and simplify as:
K⋅
ΔT (x,
Where α is the linear thermal expansion coefficient of the material, λn(n=1, 2,…) is a group of eigen values, Vn(x) is a set of eigen functions,
from the former element. At the same time, it loses Qx+dx flowing into the next element, and QW and QD due to convection through up/down and side surfaces. ΔQ is the increased heat of the element during the transmission process. The direction of heat flux is defined as positive in accordance with the arrows, conversely, the direction is negative.. In principle, the increased heat equals to the difference of obtained and lost heat fluxes. The equation can be expressed as:
q ∂T K ∂ 2T 2(Wh w + DhD ) = − ΔT + ∂t ρC ∂x 2 ρWDC ρDC
L
∞ ⎡ exp(−bt − a2λ n t )(K λ n sin( λ n L ) + h1 − h1 cos( λ n L )) t ) dx = α ∑ ⎢ ⎢ λ n νn n =1 ⎣
Fig. 2. Heat flux model of an arbitrary element of the expansion arm. QLaser is the heat flux from laser irradiation, Qx and Qx+dx are conduction heat along the arm, QW and QD are convection heat through up/down and side surfaces. The element gains QLaser and Qx, loses Qx+dx, QW and QD, and finally achieves an increased heat ΔQ.
ΔQ = QLaser + Qx − Qx + dx − QD − QW
∫0
(5)
Therefore Eq. (2) with the boundary conditions can be regarded as 567
Optics Communications 383 (2017) 566–570
S. Wang et al.
Table 1 Parameters of the Laser and the OTMA Arm.
ΔT (x, ⎧ ∞ μn Vn (x ) exp(−εn tr ) − exp(−εn t ) ⎪ ∑n =1 νn εn ( exp(2εn t 0) − 1 (exp(εn t0 ) − 1) + 1 − exp(−εn tr )) ⎪ , 2mt0 ≤ t < (2m + 1) t0 ⎪ ⎪ t ) = ⎨ ∑∞ μn Vn (x ) exp(−2εn t 0) − exp(−εn t ) (exp(ε t ) − 1), n 0 exp(2εn t 0 ) − 1 ⎪ n =1 νn εn ⎪ ⎪ (2m + 1) t0 ≤ t < 2(m + 1) t0 ⎪ (m = 0, 1, 2, …) ⎩ (12) where
μn =
2KρA q0 2h1 ρA q0 cos( λ n L1)sin( λ n R ) + sin( λ n L1)sin( λ n R ) ρDC ρDC λ n (13)
Name
Description
Given Value
R (μm) P (mW) q0 (Wm−2) f (Hz) λ (nm) L1 (μm) L (μm) L0 (μm) W (μm) D (μm) S (μm) hD (Wm−2K−1)
Radius of laser spot Laser pulse power Laser pulse power density [P/(πR2)] Laser frequency Laser wavelength Coordinate of the laser spot center Length of the arm Total length of OTMA Width of the arm Thickness of the arm Distance between two narrow bridges Coefficients of the convective heat transfer with air on the side surfaces Coefficients of the convective heat transfer with air on the upper/lower surfaces Coefficient of the convective heat transfer on the fixed end of the arm Coefficient of the convective heat transfer on the free end of the arm Thermal conductivity of the material Thermal expansion coefficient of the material Initial temperature laser absorption ratio of the expansion arm
100 2 6.4×104 0–20 650 600 1300 1500 200 20 60 500
hW (Wm−2K−1)
Using Eq. (12), we have made simulations on the temperature rise ΔT(x, t) at the center of laser beam spot (where x=L1) with the reference information [16] and the given parameters, such as 2-mW power and 0.5, 2.0, 3.0, 5.0, 10, 17 Hz (frequencies used in the experiments). The simulated results indicate that temperature rise at the center of laser beam spot periodically changes in accordance with the frequency. Meanwhile, both of the amplitude and maximum (peak) values of temperature rise decrease with the increase of frequency. The maximum temperature rises ΔTmax are 61.9, 54.6, 49.0, 42.8, 37.1, and 34.7 °C, respectively. When the initial temperature T0 is 20 °C, the maximum temperatures (T0+ΔTmax) will be 81.9, 74.6, 69.0, 62.8, 57.1 and 54.7 °C. Since the melting temperature of high density polypropylene is between 118 and 146 °C [17], the maximum temperatures of the microactuator's surface under each laser pulse frequency are all within the safe range. Meanwhile,
h1 (Wm−2K−1) h2 (Wm−2K−1) −1
−1
K (Wm K ) α (K−1) T0 (°C) ρA
30 20000 500 0.24 3.2×10−5 20 0.95
⎧ ∞ μn VLn exp(−εn tr ) − exp(−εn t ) ⎪ α ∑n =1 νn εn ( exp(2εn t 0) − 1 (exp(εn t0 ) − 1) + 1 − exp(−εn tr )) ⎪ , 2mt0 ≤ t < (2m + 1) t0 ⎪ ⎪ ΔL (t ) = ⎨ α ∑∞ μn VLn exp(−2εn t 0) − exp(−εn t ) (exp(ε t ) − 1), n 0 n =1 νn εn exp(2εn t 0 ) − 1 ⎪ ⎪ ⎪ (2m + 1) t0 ≤ t < 2(m + 1) t0 ⎪ (m = 0, 1, 2, …) ⎩ (14) where
VLn =
Fig. 3. Simulated results of dynamic optothermal expansion of the arm irradiated by laser pulse (P=2 mW, f=2 Hz).
(K λ n sin( λ n L ) + h1 − h1 cos( λ n L )) λn
(15) Similarly, the maximum expansion ΔLM can be expressed as:
According to Eq. (12) and parameters listed in Table 1, the dynamic optothermal expansion is theoretically simulated, as shown in Fig. 3. The results indicate that the expansion arm will expand and revert continuously with the same frequency of laser pulse, moreover, the arm is not able to revert to its original length.. This phenomenon can be explained on the following dynamic mechanism: During the pulse duration, expansion arm absorbs heat from laser spot, resulting in temperature rise and expansion; similarly, during the pulse interval, the arm loses heat to the environment and reverts；as the arm is alternatively irradiated by laser pulse, it is unable to sufficiently lose the heat absorbed from the former pulse, so that it can not return back to its original length before the next pulse comes. The maximum expansion ΔLM and expansion amplitude AL shown in Fig. 3 can be further discussed as follows. According to Eq. (12), when m tends to infinity, exp(−2εn (m + 1) t0 ) and exp(−εn (2m + 1) t0 )equals to zero, the expansion amplitude of the arm is derived as: ∞
AL ≈ α ∑ n =1
μn VLn (exp(2εn t0 ) + 1 − 2 exp(εn t0 )) νn εn (exp(2εn t0 ) − 1)
∞
ΔLM ≈ α ∑ n =1
μn VLn exp(2εn t0 )(1 − exp(−εn t0 )) νn εn (exp(2εn t0 ) − 1)
(17)
The relationships among ΔLM, AL and f are illustrated in Fig. 4, showing that both the maximum expansion and expansion amplitude decrease with laser frequency increasing.. In practice, the tolerance considerations should be taken into account. We have made simulations when setting the errors of geometric dimensions (R, L1, L0, L, W, D), laser parameters (P, ρA, q0), thermal parameters (hD, hW, h1, h2, K, α, T0) and all of these parameters to be 10%. The simulated maximum errors of maximum expansions ΔLM are 12.7%, 19.6%, 11.2% and 25.1%, respectively. Meanwhile, the maximum errors of expansion amplitudes AL are 12.6%, 20.1%, 17.5%, and 25.3%, respectively. These data illustrate that the errors of the parameters in our model might cause tolerances to the results. On the other hand, it should be mentioned that these errors (about 13–25%) are simulated when setting the tolerances of each parameter or even all parameters to be 10%, which would be the extreme and unlikely to happen. More importantly, the trends of all simulated curves demonstrating the dynamic behavior of optothermal
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S. Wang et al.
control circuit generates laser pulses (650 nm, 0–20 Hz, 2 mW measured at the position of microactuator) with a duty cycle of 0.5. The laser is focused by a lens and irradiates the microactuator through a beam splitter. The microactuator will then deflect with the same frequency of the laser pulse. The action or deflection of actuator is monitored by an objective/CCD/computer-combined microscopic system, which can measure actuator's optothermal deflection using subpixel motion analysis software. All parameters used in this work were listed in Table 1.. The original state of the OTMA captured by CCD is shown in Fig. 5(b). When the laser pulse irradiates the expansion arm, an obvious deflection can be observed and the switch contacts can totally touch with each other (Fig. 5(c)). Dot M within the small circle is the test point chosen to measure optothermal deflection of the OTMA. To check the dynamic properties of the OTMA, laser pulse frequency changes from 0.5 to 17 Hz. When frequencies are 0.5, 2.0, 3.0, 5.0, 10, 17 Hz, the maximum deflections are measured to be 16.6, 15.2, 13.2, 11.4, 9.2, 8.2 µm, and the deflection amplitudes are 15.5, 13.0, 10.8, 8.2, 5.9, 4.2 µm, respectively. The relationships among the maximum deflection ΔDM, deflection amplitude AD and pulse frequency f are plotted in Fig. 6. It is clear that both ΔDM and AD decrease along with frequency increasing.. As already indicated by the theoretical simulation result shown in Fig. 4, the expansion ΔL of the arm is quite small, therefore, it is difficult to realize accurate measurement for ΔL in the experiments. In practice, the deflection ΔD of the OTMA is comparatively larger and can be accurately measured. In the theoretical model, ΔD is of a corresponding relationship with ΔL. Experiment results also show that the curve trends of ΔD (ΔDM and AD) are in accordance with those of ΔL (ΔLM and AL), proving that the dynamic properties of OTMA match with the theoretical predictions quite well. Besides, even though the OTMA's deflection decreases at higher frequency, it keeps a maximum deflection of 8.2 µm and a deflection amplitude of 4.2 µm at 17 Hz, which is still sufficient for MOEMS devices. As a potential application, the microactuator mentioned above may serve as a microswitch, which can be directly controlled (on or off) by a laser beam. No electric circuit connected to power supply is demanded, and no ohmic heating current passes through the microactuator, that is, no electric or electromagnetic interference between heating current and switch-controlled current exists. With these characteristics and dynamic properties, such kinds of microactuators may provide broadened applications in MOEMS and micro/nano-technology fields.
Fig. 4. Theoretical relationships among the maximum expansion ΔLM, expansion amplitude AL and laser pulse frequency f (P=2 mW).
microactuator are nearly identical. In summary, the advantages of this optothermal actuator as well as its dynamic model include: the actuator is newly developed and made of single-layer material (rather than bi-layer one); it has a wise structure and utilizes a novel principle of converting optothermal expansion into enlarged later deflection (rather than vertical bending); detailed modelling on the dynamic properties of optothermal actuator has been made for the first time; based on the same principle, a series of optothermal actuators can be further developed, and more importantly, all of them can directly adopt the original dynamic model first proposed in this work. 3. Experiments and results As the free end of the OTMA is connected, longitudinal expansion ΔL will be finally converted and enlarged to lateral deflection ΔD. To verify the dynamic model and theoretical results, experiments involving ΔD are further performed. Choosing black high density polypropylene sheet with high linear thermal expansion coefficient as base material, several asymmetric OTMAs with the same parameters are fabricated using an excimer laser micromachining system (Optec Promaster). To avoid the influence of film sputtering for SEM observation on properties of this OTMA, another OTMA is employed in the experiment. Fig. 5(a) shows the scanning electron microscopy (SEM) image of the OTMA. It has a total length of about 1500 µm, with an expansion arm of 1300-μm length, 200 μm width and 20 μm thickness. In our dynamic model, the actuator is going to be driven in air environment. Therefore, experiments are also carried out in air environment at initial temperature (20 °C). During experiments, a laser diode controlled by
4. Conclusions This paper proposed a new method of asymmetric OTMA based on the dynamic mechanism of optothermal expansion. A comprehensive model has been developed to describe the dynamic characteristics of optothermal expansion arm. Such characteristics of the arm irradiated
Fig. 5. (a) SEM image of an OTMA, (b) original and (c) laser irradiated states of a same type of OTMA captured from optical microscope videos monitoring the process of optothermal microactuation, the laser spot is located within the bigger dashed circle.
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Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.optcom.2016.09.063. References [1] M.M. Ghazaly, K. Sato, Characteristic switching of a multilayer thin electrostatic actuator by a driving signal for an ultra-precision motion stage, Precis. Eng. 37 (1) (2013) 107–116. [2] Y.W. Park, D.Y. Kim, Development of a magnetostrictive microactuator, J. Magn. Magn. Mater. 272–276 (2004) E1765–E1766. [3] B. Watson, J. Friend, L. Yeo, Piezoelectric ultrasonic micro/milli-scale actuators, Sens. Actuator A-Phys. 152 (2009) 219–233. [4] J.Q. Ma, Y. Liu, C.P. Chen, B.Q. Li, J.R. Chu, Deformable mirrors based on piezoelectric unimorph microactuator array for adaptive optics correction, Opt. Commun. 284 (21) (2011) 5062–5066. [5] J. Kyokane, K. Tsujimoto, Y. Yanagisawa, T. Ueda, M. Fukuma, Actuator using electrostriction effect of fullerenol-doped polyurethane elastomer (PUE) films, Ieice (E87-C)T. Electron (2) (2004) 136–141. [6] T. Lalinskýa, M. Držíkb, J. Chlpíkb, M. Krnáča, Š. Haščíka, Ž. Mozolováa, I. Kostičc Thermo-mechanical, characterization of micromachined GaAs-based thermal converter using contactless optical methods, Sens. Actuator A-Phys. 123–124 (2005) 99–105. [7] J.C. Chiou, W.T. Lin, Variable optical attenuator using a thermal actuator array with dual shutters, Opt. Commun. 237 (4) (2004) 341–350. [8] R. Venditti, J.S.H. Lee, Y. Sun, D.Q. Li, An in-plane, bi-directional electrothermal MEMS actuator, J. Micromech. Microeng. 16 (10) (2006) 2067–2070. [9] P. Yang, M. Stevensona, Y. Laia, C. Mechefskea, M. Kujathb, T. Hubbard, Design, modeling and testing of a unidirectional MEMS ring thermal actuator, Sens. Actuator A-Phys. 143 (2) (2008) 352–359. [10] Y.S. Yang, L.H. Lin, H.C. Hu, C.H. Liu, A large-displacement thermal actuator designed for MEMS pitch-tunable grating, J. Micromech. Microeng. 19 (2009) 015001. [11] G. Mu, Y. Bao, C. Li, Measurement of collisional multiphoton energy deposition by a new optothermal detector, Opt. Commun. 51 (1) (1984) 25–28. [12] D. Zhang, H. Zhang, C. Liu, J. Jiang, Microscopic observation and laser-controlled micro-optothermal drive mechanism, Microsc. Res. Tech. 71 (2008) 119–124. [13] S. Zaidi, F. Lamarque, C. Prelle, O. Carton, A. Zeinert, Contactless and selective energy transfer to a bistable micro-actuator using laser heated shape memory alloy, Smart Mater. Struct. 21 (2012) 115027. [14] D. Zhang, H. Zhang, C. Liu, J. Jiang, Theoretical and experimental study of optothermal expansion and optothermal microactuator, Opt. Express 16 (17) (2008) 13476–13485. [15] Y.L. He, The mechanism of micro photo-thermal expansion and the new method of photo-thermal micro actuator (Ph.D. Thesis), Zhejiang University, 2008. [16] Typical engineering properties of polypropylene. 〈http://www.ineos.com/ globalassets/ineos-group/businesses/ineos-olefins-and-polymers-usa/products/ technical-information-patents/ineos-engineering-properties-of-pp.pdf〉. [17] J. E. Mark, Polymer data handbook, New York, 2009.
Fig. 6. Experimental results showing relationships among the maximum deflection ΔDM, deflection amplitude AD and laser pulse frequency f (P=2 mW).
by laser pulse are theoretically simulated using MATLAB (MATLAB V8.0.0.783 (R2012b), MathWorks Inc.), indicating that both of the maximum expansion and expansion amplitude decrease with the pulse frequency increasing. Experiments on the asymmetric OTMA under laser pulse irradiation with different frequency show that the OTMA deflects periodically with the same frequency of laser pulse. It is also proved that both OTMA’s maximum deflection and deflection amplitude decrease as frequency increases, agreeing with the theoretical model quite well. In addition, theoretical simulations show that OTMA is still able to keep a high expansion at 20 Hz, corresponding to a high deflection. In our follow-up work, deflection properties at higher frequency will be further studied by using high-speed photography technology. This dynamic optothermal microactuation technique has great potential in the fields of MOEMS and micro/nano-technology. Acknowledgements Financial support from National Natural Science Foundation of China (Grant Nos. 51077117 and 61540019) is gratefully acknowledged.
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Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Dynamic modelling and experimental study of asymmetric optothermal microactuator Shuying Wang, Qin Chun, Qingyang You, Yingda Wang, Haijun Zhang
crossmark
⁎
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Optothermal microactuator Dynamic modelling Deflection
This paper reports the dynamic modelling and experimental study of an asymmetric optothermal microactuator (OTMA). According to the principle of thermal flux, a theoretical model for instantaneous temperature distribution of an expansion arm is established and the expression of expansion increment is derived. Dynamic expansion properties of the arm under laser pulse irradiation are theoretically analyzed indicating that both of the maximum expansion and expansion amplitude decrease with the pulse frequency increasing. Experiments have been further carried out on an OTMA fabricated by using an excimer laser micromachining system. It is shown that the OTMA deflects periodically with the same frequency of laser pulse irradiation. Experimental results also prove that both OTMA’s maximum deflection and deflection amplitude (related to maximum expansion and expansion amplitude of the arm) decrease as frequency increases, matching with the theoretical model quite well. Even though the OTMA's deflection decrease at higher frequency, it is still capable of generating 8.2 μm maximum deflection and 4.2 μm deflection amplitude under 17 Hz/2 mW laser pulse irradiation. This work improves the potential applications of optothermal microactuators in micro-opto-electromechanical system (MOEMS) and micro/nano-technology fields.
1. Introduction With the development of micro-opto-electro-mechanical systems (MOEMS), high-performance microactuators have been increasingly required, which are considered as the key part for MOEMS devices to perform physical function. Many microactuators based on electrostatic [1], magnetic [2], piezoelectric [3,4], magnetostrictive [5], and thermal actuation [6,7] principles have been reported, among which, thermal actuation-based actuators [8,9] have been widely used in MOEMS where slow motions and large displacements are required. Electrothermal actuators [10] are capable of gaining bigger deflection angles and generating larger actuating forces, while photothermal micro-cantilevers and actuators are able to realize actuation directly by laser beam [11–13]. In our previous work [14], a kind of optothermal microactuator (OTMA) with hot/cold arms was proposed, and its static properties of expansion and deflection under continuous laser beams have been discussed. While in most of the practical applications, the MOEMS devices and OTMAs are required to work under dynamic conditions. Therefore, further efforts are needed to investigate dynamic properties of OTMA. In this paper, dynamic modelling and experimental study of an asymmetric OTMA is presented. Instantaneous temperature distribu-
⁎
tion and dynamic expansion properties the OTMA’s expansion arm are theoretically analyzed. Experiments are then conducted on such OTMA to check its dynamic properties, as well as to prove the validity of dynamic model. 2. Dynamic modelling of an OTMA The scheme of an asymmetric OTMA is shown in Fig. 1. The OTMA consists of two asymmetric arms which are joined at the free end and connected to the base through two narrow bridges at the fixed end. Heating is generated when a focused laser beam irradiates the OTMA's expansion arm (length L, width W, thickness D), causing temperature rise and volume expansion. The arm then elongates for ΔL and acquires an enlarged lateral deflection of ΔD due to connected free end.. Set the left end of the expansion arm as the coordinate origin (x=0), and the center of spot as x=L1, the free right end as x=L. A theoretical model describing the dynamic mechanism of optothermal temperature distribution and expansion is established. As shown in Fig. 2, an arbitrary element with dx length at the position x is chosen to analyze the heat transmission of the expansion arm. Within the dt period, the element gains a heat flux QLaser (QLaser is zero when the element is out of the spot) from laser irradiation, and Qx
Corresponding author. E-mail address: [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.optcom.2016.09.063 Received 29 April 2016; Received in revised form 29 August 2016; Accepted 29 September 2016 Available online 12 October 2016 0030-4018/ © 2016 Elsevier B.V. All rights reserved.
Optics Communications 383 (2017) 566–570
S. Wang et al.
partial differential equations with fixed solution: 2 ⎧ ∂T 2∂ T ⎪ ∂t = a ∂x 2 − b⋅ΔT + f (x, t ) ⎪ ⎪ K ⋅ ∂T x =0 − h1⋅ΔT (0, t ) = 0 ⎨ ∂x ⎪ ∂T ⎪ K ⋅ ∂x x = L − h2⋅ΔT (L , t ) = 0 ⎪ ΔT (x, 0) = 0 ⎩
(6)
Where a,b and f(x,t) are defined as:
a=
Fig. 1. Scheme of an asymmetric optothermal microactuator (OTMA) with its expansion arm irradiated by a laser spot.
K , ρC
b=
2(Wh w + DhD ) , ρWDC
f (x , t ) =
q (x , t ) ρDC
(7)
Solving Eq. (6) using eigen function method [15], the distribution of temperature rise can be given as follows: ∞
∑
ΔT (x, t ) =
n =1
exp(−bt − a2λ n t ) Vn (x ) νn
∫0
t
Un (ξ )exp(bξ + a2λ n ξ ) dξ
(8)
According to the relation between thermal expansion and temperature rise, the thermal expansion increment ΔL along the X direction can be expressed as:
ΔL (t ) = α
∫0
(1)
x=0
− h1⋅ΔT (0, t ) = 0
K⋅
∂T ∂x
x=L
− h2⋅ΔT (L , t ) = 0
(9)
Eqs. (8) and (9) are the general formulas of temperature rise and dynamic optothermal expansion. For an expansion arm made of certain material irradiated by a certain kind of laser, the distribution of temperature rise and the optothermal expansion can be obtained as long as all parameters are substituted into the equations. Laser pulse with a duty cycle of 0.5 and alterable frequencies is employed to analyze the dynamic properties of the expansion arm. For simplicity, the power-density distribution of laser spot is approximately assumed to be uniform. Therefore, the power-density distribution q(x,t) can be described as:
(2)
q (x , ⎧ρ q , t) = ⎨ A 0 ⎩ 0,
L1 − R ≤ x ≤ L1 + Rand 2mt0 ≤ t < (2m + 1) t0 x < L1 − Rorx > L1 + Ror (2m + 1) t0 ≤ t < 2(m + 1) t0
(m = 0, 1, 2, …)
(3)
(11)
Where q0 is the incident laser power density, ρA is the laser absorption ratio of the expansion arm, t0 the single pulse duration and 2t0 the pulse period. Within a certain laser pulse, 2mt0≤t < (2m+1)t0 stands for the “pulse-on” duration, and (2m+1)t0≤t < 2(m+1)t0 the “pulse-off” duration, set tr=t-2mt0 and εn=b+a2λn, Eq. (8) can be rewritten as:
(4)
Set the original temperature rise when t=0 is zero, that is
ΔT (x, 0) = 0
⎤ Un (ξ )exp(bξ + a2λ n ξ ) dξ ⎥ ⎥⎦
(10)
Where K, C and ρ are the thermal conductivity, heat capacity and density of the expansion arm, q is the power-density distribution of laser spot, ΔT and T=T0+ΔT are respectively the temperature rise and the real-time temperature of the element when the arm is irradiated (T0, the initial temperature), hD and hW are the coefficients of the convective heat transfer with air on the side and up/down surfaces. As the heat environment at the fixed end is different from the free end, the coefficients of the convective heat transfer are different, named h1, h2 respectively. h2 is the same with hD. The thermal boundary conditions can be expressed as:
∂T ∂x
t
2 ⎧ −1 K λ − h1h2 ⎪ λ L = nπ + ctg ( K λ (h1 + h2) ) ⎪ ⎪Vn (x ) = K λ n cos( λ n x ) + h1 sin( λ n x ) ⎨ (n = 1, 2, ⋯) L ⎪Un (t ) = ∫ Vn (x ) f (x, t ) dx 0 ⎪ ⎪ νn = ∫ L Vn (x )2dx = 1 (K2λ n + h12 )(L + h2 K ) + 1 h1 K 2 2 0 K2λn + h22 ⎩
Replace the terms of Eq. (1) by the fluxes shown in Fig. 2, and simplify as:
K⋅
ΔT (x,
Where α is the linear thermal expansion coefficient of the material, λn(n=1, 2,…) is a group of eigen values, Vn(x) is a set of eigen functions,
from the former element. At the same time, it loses Qx+dx flowing into the next element, and QW and QD due to convection through up/down and side surfaces. ΔQ is the increased heat of the element during the transmission process. The direction of heat flux is defined as positive in accordance with the arrows, conversely, the direction is negative.. In principle, the increased heat equals to the difference of obtained and lost heat fluxes. The equation can be expressed as:
q ∂T K ∂ 2T 2(Wh w + DhD ) = − ΔT + ∂t ρC ∂x 2 ρWDC ρDC
L
∞ ⎡ exp(−bt − a2λ n t )(K λ n sin( λ n L ) + h1 − h1 cos( λ n L )) t ) dx = α ∑ ⎢ ⎢ λ n νn n =1 ⎣
Fig. 2. Heat flux model of an arbitrary element of the expansion arm. QLaser is the heat flux from laser irradiation, Qx and Qx+dx are conduction heat along the arm, QW and QD are convection heat through up/down and side surfaces. The element gains QLaser and Qx, loses Qx+dx, QW and QD, and finally achieves an increased heat ΔQ.
ΔQ = QLaser + Qx − Qx + dx − QD − QW
∫0
(5)
Therefore Eq. (2) with the boundary conditions can be regarded as 567
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Table 1 Parameters of the Laser and the OTMA Arm.
ΔT (x, ⎧ ∞ μn Vn (x ) exp(−εn tr ) − exp(−εn t ) ⎪ ∑n =1 νn εn ( exp(2εn t 0) − 1 (exp(εn t0 ) − 1) + 1 − exp(−εn tr )) ⎪ , 2mt0 ≤ t < (2m + 1) t0 ⎪ ⎪ t ) = ⎨ ∑∞ μn Vn (x ) exp(−2εn t 0) − exp(−εn t ) (exp(ε t ) − 1), n 0 exp(2εn t 0 ) − 1 ⎪ n =1 νn εn ⎪ ⎪ (2m + 1) t0 ≤ t < 2(m + 1) t0 ⎪ (m = 0, 1, 2, …) ⎩ (12) where
μn =
2KρA q0 2h1 ρA q0 cos( λ n L1)sin( λ n R ) + sin( λ n L1)sin( λ n R ) ρDC ρDC λ n (13)
Name
Description
Given Value
R (μm) P (mW) q0 (Wm−2) f (Hz) λ (nm) L1 (μm) L (μm) L0 (μm) W (μm) D (μm) S (μm) hD (Wm−2K−1)
Radius of laser spot Laser pulse power Laser pulse power density [P/(πR2)] Laser frequency Laser wavelength Coordinate of the laser spot center Length of the arm Total length of OTMA Width of the arm Thickness of the arm Distance between two narrow bridges Coefficients of the convective heat transfer with air on the side surfaces Coefficients of the convective heat transfer with air on the upper/lower surfaces Coefficient of the convective heat transfer on the fixed end of the arm Coefficient of the convective heat transfer on the free end of the arm Thermal conductivity of the material Thermal expansion coefficient of the material Initial temperature laser absorption ratio of the expansion arm
100 2 6.4×104 0–20 650 600 1300 1500 200 20 60 500
hW (Wm−2K−1)
Using Eq. (12), we have made simulations on the temperature rise ΔT(x, t) at the center of laser beam spot (where x=L1) with the reference information [16] and the given parameters, such as 2-mW power and 0.5, 2.0, 3.0, 5.0, 10, 17 Hz (frequencies used in the experiments). The simulated results indicate that temperature rise at the center of laser beam spot periodically changes in accordance with the frequency. Meanwhile, both of the amplitude and maximum (peak) values of temperature rise decrease with the increase of frequency. The maximum temperature rises ΔTmax are 61.9, 54.6, 49.0, 42.8, 37.1, and 34.7 °C, respectively. When the initial temperature T0 is 20 °C, the maximum temperatures (T0+ΔTmax) will be 81.9, 74.6, 69.0, 62.8, 57.1 and 54.7 °C. Since the melting temperature of high density polypropylene is between 118 and 146 °C [17], the maximum temperatures of the microactuator's surface under each laser pulse frequency are all within the safe range. Meanwhile,
h1 (Wm−2K−1) h2 (Wm−2K−1) −1
−1
K (Wm K ) α (K−1) T0 (°C) ρA
30 20000 500 0.24 3.2×10−5 20 0.95
⎧ ∞ μn VLn exp(−εn tr ) − exp(−εn t ) ⎪ α ∑n =1 νn εn ( exp(2εn t 0) − 1 (exp(εn t0 ) − 1) + 1 − exp(−εn tr )) ⎪ , 2mt0 ≤ t < (2m + 1) t0 ⎪ ⎪ ΔL (t ) = ⎨ α ∑∞ μn VLn exp(−2εn t 0) − exp(−εn t ) (exp(ε t ) − 1), n 0 n =1 νn εn exp(2εn t 0 ) − 1 ⎪ ⎪ ⎪ (2m + 1) t0 ≤ t < 2(m + 1) t0 ⎪ (m = 0, 1, 2, …) ⎩ (14) where
VLn =
Fig. 3. Simulated results of dynamic optothermal expansion of the arm irradiated by laser pulse (P=2 mW, f=2 Hz).
(K λ n sin( λ n L ) + h1 − h1 cos( λ n L )) λn
(15) Similarly, the maximum expansion ΔLM can be expressed as:
According to Eq. (12) and parameters listed in Table 1, the dynamic optothermal expansion is theoretically simulated, as shown in Fig. 3. The results indicate that the expansion arm will expand and revert continuously with the same frequency of laser pulse, moreover, the arm is not able to revert to its original length.. This phenomenon can be explained on the following dynamic mechanism: During the pulse duration, expansion arm absorbs heat from laser spot, resulting in temperature rise and expansion; similarly, during the pulse interval, the arm loses heat to the environment and reverts；as the arm is alternatively irradiated by laser pulse, it is unable to sufficiently lose the heat absorbed from the former pulse, so that it can not return back to its original length before the next pulse comes. The maximum expansion ΔLM and expansion amplitude AL shown in Fig. 3 can be further discussed as follows. According to Eq. (12), when m tends to infinity, exp(−2εn (m + 1) t0 ) and exp(−εn (2m + 1) t0 )equals to zero, the expansion amplitude of the arm is derived as: ∞
AL ≈ α ∑ n =1
μn VLn (exp(2εn t0 ) + 1 − 2 exp(εn t0 )) νn εn (exp(2εn t0 ) − 1)
∞
ΔLM ≈ α ∑ n =1
μn VLn exp(2εn t0 )(1 − exp(−εn t0 )) νn εn (exp(2εn t0 ) − 1)
(17)
The relationships among ΔLM, AL and f are illustrated in Fig. 4, showing that both the maximum expansion and expansion amplitude decrease with laser frequency increasing.. In practice, the tolerance considerations should be taken into account. We have made simulations when setting the errors of geometric dimensions (R, L1, L0, L, W, D), laser parameters (P, ρA, q0), thermal parameters (hD, hW, h1, h2, K, α, T0) and all of these parameters to be 10%. The simulated maximum errors of maximum expansions ΔLM are 12.7%, 19.6%, 11.2% and 25.1%, respectively. Meanwhile, the maximum errors of expansion amplitudes AL are 12.6%, 20.1%, 17.5%, and 25.3%, respectively. These data illustrate that the errors of the parameters in our model might cause tolerances to the results. On the other hand, it should be mentioned that these errors (about 13–25%) are simulated when setting the tolerances of each parameter or even all parameters to be 10%, which would be the extreme and unlikely to happen. More importantly, the trends of all simulated curves demonstrating the dynamic behavior of optothermal
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control circuit generates laser pulses (650 nm, 0–20 Hz, 2 mW measured at the position of microactuator) with a duty cycle of 0.5. The laser is focused by a lens and irradiates the microactuator through a beam splitter. The microactuator will then deflect with the same frequency of the laser pulse. The action or deflection of actuator is monitored by an objective/CCD/computer-combined microscopic system, which can measure actuator's optothermal deflection using subpixel motion analysis software. All parameters used in this work were listed in Table 1.. The original state of the OTMA captured by CCD is shown in Fig. 5(b). When the laser pulse irradiates the expansion arm, an obvious deflection can be observed and the switch contacts can totally touch with each other (Fig. 5(c)). Dot M within the small circle is the test point chosen to measure optothermal deflection of the OTMA. To check the dynamic properties of the OTMA, laser pulse frequency changes from 0.5 to 17 Hz. When frequencies are 0.5, 2.0, 3.0, 5.0, 10, 17 Hz, the maximum deflections are measured to be 16.6, 15.2, 13.2, 11.4, 9.2, 8.2 µm, and the deflection amplitudes are 15.5, 13.0, 10.8, 8.2, 5.9, 4.2 µm, respectively. The relationships among the maximum deflection ΔDM, deflection amplitude AD and pulse frequency f are plotted in Fig. 6. It is clear that both ΔDM and AD decrease along with frequency increasing.. As already indicated by the theoretical simulation result shown in Fig. 4, the expansion ΔL of the arm is quite small, therefore, it is difficult to realize accurate measurement for ΔL in the experiments. In practice, the deflection ΔD of the OTMA is comparatively larger and can be accurately measured. In the theoretical model, ΔD is of a corresponding relationship with ΔL. Experiment results also show that the curve trends of ΔD (ΔDM and AD) are in accordance with those of ΔL (ΔLM and AL), proving that the dynamic properties of OTMA match with the theoretical predictions quite well. Besides, even though the OTMA's deflection decreases at higher frequency, it keeps a maximum deflection of 8.2 µm and a deflection amplitude of 4.2 µm at 17 Hz, which is still sufficient for MOEMS devices. As a potential application, the microactuator mentioned above may serve as a microswitch, which can be directly controlled (on or off) by a laser beam. No electric circuit connected to power supply is demanded, and no ohmic heating current passes through the microactuator, that is, no electric or electromagnetic interference between heating current and switch-controlled current exists. With these characteristics and dynamic properties, such kinds of microactuators may provide broadened applications in MOEMS and micro/nano-technology fields.
Fig. 4. Theoretical relationships among the maximum expansion ΔLM, expansion amplitude AL and laser pulse frequency f (P=2 mW).
microactuator are nearly identical. In summary, the advantages of this optothermal actuator as well as its dynamic model include: the actuator is newly developed and made of single-layer material (rather than bi-layer one); it has a wise structure and utilizes a novel principle of converting optothermal expansion into enlarged later deflection (rather than vertical bending); detailed modelling on the dynamic properties of optothermal actuator has been made for the first time; based on the same principle, a series of optothermal actuators can be further developed, and more importantly, all of them can directly adopt the original dynamic model first proposed in this work. 3. Experiments and results As the free end of the OTMA is connected, longitudinal expansion ΔL will be finally converted and enlarged to lateral deflection ΔD. To verify the dynamic model and theoretical results, experiments involving ΔD are further performed. Choosing black high density polypropylene sheet with high linear thermal expansion coefficient as base material, several asymmetric OTMAs with the same parameters are fabricated using an excimer laser micromachining system (Optec Promaster). To avoid the influence of film sputtering for SEM observation on properties of this OTMA, another OTMA is employed in the experiment. Fig. 5(a) shows the scanning electron microscopy (SEM) image of the OTMA. It has a total length of about 1500 µm, with an expansion arm of 1300-μm length, 200 μm width and 20 μm thickness. In our dynamic model, the actuator is going to be driven in air environment. Therefore, experiments are also carried out in air environment at initial temperature (20 °C). During experiments, a laser diode controlled by
4. Conclusions This paper proposed a new method of asymmetric OTMA based on the dynamic mechanism of optothermal expansion. A comprehensive model has been developed to describe the dynamic characteristics of optothermal expansion arm. Such characteristics of the arm irradiated
Fig. 5. (a) SEM image of an OTMA, (b) original and (c) laser irradiated states of a same type of OTMA captured from optical microscope videos monitoring the process of optothermal microactuation, the laser spot is located within the bigger dashed circle.
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Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.optcom.2016.09.063. References [1] M.M. Ghazaly, K. Sato, Characteristic switching of a multilayer thin electrostatic actuator by a driving signal for an ultra-precision motion stage, Precis. Eng. 37 (1) (2013) 107–116. [2] Y.W. Park, D.Y. Kim, Development of a magnetostrictive microactuator, J. Magn. Magn. Mater. 272–276 (2004) E1765–E1766. [3] B. Watson, J. Friend, L. Yeo, Piezoelectric ultrasonic micro/milli-scale actuators, Sens. Actuator A-Phys. 152 (2009) 219–233. [4] J.Q. Ma, Y. Liu, C.P. Chen, B.Q. Li, J.R. Chu, Deformable mirrors based on piezoelectric unimorph microactuator array for adaptive optics correction, Opt. Commun. 284 (21) (2011) 5062–5066. [5] J. Kyokane, K. Tsujimoto, Y. Yanagisawa, T. Ueda, M. Fukuma, Actuator using electrostriction effect of fullerenol-doped polyurethane elastomer (PUE) films, Ieice (E87-C)T. Electron (2) (2004) 136–141. [6] T. Lalinskýa, M. Držíkb, J. Chlpíkb, M. Krnáča, Š. Haščíka, Ž. Mozolováa, I. Kostičc Thermo-mechanical, characterization of micromachined GaAs-based thermal converter using contactless optical methods, Sens. Actuator A-Phys. 123–124 (2005) 99–105. [7] J.C. Chiou, W.T. Lin, Variable optical attenuator using a thermal actuator array with dual shutters, Opt. Commun. 237 (4) (2004) 341–350. [8] R. Venditti, J.S.H. Lee, Y. Sun, D.Q. Li, An in-plane, bi-directional electrothermal MEMS actuator, J. Micromech. Microeng. 16 (10) (2006) 2067–2070. [9] P. Yang, M. Stevensona, Y. Laia, C. Mechefskea, M. Kujathb, T. Hubbard, Design, modeling and testing of a unidirectional MEMS ring thermal actuator, Sens. Actuator A-Phys. 143 (2) (2008) 352–359. [10] Y.S. Yang, L.H. Lin, H.C. Hu, C.H. Liu, A large-displacement thermal actuator designed for MEMS pitch-tunable grating, J. Micromech. Microeng. 19 (2009) 015001. [11] G. Mu, Y. Bao, C. Li, Measurement of collisional multiphoton energy deposition by a new optothermal detector, Opt. Commun. 51 (1) (1984) 25–28. [12] D. Zhang, H. Zhang, C. Liu, J. Jiang, Microscopic observation and laser-controlled micro-optothermal drive mechanism, Microsc. Res. Tech. 71 (2008) 119–124. [13] S. Zaidi, F. Lamarque, C. Prelle, O. Carton, A. Zeinert, Contactless and selective energy transfer to a bistable micro-actuator using laser heated shape memory alloy, Smart Mater. Struct. 21 (2012) 115027. [14] D. Zhang, H. Zhang, C. Liu, J. Jiang, Theoretical and experimental study of optothermal expansion and optothermal microactuator, Opt. Express 16 (17) (2008) 13476–13485. [15] Y.L. He, The mechanism of micro photo-thermal expansion and the new method of photo-thermal micro actuator (Ph.D. Thesis), Zhejiang University, 2008. [16] Typical engineering properties of polypropylene. 〈http://www.ineos.com/ globalassets/ineos-group/businesses/ineos-olefins-and-polymers-usa/products/ technical-information-patents/ineos-engineering-properties-of-pp.pdf〉. [17] J. E. Mark, Polymer data handbook, New York, 2009.
Fig. 6. Experimental results showing relationships among the maximum deflection ΔDM, deflection amplitude AD and laser pulse frequency f (P=2 mW).
by laser pulse are theoretically simulated using MATLAB (MATLAB V8.0.0.783 (R2012b), MathWorks Inc.), indicating that both of the maximum expansion and expansion amplitude decrease with the pulse frequency increasing. Experiments on the asymmetric OTMA under laser pulse irradiation with different frequency show that the OTMA deflects periodically with the same frequency of laser pulse. It is also proved that both OTMA’s maximum deflection and deflection amplitude decrease as frequency increases, agreeing with the theoretical model quite well. In addition, theoretical simulations show that OTMA is still able to keep a high expansion at 20 Hz, corresponding to a high deflection. In our follow-up work, deflection properties at higher frequency will be further studied by using high-speed photography technology. This dynamic optothermal microactuation technique has great potential in the fields of MOEMS and micro/nano-technology. Acknowledgements Financial support from National Natural Science Foundation of China (Grant Nos. 51077117 and 61540019) is gratefully acknowledged.
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