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Integration of displacement sensor into bulk PZT thick film actuator for MEMS deformable mirror
Sensors and Actuators A 147 (2008) 242–247
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Integration of displacement sensor into bulk PZT thick film actuator for MEMS deformable mirror Xiao-Hui Xu ∗ , Yan Feng, Bao-Qing Li, Jia-Ru Chu Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei Anhui 230026, China
a r t i c l e
i n f o
Article history: Received 26 October 2007 Received in revised form 17 January 2008 Accepted 3 March 2008 Available online 16 March 2008 Keywords: Deformable mirror PZT thick film Piezoelectric sensor
a b s t r a c t Bulk PZT thick film actuator integrated with displacement sensor, the so-called self-sensing actuator, is presented in this paper. The PZT film is used as not only an actuating layer but also a displacement sensor, which is achieved by dividing the electrode on the top surface of the PZT film into two parts: central top electrode for actuating and outer annular sensor electrode for piezoelectric displacement detection. When the actuator moves, the piezoelectric charge is induced in the outer annular PZT due to the piezoelectric effect. The total amount of accumulated charge is proportional to the stress acting on the PZT, which is in turn proportional to the actuator displacement. By collecting the piezoelectric charge, the actuator displacement can be detected. A theoretical model is proposed to determine the structure parameters of the sensor and predict the sensor sensitivity. Experiments were performed on the micro-fabricated sensor integrated PZT thick film actuator, and the measured piezoelectric charge is close to the theoretical predictions. The integrated piezoelectric sensor has a displacement sensitivity of approximately 4 pC/nm. In addition, the integration of displacement sensor into the actuator needs no additional fabrication process and has no influence on the actuator performances. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Adaptive optics plays a significant role in the correction of wave aberrations and is applied in various fields such as astronomical observation [1], retina imaging [2,3] and laser shaping [4–6]. The aberrated incoming image can be compensated by the adaptive optics system, which is mainly composed of the deformable mirror (DM) and a wavefront sensor. In order to obtain better imaging quality, deformable mirror with high-actuator density is required so that high-order Zernike modes can be produced [7]. For example, the TMT program requires a deformable mirror employing a 64 × 64 actuator array with 400-m actuator spacing in order to correct the atmospheric disturbance [8]. However, it is difficult to produce such deformable mirror with large number of actuators using conventional manual assembly method. Hence, micro-fabrication method has recently been adopted to fabricate the deformable mirror, so-called MEMS DM. The MEMS DM could provide not only high-actuator density but also better performance compared with the conventional DM. An electrostatic actuated MEMS DM with a 32 × 32 actuator array is manufactured using surface fabrication techniques by Boston University [9,10]. It has a stroke of about 1 m and a resonant frequency
∗ Corresponding author. Tel.: +86 551 3607405. E-mail address: [email protected] (X.-H. Xu). 0924-4247/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2008.03.009
of several KHz. Yang et al. [11,12] reported the 2-m thick PZT thin film actuated MEMS DM including a 20 × 20 piezoelectric unimorph actuator array with 2.5mm spacing and a 20-m thick Si continuous-membrane mirror using bulk fabrication techniques. After applying a driving voltage of 50 V to the PZT thin film, the mirror shows a maximum vertical deflection of about 2.5 m. Xu et al. improved the piezoelectrically actuated MEMS DMs by replacing the PZT thin film with 40-m thick bulk PZT thick film [13], thus the stroke of the mirror was increased by a factor of about 1.5. However, with the increasing of the actuator density, the time required for the wavefront reconstruction will dramatically increase [14,15], which will severely influence the bandwidth of the adaptive optics. Moreover, after compensating the wavefront aberration, the deformable mirror must remain in that state continuously over a long period of time on some occasions [16]. But virtually environmental vibration, space radiation [17], actuator degradation and the magnitude variation of the multi-channel driving signal [18] will make the actuator deviate from its prior position. And it will be difficult to employ a wavefront sensor to monitor the mirror surface using a reference object, especially for the space-based adaptive optics. Therefore, it is important to integrate displacement sensors into the deformable mirror to monitor the mirror displacement instead of the conventional wavefront sensor. To date, few have been reported for the deformable mirror equipped with displacement sensor.
X.-H. Xu et al. / Sensors and Actuators A 147 (2008) 242–247
The paper investigates the possibility of integrating the piezoelectric displacement sensors into PZT actuator-based MEMS deformable mirror. By dividing the top electrode of the PZT film, the PZT film is used not only as the active layer but also as a sensor layer. A theoretical model was presented to determine the structure parameters and predict the induced piezoelectric charge. Experiments were performed on a fabricated self-sensing PZT actuator. The output charge of the sensor with respect to the actuator displacement was measured using a custom charge amplifier. The obtained results agree with the theoretical predictions. Meanwhile, the integration of displacement sensor shows no influence on the actuator performance and requires no additional fabrication process. It may provide the potential to miniaturize the adaptive optics system. 2. Theoretical analysis The deformable mirror discussed here consists of a continuousmembrane mirror and an underlying array of the bulk PZT actuators as shown in Fig. 1. An electric field applied perpendicular to the top and the bottom electrodes of bulk PZT ceramics induces a contraction or expansion in the lateral direction, resulting in an outof-plane deflection for the actuator. The vertical deflection acts on the portion mirror membrane mounted over the actuator. In Ref. [13], it was found that when the diameter of top electrode is 60% of the actuator membrane, the actuator can provide the maximum stroke. However, due to the piezoelectric effect of the PZT, when the actuator is actuated at an external driving voltage, piezoelectric charge will appear on the surface of the outer annual PZT. The induced piezoelectric charge can be collected by preparing a sensor electrode on the outer annular PZT, and the charge will change in proportional to the actuator deflection. Then the actuator deflection can be monitored by measuring the piezoelectric charge. To analyze the induced piezoelectric charge, an analytical model based upon the theory of plates and shells was developed. A schematic diagram of the actuator is shown in Fig. 2. The analytical
243
Fig. 2. The moment balance for the PZT actuator.
model is used to determine the stress distribution in the outer PZT which is related with the induced piezoelectric charge. The actuator is divided into two parts: the central active area covered by top electrode and the outer annular area covered by sensor electrode. According to the theory of plates and shells, for the central part of the actuator covered by top electrode, supported at r = a, the deflection at an point relative to the point O1 is [19,20] w1 (r) =
M2 (a2 − r 2 ) 2De (1 + e )
(0 ≤ r ≤ a)
(1)
where De and e are the equivalent flexural modulus and equivalent Poisson’s ratio of the actuator, respectively. M2 is the equivalent moment applied on the actuator. For the outer part of the actuator with covered sensor electrode, supported at r = b, the deflection at a point relative to the point O2 is w2 (r) =
M1 a2 [(r 2 − b2 ) + 2b2 ln(b/r)] 2De [(1 + e )a2 + (1 − e )b2 ]
(a ≤ r ≤ b)
(2)
where M1 is the moment between the central and outer part of the actuator and can be expressed as M1 = M0 − M2
(3)
where M0 is the moment caused by actuation of the PZT [21]: M0 = De
−d31 U/t1 (h/2) + (2/h)((1/E11 t1 ) + (1/E2 t2 ))(Ds1 + Ds2 )
(4)
where U is the voltage applied to the PZT film and h is the total thickness of the actuator. Ds1 , E11 and d31 are the flexural modulus, Young’s modulus and the transverse piezoelectric coefficient of the PZT film, respectively. t1 and t2 are the thickness of the PZT and silicon elastic layer, respectively. E2 and Ds2 represent the Young’s modulus and flexural modulus of the silicon layer. From the continuity condition at point O1 , one can obtain
dw1 dw2 = dr dr r=a r=a
(5)
Combining the equations above, gives the following solutions: M1 =
M0 k2 k1 + k2
(6)
M2 =
M0 k1 k1 + k2
(7)
where k1 = De (1 + e )(b2 − a2 ),
k2 = De (1 + e )a2 + (1 − e )b2
The maximum deflection of the PZT actuator at the point O is determined to be Fig. 1. Cross-section of the deformable mirror integrated with position sensor. The PZT was used not only as the actuation layer but also as the sensor media. When an external voltage was applied to the central part of the PZT, an additional piezoelectric charge will appear on the outer annular sensor electrode which will be proportional to the actuator deflection.
wmax = w1 (0) + w2 (a)
(8)
It should be noted that the actuation of a PZT actuator can cause both extension and bending. For the PZT actuator discussed here, the diameter of the actuator is much larger than its thickness, the
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Fig. 3. Dependence of the neutral surface position on the thickness of the siliconsupporting layer, The PZT thickness was set to 40 m. The material properties used for the calculation are shown in Table 1.
extension is relatively small and can be ignored [22]. In the presented model, the coupling to extension is not considered. Another simplification is to disregard the bonding layer effects on the actuator performance. In a similar study on the circular PZT actuator [23], it was found that increasing the bonding layer thickness will reduce the deflection, but this effect is not significant when the bonding/PZT thickness ratio is within 0.1. Furthermore, as for the actuator presented in this paper, the bonding layer thickness is very small. Therefore, it is reasonable to adopt this simplification. After obtaining the bending moment M1 generated at point O1 , one can obtain the radial stress in the outer annular PZT: z (9) T = 3(M1 + Mm ) 3 + (t + t − Z )3 Zeff 1 2 eff where z is the deflection from the neutral surface and Zeff is the distance between the top surface of the PZT layer and the neutral surface, and can be written as Zeff =
E1 t1 2 /2 + E2 t2 (t1 + t2 /2) E1 t1 + E2 t2
(10)
Fig. 4. The average radial stress in the outer annular PZT as a function of the thickness of silicon layer. The diameters of the actuator and top electrode are 2 and 1.2 mm, respectively. The PZT employs a thickness of 40 m. The external and internal diameters of the sensor electrode are 1.8 and 1.4 mm, respectively. The voltage applied to the central PZT is 20 V. The silicon mirror has a thickness of 40 m.
thickness of the silicon, should be larger than 23 m so that the PZT sits on above the neutral plane of the diaphragm to ensure identical stress polarity through the thickness of the PZT. For the through-thickness polarized PZT film, the induced charge in the outer annular PZT is Qout = 2d31 Tout Sout
(13)
where Sout is the area of the outer annular PZT and Tout is the average radial stress over the whole PZT thickness. Because the stress distribution through the PZT thickness is linear, it is suitable to use the average stress in the PZT to calculate the induced piezoelectric charge. The induced piezoelectric charge is proportional to the radial stress and the area of the sensor electrode. Fig. 4 shows the average stress dependence of the outer annular PZT on the thickness of the silicon layer with and without mirror. It is found that the two curves overlap with each other and are not distinguishable; this is because the stiffness of the actuator is much higher than that of the silicon mirror, then the mirror load exhibits
where Mm is the additional moment induced at the outer annular PZT due to the loading of silicon mirror and can be expressed as Mm = k=
kwmax 4De (1 + e ) ln (1 + k) b2
b r
−1
Dm b2 2De c 2
(11) (12)
where c is the actuator pitch, b the radius of the actuator, Dm the flexural modulus of the silicon mirror, and r is the distance from the actuator center. From the equation (10), it is easy to see that the neutral surface may appear above or below the bottom surface of the PZT which depends on the thickness of the silicon layer and PZT as shown in Fig. 3. To obtain high sensitivity, for a 40-m thick PZT film, the Table 1 Material parameters used in modeling Parameters
Silicon [24]
PZT [25]
E (GPa) P (Kg/m3 ) ε d31 (pm/V)
202 2300 0.3 – –
68 7500 0.3 2500 −250
Fig. 5. The average radial stress in the outer annular PZT as a function of the central displacement of the actuator. The diameters of the actuator and top electrode are 2 and 1.2 mm, respectively. The external and internal diameters of the sensor electrode are 1.8 and 1.4 mm, respectively. The PZT employs a thickness of 40 m. The thicknesses for the PZT and the silicon-supporting layer are 40 and 20 m, respectively. The silicon mirror has a thickness of 40 m.
X.-H. Xu et al. / Sensors and Actuators A 147 (2008) 242–247
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Fig. 6. Fabrication process of the sensor integrated bulk PZT actuator. The SOI wafer was thermally oxidized (a), and then PZT wafer was bonded to the SOI wafer using epoxy layer (b). The handle silicon of the SOI wafer was etched using KOH solution (c). PZT ceramic wafer was thinned to a desired thickness using a wet-etching method (d). Finally, aluminum electrode was deposited and patterned to form the actuator electrode and sensor electrode (e).
little effect on the stress of the PZT layer. Moreover, the average stress in the outer annular PZT increases with the increasing of the thickness of the silicon, but the actuator stroke will decrease if the silicon is too thick according to Ref. [13]. Hence, the thickness of the silicon should be carefully chosen according to the stroke requirement of the deformable mirror. When the silicon is 20 m in thickness, the average stress in the outer annular PZT is about 3.4 MPa without mirror, which will result in an output charge of about 1.68 × 10−9 C when the external and internal diameters of the sensor electrode are 1.8 and 1.4 mm, respectively. According to Eqs. (8) and (9), one can obtain the average stress dependence of the annular PZT on the central displacement of the actuator as show in Fig. 5. The stress increases linearly with respect to the actuator displacement. The mirror has little effect on the induced stress in the annular PZT because of the large stiffness of the actuator.
Fig. 7. SEM image of the cross-section of the PZT/epoxy/silicon sample, the thickness of the epoxy resin is less than 2 m.
3. Fabrication process The fabrication process for the bulk PZT actuators integrated with the piezoelectric sensor is depicted in Fig. 6. The (1 0 0) silicon wafer was thermal oxidized (a). Then epoxy resins were used to bond the SOI wafer and the PZT ceramics wafer. Epoxy resins were deposited onto the bulk PZT ceramics by screen-printing method. The bulk PZT ceramic contained deposited aluminum by sputtering method as the bottom electrode. After the epoxy resins were prepared, the PZT ceramics were glued to the silicon wafer and a heat treatment at 100 ◦ C for 4 h was performed (b). Fig. 7 shows the SEM image of the cross-section of the PZT/epoxy/Si sample. It is found that the thickness of the epoxy resin is less than 2 m. This indicates that it is reasonable to neglect the epoxy resin in the theoretical model. SiO2 on the backside of the wafer was patterned to open a window for KOH etching. Anisotropic etching was employed to form the Si elastic layer in KOH solution until the buried oxide (c). The buried oxide of the SOI wafer was removed in buffered oxide etchant (BOE). Then the bulk PZT ceramics were thinned using a wet-etching process [13] (d). Finally, aluminum electrode was deposited and patterned to form the actuator electrode and sensor electrode (e). Fig. 8 shows the optical photograph of the fabricated 10 × 10 PZT actuator array integrated with piezoelectric sensor. The central actuator electrode has a radius of 600 m. The outer annular electrode is square with a side length of 1.8 mm. The gap between the central and the outer annular electrodes is 100 m. The bulk PZT actuator has a dimension of 1.75 mm × 1.75 mm. The thickness for the PZT and the active layer are approximately 40 and 20 m, respectively. The fabrication and assembly of the
Fig. 8. Optical photograph of the fabricated 10 × 10 PZT actuator array integrated with piezoelectric sensors applied for deformable mirror. The central actuator electrode has a radius of 600 m. The outer annular electrode is square with a side length of 1.8 mm. The gap between the central and the outer annular electrodes is 100 m.
silicon mirror membrane can be found in our previous paper [13]. 4. Characterization Fig. 9 shows the schematic diagram of the experimental setup. The PZT actuator was driven using a signal generator. The top electrode and the sensor electrode were electrically connected using two three-dimensional adjustable conductive needles. The electrical field induced displacement was measured using laser Doppler vibrometer (MLD821, Neoark Co.). To test the piezoelectric charge generated in the outer annular PZT, a simple charge amplifier consisting of an operational amplifier OPA129 (Ti Co.) and a feedback resistance and capacitance was employed. The output voltage of the charge amplifier was measured by an oscilloscope (TDS210, Tektronix Co.). To test the displacement of the actuator, a ramp waveform was applied to the central electrode of the PZT actuator, and the generated displacement was measured by laser Doppler vibrometer
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Fig. 9. Schematic diagram of the measurement system, the output charge of the sensor was converted to the voltage by a charge amplifier. The feedback resistance R and capacitance C are chosen to be 10 M and 1.2 nF, respectively. Fig. 11. Output voltage curve of the charge amplifier vs. the driving voltage on the PZT actuator. The output voltage shows a displacement of 16%.
Furthermore, the PZT actuators are usually set in array for application in deformable mirror, thus, wiring between actuator/sensor electrodes and surrounding electrical pads is necessary. If the wiring is directly prepared onto the surface of the PZT film, the shunt capacitance between the wiring and the bottom electrode may influence the uniformity of the sensor output. To avoid this, one can deposit a polymer (such as polyimide/BCB) layer with a thickness of several microns prior to the wiring. Because the polymer usually has a much lower dielectric constant (2–3) than the PZT thick film, whose dielectric constant is about 2500, the shunt capacitance can be largely reduced approximately by an order of 100. In addition, the gap between the wiring should be as large as possible to avoid the effect of electromagnetic induction. According to the experimental results, a gap of 100 m is large enough. Fig. 10. Displacement curve of the PZT actuator vs. driven voltage. The PZT actuator shows a displacement of 12%.
as shown in Fig. 10. The actuator shows a maximum deflection of about 0.5 m, which is identical with that of the actuator without integrated sensor as reported in Ref. [13]. This indicates that the integration of the sensor has no influence on the stroke of the PZT actuator. In addition, the measured piezoelectric displacement is larger than the theoretical value (∼0.3 m), probably because of the influence of the boundary of the actuator which can not be completely fixed during the experiment. The displacement hysteresis of the PZT was observed to be about 12%. The hysteresis is the intrinsic property of PZT material, but it can be reduced by using some additional methods such as the Q–V control method [26] or the method of stepping in the same way [11,13]. While the PZT actuator was driven with the ramp waveform, the output of the charge amplifier was also measured using the oscilloscope as show in Fig. 11. The output voltage of the sensor has a peak-to-peak value of approximately 2 V. According to the output voltage of the charge amplifier, the induced piezoelectric charge is calculated to be 2 × 10−9 C which is close to the theoretical value. Then, a charge sensitivity of approximately 4 pC/nm is obtained. The output voltage also shows a hysteresis of about 16%. The hysteresis is larger than that of the displacement hysteresis of the actuator; this is because the output voltage hysteresis was caused not only by the displacement hysteresis of the PZT actuator but also the discharging through the resistance R in the charge amplifier circuit. By increasing the discharge time constant ( = RC) of the circuit, the hysteresis can be further reduced.
5. Conclusion A self-sensing PZT thick film actuator was developed in this paper for the MEMS deformable mirror. By collecting the piezoelectric charge induced in the outer annular PZT, the actuator displacement can be detected. A theoretical model was developed to predict the generated piezoelectric charge. Experiments performed on the micro-fabricated self-sensing PZT actuators show that the sensor has a sensitivity of about 4 pC/nm. Besides, the sensor only requires no additional fabrication process and does not influence the performance of the actuator. It may provide the potential for the microminiaturization of the adaptive optics system. Acknowledgements This work is supported by the Innovative Foundation of Chinese Academic of Sciences and the National Science Foundation (no. 50605061). The authors want to thank Kunshan Jingfeng Electronic Co. Ltd. for providing the bulk PZT wafer. References [1] D. Gavel, MEMS for the next generation of giant astronomical telescopes, in: Proceedings of SPIE, 2006, pp. 611307–611311. [2] D.A. Horsley, H. Park, S.P. Laut, J.S. Werner, Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry, in: Proceedings of SPIE, 2005, pp. 133–144. [3] N. Doble, Use of a microelectromechanical mirror for adaptive optics in human eyes, Opt. Lett. 27 (2002) 1537–1539. [4] C. Radzewicz, P. Wasylczyk, W. Wasilewski, Piezo-driven deformable mirror for femtosecond pulse shaping, Opt. Lett. 29 (2004) 177–179.
X.-H. Xu et al. / Sensors and Actuators A 147 (2008) 242–247 [5] U. Wittrock, P. Welp, Adaptive laser resonator control with deformable MOEMS mirrors, in: Proceedings of SPIE, 2006, p. 61130C. [6] G.-Y. Yoon, T. Imani, H. Daido, T. Jitsuno, Y. Kato, M. Nakatsuka, Enhancement of X-ray lasing due to wavefront correction of line-focusing optics with a largeaperture deformable mirror, Appl. Phys. Lett. 72 (1998) 2785–2787. [7] L. Zhu, P.-C. Sun, D.-U. Bartsch, W.R. Freeman, Y. Fainman, Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror, Appl. Opt. 38 (1999) 6019–6026. [8] D. Gavel, MEMS development for astronomical instrumentation at the Lick Observatory for adaptive optics, in: Proceedings of SPIE, 2007, pp. 646702–646707. [9] S.A. Cornelissen, P.A. Bierden, T.G. Bifano, Development of a 4096 element MEMS continuous membrane deformable mirror for high contrast astronomical imaging, in: Proceedings of SPIE, 2006, p. 630606. [10] J.W. Evans, B. Macintosh, L. Poyneer, Demonstrating sub-nm closed loop MEMS flattening, Opt. Express 14 (2006) 5558–5570. [11] Y. Hishinuma, E.-H. Yang, Piezoelectric unimorph microactuator arrays for single-crystal silicon continuous-membrane deformable mirror, J. Microelectromech. Syst. 15 (2) (2006) 370–410. [12] E.-H. Yang, Y. Hishinuma, J.-G. Cheng, Thin-film piezoelectric unimorph actuator-based deformable mirror with a transferred silicon membrane, J. Microelectromech. Syst. 15 (5) (2006) 1214–1225. [13] X.-H. Xu, B.-Q. Li, Y. Feng, J.R. Chu, Design, fabrication and characterization of bulk PZT actuated MEMS deformable mirror, J. Micromech. Microeng. 17 (12) (2007) 2439–2446. [14] R.A. Carreras, D.K. Marker, Proposed adaptive optics control loop for a continuous face sheet, MEMS based deformable membrane mirror, in: Proceedings of SPIE, vol. 6306, 2006, pp. 630607–630609. [15] L. Zhu, P.-C. Sun, D.-U. Bartsch, W.R. Freeman, Y. Fainman, Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation, Appl. Opt. 38 (1999) 168–176. [16] I.W. Jung, Y.A. Peter, Y.A. Peter, O. Solgaard, Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in spacebased telescopes, IEEE J. Select. Top. Quant. Electron. 13 (2) (2007) 162–167. [17] T.F. Miyahira, H.N. Becker, S.S. McClure, L.D. Edmonds, A.H. Johnston, Total dose degradation of MEMS optical mirrors, IEEE Trans. Nucl. Sci. 50 (2003) 1860–1866. [18] A.N. Simonov, S. Hong, G. Vdovin, Piezoelectric deformable mirror with adaptive multiplexing control, Opt. Eng. 45 (2006) 070501–70503. [19] M. Bu, T. Melvin, G. Ensell, J.S. Wilkinson, A.G.R. Evans, Design and theoretical evaluation of a novel microfluidic device to be used for PCR, J. Micromech. Microeng. 13 (2003) 125–130. [20] T. Zhang, Q.M. Wang, Performance evaluation of a valveless micropump driven by a ring-type piezoelectric actuator, IEEE Trans. Ultrasonics Ferroelectr. Frequency Control 53 (2) (2006) 463–473.
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[21] K. Michael, Silicon micromachined pumps employing piezoelectric membrane actuation for microfluidic system, PhD dissertation, University of Southampton (UK), 1997, pp. 70–74. [22] M.R. Steel, F. Harrison, P.G. Harper, The piezoelectric bimorph: an experimental and theoretical study of its quasistatic response, J. Phys. D: Appl. Phys. 11 (1978) 979–989. [23] S. Li, S. Chen, Analytical analysis of a circular PZT actuator for valveless micropumps, Sens. Actuat. A: Phys. 104 (2003) 151–161. [24] B. Bhushan, X. Li, Micromechanical and tribological characterization of doped single-crystal silicon and polysilicon films for microelectromechanical systems devices, J. Mater. Res. 12 (1) (1997) 54–63. [25] D.F. Bahr, J.S. Robach, J.S. Wright, L.F. Francis, W.W. Gerberich, Mechanical deformation of PZT thin films for MEMS applications, Mater. Sci. Eng. 259 (1999) 126–131. [26] R. Perez, J. Agnus, C. Clevy, A. Hubert, N. Chaillet, Modeling fabrication and validation of a high-performance 2-DoF piezoactuator for micromanipulation, in: IEEE/ASME Transactions on Mechatronics, 2005, pp. 161–171.
Biographies Xiaohui Xu received his bachelor’s degree in 2003 from University of Science and Technology of China (USTC). He is now a PhD candidate at USTC. His research interests include microfabrication technologies, MEMS actuator and sensor designs, and MEMS-based deformable mirror. Yan Feng received the BS degree in 2004 from University of Science and Technology of China (USTC). She is now a PhD candidate at USTC. Her research interests include microfabrication technologies of PZT thin/thick film and PZT-based acoustic devices. Baoqing Li received the BS and MS degrees in 2000 and 2003, respectively, from University of Science and Technology of China (USTC). He is now a PhD candidate at USTC. His research interests include microfluidic technology and adaptive optics. Jiaru Chu received his PhD degree in 1997 from USTC. In 1998–2000, he worked as an NEDO industrial technology researcher in the Mechanical Engineering Laboratory, AIST/MITI (Japan). He is currently a Professor of the Department of Precision Machinery and Precision Instrumentation (USTC) and the Vice Dean of School of Engineering. His research interests include integrated microsensors and microactuators, novel fabrication techniques for micro- and nano-devices, and packaging techniques for micro/nano-systems.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Integration of displacement sensor into bulk PZT thick film actuator for MEMS deformable mirror Xiao-Hui Xu ∗ , Yan Feng, Bao-Qing Li, Jia-Ru Chu Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei Anhui 230026, China
a r t i c l e
i n f o
Article history: Received 26 October 2007 Received in revised form 17 January 2008 Accepted 3 March 2008 Available online 16 March 2008 Keywords: Deformable mirror PZT thick film Piezoelectric sensor
a b s t r a c t Bulk PZT thick film actuator integrated with displacement sensor, the so-called self-sensing actuator, is presented in this paper. The PZT film is used as not only an actuating layer but also a displacement sensor, which is achieved by dividing the electrode on the top surface of the PZT film into two parts: central top electrode for actuating and outer annular sensor electrode for piezoelectric displacement detection. When the actuator moves, the piezoelectric charge is induced in the outer annular PZT due to the piezoelectric effect. The total amount of accumulated charge is proportional to the stress acting on the PZT, which is in turn proportional to the actuator displacement. By collecting the piezoelectric charge, the actuator displacement can be detected. A theoretical model is proposed to determine the structure parameters of the sensor and predict the sensor sensitivity. Experiments were performed on the micro-fabricated sensor integrated PZT thick film actuator, and the measured piezoelectric charge is close to the theoretical predictions. The integrated piezoelectric sensor has a displacement sensitivity of approximately 4 pC/nm. In addition, the integration of displacement sensor into the actuator needs no additional fabrication process and has no influence on the actuator performances. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Adaptive optics plays a significant role in the correction of wave aberrations and is applied in various fields such as astronomical observation [1], retina imaging [2,3] and laser shaping [4–6]. The aberrated incoming image can be compensated by the adaptive optics system, which is mainly composed of the deformable mirror (DM) and a wavefront sensor. In order to obtain better imaging quality, deformable mirror with high-actuator density is required so that high-order Zernike modes can be produced [7]. For example, the TMT program requires a deformable mirror employing a 64 × 64 actuator array with 400-m actuator spacing in order to correct the atmospheric disturbance [8]. However, it is difficult to produce such deformable mirror with large number of actuators using conventional manual assembly method. Hence, micro-fabrication method has recently been adopted to fabricate the deformable mirror, so-called MEMS DM. The MEMS DM could provide not only high-actuator density but also better performance compared with the conventional DM. An electrostatic actuated MEMS DM with a 32 × 32 actuator array is manufactured using surface fabrication techniques by Boston University [9,10]. It has a stroke of about 1 m and a resonant frequency
∗ Corresponding author. Tel.: +86 551 3607405. E-mail address: [email protected] (X.-H. Xu). 0924-4247/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2008.03.009
of several KHz. Yang et al. [11,12] reported the 2-m thick PZT thin film actuated MEMS DM including a 20 × 20 piezoelectric unimorph actuator array with 2.5mm spacing and a 20-m thick Si continuous-membrane mirror using bulk fabrication techniques. After applying a driving voltage of 50 V to the PZT thin film, the mirror shows a maximum vertical deflection of about 2.5 m. Xu et al. improved the piezoelectrically actuated MEMS DMs by replacing the PZT thin film with 40-m thick bulk PZT thick film [13], thus the stroke of the mirror was increased by a factor of about 1.5. However, with the increasing of the actuator density, the time required for the wavefront reconstruction will dramatically increase [14,15], which will severely influence the bandwidth of the adaptive optics. Moreover, after compensating the wavefront aberration, the deformable mirror must remain in that state continuously over a long period of time on some occasions [16]. But virtually environmental vibration, space radiation [17], actuator degradation and the magnitude variation of the multi-channel driving signal [18] will make the actuator deviate from its prior position. And it will be difficult to employ a wavefront sensor to monitor the mirror surface using a reference object, especially for the space-based adaptive optics. Therefore, it is important to integrate displacement sensors into the deformable mirror to monitor the mirror displacement instead of the conventional wavefront sensor. To date, few have been reported for the deformable mirror equipped with displacement sensor.
X.-H. Xu et al. / Sensors and Actuators A 147 (2008) 242–247
The paper investigates the possibility of integrating the piezoelectric displacement sensors into PZT actuator-based MEMS deformable mirror. By dividing the top electrode of the PZT film, the PZT film is used not only as the active layer but also as a sensor layer. A theoretical model was presented to determine the structure parameters and predict the induced piezoelectric charge. Experiments were performed on a fabricated self-sensing PZT actuator. The output charge of the sensor with respect to the actuator displacement was measured using a custom charge amplifier. The obtained results agree with the theoretical predictions. Meanwhile, the integration of displacement sensor shows no influence on the actuator performance and requires no additional fabrication process. It may provide the potential to miniaturize the adaptive optics system. 2. Theoretical analysis The deformable mirror discussed here consists of a continuousmembrane mirror and an underlying array of the bulk PZT actuators as shown in Fig. 1. An electric field applied perpendicular to the top and the bottom electrodes of bulk PZT ceramics induces a contraction or expansion in the lateral direction, resulting in an outof-plane deflection for the actuator. The vertical deflection acts on the portion mirror membrane mounted over the actuator. In Ref. [13], it was found that when the diameter of top electrode is 60% of the actuator membrane, the actuator can provide the maximum stroke. However, due to the piezoelectric effect of the PZT, when the actuator is actuated at an external driving voltage, piezoelectric charge will appear on the surface of the outer annual PZT. The induced piezoelectric charge can be collected by preparing a sensor electrode on the outer annular PZT, and the charge will change in proportional to the actuator deflection. Then the actuator deflection can be monitored by measuring the piezoelectric charge. To analyze the induced piezoelectric charge, an analytical model based upon the theory of plates and shells was developed. A schematic diagram of the actuator is shown in Fig. 2. The analytical
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Fig. 2. The moment balance for the PZT actuator.
model is used to determine the stress distribution in the outer PZT which is related with the induced piezoelectric charge. The actuator is divided into two parts: the central active area covered by top electrode and the outer annular area covered by sensor electrode. According to the theory of plates and shells, for the central part of the actuator covered by top electrode, supported at r = a, the deflection at an point relative to the point O1 is [19,20] w1 (r) =
M2 (a2 − r 2 ) 2De (1 + e )
(0 ≤ r ≤ a)
(1)
where De and e are the equivalent flexural modulus and equivalent Poisson’s ratio of the actuator, respectively. M2 is the equivalent moment applied on the actuator. For the outer part of the actuator with covered sensor electrode, supported at r = b, the deflection at a point relative to the point O2 is w2 (r) =
M1 a2 [(r 2 − b2 ) + 2b2 ln(b/r)] 2De [(1 + e )a2 + (1 − e )b2 ]
(a ≤ r ≤ b)
(2)
where M1 is the moment between the central and outer part of the actuator and can be expressed as M1 = M0 − M2
(3)
where M0 is the moment caused by actuation of the PZT [21]: M0 = De
−d31 U/t1 (h/2) + (2/h)((1/E11 t1 ) + (1/E2 t2 ))(Ds1 + Ds2 )
(4)
where U is the voltage applied to the PZT film and h is the total thickness of the actuator. Ds1 , E11 and d31 are the flexural modulus, Young’s modulus and the transverse piezoelectric coefficient of the PZT film, respectively. t1 and t2 are the thickness of the PZT and silicon elastic layer, respectively. E2 and Ds2 represent the Young’s modulus and flexural modulus of the silicon layer. From the continuity condition at point O1 , one can obtain
dw1 dw2 = dr dr r=a r=a
(5)
Combining the equations above, gives the following solutions: M1 =
M0 k2 k1 + k2
(6)
M2 =
M0 k1 k1 + k2
(7)
where k1 = De (1 + e )(b2 − a2 ),
k2 = De (1 + e )a2 + (1 − e )b2
The maximum deflection of the PZT actuator at the point O is determined to be Fig. 1. Cross-section of the deformable mirror integrated with position sensor. The PZT was used not only as the actuation layer but also as the sensor media. When an external voltage was applied to the central part of the PZT, an additional piezoelectric charge will appear on the outer annular sensor electrode which will be proportional to the actuator deflection.
wmax = w1 (0) + w2 (a)
(8)
It should be noted that the actuation of a PZT actuator can cause both extension and bending. For the PZT actuator discussed here, the diameter of the actuator is much larger than its thickness, the
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Fig. 3. Dependence of the neutral surface position on the thickness of the siliconsupporting layer, The PZT thickness was set to 40 m. The material properties used for the calculation are shown in Table 1.
extension is relatively small and can be ignored [22]. In the presented model, the coupling to extension is not considered. Another simplification is to disregard the bonding layer effects on the actuator performance. In a similar study on the circular PZT actuator [23], it was found that increasing the bonding layer thickness will reduce the deflection, but this effect is not significant when the bonding/PZT thickness ratio is within 0.1. Furthermore, as for the actuator presented in this paper, the bonding layer thickness is very small. Therefore, it is reasonable to adopt this simplification. After obtaining the bending moment M1 generated at point O1 , one can obtain the radial stress in the outer annular PZT: z (9) T = 3(M1 + Mm ) 3 + (t + t − Z )3 Zeff 1 2 eff where z is the deflection from the neutral surface and Zeff is the distance between the top surface of the PZT layer and the neutral surface, and can be written as Zeff =
E1 t1 2 /2 + E2 t2 (t1 + t2 /2) E1 t1 + E2 t2
(10)
Fig. 4. The average radial stress in the outer annular PZT as a function of the thickness of silicon layer. The diameters of the actuator and top electrode are 2 and 1.2 mm, respectively. The PZT employs a thickness of 40 m. The external and internal diameters of the sensor electrode are 1.8 and 1.4 mm, respectively. The voltage applied to the central PZT is 20 V. The silicon mirror has a thickness of 40 m.
thickness of the silicon, should be larger than 23 m so that the PZT sits on above the neutral plane of the diaphragm to ensure identical stress polarity through the thickness of the PZT. For the through-thickness polarized PZT film, the induced charge in the outer annular PZT is Qout = 2d31 Tout Sout
(13)
where Sout is the area of the outer annular PZT and Tout is the average radial stress over the whole PZT thickness. Because the stress distribution through the PZT thickness is linear, it is suitable to use the average stress in the PZT to calculate the induced piezoelectric charge. The induced piezoelectric charge is proportional to the radial stress and the area of the sensor electrode. Fig. 4 shows the average stress dependence of the outer annular PZT on the thickness of the silicon layer with and without mirror. It is found that the two curves overlap with each other and are not distinguishable; this is because the stiffness of the actuator is much higher than that of the silicon mirror, then the mirror load exhibits
where Mm is the additional moment induced at the outer annular PZT due to the loading of silicon mirror and can be expressed as Mm = k=
kwmax 4De (1 + e ) ln (1 + k) b2
b r
−1
Dm b2 2De c 2
(11) (12)
where c is the actuator pitch, b the radius of the actuator, Dm the flexural modulus of the silicon mirror, and r is the distance from the actuator center. From the equation (10), it is easy to see that the neutral surface may appear above or below the bottom surface of the PZT which depends on the thickness of the silicon layer and PZT as shown in Fig. 3. To obtain high sensitivity, for a 40-m thick PZT film, the Table 1 Material parameters used in modeling Parameters
Silicon [24]
PZT [25]
E (GPa) P (Kg/m3 ) ε d31 (pm/V)
202 2300 0.3 – –
68 7500 0.3 2500 −250
Fig. 5. The average radial stress in the outer annular PZT as a function of the central displacement of the actuator. The diameters of the actuator and top electrode are 2 and 1.2 mm, respectively. The external and internal diameters of the sensor electrode are 1.8 and 1.4 mm, respectively. The PZT employs a thickness of 40 m. The thicknesses for the PZT and the silicon-supporting layer are 40 and 20 m, respectively. The silicon mirror has a thickness of 40 m.
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Fig. 6. Fabrication process of the sensor integrated bulk PZT actuator. The SOI wafer was thermally oxidized (a), and then PZT wafer was bonded to the SOI wafer using epoxy layer (b). The handle silicon of the SOI wafer was etched using KOH solution (c). PZT ceramic wafer was thinned to a desired thickness using a wet-etching method (d). Finally, aluminum electrode was deposited and patterned to form the actuator electrode and sensor electrode (e).
little effect on the stress of the PZT layer. Moreover, the average stress in the outer annular PZT increases with the increasing of the thickness of the silicon, but the actuator stroke will decrease if the silicon is too thick according to Ref. [13]. Hence, the thickness of the silicon should be carefully chosen according to the stroke requirement of the deformable mirror. When the silicon is 20 m in thickness, the average stress in the outer annular PZT is about 3.4 MPa without mirror, which will result in an output charge of about 1.68 × 10−9 C when the external and internal diameters of the sensor electrode are 1.8 and 1.4 mm, respectively. According to Eqs. (8) and (9), one can obtain the average stress dependence of the annular PZT on the central displacement of the actuator as show in Fig. 5. The stress increases linearly with respect to the actuator displacement. The mirror has little effect on the induced stress in the annular PZT because of the large stiffness of the actuator.
Fig. 7. SEM image of the cross-section of the PZT/epoxy/silicon sample, the thickness of the epoxy resin is less than 2 m.
3. Fabrication process The fabrication process for the bulk PZT actuators integrated with the piezoelectric sensor is depicted in Fig. 6. The (1 0 0) silicon wafer was thermal oxidized (a). Then epoxy resins were used to bond the SOI wafer and the PZT ceramics wafer. Epoxy resins were deposited onto the bulk PZT ceramics by screen-printing method. The bulk PZT ceramic contained deposited aluminum by sputtering method as the bottom electrode. After the epoxy resins were prepared, the PZT ceramics were glued to the silicon wafer and a heat treatment at 100 ◦ C for 4 h was performed (b). Fig. 7 shows the SEM image of the cross-section of the PZT/epoxy/Si sample. It is found that the thickness of the epoxy resin is less than 2 m. This indicates that it is reasonable to neglect the epoxy resin in the theoretical model. SiO2 on the backside of the wafer was patterned to open a window for KOH etching. Anisotropic etching was employed to form the Si elastic layer in KOH solution until the buried oxide (c). The buried oxide of the SOI wafer was removed in buffered oxide etchant (BOE). Then the bulk PZT ceramics were thinned using a wet-etching process [13] (d). Finally, aluminum electrode was deposited and patterned to form the actuator electrode and sensor electrode (e). Fig. 8 shows the optical photograph of the fabricated 10 × 10 PZT actuator array integrated with piezoelectric sensor. The central actuator electrode has a radius of 600 m. The outer annular electrode is square with a side length of 1.8 mm. The gap between the central and the outer annular electrodes is 100 m. The bulk PZT actuator has a dimension of 1.75 mm × 1.75 mm. The thickness for the PZT and the active layer are approximately 40 and 20 m, respectively. The fabrication and assembly of the
Fig. 8. Optical photograph of the fabricated 10 × 10 PZT actuator array integrated with piezoelectric sensors applied for deformable mirror. The central actuator electrode has a radius of 600 m. The outer annular electrode is square with a side length of 1.8 mm. The gap between the central and the outer annular electrodes is 100 m.
silicon mirror membrane can be found in our previous paper [13]. 4. Characterization Fig. 9 shows the schematic diagram of the experimental setup. The PZT actuator was driven using a signal generator. The top electrode and the sensor electrode were electrically connected using two three-dimensional adjustable conductive needles. The electrical field induced displacement was measured using laser Doppler vibrometer (MLD821, Neoark Co.). To test the piezoelectric charge generated in the outer annular PZT, a simple charge amplifier consisting of an operational amplifier OPA129 (Ti Co.) and a feedback resistance and capacitance was employed. The output voltage of the charge amplifier was measured by an oscilloscope (TDS210, Tektronix Co.). To test the displacement of the actuator, a ramp waveform was applied to the central electrode of the PZT actuator, and the generated displacement was measured by laser Doppler vibrometer
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Fig. 9. Schematic diagram of the measurement system, the output charge of the sensor was converted to the voltage by a charge amplifier. The feedback resistance R and capacitance C are chosen to be 10 M and 1.2 nF, respectively. Fig. 11. Output voltage curve of the charge amplifier vs. the driving voltage on the PZT actuator. The output voltage shows a displacement of 16%.
Furthermore, the PZT actuators are usually set in array for application in deformable mirror, thus, wiring between actuator/sensor electrodes and surrounding electrical pads is necessary. If the wiring is directly prepared onto the surface of the PZT film, the shunt capacitance between the wiring and the bottom electrode may influence the uniformity of the sensor output. To avoid this, one can deposit a polymer (such as polyimide/BCB) layer with a thickness of several microns prior to the wiring. Because the polymer usually has a much lower dielectric constant (2–3) than the PZT thick film, whose dielectric constant is about 2500, the shunt capacitance can be largely reduced approximately by an order of 100. In addition, the gap between the wiring should be as large as possible to avoid the effect of electromagnetic induction. According to the experimental results, a gap of 100 m is large enough. Fig. 10. Displacement curve of the PZT actuator vs. driven voltage. The PZT actuator shows a displacement of 12%.
as shown in Fig. 10. The actuator shows a maximum deflection of about 0.5 m, which is identical with that of the actuator without integrated sensor as reported in Ref. [13]. This indicates that the integration of the sensor has no influence on the stroke of the PZT actuator. In addition, the measured piezoelectric displacement is larger than the theoretical value (∼0.3 m), probably because of the influence of the boundary of the actuator which can not be completely fixed during the experiment. The displacement hysteresis of the PZT was observed to be about 12%. The hysteresis is the intrinsic property of PZT material, but it can be reduced by using some additional methods such as the Q–V control method [26] or the method of stepping in the same way [11,13]. While the PZT actuator was driven with the ramp waveform, the output of the charge amplifier was also measured using the oscilloscope as show in Fig. 11. The output voltage of the sensor has a peak-to-peak value of approximately 2 V. According to the output voltage of the charge amplifier, the induced piezoelectric charge is calculated to be 2 × 10−9 C which is close to the theoretical value. Then, a charge sensitivity of approximately 4 pC/nm is obtained. The output voltage also shows a hysteresis of about 16%. The hysteresis is larger than that of the displacement hysteresis of the actuator; this is because the output voltage hysteresis was caused not only by the displacement hysteresis of the PZT actuator but also the discharging through the resistance R in the charge amplifier circuit. By increasing the discharge time constant ( = RC) of the circuit, the hysteresis can be further reduced.
5. Conclusion A self-sensing PZT thick film actuator was developed in this paper for the MEMS deformable mirror. By collecting the piezoelectric charge induced in the outer annular PZT, the actuator displacement can be detected. A theoretical model was developed to predict the generated piezoelectric charge. Experiments performed on the micro-fabricated self-sensing PZT actuators show that the sensor has a sensitivity of about 4 pC/nm. Besides, the sensor only requires no additional fabrication process and does not influence the performance of the actuator. It may provide the potential for the microminiaturization of the adaptive optics system. Acknowledgements This work is supported by the Innovative Foundation of Chinese Academic of Sciences and the National Science Foundation (no. 50605061). The authors want to thank Kunshan Jingfeng Electronic Co. Ltd. for providing the bulk PZT wafer. References [1] D. Gavel, MEMS for the next generation of giant astronomical telescopes, in: Proceedings of SPIE, 2006, pp. 611307–611311. [2] D.A. Horsley, H. Park, S.P. Laut, J.S. Werner, Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry, in: Proceedings of SPIE, 2005, pp. 133–144. [3] N. Doble, Use of a microelectromechanical mirror for adaptive optics in human eyes, Opt. Lett. 27 (2002) 1537–1539. [4] C. Radzewicz, P. Wasylczyk, W. Wasilewski, Piezo-driven deformable mirror for femtosecond pulse shaping, Opt. Lett. 29 (2004) 177–179.
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Biographies Xiaohui Xu received his bachelor’s degree in 2003 from University of Science and Technology of China (USTC). He is now a PhD candidate at USTC. His research interests include microfabrication technologies, MEMS actuator and sensor designs, and MEMS-based deformable mirror. Yan Feng received the BS degree in 2004 from University of Science and Technology of China (USTC). She is now a PhD candidate at USTC. Her research interests include microfabrication technologies of PZT thin/thick film and PZT-based acoustic devices. Baoqing Li received the BS and MS degrees in 2000 and 2003, respectively, from University of Science and Technology of China (USTC). He is now a PhD candidate at USTC. His research interests include microfluidic technology and adaptive optics. Jiaru Chu received his PhD degree in 1997 from USTC. In 1998–2000, he worked as an NEDO industrial technology researcher in the Mechanical Engineering Laboratory, AIST/MITI (Japan). He is currently a Professor of the Department of Precision Machinery and Precision Instrumentation (USTC) and the Vice Dean of School of Engineering. His research interests include integrated microsensors and microactuators, novel fabrication techniques for micro- and nano-devices, and packaging techniques for micro/nano-systems.