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Design and fabrication of silicon-based 8×8 MEMS optical switch array
ARTICLE IN PRESS Microelectronics Journal 40 (2009) 83–86
Contents lists available at ScienceDirect
Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
Design and fabrication of silicon-based 8 8 MEMS optical switch array Cuiping Jia a,, Jingran Zhou b, Wei Dong b, Weiyou Chen b a b
College of Physics Science and Technology, China University of Petroleum (East China), Beier Road 271, Dongying, Shandong 257061, PR China College of Electronic Science and Engineering, State Key Laboratory on Integrate Optoelectronics, Jilin University, Qianjin Road, 119 Changchun, Jilin 130012, PR China
a r t i c l e in fo
abstract
Article history: Received 25 April 2008 Accepted 14 June 2008 Available online 8 August 2008
Silicon-based torsion-beam 8 8 optical switch array are designed and fabricated with bulk silicon micromachining technology. Torsion beams and cantilever beams with reflective micromirror situated on the same wafer are fabricated on (11 0) silicon. During fabricating the torsion beam actuating structure, the etched hillocks on (11 0) plane are obstacles to achieve smooth torsion beam. It is put forward the reasonable ratios mixtures of HF, HNO3 and CH3COOH to improve the processes of fabricating torsion beam actuating structure. The slanted under electrodes that can reduce the actuating voltage are designed and fabricated on tilting (111) plane by wet chemical etching. According to the etching characteristics of (111) silicon in KOH solution, two designed photomask patterns are proposed in this paper. According to the experimental results, for the 180 mm displacement of mirrors, the device presents the switching time less than 6 ms and the actuating voltage about 65 V. It shows that this optical switch array can make the meet of the optical communication network. Crown Copyright & 2008 Published by Elsevier Ltd. All rights reserved.
Keywords: Optical switch array Mirror Actuating voltage MEMS
1. Introduction Optical matrix switching is one kind of key components for optical communication networks including the optical path crossconnect and reconfigurable optical add-drop multiplexing. Current optical matrix switching devices under development include opto-mechanical [1], waveguide [2], liquid-crystal [3] and microelectromechanical systems (MEMS) [4–7]-based technology .The optic-fiber switches developed using MEMS technology have the benefits of small size, lightweight, insensitivity to wavelength and polarization, and low power consumption, so which have been intensively researched in recent years. In the considerable variety of MEMS optical switches that have emerged constantly up to the present, the core of MEMS switches is an array of mirrors capable of redirecting light either in free space or within a waveguide framework. It has been reported that waveguide 8 8 optical switch array based on electrostatic force have been demonstrated with an actuating voltage of 120 V [2]. In this paper, silicon-based 8 8 MEMS optical switches array are presented, which have torsion beam electrostatic actuators. To improve the fabrication processes of torsion beam actuating structure, it is put forward a better way of polishing in the mixture solution of HF, HNO3 and CH3COOH. The low actuating voltage can be accomplished by using slanted under electrodes which are fabricated on the tilting (111) silicon wafer, two designed
Corresponding author. Tel.: +86 546 8391947.
E-mail address: [email protected] (C. Jia).
photomask figures are proposed. For the 180 mm displacement of mirrors, the optical switches present the performance of the switching time less than 6 ms and the actuating voltage about 65 V.
2. Structure and principle Overview of 8 8 MEMS optical switches array is shown in Fig. 1. It consists of upper electrodes with mirrors chip, slanted under electrodes chip and fiber collimators. Upper electrode structure of optical switch unit can be obviously seen in the schematic view in Fig. 2, the torsion beam and cantilever beam with mirror are all situated on the same wafer. Mirror is parallel to the torsion beam. Slanted under electrodes are matched with the corresponding cantilever beams. Optical switch is characterized by two states of vertical mirror positioning: one is bar state, the other is cross-state. 8 8 optical switch array switch the signals by applying actuating voltages to the associated actuator with micromirror, the incoming optical signal is reflected into the selected output port, as the result, the light channel selectivity is performed.
3. Fabrication of upper electrode Upper electrode consists of the torsion beam and cantilever beam with mirror. Based on the crystal characteristics of (11 0) silicon, smooth {111} planes vertical to the (11 0) surface plane can be obtained by anisotropic wet chemical etching [8–11]. Upper electrodes of optical switch array are fabricated on N-type
0026-2692/$ - see front matter Crown Copyright & 2008 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.06.047
ARTICLE IN PRESS 84
C. Jia et al. / Microelectronics Journal 40 (2009) 83–86
Fig. 3. Optical switch unit with non-uniform.
Fig. 1. Overview of 8 8 MEMS optical switch array.
Fig. 2. Schematic view of optical switch unit.
(11 0) silicon with thickness 300 mm and 4–8 O m resistivity. LPCVD silicon nitride is used as masking material. Based on the transmission theory of Gaussian beam and light distance (the longest 4.8 cm) in this optical switch array, the dimension of mirror should be at least 180 mm 600 mm to make the need of fully reflecting the light beam. During mirror etched in KOH solutions, undercutting exists on the tips of mirror for different etch rates along different crystallographic directions. As a result, the mirror becomes smaller contrasting to the dimension of photomask. It can be corrected by the corner compensation to ensure large enough mirror. Among the rectangular, triangle and rhombus compensation structure, the rhombus compensation is the best choice [12]. Dimension of the torsion beam is sensitive to the actuating voltage of optical switch [13]. During upper electrode chip etched in KOH solutions, the etched hillocks on (11 0) plane are obstacles to achieve smooth torsion beam, as non-uniform torsion beam is shown in Fig. 3. It can be settled by polishing in the reasonable ratio mixtures of 6.5 ml HF+54 ml HNO3+25 ml CH3COOH for 20 min at room temperature. In the end, the etched (11 0) planes become smooth and reaction residues on the mirror can be etched away. Optical switch with uniform torsion beam can be obtained, which can be seen from Fig. 4.
4. Fabrication of slanted under electrodes According to the cantilever structure and the height of mirror, a tilting 4.51 (111) silicon wafer is needed to fabricate the slanted
Fig. 4. Optical switch unit with uniform torsion beam.
under electrode array. The starting material consists of 500 mm thick, N-type tilting 4.51 /111S-oriented double-sided polished silicon wafer with 4–8 O m resistivity. The LPCVD silicon nitride is also used as masking material. The wafer is etched in aqueous KOH solution due to the smooth surface morphology. Photomask is designed to compensate the fast etching profile in /11 0S direction so that slanted under electrode would have large enough space to guarantee actuating cantilever. The designed two photomasks are proposed as shown in Fig. 5. Relationship of the structure parameters between the photomask and the afteretching pattern is introduced as following: W ¼ W 0 þ 2Rð1 1 0Þ T L ¼ L0 þ Rð1 1 1Þ
T¼
1 1 þ T sin a sin b
H R0ð1 1 1Þ0
where R(11 0), R(111) and R0 (111) are (11 0) plane, (111)plane, tilting (111) plane etching ratio in the KOH solution, respectively. a ¼ 4.51, b ¼ 70.531+a. T is the etching time. Length of the middle of the photomask, which is marked by l in Fig. 5, is not essential to the result, which just only should meet loL0. After designed pattern enough etched in KOH solution, the rectangular can be obtained. The length and width of the rectangular are large enough for the actuating upper electrode of the optical switch. Planform SEM and side-view SEM of slanted
ARTICLE IN PRESS C. Jia et al. / Microelectronics Journal 40 (2009) 83–86
85
Fig. 5. Designed photomasks of slanted under electrode.
a square wave to the optical switch and comparing the actuating signals and the photo-electric signals simultaneously using a digitizing oscilloscope, which are less than 6 ms. Cross-talk among different channels is measured below 40 dB.
6. Conclusions
Fig. 6. Planform SEM of single under electrode.
In this paper, silicon-based 8 8 MEMS optical switches array are presented, which have torsion beam electrostatic actuators. During the torsion beam actuating structure etched in KOH solutions, the etched hillocks on (11 0) plane are obstacles to achieve smooth torsion beam. To improve the fabrication processes of torsion beam actuating structure, it is put forward a better way of polishing in the mixture solution of HF, HNO3 and CH3COOH, in the end, the uniform torsion beam can be obtained. The low actuating voltage can be accomplished by using slanted under electrodes which are fabricated on the tilting (111) silicon wafer, two designed photomask figures are proposed. For the 180 mm displacement of mirrors, the optical switches present the switching time less than 6 ms and the actuating voltage about 65 V. The whole optical switch array device has simple structure, good integration and low cost. According to the experimental results, it shows that optical switch array can be widely used in the field of DWDM communication and make the meet of the optical communication network.
Acknowledgments Fig. 7. Side view SEM of under electrode.
under electrode are shown in Fig. 6 and Fig. 7, respectively. Smooth slanted underside is obvious and can be seen in Fig. 7.
Thanks to the Sciences Foundation of China University of Petroleum (East China) Nationalities (no. Y071809) for the Support. References
5. Measuring results The optical switch performance largely depends on the structure and the assembling effect. Therefore, the fabricated optical switch chips and the optical fibers should be integrated and packaged, besides, upper electrode chip and slanted under electrode chip should be bonded closely. The experimental data show that electrostatic yielding voltages for actuating the mirrors 180 mm are in the range of 65.270.5 V based on the fabricated slanted under electrodes. It is relatively lower than conventional mechanical devices. Insertion losses of different ports are greatly different, according to the diversity of collimators, the transmission distance, and the coupling error. Measurements indicate that the optical switches own the best insertion loss of 5 dB at the wavelength of 1.55 mm. Switching times are measured by applying
[1] A.Q. Liu, B. Zhao, F. Chollet, Q. Zou, A. Asundi, H. Fujita, Micro-optomechanical grating switches, Sensor. Actuator. 86 (2000) 127–134. [2] N. Iyer, C.H. Mastrangelo, S. Akkaraju, C. Brophy, T.G. McDonald, R. Dureiko, E.T. Carlen, A two-dimensional optical cross-connect with integrated waveguides and surface micromachined crossbar switches, Sensor. Actuator. A 109 (2004) 231–241. [3] F. Pain, R. CoquilE, B. Vinouze, N. Wolffer, P. Gravey, Comparison of twisted and parallel nematic liquid crystal polarisation controllers. Application to a 4 4 free space optical switch at 1.5 mm, Opt. Commun. 139 (1997) 199–204. [4] S.B. Wang, S.B. Zhou, G. Huang, B.F. Xiong, S.H. Chen, X.J. Yi, Fabrication of 128 128 element optical switch array by micromachining technology, Microprocess. Microsyst. 29 (2005) 21–25. [5] Xiaohua Ma, Geng-Sheng Kuo, A novel integrated multistage optical MEMSmirror switch architecture design with shuffle Benes inter-stage connecting principle, Opt. Commun. 242 (2004) 179–189. [6] J. Li, X.M. Zhang, A.Q. Liu, C. Lu, J.Z. Hao, A monolithically integrated photonic MEMS subsystem for optical network applications, Opt. Commun. 249 (2005) 579–586.
ARTICLE IN PRESS 86
C. Jia et al. / Microelectronics Journal 40 (2009) 83–86
[7] Z.F. Wang, W. Cao, X.C. Shan, J.F. Xu, S.P. Lim, W. Noell, N.F. de Rooij, Development of 1 4 MEMS-based optical switch, Sensor. Actuator. A 114 (2004) 80–87. [8] M. Giousouf, F. Assmus, H. Ku¨ck, Structuring of convex corners using a reoxidation process-application to a tuning fork resonator made from (11 0)silicon, Sensor. Actuator. 76 (1999) 416–424. [9] Yuji Uenishi, Masahiro Tsugai, Mehran Mehregany, Micro-opto-mechanical devices fabrication by anisotropic etching of (110) silicon, IEEE (1994) 319–324. [10] Ernest Bassous, Fabrication of novel three-dimensional microstructures by the anisotropic etching of (1 0 0) and (11 0) silicon, IEEE Trans. Electron Dev. ED-25 (10) (1978) 1178–1185.
[11] D.R. Ciarlo, A latching accelerometer fabricated by the anisotropic etching of (11 0) oriented silicon wafers, J. Micromech. Microeng. 2 (1992) 12–13. [12] Byungwook Kim, Dong-il Dan Cho, Aqueous KOH etching of silicon (11 0) etch characteristics and compensation methods for convex corners, J. Electrochem. Soc. 145 (7) (1998) 2499–2508. [13] Dongming Sun, Wei Dong, Wenbin Guo, Caixia Liu, Guodong Wang, Xin Yan, Baokun Xu, Wwiyou Chen, Michael Kraft, Study on actuating voltage and switching time of a MOEMS optical switch, Opt. Laser Technol. 37 (2005) 601–607.
Contents lists available at ScienceDirect
Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
Design and fabrication of silicon-based 8 8 MEMS optical switch array Cuiping Jia a,, Jingran Zhou b, Wei Dong b, Weiyou Chen b a b
College of Physics Science and Technology, China University of Petroleum (East China), Beier Road 271, Dongying, Shandong 257061, PR China College of Electronic Science and Engineering, State Key Laboratory on Integrate Optoelectronics, Jilin University, Qianjin Road, 119 Changchun, Jilin 130012, PR China
a r t i c l e in fo
abstract
Article history: Received 25 April 2008 Accepted 14 June 2008 Available online 8 August 2008
Silicon-based torsion-beam 8 8 optical switch array are designed and fabricated with bulk silicon micromachining technology. Torsion beams and cantilever beams with reflective micromirror situated on the same wafer are fabricated on (11 0) silicon. During fabricating the torsion beam actuating structure, the etched hillocks on (11 0) plane are obstacles to achieve smooth torsion beam. It is put forward the reasonable ratios mixtures of HF, HNO3 and CH3COOH to improve the processes of fabricating torsion beam actuating structure. The slanted under electrodes that can reduce the actuating voltage are designed and fabricated on tilting (111) plane by wet chemical etching. According to the etching characteristics of (111) silicon in KOH solution, two designed photomask patterns are proposed in this paper. According to the experimental results, for the 180 mm displacement of mirrors, the device presents the switching time less than 6 ms and the actuating voltage about 65 V. It shows that this optical switch array can make the meet of the optical communication network. Crown Copyright & 2008 Published by Elsevier Ltd. All rights reserved.
Keywords: Optical switch array Mirror Actuating voltage MEMS
1. Introduction Optical matrix switching is one kind of key components for optical communication networks including the optical path crossconnect and reconfigurable optical add-drop multiplexing. Current optical matrix switching devices under development include opto-mechanical [1], waveguide [2], liquid-crystal [3] and microelectromechanical systems (MEMS) [4–7]-based technology .The optic-fiber switches developed using MEMS technology have the benefits of small size, lightweight, insensitivity to wavelength and polarization, and low power consumption, so which have been intensively researched in recent years. In the considerable variety of MEMS optical switches that have emerged constantly up to the present, the core of MEMS switches is an array of mirrors capable of redirecting light either in free space or within a waveguide framework. It has been reported that waveguide 8 8 optical switch array based on electrostatic force have been demonstrated with an actuating voltage of 120 V [2]. In this paper, silicon-based 8 8 MEMS optical switches array are presented, which have torsion beam electrostatic actuators. To improve the fabrication processes of torsion beam actuating structure, it is put forward a better way of polishing in the mixture solution of HF, HNO3 and CH3COOH. The low actuating voltage can be accomplished by using slanted under electrodes which are fabricated on the tilting (111) silicon wafer, two designed
Corresponding author. Tel.: +86 546 8391947.
E-mail address: [email protected] (C. Jia).
photomask figures are proposed. For the 180 mm displacement of mirrors, the optical switches present the performance of the switching time less than 6 ms and the actuating voltage about 65 V.
2. Structure and principle Overview of 8 8 MEMS optical switches array is shown in Fig. 1. It consists of upper electrodes with mirrors chip, slanted under electrodes chip and fiber collimators. Upper electrode structure of optical switch unit can be obviously seen in the schematic view in Fig. 2, the torsion beam and cantilever beam with mirror are all situated on the same wafer. Mirror is parallel to the torsion beam. Slanted under electrodes are matched with the corresponding cantilever beams. Optical switch is characterized by two states of vertical mirror positioning: one is bar state, the other is cross-state. 8 8 optical switch array switch the signals by applying actuating voltages to the associated actuator with micromirror, the incoming optical signal is reflected into the selected output port, as the result, the light channel selectivity is performed.
3. Fabrication of upper electrode Upper electrode consists of the torsion beam and cantilever beam with mirror. Based on the crystal characteristics of (11 0) silicon, smooth {111} planes vertical to the (11 0) surface plane can be obtained by anisotropic wet chemical etching [8–11]. Upper electrodes of optical switch array are fabricated on N-type
0026-2692/$ - see front matter Crown Copyright & 2008 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.06.047
ARTICLE IN PRESS 84
C. Jia et al. / Microelectronics Journal 40 (2009) 83–86
Fig. 3. Optical switch unit with non-uniform.
Fig. 1. Overview of 8 8 MEMS optical switch array.
Fig. 2. Schematic view of optical switch unit.
(11 0) silicon with thickness 300 mm and 4–8 O m resistivity. LPCVD silicon nitride is used as masking material. Based on the transmission theory of Gaussian beam and light distance (the longest 4.8 cm) in this optical switch array, the dimension of mirror should be at least 180 mm 600 mm to make the need of fully reflecting the light beam. During mirror etched in KOH solutions, undercutting exists on the tips of mirror for different etch rates along different crystallographic directions. As a result, the mirror becomes smaller contrasting to the dimension of photomask. It can be corrected by the corner compensation to ensure large enough mirror. Among the rectangular, triangle and rhombus compensation structure, the rhombus compensation is the best choice [12]. Dimension of the torsion beam is sensitive to the actuating voltage of optical switch [13]. During upper electrode chip etched in KOH solutions, the etched hillocks on (11 0) plane are obstacles to achieve smooth torsion beam, as non-uniform torsion beam is shown in Fig. 3. It can be settled by polishing in the reasonable ratio mixtures of 6.5 ml HF+54 ml HNO3+25 ml CH3COOH for 20 min at room temperature. In the end, the etched (11 0) planes become smooth and reaction residues on the mirror can be etched away. Optical switch with uniform torsion beam can be obtained, which can be seen from Fig. 4.
4. Fabrication of slanted under electrodes According to the cantilever structure and the height of mirror, a tilting 4.51 (111) silicon wafer is needed to fabricate the slanted
Fig. 4. Optical switch unit with uniform torsion beam.
under electrode array. The starting material consists of 500 mm thick, N-type tilting 4.51 /111S-oriented double-sided polished silicon wafer with 4–8 O m resistivity. The LPCVD silicon nitride is also used as masking material. The wafer is etched in aqueous KOH solution due to the smooth surface morphology. Photomask is designed to compensate the fast etching profile in /11 0S direction so that slanted under electrode would have large enough space to guarantee actuating cantilever. The designed two photomasks are proposed as shown in Fig. 5. Relationship of the structure parameters between the photomask and the afteretching pattern is introduced as following: W ¼ W 0 þ 2Rð1 1 0Þ T L ¼ L0 þ Rð1 1 1Þ
T¼
1 1 þ T sin a sin b
H R0ð1 1 1Þ0
where R(11 0), R(111) and R0 (111) are (11 0) plane, (111)plane, tilting (111) plane etching ratio in the KOH solution, respectively. a ¼ 4.51, b ¼ 70.531+a. T is the etching time. Length of the middle of the photomask, which is marked by l in Fig. 5, is not essential to the result, which just only should meet loL0. After designed pattern enough etched in KOH solution, the rectangular can be obtained. The length and width of the rectangular are large enough for the actuating upper electrode of the optical switch. Planform SEM and side-view SEM of slanted
ARTICLE IN PRESS C. Jia et al. / Microelectronics Journal 40 (2009) 83–86
85
Fig. 5. Designed photomasks of slanted under electrode.
a square wave to the optical switch and comparing the actuating signals and the photo-electric signals simultaneously using a digitizing oscilloscope, which are less than 6 ms. Cross-talk among different channels is measured below 40 dB.
6. Conclusions
Fig. 6. Planform SEM of single under electrode.
In this paper, silicon-based 8 8 MEMS optical switches array are presented, which have torsion beam electrostatic actuators. During the torsion beam actuating structure etched in KOH solutions, the etched hillocks on (11 0) plane are obstacles to achieve smooth torsion beam. To improve the fabrication processes of torsion beam actuating structure, it is put forward a better way of polishing in the mixture solution of HF, HNO3 and CH3COOH, in the end, the uniform torsion beam can be obtained. The low actuating voltage can be accomplished by using slanted under electrodes which are fabricated on the tilting (111) silicon wafer, two designed photomask figures are proposed. For the 180 mm displacement of mirrors, the optical switches present the switching time less than 6 ms and the actuating voltage about 65 V. The whole optical switch array device has simple structure, good integration and low cost. According to the experimental results, it shows that optical switch array can be widely used in the field of DWDM communication and make the meet of the optical communication network.
Acknowledgments Fig. 7. Side view SEM of under electrode.
under electrode are shown in Fig. 6 and Fig. 7, respectively. Smooth slanted underside is obvious and can be seen in Fig. 7.
Thanks to the Sciences Foundation of China University of Petroleum (East China) Nationalities (no. Y071809) for the Support. References
5. Measuring results The optical switch performance largely depends on the structure and the assembling effect. Therefore, the fabricated optical switch chips and the optical fibers should be integrated and packaged, besides, upper electrode chip and slanted under electrode chip should be bonded closely. The experimental data show that electrostatic yielding voltages for actuating the mirrors 180 mm are in the range of 65.270.5 V based on the fabricated slanted under electrodes. It is relatively lower than conventional mechanical devices. Insertion losses of different ports are greatly different, according to the diversity of collimators, the transmission distance, and the coupling error. Measurements indicate that the optical switches own the best insertion loss of 5 dB at the wavelength of 1.55 mm. Switching times are measured by applying
[1] A.Q. Liu, B. Zhao, F. Chollet, Q. Zou, A. Asundi, H. Fujita, Micro-optomechanical grating switches, Sensor. Actuator. 86 (2000) 127–134. [2] N. Iyer, C.H. Mastrangelo, S. Akkaraju, C. Brophy, T.G. McDonald, R. Dureiko, E.T. Carlen, A two-dimensional optical cross-connect with integrated waveguides and surface micromachined crossbar switches, Sensor. Actuator. A 109 (2004) 231–241. [3] F. Pain, R. CoquilE, B. Vinouze, N. Wolffer, P. Gravey, Comparison of twisted and parallel nematic liquid crystal polarisation controllers. Application to a 4 4 free space optical switch at 1.5 mm, Opt. Commun. 139 (1997) 199–204. [4] S.B. Wang, S.B. Zhou, G. Huang, B.F. Xiong, S.H. Chen, X.J. Yi, Fabrication of 128 128 element optical switch array by micromachining technology, Microprocess. Microsyst. 29 (2005) 21–25. [5] Xiaohua Ma, Geng-Sheng Kuo, A novel integrated multistage optical MEMSmirror switch architecture design with shuffle Benes inter-stage connecting principle, Opt. Commun. 242 (2004) 179–189. [6] J. Li, X.M. Zhang, A.Q. Liu, C. Lu, J.Z. Hao, A monolithically integrated photonic MEMS subsystem for optical network applications, Opt. Commun. 249 (2005) 579–586.
ARTICLE IN PRESS 86
C. Jia et al. / Microelectronics Journal 40 (2009) 83–86
[7] Z.F. Wang, W. Cao, X.C. Shan, J.F. Xu, S.P. Lim, W. Noell, N.F. de Rooij, Development of 1 4 MEMS-based optical switch, Sensor. Actuator. A 114 (2004) 80–87. [8] M. Giousouf, F. Assmus, H. Ku¨ck, Structuring of convex corners using a reoxidation process-application to a tuning fork resonator made from (11 0)silicon, Sensor. Actuator. 76 (1999) 416–424. [9] Yuji Uenishi, Masahiro Tsugai, Mehran Mehregany, Micro-opto-mechanical devices fabrication by anisotropic etching of (110) silicon, IEEE (1994) 319–324. [10] Ernest Bassous, Fabrication of novel three-dimensional microstructures by the anisotropic etching of (1 0 0) and (11 0) silicon, IEEE Trans. Electron Dev. ED-25 (10) (1978) 1178–1185.
[11] D.R. Ciarlo, A latching accelerometer fabricated by the anisotropic etching of (11 0) oriented silicon wafers, J. Micromech. Microeng. 2 (1992) 12–13. [12] Byungwook Kim, Dong-il Dan Cho, Aqueous KOH etching of silicon (11 0) etch characteristics and compensation methods for convex corners, J. Electrochem. Soc. 145 (7) (1998) 2499–2508. [13] Dongming Sun, Wei Dong, Wenbin Guo, Caixia Liu, Guodong Wang, Xin Yan, Baokun Xu, Wwiyou Chen, Michael Kraft, Study on actuating voltage and switching time of a MOEMS optical switch, Opt. Laser Technol. 37 (2005) 601–607.