新型栅结构双向MEMS惯性传感器研究
|
摘要
微电子机械系统(MEMS)是一个发展十分迅速、应用日渐广泛的领域,其中以加速度计为代表的MEMS传感器是目前应用最为广泛的MEMS器件。电容式MEMS加速度计具有灵敏度高、温度系数小、功耗和成本低等优点,在汽车工业、消费类产品、石油探测、导航等领域具有十分广泛的应用。
对电容式加速度计的基本原理、基本结构和基本检测原理进行了分析;比较了电容式MEMS器件的几种主要检测方式,选用了基于变面积检测原理的栅型结构作为检测电容结构;分析了加速度计的气体阻尼,证明工作在滑膜阻尼状态下的栅型结构器件具有更小的气体阻尼,可以有效提高器件的分辨率;分析了静电力对电容式器件的影响,说明栅型结构的电容式加速度计可以通过提高检测电压来提高器件的分辨率。
根据上述的理论分析设计了一个基于栅型检测电容结构的双轴电容式MEMS加速度计,主要由支撑梁、连接梁、带有栅型检测电极的质量块、玻璃衬底和淀积在玻璃衬底上的铝检测电极组成。设计了阻尼调整梳齿,用来调节器件的阻尼特性;在器件的敏感运动方向上设计了冲击保护结构,保护器件免受大的冲击的破坏。
使用有限元分析软件ANSYS对设计的加速度计进行了分析:通过模态分析证明了加速度计的敏感运动方向和设计要求相一致;通过静态灵敏度分析证明了加速度计在x-轴和y-轴上具有几乎相同的灵敏度;通过强度分析证明加速度计可以承受1000g加速度信号的冲击;通过横向效应分析证明了器件的横向效应近似为0。
由于电容式MEMS器件的小尺寸特性,电容边缘效应对电容式MEMS器件具有十分重要的影响,对栅型电容和平行板电容的边缘效应进行了分析比较。利用电磁场分析软件ANSOFT-Maxwell分析了电容边缘效应对栅型结构电容值的影响,包括栅型电容随着电容极板长度、宽度、交叠宽度、极板厚度、极板间距、栅型条密度变化时的变化情况,结果表明:边缘效应会引起栅型电容随交叠长度和宽度的非线性变化;栅型电容会随着栅型条宽度和极板厚度增加而增加;相同交叠面积下增大栅型条密度可以提高灵敏度,但是会降低器件线性度。此外结合设计的加速度计器件的结构,对边缘效应对该器件的影响进行了分析。
设计了双轴MEMS加速度计的版图;介绍了MEMS器件的主流工艺;根据体硅工艺,设计了加速度计制作的工艺流程,并对主要的工艺进行了介绍;分析了DRIE工艺引起的微负载效应,并针对这一效应对器件结构进行了改进;制作了双轴MEMS加速度计,证明了器件工艺设计的可行性;对器件进行了初步的静态测试,测得器件在x-轴和y-轴的电容灵敏度分别为0.53pF/g和0.49pF/g,证明了所设计的器件满足双向加速度信号检测的要求;利用一个基于栅型结构的谐振器分析了栅型结构的阻尼特性,证明栅型结构器件在常压下具有较低的气体阻尼和较高的品质因数,从而具有较好的动态性能。
Micro-Electro-Mechanical-System is a rapidly-developing and ever-growing area, and with the representative of accelerometer, MEMS sensors are the most widely-used MEMS devices at present. With the advantage of high-sensitivity, low-temperature coefficient, as well as low power consumption and low cost, capacitive accelerometer has been widely used in the area of auto industry, consumer commodities, oil exploration and navigation etc.
Basic principle, structure and detecting principle of capacitive accelerometer are analyzed in this thesis, and major detecting methods of capacitive MEMS devices are compared, and then the method of area-change with the structure of grid strip capacitors were adopted in the structure design. Air damping of the accelerometer is analyzed which proves that the grid strip structure which works on the condition of slide-film damping has low air damping and it can effectively improve the resolution of the device; effects of electrostatic force is also simulated which indicating that the resolution of the designed accelerometer can be improved through voltage increase of detecting signal.
A biaxial capacitive MEMS accelerometer based on grid strip structure is designed according to analyses above, which consists of supporting beam, connecting beam, proof mass with grid strip detecting electrodes, glass substrate and aluminum detecting electrodes deposited on glass substrate. Damping adjustment combs were designed to adjust damping property of the designed accelerometer; anti-collision structure is designed on the sensitive axes to protect the accelerometer from damage induced by large acceleration.
Finite element analysis software ANSYS was employed to analyze the performances of the designed accelerometer, including modal analyses which proves that the sensitive moving direction is the same as the requirement of design; the static sensitivity analyses which prove that the accelerometer has nearly the same sensitivity on x- and y- axes; strength analyses which proves that the accelerometer can sustain 1000g acceleration; transverse analyses which prove that the transverse effect of the accelerometer is near 0.
Because of the small-scale character of capacitive MEMS devices, capacitor fringe effects are proved to have significant influence on capacitance of capacitive MEMS devices. Fringe effect of grid strip structure and parallel structure is analyzed and compared. Electro-Magnetic field analyzing software ANSOFT-Maxwell was employed to simulate the impact of fringe effect on grid strip capacitors, including the capacitance change of grid strip capacitors with the change of electrode length, width, overlap width, plate thickness, plates distance and grid strip density etc, and the analyzed results shows that the fringe effect would cause nonlinear change of grid strip capacitors with the change of overlap length and width; and that the capacitance would increase with the increase of grid strip width and plate thickness; and that the sensitivity can be improved by increase of grid strip density under the same area, however the linearity of the devices would decrease correspondently. Otherwise, influence of capacitor fringe effect on the designed accelerometer is analyzed combined with the size of the accelerometer.
Layout of the designed biaxial MEMS accelerometer is designed. Then the main manufacturing processes are introduced and then the manufacturing flow of the accelerometer was designed based on bulk-silicon micromachining; the main processes of the fabrication are also introduced. Micro-loading effect induced by DRIE process was analyzed and the accelerometer structure was modified to cope with this effect. The designed accelerometer was manufactured which proves the feasibility of the designed process and then primary static test was issued which show that the capacitance sensitivities of the manufactured accelerometer are 0.53pF/g and 0.49pF/g on x- and y- axis respectively, which indicates that the designed accelerometer can fulfill the needs of biaxial acceleration detection; at last the damping performance of grid strip structure was analyzed by using a resonator with grid strip structure, which proves that devices with grid strip structure has low air damping and high Q factor and thus good dynamic performance.
对电容式加速度计的基本原理、基本结构和基本检测原理进行了分析;比较了电容式MEMS器件的几种主要检测方式,选用了基于变面积检测原理的栅型结构作为检测电容结构;分析了加速度计的气体阻尼,证明工作在滑膜阻尼状态下的栅型结构器件具有更小的气体阻尼,可以有效提高器件的分辨率;分析了静电力对电容式器件的影响,说明栅型结构的电容式加速度计可以通过提高检测电压来提高器件的分辨率。
根据上述的理论分析设计了一个基于栅型检测电容结构的双轴电容式MEMS加速度计,主要由支撑梁、连接梁、带有栅型检测电极的质量块、玻璃衬底和淀积在玻璃衬底上的铝检测电极组成。设计了阻尼调整梳齿,用来调节器件的阻尼特性;在器件的敏感运动方向上设计了冲击保护结构,保护器件免受大的冲击的破坏。
使用有限元分析软件ANSYS对设计的加速度计进行了分析:通过模态分析证明了加速度计的敏感运动方向和设计要求相一致;通过静态灵敏度分析证明了加速度计在x-轴和y-轴上具有几乎相同的灵敏度;通过强度分析证明加速度计可以承受1000g加速度信号的冲击;通过横向效应分析证明了器件的横向效应近似为0。
由于电容式MEMS器件的小尺寸特性,电容边缘效应对电容式MEMS器件具有十分重要的影响,对栅型电容和平行板电容的边缘效应进行了分析比较。利用电磁场分析软件ANSOFT-Maxwell分析了电容边缘效应对栅型结构电容值的影响,包括栅型电容随着电容极板长度、宽度、交叠宽度、极板厚度、极板间距、栅型条密度变化时的变化情况,结果表明:边缘效应会引起栅型电容随交叠长度和宽度的非线性变化;栅型电容会随着栅型条宽度和极板厚度增加而增加;相同交叠面积下增大栅型条密度可以提高灵敏度,但是会降低器件线性度。此外结合设计的加速度计器件的结构,对边缘效应对该器件的影响进行了分析。
设计了双轴MEMS加速度计的版图;介绍了MEMS器件的主流工艺;根据体硅工艺,设计了加速度计制作的工艺流程,并对主要的工艺进行了介绍;分析了DRIE工艺引起的微负载效应,并针对这一效应对器件结构进行了改进;制作了双轴MEMS加速度计,证明了器件工艺设计的可行性;对器件进行了初步的静态测试,测得器件在x-轴和y-轴的电容灵敏度分别为0.53pF/g和0.49pF/g,证明了所设计的器件满足双向加速度信号检测的要求;利用一个基于栅型结构的谐振器分析了栅型结构的阻尼特性,证明栅型结构器件在常压下具有较低的气体阻尼和较高的品质因数,从而具有较好的动态性能。
Micro-Electro-Mechanical-System is a rapidly-developing and ever-growing area, and with the representative of accelerometer, MEMS sensors are the most widely-used MEMS devices at present. With the advantage of high-sensitivity, low-temperature coefficient, as well as low power consumption and low cost, capacitive accelerometer has been widely used in the area of auto industry, consumer commodities, oil exploration and navigation etc.
Basic principle, structure and detecting principle of capacitive accelerometer are analyzed in this thesis, and major detecting methods of capacitive MEMS devices are compared, and then the method of area-change with the structure of grid strip capacitors were adopted in the structure design. Air damping of the accelerometer is analyzed which proves that the grid strip structure which works on the condition of slide-film damping has low air damping and it can effectively improve the resolution of the device; effects of electrostatic force is also simulated which indicating that the resolution of the designed accelerometer can be improved through voltage increase of detecting signal.
A biaxial capacitive MEMS accelerometer based on grid strip structure is designed according to analyses above, which consists of supporting beam, connecting beam, proof mass with grid strip detecting electrodes, glass substrate and aluminum detecting electrodes deposited on glass substrate. Damping adjustment combs were designed to adjust damping property of the designed accelerometer; anti-collision structure is designed on the sensitive axes to protect the accelerometer from damage induced by large acceleration.
Finite element analysis software ANSYS was employed to analyze the performances of the designed accelerometer, including modal analyses which proves that the sensitive moving direction is the same as the requirement of design; the static sensitivity analyses which prove that the accelerometer has nearly the same sensitivity on x- and y- axes; strength analyses which proves that the accelerometer can sustain 1000g acceleration; transverse analyses which prove that the transverse effect of the accelerometer is near 0.
Because of the small-scale character of capacitive MEMS devices, capacitor fringe effects are proved to have significant influence on capacitance of capacitive MEMS devices. Fringe effect of grid strip structure and parallel structure is analyzed and compared. Electro-Magnetic field analyzing software ANSOFT-Maxwell was employed to simulate the impact of fringe effect on grid strip capacitors, including the capacitance change of grid strip capacitors with the change of electrode length, width, overlap width, plate thickness, plates distance and grid strip density etc, and the analyzed results shows that the fringe effect would cause nonlinear change of grid strip capacitors with the change of overlap length and width; and that the capacitance would increase with the increase of grid strip width and plate thickness; and that the sensitivity can be improved by increase of grid strip density under the same area, however the linearity of the devices would decrease correspondently. Otherwise, influence of capacitor fringe effect on the designed accelerometer is analyzed combined with the size of the accelerometer.
Layout of the designed biaxial MEMS accelerometer is designed. Then the main manufacturing processes are introduced and then the manufacturing flow of the accelerometer was designed based on bulk-silicon micromachining; the main processes of the fabrication are also introduced. Micro-loading effect induced by DRIE process was analyzed and the accelerometer structure was modified to cope with this effect. The designed accelerometer was manufactured which proves the feasibility of the designed process and then primary static test was issued which show that the capacitance sensitivities of the manufactured accelerometer are 0.53pF/g and 0.49pF/g on x- and y- axis respectively, which indicates that the designed accelerometer can fulfill the needs of biaxial acceleration detection; at last the damping performance of grid strip structure was analyzed by using a resonator with grid strip structure, which proves that devices with grid strip structure has low air damping and high Q factor and thus good dynamic performance.
引文
[1] R. Feymann, A talk at annual meeting of the American Physical California Institute of the Technology on Dec. 26, 1959.
[2] K. E. Peterson, "Silicon as a mechanical material", Proc. IEEE, Vol. 70, May 1982, pp. 420-457.
[3] L. S. Fan, Y. C. Tai, et al., "IC-processed electrostatic micro-motors", Proc. of 1988 IEEE Int. Electr. Devices Meeting, San Francisco, CA, Dec. 1998.
[4] O'Commor, MEMS-Microelectromechanical system, Mechanical Engineering, Feb., pp.40-47, (1992).
[5] Analog Devices. Monolithic Accelerometer with Signal Conditioning ADXL50, Rev. B, 1996.
[6]柴焕欣.2006-2013年全球MEMS市场规模预测[EB/OL].[2009-7-2]. http://www.digitimes. com.tw.
[7]高强业.硅微加速度计的特性及应用研究[D].长沙:国防科技大学. 2003.
[8]柴焕欣. 2006~2013年全球MEMS加速器市场规模预测[EB/OL].[2009-7-2]. http://www. digitimes.com.tw.
[9]王亚峰,宋晓辉.新型传感器技术及应用[M].北京:中国计量出版社,2009.
[10] Partridge, A.; Reynolds, J.K.; Chui, B.W.; Chow, E.M.; Fitzgerald, A.M.; Zhang, L.; Maluf, N.I.; Kenny, T.W. A high-performance planar piezoresistive accelerometer[J]. Journal of Microelectromechanical Systems. 2000, 9(1):58-66
[11] A.T. Kollias, J.N. Avaritsiotis. A study on the performance of bending mode piezoelectric accelerometers[J]. Sensors and Actuators A: Physical, 2005,121(2):434-442
[12] C. Yeh and K. Najafi, A low-voltage bulk-silicon tunneling based Microaccelerometer[J], in Tech. Dig. IEEE Int. ElectronDevices Meeting (IEDM), Washington, DC. 1995:593-596.
[13] A. Chaehoi, F. Mailly, L. Latorre, P. Nouet. Experimental and finite-element study of convective accelerometer on CMOS[J]. Sensors and Actuators A: Physical, 2006. 132:78–84.
[14] JoséMaría Gómez et al. Balance Interface Circuit Based on Floating MOSFET Capacitors for Micro-Machined Capacitive Accelerometers[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2006, 53(7):546-552.
[15]江建明,娄利飞,汪家友,杨银堂.单片集成MEMS技术[J].传感器技术, 2005,24(3):1-3.
[16]杨邦朝,张经国.多芯片组件(MCM)技术及其应用[M].成都:电子科技大学出版社2001.
[17] Colibrys. Inc. Vibration sensing[EB/OL]. http://www.colibrys.com.
[18] Chih-ming Sun, ChuanWei Wang, Weileun Fang. On the sensitivity improvement of CMOS capacitive accelerometer[J]. Sensors and Actuators A. 2008.141:347–352
[19] Dong Linxi, Che Lufeng, Wang Yuelin. The effect of non-parallel combs of the capacitive micro-sensor on the reliable operation range[J]. Chinese Journal of Semiconductors, 2005, 26 (2):373-378
[20] Dong Linxi, et al. Effects of Non-Parallel Combs on Reliable Operation Conditions of Capacitive InertialSensor for Step and Shock Signals[J]. Sensors and Actuators, 2005, 121(2): 395-404.
[21] B. Li, D. Lu and W. Wang, Micromachined accelerometer with area-changed capacitance[J], Mechatronics. 2001,11:811-819
[22]何洪涛等,梳指差分电容式体硅微加速度计,微纳电子技术,2002, 11: 25-28
[23]徐玮鹤.硅四层键合MEMS电容式加速度传感器研究[D].上海:中国科学院上海微系统与信息技术研究所,2007.
[24] Dong Linxi, Yan Haixia, Qian Xian, Sun Lingling. A Novel Capacitive Biaxial Microaccelerometer Based on the Slide-Film Damping Effect[J]. 2008, 29(2):219-213
[25] Josselin V, Touboul P, Kielbasa R. Capacitive Detection Scheme for Space Accelerometers Applications[J].Sensors and Actuators. 1999,78:9298.
[26] Leuthold H, Rudolf F. An ASIC for High-Resolution Capacitive Micro-Accelerometers[J]. Sensor and Actuators. A: Physical.1990:278-281.
[27] Yufeng Dong, Michael Kraft and William Redman-White. Force feedback linearization for higher-order electromechanical sigma–delta modulators[J]. Journal of Micromechanics and Microengineering. 2006,16: 54–60
[28] Haluk Külah, Junseok Chae, Navid Yazdi and Khalil Najafi. Noise Analysis and Characterization of a Sigma-Delta Capacitive Microaccelerometer[J]. IEEE Journal of Solid-state circuits, 2006, 41(2): 352-361.
[29] T. B. Gabrielson, Mechanical-thermal noise in micromachined acoustic and vibration sensors, IEEE Trans. Electron Dev. 1993, 40,(5):903
[30] P. R. Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits, 3rd ed: Wiley, 1977.
[31] Pejman Monajemi, Farrokh Ayazi. Design Optimization and Implementation of a Microgravity Capacitive HARPSS Accelerometer[J]. IEEE Sensors Journal, 2006, 6(1):39-46.
[32] H. B. Palmer, Capacitance of a parallel-plate capacitor by the Schwartz-Christoffel transformation[J], Trans. AIEE, 1927, 56(4) : 363.
[33] R. S. Elliott, Electromagnetics[M], 1966 ,182-189
[34] W. H. Chang, Analytic IC-metal-line capacitance formulas[J]. Microwave Theory Tech. 1977.25(3): 712
[35] C. P. Yuan, T. N. Trick. A simple formula for the estimation of the capacitance of two-dimensional interconnects in VLSI circuits[J]. Electron Device. 1982. 3(4): 391-393
[36] H. Yang, Microgyroscope and microdynamics[C]. Ph. D. Dissertation, 2000: 44-48
[37]关荣峰. MEMS器件设计、封装工艺及应用研究[D].武汉:华中科技大学,2005.
[38]孙以材,庞冬青.微电子机械加工系统(MEMS)技术基础[M].北京:冶金工业出版社2009.
[39] (美)肯·吉列奥(Ken Gilleo). MEMS/MOEMS封装技术[M].北京:化学工业出版社,2008.
[40]刘晓明,朱钟淦.微机电系统设计与制造[M].北京:国防工业出版社.2006.
[41]陈永.基于滑膜阻尼效应的音叉式微机械陀螺研究[D].上海:中国科学院上海微系统与信息技术研究所,2004.
[42] Innam Lee, Gil Ho Yoon, Jungyul Park, Seonho Seok, Kukjin Chun, Kyo-Il Lee. Development and analysis of the vertical capacitive accelerometer[J]. Sensors and Actuators. 2005. 18 (8):8-18
[43] Minhang Bao. Analysis and Design Principles of MEMS Devices[M]. Elsevier Science, 2005.
[44] H. Hosaka, K. Itao, S. Kuroda, Damping characteristics of beam-shaped microstructures[J], Sensors and Actuators. A, 1995, 49:87-95.
[45]孟光,张文明.微机电系统动力学[M].北京:科学出版社.2008.
[46] Y. Cho, et al, Viscous damping model for laterally oscillating microstructures[J]. Microelectromechanical Systems. 1994, 3(2):81-86.
[47] R. Puers, D. Lapadatu, Electrostatic forces and their effects on capacitive mechanical sensors[J], Sensors and Actuators. A, 1996, 56:203-210.
[48] Chabloz M, Jiao J, Yoshida Y, et al. A Method to Evade Microloading Effect in Deep Reactive Ion Etching for Anodically Bonged Glass-Silicon Structures. Proc. IEEE Micro ElectroMechanical System Workshop(MEMS’00), Miyazaki, Japan, 2000.
[49]董林玺.微机械电容式传感器及其相关特性研究[D].杭州:浙江大学.2004.
[50] G. Walks, D. I. Pomerantz. Field assisted glass-metal sealing[J]. J Appl. Phys., 1969, 40(10): 3946-3969.
[2] K. E. Peterson, "Silicon as a mechanical material", Proc. IEEE, Vol. 70, May 1982, pp. 420-457.
[3] L. S. Fan, Y. C. Tai, et al., "IC-processed electrostatic micro-motors", Proc. of 1988 IEEE Int. Electr. Devices Meeting, San Francisco, CA, Dec. 1998.
[4] O'Commor, MEMS-Microelectromechanical system, Mechanical Engineering, Feb., pp.40-47, (1992).
[5] Analog Devices. Monolithic Accelerometer with Signal Conditioning ADXL50, Rev. B, 1996.
[6]柴焕欣.2006-2013年全球MEMS市场规模预测[EB/OL].[2009-7-2]. http://www.digitimes. com.tw.
[7]高强业.硅微加速度计的特性及应用研究[D].长沙:国防科技大学. 2003.
[8]柴焕欣. 2006~2013年全球MEMS加速器市场规模预测[EB/OL].[2009-7-2]. http://www. digitimes.com.tw.
[9]王亚峰,宋晓辉.新型传感器技术及应用[M].北京:中国计量出版社,2009.
[10] Partridge, A.; Reynolds, J.K.; Chui, B.W.; Chow, E.M.; Fitzgerald, A.M.; Zhang, L.; Maluf, N.I.; Kenny, T.W. A high-performance planar piezoresistive accelerometer[J]. Journal of Microelectromechanical Systems. 2000, 9(1):58-66
[11] A.T. Kollias, J.N. Avaritsiotis. A study on the performance of bending mode piezoelectric accelerometers[J]. Sensors and Actuators A: Physical, 2005,121(2):434-442
[12] C. Yeh and K. Najafi, A low-voltage bulk-silicon tunneling based Microaccelerometer[J], in Tech. Dig. IEEE Int. ElectronDevices Meeting (IEDM), Washington, DC. 1995:593-596.
[13] A. Chaehoi, F. Mailly, L. Latorre, P. Nouet. Experimental and finite-element study of convective accelerometer on CMOS[J]. Sensors and Actuators A: Physical, 2006. 132:78–84.
[14] JoséMaría Gómez et al. Balance Interface Circuit Based on Floating MOSFET Capacitors for Micro-Machined Capacitive Accelerometers[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2006, 53(7):546-552.
[15]江建明,娄利飞,汪家友,杨银堂.单片集成MEMS技术[J].传感器技术, 2005,24(3):1-3.
[16]杨邦朝,张经国.多芯片组件(MCM)技术及其应用[M].成都:电子科技大学出版社2001.
[17] Colibrys. Inc. Vibration sensing[EB/OL]. http://www.colibrys.com.
[18] Chih-ming Sun, ChuanWei Wang, Weileun Fang. On the sensitivity improvement of CMOS capacitive accelerometer[J]. Sensors and Actuators A. 2008.141:347–352
[19] Dong Linxi, Che Lufeng, Wang Yuelin. The effect of non-parallel combs of the capacitive micro-sensor on the reliable operation range[J]. Chinese Journal of Semiconductors, 2005, 26 (2):373-378
[20] Dong Linxi, et al. Effects of Non-Parallel Combs on Reliable Operation Conditions of Capacitive InertialSensor for Step and Shock Signals[J]. Sensors and Actuators, 2005, 121(2): 395-404.
[21] B. Li, D. Lu and W. Wang, Micromachined accelerometer with area-changed capacitance[J], Mechatronics. 2001,11:811-819
[22]何洪涛等,梳指差分电容式体硅微加速度计,微纳电子技术,2002, 11: 25-28
[23]徐玮鹤.硅四层键合MEMS电容式加速度传感器研究[D].上海:中国科学院上海微系统与信息技术研究所,2007.
[24] Dong Linxi, Yan Haixia, Qian Xian, Sun Lingling. A Novel Capacitive Biaxial Microaccelerometer Based on the Slide-Film Damping Effect[J]. 2008, 29(2):219-213
[25] Josselin V, Touboul P, Kielbasa R. Capacitive Detection Scheme for Space Accelerometers Applications[J].Sensors and Actuators. 1999,78:9298.
[26] Leuthold H, Rudolf F. An ASIC for High-Resolution Capacitive Micro-Accelerometers[J]. Sensor and Actuators. A: Physical.1990:278-281.
[27] Yufeng Dong, Michael Kraft and William Redman-White. Force feedback linearization for higher-order electromechanical sigma–delta modulators[J]. Journal of Micromechanics and Microengineering. 2006,16: 54–60
[28] Haluk Külah, Junseok Chae, Navid Yazdi and Khalil Najafi. Noise Analysis and Characterization of a Sigma-Delta Capacitive Microaccelerometer[J]. IEEE Journal of Solid-state circuits, 2006, 41(2): 352-361.
[29] T. B. Gabrielson, Mechanical-thermal noise in micromachined acoustic and vibration sensors, IEEE Trans. Electron Dev. 1993, 40,(5):903
[30] P. R. Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits, 3rd ed: Wiley, 1977.
[31] Pejman Monajemi, Farrokh Ayazi. Design Optimization and Implementation of a Microgravity Capacitive HARPSS Accelerometer[J]. IEEE Sensors Journal, 2006, 6(1):39-46.
[32] H. B. Palmer, Capacitance of a parallel-plate capacitor by the Schwartz-Christoffel transformation[J], Trans. AIEE, 1927, 56(4) : 363.
[33] R. S. Elliott, Electromagnetics[M], 1966 ,182-189
[34] W. H. Chang, Analytic IC-metal-line capacitance formulas[J]. Microwave Theory Tech. 1977.25(3): 712
[35] C. P. Yuan, T. N. Trick. A simple formula for the estimation of the capacitance of two-dimensional interconnects in VLSI circuits[J]. Electron Device. 1982. 3(4): 391-393
[36] H. Yang, Microgyroscope and microdynamics[C]. Ph. D. Dissertation, 2000: 44-48
[37]关荣峰. MEMS器件设计、封装工艺及应用研究[D].武汉:华中科技大学,2005.
[38]孙以材,庞冬青.微电子机械加工系统(MEMS)技术基础[M].北京:冶金工业出版社2009.
[39] (美)肯·吉列奥(Ken Gilleo). MEMS/MOEMS封装技术[M].北京:化学工业出版社,2008.
[40]刘晓明,朱钟淦.微机电系统设计与制造[M].北京:国防工业出版社.2006.
[41]陈永.基于滑膜阻尼效应的音叉式微机械陀螺研究[D].上海:中国科学院上海微系统与信息技术研究所,2004.
[42] Innam Lee, Gil Ho Yoon, Jungyul Park, Seonho Seok, Kukjin Chun, Kyo-Il Lee. Development and analysis of the vertical capacitive accelerometer[J]. Sensors and Actuators. 2005. 18 (8):8-18
[43] Minhang Bao. Analysis and Design Principles of MEMS Devices[M]. Elsevier Science, 2005.
[44] H. Hosaka, K. Itao, S. Kuroda, Damping characteristics of beam-shaped microstructures[J], Sensors and Actuators. A, 1995, 49:87-95.
[45]孟光,张文明.微机电系统动力学[M].北京:科学出版社.2008.
[46] Y. Cho, et al, Viscous damping model for laterally oscillating microstructures[J]. Microelectromechanical Systems. 1994, 3(2):81-86.
[47] R. Puers, D. Lapadatu, Electrostatic forces and their effects on capacitive mechanical sensors[J], Sensors and Actuators. A, 1996, 56:203-210.
[48] Chabloz M, Jiao J, Yoshida Y, et al. A Method to Evade Microloading Effect in Deep Reactive Ion Etching for Anodically Bonged Glass-Silicon Structures. Proc. IEEE Micro ElectroMechanical System Workshop(MEMS’00), Miyazaki, Japan, 2000.
[49]董林玺.微机械电容式传感器及其相关特性研究[D].杭州:浙江大学.2004.
[50] G. Walks, D. I. Pomerantz. Field assisted glass-metal sealing[J]. J Appl. Phys., 1969, 40(10): 3946-3969.