Springer Handbook of Nanotechnology pp 1703-1748 | Cite as
Thermo- and Electromechanical Behavior of Thin-Film Micro and Nanostructures
Abstract
Applications using thin-film micro- and nanomechanical structures for actuation and sensing require the coupling of energy between various physical domains. This chapter focuses on two important couplings: thermomechanics and electromechanics. Thermomechanical phenomena is considered in Sect. 54.1, where we describe broad aspects of the deformation characteristics and stress states that arise when dealing with a large class of thin-film microstructures. These include the origin of stresses in multilayer films and their qualitative evolution through processing and release from the substrate. A basic framework is described for the analysis of the thermomechanics of multilayer films, emphasizing the linear response. Issues of geometric and material nonlinearity are then taken up, and equal emphasis is put on the generality of the analysis approach and specific applications. As much as possible, we show comparisons between theoretical predictions and companion experimental results.
A common use of electromechanics in microsystems involves the application of an electric potential between two electrodes where one is fixed and the other is connected to a deformable elastic structure. The electric potential produces an electric field and an associated electrostatic force that deforms the structure, and in turn alters the electrostatic force, resulting in fully-coupled nonlinear behavior. At some point an instability can occur where the deformable structure snaps into contact with the fixed electrode. This phenomena, called pull-in, is often used for switching applications. In Sect. 54.2 we describe the basic electromechanical phenomena using a parallel-plate electrostatic actuator as a reference. We discuss many important phenomena including pull-in, external forcing, stabilization, time response, the effects of dielectric charging, and breakdown of gases in small gaps. We address these phenomena for a wide range of micromechanical structures including cantilevered beams and plates, torsionally suspended plates, and zipper actuators with curved electrodes.
Keywords
Cantilever Beam Breakdown Voltage Multilayer Film Transformation Strain Electrostatic ActuatorAbbreviations
- AC
alternating current
- BE
boundary element
- CD
compact disc
- CD
critical dimension
- DC
direct current
- ESD
electrostatic discharge
- FD
finite difference
- FE
finite element
- FEM
finite element modeling
- HF
hydrofluoric acid
- MEMS
microelectromechanical system
- OTS
octadecyltrichlorosilane
- RF
radio-frequency
- RH
relative humidity
- SAM
scanning acoustic microscopy
- SAM
self-assembled monolayer
References
- 54.1.M. Madou: Fundamentals of Microfabrication (CRC, Boca Raton 1997)Google Scholar
- 54.2.M. Gad-el-Hak: The MEMS Handbook (CRC, Boca Raton 2001)CrossRefGoogle Scholar
- 54.3.J. J. Sniegowski, M. P. de Boer: IC-compatible polysilicon surface micromachining, Annu. Rev. Mater. Sci. 30, 299–333 (2000)CrossRefGoogle Scholar
- 54.4.C. H. Mastrangelo: Adhesion-related failure mechanisms in microelectromechanical devices, Tribol. Lett. 3, 223–238 (1997)CrossRefGoogle Scholar
- 54.5.M. P. de Boer, T. M. Mayer: Tribology of MEMS, MRS Bull. 26, 302–304 (2001)CrossRefGoogle Scholar
- 54.6.R. C. Cammarata, K. Sieradzki: Surface and interface stresses, Ann. Rev. Mater. Sci. 24, 215–234 (1994)CrossRefGoogle Scholar
- 54.7.J. Diao, K. Gall, M. L. Dunn: Atomistic simulation of the structure and elastic properties of gold nanowires, J. Mech. Phys. Solids 52, 1935–1962 (2004)CrossRefGoogle Scholar
- 54.8.W. D. Nix: Mechanical properties of thin films, Metall. Trans. A 20A, 2217–2245 (1989)CrossRefGoogle Scholar
- 54.9.C. Y. Hui, H. D. Conway, Y. Y. Lin: A reexamination of residual stresses in thin films and of the validity of Stoney's estimate, J. Electron. Packaging 122, 267–273 (2000)CrossRefGoogle Scholar
- 54.10.D. B. Bogy, K. C. Wang: Stress singularities at interface corners in bonded dissimilar materials, Int. J. Solids Struct. 7, 993–1005 (1971)CrossRefGoogle Scholar
- 54.11.V. L. Hein, F. Erdogan: Stress singularities in a two material wedge, Int. J. Fract. Mech. 7, 317–330 (1971)Google Scholar
- 54.12.E. D. Reedy, T. R. Guess: Nucleation and propagation of an edge crack in a uniformly cooled epoxy/glass bimaterial, Int. J. Solids Struct. 39, 325–340 (2002)CrossRefGoogle Scholar
- 54.13.M. D. Thouless: Modeling the development and relaxation of stresses in films, Annu. Rev. Mater. Sci. 25, 69–96 (1995)CrossRefGoogle Scholar
- 54.14.N. D. Masters, M. P. de Boer, B. D. Jensen, M. S. Baker, D. Koester: Side-by-side comparison of passive MEMS residual strain test structures under residual compression. In: Mechanical Properties of Structural Films. In: Mechanical Properties of Structural Films, Vol. 1413, ed. by C. L. Muhlstein, S. B. Brown (ASTM STP, West Conshohocken 2001) pp. 168–200CrossRefGoogle Scholar
- 54.15.M. W. Hyer: Calculation of the room-temperature shapes of unsymmetric laminates, J. Compos. Mater. 15, 296–310 (1981)Google Scholar
- 54.16.M. W. Hyer: The room-temperature shape of four-layer unsymmetric cross-ply laminates, J. Compos. Mater. 16, 318–340 (1982)CrossRefGoogle Scholar
- 54.17.D. E. Fahnline, C. B. Masters, N. J. Salamon: Thin film stress from nonspherical substrate bending measurements, J. Vac. Sci. Technol. A 9, 2483–2487 (1991)CrossRefGoogle Scholar
- 54.18.C. B. Masters, N. J. Salamon: Geometrically nonlinear stress-deflection relations for thin film/substrate systems, Int. J. Eng. Sci. 31, 915–925 (1993)CrossRefGoogle Scholar
- 54.19.C. B. Masters, N. J. Salamon: Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison, J. Appl. Mech. 61, 872–878 (1994)CrossRefGoogle Scholar
- 54.20.M. Finot, S. Suresh: Small and large deformation of thick and thin film multilayers: effects of layer geometry, plasticity and compositional gradients, J. Mech. Phys. Solids 44, 683–721 (1996)CrossRefGoogle Scholar
- 54.21.M. Finot, I. A. Blech, S. Suresh, H. Fujimoto: Large deformation and geometric instability of substrates with thin film deposits, J. Appl. Phys. 81, 3457–3464 (1997)CrossRefGoogle Scholar
- 54.22.L. B. Freund: The stress distribution and curvature of a general compositionally graded semiconductor layer, J. Cryst. Growth 132, 341–344 (1993)CrossRefGoogle Scholar
- 54.23.L. B. Freund: Some elementary connections between curvature and mismatch strain in compositionally graded thin films, J. Mech. Phys. Solids 44, 723–736 (1996)CrossRefGoogle Scholar
- 54.24.L. B. Freund: Substrate curvature due to thin film mismatch strain in the nonlinear deformation range, J. Mech. Phys. Solids 48, 1159–1174 (2000)CrossRefGoogle Scholar
- 54.25.N. J. Salamon, C. B. Masters: Bifurcation in isotropic thin film/substrate plates, Int. J. Solids Struct. 32, 473–481 (1995)CrossRefGoogle Scholar
- 54.26.R. M. Jones: Mechanics of Composite Materials, 2nd edn. (Taylor & Francis, London 1999)Google Scholar
- 54.27.M. W. Hyer: Stress Analysis of Fiber-Reinforced Composite Materials (McGraw–Hill, Boston 1998)Google Scholar
- 54.28.G. G. Stoney: The tension of metallic films deposited by electrolysis, Proc. R. Soc. Lond. A 82, 172–175 (1909)CrossRefGoogle Scholar
- 54.29.C. D. Pionke, G. Wempner: The various approximations of the bimetallic thermostatic strip, J. Appl. Mech. 58, 1015–1020 (1991)CrossRefGoogle Scholar
- 54.30.P. Krulevitch, G. C. Johnson: Curvature of a cantilever beam subjected to an equibiaxial bending moment, Mater. Res. Symp. Proc. 518, 67–72 (1998)Google Scholar
- 54.31.S. R. Swanson: Introduction to Design and Analysis with Advanced Composite Materials (Prentice-Hall, Upper Siddel River 1997)Google Scholar
- 54.32.M. L. Dunn, Y. Zhang, V. Bright: Deformation and structural stability of layered plate microstructures subjected to thermal loading, J. Microelectromech. Syst. 11, 372–383 (2002)CrossRefGoogle Scholar
- 54.33.J. A. King: Materials Handbook for Hybrid Microelectronics (Teledyne Microelectronics, Los Angeles 1988)Google Scholar
- 54.34.W. N. Sharpe: Mechanical properties of MEMS materials. In: The CRC Handbook of MEMS, ed. by M. Gad-el-Hak (CRC, Boca Raton 2001) Chap. 3Google Scholar
- 54.35.Y. Zhang, M. L. Dunn: Deformation of blanketed and patterned bilayer thin film microstructures during post-release thermal and cyclic thermal loading, J. Microelectromech. Syst. 12, 788–796 (2003)CrossRefGoogle Scholar
- 54.36.B. D. Harper, C.-P. Wu: A geometrically nonlinear model for predicting the intrinsic film stress by the bending plate method, Int. J. Solids Struct. 26, 511–525 (1990)CrossRefGoogle Scholar
- 54.37.J. W. Gibbs: The Collected Works of J. Willard Gibbs (Longmans, New York 1928)Google Scholar
- 54.38.R. Shuttleworth: The Surface Tension of Solids, Proc. R. Soc. London A 63, 444–457 (1950)Google Scholar
- 54.39.J. Diao, K. Gall, M. L. Dunn: Surface and stress induced phase transformation in metal nanowires, Nature Mater. 977, 1–5 (2003)Google Scholar
- 54.40.L. G. Zhou, H. Huang: Are surfaces elastically softer or stiffer?, Appl. Phys. Lett. 84, 1940–1942 (2004)CrossRefGoogle Scholar
- 54.41.R. Dingreville, J. Qu, M. Cherkaoui: Surface free energy and its effect on the elastic behavior of nano-sized particles, wires, and films, J. Mech. Phys. Solids, in press (2005)Google Scholar
- 54.42.R. E. Miller, V. B. Shenoy: Size dependent elastic properties of nanosized structural elements, Nanotechnology 11, 139–147 (2000)CrossRefGoogle Scholar
- 54.43.K. Gall, J. Diao, M. L. Dunn: The strength of gold nanowires, Nanoletters 4, 2431–2436 (2004)Google Scholar
- 54.44.Y. L. Shen, S. Suresh: Thermal cycling and stress relaxation response of Si-Al and Si-Al-SiO2 layered thin films, Acta. Metall. Mater. 43, 3915–3926 (1995)CrossRefGoogle Scholar
- 54.45.S. P. Baker, A. Kretschmann, E. Arzt: Thermomechanical behavior of different texture components in Cu thin films, Acta Mater. 49, 2145–2160 (2001)CrossRefGoogle Scholar
- 54.46.D. C. Miller, C. F. Herrmann, H. J. Maier, S. M. George, C. R. Stoldt, K. Gall: Intrinsic stress development and microstructure evolution of Au/Cr/Si multilayer thin films subject to annealing, Scripta Materialia 52, 873–879 (2005)CrossRefGoogle Scholar
- 54.47.W. D. Nix: Elastic and plastic properties of thin films on substrates, Mater. Sci. Eng. A 234-236, 37–44 (1997)CrossRefGoogle Scholar
- 54.48.C. Thompson: The yield stress of polycrystalline thin films, J. Mater. Res. 8, 237–238 (1993)CrossRefGoogle Scholar
- 54.49.H. Gao, Y. Huang, W. D. Nix, J. W. Hutchinson: Mechanism-based strain gradient plasticity – I. Theory, J. Mech. Phys. Solids 47, 1239–1263 (1999)CrossRefGoogle Scholar
- 54.50.H. D. Espinosa, B. C. Prorok, M. Fischer: A novel method for measuring elasticity, plasticity, and fracture of thin films and MEMS materials, J. Mech. Phys. Solids 51, 47–67 (2003)CrossRefGoogle Scholar
- 54.51.D. C. Miller, M. L. Dunn, V. M. Bright: Thermally induced change in deformation of multimorph MEMS structures, Proc. SPIE 4558, 32–44 (2001)CrossRefGoogle Scholar
- 54.52.D. J. Vickers-Kirby, R. L. Kubena, F. P. Stratton, R. J. Joyce, D. T. Chang, J. Kim: Anelastic creep phenomena in thin film metal plated cantilevers for MEMS, Mater. Res. Soc. Symp. 657, EE2.5.1–EE2.5.6 (2001)Google Scholar
- 54.53.R. M. Keller, S. P. Baker, E. Arzt: Stress–temperature behavior of unpassivated thin copper films, Acta Mater. 47, 415–426 (1999)CrossRefGoogle Scholar
- 54.54.M. D. Thouless, J. Cupta, J. M. E. Harper: Stress development and relaxation in copper films during thermal cycling, J. Mater. Res. 8, 1845–1852 (1993)CrossRefGoogle Scholar
- 54.55.M. D. Thouless, K. P. Rodbell, C. Cabral Jr.: Effect of a surface layer on the stress relaxation of thin films, J. Vac. Sci. Technol. 14, 2454–2461 (1996)CrossRefGoogle Scholar
- 54.56.R. P. Vinci, E. M. Zielinski, J. C. Bravman: Thermal stress and strain in copper thin films, Thin Solid Films 262, 142–153 (1995)CrossRefGoogle Scholar
- 54.57.J. Koike, S. Utsunomiya, Y. Shimoyama, K. Maruyama, H. Oikawa: Thermal cycling fatigue and deformation mechanism in aluminum alloy thin films on silicon, J. Mater. Res. 13, 3256–3264 (1998)CrossRefGoogle Scholar
- 54.58.Y. Zhang, M. L. Dunn: Geometric and Material Nonlinearity During the Deformation of Micron-Scale Thin-Film Bilayers Subject to Thermal Loading, J. Mech. Phys. Solids 52, 2101–2126 (2004)CrossRefGoogle Scholar
- 54.59.K. Gall, M. L. Dunn, Y. Zhang, B. Corff: Thermal cycling response of layered gold/polysilicon MEMS structures, Mech. Mater. 36, 45–55 (2004)CrossRefGoogle Scholar
- 54.60.S. D. Senturia: Microsystems Design (Kluwer Academic, Dordrecht 2001)Google Scholar
- 54.61.M. P. de Boer, N. F. Smith, N. D. Masters, M. B. Sinclair, E. J. Pryputniewicz: Integrated platform for testing MEMS mechanical properties at the wafer scale by the IMaP methodology. In: Mechanical Properties of Structural Films, ASTM STP 1413, 85–95 (2001)Google Scholar
- 54.62.Z. J. Yao, S. Chen, S. Eshelman, D. Denniston, C. Goldsmith: Micromachined low-loss microwave switches, J. Microelectromech. Syst. 8, 129–134 (1999)CrossRefGoogle Scholar
- 54.63.B. McCarthy, G. G. Adams, N. E. McGruer, D. Potter: A dynamic model, including contact bounce of an electrostatically actuated microswitch, J. Microelectromech. Syst. 11, 276–283 (2002)CrossRefGoogle Scholar
- 54.64.H.-S. Lee, C. H. Leung, J. Shih, S.-C. Chang, S. Lorincz, I. Nedelescu: Integrated microrelays: Concept and initial results, J. Microelectromech. Syst. 11, 147–153 (2002)CrossRefGoogle Scholar
- 54.65.S. J. Cunningham, S. Tatic-Lucic, J. Carper, J. Lindsey, L. Spangler: A high aspect ratio accelerometer fabricated using anodic bonding, dissolved wafer, and deep RIE processes, Proc. Transducers '99, the 10th Intl. Conf. Solid-State Sensors and Actuators 1999, ed. by M. Esashi (IEE Jpn., Sendai 1999) 1522–1525Google Scholar
- 54.66.L. Spangler, C. Kemp: ISAAC: integrated silicon automotive acceleromter, Sens. Actuators A 54, 523–529 (1996)CrossRefGoogle Scholar
- 54.67.M. T. A. Saif, B. E. Alaca, H. Sehitoglu: Analytical modeling of electrostatic membrane actuator for micropumps, J. Microelectromech. Syst. 8, 335–345 (1999)CrossRefGoogle Scholar
- 54.68.C. Huang, C. Christophorou, K. Najafi, A. Naguib, H. M. Naguib: An electrostatic microactuator system for application in high-speed jets, J. Microelectromech. Syst. 11, 222–235 (2002)CrossRefGoogle Scholar
- 54.69.H. Toshiyoshi, H. Fujita: Electrostatic micro torsion mirrors for optical switch matrix, J. Microelectromech. Syst. 5, 231–237 (1996)CrossRefGoogle Scholar
- 54.70.H. Toshiyoshi, W. Piyawattanametha, C.-T. Chan, M. C. Wu: Linearization of electrostatically actuated surface micromachined 2-D optical scanner, J. Microelectromech. Syst. 10, 205–214 (2001)CrossRefGoogle Scholar
- 54.71.M. Fischer, M. Giousouf, J. Schaepperle, D. Eichner, M. Weinmann, W. von Münch, F. Assmus: Electrostatically deflectable polysilicon micromirrors – dynamic behaviour and comparison with the results from FEM modelling with Ansys, Sens. Actuators A 67, 89–95 (1998)CrossRefGoogle Scholar
- 54.72.P. K. C. Wang, R. C. Gutierrez, R. K. Bartman: A method for designing electrostatic-actuator electrode pattern in micromachined deformable mirrors, Sens. Actuators A 55, 211–217 (1996)CrossRefGoogle Scholar
- 54.73.P. K. C. Wang, F. Y. Hadaegh: Computation of static shapes and voltages for micromachined deformable mirrors with nonlinear electrostatic actuators, J. Microelectromech. Syst. 5, 205–220 (1996)CrossRefGoogle Scholar
- 54.74.J. Bühler, J. Funk, J. G. Korvink, F.-P. Steiner, P. M. Sarro, H. Baltes: Electrostatic aluminum micromirrors using double-pass metallization, J. Microelectromech. Syst. 6, 126–135 (1997)CrossRefGoogle Scholar
- 54.75.M. Fischer, H. Graef, W. von Münch: Electrostatically deflectable polysilicon torsional mirrors, Sens. Actuators A 44, 83–89 (1994)CrossRefGoogle Scholar
- 54.76.H. Schenk, P. Dürr, D. Kunze, H. Lakner, H. Kück: An electrostatically excited 2D-micro-scanning-mirror with an in-plane configuration of the driving electrodes, Proc. IEEE MEMS 2000, The 13rd Ann. Intl. Conf. Micro Electro Mechanical Systems, Miyazaki 2000, ed. by I. Shimoyama, H. Kuwano (IEEE, Piscataway 2000)Google Scholar
- 54.77.Y. Nemirovsky, O. Bochobza-Degani: Methodology and model for the pull-in parameters of electrostatic actuators, J. Microelectromech. Syst. 10, 601–615 (2001)CrossRefGoogle Scholar
- 54.78.G. Li, N. R. Aluru: A Lagrangian approach for electrostatics analysis of deformable conductors, J. Microelectromech. Syst. 11, 245–254 (2002)CrossRefGoogle Scholar
- 54.79.N. R. Aluru, J. White: A multilevel Newton method for mixed-energy domain simulation of MEMS, J. Microelectromech. Syst. 8, 299–308 (1999)CrossRefGoogle Scholar
- 54.80.J. I. Seeger, S. B. Crary: Stabilization of electrostatically actuated mechanical devices, Proc. Transducers '97, 1997 Intl. Conf. Solid-State Sensors and Actuators, Chicago 1997, ed. by K. Wise (IEEE, Piscataway 1997) 1133–1136Google Scholar
- 54.81.E. S. Hung, S. D. Senturia: Extending the travel range of analog-tuned electrostatic actuators, J. Microelectromech. Syst. 8, 497–505 (1999)CrossRefGoogle Scholar
- 54.82.R. Nadal-Guardia, A. Dehe, R. Aigner, L. M. Castaner: Current drive methods to extend the range of travel of electrostatic microactuators beyond the voltage pull-in point, J. Microelectromech. Syst. 11, 255–263 (2002)CrossRefGoogle Scholar
- 54.83.G. J. O'Brien, D. J. Monk, L. Lin: Electrostatic latch and release; a theoretical and empirical study, Proc. Micro-Electro-Mechanical Syst. (MEMS) 2000, MEMS-Vol. 2, The 2000 ASME Intl. Mech. Eng. Cong. and Expo., Orlando 2000, ed. by A. J. Malshe, Q. Tan, A. P. Lee, F. R. Forster, R. S. Kenten (ASME, New York 2000) 19–26Google Scholar
- 54.84.B. Choi, E. G. Lovell: Improved analysis of microbeams under mechanical and electrostatic loads, J. Micromech. Microeng. 7, 24–29 (1997)CrossRefGoogle Scholar
- 54.85.D. Elata, O. Bochobza-Degani, S. Feldman, Y. Nemirovski: Secondary DOF and Their Effect on the Instability of Electrostatic MEMS Devices (Proc. MEMS 2003, Kyoto, Japan 2003) pp. 177–181Google Scholar
- 54.86.Y. Zhang, M. L. Dunn: A vertical electrostatic actuator with extended digital range via tailored topology. In: Smart Structures and Materials 2002: Smart Electronics, MEMS, and Nanotechnology, Vol. 4700, ed. by V. K. Varadan (Proceedings of SPIE – The International Society for Optical Engineering, Bellingham, Washington 2002) pp. 147–156Google Scholar
- 54.87.O. Degani, E. Socher, A. Lipson, T. Leitner, D. J. Setter, S. Kaldor, Y. Nemirovsky: Pull-in study of an electrostatic torsion microactuator, J. Microelectromech. Syst. 7, 373–379 (1998)CrossRefGoogle Scholar
- 54.88.Z. Xiao, X. Wu, W. Peng, K. R. Farmer: An angled-based design approach for rectangular electrostatic actuators, J. Microelectromech. Syst. 10, 561–568 (2001)CrossRefGoogle Scholar
- 54.89.E. S. Hung, S. D. Senturia: Generating efficient dynamical models for microelectromechanical systems from a few finite-element simulation runs, J. Microelectromech. Syst. 8, 280–289 (1999)CrossRefGoogle Scholar
- 54.90.E. S. Hung, S. D. Senturia: Leveraged bending for full-gap positioning with electrostatic actuation, Tech. Dig. Solid-State Sensors and Actuators Hilton Head '98, Hilton Head Island 1998, ed. by A. J. Ricco (Transducers Research Foundation, Cleveland Heights 1998) 83–86Google Scholar
- 54.91.J. R. Gilbert, S. D. Senturia: Two-phase actuators: Stable zipping devices without fabrication of curved structures, Tech. Dig. Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, USA 1996, ed. by R. T. Howe (Transducers Research Foundation, Cleveland Heights 1996) 98–100Google Scholar
- 54.92.J. R. Gilbert, R. Legtenberg, S. D. Senturia: 3D coupled electro-mechanics for MEMS: Application of CoSolve-EM, Proc. IEEE MEMS Conference, Amsterdam 1995, ed. by M. Elwenspoek, N. de Rooij (IEEE, Piscataway 1995) 122–127Google Scholar
- 54.93.J. R. Gilbert, G. K. Ananthasuresh, S. D. Senturia: 3D modeling of contact problems and hysteresis in coupled electro-mechanics, Proc. IEEE MEMS 1996, The ninth Ann. Intl. Workshop on Micro Electro Mechanical Syst., San Diego 1996, ed. by M. G. Allen, M. L. Reed (IEEE, Piscataway 1996) 127–132Google Scholar
- 54.94.Y.-H. Jin, K.-S. Seo, Y.-H. Cho, S.-S. Lee, K.-C. Song, J.-U. Bu: An integrated SOI optical microswitch using electrostatic micromirror actuators with insulated touch-down beams and curved electrodes, Proc. Micro-Electro-Mechanical Syst. (MEMS) 2000, MEMS-Vol. 2, The 2000 ASME Intl. Mech. Eng. Cong. and Expo., Orlando 2000, ed. by A. J. Malshe, Q. Tan, A. P. Lee, F. R. Forster, R. S. Kenten (ASME, New York 2000) 177–181Google Scholar
- 54.95.R. Legtenberg, E. Berenschot, M. Elwenspoeke, J. Fluitman: Electrostatic curved electrode actuators, Proc. IEEE MEMS Conference, Amsterdam 1995 (IEEE, Piscataway 1995) 37–42Google Scholar
- 54.96.R. Legtenberg, J. Gilbert, S. D. Senturia, M. Elwenspoek: Electrostatic curved electrode actuators, J. Microelectromech. Syst. 6, 257–265 (1997)CrossRefGoogle Scholar
- 54.97.D. DeReus: Personal communications and internal reports (2002)Google Scholar
- 54.98.P. M. Osterberg, S. D. Senturia: M-TEST: A test chip for MEMS material property measurement using electrostatically actuated test structures, J. Microelectromech. Syst. 6, 107–118 (1997)CrossRefGoogle Scholar
- 54.99.L. M. Castaner, S. D. Senturia: Speed-energy optimization of electrostatic actuators based on pull-in, IEEE J. Microelectromech. Syst. 8, 290–298 (1999)CrossRefGoogle Scholar
- 54.100.L. Castaner, A. Rodriguez, J. Pons, S. D. Senturia: Measurement of power-speed product of electrostatic actuators, Proc. Transducers '99, the 10th Intl. Conf. Solid-State Sensors and Actuators, Sendai 1999, ed. by M. Esashi (IEE Jpn., Tokyo 1999) 1772–1775Google Scholar
- 54.101.L. Castaner, A. Rodriguez, J. Pons, S. D. Senturia: Pull-in time-energy product of electrostatic actuators: Comparison of experiments and simulation, Sens. Actuators 83, 263–269 (2000)CrossRefGoogle Scholar
- 54.102.J. Pons-Nin, A. Rodriguez, L. M. Castaner: Voltage and pull-in time in current drive of electrostatic actuators, J. Microelectromech. Syst. 11, 196–205 (2002)CrossRefGoogle Scholar
- 54.103.C. Cabuz, E. I. Cabuz, T. R. Ohnstein, J. Neus, R. Maboudian: Factors enhancing the reliability of touch-mode electrostatic actuators, Sens. Actuators 79, 245–250 (2000)CrossRefGoogle Scholar
- 54.104.J. Wibbeler, G. Pfeifer, M. Hietschold: Parasitic charging of dielectric surfaces in capacitive microelectromechanical systems (MEMS), Sens. Actuators A 71, 74–80 (1998)CrossRefGoogle Scholar
- 54.105.H. Kubo, T. Namura, K. Yoneda, H. Ohishi, Y. Todokoro: Evaluation of charge build-up in wafer processing by using MOS capacitors with charge collecting electrodes, ICMTS 1995 Proc. IEEE Intl. Conf. Microelectronic Test Structures, Vol. 8, Nara 1995, ed. by T. Sugano, K. Asada (IEEE, Piscataway 1995) 5–9Google Scholar
- 54.106.E. K. Chan, K. Garikipati, R. W. Dutton: Characterization of contact electromechanics through capacitance–voltage measurement and simulations, IEEE J. Microelectromech. Syst. 8, 208–217 (1999)CrossRefGoogle Scholar
- 54.107.P. G. Slade, E. D. Taylor: Electrical breakdown in atmospheric air between closely spaced (0.2 μ m–40 μ m) electrical contacts, Proc. 47th IEEE Holm Conf. Electrical Contacts, Montreal 2001, ed. by K. Leung (IEEE, Piscataway 2001) 245–250Google Scholar
- 54.108.J-M. Torres, R. S. Dhariwal: Electric field breakdown at micrometer separations, Nanotechnology 10, 102–107 (1999)CrossRefGoogle Scholar
- 54.109.R. Longwitz, H. van Lintel, R. Carr, C. Hollenstein, P. Renaud: Study of gas ionization schemes for microdevices, Proc. Transducers '01, Eurosensors XV, The 11st Intl. Conf. Solid-State Sensors and Actuators, Munich 2001, ed. by O. Obermeier (Springer, Berlin Heidelberg New York 2001) 1258–1261Google Scholar
- 54.110.D. K. Davies, M. F. Biondi: Vacuum breakdown between plane-parallel copper plates, J. Appl. Phys. 37, 2969–2977 (1966)CrossRefGoogle Scholar
- 54.111.T. Ono, D. Y. Sim, M. Esashi: Micro-discharge and electric breakdown in a micro-gap, J. Micromech. Microeng. 10, 445–451 (2000)CrossRefGoogle Scholar