comsol MEMS模块简易教程.pdf-资料库

COMSOL Multiphysics ™ M E M S M o d u l e M n i i c o u r s e V E R S I O N 3 . 3

How to contact COMSOL: Benelux COMSOL BV Röntgenlaan 19 2719 DX Zoetermeer The Netherlands Phone: +31 (0) 79 363 4230 Fax: +31 (0) 79 361 4212 info@femlab.nl www.femlab.nl Denmark COMSOL A/S Diplomvej 376 2800 Kgs. Lyngby Phone: +45 88 70 82 00 Fax: +45 88 70 80 90 info@comsol.dk www.comsol.dk Finland COMSOL OY Lauttasaarentie 52 FIN-00200 Helsinki Phone: +358 9 2510 400 Fax: +358 9 2510 4010 info@comsol.fi www.comsol.fi France COMSOL France WTC, 5 pl. Robert Schuman F-38000 Grenoble Phone: +33 (0)4 76 46 49 01 Fax: +33 (0)4 76 46 07 42 info@comsol.fr www.comsol.fr Germany FEMLAB GmbH Berliner Str. 4 D-37073 Göttingen Phone: +49-551-99721-0 Fax: +49-551-99721-29 info@femlab.de www.femlab.de Italy COMSOL S.r.l. Via Vittorio Emanuele II, 22 25122 Brescia Phone: +39-030-3793800 Fax: +39-030-3793899 info.it@comsol.com www.it.comsol.com Norway COMSOL AS Søndre gate 7 NO-7485 Trondheim Phone: +47 73 84 24 00 Fax: +47 73 84 24 01 info@comsol.no www.comsol.no Sweden COMSOL AB Tegnérgatan 23 SE-111 40 Stockholm Phone: +46 8 412 95 00 Fax: +46 8 412 95 10 info@comsol.se www.comsol.se Switzerland FEMLAB GmbH Technoparkstrasse 1 CH-8005 Zürich Phone: +41 (0)44 445 2140 Fax: +41 (0)44 445 2141 info@femlab.ch www.femlab.ch United Kingdom COMSOL Ltd. Studio G8 Shepherds Building Rockley Road London W14 0DA Phone:+44-(0)-20 7348 9000 Fax: +44-(0)-20 7348 9020 info.uk@comsol.com www.uk.comsol.com United States COMSOL, Inc. 1 New England Executive Park Suite 350 Burlington, MA 01803 Phone: +1-781-273-3322 Fax: +1-781-273-6603 COMSOL, Inc. 1100 Glendon Avenue, 17th Floor Los Angeles, CA 90024 Phone: +1-310-689-7250 Fax: +1-310-689-7527 COMSOL, Inc. 744 Cowper Street Palo Alto, CA 94301 Phone: +1-650-324-9935 Fax: +1-650-324-9936 info@comsol.com www.comsol.com For a complete list of international representatives, visit www.comsol.com/contact Company home page www.comsol.com COMSOL user forums www.comsol.com/support/forums COMSOL Multiphysics MEMS Module Minicourse © COPYRIGHT 1994–2006 by COMSOL AB. All rights reserved Patent pending The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from COMSOL AB. COMSOL, COMSOL Multiphysics, and COMSOL Script are trademarks of COMSOL AB. Other product or brand names are trademarks or registered trademarks of their respective holders. Version: September 2006 COMSOL 3.3

C O N T E N T S Preface Solving Electro-Thermo-Mechanical Problems 2 3 Microresistor Beam 4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4 Model Definition . . . . . . . . . . . . . . . . . . . . . . . 4 Results and Discussion. . . . . . . . . . . . . . . . . . . . . 5 Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . . . 6 Modeling Using the Graphical User Interface . . . . . . . . . . . . 7 Solving Piezoelectric Problems 22 A Piezoelectric Shear Actuated Beam 23 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 23 Model Definition . . . . . . . . . . . . . . . . . . . . . . . 23 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . . . 26 References . . . . . . . . . . . . . . . . . . . . . . . . . 27 Modeling Using the Graphical User Interface . . . . . . . . . . . . 27 Eigenfrequency Analysis . . . . . . . . . . . . . . . . . . . . 32 Frequency-Response Analysis . . . . . . . . . . . . . . . . . . 33 Appendix: Geometry Modeling . . . . . . . . . . . . . . . . . 35 Low-Voltage Electroosmotic Micropump 38 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 38 Model Definition . . . . . . . . . . . . . . . . . . . . . . . 41 Results and Discussion. . . . . . . . . . . . . . . . . . . . . 42 Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . . . 45 References . . . . . . . . . . . . . . . . . . . . . . . . . 46 Modeling Using the Graphical User Interface . . . . . . . . . . . . 46 Appendix—Geometry Modeling . . . . . . . . . . . . . . . . . 54 C O N T E N T S | i

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M E M S M o d u l e M i n i c o u r s e | 1

Preface Mathematical modeling has become a very important part of the research and development work in engineering and science. Retaining a competitive edge requires a fast path between ideas and prototypes, and in this regard mathematical modeling and simulation provide a valuable shortcut for understanding both qualitative and quantitative aspects of scientific and engineering design. This minicourse gives you an introduction into the modeling of microscale systems using COMSOL Multiphysics and the MEMS Module. It takes you though several fields of science commonly encountered when modeling MEMS: electrical and structural problems, piezoelectricity, and microfluidics. You do not require any prior expertise in mathematical modeling or COMSOL Multiphysics in order to find it rewarding. Enjoy your modeling! The COMSOL team 2 | M E M S M O D U L E M I N I C O U R S E

Solving Electro-Thermo-Mechanical Problems Electro-mechanical actuators and sensors constitute the backbone of the whole MEMS area. The mechanical movement they provide differentiate MEMS devices from conventional microelectronics where the mechanics is designed to be fixed and only electric (wanted) and heat currents (side effect) are observed. The MEMS Module contains several example models of MEMS actuators and sensors such as cantilever beams, comb drives, micromirrors, resonators, thermomechanical microvalves, pressure sensors, and accelerometers. You can make a quick 3D analysis of the electrostatic field and calculate capacitance values based on that using Electrostatic application mode alone. Or you can model pure continuum mechanics, like how residual stresses affect on the resonant frequencies, by using Structural Mechanics application modes. Using Moving Mesh application mode you can accurately combine movements and geometry changes in your own models. Lastly you can create fully electro-thermo-structural couplings, like in the following example of a microresistor beam. The application in this example is to move the structure by conducting a current through conductive layers and generate a temperature increase that leads to a displacement through thermal expansion. M E M S M O D U L E M I N I C O U R S E | 3

Microresistor Beam Introduction This example illustrates the ability to couple thermal, electrical, and structural analysis in one model. This particular application moves a beam by passing a current through it; the current generates heat, and the temperature increase leads to displacement through thermal expansion. The model estimates how much current and increase in temperature are necessary to displace the beam. Although the model involves rather simple 3D geometry and straightforward physics, it provides a good example of multiphysics modeling because it contains several appli- cation modes added incrementally to the model. Note that this model of a microresis- tor beam also appears in the companion MEMS Module Model Library in the Actuators Models folder under the name micro_beam3d. Model Definition Figure 1: Microbeam geometry. A copper microbeam has a length of 13 µm plus a height and width of 1 µm. Feet at both end bond it rigidly to a substrate. An electrical potential of 0.2 V applied between the feet induces an electric current. Due to the material’s resistivity, the current heats up the structure. Because the beam operates in the open, the generated heat dissipates into the air. The thermally induced stress loads the material and deforms the beam. 4 | M E M S M O D U L E M I N I C O U R S E

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