Mathematical Modeling of Electrostatic MEMS with Tailored Dielectric Properties

Abstract

<html xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:w=3D"urn:schemas-microsoft-com:office:word" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dwindows-1252"> <meta name=3DProgId content=3DWord.Document> <meta name=3DGenerator content=3D"Microsoft Word 11"> <meta name=3DOriginator content=3D"Microsoft Word 11"> <link rel=3DFile-List href=3D"Resumen1_archivos/filelist.xml"> <title>Resumen</title> <!--[if gte mso 9]><xml> <o:DocumentProperties> <o:Author>Biblioteca de Ciencias y Tecnología</o:Author> <o:Template>Normal</o:Template> <o:LastAuthor>Biblioteca de Ciencias y Tecnología</o:LastAuthor> <o:Revision>1</o:Revision> <o:TotalTime>0</o:TotalTime> <o:Created>2007-07-05T00:31:00Z</o:Created> <o:LastSaved>2007-07-05T00:31:00Z</o:LastSaved> <o:Pages>1</o:Pages> <o:Words>166</o:Words> <o:Characters>918</o:Characters> <o:Company>UCLA</o:Company> <o:Lines>7</o:Lines> <o:Paragraphs>2</o:Paragraphs> <o:CharactersWithSpaces>1082</o:CharactersWithSpaces> <o:Version>11.6568</o:Version> </o:DocumentProperties> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:SpellingState>Clean</w:SpellingState> <w:GrammarState>Clean</w:GrammarState> <w:HyphenationZone>21</w:HyphenationZone> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState=3D"false" LatentStyleCount=3D"156"> </w:LatentStyles> </xml><![endif]--> <style> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} h4 {mso-margin-top-alt:auto; margin-right:0cm; mso-margin-bottom-alt:auto; margin-left:0cm; mso-pagination:widow-orphan; mso-outline-level:4; font-size:12.0pt; font-family:"Times New Roman"; font-weight:bold;} p {mso-margin-top-alt:auto; margin-right:0cm; mso-margin-bottom-alt:auto; margin-left:0cm; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} span.SpellE {mso-style-name:""; mso-spl-e:yes;} @page Section1 {size:595.3pt 841.9pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style> <!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabla normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} </style> <![endif]--> </head> <body lang=3DES style=3D'tab-interval:35.4pt'> <div class=3DSection1> <h4 align=3Dcenter style=3D'text-align:center'><span class=3DSpellE><span lang=3DEN-US style=3D'font-size:10.0pt;mso-ansi-language:EN-US'>Resumen</span></span><span lang=3DEN-US style=3D'font-size:10.0pt;mso-ansi-language:EN-US'><o:p></o:p></span></h4> <p style=3D'text-align:justify'><span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>The&quot;pull-in&quot; or &quot;snap-down&quot; instability in <span class=3DSpellE>electrostatically</span> actuated <span class=3DSpellE>microelectromechanical</span> systems (MEMS)presents a ubiquitous challenge in MEMS technology of great importance.In this instability, when applied voltages are increased beyond acritical value, there is no longer a steady-state configuration ofthe device where mechanical members remain separate. This severely restrictsthe range of stable operation of many devices. In anattempt to reduce the effects of this instability, researchers havesuggested spatially tailoring the dielectric properties of MEMS devices. Here,a mathematical model of an idealized <span class=3DSpellE>electrostatically</span> actuated MEMS deviceis constructed and analyzed for the purpose of investigating thispossibility. The pull-in instability is characterized in terms of thebifurcation diagram for the mathematical model. Variations in this bifurcationdiagram for various dielectric profiles are studied, yielding insight intohow this technique may be used to increase the stablerange of operation of <span class=3DSpellE>electrostatically</span> actuated MEMS devices.^<o:p></o:p></span> <p style=3D'text-align:justify'><span lang=3DEN-US style=3D'font-size:11.0pt; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span> </div> </body> </html>