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XRESIDUALSTRESSESINMICRO2ELECTRO2MECHANICALSYSTEMS1,2121(1.,100080)(2.,100871)QIANJin1,2LIUCheng1ZHANGDacheng2ZHAOYapu1(1.StateKeyLaboratoryofNonlinearMechanics(LNM),InstituteofMechanicsChineseAcademyofSciences,Beijing100080,China)(2.InstituteofMicroelectronics,PekingUniversity,Beijing100871,China)(MST),MEMS,,Stoney,MEMS,AbstractResidualstressesinthinfilmsarealwaysamajorconcerninmicromachiningtechnology.Indesign,fabricationandpackagingprocessesofMEMS,residualstressesallthroughoperateasaninfluentialfactor.Thederivationofresidualstressesinthinfilmsisconsideredinthispaper,andsomemeasurementsareintroduced.TheStoneyformulaanditsextensions,arediscussedtocalcu2lateresidualstressesinthinfilms.Residualstressesaffectmechanicalbehaviorofmicrostructuresstrongly,suchasbucklingandadhe2sionofmicrobeams.KeywordsMicro2electro2mechanicalsystem;Residualstresses;Thinfilms;Buckling;Adhesion;ResonantfrequencyCorrespondent:ZHAOYapu,E2mail:yzhao@lnm.imech.ac.cn,Fax:+86210262561284Thefundingforthisprojectwasprovidedbyasubprojectof973ProjectentitledMOEMS.Contract(No.G19990331103).Manuscriptreceived20010627,inrevisedform20010828.1(MEMS)IC(Inte2grateCircuit),MEMS,,21[1],(MEMS)IC,,,,[1,2],,;,,2,(extrin2sicstress)(intrinsicstress),,,[3]th=[f(T)-s(T)]dT(1),f,sHookes,th=E1-fth(2)E1Fig.1Edgedislocationbylatticemismatch,,,1,JournalofMechanicalStrength2001,23(4):393401X20010627,20010828(973)(G19990331103)©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(as-af)Paf,,aiHoffman[4]i=Ef1-fx-aa=Ef1-fLg(3)a,x-a,,Lg[5],GPa,GPa,TFD,,,,[5]Pµ(dpPdn)1(n20-n10)(4)(dpPdn)1,n10n20,(dpPdn)1,,,,33.1Stoney,,,,,Stoney[6]f=E1-st2s6rtf(5)fs,t,r,EStoney,,Stoney[7]1)tfnts,2)EfEs3),4),5)6),,,Stoney3.2MEMS,,,,,Stoney,,,,nStoney[8]1r1+1r2++1rn=1-Es6t2s(f1tf1+f2tf2++fntfn)(6)1,2,,n,,(5)3.32,tfts,,,rr(r,z)(r,z),U(r,z)=E2(1-2)[rr(r,z)2+(r,z)2+2rr(r,z)(r,z)](7)rr,3rr=u(r)-zw(r)+m(8a)=u(r)r-zw(r)r+m(8b)(8a)(8b)m,u(r)w(r)2(Fig.2)3Fig.3Theextensionalstrainarisingfromrotationofthesubstratemidplane3942001©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(r)w(r)u(r)=0r+mw(r)=r2P2(9)0,(9)(8),(8)(7),0V(0,)=2R0tf+tsP2-tsP2U(r,z)rdrdz(10)5VP50=0,5VP5=0=6mtslm1+l1+lm(4+6l+4l2)+l4m2(11)l=tfPts,,m=EfPEstfnts(l0),(11)Stoney,m=1l=0.1,Stoney30%[9]3.4Stoney,,,4(),,,,(a)(a)Microcantileverbeforerelease(b)(b)Curved2upofmicrocantileverafterrelease(c)(c)Curved2downofmicrocantileverafterrelease4Fig.4Microcantileverwithastressgradientbeforeandafterrelease,total=k=0kztP2k(12)z,tk=1()=0ztP21(13)(13),5(a)(a)Tensilestressgradientthroughfilmthickness(b)(b)Compressivestressgradientthroughfilmthickness5()Fig.5Gradientdistributionofresidualstressthroughfilmthickness(firstorderapproximation)4,,,,,MEMS,,MEMS,,,MEMS,,(Mi2cro2rotating2structures)[10]X[11]X,,X,234:395©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.,,,Stoney6Fig.6Polysiliconfilmstressvs.depositiontemperatureKrulevitch[12](LPVCD)6,605,,630700,,,,,CCl42O2,,78605650,70.2m,,0.2m,600,LPCVD,(TEM),,,,630,(8)TEM,7007(605)Fig.7Stressprofileofthepolysiliconfilmat6058(650)Fig.8Stressprofileofthepolysiliconfilmat6504.2XX,10m[13]X,,Bragg2dsin=n(14)(,d,),,;,,,XPVD,(9)3962001©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(a)Eulerian(a)OpenEuleriancradle(b)(b)Areadetector11XFig.11X2raydiffractionsystems9PVDFig.9SchematicofthethreetypesoflatticedistortionsfoundinPVDthinfilms,,,10Fig.10StressandstrainstatesonthesurfaceofspecimenXsin2,10,123X,X(),3=0(),,=1+Esin2-E(1+2)(15)(hkl),=d-d0d0(16)d(hkl);d0(hkl)(14)(15)(16)=-E2(1+)180cot05(2)5sin2=KM(17)K=-E2(1+)180cot0,M=5(2)5sin22-sin22-sin2M11abX[14]XXX,,,MEMSX[15]XNiTi1823K1,NiTi,NiTiNiTi,,,,234:397©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.,,,,Kusaka[16]X{111}Al12Al,()Al,350350,T,(3),Al350,,12AlFig.12ResidualstressesinAlfilmsexperiencingdifferentheattreatmentChollet[17]XTiC,(2)213;47Cr;89TiC(),CrTiC,TiC,,TiC,Cr457,TiC,6TiC,TiC,2TiCTab.2ResidualstressesinTiCthinfilmswithdifferenttypesofsteelsubstratePMPa1-2950-15592-2852-9743-2707-14534-2563-22665-2994-26536-2586-31167-2727-23608-2178-16439-2163-15384.3MEMSMEMS,4.14.2,,,,,(),,(4),(dpPdn)1,CoSi2,BPSiCoSi2BSiCoSi2BSi,B,,[18]5,MEMS,MEMS,,:,;,(13)[19]()143982001©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.()Fig.13BucklingofmicrobridgebyCompressivestress(doubly2clampedbeam),,[20](peelnumber),5.314Fig.14MicrocantileveradheringtosubstrateMEMS(),15,,5.415SEMFig.15SEMofcomb2structure5.15b,,16,(E)16Fig.16Curved2upofmicrocantileverbycompressivestress=0-1(tP2)z(18)M=tP2-tP2Wzdz(19)(18)(19),M=-16Wt21(20),=-112EWt3M(21)(21),=12Et1(22),=12E1-t1(23)5.2hA,I=(1P12)Ah2P,PPq(x),w,,E,,[21]EI54w5x4+P52w5x2+A52w5t2=-q(x)(24),q(x)Pw(x,t)X(x)T(t),(24)1Td2Tdt2=-EIA1Xd4Xdx4-PA1Xd2Xdx2=-2(25),(25)T(t)=C1cos(t+)(26a)X(
本文标题:微电子机械系统中的残余应力问题
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