..Schematicoftheelectrodes.Notethattheshadedareascorrespondtothenichromecoating.TheresolutionoftheinstrumentwasdeterminedinIIandIII.Fordry,isothermalconditions,thecapacitancecellcanmeasurerelativechangesinthicknessontheorderof,fora.-mmthicksample;thiscorrespondstoaresolutionontheorderofm.Underdryconditionsinwhichthetemperatureischanged,thereproducibilityofarelativethicknesschange(e.g.,forCTEmeathandonlyairetweentheelectrodes,thevacuumcapacitanceisobtainedromthemeasuredcapacitanceCbyairvacCC()whereairisthedielectricconstantofair.Inthreepreviouspapers,thedesignanddatareductiontechniqueswerepresentedforourthree-terminalcapacitance-basedmetrologyforthinpolymerfilmmeasurements.Thefirstpaper(I)describedtheinitialdesignbasedongold-coatedZerodur.However,severalproblemswereencountered.ItwasdiscoveredthatZerodurdisplaysferroelectricbehavior,withanapparentCurietemperatureof℃asdeterminedbyfittingwithaCurie–Weisslaw.TherapidchangeinthedielectricconstantoftheZeroduralongwithacouplingfromthecentralcontactthroughtheguardgaptothehighelectrodecreatedanapparentnegativethermalexpansion.Thesecondproblemwiththeinitialdesignwaswiththegoldcoating.Thiscoatinghadthetendencyto―snowplow‖whenscratchesformedinthesurfacecreatingraisedareaswhichwouldresultinshortswhenmeasurementswereperformedonthinsamples.Thesecondproblemwiththegoldwasthatitunderwentmechanicalcreepunderloading.Toresolvetheseproblems,anewelectrodewasdesignedfromfusedquartzcoatedwithnichrome.Agroovefilledwithconductivesilverpaintwasaddedtothebacksideofthebottomelectrodearoundthecentralcontacttointerceptanyfieldlinesbetweenthecentralwirecontactthroughtheguardgaptothehighelectrode.Thenewdesignwasdescribedinthesecondpaper(II)alongwiththermalexpansionmeasurementson-orientedsinglecrystalsapphire(OAl)anda-mthickinnerlayerdielectricmaterial[].ItwasrecognizedinIIthatthedatareductionwassimpleaslongastheairfillingthegapbetweenthecapacitorplateswasdry.However,toexpandtheutilityofthecapacitancecelltohygrothermalexpansion(i.e.,swellinginahumidenvironment),thethirdpaper(III)describedthedatareductiontechniquesnecessaryforuseofthecapacitancecellunderhumidconditions.Fig..Schematicoftheelectrodes.Notethattheshadedareascorrespondtothenichromecoating.TheresolutionoftheinstrumentwasdeterminedinIIandIII.Fordry,isothermalconditions,thecapacitancecellcanmeasurerelativechangesinthicknessontheorderof,fora.-mmthicksample;thiscorrespondstoaresolutionontheorderofm.Underdryconditionsinwhichthetemperatureischanged,thereproducibilityofarelativethicknesschange(e.g.,forCTEmea误差值.mmHg(帕)。正如论文Ⅱ中,电解槽内温度校正用过一个黏贴在电解槽热导体上热电阻器(RTD)来实现。RTD是NIST通过ITS-中温度计测量标准参考值来设计。在论文Ⅱ中,因为我们使用是干燥空气净化,所以我们可以用理想气体定律来校正,以确定空气摩尔体积airv来计算vacCpRTvair()式中T——绝对温度;P——压力;R——气体常数(.KmolkpaLR)[]。从这个等式和干燥空气摩尔空气体积常数可得molLP.[],该电极空气分离介电常数为aieairaieairairvPvP()III.测量A.电解槽校正使用()样品计算厚度,必须知道有效面积。为了确定该值随温度变化而如何变化,在论文Ⅱ中,我们用过Zerodur样品得到面积和厚度校正约为.mm。在论文Ⅱ中,Zerodur实际尺寸由一个专门测定球平面游标卡尺和一个线性电压位移传感(LVDT)误差为mm。该电解槽通过论文Ⅱ所述Zerodur样品。测量温度分别在℃,℃,℃,℃,℃,C,and℃。电解槽内温度在每个温度段测量三次,每次测量后都记录电容vacC值,大约用小时,秒采样一次(总共有个数据点)。在A区采用℃电容量vacC来测量。在较高温度下所有测量值A都将通过Zerodur膨胀和收缩根据随温度变化函数(.KZerodur)来校正。该电极有效半径与温度关系如图图底部电极有效半径随温度变化和使用Zerodur校正其膨胀测量。图型单晶硅随温度变化曲线所显示数据B.p型单晶硅为了证明该电解槽能精密测量,并提供准确热膨胀值,一个单端.毫米厚圆片,以P型晶体硅为中心,厘米电阻划分(以划线)成三块。每片约为cm。这些材料用蒸馏水和乙醇清洗。电解槽组装就跟论文II中描述一样,放置在真空炉中约小时以成为有效地样品。测量分别在℃,℃,℃,℃,℃,and℃,每点采样两次(在环境与压缩机室内点不采样)。圆晶片厚度通过图三所示温度数据对应有效半径来确定。从图分析结果可以得到硅晶体管厚度。应该指出是标准引用在℃标准数据,而我们已经测量℃数据。因此,标准参数相对扩张数据可以从图中得到S等式KST()式中T是在温度T下膨胀系数。很明显,这两组数据在试验上有一定误差。(在℃温度下进行重复测量数据,以便较小误差)。这里得到一些电容电解池关键结论。首先,取消先前设计限制;对硅样品检测。第二,结果表明,电容电解池产生数据与文献基本一致。最后,我们进一步证实了样品TMAS测量技术优势。通过研究数据结果表明此设计可行性。这项研究是NIST研究人员之一,IBM公司恩迪科特,微电子和计算机技术公司,NavalSurfaceWarfareCenter—CraneDivision,CALCE电子产品和系统中心,马里兰大学,康奈尔大学,德克萨斯大学奥斯汀分校,普渡大学和半导体研究公司(SRC)利用各种TMAs技术对单晶硅热膨胀系数测量。用一个.毫米单晶硅样品作为研究对象。硅膨胀系数所有实际值分别在相应温度范围to。我们样品虽然只有一般一半厚,但我们实验误差值相对较小。(应当指出,我们总精度与实际厚度无关,主要误差是由于电极/样品间影响。因此,如果我们用较厚样品,在研究中循环测量,将能减小我们测量结果误差)最后,应该提到是由于硅是―最坏情况―在新电容电解池中,就认为它是没有必要对金属单晶样品进行更高热膨胀系数测量。但是,对连接在架空可得保护环高、低电极版间硅晶体测量,就如同是在硅晶体样品上测量。测量电容量保持一致,这表明,导电材料也可以用来测量。IV.结论我们已提出并设计了半导体材料(以及电介质)测量和我们电容电解槽实现。通过热膨胀系数得到了我们新型电容电解槽,对于P型单晶硅能力已经得到了证明,测量单元选材需通过热膨胀值来确定。因此,很明显,这也可以计量硅片上聚合物薄膜。此外,这种单元还可以用来研究湿热扩张(水分存在引起肿胀)可通过利用在III描述数据复位技术来实现。因此,这种技术广泛应用于内层介电层以及复合材料结构微电子包装领域。鸣谢作者在此感谢半导体电子部门NISTJr.Ehrstein博士提供硅样品。thandonlyairetweentheelectrodes,thevacuumcapacitanceisobtainedromthemeasuredcapacitanceCbyairvacCC()whereairisthedielectricconstantofair.Inthreepreviouspapers,thedesignanddatareductiontechniqueswerepresentedforourthree-terminalcapacitance-basedmetrologyforthinpolymerfilmmeasurements.Thefirstpaper(I)describedtheinitialdesignbasedongold-coatedZerodur.However,severalproblemswereencountered.Itwasdi中文字作者:ChadR.Snyder,MemberFrederickI.Mopsik国籍:America出处:IEEETRANSACTIONSONINSTRUMENTATIONANDEASUREMENTAPrecisionCapacitanceCellforMeasurementofThinFilmOut-of-PlaneExpansion–PartIII:ConductingandSemiconductingMaterialsAbstract—Thispaperdescribestheconstruction,calibration,anduseofaprecisioncapacitance-basedmetrologyforthemeasurementofthethermalandhygrothermal(swelling)expansionofthinfilms.Itisdemonstratedthatwiththisversionofourcapacitancecell,materialsranginginelectricalpropertiesfrominsulatorstoconductorscanbemeasured.Theresultsofourmeasurementsonp-type-orientedsinglecrystalsiliconarecomparedtotherecommendedstandardreferencevaluesfromtheliteratureandareshowntobeinexcellentagreement.IndexTerms—Capacitancecell,coefficientofthermalexpansion(CTE),guardedelectrode,highsensitivitydisplacement,innerlayerdielectrics,polymers,thinfilms.I.INTRODUCTIONTHEcoefficientofthermalexpansion(CTE)isakeydesignparameterinmanyapplications.Itisusedforestimatingdimensionaltolerancesandthermalstressmismatches.Thelatterisofgreatimportancetotheelectronicsindustry,wherethermalstressescanleadtodevicefailure.Foraccuratemodelingofthesesystems,reliablevaluesareneededfortheCTE.Traditionally,displacementgaugetechniquessuchasthermomechanicalanalysis(TMA)havebeenutilizedfordeterminingtheCTE.However,standardtestmethodsbasedonthesetechniquesarelimitedtodimensionsgreaterthanmm[-].Thisisproblematicformaterialswhichcanbeformedonlyasthinlayers(suchascoatingsandcertaininnerlayerdielectrics).Additionally,thereissomequestionastowhethervaluesobtainedonlargersamples(bulkmaterial)arethesameasthoseobtainedforthinfilms,evenwhentheeffectsoflateralconstraintsareincludedinthecalculations.Ithaslongbeenrecognizedthatcapacitance-basedmeasurements,inprinciple,canofferthenecessaryresolutionforthesefilms.Forapairofplane-parallelplatecapacitors,ifthesampleisusedtosetthespacingoftheplatesdwhilebeingoutsideofthemeasurementpath,thenforaconstanteffectiveareaoftheplatesA,thecapacitanceinavacuumvacCisgivenbythewell-knownequationdACvac()whereisthepermittivityoffreespace(mpF.).Withthesampleoutsideofthemeasurementpathandonlyairetweentheelectrodes,thevacuumcapacitanceisobtainedromthemeasuredcapacitanceCbyairvacCC()whereairisthedielectricconstantofair.Inthreepreviouspapers,thedesignanddatareductiontechniqueswerepresentedforourthree-terminalcapacitance-basedmetrologyforthinpolymerfilmmeasurements.Thefirstpaper(I)describedtheinitialdesignbasedongold-coatedZerodur.However,severalproblemswereencountered.ItwasdiscoveredthatZerodurdisplaysferroelectricbehavior,withanapparentCurietemperatureof℃asdeterminedbyfittingwithaCurie–Weisslaw.TherapidchangeinthedielectricconstantoftheZeroduralongwithacouplingfromthecentralcontactthroughtheguardgaptothehighelectrodecreatedanapparentnegativethermalexpansion.Thesecondproblemwiththeinitialdesignwaswiththegoldcoating.Thiscoatinghadthetendencyto―snowplow‖whenscratchesformedinthesurfacecreatingraisedareaswhichwouldresultinshortswhenmeasurementswereperformedonthinsamples.Thesecondproblemwiththegoldwasthatitunderwentmechanicalcreepunderloading.Toresolvetheseproblems,anewelectrodewasdesignedfromfusedquartzcoatedwithnichrome.Agroovefilledwithconductivesilverpaintwasaddedtothebacksideofthebottomelectrodearoundthecentralcontacttointerceptanyfieldlinesbetweenthecentralwirecontactthroughtheguardgaptothehighelectrode.Thenewdesignwasdescribedinthesecondpaper(II)alongwiththermalexpansionmeasurementson-orientedsinglecrystalsapphire(OAl)anda-mthickinnerlayerdielectricmaterial[].ItwasrecognizedinIIthatthedatareductionwassimpleaslongastheairfillingthegapbetweenthecapacitorplateswasdry.However,toexpandtheutilityo 中文3550字作者:ChadR.Snyder,MemberFrederickI.Mopsik国籍:America出处:IEEETRANSACTIONSONINSTRUMENTATIONANDEASUREMENTAPrecisionCapacitanceCellforMeasurementofThinFilmOut-of-PlaneExpansion–PartIII:ConductingandSemiconductingMaterialsAbstract—Thispaperdescribestheconstruction,calibration,anduseofaprecisioncapacitance-basedmetrologyforthemeasurementofthethermalandh