1、Designation: E2245 11Standard Test Method forResidual Strain Measurements of Thin, Reflecting FilmsUsing an Optical Interferometer1This standard is issued under the fixed designation E2245; the number immediately following the designation indicates the year oforiginal adoption or, in the case of rev
2、ision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers a procedure for measuring thecompressive residual strain in thin films. It
3、applies only tofilms, such as found in microelectromechanical systems(MEMS) materials, which can be imaged using an opticalinterferometer, also called an interferometric microscope. Mea-surements from fixed-fixed beams that are touching the under-lying layer are not accepted.1.2 This test method use
4、s a non-contact optical interfero-metric microscope with the capability of obtaining topographi-cal 3-D data sets. It is performed in the laboratory.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this s
5、tandard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E2244 Test Method for In-Plane Length Measurements ofThin, Reflecting Films Using an Optical InterferometerE2246 Test Metho
6、d for Strain Gradient Measurements ofThin, Reflecting Films Using an Optical InterferometerE2444 Terminology Relating to Measurements Taken onThin, Reflecting FilmsE2530 Practice for Calibrating the Z-Magnification of anAtomic Force Microscope at Subnanometer DisplacementLevels Using Si(111) Monatom
7、ic Steps2.2 SEMI Standard:3MS2 Test Method for Step Height Measurements of ThinFilms3. Terminology3.1 Definitions:3.1.1 The following terms can be found in TerminologyE2444.3.1.2 2-D data trace, na two-dimensional group of pointsthat is extracted from a topographical 3-D data set and that isparallel
8、 to the xz-oryz-plane of the interferometric micro-scope.3.1.3 3-D data set, na three-dimensional group of pointswith a topographical z-value for each (x, y) pixel locationwithin the interferometric microscopes field of view.3.1.4 anchor, nin a surface-micromachining process, theportion of the test
9、structure where a structural layer is inten-tionally attached to its underlying layer.3.1.5 anchor lip, nin a surface-micromachining process,the freestanding extension of the structural layer of interestaround the edges of the anchor to its underlying layer.3.1.5.1 DiscussionIn some processes, the w
10、idth of theanchor lip may be zero.3.1.6 bulk micromachining, adja MEMS fabrication pro-cess where the substrate is removed at specified locations.3.1.7 cantilever, na test structure that consists of a free-standing beam that is fixed at one end.3.1.8 fixed-fixed beam, na test structure that consists
11、 of afreestanding beam that is fixed at both ends.3.1.9 in-plane length (or deflection) measurement, ntheexperimental determination of the straight-line distance be-tween two transitional edges in a MEMS device.3.1.9.1 DiscussionThis length (or deflection) measure-ment is made parallel to the underl
12、ying layer (or the xy-planeof the interferometric microscope).3.1.10 interferometer, na non-contact optical instrumentused to obtain topographical 3-D data sets.3.1.10.1 DiscussionThe height of the sample is measuredalong the z-axis of the interferometer. The x-axis is typicallyaligned parallel or p
13、erpendicular to the transitional edges to bemeasured.1This test method is under the jurisdiction of ASTM Committee E08 on Fatigueand Fracture and is the direct responsibility of Subcommittee E08.05 on CyclicDeformation and Fatigue Crack Formation.Current edition approved Nov. 1, 2011. Published Dece
14、mber 2011. Originallyapproved in 2002. Last previous edition approved in 2005 as E2245 05.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Sum
15、mary page onthe ASTM website.3For referenced Semiconductor Equipment and Materials International (SEMI)standards, visit the SEMI website, www.semi.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.11 MEMS, adjmicroelectromechan
16、ical systems.3.1.12 microelectromechanical systems, adjin general,this term is used to describe micron-scale structures, sensors,actuators, and technologies used for their manufacture (such as,silicon process technologies), or combinations thereof.3.1.13 residual strain, nin a MEMS process, the amou
17、ntof deformation (or displacement) per unit length constrainedwithin the structural layer of interest after fabrication yetbefore the constraint of the sacrificial layer (or substrate) isremoved (in whole or in part).3.1.14 sacrificial layer, na single thickness of materialthat is intentionally depo
18、sited (or added) then removed (inwhole or in part) during the micromachining process, to allowfreestanding microstructures.3.1.15 stiction, nadhesion between the portion of a struc-tural layer that is intended to be freestanding and its underlyinglayer.3.1.16 (residual) strain gradient, na through-t
19、hicknessvariation (of the residual strain) in the structural layer ofinterest before it is released.3.1.16.1 DiscussionIf the variation through the thicknessin the structural layer is assumed to be linear, it is calculated tobe the positive difference in the residual strain between the topand bottom
20、 of a cantilever divided by its thickness. Directionalinformation is assigned to the value of “s.”3.1.17 structural layer, na single thickness of materialpresent in the final MEMS device.3.1.18 substrate, nthe thick, starting material (oftensingle crystal silicon or glass) in a fabrication process t
21、hat canbe used to build MEMS devices.3.1.19 support region, nin a bulk-micromachining pro-cess, the area that marks the end of the suspended structure.3.1.20 surface micromachining, adja MEMS fabricationprocess where micron-scale components are formed on asubstrate by the deposition (or addition) an
22、d removal (in wholeor in part) of structural and sacrificial layers.3.1.21 test structure, na component (such as, a fixed-fixedbeam or cantilever) that is used to extract information (such as,the residual strain or the strain gradient of a layer) about afabrication process.3.1.22 transitional edge,
23、nthe side of a MEMS structurethat is characterized by a distinctive out-of-plane verticaldisplacement as seen in an interferometric 2-D data trace.3.1.23 underlying layer, nthe single thickness of materialdirectly beneath the material of interest.3.1.23.1 DiscussionThis layer could be the substrate.
24、3.2 Symbols:3.2.1 For Calibration:s6same= the maximum of two uncalibrated values (ssame1and ssame2) where ssame1is the standard deviation of the sixstep height measurements taken on the physical step heightstandard at the same location before the data session and ssame2is the standard deviation of t
25、he six measurements taken at thissame location after the data sessionscert= the certified one sigma uncertainty of the physicalstep height standard used for calibrationsnoise= the standard deviation of the noise measurement,calculated to be one-sixth the value of Rtaveminus RavesRave= the standard d
26、eviation of the surface roughnessmeasurement, calculated to be one-sixth the value of Ravesxcal= the standard deviation in a ruler measurement in theinterferometric microscopes x-direction for the given combi-nation of lensessycal= the standard deviation in a ruler measurement in theinterferometric
27、microscopes y-direction for the given combi-nation of lensescalx= the x-calibration factor of the interferometric micro-scope for the given combination of lensescaly= the y-calibration factor of the interferometric micro-scope for the given combination of lensescalz= the z-calibration factor of the
28、interferometric micro-scope for the given combination of lensescert = the certified (that is, calibrated) value of the physicalstep height standardrulerx= the interferometric microscopes maximum field ofview in the x-direction for the given combination of lenses asmeasured with a 10-m grid (or finer
29、 grid) rulerrulery= the interferometric microscopes maximum field ofview in the y-direction for the given combination of lenses asmeasured with a 10-m grid (or finer grid) rulerscopex= the interferometric microscopes maximum field ofview in the x-direction for the given combination of lensesscopey=
30、the interferometric microscopes maximum field ofview in the y-direction for the given combination of lensesxres= the calibrated resolution of the interferometric micro-scope in the x-directionz6same= the uncalibrated average of the six calibration mea-surements from which s6sameis foundzdrift= the u
31、ncalibrated positive difference between the av-erage of the six calibration measurements taken before the datasession (at the same location on the physical step heightstandard used for calibration) and the average of the sixcalibration measurements taken after the data session (at thissame location)
32、zlin= over the instruments total scan range, the maximumrelative deviation from linearity, as quoted by the instrumentmanufacturer (typically less than 3 %)zres= the calibrated resolution of the interferometric micro-scope in the z-directionzave= the average of the calibration measurements takenalon
33、g the physical step height standard before and after the datasession3.2.2 For In-plane Length Measurement:a = the misalignment angleL = the in-plane length measurement of the fixed-fixed beamLoffset= the in-plane length correction term for the given typeof in-plane length measurement taken on simila
34、r structureswhen using similar calculations and for the given combinationof lenses for a given interferometric microscopev1end= one endpoint of the in-plane length measurementv2end= another endpoint of the in-plane length measurementx1uppert= the calibrated x-value that most appropriately lo-cates t
35、he upper corner associated with Edge 1 in Trace tx2uppert= the calibrated x-value that most appropriately lo-cates the upper corner associated with Edge 2 in Trace tya8= the calibrated y-value associated with Trace a8E2245 112ye8= the calibrated y-value associated with Trace e83.2.3 For Residual Str
36、ain Measurement:drcorrection= the relative residual strain correction termr= the residual strainAF= the amplitude of the cosine function used to model thefirst abbreviated data traceAS= the amplitude of the cosine function used to model thesecond abbreviated data traceL0= the calibrated length of th
37、e fixed-fixed beam if there areno applied axial-compressive forcesLc= the total calibrated length of the curved fixed-fixedbeam (as modeled with two cosine functions) with v1endandv2endas the calibrated v values of the endpointsLcF= the calibrated length of the cosine function modelingthe first curv
38、e with v1endand i as the calibrated v values of theendpointsLcS= the calibrated length of the cosine function modelingthe second curve with i and v2endas the calibrated v values ofthe endpointsLe8= the calibrated effective length of the fixed-fixed beamcalculated as a straight-line measurement betwe
39、en veFand veSn1t= indicative of the data point uncertainty associated withthe chosen value for x1uppert, with the subscript “t” referring tothe data trace. If it is easy to identify one point that accuratelylocates the upper corner of Edge 1, the maximum uncertaintyassociated with the identification
40、 of this point is n1txrescalx,where n1t=1.n2t= indicative of the data point uncertainty associated withthe chosen value for x2uppert, with the subscript “t” referring tothe data trace. If it is easy to identify one point that accuratelylocates the upper corner of Edge 2, the maximum uncertaintyassoc
41、iated with the identification of this point is n2txrescalx,where n2t=1.s = equals 1 for fixed-fixed beams deflected in the minusz-direction of the interferometric microscope, and equals 1 forfixed-fixed beams deflected in the plus z-directiont = the thickness of the suspended, structural layerveF= t
42、he calibrated v value of the inflection point of thecosine function modeling the first abbreviated data traceveS= the calibrated v value of the inflection point of thecosine function modeling the second abbreviated data trace3.2.4 For Combined Standard Uncertainty Calculations:r-high= in determining
43、 the combined standard uncertaintyvalue for the residual strain measurement, the highest value forrgiven the specified variationsr-low= in determining the combined standard uncertaintyvalue for the residual strain measurement, the lowest value forrgiven the specified variationssLrepeat(samp)8= the i
44、n-plane length repeatability standarddeviation (for the given combination of lenses for the giveninterferometric microscope) as obtained from test structuresfabricated in a process similar to that used to fabricate thesample and when the transitional edges face each othersrepeat(samp)= the relative
45、residual strain repeatability stan-dard deviation as obtained from fixed-fixed beams fabricated ina process similar to that used to fabricate the sampleRave= the calibrated surface roughness of a flat and leveledsurface of the sample material calculated to be the average ofthree or more measurements
46、, each measurement taken from adifferent 2-D data traceRtave= the calibrated peak-to-valley roughness of a flat andleveled surface of the sample material calculated to be theaverage of three or more measurements, each measurementtaken from a different 2-D data traceUr= the expanded uncertainty of a
47、residual strain measure-mentucr= the combined standard uncertainty of a residual strainmeasurementucert= the component in the combined standard uncertaintycalculation for residual strain that is due to the uncertainty ofthe value of the physical step height standard used forcalibrationucorrection= t
48、he component in the combined standard uncer-tainty calculation for residual strain that is due to the uncer-tainty of the correction termudrift= the component in the combined standard uncertaintycalculation for residual strain that is due to the amount of driftduring the data sessionuL= the componen
49、t in the combined standard uncertaintycalculation for residual strain that is due to the measurementuncertainty of Lulinear= the component in the combined standard uncertaintycalculation for residual strain that is due to the deviation fromlinearity of the data scanunoise= the component in the combined standard uncertaintycalculation for residual strain that is due to interferometricnoiseuRave= the component in the combined standard uncertaintycalculation for residual strain that is due to the samples surfaceroughnessurepeat(samp)= th
