1、Designation: E2245 11 (Reapproved 2018)Standard 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,
2、in the case of revision, 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
3、in thin films. It 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 Th
4、is test method uses 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
5、the user of this standard to establish appro-priate safety, health, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.4 This international standard was developed in accor-dance with internationally recognized principles on standard-ization establis
6、hed in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E2244 Test Method for In-Plane Length Measurements ofThin, Reflect
7、ing Films Using an Optical InterferometerE2246 Test Method 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
8、 at Subnanometer DisplacementLevels Using Si(111) Monatomic Steps (Withdrawn2015)32.2 SEMI Standard:4MS2 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 poi
9、ntsthat is extracted from a topographical 3-D data set and that isparallel 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
10、.1.4 anchor, nin a surface-micromachining process, theportion of the test 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
11、 anchor to its underlying layer.3.1.5.1 DiscussionIn some processes, the width 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 i
12、s fixed at one end.3.1.8 fixed-fixed beam, na test structure that consists 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.1This test meth
13、od 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 May 1, 2018. Published May 2018. Originallyapproved in 2002. Last previous edition approved in 2
14、011 as E2245 111. DOI:10.1520/E224511R182For 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 Summary page onthe ASTM website.3The last approved ve
15、rsion of this historical standard is referenced onwww.astm.org.4For referenced Semiconductor Equipment and Materials International (SEMI)standards, visit the SEMI website, www.semi.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesTh
16、is international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (
17、TBT) Committee.13.1.9.1 DiscussionThis length (or deflection) measure-ment is made parallel to the underlying 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 t
18、he sample is measuredalong the z-axis of the interferometer. The x-axis is typicallyaligned parallel or perpendicular to the transitional edges to bemeasured.3.1.11 MEMS, adjmicroelectromechanical systems.3.1.12 microelectromechanical systems, adjin general,this term is used to describe micron-scale
19、 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 amountof deformation (or displacement) per unit length constrainedwithin the structural layer of interest after
20、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 deposited (or added) then removed (inwhole or in part) during the micromachining process, to allowfreestanding m
21、icrostructures.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-thicknessvariation (of the residual strain) in the structural layer ofinterest before it is released.3.1.16.1
22、 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 of a cantilever divided by its thickness. Directionalinformation is assigned to the value of “s.”3.1.17 str
23、uctural layer, na single thickness of materialpresent in the final MEMS device.3.1.18 substrate, nthe thick, starting material (often singlecrystal silicon or glass) in a fabrication process that can be usedto build MEMS devices.3.1.19 support region, nin a bulk-micromachiningprocess, the area that
24、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) and removal (in wholeor in part) of structural and sacrificial layers.3.1.21 test structure, na component (such
25、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, nthe side of a MEMS structurethat is characterized by a distinctive out-of-plane verticaldisplacement as seen
26、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.3.2 Symbols:3.2.1 For Calibration: 6same= the maximum of two uncali-brated values (same1and same2) where same1
27、is the standarddeviation of the six step height measurements taken on thephysical step height standard at the same location before thedata session and same2is the standard deviation of the sixmeasurements taken at this same location after the data sessioncert= the certified one sigma uncertainty of
28、the physicalstep height standard used for calibrationnoise= the standard deviation of the noise measurement,calculated to be one-sixth the value of Rtaveminus RaveRave= the standard deviation of the surface roughnessmeasurement, calculated to be one-sixth the value of Ravexcal= the standard deviatio
29、n in a ruler measurement in theinterferometric microscopes x-direction for the given combi-nation of lensesycal= the standard deviation in a ruler measurement in theinterferometric microscopes y-direction for the given combi-nation of lensescalx= the x-calibration factor of the interferometric micro
30、-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 interferometric micro-scope for the given combination of lensescert = the certified (that is, calibrated) value of the
31、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 grid) rulerrulery= the interferometric microscopes maximum field ofview in the y-direction for the given combination o
32、f 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= the interferometric microscopes maximum field ofview in the y-direction for the given combination of lensesxres= the ca
33、librated resolution of the interferometric micro-scope in the x-directionz6same= the uncalibrated average of the six calibrationmeasurements from which 6sameis foundzdrift= the uncalibrated positive difference between the av-erage of the six calibration measurements taken before the datasession (at
34、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)zlin= over the instruments total scan range, the maximumrelative deviation from linearity, as quoted by the instrumentmanu
35、facturer (typically less than 3 %)zres= the calibrated resolution of the interferometric micro-scope in the z-directionzave= the average of the calibration measurements takenalong the physical step height standard before and after the datasession3.2.2 For In-plane Length Measurement: = the misalign-
36、ment angleL = the in-plane length measurement of the fixed-fixed beamE2245 11 (2018)2Loffset= the in-plane length correction term for the given typeof in-plane length measurement taken on similar structureswhen using similar calculations and for the given combinationof lenses for a given interferome
37、tric 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 the upper corner associated with Edge 1 in Trace tx2uppert= the calibrated x-value that most appropriately
38、lo-cates the upper corner associated with Edge 2 in Trace tya= the calibrated y-value associated with Trace aye= the calibrated y-value associated with Trace e3.2.3 For Residual Strain Measurement: rcorrection= therelative residual strain correction termr= the residual strainAF= the amplitude of the
39、 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 the fixed-fixed beam if there areno applied axial-compressive forcesLc= the total calibrated length of the curved fixed-fi
40、xedbeam (as modeled with two cosine functions) with v1endandv2endas the calibrated v values of the endpointsLcF= the calibrated length of the cosine function modelingthe first curve with v1endand i as the calibrated v values of theendpointsLcS= the calibrated length of the cosine function modelingth
41、e second curve with i and v2endas the calibrated v values ofthe endpointsLe= the calibrated effective length of the fixed-fixed beamcalculated as a straight-line measurement between veFand veSn1t= indicative of the data point uncertainty associated withthe chosen value for x1uppert, with the subscri
42、pt “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 of this point is n1txrescalx,where n1t=1.n2t= indicative of the data point uncertainty associated withthe chosen value f
43、or 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 uncertaintyassociated with the identification of this point is n2txrescalx,where n2t=1.s = equals 1 for fixed-fixed beams deflected in th
44、e 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= the calibrated v value of the inflection point of thecosine function modeling the first abbreviated data traceveS= the cal
45、ibrated 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 the combined standard uncertaintyvalue for the residual strain measurement, the highest value forrgiven the specified va
46、riationsr-low= in determining the combined standard uncertaintyvalue for the residual strain measurement, the lowest value forrgiven the specified variationsLrepeat(samp)= the in-plane length repeatability standard de-viation (for the given combination of lenses for the giveninterferometric microsco
47、pe) as obtained from test structuresfabricated in a process similar to that used to fabricate thesample and when the transitional edges face each otherrepeat(samp)= the relative residual strain repeatability stan-dard deviation as obtained from fixed-fixed beams fabricated ina process similar to tha
48、t 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, each measurement taken from adifferent 2-D data traceRtave= the calibrated peak-to-valley roughness of a flat andleveled
49、 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 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= the component in the combined standard u
