1、Designation: E2245 111Standard 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 re
2、vision, 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.1NOTEReference (1) was editorially revised in September 2013.1. Scope1.1 This test method covers a procedure f
3、or measuring thecompressive residual strain 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 t
4、he under-lying layer are not accepted.1.2 This 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, associat
5、ed with its use. It is theresponsibility of the user of this standard 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, Re
6、flecting 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 Micro
7、scope at Subnanometer DisplacementLevels Using Si(111) Monatomic 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 e
8、xtracted 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.3.1.4 anchor,
9、 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 anchor to i
10、ts 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 is fixed at o
11、ne 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 method is under
12、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 December 2011. Originallyapproved in 2002. Last previous edition approved in 2005 as
13、 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 Summary page onthe ASTM website.3For referenced Semiconductor Equipment and Materia
14、ls 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 States13.1.9.1 DiscussionThis length (or deflection) measure-ment is made parallel to the underlying layer (or the xy-plan
15、eof 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 perpendicular to the transi
16、tional edges to bemeasured.3.1.11 MEMS, adjmicroelectromechanical 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
17、 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 fabrication yetbefore the constraint of the sacrificial layer (or substrate) isremoved (in whole or in part).3.1.14 sacrificial lay
18、er, na single thickness of materialthat is intentionally deposited (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 un
19、derlyinglayer.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 DiscussionIf the variation through the thicknessin the structural layer is assumed to be linear, it is calculated tobe the positiv
20、e 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 structural layer, na single thickness of materialpresent in the final MEMS device.3.1.18 substrate, nthe thick, starting material (oft
21、en 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 marks the end of the suspended structure.3.1.20 surface micromachining, adja MEMS fabricationprocess where micron-scale components
22、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 as, a fixed-fixedbeam or cantilever) that is used to extract information (such as,the residual strain or the strain gradient of a l
23、ayer) 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 in an interferometric 2-D data trace.3.1.23 underlying layer, nthe single thickness of materialdirectly beneath the material of int
24、erest.3.1.23.1 DiscussionThis layer could be the substrate.3.2 Symbols:3.2.1 For Calibration:6same= the maximum of two uncalibrated values (same1and same2) where same1is the standard deviation of the sixstep height measurements taken on the physical step heightstandard at the same location before th
25、e data session and same2is the standard deviation of the six measurements taken at thissame location after the data sessioncert= the certified one sigma uncertainty of the physicalstep height standard used for calibrationnoise= the standard deviation of the noise measurement,calculated to be one-six
26、th the value of Rtaveminus RaveRave= the standard deviation of the surface roughnessmeasurement, calculated to be one-sixth the value of Ravexcal= the standard deviation in a ruler measurement in theinterferometric microscopes x-direction for the given combi-nation of lensesycal= the standard deviat
27、ion in a ruler measurement in theinterferometric 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 combinatio
28、n 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 physicalstep height standardrulerx= the interferometric microscopes maximum field ofview in the x-direction for the given combinatio
29、n 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 of lenses asmeasured with a 10-m grid (or finer grid) rulerscopex= the interferometric microscopes maximum field ofview in the x-dire
30、ction for the given combination of lensesscopey= 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 calibrationmeas
31、urements from which 6sameis foundzdrift= the uncalibrated 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
32、 after the data session (at thissame location)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 ave
33、rage of the calibration measurements takenalong the physical step height standard before and after the datasession3.2.2 For In-plane Length Measurement: = the misalignment angleE2245 1112L = the in-plane length measurement of the fixed-fixed beamLoffset= the in-plane length correction term for the g
34、iven typeof in-plane length measurement taken on similar 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= th
35、e 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 lo-cates the upper corner associated with Edge 2 in Trace tya= the calibrated y-value associated with Trace aye= the calibrated y-value ass
36、ociated with Trace e3.2.3 For Residual Strain Measurement:rcorrection= 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
37、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-fixedbeam (as modeled with two cosine functions) with v1endandv2endas the calibrated v values of the endpointsLcF= the calibrated length of t
38、he cosine function modelingthe first curve 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 endpointsLe= the calibrated effective length of the fixed-fixed beamcalcula
39、ted as a straight-line measurement between 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 uncer
40、taintyassociated with the identification 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
41、 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 the minusz-direction of the interferometric microscope, and equals 1 forfixed-fixed beams deflected in the plus z-directiont = the thickness
42、of the suspended, structural layerveF= the 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 Uncerta
43、inty Calculations:r-high= in determining 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 sp
44、ecified variationsLrepeat(samp)= the in-plane length repeatability standard de-viation (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 fac
45、e each otherrepeat(samp)= the relative 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 t
46、he average ofthree or more measurements, 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
47、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 sta
48、ndard used forcalibrationucorrection= the 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 drift
49、during the data sessionuL= the component 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 stra
