1、Designation: E2246 11Standard Test Method forStrain Gradient Measurements of Thin, Reflecting FilmsUsing an Optical Interferometer1This standard is issued under the fixed designation E2246; 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 thestrain gradient in thin, reflecting films. It
3、applies only to films,such as found in microelectromechanical systems (MEMS)materials, which can be imaged using an optical interferometer,also called an interferometric microscope. Measurements fromcantilevers that are touching the underlying layer are notaccepted.1.2 This test method uses a non-co
4、ntact 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 standard to
5、 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 InterferometerE2245 Test Method for Resi
6、dual Strain 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) Monatomic Steps2.
7、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 to the xz
8、-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 structure
9、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 width of th
10、eanchor 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 of afrees
11、tanding 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 underlying layer
12、 (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 perpendicul
13、ar 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 January 2012.
14、Originallyapproved in 2002. Last previous edition approved in 2005 as E2246 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 o
15、nthe 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, adjmicroelectromechanical system
16、s.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 amountof deform
17、ation (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 deposited (or a
18、dded) 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-thicknessvar
19、iation (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 of a canti
20、lever 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 that canbe u
21、sed 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) and removal (
22、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, nthe side o
23、f 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.3.2 Symbols
24、: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 the six meas
25、urements taken at thissame location after the data sessionscert= the certified one sigma uncertainty of the physicalstep height standard used for calibrationsxcal= the standard deviation in a ruler measurement in theinterferometric microscopes x-direction for the given combi-nation of lensessycal= t
26、he 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-scope for the given combination of lensescaly= the y-calibration factor of the interferometric micro-scope for th
27、e 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 physicalstep height standardrulerx= the interferometric microscopes maximum field ofview in the x-direction for th
28、e 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 of lenses asmeasured with a 10-m grid (or finer grid) rulerscopex= the interferometric microscopes maximum field of
29、view 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 calibrated resolution of the interferometric micro-scope in the x-directionz6same= the uncalibrated average of the s
30、ix calibration mea-surements from which s6sameis 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 sixcalibrati
31、on 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 instrumentmanufacturer (typically less than 3 %)zres= the calibrated resolution of the interferometric micro-scope in the z-d
32、irectionzave= the average of the calibration measurements takenalong the physical step height standard before and after the datasession3.2.2 For Strain Gradient Calculations:a = the misalignment anglea = the x- (or y-) coordinate of the origin of the circle ofradius Rint. An arc of this circle model
33、s the out-of-plane shapein the z-direction of the surface of the cantilever that ismeasured with the interferometric microscopeb = the z-coordinate of the origin of the circle of radius Rint.An arc of this circle models the out-of-plane shape in thez-direction of the surface of the cantilever that i
34、s measured withthe interferometric microscopeL = the in-plane length measurement of the cantilevern1t= 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 accuratelyE2246 11
35、2locates the upper corner of Edge 1, the maximum uncertaintyassociated with the identification of this point is n1txrescalx,where n1t=1.Rint= the radius of the circle with an arc that models theshape of the surface of the cantilever that is measured with theinterferometric microscopes = equals 1 for
36、 cantilevers deflected in the minus z-directionof the interferometric microscope, and equals 1 for cantileversdeflected in the plus z-directionsg= the strain gradient as calculated from three data pointssg0= the strain gradient when the residual strain equals zerosgcorrection= the strain gradient co
37、rrection term for the givendesign lengtht = the thickness of the suspended, structural layerx1ave= the calibrated average of x1upperaand x1upperex1uppert= the calibrated x-value along Edge 1 locating theupper corner of the transitional edge using Trace tx2uppert= the calibrated x-value along Edge 2
38、locating theupper corner of the transitional edge using Trace tyt= the calibrated y-value associated with Trace t3.2.3 For Combined Standard Uncertainty Calculations:srepeat(samp)= the relative strain gradient repeatability stan-dard deviation as obtained from cantilevers fabricated in aprocess simi
39、lar 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, each measurement taken from adifferent 2-D data traceRtave= the calibrated peak-to-valley roughness of a flat
40、andleveled surface of the sample material calculated to be theaverage of three or more measurements, each measurementtaken from a different 2-D data tracesg-high= in determining the combined standard uncertaintyvalue for the strain gradient measurement, the highest value forsggiven the specified var
41、iationssg-low= in determining the combined standard uncertaintyvalue for the strain gradient measurement, the lowest value forsggiven the specified variationsUsg= the expanded uncertainty of a strain gradient measure-mentucert= the component in the combined standard uncertaintycalculation for strain
42、 gradient that is due to the uncertainty ofthe value of the physical step height standard used forcalibrationucorrection= the component in the combined standard uncer-tainty calculation for strain gradient that is due to the uncer-tainty of the correction termucsg= the combined standard uncertainty
43、of a strain gradientmeasurementudrift= the component in the combined standard uncertaintycalculation for strain gradient that is due to the amount of driftduring the data sessionulinear= the component in the combined standard uncertaintycalculation for strain gradient that is due to the deviation fr
44、omlinearity of the data scanunoise= the component in the combined standard uncertaintycalculation for strain gradient that is due to interferometricnoiseuRave= the component in the combined standard uncertaintycalculation for strain gradient that is due to the samplessurface roughnessurepeat(samp)=
45、the component in the combined standard un-certainty calculation for strain gradient that is due to therepeatability of measurements taken on cantilevers processedsimilarly to the one being measuredurepeat(shs)= the component in the combined standard uncer-tainty calculation for strain gradient that
46、is due to the repeat-ability of measurements taken on the physical step heightstandarduW= the component in the combined standard uncertaintycalculation for strain gradient that is due to the measurementuncertainty across the width of the cantileveruxcal= the component in the combined standard uncert
47、aintycalculation for strain gradient that is due to the uncertainty ofthe calibration in the x-directionuxres= the component in the combined standard uncertaintycalculation for strain gradient that is due to the resolution of theinterferometric microscope in the x-directionuzres= the component in th
48、e combined standard uncertaintycalculation for strain gradient that is due to the resolution of theinterferometric microscope in the z-direction3.2.4 For Round Robin Measurements:Ldes= the design length of the cantilevern = the number of repeatability or reproducibility measure-mentssgave= the avera
49、ge strain gradient value for the repeatabilityor reproducibility measurements that is equal to the sum of thesgvalues divided by nucgave= the average combined standard uncertainty value forthe strain gradient measurements that is equal to the sum of theucsgvalues divided by n3.2.5 For Adherence to the Top of the Underlying Layer:A = in a surface micromachining process, the minimumthickness of the structural layer of interest as measured fromthe top of the structural layer in the anchor area to the top of theunderlying layerH = in a surface m
