1、Designation: E2246 11 (Reapproved 2018)Standard 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,
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 thestrain gradient in thin, ref
3、lecting films. It 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 me
4、thod 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 the user o
5、f 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 established in the
6、 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, Reflecting Films
7、Using an Optical InterferometerE2245 Test Method for Residual 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 Subnan
8、ometer 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 pointsthat is
9、 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.3.1.4 ancho
10、r, 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
11、 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 is fixed at
12、 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 method is unde
13、r 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 2011 as E22
14、46 111. DOI:10.1520/E224611R182For 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 version of t
15、his 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 StatesThis interna
16、tional 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 (TBT) Commi
17、ttee.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 the sample
18、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 structure
19、s, 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 fabricatio
20、n 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 microstruct
21、ures.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 Discussio
22、nIf 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 structural la
23、yer, 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 marks the
24、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 as, a fixe
25、d-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 in an inte
26、rferometric 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 same1is the sta
27、ndarddeviation 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 the physic
28、alstep height standard used for calibrationxcal= the standard deviation 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-natio
29、n 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 interferometric micro-scope for the given combina
30、tion 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 grid) rulerrulery= the interferometric microscop
31、es 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= the interferometric microscopes maximum field ofv
32、iew 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 calibrationmeasurements from which 6sameis foundzdrift= the uncalibrated positive difference between the av-erage
33、 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)zlin= over the instruments total scan range, the max
34、imumrelative 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 takenalong the physical step height standard before and after
35、 the datasession3.2.2 For Strain Gradient Calculations: = the misalign-ment anglea = the x- (or y-) coordinate of the origin of the circle ofradius Rint. An arc of this circle models the out-of-plane shapein the z-direction of the surface of the cantilever that ismeasured with the interferometric mi
36、croscopeE2246 11 (2018)2b = 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 is measured withthe interferometric microscopeL = the in-plane length measurement of the cantilevern1t=
37、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 of this point is
38、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 cantilevers deflected in the minus z-directionof the interferometric microscope, and equals 1 for cantileversde
39、flected 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 correction term for the givendesign lengtht = the thickness of the suspended, structural layerx1ave= the calibrate
40、d 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 locating theupper corner of the transitional edge using Trace tyt= the calibrated y-value associated with Trace
41、t3.2.3 For Combined Standard Uncertainty Calculations:repeat(samp)= the relative strain gradient repeatability standarddeviation as obtained from cantilevers fabricated in a processsimilar to that used to fabricate the sampleRave= the calibrated surface roughness of a flat and leveledsurface of the
42、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 surface of the sample material calculated to be theaverage of three or more measurements, each measureme
43、nttaken 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 variationssg-low= in determining the combined standard uncertaintyvalue for the strain gradient measurement, the lowes
44、t value forsggiven the specified variationsUsg= the expanded uncertainty of a strain gradient measure-mentucert= the component in the combined standard uncertaintycalculation for strain gradient that is due to the uncertainty ofthe value of the physical step height standard used forcalibrationucorre
45、ction= 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 of a strain gradientmeasurementudrift= the component in the combined standard uncertaintycalculation for strain gra
46、dient 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 fromlinearity of the data scanunoise= the component in the combined standard uncertaintycalculation for strain gradie
47、nt that is due to interferometricnoiseuRave= the component in the combined standard uncertaintycalculation for strain gradient that is due to the samplessurface roughnessurepeat(samp)= the component in the combined standard un-certainty calculation for strain gradient that is due to therepeatability
48、 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 is due to the repeat-ability of measurements taken on the physical step heightstandarduW= the component in the comb
49、ined standard uncertaintycalculation for strain gradient that is due to the measurementuncertainty across the width of the cantileveruxcal= the component in the combined standard uncertaintycalculation 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 the combined standard uncertaintycalculation for st
