1、Designation: E2246 111Standard 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 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 thestrain gradient in thin, reflecting 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 under
4、lying layer are notaccepted.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, associated with it
5、s 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, Reflecting F
6、ilms 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 S
7、ubnanometer 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 extracted f
8、rom 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, nin a sur
9、face-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 its underly
10、ing 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 one end.3.1
11、.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 the jurisd
12、iction 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. Originallyapproved in 2002. Last previous edition approved in 2005 as E2246 05.2
13、For 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 Materials Internat
14、ional (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-planeof the int
15、erferometric 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 transitional edge
16、s 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 thereof.3.
17、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 layer, na sing
18、le 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 underlyinglay
19、er.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 positive differenc
20、e 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 (often singlecr
21、ystal 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 are formed
22、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 layer) about
23、 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 interest.3.1.2
24、3.1 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 the data sess
25、ion 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 calibrationxcal= the standard deviation in a ruler measurement in theinterferometric microscopes x-di
26、rection 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-scope for the given combination of lensescaly= the y-calibrati
27、on 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 physicalstep height standardrulerx= the interferometric microsc
28、opes 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 of lenses asmeasured with a 10-m grid (or finer grid) rulerscope
29、x= 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 calibrated resolution of the interferometric micro-scope in the x
30、-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 the same location on the physical step heightstandard used for
31、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 instrumentmanufacturer (typically less than 3 %)zres= the calibrated resoluti
32、on 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 Strain Gradient Calculations: = the misalignment anglea = the x- (or y-) coordinate of the origin of the ci
33、rcle 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 microscopeE2246 1112b = the z-coordinate of the origin of the circle of radius Rint.An arc of this circle models the out-of-plane shape
34、in thez-direction of the surface of the cantilever that is 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
35、 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.Rint= the radius of the circle with an arc that models theshape of the surface of the cantilever that is measured wi
36、th theinterferometric microscopes = equals 1 for 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
37、 equals zerosgcorrection= the strain gradient correction 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
38、 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 t3.2.3 For Combined Standard Uncertainty Calculations:repeat(samp)= the relative strain gradient repeatability stan-dard deviation as obtain
39、ed from cantilevers fabricated in aprocess 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, each measurement taken from adifferent 2-D data traceRtave= the
40、 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 tracesg-high= in determining the combined standard uncertaintyvalue for the strain gradient measurement,
41、 the highest value forsggiven the specified variationssg-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 comb
42、ined standard uncertaintycalculation for strain 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 correcti
43、on termucsg= the combined standard uncertainty 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
44、strain gradient that is due to the deviation fromlinearity 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
45、 to the samplessurface roughnessurepeat(samp)= 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 unc
46、er-tainty calculation for strain gradient that 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
47、= 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 microsco
48、pe in the x-directionuzres= the component in the 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 o
49、r reproducibility measure-mentssgave= the average 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 a
