1、Designation: E 2245 05Standard Test Method forResidual Strain Measurements of Thin, Reflecting FilmsUsing an Optical Interferometer1This standard is issued under the fixed designation E 2245; the number immediately following the designation indicates the year oforiginal adoption or, in the case of r
2、evision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers a procedure for measuring thecompressive residual strain in thin films.
3、It applies only tofilms, such as found in microelectromechanical systems(MEMS) materials, which can be imaged using an opticalinterferometer. Measurements from fixed-fixed beams that aretouching the underlying layer are not accepted.1.2 This test method uses a non-contact optical interferom-eter wit
4、h the capability of obtaining topographical 3-D datasets. 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 establish appro-priate safety and health pract
5、ices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E 2244 Test Method for In-Plane Length Measurements ofThin, Reflecting Films Using an Optical InterferometerE 2246 Test Method for Strain Gradient Measurements ofThin, Reflecting F
6、ilms Using an Optical Interferometer3. Terminology3.1 Definitions:3.1.1 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-oryz-plane of the interferometer.3.1.2 3-D data set, na three-dimensional group of pointswith a
7、topographical z-value for each (x, y) pixel locationwithin the interferometers field of view.3.1.3 anchor, nin a surface-micromachining process, theportion of the test structure where a structural layer is inten-tionally attached to its underlying layer.3.1.4 anchor lip, nin a surface-micromachining
8、 process,the freestanding extension of the structural layer of interestaround the edges of the anchor to its underlying layer.3.1.4.1 DiscussionIn some processes, the width of theanchor lip may be zero.3.1.5 bulk micromachining, adja MEMS fabrication pro-cess where the substrate is removed at specif
9、ied locations.3.1.6 cantilever, na test structure that consists of a free-standing beam that is fixed at one end.3.1.7 fixed-fixed beam, na test structure that consists of afreestanding beam that is fixed at both ends.3.1.8 in-plane length (or deflection) measurement, ntheexperimental determination
10、of the straight-line distance be-tween two transitional edges in a MEMS device.3.1.8.1 DiscussionThis length (or deflection) measure-ment is made parallel to the underlying layer (or the xy-planeof the interferometer).3.1.9 interferometer, na non-contact optical instrumentused to obtain topographica
11、l 3-D data sets.3.1.9.1 DiscussionThe height of the sample is measuredalong the z-axis of the interferometer. The interferometersx-axis is typically aligned parallel or perpendicular to thetransitional edges to be measured.3.1.10 MEMS, adjmicroelectromechanical system.3.1.11 microelectromechanical s
12、ystems, adjin general,this term is used to describe micron-scale structures, sensors,actuators or the technologies used for their manufacture (suchas, silicon process technologies), or combinations thereof.3.1.12 out-of-plane measurements, nexperimental datataken on structures that are curved in the
13、 interferometersz-direction (that is, perpendicular to the underlying layer).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 (
14、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 microstructures.3.1.15 stiction, nadhesion between the portion o
15、f a struc-tural layer that is intended to be freestanding and its underlyinglayer.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
16、 Nov. 1, 2005. Published December 2005. Originallyapproved in 2002. Last previous edition approved in 2002 as E 2245 02.2For 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
17、 to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.16 (residual) strain gradient, na through-thicknessvariation (of the residual strain) in the structural layer ofinterest b
18、efore 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 cantilever divided by its thickness. Directionalinformation is assigned t
19、o 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 used to build MEMS devices.3.1.19 support region, nin a bulk-micromac
20、hining 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 (in wholeor in part) of structural and sacrificial layers.3.1.21 test
21、 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 of a MEMS structurethat is characterized by a distinctive out-of-plan
22、e 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:3.2.1 For Calibration:sxcal= the standard deviation in a ruler meas
23、urement in theinterferometers x-direction for the given combination of lensessycal= the standard deviation in a ruler measurement in theinterferometers y-direction for the given combination of lensesszcal= the standard deviation of the step height measure-ments on the double-sided step height standa
24、rdcalx= the x-calibration factor of the interferometer for thegiven combination of lensescaly= the y-calibration factor of the interferometer for thegiven combination of lensescalz= the z-calibration factor of the interferometer for thegiven combination of lensescert = the certified value of the dou
25、ble-sided step heightstandardinterx= the interferometers maximum field of view in thex-direction for the given combination of lensesintery= the interferometers maximum field of view in they-direction for the given combination of lensesmean = the mean value of the step-height measurements(on the doub
26、le-sided step height standard) used to calculatecalzrulerx= the interferometers maximum field of view in thex-direction for the given combination of lenses as measuredwith a 10-m grid (or finer grid) rulerrulery= the interferometers maximum field of view in they-direction for the given combination o
27、f lenses as measuredwith a 10-m grid (or finer grid) ruler3.2.2 For Alignment:x1lower= the x-data value along Edge “1” locating the lowerpart of the transitional edgex1upper= the x-data value along Edge “1” locating the upperpart of the transitional edgex2lower= the x-data value along Edge “2” locat
28、ing the lowerpart of the transitional edgex2upper= the x-data value along Edge “2” locating the upperpart of the transitional edgexlower= the x-data value along the transitional edge ofinterest locating the lower part of the transitionxupper= the x-data value along the transitional edge ofinterest l
29、ocating the upper part of the transition3.2.3 For In-plane Length Measurement:L = the in-plane length measurement of the fixed-fixedbeamLmax= the maximum in-plane length measurement of thefixed-fixed beamLmin= the minimum in-plane length measurement of thefixed-fixed beamx1ave= an endpoint of the in
30、-plane length measurement(that is, the average of x1minand x1max)x1max= the value for x1upperused in the calculation of Lmaxx1min= the value for x1lowerused in the calculation of Lminx2ave= the other endpoint of the in-plane length measure-ment (that is, the average of x2minand x2max)x2max= the valu
31、e for x2upperused in the calculation of Lmaxx2min= the value for x2lowerused in the calculation of Lmin3.2.4 For Residual Strain Measurement:er= the residual strainAF= the amplitude of the cosine function used to model thefirst abbreviated data trace (or curve #1)AS= the amplitude of the cosine func
32、tion used to model thesecond abbreviated data trace (or curve #2)L0= the length of the fixed-fixed beam if there were noapplied axial-compressive forceLc= the total length of the curved fixed-fixed beam (asmodeled with two cosine functions) with x1aveand x2aveas thex values of the endpointsLcF= the
33、length of the cosine function modeling the firstcurve (or curve #1) with x1aveand x3Fas the x values of theendpointsLcS= the length of the cosine function modeling the secondcurve (or curve #2) with x1Sand x2aveas the x values of theendpointsLe8 = the effective length of the fixed-fixed beam. This i
34、s astraight-line measurement between xeFand xeSs = equals 1 for fixed-fixed beams deflected in the minusz-direction of the interferometer, and equals 1 for fixed-fixedbeams deflected in the plus z-directiont = the thickness of the suspended, structural layertsupport= in a bulk-micromachining process
35、, the thicknessof the support region where it is intersected by the interfero-metric 2-D data trace of interestxeF= the x value of the inflection point of the cosinefunction modeling the first abbreviated data trace (or curve #1)E2245052xeS= the x value of the inflection point of the cosinefunction
36、modeling the second abbreviated data trace (or curve#2)zupper= the z-data value associated with xupperzupper-t= in a bulk-micromachining process, the value for zwhen the thickness of the support region, tsupport, is subtractedfrom zupper3.2.5 For Combined Standard Uncertainty Calculations:er-high= i
37、n determining the combined standard uncertaintyvalue for the residual strain measurement, the highest value forergiven the specified variationser-low= in determining the combined standard uncertaintyvalue for the residual strain measurement, the lowest value forergiven the specified variationsssampl
38、e= the standard deviation in a height measurementdue to the samples peak-to-valley surface roughness as mea-sured with the interferometerLc-max= the total length of the curved fixed-fixed beam (asmodeled with two cosine functions) with x1maxand x2maxas thex values of the endpointsLc-min= the total l
39、ength of the curved fixed-fixed beam (asmodeled with two cosine functions) with x1minand x2minas thex values of the endpointsRtave= the peak-to-valley roughness of a flat and leveledsurface of the sample material calculated to be the average ofthree or more measurements, each measurement of which is
40、taken from a different 2-D data traceuc= the combined standard uncertainty value (that is, theestimated standard deviation of the result)uL= the component in the combined standard uncertaintycalculation for residual strain that is due to the measurementuncertainty of Lusamp= the component in the com
41、bined standard uncer-tainty calculation for residual strain that is due to the samplespeak-to-valley surface roughness as measured with the inter-ferometeruW= the component in the combined standard uncertaintycalculation for residual strain that is due to the measurementuncertainty across the width
42、of the fixed-fixed beamuxcal= the component in the combined standard uncertaintycalculation for residual strain that is due to the uncertainty ofthe calibration in the x-directionuxres= the component in the combined standard uncertaintycalculation for residual strain that is due to the resolution of
43、 theinterferometer in the x-direction as pertains to the chosen datapoints along the fixed-fixed beamuxresL= the component in the combined standard uncer-tainty calculation for residual strain that is due to the resolutionof the interferometer in the x-direction as pertains to thein-plane length mea
44、surementuzcal= the component in the combined standard uncertaintycalculation for residual strain that is due to the uncertainty ofthe calibration in the z-directionuzres= the component in the combined standard uncertaintycalculation for residual strain that is due to the resolution of theinterferome
45、ter in the z-directionw1/2= the half width of the interval from er-lowto er-highxres= the resolution of the interferometer in the x-directionzres= the resolution of the interferometer in the z-direction3.2.6 For Round Robin Measurements:erave= the average residual strain value for the reproduc-ibili
46、ty or repeatability measurements. It is equal to the sum ofthe ervalues divided by n.Ldes= the design length of the fixed-fixed beamn = the number of reproducibility or repeatability measure-mentsucave= the average combined standard uncertainty value forthe reproducibility or repeatability measureme
47、nts. It is equal tothe sum of the ucvalues divided by n.3.2.7 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 theunderly
48、ing layerH = in a surface micromachining process, the anchor etchdepth, which is the amount the underlying layer is etched awayin the interferometers minus z-direction during the patterningof the sacrificial layerJ = in a surface micromachining process, the positivedistance (equal to the sum of ja,
49、jb, jc, and jd) between thebottom of the suspended, structural layer and the top of theunderlying layerja= in a surface micromachining process, half the peak-to-peak value of the roughness of the underside of the suspended,structural layer in the interferometers z-direction. This is dueto the roughness of the topside of the sacrificial layer.jb= in a surface micromachining process, the tilting com-ponent of the suspended, structural layer that accounts for thedeviation in the distance between the bottom of the suspended,structural layer and
