1、Designation: E 2246 05Standard Test Method forStrain Gradient Measurements of Thin, Reflecting FilmsUsing an Optical Interferometer1This standard is issued under the fixed designation E 2246; 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 thestrain gradient in thin, reflecting films.
3、It applies only to films,such as found in microelectromechanical systems (MEMS)materials, which can be imaged using an optical interferometer.Measurements from cantilevers that are touching the underly-ing layer are not accepted.1.2 This test method uses a non-contact optical interferom-eter with th
4、e 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 practices
5、 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 2245 Test Method for Residual Strain Measurements ofThin, Reflecting Films
6、 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 topo
7、graphical 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 pro
8、cess,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 specified
9、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 of t
10、he 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 topographical 3-
11、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 syste
12、ms, 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 int
13、erferometersz-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 (or s
14、ubstrate) 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 of a
15、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 Nov
16、. 1, 2005. Published December 2005. Originallyapproved in 2002. Last previous edition approved in 2002 as E 2246 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 to
17、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 befor
18、e 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 to th
19、e 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-micromachini
20、ng 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 str
21、ucture, na component (such as, a cantileveror a fixed-fixed beam) that is used to extract information (suchas, the strain gradient or the residual strain 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
22、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 measur
23、ement 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 standard
24、calx= 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 doubl
25、e-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 double
26、-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 of
27、lenses as measuredwith a 10-m grid (or finer grid) ruler3.2.2 For Alignment:L = the in-plane length measurement of the cantileverx1lower= 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
28、 edgex3lower= the x-data value along Edge “3” locating the lowerpart of the transitional edgex3upper= the x-data value along Edge “3” locating the upperpart of the transitional edgex4lower= the x-data value along Edge “4” locating the lowerpart of the transitional edgex4upper= the x-data value along
29、 Edge “4” 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 locating the upper part of the transition3.2.3 For Strain Gradient Calcula
30、tions:a = 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 topmost surface of the cantileverb = the z-coordinate of the origin of the circle of radius Rint.An arc of this circle models the out-of-plane s
31、hape in thez-direction of the topmost surface of the cantileverRint= the radius of the circle with an arc that models theshape of the topmost surface of the cantilever as measured withthe interferometers = equals 1 for cantilevers deflected in the minusz-direction of the interferometer, and equals 1
32、 for cantileversdeflected in the plus z-directionsg= the strain gradient as calculated from three data pointssg0= the strain gradient when the residual strain equals zerot = the thickness of the suspended, structural layertsupport= in a bulk-micromachining process, the thicknessof the support region
33、 where it is intersected by the interfero-metric 2-D data trace of interestx1ave= the average of x1lowerand x1upperx2ave= the average of x2lowerand x2upperx2lower= the x-data value along Edge “2” locating the lowerpart of the transitional edgex2upper= the x-data value along Edge “2” locating the upp
34、erpart of the transitional edgezupper= 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 zupper3.2.4 For Combined Standard Uncertainty Calculations:ssample= the standard deviation in
35、 a height measurementdue to the samples peak-to-valley surface roughness as mea-sured with the interferometerRtave= 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 istaken from a dif
36、ferent 2-D data tracesg-high= in determining the combined standard uncertaintyvalue for the strain gradient measurement, the highest value forsggiven the specified variationsE2246052sg-low= in determining the combined standard uncertaintyvalue for the strain gradient measurement, the lowest value fo
37、rsggiven the specified variationsuc= the combined standard uncertainty value (that is, theestimated standard deviation of the result)usamp= the component in the combined standard uncer-tainty calculation for strain gradient that is due to the samplespeak-to-valley surface roughness as measured with
38、the inter-ferometeruW= 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 uncertaintycalculation for strain gradient that is due to the uncertainty
39、 ofthe calibration in the x-directionuxres= the component in the combined standard uncertaintycalculation for strain gradient that is due to the resolution of theinterferometer in the x-directionuzcal= the component in the combined standard uncertaintycalculation for strain gradient that is due to t
40、he uncertainty ofthe calibration in the z-directionuzres= the component in the combined standard uncertaintycalculation for strain gradient that is due to the resolution of theinterferometer in the z-directionw1/2= the half width of the interval from sg-lowto sg-highxres= the resolution of the inter
41、ferometer in the x-directionzres= the resolution of the interferometer in the z-direction3.2.5 For Round Robin Measurements:Ldes= the design length of the cantilevern = the number of reproducibility or repeatability measure-mentssgave= the average strain gradient value for the reproduc-ibility or re
42、peatability measurements. It is equal to the sum ofthe sgvalues divided by n.ucave= the average combined standard uncertainty value forthe reproducibility or repeatability measurements. It is equal tothe sum of the ucvalues divided by n.3.2.6 For Adherence to the Top of the Underlying Layer:A = in a
43、 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 micromachining process, the anchor etchdepth, which is the amount the underlying layer is etc
44、hed 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, jb, jc, and jd) between thebottom of the suspended, structural layer and the top of theunderlying layerja= in a surface
45、 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 susp
46、ended, structural layer that accounts for thedeviation in the distance between the bottom of the suspended,structural layer and the top of the underlying layer that is notdue to residue or the roughness of the surfaces.This componentcan be positive or negative.jc= in a surface micromachining process
47、, the height in theinterferometers z-direction of any residue present between thebottom of the suspended, structural layer and the top of theunderlying layerjd= in a surface micromachining process, half the peak-to-peak value of the surface roughness of the topside of theunderlying layerzreg#1= in a
48、 surface micromachining process, the interfero-metric z value of the point of maximum deflection along thecantilever with respect to the anchor lipzreg#2= in a surface micromachining process, a representa-tive interferometric z value of the group of points within thelarge anchor area3.2.7 Discussion
49、The symbols above are used throughoutthis test method. However, when referring to y values, the letter“y” can replace the first letter in the symbols above that startwith the letter “x.”4. Summary of Test Method4.1 Acantilever is shown in Figs. 1-3.After fabrication, thiscantilever bends in the out-of-plane z-direction. An opticalinterferometer (such as shown in Fig. 4) is used to obtain atopographical 3-D data set. Two-D data traces beside thecantilever (such as shown in Fig. 5) and along the top of thecantilever (such as shown in Fig. 6)
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