1、Designation: E2244 11Standard Test Method forIn-Plane Length Measurements of Thin, Reflecting FilmsUsing an Optical Interferometer1This standard is issued under the fixed designation E2244; 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 measuringin-plane lengths (including deflections) of patter
3、ned thin films.It applies only to films, such as found in microelectromechani-cal systems (MEMS) materials, which can be imaged using anoptical interferometer, also called an interferometric micro-scope.1.2 There are other ways to determine in-plane lengths.Using the design dimensions typically prov
4、ides more precisein-plane length values than using measurements taken with anoptical interferometric microscope. (Interferometric measure-ments are typically more precise than measurements taken withan optical microscope.) This test method is intended for usewhen interferometric measurements are pre
5、ferred over usingthe design dimensions (for example, when measuring in-planedeflections and when measuring lengths in an unproven fabri-cation process).1.3 This test method uses a non-contact optical interfero-metric microscope with the capability of obtaining topographi-cal 3-D data sets. It is per
6、formed in the laboratory.1.4 The maximum in-plane length measured is determinedby the maximum field of view of the interferometric micro-scope at the lowest magnification. The minimum deflectionmeasured is determined by the interferometric microscopespixel-to-pixel spacing at the highest magnificati
7、on.1.5 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 and determine the applica-bility of regulatory limitations prior to use.2. Reference
8、d Documents2.1 ASTM Standards:2E2245 Test Method for Residual Strain Measurements ofThin, Reflecting Films Using an Optical InterferometerE2246 Test Method for Strain Gradient Measurements ofThin, Reflecting Films Using an Optical InterferometerE2444 Terminology Relating to Measurements Taken onThin
9、, Reflecting FilmsE2530 Practice for Calibrating the Z-Magnification of anAtomic Force Microscope at Subnanometer 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
10、 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-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
11、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 where a structural layer is inten-tionally attached to its underlying layer.3.1.5 anchor lip, nin a surface-micromachining process,the f
12、reestanding 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 theanchor lip may be zero.3.1.6 bulk micromachining, adja MEMS fabrication pro-cess where the substrate is removed at specified locations.
13、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 afreestanding beam that is fixed at both ends.3.1.9 in-plane length (or deflection) measurement, ntheexperimental determination of the straigh
14、t-line distance be-tween two transitional edges in a MEMS device.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. Pu
15、blished December 2011. Originallyapproved in 2002. Last previous edition approved in 2005 as E2244 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
16、Document Summary page onthe 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.3.1.9.1 DiscussionThis
17、 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 is measuredalong the z-axis
18、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 structures, sensors,actuators, and te
19、chnologies used for their manufacture (such as,silicon process technologies), or combinations thereof.3.1.13 sacrificial layer, na single thickness of materialthat is intentionally deposited (or added) then removed (inwhole or in part) during the micromachining process, to allowfreestanding microstr
20、uctures.3.1.14 structural layer, na single thickness of materialpresent in the final MEMS device.3.1.15 substrate, nthe thick, starting material (oftensingle crystal silicon or glass) in a fabrication process that canbe used to build MEMS devices.3.1.16 support region, nin a bulk-micromachining pro-
21、cess, the area that marks the end of the suspended structure.3.1.17 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.3.1.18 test structure,
22、 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.3.1.19 transitional edge, nthe side of a MEMS structurethat is characterized by a distinctive out-of-plane verticald
23、isplacement as seen in an interferometric 2-D data trace.3.1.20 underlying layer, nthe single thickness of materialdirectly beneath the material of interest.3.1.20.1 DiscussionThis layer could be the substrate.3.2 Symbols:3.2.1 For Calibration:sxcal= the standard deviation in a ruler measurement in
24、theinterferometric microscopes x-direction for the given combi-nation of lensessycal= 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 combin
25、ation 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 combination of lensescert = the certified (that is, calibrated) value of the physicalstep height standar
26、drulerx= 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 microscopes maximum field ofview in the y-direction for the given combination of lenses asmeasured with a
27、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 ofview in the y-direction for the given combination of lenseszave= the average of the calibration me
28、asurements takenalong the physical step height standard before and after the datasession3.2.2 For In-plane Length Measurement:a = the misalignment anglesrepeat(samp)8= the in-plane length repeatability standard de-viation (for the given combination of lenses for the giveninterferometric microscope)
29、as obtained from test structuresfabricated in a process similar to that used to fabricate thesample and for the same or a similar type of measurementL = the in-plane length measurement that accounts for mis-alignment and includes the in-plane length correction term,LoffsetLalign= the in-plane length
30、, after correcting for misalign-ment, used to calculate LLmeas= the measured in-plane length used to calculate LalignLoffset= the in-plane length correction term for the given typeof in-plane length measurement on similar structures, whenusing similar calculations, and for a given magnification of a
31、given interferometric microscopen1t= 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
32、 the identification of this point is n1txrescalx,where n1t=1.n2t= indicative of the data point uncertainty associated withthe chosen value for x2uppert, with the subscript “t” referring tothe data trace. If it is easy to identify one point that accuratelylocates the upper corner of Edge 2, the maxim
33、um uncertaintyassociated with the identification of this point is n2txrescalx,where n2t=1.UL= the expanded uncertainty of an in-plane length mea-surementualign= the component in the combined standard uncertaintycalculation for an in-plane length measurement that is due toalignment uncertaintyucL= th
34、e combined standard uncertainty for an in-planelength measurementuL= the component in the combined standard uncertaintycalculation for an in-plane length measurement that is due tothe uncertainty in the calculated lengthuoffset= the component in the combined standard uncertaintycalculation for an in
35、-plane length measurement that is due tothe uncertainty of the value for Loffseturepeat(L)= the component in the combined standard uncer-tainty calculation for an in-plane length measurement that isdue to the uncertainty of the four measurements taken on thetest structure at different locationsE2244
36、 112urepeat(samp)= the component in the combined standard un-certainty calculation for an in-plane length measurement that isdue to the repeatability of measurements taken on test struc-tures processed similarly to the sample, using the samecombination of lenses for the given interferometric microsc
37、opefor the measurement, and for the same or a similar type ofmeasurementuxcal= the component in the combined standard uncertaintycalculation for an in-plane length measurement that is due tothe uncertainty of the calibration in the x-directionx1uppert= the uncalibrated x-value that most appropriatel
38、ylocates the upper corner associated with Edge 1 using Trace tx2uppert= the uncalibrated x-value that most appropriatelylocates the upper corner associated with Edge 2 using Trace txres= the uncalibrated resolution of the interferometric mi-croscope in the x-direction for the given combination of le
39、nsesya8= the uncalibrated y-value associated with Trace a8ye8= the uncalibrated y-value associated with Trace e83.2.3 For Round Robin Measurements:DL = for the given value of Ldes, Laveminus LdesDLave= the average value of DL over the given range of LdesvaluesLave= the average in-plane length value
40、for the repeatabilityor reproducibility measurements that is equal to the sum of theL values divided by nLdes= the design lengthmag = the magnification used for the measurementn = the number of repeatability or reproducibility measure-mentsucLave= the average combined standard uncertainty value fort
41、he in-plane length measurements that is equal to the sum of theucLvalues divided by n3.2.4 DiscussionThe symbols above are used throughoutthis test method. However, the letter “D” can replace the letter“L” in the symbols above when referring to in-plane deflectionmeasurements, which would imply repl
42、acing the word “length”with the word “deflection.” Also, when referring to y values,the letter “y” can replace the first letter in the symbols (or thesubscript of the symbols) above that start with the letter “x.”4. Summary of Test Method4.1 Any in-plane length measurement can be made if eachend is
43、defined by a transitional edge. Consider the surface-micromachined fixed-fixed beam shown in Figs. 1 and 2.Anoptical interferometric microscope (such as shown in Fig. 3)isused to obtain a topographical 3-D data set. Four 2-D datatraces (one of which is shown in Fig. 4) are extracted from this3-D dat
44、a set for the analysis of the transitional edges ofinterest.4.2 To obtain the endpoints of the in-plane length measure-ment for a surface-micromachined structure, four steps aretaken: (1) select the two transitional edges, (2) align thetransitional edges in the field of view, (3) obtain a 3-D data s
45、et,and (4) obtain the endpoints and associated uncertainties. (Thisprocedure may need to be modified for a bulk-micromachinedstructure.)4.3 From each of the four data traces, the x-values (x1uppertand x2uppert) are obtained at the transitional edges defining L,where the subscript t is a8, a, e,ore8
46、to identify Trace a8, a, e,or e8, respectively. The uncertainties (n1tand n2t) associatedwith these x-values are also obtained. The misalignment angle,a, is calculated from the data obtained from the two outermostdata traces (a8 and e8) along with the corresponding y-values(ya8and ye8) associated wi
47、th these traces. The in-plane length,L, is the average of the four calibrated values for(x2uppert x1uppert) times cos(a) plus Loffset, the in-plane lengthcorrection term.FIG. 1 Three-Dimensional View of Surface-Micromachined Fixed-Fixed BeamE2244 1134.4 Alternatively for a surface-micromachining pro
48、cess, ifthe transitional edges that define L face the same way (forexample, two right-hand edges) and have similar slopes andmagnitudes, the values for x1lowertand x2lowertcan be usedinstead of x1uppertand x2uppertif the sum of the uncertainties(n1t+ n2t) for the lower values are typically less than
49、 the sumof the uncertainties for the upper values. Due to the similaritiesof the edges involved, the length correction term, Loffset,issetequal to zero in the calculation of L.4.5 The equations used to find the combined standarduncertainty are given in Annex A1.5. Significance and Use5.1 In-plane length measurements can be used in calcula-tions of parameters, such as residual strain and Youngsmodulus.NOTE 1The underlying layer is beneath this test structure.NOTE 2The structural layer of interest is included in both the light and dark gray are
