1、Designation: E2244 11 (Reapproved 2018)Standard 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,
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 measuringin-plane lengths (including defl
3、ections) of patterned 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 dimensi
4、ons typically provides 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 me
5、asurements are preferred 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 da
6、ta sets. It is performed 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 h
7、ighest magnification.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, health, and environmental practices and deter-mine the applicability of regulatory lim
8、itations prior to use.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organizatio
9、n TechnicalBarriers to Trade (TBT) Committee.2. Referenced 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 Interferomet
10、erE2444 Terminology Relating to Measurements Taken onThin, Reflecting FilmsE2530 Practice for Calibrating the Z-Magnification of anAtomic Force Microscope at Subnanometer DisplacementLevels Using Si(111) Monatomic Steps (Withdrawn2015)32.2 SEMI Standard:4MS2 Test Method for Step Height Measurements
11、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 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
12、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 surface-micromachining process, theportion of the test structure where a structural layer is inten-tionally attached to its und
13、erlying layer.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 May 1, 2018. Published May 2018. Originallyapproved in 2002. Last p
14、revious edition approved in 2011 as E2244 111. DOI:10.1520/E224411R18.2For 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 Document Summary page onthe ASTM
15、 website.3The last approved version of this 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,
16、PA 19428-2959. United StatesThis international 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
17、 Technical Barriers to Trade (TBT) Committee.13.1.5 anchor lip, nin a surface-micromachining process,the freestanding extension of the structural layer of interestaround the edges of the anchor to its underlying layer.3.1.5.1 DiscussionIn some processes, the width of theanchor lip may be zero.3.1.6
18、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.3.1.8 fixed-fixed beam, na test structure that consists of afreestanding beam that is fixed at
19、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.3.1.9.1 DiscussionThis length (or deflection) measure-ment is made parallel to the underlying layer (or the xy-planeof the interf
20、erometric 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 edges t
21、o 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.3.1.1
22、3 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.3.1.14 structural layer, na single thickness of materialpresent in the final MEMS device.3.1.15 sub
23、strate, nthe thick, starting material (often singlecrystal silicon or glass) in a fabrication process that can be usedto build MEMS devices.3.1.16 support region, nin a bulk-micromachiningprocess, the area that marks the end of the suspended structure.3.1.17 surface micromachining, adja MEMS fabrica
24、tionprocess 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, na component (such as, a fixed-fixedbeam or cantilever) that is used to extract information (such as,the res
25、idual 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 verticaldisplacement as seen in an interferometric 2-D data trace.3.1.20 underlying layer, nthe single thickness of ma
26、terialdirectly beneath the material of interest.3.1.20.1 DiscussionThis layer could be the substrate.3.2 Symbols:3.2.1 For Calibration: xcal= the standard deviation in aruler measurement in the interferometric microscopesx-direction for the given combination of lensesycal= the standard deviation in
27、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-calibration factor of the interferometric micro-scope for the given combination of le
28、nsescalz= 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 microscopes maximum field ofview in the x-direction for the given combination of le
29、nses 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) rulerscopex= the interferometric microscopes maximum field ofview in the x-direction f
30、or 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 measurements takenalong the physical step height standard before and after the datasession3.2.2 For In-plane Lengt
31、h Measurement: = the misalign-ment anglerepeat(samp)= the in-plane length repeatability standard de-viation (for the given combination of lenses for the giveninterferometric microscope) as obtained from test structuresfabricated in a process similar to that used to fabricate thesample and for the sa
32、me 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, after correcting formisalignment, used to calculate LLmeas= the measured in-plane length used to calculate Lalig
33、nLoffset= 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 agiven interferometric microscopen1t= indicative of the data point uncertainty associated withthe chosen value for x1
34、uppert, 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 n1txrescalx,where n1t=1.n2t= indicative of the data point uncertainty associate
35、d 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 maximum uncertaintyassociated with the identification of this point is n2txrescalx,where n2t=1.UL= the expanded uncertain
36、ty of an in-plane length mea-surementE2244 11 (2018)2ualign= the component in the combined standard uncertaintycalculation for an in-plane length measurement that is due toalignment uncertaintyucL= the combined standard uncertainty for an in-planelength measurementuL= the component in the combined s
37、tandard 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-plane length measurement that is due tothe uncertainty of the value for Loffseturepeat(L)= the comp
38、onent 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 locationsurepeat(samp)= the component in the combined standard un-certainty calculation for an in-plane length mea
39、surement 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 microscopefor the measurement, and for the same or a similar type ofmeasurementuxcal= the component in the combined
40、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 appropriatelylocates the upper corner associated with Edge 1 using Trace tx2uppert= the uncalibrated x-value that most ap
41、propriatelylocates 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 lensesya= the uncalibrated y-value associated with Trace aye= the uncalibrated y-value associated with Trace e3
42、.2.3 For Round Robin Measurements: L = for the givenvalue of Ldes, Laveminus LdesLave= the average value of L over the given range of LdesvaluesLave= the average in-plane length value for the repeatabilityor reproducibility measurements that is equal to the sum of theL values divided by nLdes= the d
43、esign lengthmag = the magnification used for the measurementn = the number of repeatability or reproducibility measure-mentsucLave= the average combined standard uncertainty value forthe in-plane length measurements that is equal to the sum of theucLvalues divided by n3.2.4 DiscussionThe symbols abo
44、ve 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 replacing the word “length”with the word “deflection.” Also, when referring to y values,the letter “y” can replace the f
45、irst 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 defined by a transitional edge. Consider the surface-micromachined fixed-fixed beam shown in Figs. 1 and 2.Anoptical
46、 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 data set for the analysis of the transitional edges ofinterest.FIG. 1 Three-Dimensional View of Surface-Micromachined F
47、ixed-Fixed BeamE2244 11 (2018)34.2 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 set,and (4) obtain the endpoin
48、ts 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 a, a, e,ore to identify Trace a, a, e,or e,
49、 respectively. The uncertainties (n1tand n2t) associatedwith these x-values are also obtained. The misalignment angle, is calculated from the data obtained from the two outermostdata traces (a and e) along with the corresponding y-values (yaand ye) associated with these traces. The in-plane length, L,isthe average of the four calibrated values for (x2uppert x1uppert)times cos() plus Loffset, the in-plane length correction term.4.4 Alternatively for a surface-micromachining process, ifthe transitional edges that define L
