1、Designation: E2244 111Standard 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 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 measuringin-plane lengths (including deflections) 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 determi
4、ne in-plane lengths.Using the design dimensions 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 metho
5、d is intended for usewhen interferometric measurements 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 c
6、apability of obtaining topographi-cal 3-D data 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 interferometri
7、c microscopespixel-to-pixel spacing at the highest 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 and health practices and determine the appl
8、ica-bility of regulatory limitations prior to use.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 Interfe
9、rometerE2444 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 Steps2.2 SEMI Standard:3MS2 Test Method for Step Height Measurements of ThinFilms
10、3. 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 set, na thre
11、e-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 underlying laye
12、r.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 underlying layer.1This test method is under the jurisdiction of ASTM Committee E08 on Fatigueand Fracture and is the direct responsibility of S
13、ubcommittee E08.05 on CyclicDeformation and Fatigue Crack Formation.Current edition approved Nov. 1, 2011. Published 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 Cust
14、omer 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 International (SEMI)standards, visit the SEMI website, www.semi.org.Copyright ASTM International
15、, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.5.1 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
16、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 straight-line distance be-tween t
17、wo 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 interferometric microscope).3.1.10 interferometer, na non-contact optical instrumentused to obtain topographical 3-D data sets.3.1.10.1 Di
18、scussionThe height of the sample is measuredalong the z-axis 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 t
19、o describe micron-scale structures, sensors,actuators, and technologies 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) dur
20、ing the micromachining process, to allowfreestanding microstructures.3.1.14 structural layer, na single thickness of materialpresent in the final MEMS device.3.1.15 substrate, nthe thick, starting material (often singlecrystal silicon or glass) in a fabrication process that can be usedto build MEMS
21、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 fabricationprocess where micron-scale components are formed on asubstrate by the deposition (or addition) and removal (in wholeor in part)
22、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 residual strain or the strain gradient of a layer) about afabrication process.3.1.19 transitional edge, nthe side of a MEMS structureth
23、at 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 materialdirectly beneath the material of interest.3.1.20.1 DiscussionThis layer could be the substrate.3.2 Symbols:3.2.1 For Calibrati
24、on:xcal= the standard deviation in a ruler measurement in theinterferometric microscopes x-direction 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 facto
25、r 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 lensescalz= the z-calibration factor of the interferometric micro-scope for the given combination of lensescert = the certified (that
26、 is, calibrated) value of the physicalstep height standardrulerx= 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-directi
27、on 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 for the given combination of lensesscopey= the interferometric microscopes maximum field ofview in the y-direction for the given com
28、bination of lenseszave= the average of the calibration measurements takenalong the physical step height standard before and after the datasession3.2.2 For In-plane Length Measurement: = the misalignment anglerepeat(samp)= the in-plane length repeatability standard de-viation (for the given combinati
29、on of lenses for the giveninterferometric microscope) 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 len
30、gth correction term,LoffsetLalign= the in-plane length, after correcting formisalignment, 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 simi
31、lar calculations, and for a given magnification of agiven 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 corn
32、er of Edge 1, the maximum uncertaintyassociated with 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 acc
33、uratelylocates the upper corner of Edge 2, the maximum 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 me
34、asurement that is due toalignment uncertaintyE2244 1112ucL= the 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 compo
35、nent in the combined standard uncertaintycalculation for an in-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 measu
36、rements taken on thetest structure at different locationsurepeat(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 samecombin
37、ation of lenses for the given interferometric microscopefor 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-directionx1up
38、pert= the uncalibrated x-value that most appropriatelylocates 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-crosco
39、pe 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 e3.2.3 For Round Robin Measurements:L = for the given value of Ldes, Laveminus LdesLave= the average value of L over the given range of Ldes
40、valuesLave= the average in-plane length value 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 av
41、erage combined standard uncertainty value forthe 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
42、deflectionmeasurements, which would imply replacing 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
43、 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 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 s
44、hown in Fig. 4) are extracted from this3-D data 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
45、 in the field of view, (3) obtain a 3-D data set,FIG. 1 Three-Dimensional View of Surface-Micromachined Fixed-Fixed BeamE2244 1113and (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
46、, 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, respectively. The uncertainties (n1tand n2t) associatedwith these x-values are also obtained. The misalignment angle, is calculated from the da
47、ta 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 Alternati
48、vely for a surface-micromachining process, 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
49、 lower values are typically less than 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.NOTE 1The underlying layer is beneath this test structure.NOTE 2The structural layer of interest is included in both the light and dark gray areas.NOTE 3The light gray area is suspended in air after fabrication.NOTE 4The dark gray areas (the anchors) are the designed cuts in the sacrificial layer. This is
