1、Designation: E 2244 05Standard Test Method forIn-Plane Length Measurements of Thin, Reflecting FilmsUsing an Optical Interferometer1This standard is issued under the fixed designation E 2244; 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 measuringin-plane lengths (including deflections) of pat
3、terned thin films.It applies only to films, such as found in microelectromechani-cal systems (MEMS) materials, which can be imaged using anoptical interferometer.1.2 There are other ways to determine in-plane lengths.Using the design dimensions typically provides more precisein-plane length values t
4、han using measurements taken with anoptical interferometer. (Interferometric measurements are typi-cally more precise than measurements taken with an opticalmicroscope.) This test method is intended for use wheninterferometric measurements are preferred over using thedesign dimensions (for example,
5、when measuring in-planedeflections and when measuring lengths in an unproven fabri-cation process).1.3 This test method uses a non-contact optical interferom-eter with the capability of obtaining topographical 3-D datasets. It is performed in the laboratory.1.4 The maximum in-plane length measured i
6、s determinedby the maximum field of view of the interferometer at thelowest magnification. The minimum deflection measured isdetermined by the interferometers pixel-to-pixel spacing at thehighest magnification.1.5 This standard does not purport to address all of thesafety concerns, if any, associate
7、d 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. Referenced Documents2.1 ASTM Standards:2E 2245 Test Method for Residual Strain Measurements ofThin, Re
8、flecting Films Using an Optical InterferometerE 2246 Test Method for Strain Gradient Measurements ofThin, Reflecting Films 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
9、 isparallel to the xz-oryz-plane of the interferometer.3.1.2 3-D data set, na three-dimensional group of pointswith a 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 wher
10、e a structural layer is inten-tionally attached to its underlying layer.3.1.4 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.3.1.4.1 DiscussionIn some processes, the width of theanc
11、hor lip may be zero.3.1.5 bulk micromachining, adja MEMS fabrication pro-cess where the substrate is removed at specified 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 afreestand
12、ing beam that is fixed at both ends.3.1.8 in-plane length (or deflection) measurement, ntheexperimental determination 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
13、 the xy-planeof the interferometer).3.1.9 interferometer, na non-contact optical instrumentused to obtain topographical 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
14、 to thetransitional edges to be measured.3.1.10 MEMS, adjmicroelectromechanical system.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 app
15、roved Nov. 1, 2005. Published December 2005. Originallyapproved in 2002. Last previous edition approved in 2002 as E 2244 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,
16、refer 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.3.1.11 microelectromechanical systems, adjin general,this term is used to describe micron-scale structures, sensors,actua
17、tors or the technologies used for their manufacture (suchas, silicon process technologies), or combinations thereof.3.1.12 sacrificial layer, na single thickness of materialthat is intentionally deposited (or added) then removed (inwhole or in part) during the micromachining process, to allowfreesta
18、nding microstructures.3.1.13 structural layer, na single thickness of materialpresent in the final MEMS device.3.1.14 substrate, nthe thick, starting material (oftensingle crystal silicon or glass) in a fabrication process that canbe used to build MEMS devices.3.1.15 support region, nin a bulk-micro
19、machining pro-cess, the area that marks the end of the suspended structure.3.1.16 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.3.1.17 t
20、est 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.3.1.18 transitional edge, nthe side of a MEMS structurethat is characterized by a distinctive out-of-p
21、lane verticaldisplacement as seen in an interferometric 2-D data trace.3.1.19 underlying layer, nthe single thickness of materialdirectly beneath the material of interest.3.1.19.1 DiscussionThis layer could be the substrate.3.2 Symbols:3.2.1 For Calibration:sxcal= the standard deviation in a ruler m
22、easurement 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 lensescalx= the x-calibration factor of the interferometer for thegiven combination of lensescaly= the y
23、-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 double-sided step heightstandardinterx= the interferometers maximum field of view in thex-direction for
24、 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-sided step height standard) used to calculatecalzrulerx= the interferometers maximum field of vie
25、w 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 lenses as measuredwith a 10-m grid (or finer grid) ruler3.2.2 For Alignment:x1lower= the x-data va
26、lue 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” locating the lowerpart of the transitional edgex2upper= the x-data value along Edge “2” locating the uppe
27、rpart 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 In-plane Length Measurement:L = the in-plane lengt
28、h measurementLmax= the maximum in-plane length measurementLmin= the minimum in-plane length measurementsep = the average calibrated separation between two inter-ferometric pixels (in either the x-ory-direction) as applies toa given measurement or sep =(sep1+ sep2)/2sep1= the average calibrated separ
29、ation between two inter-ferometric pixels at one end of the in-plane length measure-mentsep2= the average calibrated separation between two inter-ferometric pixels at the other end of the in-plane lengthmeasurementtsupport= in a bulk-micromachining process, the thicknessof the support region where i
30、t is intersected by the interfero-metric 2-D data trace of interestuc= the combined standard uncertainty value (that is, theestimated standard deviation of the result)uL= the component in the combined standard uncertaintycalculation that is due to the uncertainty in the calculatedlengthuxcal= the co
31、mponent in the combined standard uncertaintycalculation that is due to the uncertainty of the calibration inthe x-directionuxres= the component in the combined standard uncertaintycalculation that is due to the resolution of the interferometer inthe x-directionx1max= the smaller of the two x values
32、(x1loweror x1upper)used to calculate Lmaxx1min= the larger of the two x values (x1loweror x1upper)used to calculate Lminx2max= the larger of the two x values (x2loweror x2upper)used to calculate Lmaxx2min= the smaller of the two x values (x2loweror x2upper)used to calculate Lminxres= the resolution
33、of the interferometer in the x-directionzupper= 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 Round Robin Measurements:DL = for the given value of Ldes, Laveminus
34、 LdesDLave= the average value of DL over the given range ofLdesvaluesE2244052Lave= the average in-plane length value for the reproduc-ibility or repeatability measurements. It is equal to the sum ofthe L values divided by nLdes= the design lengthmag = the magnification used for the measurementn = th
35、e number of reproducibility or repeatability measure-mentsucave= the average combined standard uncertainty value forthe reproducibility or repeatability measurements. It is equal tothe sum of the ucvalues divided by n3.2.5 DiscussionThe symbols above are used throughoutthis test method. However, the
36、 letter “D” can replace the letter“L” in the symbols above when referring to in-plane deflectionmeasurements. Also, when referring to y values, the letter “y”can replace the first letter in the symbols above that start withthe letter “x.”4. Summary of Test Method4.1 Any in-plane length measurement c
37、an be made if eachend is defined by a transitional edge. Consider the surface-micromachined fixed-fixed beam shown in Figs. 1 and 2.Anoptical interferometer (such as shown in Fig. 3) is used toobtain a topographical 3-D data set. A 2-D data trace (such asFIG. 1 Three-Dimensional View of Surface-Micr
38、omachined Fixed-Fixed BeamNOTE 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 i
39、n the sacrificial layer. This is where the structural layer contacts the underlying layer.NOTE 5The 2-D data traces (“a” and “e”) are used to ensure alignment.NOTE 6A 2-D data trace (“a” or “e”) is used to determine L.FIG. 2 Top View of Fixed-Fixed Beam in Fig. 1E2244053shown in Fig. 4) is extracted
40、 from this 3-D data set for theanalysis of the transitional edges of interest.4.2 To obtain the endpoints of the in-plane length measure-ment for a surface-micromachined structure, four steps aretaken: (1) select four transitional edges, (2) obtain a 3-D dataset, (3) ensure alignment, and (4) determ
41、ine the endpoints.(This procedure is presented in Appendix X1 for a bulk-micromachined structure or a surface-micromachined structurewith transitional edges greater than 8 m in height.)4.3 At the transitional edges defining L, the endpoints arex1min, x1max, x2min, and x2max. Lminand Lmaxare calculat
42、edfrom these values. L is the average of Lminand Lmax.4.4 Alternatively 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, a different approach can be taken. Here, L is thepositive d
43、ifference between the endpoints x1lowerand x2lower(or x1upperand x2upper).FIG. 3 Schematic of an Optical InterferometerFIG. 4 2-D Data Trace Used to Find x1min, x1max, x2min, and x2maxTABLE 1 Interferometer Pixel-to-Pixel Spacing RequirementsMagnification, 3 Pixel-to-pixel spacing, m5 1.5710 0.8320
44、0.3940 0.2180 0.11E22440545. Significance and Use5.1 In-plane length measurements are used in calculationsof parameters, such as residual strain and Youngs modulus.5.2 In-plane deflection measurements are required for spe-cific test structures. Parameters, including residual strain, arecalculated gi
45、ven these in-plane deflection measurements.6. Apparatus36.1 Non-contact Optical Interferometer, capable of obtain-ing a topographical 3-D data set and exporting a 2-D data trace.Fig. 3 is a schematic of such an interferometer. However, anynon-contact optical interferometer that has pixel-to-pixel sp
46、ac-ings as specified in Table 1 and that is capable of performingthe test procedure with a vertical resolution less than 1 nm ispermitted. The interferometer must be capable of measuringstep heights to at least 5 m higher than the step height to bemeasured.NOTE 1Table 1 does not include magnificatio
47、ns at or less than 2.53because the pixel-to-pixel spacings will be too large for this work or thepossible introduction of a second set of interferometric fringes in the dataset at these magnifications can adversely affect the data, or both.Therefore, magnifications at or less than 2.53 shall not be
48、used.NOTE 2The 1 nm resolution is not mandatory for this test method. Inreality, the vertical resolution can be as much as 5 nm. However, theconstraint is supplied to alert the user of this instrumental constraint forout-of-plane measurements leading to residual strain and strain gradientcalculation
49、s.6.2 10-m-grid (or finer grid) Ruler, for calibrating theinterferometer in the xy-plane. This ruler should be longer thanthe maximum field of view at the lowest magnification.6.3 Double-sided Step Height Standard, for calibrating theinterferometer in the out-of-plane z-direction.7. Test Units7.1 The two transitional edges (for example, Edges “1” and“2” in Figs. 1 and 2) defining the in-plane length (or deflection)measurement.NOTE 3In a surface-micromachining process, if a transitional edge ison one side of an anchor lip, the anchor l
