ASTM E2244-02

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: E 2244 – 02
Standard Test Method for
In-Plane Length Measurements of Thin, Reflecting Films
Using an Optical Interferometer
This standard is issued under the fixed designation E2244; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 3. Terminology
1.1 This test method covers a procedure for measuring 3.1 Definitions:
in-plane lengths (including deflections) of patterned thin films. 3.1.1 2-D data trace, n—a two-dimensional data trace that
It applies only to films, such as found in microelectromechani- is extracted from a topographical 3-D data set and that is
cal systems (MEMS) materials, which can be imaged using an parallel to the xz-or yz-plane of the interferometer.
interferometer. 3.1.1.1 Discussion—The height of the sample is measured
1.2 There are other ways to determine in-plane lengths. along the z-axis of the interferometer. The interferometer’s
Using the design dimensions typically provides more precise x-axis (as shown in Figs. 1 and 2) is typically aligned parallel
in-plane length values than using measurements taken with an or perpendicular to the transitional edges to be measured.
optical interferometer. (Interferometric measurements are typi- 3.1.2 3-D data set, n—a three-dimensional data set with a
cally more precise than measurements taken with an optical topographical z-data value for each (x, y) pixel location within
microscope.) This test method is intended for use when the interferometer’s field of view.
interferometric measurements are preferred over using the 3.1.3 anchor, n—in a surface-micromachining process, the
design dimensions (for example, when measuring in-plane portion of the test structure where the mechanical layer makes
deflections and when measuring lengths in an unproven fabri- contact with the underlying layer (see Fig. 2).
cation process). 3.1.4 anchor lip, n—in a surface-micromachining process,
1.3 This test method uses a non-contact optical interferom- the extension of the mechanical layer around the edges of the
eter with the capability of obtaining topographical 3-D data anchor (see Fig. 2).
sets. It is performed in the laboratory. 3.1.5 bulk micromachining, adj—a MEMS fabrication pro-
1.4 The maximum in-plane length measured is determined cess where the substrate is removed at specified locations,
by the maximum field of view of the interferometer at the which can create structures suspended in air.
lowest magnification. The minimum deflection measured is 3.1.6 cantilever, n—a test structure that consists of a beam
determinedbytheinterferometer’spixel-to-pixelspacingatthe suspended in air and anchored or supported at one end.
highest magnification. 3.1.7 fixed-fixed beam, n—a test structure that consists of a
1.5 This standard does not purport to address all of the beam suspended in air and anchored or supported at both ends
safety concerns, if any, associated with its use. It is the (see Figs. 1 and 2, and Fig. X1.1).
responsibility of the user of this standard to establish appro- 3.1.8 in-plane length measurement, n—a length (or deflec-
priate safety and health practices and determine the applica- tion)measurementmadeparalleltotheunderlyinglayer(orthe
bility of regulatory limitations prior to use. xy-plane).
3.1.9 interferometer, n—a non-contact optical instrument
2. Referenced Documents
(suchasshowninFig.3)usedtoobtaintopographical3-Ddata
2.1 ASTM Standards:
sets.
E2245 Test Method for Residual Strain Measurements of 3.1.10 mechanical layer, n—in a surface-micromachining
Thin, Reflecting Films Using an Optical Interferometer
process, the patterned layer (as shown in Fig. 2) that is
E2246 Test Method for Strain Gradient Measurements of anchoredtotheunderlyinglayerwherecutsaredesignedinthe
Thin, Reflecting Films Using an Optical Interferometer
sacrificial layer and that is suspended in air where no cuts are
designed in the sacrificial layer.
3.1.11 MEMS, adj—microelectromechanical systems.
This test method is under the jurisdiction ofASTM Committee E08 on Fatigue
3.1.12 sacrificial layer, n—in a surface-micromachining
and Fracture and is the direct responsibility of Subcommittee E08.05 on Cyclic
process, the layer fabricated between the mechanical layer and
Deformation and Fatigue Crack Formation.
Current edition approved Oct. 10, 2002. Published November 2002. the underlying layer.This layer is removed after fabrication. If
Annual Book of ASTM Standards, Vol 03.01.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E2244–02
FIG. 1 Three-Dimensional View of Surface-Micromachined Fixed-Fixed Beam
NOTE 1—The underlying layer is beneath this test structure.
NOTE 2—The mechanical layer is included in both the light and dark gray areas.
NOTE 3—The dark gray areas (the anchors) are the designed cuts in the sacrificial layer. This is where the mechanical layer contacts the underlying
layer.
NOTE 4—The light gray area is suspended in air after fabrication.
NOTE 5—The 2-D data traces (“a” and “e”) are used to ensure alignment.
NOTE 6—A 2-D data trace (“a” or “e”) is used to determine L.
FIG. 2 Top View of Fixed-Fixed Beam in Fig. 1
cuts are designed in this sacrificial layer (as shown in Fig. 2), 3.1.15 surface micromachining, adj—a MEMS fabrication
an anchor is created allowing the mechanical layer to contact
process where thin, sacrificial layers are removed, which can
the underlying layer in that region.
create structures suspended in air.
3.1.13 substrate, n—the thick, starting material in a MEMS
3.1.16 test structure, n—a structure (such as, a fixed-fixed
fabrication process.
beamorcantilever)thatisusedtoextractinformation(suchas,
3.1.14 support region, n—in a bulk-micromachining pro-
the residual strain or the strain gradient of a layer) about a
cess, the region that marks the end of the suspended structure.
fabrication process.
This region is suspended in air, attached to the substrate, or
both.
E2244–02
FIG. 3 Sketch of Optical Interferometer
3.1.17 transitional edge, n—an edge of a MEMS structure cal-x = the x-calibration factor of the interferometer for the
(such as Edge “1” in Fig. 2) that is characterized by a
given combination of lenses
distinctiveout-of-planeverticaldisplacement(asshowninFig.
cal-y = the y-calibration factor of the interferometer for the
4).
given combination of lenses
3.1.18 underlying layer, n—in a surface-micromachining
cal-z = the z-calibration factor of the interferometer for the
process, the layer directly beneath the mechanical layer after
given combination of lenses
the sacrificial layer is removed.
cert = the certified value of the double-sided step height
3.2 Symbols:
standard
3.2.1 For Calibration:
FIG. 4 2-D Data Trace Used to Find x1 , x1 , x2 , and x2
min max min max
E2244–02
inter-x = theinterferometer’smaximumfieldofviewinthe z = in a bulk-micromachining process, the value for z
upper-t
x-direction for the given combination of lenses when the thickness of the support region, t , is subtracted
support
inter-y = theinterferometer’smaximumfieldofviewinthe from z
upper
y-direction for the given combination of lenses 3.2.4 Discussion—The symbols above are used throughout
mean = the mean value of the step-height measurements this test method. However, the letter “D” can replace the letter
(on the double-sided step height standard) used to calculate “L” in the symbols above when referring to in-plane deflection
cal-z measurements. Also, when referring to y values, the letter “y”
ruler-x = theinterferometer’smaximumfieldofviewinthe can replace the first letter in the symbols above that start with
x-direction for the given combination of lenses as measured the letter “x.”
with a 10-µm grid ruler
4. Summary of Test Method
ruler-y = theinterferometer’smaximumfieldofviewinthe
y-direction for the given combination of lenses as measured
4.1 Any in-plane length measurement can be made if each
with a 10-µm grid ruler
endisdefinedbyatransitionaledge.Toobtaintheendpointsof
3.2.2 For Alignment:
the in-plane length measurement for a surface-micromachined
x1 = the x-datavaluealongEdge“1”(suchasshownin
lower structure,fourstepsaretaken:(1)selectfourtransitionaledges,
Fig. 4) locating the lower part of the transition
(2) obtain a 3-D data set, (3) ensure alignment, and (4)
x1 = the x-datavaluealongEdge“1”(suchasshownin
upper determine the endpoints. (This procedure is presented in
Fig. 4) locating the upper part of the transition
Appendix X1 for a bulk-micromachined structure.)
x2 = the x-datavaluealongEdge“2”(suchasshownin
lower 4.2 At the transitional edges defining L, the endpoints are
Fig. 4) locating the lower part of the transition
x1 , x1 , x2 , and x2 . L and L are calculated
min max min max min max
x2 = the x-datavaluealongEdge“2”(suchasshownin
upper from these values. L is the average of L and L .
min max
Fig. 4) locating the upper part of the transition
4.3 Alternatively for a surface-micromachining process, if
x = the x-data value along the transitional edge of
lower the transitional edges that define L face the same way (for
interest locating the lower part of the transition (see Fig. 4)
example, two right-hand edges) and have similar slopes and
x = the x-data value along the transitional edge of
upper magnitudes, a different approach can be taken. Here, L is the
interest locating the upper part of the transition (see Fig. 4)
positive difference between the endpoints x1 and x2
lower lower
3.2.3 For In-plane Length Measurement:
(or x1 and x2 ).
upper upper
L = the in-plane length measurement
L = the maximum in-plane length measurement
5. Significance and Use
max
L = the minimum in-plane length measurement
min
5.1 In-plane length measurements are used in calculations
sep = the average calibrated separation between two inter-
of parameters, such as residual strain and Young’s modulus.
ferometric pixels (in either the x-or y-direction) as applies to
5.2 In-plane deflection measurements are required for spe-
a given measurement or sep=(sep + sep)/2
1 2
cific test structures. Parameters, including residual strain, are
sep = the average calibrated separation between two inter-
calculated given these in-plane deflection measurements.
ferometric pixels at one end of the in-plane length measure-
ment 4
6. Apparatus
sep = the average calibrated separation between two inter-
6.1 Non-contact Optical Interferometer, capable of obtain-
ferometric pixels at the other end of the in-plane length
ing a topographical 3-D data set and has software that can
measurement
export a 2-D data trace. Fig. 3 is a sketch of a suitable
t = in a bulk-micromachining process, the thickness
support
non-contact optical interferometer. However, any non-contact
of the support region where it is intersected by the 2-D data
opticalinterferometerthathaspixel-to-pixelspacingsasspeci-
trace of interest (such as, Trace “a” or “e” in Fig. X1.1, as
fied in Table 1 and that is capable of performing the test
shown in Fig. X1.2)
procedurewithaverticalresolutionlessthan1nmispermitted.
u = the combined standard uncertainty value (that is, the
c
The interferometer must be capable of measuring step heights
estimated standard deviation of the result)
from 0.1 nm to at least 10 µm higher than the step height to be
x1 = the smaller of the two x values (x1 or x1 )
max lower upper
measured.
used to calculate L
max
x1 = the larger of the two x values (x1 or x1 )
min lower upper
used to calculate L
min
x2 = the larger of the two x values (x2 or x2 )
max lower upper
ThesameapparatusisusedasinTestMethodE2245andTestMethodE2246.
used to calculate L
max
x2 = the smaller of the two x values (x2 or x2 )
min lower upper
TABLE 1 Interferometer Pixel-to-Pixel Spacing Requirements
used to calculate L
min
z = the z-data value associated with x Magnification, 3 Pixel-to-pixel spacing, µm
upper upper
5 < 1.57
10 < 0.83
20 < 0.39
Taylor, B. N. and Kuyatt, C. E., “Guidelines for Evaluating and Expressing the
40 < 0.21
Uncertainty of NIST Measurement Results,” NIST Technical Note 1297, National 80 < 0.11
Institute of Standards and Technology, September 1994.
E2244–02
NOTE 1—The 1 nm resolution is not mandatory for this test method. In NOTE 4—Obtain at least five data sets representative of the field of
reality, the vertical resolution can be as much as 5 nm. However, the view.
constraint is supplied to alert the user of this instrumental constraint for
8.1.2.9 Foreach3-Ddataset,extracta2-Ddatatraceinthe
out-of-plane measurements leading to residual strain and strain gradient
xz-plane at the same location on the ruler, if possible.
calculations.
8.1.2.10 Record in tabular form the ruler measurements
6.2 10-µm-grid Ruler, for calibrating the interferometer in
versus x for each y.
the xy-plane.
8.1.2.11 Orient the ruler in the y-direction along the left-
6.3 Double-sided Step Height Standard, for calibrating the
hand edge of the field of view. Repeat the above steps in a
interferometer in the out-of-plane z-direction.
similar manner.
7. Test Units
NOTE 5—This step can be skipped if the in-plane measurements are
restricted to the x-direction due to a smaller pixel-to-pixel spacing in that
7.1 The two transitional edges (for example, Edges “1” and
direction.
“2”inFigs.1and2)definingthein-planelength(ordeflection)
8.1.2.12 By interpolating or extrapolating, or both, use the
measurement.
newly created calibrated lookup table(s) to find the calibrated
NOTE 2—In a surface-micromachining process, if a transitional edge is
x (and/or y) values for pertinent pixels within the field of view.
on one side of an anchor lip, the anchor lip should be wide enough to
8.2 Calibrate the interferometer in the out-of-plane
include at least three data points. If the pixel-to-pixel spacing is 1.56 µm,
z-direction using the certified value of a double-sided step
then the anchor lip should be at least 3.2 times greater (or 5.0 µm).
height standard. Do this for each combination of lenses used
8. Calibration
for the measurements.
8.1 Calibrate the interferometer in the x- and y-directions 6
NOTE 6—Calibrating the step height at NIST lowers the total uncer-
using a 10-µm-grid ruler. Do this for each combination of
tainty in the certified value.
lenses used for the measurements. Calibrate in the xy-plane on
8.2.1 Before the data session, record the height of the step
a yearly basis.
height standard at six locations, three on each side of the step
8.1
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