ASTM E2245-02
(Test Method)Standard Test Method for Residual Strain Measurements of Thin, Reflecting Films Using an Optical Interferometer
Standard Test Method for Residual Strain Measurements of Thin, Reflecting Films Using an Optical Interferometer
SCOPE
1.1 This test method covers a procedure for measuring the compressive residual strain in thin films. It applies only to films, such as found in microelectromechanical systems (MEMS) materials, which can be imaged using an interferometer. Measurements from fixed-fixed beams that are touching the underlying layer are not accepted.
1.2 This test method uses a non-contact optical interferometer with the capability of obtaining topographical 3-D data sets. It is performed in the laboratory.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E 2245 – 02
Standard Test Method for
Residual Strain Measurements of Thin, Reflecting Films
Using an Optical Interferometer
This standard is issued under the fixed designation E2245; 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 3.1.3 anchor, n—in a surface-micromachining process, the
portion of the test structure where the mechanical layer makes
1.1 This test method covers a procedure for measuring the
contact with the underlying layer (see Figs. 1 and 2).
compressive residual strain in thin films. It applies only to
3.1.4 anchor lip, n—in a surface-micromachining process,
films, such as found in microelectromechanical systems
the extension of the mechanical layer around the edges of the
(MEMS) materials, which can be imaged using an interferom-
anchor (see Figs. 2 and 3).
eter. Measurements from fixed-fixed beams that are touching
3.1.5 bulk micromachining, adj—a MEMS fabrication pro-
the underlying layer are not accepted.
cess where the substrate is removed at specified locations,
1.2 This test method uses a non-contact optical interferom-
which can create structures suspended in air.
eter with the capability of obtaining topographical 3-D data
3.1.6 cantilever, n—a test structure that consists of a beam
sets. It is performed in the laboratory.
suspended in air and anchored or supported at one end.
1.3 This standard does not purport to address all of the
3.1.7 fixed-fixed beam, n—a test structure that consists of a
safety concerns, if any, associated with its use. It is the
beam suspended in air and anchored or supported at both ends
responsibility of the user of this standard to establish appro-
(see Figs. 1-3, and Fig. X1.1).
priate safety and health practices and determine the applica-
3.1.8 in-plane length measurement, n—a length (or deflec-
bility of regulatory limitations prior to use.
tion)measurementmadeparalleltotheunderlyinglayer(orthe
2. Referenced Documents
xy-plane).
3.1.9 interferometer, n—a non-contact optical instrument
2.1 ASTM Standards:
(suchasshowninFig.4)usedtoobtaintopographical3-Ddata
E2244 Test Method for In-Plane Length Measurements of
sets.
Thin, Reflecting Films Using an Optical Interferometer
3.1.10 mechanical layer, n—in a surface-micromachining
E2246 Test Method for Strain Gradient Measurements of
process, the patterned layer (as shown in Fig. 2) that is
Thin, Reflecting Films Using an Optical Interferometer
anchoredtotheunderlyinglayerwherecutsaredesignedinthe
3. Terminology
sacrificial layer and that is suspended in air where no cuts are
designed in the sacrificial layer.
3.1 Definitions:
3.1.11 MEMS, adj—microelectromechanical systems.
3.1.1 2-D data trace, n—a two-dimensional data trace that
3.1.12 out-of-plane, adj—perpendicular (in the z-direction)
is extracted from a topographical 3-D data set and that is
to the underlying layer.
parallel to the xz-or yz-plane of the interferometer.
3.1.13 out-of-plane measurements, n—measurements taken
3.1.1.1 Discussion—The height of the sample is measured
on structures that are curved out-of-plane in the z-direction.
along the z-axis of the interferometer. The interferometer’s
3.1.14 residual strain, n—inasurface-micromachiningpro-
x-axis (as shown in Figs. 1-3) is typically aligned parallel or
cess,thestrainpresentinthemechanicallayerafterfabrication
perpendicular to the transitional edges to be measured.
yet before the sacrificial layer is removed. In a bulk-
3.1.2 3-D data set, n—a three-dimensional data set with a
micromachining process, the strain present in the suspended
topographical z-data value for each (x, y) pixel location within
layer after fabrication yet before the substrate is removed at
the interferometer’s field of view.
specified locations.
3.1.15 sacrificial layer, n—in a surface-micromachining
This test method is under the jurisdiction ofASTM Committee E08 on Fatigue
process, the layer fabricated between the mechanical layer and
and Fracture and is the direct responsibility of Subcommittee E08.05 on Cyclic
the underlying layer.This layer is removed after fabrication. If
Deformation and Fatigue Crack Formation.
cuts are designed in this sacrificial layer (as shown in Fig. 2),
Current edition approved Oct. 10, 2002. Published November 2002.
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.
E2245–02
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.
FIG. 2 Design Dimensions for Fixed-Fixed Beam in Fig. 1
an anchor is created allowing the mechanical layer to contact 3.1.20 surface micromachining, adj—a MEMS fabrication
the underlying layer in that region. process where thin, sacrificial layers are removed, which can
create structures suspended in air.
3.1.16 stiction, n—in a surface-micromachining process, a
3.1.21 test structure, n—a structure (such as, a fixed-fixed
structure exhibits this when a non-anchored portion of the
beamorcantilever)thatisusedtoextractinformation(suchas,
mechanical layer adheres to the top of the underlying layer.
the residual strain or the strain gradient of a layer) about a
3.1.17 strain gradient, n—the positive difference in the
fabrication process.
strainbetweenthetopandbottomofacantileverdividedbyits
3.1.22 transitional edge, n—an edge of a MEMS structure
thickness.
(such as Edge “1” in Fig. 3) that is characterized by a
3.1.18 substrate, n—the thick, starting material in a MEMS
distinctiveout-of-planeverticaldisplacement(asshowninFig.
fabrication process.
5).
3.1.19 support region, n—in a bulk-micromachining pro-
3.1.23 underlying layer, n—in a surface-micromachining
cess, the region that marks the end of the suspended structure. process, the layer directly beneath the mechanical layer after
This region is suspended in air, attached to the substrate, or
the sacrificial layer is removed.
both. 3.2 Symbols:
E2245–02
NOTE 1—The 2-D data traces (“a” and “e”) are used to ensure alignment and determine L.
NOTE 2—Trace “c” is used to determine the residual strain and ascertain if the fixed-fixed beam is adhered to the top of the underlying layer.
NOTE 3—Traces “b,” “c,” and “d” are used in the calculation of u .
W
FIG. 3 Top View of Fixed-Fixed Beam
FIG. 4 Sketch of Optical Interferometer
3.2.1 For Calibration: mean = the mean value of the step-height measurements
cal-x = the x-calibration factor of the interferometer for the (on the double-sided step height standard) used to calculate
given combination of lenses
cal-z
cal-y = the y-calibration factor of the interferometer for the
ruler-x = theinterferometer’smaximumfieldofviewinthe
given combination of lenses
x-direction for the given combination of lenses as measured
cal-z = the z-calibration factor of the interferometer for the
with a 10-µm grid ruler
given combination of lenses
ruler-y = theinterferometer’smaximumfieldofviewinthe
cert = the certified value of the double-sided step height
y-direction for the given combination of lenses as measured
standard
with a 10-µm grid ruler
inter-x = theinterferometer’smaximumfieldofviewinthe
3.2.2 For Alignment:
x-direction for the given combination of lenses
x1 = the x-datavaluealongEdge“1”(suchasshownin
inter-y = theinterferometer’smaximumfieldofviewinthe
lower
y-direction for the given combination of lenses Fig. 5) locating the lower part of the transition
E2245–02
FIG. 5 2-D Data Trace Used to Find x1 , x1 , x2 , and x2
min max min max
x1 = the x-datavaluealongEdge“1”(suchasshownin A = the amplitude of the cosine function used to model
upper F
Fig. 5) locating the upper part of the transition curve #1 in Fig. 7
x2 = the x-datavaluealongEdge“2”(suchasshownin A = the amplitude of the cosine function used to model
S
lower
Fig. 5) locating the lower part of the transition curve #2 in Fig. 7
x2 = the x-datavaluealongEdge“2”(suchasshownin L = the total length of the curved fixed-fixed beam (as
c
upper
Fig. 5) locating the upper part of the transition modeled with two cosine functions) with x1 and x2 as the
ave ave
x values of the endpoints
x = the x-data value along the transitional edge of
lower
L = the length of the cosine function modeling curve #1
interest locating the lower part of the transition (see Fig. 5)
cF
in Fig. 7 with x1 and x as the x values of the endpoints
x = the x-data value along the transitional edge of
ave 3F
upper
L = thelengthofthecosinefunctionmodelingcurve#2in
interest locating the upper part of the transition (see Fig. 5)
cS
Fig. 7 with x and x2 as the x values of the endpoints
3.2.3 For In-plane Length Measurement:
1S ave
L 8 = the effective length of the fixed-fixed beam. This is a
L = the in-plane length measurement of the fixed-fixed
e
straight-line measurement between x and x
beam (see Fig. 2 or Fig. 3)
eF eS
L = the length of the fixed-fixed beam if there were no
L = the maximum in-plane length measurement of the
max
applied axial-compressive force
fixed-fixed beam (see Fig. 5)
s = equals 1 for fixed-fixed beams deflected in the −z-
L = the minimum in-plane length measurement of the
min
direction, and equals −1 for fixed-fixed beams deflected in the
fixed-fixed beam (see Fig. 5)
+z-direction
x1 = an endpoint of the in-plane length measurement
ave
t = the thickness of the suspended layer, such as shown in
(that is, the average of x1 and x1 )
min max
Fig. X2.1 (1-3) for a surface-micromachining process
x1 = the value for x1 used in the calculation of L
max upper max
t = in a bulk-micromachining process, the thickness
x1 = the value for x1 used in the calculation of L support
min lower min
of the support region where it is intersected by the 2-D data
x2 = the other endpoint of the in-plane length measure-
ave
trace of interest (such as, Trace “a” or “e” in Fig. X1.1, as
ment (that is, the average of x2 and x2 )
min max
shown in Fig. X1.2)
x2 = the value for x2 used in the calculation of L
max upper max
x = the x value of the inflection point of the cosine
eF
x2 = the value for x2 used in the calculation of L
min lower min
function modeling curve #1 in Fig. 7
3.2.4 For Residual Strain Measurement:
x = the x value of the inflection point of the cosine
eS
e = in a surface-micromachining process, the residual
r
function modeling curve #2 in Fig. 7
strain present in the mechanical layer after fabrication yet
z = the z-data value associated with x
upper upper
before the sacrificial layer is removed. The data in Figs. 5 and
6 are used for this calculation. In a bulk-micromachining
process, the residual strain present in the suspended layer after
fabrication yet before the substrate is removed at specified
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
locations. this standard.
E2245–02
FIG. 6 2-D Data Trace Along a Fixed-Fixed Beam
NOTE—The data above has been exaggerated.
FIG. 7 First and Second Curves Used to Find Residual Strain
z = in a bulk-micromachining process, the value for z e = in determining the combined standard uncertainty
upper-t r-low
when the thickness of the support region, t , is subtracted
value for the residual strain measurement, the lowest value for
support
from z
e given the specified variations
upper
r
3.2.5 For Combined Standard Uncertainty Calculations:
L = the total length of the curved fixed-fixed beam (as
c-max
e = in determining the combined standard uncertainty
r-high
modeledwithtwocosinefunctions)withx1 andx2 asthe
max max
valuefortheresidualstrainmeasurement,thehighestvaluefor
x values of the endpoints
e given the specified variations
r
E2245–02
L = the total length of the curved fixed-fixed beam (as 4.3 Tocalculatetheresidualstrain:(1)solvethreeequations
c-min
modeledwithtwocosinefunctions)with x1 and x2 asthe for three unknowns to obtain each cosine function, (2) plot the
min min
x values of the endpoints functions with the data, (3) calculate the length of the curved
u = the component in the combined standard uncertainty fixed-fixed beam, and (4) calculate the residual strain.
1pt
calculation that is due to the measurement uncertainty of one
5. Significance and Use
data point
u = the combined standard uncertainty value (that is, the 5.1 Residual strain measurements are an aid in the design
c
andfabricationofMEMSdevices.Thevalueforresidualstrain
estimated standard deviation of the result) (4).
u = the component in the combined standard uncertainty is used in Young’s modulus calculations.
L
calculation that is due to the measurement uncertainty of L
6. Interferences
u = the component in the combined standard uncertainty
W
6.1 Measurements from fixed-fixed beams that are touching
calculation that is due to the measurement uncertainty across
the width of the fixed-fixed beam the underlying layer (as ascertained in Appendix X2) are not
accepted.
w = the half width of the interval from e to e
1/2 r-low r-high
3.2.6 For Adherence to the Top of the Underlying Layer:
7. Apparatus
A = the minimum thickness of the mechanical layer as
7.1 Non-contact Optical Interferometer, capable of obtain-
measured from the top of the mechanical layer in the anchor
area (or region #2 in Fig. X2.2) to the top of the underlying ing a topographical 3-D data set and has software that can
export a 2-D data trace. Fig. 4 is a sketch of a suitable
layer (as shown in Fig. X2.1) and as specified in the reference
(3) non-contact optical interferometer. However, any non-contact
opticalinterferometerthathaspixel-to-pixelspacingsasspeci-
H = the anchor etch depth (as shown in Fig. X2.1). The
amount the underlying layer is etched away in the z-direction fied in Table 1 and that is capable of performing the test
during the patterning of the sacrificial layer.
J = this dimension (as shown in Fig. X2.1) incorporates j ,
TABLE 1 Interferometer Pixel-to-Pixel Spacing Requirements
a
j , j , and j , as shown in Figs. X2.3 and X2.4 (3)
b c d Magnification, 3 Pixel-to-pixel spacing, µm
j = the roughness of the underside of the suspended,
a
5 < 1.57
mechanicallayerinthe z-direction(asshowninFigs.X2.3and 10 < 0.83
20 < 0
...
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