ASTM E2244-11(2018)
(Test Method)Standard Test Method for In-Plane Length Measurements of Thin, Reflecting Films Using an Optical Interferometer (Withdrawn 2023)
Standard Test Method for In-Plane Length Measurements of Thin, Reflecting Films Using an Optical Interferometer (Withdrawn 2023)
SIGNIFICANCE AND USE
5.1 In-plane length measurements can be used in calculations of parameters, such as residual strain and Young's modulus.
5.2 In-plane deflection measurements are required for specific test structures. Parameters, including residual strain, are calculated given the in-plane deflection measurements.
SCOPE
1.1 This test method covers a procedure for measuring in-plane lengths (including deflections) of patterned thin films. It applies only to films, such as found in microelectromechanical systems (MEMS) materials, which can be imaged using an optical interferometer, also called an interferometric microscope.
1.2 There are other ways to determine in-plane lengths. Using the design dimensions typically provides more precise in-plane length values than using measurements taken with an optical interferometric microscope. (Interferometric measurements are typically more precise than measurements taken with an optical microscope.) This test method is intended for use when interferometric measurements are preferred over using the design dimensions (for example, when measuring in-plane deflections and when measuring lengths in an unproven fabrication process).
1.3 This test method uses a non-contact optical interferometric microscope with the capability of obtaining topographical 3-D data sets. It is performed in the laboratory.
1.4 The maximum in-plane length measured is determined by the maximum field of view of the interferometric microscope at the lowest magnification. The minimum deflection measured is determined by the interferometric microscope’s pixel-to-pixel spacing at the highest magnification.
1.5 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
WITHDRAWN RATIONALE
This test method covers a procedure for measuring in-plane lengths (including deflections) of patterned thin films. It applies only to films, such as found in microelectromechanical systems (MEMS) materials, which can be imaged using an optical interferometer, also called an interferometric microscope.
Formerly under the jurisdiction of Committee E08 on Fatigue and Fracture, this test method was withdrawn in November 2023. This standard is being withdrawn without replacement due to its limited use by industry.
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This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation:E2244 −11 (Reapproved 2018)
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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This test method covers a procedure for measuring
in-plane lengths (including deflections) of patterned thin films.
2. Referenced Documents
It applies only to films, such as found in microelectromechani-
2.1 ASTM Standards:
cal systems (MEMS) materials, which can be imaged using an
optical interferometer, also called an interferometric micro- E2245Test Method for Residual Strain Measurements of
Thin, Reflecting Films Using an Optical Interferometer
scope.
E2246Test Method for Strain Gradient Measurements of
1.2 There are other ways to determine in-plane lengths.
Thin, Reflecting Films Using an Optical Interferometer
Using the design dimensions typically provides more precise
E2444Terminology Relating to Measurements Taken on
in-plane length values than using measurements taken with an
Thin, Reflecting Films
optical interferometric microscope. (Interferometric measure-
E2530Practice for Calibrating the Z-Magnification of an
mentsaretypicallymoreprecisethanmeasurementstakenwith
Atomic Force Microscope at Subnanometer Displacement
an optical microscope.) This test method is intended for use
Levels Using Si(111) Monatomic Steps (Withdrawn
when interferometric measurements are preferred over using
2015)
the design dimensions (for example, when measuring in-plane
2.2 SEMI Standard:
deflections and when measuring lengths in an unproven fabri-
MS2Test Method for Step Height Measurements of Thin
cation process).
Films
1.3 This test method uses a non-contact optical interfero-
metricmicroscopewiththecapabilityofobtainingtopographi-
3. Terminology
cal 3-D data sets. It is performed in the laboratory.
3.1 Definitions:
1.4 The maximum in-plane length measured is determined
3.1.1 The following terms can be found in Terminology
by the maximum field of view of the interferometric micro-
E2444.
scope at the lowest magnification. The minimum deflection
3.1.2 2-D data trace, n—a two-dimensional group of points
measured is determined by the interferometric microscope’s
that is extracted from a topographical 3-D data set and that is
pixel-to-pixel spacing at the highest magnification.
parallel to the xz-or yz-plane of the interferometric micro-
1.5 This standard does not purport to address all of the
scope.
safety concerns, if any, associated with its use. It is the
3.1.3 3-D data set, n—a three-dimensional group of points
responsibility of the user of this standard to establish appro-
with a topographical z-value for each (x, y) pixel location
priate safety, health, and environmental practices and deter-
within the interferometric microscope’s field of view.
mine the applicability of regulatory limitations prior to use.
3.1.4 anchor, n—in a surface-micromachining process, the
1.6 This international standard was developed in accor-
portion of the test structure where a structural layer is inten-
dance with internationally recognized principles on standard-
tionally attached to its underlying layer.
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
This test method is under the jurisdiction ofASTM Committee E08 on Fatigue Standards volume information, refer to the standard’s Document Summary page on
and Fracture and is the direct responsibility of Subcommittee E08.05 on Cyclic the ASTM website.
Deformation and Fatigue Crack Formation. The last approved version of this historical standard is referenced on
Current edition approved May 1, 2018. Published May 2018. Originally www.astm.org.
ɛ1 4
approved in 2002. Last previous edition approved in 2011 as E2244–11 . DOI: For referenced Semiconductor Equipment and Materials International (SEMI)
10.1520/E2244–11R18. standards, visit the SEMI website, www.semi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2244−11 (2018)
3.1.5 anchor lip, n—in a surface-micromachining process, 3.2.1 For Calibration: σ =the standard deviation in a
xcal
the freestanding extension of the structural layer of interest ruler measurement in the interferometric microscope’s
around the edges of the anchor to its underlying layer. x-direction for the given combination of lenses
3.1.5.1 Discussion—In some processes, the width of the σ =the standard deviation in a ruler measurement in the
ycal
anchor lip may be zero. interferometric microscope’s y-direction for the given combi-
nation of lenses
3.1.6 bulk micromachining, adj—a MEMS fabrication pro-
cal =the x-calibration factor of the interferometric micro-
x
cess where the substrate is removed at specified locations.
scope for the given combination of lenses
3.1.7 cantilever, n—a test structure that consists of a free-
cal =the y-calibration factor of the interferometric micro-
y
standing beam that is fixed at one end.
scope for the given combination of lenses
3.1.8 fixed-fixed beam, n—a test structure that consists of a
cal =the z-calibration factor of the interferometric micro-
z
freestanding beam that is fixed at both ends.
scope for the given combination of lenses
3.1.9 in-plane length (or deflection) measurement, n—the
cert=the certified (that is, calibrated) value of the physical
experimental determination of the straight-line distance be-
step height standard
tween two transitional edges in a MEMS device.
ruler =the interferometric microscope’s maximum field of
x
3.1.9.1 Discussion—This length (or deflection) measure- view in the x-direction for the given combination of lenses as
ment is made parallel to the underlying layer (or the xy-plane
measured with a 10-µm grid (or finer grid) ruler
of the interferometric microscope).
ruler =the interferometric microscope’s maximum field of
y
view in the y-direction for the given combination of lenses as
3.1.10 interferometer, n—a non-contact optical instrument
measured with a 10-µm grid (or finer grid) ruler
used to obtain topographical 3-D data sets.
scope =the interferometric microscope’s maximum field of
3.1.10.1 Discussion—The height of the sample is measured x
view in the x-direction for the given combination of lenses
along the z-axis of the interferometer. The x-axis is typically
scope =the interferometric microscope’s maximum field of
aligned parallel or perpendicular to the transitional edges to be y
view in the y-direction for the given combination of lenses
measured.
z¯ =the average of the calibration measurements taken
ave
3.1.11 MEMS, adj—microelectromechanical systems.
alongthephysicalstepheightstandardbeforeandafterthedata
3.1.12 microelectromechanical systems, adj—in general,
session
this term is used to describe micron-scale structures, sensors,
3.2.2 For In-plane Length Measurement: α=the misalign-
actuators,andtechnologiesusedfortheirmanufacture(suchas,
ment angle
silicon process technologies), or combinations thereof.
σ =the in-plane length repeatability standard de-
repeat(samp)'
3.1.13 sacrificial layer, n—a single thickness of material
viation (for the given combination of lenses for the given
that is intentionally deposited (or added) then removed (in
interferometric microscope) as obtained from test structures
whole or in part) during the micromachining process, to allow
fabricated in a process similar to that used to fabricate the
freestanding microstructures.
sample and for the same or a similar type of measurement
L=the in-plane length measurement that accounts for mis-
3.1.14 structural layer, n—a single thickness of material
alignment and includes the in-plane length correction term,
present in the final MEMS device.
L
offset
3.1.15 substrate, n—thethick,startingmaterial(oftensingle
L = the in-plane length, after correcting for
align
crystalsiliconorglass)inafabricationprocessthatcanbeused
misalignment, used to calculate L
to build MEMS devices.
L =the measured in-plane length used to calculate L
meas align
3.1.16 support region, n—in a bulk-micromachining
L =thein-planelengthcorrectiontermforthegiventype
offset
process,theareathatmarkstheendofthesuspendedstructure.
of in-plane length measurement on similar structures, when
3.1.17 surface micromachining, adj—a MEMS fabrication
using similar calculations, and for a given magnification of a
process where micron-scale components are formed on a
given interferometric microscope
substratebythedeposition(oraddition)andremoval(inwhole
n1 =indicative of the data point uncertainty associated with
t
or in part) of structural and sacrificial layers.
the chosen value for x1 , with the subscript “t” referring to
uppert
the data trace. If it is easy to identify one point that accurately
3.1.18 test structure, n—acomponent(suchas,afixed-fixed
locates the upper corner of Edge 1, the maximum uncertainty
beamorcantilever)thatisusedtoextractinformation(suchas,
associated with the identification of this point is n1x cal ,
the residual strain or the strain gradient of a layer) about a
t res x
where n1=1.
fabrication process. t
n2 =indicative of the data point uncertainty associated with
t
3.1.19 transitional edge, n—the side of a MEMS structure
the chosen value for x2 , with the subscript “t” referring to
uppert
that is characterized by a distinctive out-of-plane vertical
the data trace. If it is easy to identify one point that accurately
displacement as seen in an interferometric 2-D data trace.
locates the upper corner of Edge 2, the maximum uncertainty
3.1.20 underlying layer, n—the single thickness of material
associated with the identification of this point is n2x cal ,
t res x
directly beneath the material of interest.
where n2=1.
t
3.1.20.1 Discussion—This layer could be the substrate.
U =the expanded uncertainty of an in-plane length mea-
L
3.2 Symbols: surement
E2244−11 (2018)
FIG. 1Three-Dimensional View of Surface-Micromachined Fixed-Fixed Beam
u =the component in the combined standard uncertainty 3.2.3 For Round Robin Measurements: ∆L=for the given
align
calculation for an in-plane length measurement that is due to value of L , L minus L
des ave des
alignment uncertainty
∆L =theaveragevalueof∆Loverthegivenrangeof L
ave des
u =the combined standard uncertainty for an in-plane
cL values
length measurement
L =the average in-plane length value for the repeatability
ave
u =the component in the combined standard uncertainty
L
or reproducibility measurements that is equal to the sum of the
calculation for an in-plane length measurement that is due to
L values divided by n
the uncertainty in the calculated length
L =the design length
des
u =the component in the combined standard uncertainty
offset
mag=the magnification used for the measurement
calculation for an in-plane length measurement that is due to
n=the number of repeatability or reproducibility measure-
the uncertainty of the value for L
offset
u =the component in the combined standard uncer- ments
repeat(L)
tainty calculation for an in-plane length measurement that is
u =theaveragecombinedstandarduncertaintyvaluefor
cLave
due to the uncertainty of the four measurements taken on the
thein-planelengthmeasurementsthatisequaltothesumofthe
test structure at different locations
u values divided by n
cL
u =the component in the combined standard un-
repeat(samp)
3.2.4 Discussion—The symbols above are used throughout
certaintycalculationforanin-planelengthmeasurementthatis
this test method. However, the letter “D” can replace the letter
due to the repeatability of measurements taken on test struc-
“L” in the symbols above when referring to in-plane deflection
tures processed similarly to the sample, using the same
measurements,whichwouldimplyreplacingtheword“length”
combinationoflensesforthegiveninterferometricmicroscope
with the word “deflection.” Also, when referring to y values,
for the measurement, and for the same or a similar type of
the letter “y” can replace the first letter in the symbols (or the
measurement
subscript of the symbols) above that start with the letter “x.”
u =the component in the combined standard uncertainty
xcal
calculation for an in-plane length measurement that is due to
4. Summary of Test Method
the uncertainty of the calibration in the x-direction
4.1 Any in-plane length measurement can be made if each
x1 =the uncalibrated x-value that most appropriately
uppert
locates the upper corner associated with Edge 1 using Trace t end is defined by a transitional edge. Consider the surface-
x2 =the uncalibrated x-value that most appropriately micromachined fixed-fixed beam shown in Figs. 1 and 2.An
uppert
locates the upper corner associated with Edge 2 using Trace t optical interferometric microscope (such as shown in Fig. 3)is
x =the uncalibrated resolution of the interferometric mi- used to obtain a topographical 3-D data set. Four 2-D data
res
croscope in the x-direction for the given combination of lenses traces(oneofwhichisshowninFig.4)areextractedfromthis
y =the uncalibrated y-value associated with Trace a' 3-D data set for the analysis of the transitional edges of
a'
y =the uncalibrated y-value associated with Trace e' interest.
e'
E2244−11 (2018)
NOTE 1—The underlying layer is beneath this test structure.
NOTE 2—The structural layer of interest is included in both the light and dark gray areas.
NOTE 3—The light gray area is suspended in air after fabrication.
NOTE4—Thedarkgrayareas(theanchors)arethedesignedcutsinthesacrificiallayer.Thisiswherethestructurallayercontactstheunderlyinglayer.
NOTE 5—The 2-D data traces (a' and e') are used to determine the misalignment angle, α.
NOTE 6—The 2-D data traces (a', a, e, and e' ) are used to determine L.
FIG. 2Top View of Fixed-Fixed Beam in Fig. 1
FIG. 3Schematic of an Optical Interferometric Microscope
4.2 To obtain the endpoints of the in-plane length measure- α, is calculated from the data obtained from the two outermost
ment for a surface-micromachined structure, four steps are datatrac
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2244 − 11 (Reapproved 2018)
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. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This test method covers a procedure for measuring
in-plane lengths (including deflections) of patterned thin films.
2. Referenced Documents
It applies only to films, such as found in microelectromechani-
cal systems (MEMS) materials, which can be imaged using an 2.1 ASTM Standards:
E2245 Test Method for Residual Strain Measurements of
optical interferometer, also called an interferometric micro-
scope. Thin, Reflecting Films Using an Optical Interferometer
E2246 Test Method for Strain Gradient Measurements of
1.2 There are other ways to determine in-plane lengths.
Thin, Reflecting Films Using an Optical Interferometer
Using the design dimensions typically provides more precise
E2444 Terminology Relating to Measurements Taken on
in-plane length values than using measurements taken with an
Thin, Reflecting Films
optical interferometric microscope. (Interferometric measure-
E2530 Practice for Calibrating the Z-Magnification of an
ments are typically more precise than measurements taken with
Atomic Force Microscope at Subnanometer Displacement
an optical microscope.) This test method is intended for use
Levels Using Si(111) Monatomic Steps (Withdrawn
when interferometric measurements are preferred over using
2015)
the design dimensions (for example, when measuring in-plane
2.2 SEMI Standard:
deflections and when measuring lengths in an unproven fabri-
MS2 Test Method for Step Height Measurements of Thin
cation process).
Films
1.3 This test method uses a non-contact optical interfero-
metric microscope with the capability of obtaining topographi-
3. Terminology
cal 3-D data sets. It is performed in the laboratory.
3.1 Definitions:
1.4 The maximum in-plane length measured is determined
3.1.1 The following terms can be found in Terminology
by the maximum field of view of the interferometric micro-
E2444.
scope at the lowest magnification. The minimum deflection
3.1.2 2-D data trace, n—a two-dimensional group of points
measured is determined by the interferometric microscope’s
that is extracted from a topographical 3-D data set and that is
pixel-to-pixel spacing at the highest magnification.
parallel to the xz- or yz-plane of the interferometric micro-
1.5 This standard does not purport to address all of the
scope.
safety concerns, if any, associated with its use. It is the
3.1.3 3-D data set, n—a three-dimensional group of points
responsibility of the user of this standard to establish appro-
with a topographical z-value for each (x, y) pixel location
priate safety, health, and environmental practices and deter-
within the interferometric microscope’s field of view.
mine the applicability of regulatory limitations prior to use.
3.1.4 anchor, n—in a surface-micromachining process, the
1.6 This international standard was developed in accor-
portion of the test structure where a structural layer is inten-
dance with internationally recognized principles on standard-
tionally attached to its underlying layer.
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
This test method is under the jurisdiction of ASTM Committee E08 on Fatigue Standards volume information, refer to the standard’s Document Summary page on
and Fracture and is the direct responsibility of Subcommittee E08.05 on Cyclic the ASTM website.
Deformation and Fatigue Crack Formation. The last approved version of this historical standard is referenced on
Current edition approved May 1, 2018. Published May 2018. Originally www.astm.org.
ɛ1 4
approved in 2002. Last previous edition approved in 2011 as E2244 – 11 . DOI: For referenced Semiconductor Equipment and Materials International (SEMI)
10.1520/E2244–11R18. standards, visit the SEMI website, www.semi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2244 − 11 (2018)
3.1.5 anchor lip, n—in a surface-micromachining process, 3.2.1 For Calibration: σ = the standard deviation in a
xcal
the freestanding extension of the structural layer of interest ruler measurement in the interferometric microscope’s
around the edges of the anchor to its underlying layer. x-direction for the given combination of lenses
3.1.5.1 Discussion—In some processes, the width of the σ = the standard deviation in a ruler measurement in the
ycal
anchor lip may be zero. interferometric microscope’s y-direction for the given combi-
nation of lenses
3.1.6 bulk micromachining, adj—a MEMS fabrication pro-
cal = the x-calibration factor of the interferometric micro-
cess where the substrate is removed at specified locations. x
scope for the given combination of lenses
3.1.7 cantilever, n—a test structure that consists of a free-
cal = the y-calibration factor of the interferometric micro-
y
standing beam that is fixed at one end.
scope for the given combination of lenses
3.1.8 fixed-fixed beam, n—a test structure that consists of a
cal = the z-calibration factor of the interferometric micro-
z
freestanding beam that is fixed at both ends.
scope for the given combination of lenses
3.1.9 in-plane length (or deflection) measurement, n—the cert = the certified (that is, calibrated) value of the physical
experimental determination of the straight-line distance be- step height standard
tween two transitional edges in a MEMS device.
ruler = the interferometric microscope’s maximum field of
x
3.1.9.1 Discussion—This length (or deflection) measure-
view in the x-direction for the given combination of lenses as
ment is made parallel to the underlying layer (or the xy-plane measured with a 10-µm grid (or finer grid) ruler
of the interferometric microscope).
ruler = the interferometric microscope’s maximum field of
y
view in the y-direction for the given combination of lenses as
3.1.10 interferometer, n—a non-contact optical instrument
measured with a 10-µm grid (or finer grid) ruler
used to obtain topographical 3-D data sets.
scope = the interferometric microscope’s maximum field of
3.1.10.1 Discussion—The height of the sample is measured
x
view in the x-direction for the given combination of lenses
along the z-axis of the interferometer. The x-axis is typically
scope = the interferometric microscope’s maximum field of
aligned parallel or perpendicular to the transitional edges to be
y
view in the y-direction for the given combination of lenses
measured.
z¯ = the average of the calibration measurements taken
ave
3.1.11 MEMS, adj—microelectromechanical systems.
along the physical step height standard before and after the data
3.1.12 microelectromechanical systems, adj—in general,
session
this term is used to describe micron-scale structures, sensors,
3.2.2 For In-plane Length Measurement: α = the misalign-
actuators, and technologies used for their manufacture (such as,
ment angle
silicon process technologies), or combinations thereof.
σ = the in-plane length repeatability standard de-
repeat(samp)'
3.1.13 sacrificial layer, n—a single thickness of material
viation (for the given combination of lenses for the given
that is intentionally deposited (or added) then removed (in
interferometric microscope) as obtained from test structures
whole or in part) during the micromachining process, to allow
fabricated in a process similar to that used to fabricate the
freestanding microstructures.
sample and for the same or a similar type of measurement
L = the in-plane length measurement that accounts for mis-
3.1.14 structural layer, n—a single thickness of material
alignment and includes the in-plane length correction term,
present in the final MEMS device.
L
offset
3.1.15 substrate, n—the thick, starting material (often single
L = the in-plane length, after correcting for
align
crystal silicon or glass) in a fabrication process that can be used
misalignment, used to calculate L
to build MEMS devices.
L = the measured in-plane length used to calculate L
meas align
3.1.16 support region, n—in a bulk-micromachining
L = the in-plane length correction term for the given type
offset
process, the area that marks the end of the suspended structure.
of in-plane length measurement on similar structures, when
3.1.17 surface micromachining, adj—a MEMS fabrication
using similar calculations, and for a given magnification of a
process where micron-scale components are formed on a
given interferometric microscope
substrate by the deposition (or addition) and removal (in whole
n1 = indicative of the data point uncertainty associated with
t
or in part) of structural and sacrificial layers.
the chosen value for x1 , with the subscript “t” referring to
uppert
the data trace. If it is easy to identify one point that accurately
3.1.18 test structure, n—a component (such as, a fixed-fixed
locates the upper corner of Edge 1, the maximum uncertainty
beam or cantilever) that is used to extract information (such as,
associated with the identification of this point is n1 x cal ,
the residual strain or the strain gradient of a layer) about a t res x
where n1 =1.
fabrication process.
t
n2 = indicative of the data point uncertainty associated with
t
3.1.19 transitional edge, n—the side of a MEMS structure
the chosen value for x2 , with the subscript “t” referring to
uppert
that is characterized by a distinctive out-of-plane vertical
the data trace. If it is easy to identify one point that accurately
displacement as seen in an interferometric 2-D data trace.
locates the upper corner of Edge 2, the maximum uncertainty
3.1.20 underlying layer, n—the single thickness of material
associated with the identification of this point is n2 x cal ,
t res x
directly beneath the material of interest.
where n2 =1.
t
3.1.20.1 Discussion—This layer could be the substrate.
U = the expanded uncertainty of an in-plane length mea-
L
3.2 Symbols: surement
E2244 − 11 (2018)
FIG. 1 Three-Dimensional View of Surface-Micromachined Fixed-Fixed Beam
u = the component in the combined standard uncertainty 3.2.3 For Round Robin Measurements: ΔL = for the given
align
calculation for an in-plane length measurement that is due to value of L , L minus L
des ave des
alignment uncertainty
ΔL = the average value of ΔL over the given range of L
ave des
u = the combined standard uncertainty for an in-plane
cL values
length measurement
L = the average in-plane length value for the repeatability
ave
u = the component in the combined standard uncertainty
L
or reproducibility measurements that is equal to the sum of the
calculation for an in-plane length measurement that is due to
L values divided by n
the uncertainty in the calculated length
L = the design length
des
u = the component in the combined standard uncertainty
offset
mag = the magnification used for the measurement
calculation for an in-plane length measurement that is due to
n = the number of repeatability or reproducibility measure-
the uncertainty of the value for L
offset
ments
u = the component in the combined standard uncer-
repeat(L)
tainty calculation for an in-plane length measurement that is
u = the average combined standard uncertainty value for
cLave
due to the uncertainty of the four measurements taken on the
the in-plane length measurements that is equal to the sum of the
test structure at different locations
u values divided by n
cL
u = the component in the combined standard un-
repeat(samp)
3.2.4 Discussion—The symbols above are used throughout
certainty calculation for an in-plane length measurement that is
this test method. However, the letter “D” can replace the letter
due to the repeatability of measurements taken on test struc-
“L” in the symbols above when referring to in-plane deflection
tures processed similarly to the sample, using the same
measurements, which would imply replacing the word “length”
combination of lenses for the given interferometric microscope
with the word “deflection.” Also, when referring to y values,
for the measurement, and for the same or a similar type of
the letter “y” can replace the first letter in the symbols (or the
measurement
subscript of the symbols) above that start with the letter “x.”
u = the component in the combined standard uncertainty
xcal
calculation for an in-plane length measurement that is due to
4. Summary of Test Method
the uncertainty of the calibration in the x-direction
x1 = the uncalibrated x-value that most appropriately 4.1 Any in-plane length measurement can be made if each
uppert
end is defined by a transitional edge. Consider the surface-
locates the upper corner associated with Edge 1 using Trace t
x2 = the uncalibrated x-value that most appropriately micromachined fixed-fixed beam shown in Figs. 1 and 2. An
uppert
locates the upper corner associated with Edge 2 using Trace t optical interferometric microscope (such as shown in Fig. 3) is
x = the uncalibrated resolution of the interferometric mi- used to obtain a topographical 3-D data set. Four 2-D data
res
croscope in the x-direction for the given combination of lenses traces (one of which is shown in Fig. 4) are extracted from this
y = the uncalibrated y-value associated with Trace a' 3-D data set for the analysis of the transitional edges of
a'
y = the uncalibrated y-value associated with Trace e' interest.
e'
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NOTE 1—The underlying layer is beneath this test structure.
NOTE 2—The structural layer of interest is included in both the light and dark gray areas.
NOTE 3—The light gray area is suspended in air after fabrication.
NOTE 4—The dark gray areas (the anchors) are the designed cuts in the sacrificial layer. This is where the structural layer contacts the underlying layer.
NOTE 5—The 2-D data traces (a' and e') are used to determine the misalignment angle, α.
NOTE 6—The 2-D data traces (a', a, e, and e' ) are used to determine L.
FIG. 2 Top View of Fixed-Fixed Beam in Fig. 1
FIG. 3 Schematic of an Optical Interferometric Microscope
4.2 To obtain the endpoints of the in-plane length me
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