Data
analysis sheet for residual strain
measurements
Figure
RS.1.1.
Top view of fixed-fixed beam used to
measure residual strain.
To obtain the
following measurements, consult ASTM
standard test method E 2245 entitled
"Standard Test Method for Residual
Strain Measurements of Thin,
Reflecting Films
Using an Optical Interferometer."
date data taken (optional) =
/
/
identifying words (optional)
=
instrument used (optional)
=
fabrication facility/process
(optional) =
test chip name (optional)
=
test chip number (optional)
=
filename of 3-D data set
(optional) =
filename of 2-D data traces
(optional) =
Table 1 - Preliminary
ESTIMATES
Description
1
material =
material
2
t =
μm
beam thickness
3
design length =
μm
design
length
4
design width =
μm
design width (needed for test
structure identification purposes only)
5
which beam?
which fixed-fixed beam on the test
chip, where "first" corresponds to the topmost fixed-fixed
beam in the column or array that has the specified length?
6
magnification =
×
magnification
7
orientation =
0°
90°
other
orientation of the fixed-fixed beam on
the chip
8
calx =
x-calibration factor (for the given magnification)
9
interx
=
μm
maximum field of view (for the given
magnification)
10
σxcal =
μm
one sigma
uncertainty in a ruler
measurement (for the given
magnification)
11
xres
=
μm
uncalibrated resolution
of the interferometer in the
x-direction
12
calz =
z-calibration factor (for the given magnification)
13
cert =
μm
certified value of physical step
height used for calibration
14
σzcal
=
μm
standard deviation of step height
measurements (on double-sided physical step height)
15
zres
=
μm
calibrated resolution
of the interferometer in the
z-direction
16
Rtave
=
μm
calibrated peak-to-valley roughness of a flat and
leveled surface of the sample material calculated to be the
average of three or more measurements, each measurement of
which is taken from a different 2-D data trace
17
aligned?
alignment ensured ?
18
leveled?
data leveled ?
19
stiction?
Is this fixed-fixed beam exhibiting
stiction ?
(If
it is exhibiting stiction, do not fill out the remainder of
this form.)
Table 2 -
INPUTS
(uncalibrated values from Trace
"a" or "e")
Notes
20
x1max
(i.e., x1upper)
=
μm
21
x1min
(i.e., x1lower)
=
μm
(x1min > x1max)
22
x2min
(i.e., x2lower)
=
μm
(x2min > x1min)
23
x2max
(i.e., x2upper)
=
μm
(x2max > x2min)
Table 3 -
INPUTS
(uncalibrated values from Trace
"b")
Notes
24
x1F
=
μm
z1F =
μm
(x1ave
< x1F calx)
25
x2F
=
μm
z2F
=
μm
(inflection point)
( x1F <
x2F
< x3F )
26
x3F
=
μm
z3F
=
μm
(most deflected point) (
x1S = x3F
; z1S
= z3F
)
27
x2S
=
μm
z2S
=
μm
(inflection point)
28
x3S
=
μm
z3S
=
μm
(
x3S calx <
x2ave
)(
x1S < x2S
< x3S )
Table 4 -
INPUTS
(uncalibrated values from Trace
"c")
Notes
29
x1F
=
μm
z1F
=
μm
(x1ave
< x1F calx)
30
x2F
=
μm
z2F
=
μm
(inflection point)(
x1F < x2F
< x3F )
31
x3F
=
μm
z3F
=
μm
(most deflected point)(
x1S = x3F
; z1S = z3F
)
32
x2S
=
μm
z2S
=
μm
(inflection point)
33
x3S
=
μm
z3S
=
μm
(
x3S calx
< x2ave )(
x1S < x2S
< x3S )
Table 5 -
INPUTS
(uncalibrated values from Trace
"d")
AF= μm from Trace "b"
w1F= from
Trace "b"
AS=
μm
from Trace "b"
w3S=from Trace "b"
xeF=
μm
from Trace "b"
xeS=
μm
from Trace "b"
εr0
=
× 10-6
from Trace "b"
εr
=× 10-6
from Trace "b"
AF=
μm from Trace "c"
w1F= from Trace "c"
AS=
μm
from Trace "c"
w3S= from Trace "c"
xeF= μm
from Trace "c"
xeS= μm
from Trace "c"
εr0=
× 10-6 from
Trace "c" εr=× 10-6 from
Trace "c"(USE THIS VALUE)
usamp=× 10-6 from
Trace "c"
uW =× 10-6
from two or three traces
uxcal= × 10-6
from Trace "c" uL=× 10-6
from Trace "c"
uzcal=× 10-6 from
Trace "c"
uzres =× 10-6 from
Trace "c"
uxres =× 10-6 from
Trace "c"
uxresL =× 10-6 from
Trace "c"
ucer= SQRT[usamp2
+ uW2
+ uxcal2
+ uL2
+ uzcal2
+ uzres2
+ uxres2
+ uxresL2]
(Each of the standard
uncertainty components is
obtained using a Type B
analysis.) ucer =× 10-6 from
two or three traces
AF=
μm from Trace "d"
w1F= from
Trace "d"
AS=
μm
from Trace "d"
w3S= from Trace "d"
xeF=
μm
from Trace "d"
xeS= μm
from Trace "d"
εr0
=
× 10-6
from Trace "d"
εr
=× 10-6 from
Trace "d"
Report the results as follows: Since it can be assumed that the
estimated values of the
uncertainty components are
approximately uniformly
or Gaussianly distributed with
approximate combined standard
uncertainty
ucer, the residual strain is believed to lie in the
interval
er
±
ucer
(expansion factor k=1)
representing a level of
confidence of approximately 68 %.
Modify the
input data, given the
information supplied in any
flagged statement below, if
applicable, then recalculate:
1.
Please fill
out the entire form.
2.
The value
for
t should be between
0.000
μm
and 10.000
μm.
3.
The value
for the design length should be
between
0
μm
and 1000
μm.
4.
The measured
value for
L is more than 3ucL
from the design length.
5.
The value
for the design width should be
between 0
μm
and 60
μm.
6.
Is the
magnification appropriate given
the design length ?
7.
Magnifications at or
less than
2.5× shall not be used.
8.
Is 0.95 < calx<
1.05 but not equal to
"1"? If not,
recheck your
x-calibration.
9.
The value for
interxshould be between 0
μm
and 1500
μm.
10.
The value for
σxcal should be between 0
μm
and 4
μm.
11.
The value for
xres should be between 0
μm
and 2.00
μm.
12.
Is 0.95 <
calz< 1.05 but not
equal to "1" ? If not,
recheck your
z-calibration.
13.
The value
for cert should be
greater than 0 μm and less than
25 μm.
14.
The value for
σzcal
should be between 0
μm
and 0.050
μm.
15.
The value
for
zresshould be greater than 0 μm
and less than or equal to 0.005
μm.
16.
The value for
Rtave
should be between 0
μm
and 0.100
μm.
17.
Alignment
has not been ensured.
18.
Data has not
been leveled.
19.
x1minshould be greater
than x1max.
20.
x2minshould be greater
than
x1min.
21.
x2maxshould be greater
than
x2min.
22.
The
calibrated values for
x1minand
x1maxare
greater than 10 μm apart.
23.
The
calibrated values for
x2minand
x2max
are greater
than 10 μm apart.
24.
In Traces
"b," "c," and "d," the value for
s is not the same.
25.
x1ave
should be
< (x1F calx) in all
traces.
26.
(x3S calx) should be <
x2ave
in all
traces.
27.
In
all traces, make sure (
x1F
< x2F < x3F ).
28.
In
all traces, make sure (
x1S
< x2S < x3S
).
29.
For Trace
"b," | [(x2F calx)
− xeF] | =μm. This
should be < 5 μm. If it is not, choose
(x2F,
z2F)
such that (x2F
calx) is closer to
xeF
=
μm.
30.
For Trace
"b," | [(x2S calx)
− xeS] |
=
μm. This should be < 5 μm. If it is not, choose
(x2S,
z2S)
such that (x2S
calx) is closer to
xeS
=
μm.
31.
For Trace
"c," | [(x2F calx)
− xeF] | =μm. This
should be < 5 μm. If it is not, choose
(x2F,
z2F)
such that (x2F
calx) is closer to
xeF
=
μm.
32.
For Trace
"c," | [(x2S calx)
− xeS] | =μm. This
should be < 5 μm. If it is not, choose
(x2S,
z2S)
such that (x2S
calx) is closer to
xeS
=
μm.
33.
For Trace "d," | [(x2F calx)
− xeF] | =
μm. This should be
< 5 μm. If it is not, choose
(x2F,
z2F)
such that (x2Fcalx) is closer
to xeF
=
μm.
34.
For Trace "d," | [(x2S calx)
− xeS] | =
μm. This
should be < 5 μm. If it is not, choose
(x2S,
z2S)
such that (x2S
calx) is closer to
xeS
=
μm.
