Data
analysis sheet for strain gradient
measurements
Figure
SG.1.1.
Top view of cantilever test
structure used to measure strain
gradient.
To obtain the
following measurements, consult ASTM
standard test method E 2246 entitled
"Standard Test Method for Strain
Gradient 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
design length =
μm
design
length
3
design width =
μm
design width (needed for test
structure identification purposes only)
4
which cantilever?
which cantilever on the test chip,
where "first" corresponds to the topmost cantilever in the
column or array that has the specified length?
5
magnification =
×
magnification
6
orientation =
orientation of the cantilever on the
chip
7
calx =
x-calibration factor (for the given magnification)
8
interx
=
μm
maximum field of view (for the given
magnification)
9
σxcal =
μm
one sigma
uncertainty in a ruler
measurement (for the given
magnification)
10
xres
=
μm
uncalibrated resolution
of the interferometer in the
x-direction
11
calz =
z-calibration factor (for the given magnification)
12
cert =
μm
certified value of double-sided
physical step height used for calibration
13
σzcal
=
μm
standard deviation of step height
measurements (on double-sided physical step height)
14
zres
=
μm
calibrated resolution
of the interferometer in the
z-direction
15
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
16
aligned?
Yes
No
alignment ensured ?
17
leveled?
Yes
No
data leveled ?
18
stiction?
Yes
No
Is this cantilever 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
19
x1max
(i.e., x1upper)
=
μm
20
x1min
(i.e., x1lower)
=
μm
(x1min > x1max)
Table 3 -
INPUTS (uncalibrated values from Trace "b")
Notes
21
x1
=
μm
z1
=
μm
(x1ave <
x1 calx)
22
x2
=
μm
z2
=
μm
(x1ave <
x2 calx)
23
x3
=
μm
z3
=
μm
(x1ave <
x3 calx)
Table 4 -
INPUTS (uncalibrated values from Trace "c")
Notes
24
x1
=
μm
z1
=
μm
(x1ave <
x1 calx)
25
x2
=
μm
z2
=
μm
(x1ave <
x2 calx)
26
x3
=
μm
z3
=
μm
(x1ave <
x3 calx)
Table 5 -
INPUTS (uncalibrated values from Trace "d")
Notes
27
x1
=
μm
z1
=
μm
(x1ave <
x1 calx)
28
x2
=
μm
z2
=
μm
(x1ave <
x2 calx)
29
x3
=
μm
z3
=
μm
(x1ave <
x3 calx)
OUTPUTS (calibrated
values):
x1ave
=
μm
s =
from Trace "c"
s = 1 (for downward bending
cantilevers or
if data was taken from the
bottom of an upward bending
cantilever)
s = −1 (for upward bending
cantilevers unless
data was taken from the bottom
of an upward bending cantilever)
Rint
=
μm from Trace
"b"
a
=
μm from Trace
"b" b
=
μm from Trace
"b"
sg=
m−1
from Trace "b"
Rint
=
μm from Trace
"c"
a
=
μm from Trace
"c" b
=
μm from Trace
"c" sg=
m−1
from Trace "c"
(USE THIS VALUE)
uW=
m−1 from
two or three traces
usamp=
m−1 from
Trace "c"
uxcal=
m−1
from Trace "c"
uzcal=
m−1
from Trace "c"
uzres=
m−1
from Trace "c"
uxres=
m−1
from Trace "c" ucsg
= SQRT[uW2
+ usamp2
+ uxcal2
+ uzcal2
+ uzres2
+ uxres2]
(Each of the
standard uncertainty components
is obtained using a Type B
analysis.)
ucsg=
m−1 from
two or three traces
Rint
=
μm from Trace
"d"
a
=
μm from Trace
"d" b
=
μm from Trace
"d"
sg=
m−1
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
ucsg, the strain gradient is believed to lie in the
interval
sg
±
ucsg (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 the design length should be
between 0 μm and 1000 μm.
3.
The value
for the design width should be
between 0 μm and 60 μm.
4.
Is the
magnification appropriate given
the design length ?
5.
Magnifications at or
less than 2.5×
shall not be used.
6.
Is 0.95 < calx<
1.05 but not equal to
"1"? If not,
recheck your x-calibration.
7.
The value for interx
should be between
0
μm
and 1500
μm.
8.
The value for
σxcal
should be between 0
μm
and 4
μm.
9.
The value for
xres
should be between 0
μm
and 2.00
μm.
10.
Is 0.95 <
calz < 1.05 but not equal to
"1"? If not, recheck your
z-calibration.
11.
The value
for cert should be
greater than 0 μm and less than
25 μm.
12.
The value
for
σzcal
should be between 0 μm and 0.050
μm.
13.
The value for zres
should be greater than 0
μm and less than or
equal to 0.005 μm.
14.
The value for
Rtave
should be between 0 μm
and 0.100 μm.
15.
Alignment has not been
ensured.
16.
Data has not been
leveled.
17.
x1min
should be greater than
x1max.
18.
The
calibrated values for x1min
and x1max are
greater than 10 μm apart.
19.
In Trace
"b," the calibrated values of
x1,
x2, and x3
should be > x1ave.
20.
In Trace
"c," the calibrated values of
x1,
x2, and x3
should be > x1ave.
21.
In Trace
"d," the calibrated values of
x1,
x2, and x3
should be > x1ave.
22.
In Traces
"b," "c," and "d," the value for
s is not the same.