Data
analysis sheet for in-plane length
measurements with two ends anchored
(or for an inside edge-to-inside
edge length measurement)
Figure L.1.1.
Top view of a fixed-fixed beam test
structure depicting the measurement
to be made, where Edge 1 and
Edge 2 are considered inside edges.
To obtain the
following measurements, consult ASTM
standard test method E 2244 entitled
"Standard Test Method for In-Plane
Length Measurements of Thin,
Reflecting Films
Using an Optical Interferometer."
date data taken (optional) =
/
/
Table 1 - Preliminary
ESTIMATES
Description
1
material =
material
2
design length =
μm
design
length
3
which?
which iteration of the test structure
where "first" corresponds to the topmost or
leftmost test structure in
the column or array of the same material that has the specified length?
4
magnification =
×
magnification
5
orientation
=
orientation on the chip
6
calx =
x-calibration factor (for the given magnification)
7
interx
=
μm
interferometer's maximum field of view
(for the given magnification)
8
σxcal =
μm
one sigma
uncertainty in a ruler
measurement (for the given
magnification)
9
xres
=
μm
uncalibrated resolution
of the interferometer in the
x-direction
10
calz =
z-calibration factor (for the given magnification)
11
aligned?
alignment ensured ?
12
leveled?
data leveled ?
Table 2 -
INPUTS
(uncalibrated values)
Notes
13
x1max
(i.e., x1upper)
=
μm
14
x1min
(i.e., x1lower)
=
μm
(x1min > x1max)
15
x2min
(i.e., x2lower)
=
μm
(x2min > x1min)
16
x2max
(i.e., x2upper)
=
μm
(x2max > x2min)
Table 3 -
OUTPUTS
(calibrated values)
Equation
17
Lmin =
μm
Lmin = (
x2min – x1min )
calx
18
Lmax =
μm
Lmax = ( x2max
– x1max
)
calx
19
L =
μm
in plane length L
= (Lmin
+ Lmax ) / 2
20
uL =
μm
uL = (
Lmax – Lmin
) / 6
21
uxcal
=
μm
uxcal = (σxcal
/ interx)( L / calx
)
22
uxres =
μm
uxres = xres calx/ 1.732
23
ucL =
μm
combined standard uncertainty ucL = SQRT
[ uL2
+
uxcal2
+
uxres2]
where each of the standard uncertainty
components is obtained using a Type B analysis
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
ucL, the
in-plane length
is believed to lie in the
interval L
±
ucL (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
design length should be between
0
μm and 1050
μm.
3.
The measured value for L
is more than
3ucL from the
design length.
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 1.57
μm.
10.
Is 0.95 <
calz < 1.05 but not equal to
"1" ? If not, recheck your
z-calibration.
11.
Alignment
has not been ensured.
12.
Data has not been
leveled.
13.
x1min
should be greater than
x1max.
14.
x2min
should be greater than
x1min.
15.
x2max
should be greater than
x2min.
16.
The calibrated values
for x1min
and x1max
are greater than 10 μm
apart.
17.
The calibrated values for x2min
and x2max are
greater than 10 μm apart.