Data
analysis sheet for in-plane length
measurements with one end anchored
(or for an inside edge-to-outside
edge length measurement from two
data traces)
Figure L.3.1.
Top view of a cantilever test
structure depicting the measurement
to be made, where Edge 1 is
considered an inside edge and Edge 2
is considered an outside edge.
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) =
/
/
filename of 3-D data set
(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., x2upper)
=
μm
(x2min > x1min)
16
x2max
(i.e., x2lower)
=
μm
(x2max > x2min)
Table 3
- OUTPUTS (calibrated values)
Notes
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 = xrescalx/ 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
1000
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
interxshould
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.