Data
analysis sheet for in-plane
deflection measurements from
released part to released part
Figure L.5.1.
Top view of bow-tie test structure
depicting the measurement to be
made.
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
D =
μm
design
dimension for D
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 design dimension for D?
4
which bow-tie?
which
bow-tie array ?
5
magnification =
×
magnification
6
orientation =
orientation on the chip
7
calx =
x-calibration factor (for the given magnification)
8
interx
=
μm
interferometer's 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
aligned?
alignment ensured ?
13
leveled?
data leveled ?
Table 2 -
INPUTS (uncalibrated values)
Notes
14
x1max
(i.e., x1upper)
=
μm
15
x1min
(i.e., x1lower)
=
μm
(x1min > x1max)
16
x2min
(i.e., x2lower)
=
μm
(x2min
> x1min)
17
x2max
(i.e., x2upper)
=
μm
(x2max > x2min)
Table 3 -
OUTPUTS (calibrated values)
Notes
18
Dmin =
μm
Dmin = (
x2min − x1min )
calx
19
Dmax =
μm
Dmax = ( x2max
− x1max
)
calx
20
D
=
μm
in-plane deflection D
= (Dmin
+ Dmax ) / 2
21
uD =
μm
uD = (Dmax
−
Dmin ) / 6
22
uxcal =
μm
uxcal = (σxcal
/ interx) ( D /
calx )
23
uxres =
μm
uxres = xrescalx
/ 1.732
24
ucD =
μm
combined standard uncertainty ucD
= SQRT [ uD2
+ 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
ucD, the
in-plane deflection is believed to
lie in the interval D
±
ucD (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 D should be
between 0 μm and 50 μm.
3.
The measured
value for D
is more than 5 μm from the
design dimension.
4.
Is the
magnification appropriate given
the design dimension for
D ?
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.