Data
analysis sheet for step height
measurements taken during
different
data sessions from two step
height test structures.
a)
b)
Figure SH.3.1.For a CMOS step height test
structure: a) a design rendition and
b) a cross-section.
To obtain the
following measurements, consult SEMI
standard test method MS2 entitled
"Test Method for Step Height
Measurements of Thin Films."
date first 3-D data set taken
(optional) =
/
/
date second 3-D data set taken
(optional) =
/
/
Table 1 - Preliminary
INPUTS
First Test
Structure
Second Test
Structure
Description
1
proc =
which process?
2
which =
For CMOS SRM chips,
which test structure?
For MUMPs chips, which
quad?
3
which2 =
Which platform, where
"first" corresponds to
the leftmost or
bottommost platform in
the test structure,
counting the reference
platform?
4
which3 =
For CMOS chips, which
iteration of the test
structure where "first"
corresponds to the
topmost test structure
in the column?
5
orient =
orientation of the test
structure on the test
chip
6
mag
=
×
×
magnification
7
align =
alignment ensured?
8
level =
data leveled?
9
cert =
μm
μm
certified value of
physical step height
standard used for calibration
10
σcert
=
μm
μm
certified one sigma
uncertainty of the
certified physical step
height standard used for
calibration
11
zrepeat(shs)=
μm
μm
maximum uncalibrated
range of the six
calibration measurements
taken before the data
session at the same
location on the physical
step height or after the
data session
at the same location on
the physical step height
(whichever is larger)
12
z6
=
μm
μm
the uncalibrated average
of the six calibration
measurements from which
zrepeat(shs)
was found
13
zdrift
=
μm
μm
uncalibrated drift in
the calibration data
(i.e., the uncalibrated
positive difference
between the average of
the six calibration
measurements taken
before the data session
at the same location on
the physical step height
and the average of the
six calibration
measurements taken after
the data session at the
same location on the
physical step height)
14
calz
=
the
z-calibration
factor = the certified
value of the physical
step height standard divided by
the average of the
twelve calibration
measurements taken
at the same location on
the physical step height
15
zperc
=
%
%
if
applicable, over the
instrument's total scan
range, the maximum
percent deviation from
linearity, as quoted by
the instrument
manufacturer (typically
less than 3%)
16
σroughLX=
μm
the uncalibrated surface
roughness of platLX
measured as the smallest
of all the values
obtained for
σplatLXt.
(However, if the
surfaces of platLX,
platMY, platLr,
and platMr all
have identical
compositions, then it is
measured as the smallest
of all the values
obtained for
σplatLXt,
σplatMYt,
σplatLrDt,
and
σplatMrDt
in which case
σroughLX=
σroughMY.)
17
σroughMY=
μm
the uncalibrated surface
roughness of platMY
measured as the smallest
of all the values
obtained for
σplatMYt.
(However, if the
surfaces of platLX,
platMY, platLr,
and platMr all
have identical
compositions, then it is
measured as the smallest
of all the values
obtained for
σplatLXt,
σplatMYt,
σplatLrDt,
and
σplatMrDt
in which case
σroughLX=
σroughMY.)
Nomenclature:
"L" and "M" refer
to the test structure number ("1,"
"2," "3," etc.),
"X" and "Y" refer
to the platform letter ("A,"
"B," "C," etc.),
"r" refers to the
reference platform,
"D" directionally
indicates which reference
platform ("N," "S,"
"E," or "W"), and
"t" indicates which data
trace ("a," "b,"
or "c").
Table 2a - Uncalibrated
REFERENCE PLATFORM
INPUTS
(in
μm)
First Test Structure
Second Test Structure
1a
4a
1b
4b
2a
5a
2b
5b
3a
6a
3b
6b
Table 2b - Calibrated
REFERENCE PLATFORM
CALCULATIONS
(in
μm)
First Test Structure
Second Test Structure
7a
8a
7b
8b
Note 1:
platLr = AVE(platLrWa,
platLrWb, platLrWc, platLrEa,
platLrEb, platLrEc) calz
Note 2:
splatLr = STDEV(platLrWa,
platLrWb, platLrWc, platLrEa,
platLrEb, platLrEc) calz
Note 3: The calculations
for the second test structure
are similar to the calculations
for the first test structure
given in Notes
1 and 2.
Table 3a - Uncalibrated
PLATFORM INPUTS
(in
μm)
First Test Structure
Second Test Structure
9a
9b
10a
10b
11a
11b
12a
platLXa
=
12b
platMYa
=
13a
platLXb
=
13b
platMYb
=
14a
platLXc
=
14b
platMYc
=
Table 3b - Calibrated
PLATFORM CALCULATIONS
(in
μm)
First Test Structure
Second Test Structure
15a
15b
16a
16b
17a
platLXave
=
17b
platMYave
=
18a
18b
19a
19b
20a
20b
21a
21b
22a
22b
23a
23b
24a
24b
Note 4:
platLX = calz AVE(platLXa,
platLXb, platLXc)-
platLr
Note 5:
splatLX =
calz STDEV(platLXa,
platLXb, platLXc)
Note 6:
σplatLXave
=
calz AVE(σplatLXa,
σplatLXb,
σplatLXc)
Note 7:
uLplatLX =
σplatLXave
-
calzσroughLX
Note 8:
uWplatLX = SQRT(splatLX2+splatLr2)
Note 9:
ucertLX = |σcertplatLX
/ cert|
Note 10:
urepeat(shs)LX
= |zrepeat(shs)platLX
/ [2(1.732) z6]|
Note 11:
udriftLX = |(zdriftcalz) platLX
/ [2(1.732) cert]|
Note 12:
ulinearLX
= |zpercplatLX
/ (1.732)|
Note 13:
uplatLX = SQRT(uLplatLX2+uWplatLX2+ucertLX2+urepeat(shs)LX2+udriftLX2+ulinearLX2) (Each
of the standard uncertainty
components is obtained using a
Type B analysis,
except for uWplatLX,
which uses a Type A analysis.)
Note 14: The
calculations for the second test
structure are similar to the
calculations for the first
test structure given in Notes
4 through 13, inclusive.
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
ucSH, the step
height is believed to lie in the
interval stepLXMY
±
ucSH (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.
he
Preliminary Inputs
Table.
2.
3a.
3b.
4a.
4b.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
σplatLXt
and
σplatMYt
should be between 0.0
μm
and 0.02
μm,
inclusive.