Data
analysis sheet for thickness
measurements in MEMS processes using
optomechanical technique.
a)
b)
Figure T.3.1.
For a fixed-fixed beam test
structure a) a design rendition and
b) a cross-sectional side view of a
pegged beam.
To obtain the
measurements in this data sheet, consult
the following: [1] J.C.
Marshall, "New Optomechanical
Technique for Measuring Layer
Thickness in MEMS Processes," Journal of Microelectromechanical
Systems, Vol. 10, No. 1, March 2001. [2] SEMI
MS2,
"Test Method for Step Height
Measurements of Thin Films."
Note:
A stylus profilometer is typically
used to measure A. An optical
interferometer is typically used to
measure B. The
platforms are assumed to be reflective
with no secondary fringe effect.
date data
taken (optional) =
/
/
Table 1 -
Preliminary
INPUTS
To Measure A
To Measure B
Description
1
mat =
composition of the thin
film layer
2
orient =
orientation of the test
structure on the chip
3
=
×
×
magnification
4
alignN =
alignment ensured?
5
levelN =
data leveled?
6
µm
µm
certified value of
physical step
height used for
calibration
7
µm
µm
certified one sigma
uncertainty of the certified
physical step height
used for calibration
8
N =
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)
9
6N
=
µm
µm
the uncalibrated average
of the six calibration
measurements from which
zrepeat
was found
10
N =
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.
11
the
z-calibration
factor = the certified
value of the physical step height
divided by the
average of the twelve
calibration measurements
taken at the same
location on the physical
step height
12
N=
%
%
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%)
13
µm
anchor etch depth
14
µm
range of the anchor etch
depth (as provided by
the processing facility)
15
µm
estimated value for the
dimension J
(if known); otherwise
input 0.0
µm
16
µm
estimated value for the
combined standard
uncertainty of Jest
(if Jest
is known and inputted); otherwise
input 0.0
µm
17
µm
the uncalibrated surface
roughness of platX
measured as the smallest
of all the values
obtained for
σplatXt.
(However, if the
surfaces of platX,
platY, and
platZ all have
identical compositions,
then it is measured as
the smallest of all the
values obtained for
σplatXt,
σplatYt1,
σplatYt2,
and
σplatZt
in which case
σroughX
= σroughY
= σroughZ.)
18
µm
the uncalibrated surface
roughness of platY
measured as the smallest
of all the values
obtained for
σplatYt1
and
σplatYt2.
(However, if the
surfaces of platX,
platY, and
platZ all have
identical compositions,
then it is measured as
the smallest of all the
values obtained for
σplatXt,
σplatYt1,
σplatYt2, and
σplatZt
in which case
σroughX
= σroughY
= σroughZ.)
19
µm
the uncalibrated surface
roughness of platZ
measured as the smallest
of all the values
obtained for
σplatZt.
(However, if the
surfaces of platX,
platY, and
platZ all have
identical compositions,
then it is measured as
the smallest of all the
values obtained for
σplatXt,
σplatYt1,
σplatYt2, and
σplatZt
in which case
σroughX
= σroughY
= σroughZ.)
Nomenclature:
"platX"
refers to the height
measurement taken from the top of the
underlying layer,
"platY" refers
to the height measurement
taken from the top of the
anchor, "platZ" refers
to the height measurement
taken from the top of the
pegged portion of the beam,
"t" indicates which
data trace ("a," "b,"
or "c"), and "N"
indicates which measurement
("A" or "B").
Table 2 -
MINIMUM AND DELTA HEIGHT
MEASUREMENTS
Uncalibrated
PLATFORM INPUTS
(in
µm) used to find A typically
with a stylus
profilometer
Uncalibrated
PLATFORM INPUTS
(in
µm) used to find B typically with an
optical interferometer
20
26
32
38
21
27
33
39
22
28
34
40
23
29
35
41
24
30
36
42
25
31
37
43
Note 1:
The platform
height measurements are
platXt, platYt1,
platYt2, and platZt.
Note
2: The
standard deviations of the
platform height measurements are
σplatXt,σplatYt1,
σplatYt2, andσplatZt.
Note 18:
C = A + B
and ucC
= SQRT(ucstepA2
+ ucstepB2) Note
19:
J = B
- H
and ucJ
= SQRT(ucstepB2
+ ucH2)
where
ucH =
ΔH
/ 6 Note
20:
aa =
A
+ H
and ucaa= SQRT(ucstepA2
+ ucH2) Note
21:
ab =
C
- Jest
and ucab= SQRT(ucC2
+ ucJest2) Note
22:
The
thickness of the suspended
layer,
a,
is the value specified for
aa
or
ab
(whichever has the smaller
combined standard uncertainty
value) unless Jest=0
in which case
a
=
aa.
Report the results as follows: Since it can be assumed that the
possible estimated values are either approximately uniformly
distributed or Gaussian with approximate standard deviation
uca, the
thicknessis believed to lie in the
interval a ±
uca with a level of
confidence of approximately 68 % assuming a Gaussian distribution.
Modify the input data,
given the information
supplied in any flagged
statement below, if
applicable, then
recalculate:
1.
2.
the magnifications
appropriately greater
than 2.5×?
3a.
3b.
4a.
4b.
5.
6.
7.
8.
N
- 0.100 µm)/calzN
and (certN+ 0.100
µm)/calzN
and not equal to 0.0
µm.
9.
N
should be between 0.000
µm and 0.050 µm,
inclusive.
10.
N
should be between 0.900
and 1.100, but not equal
to 1.000.
11.
N
should be between 0.0
% and 3.0 %, inclusive.
12.
ΔH,
Jest,
and ucJest
should be greater than
or equal to 0.0
µm and less than 0.50
µm.
13.
14.
15.
16.
platYt2, and
platZt) should be between
-2.500 µm and
2.500 µm.
