Data
analysis sheet for thickness
measurements in a
surface-micromachining MEMS
process using an optomechanical
technique.
a)
b)
Figure T.3.1.
For a cantilever 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 (optional) =
/
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comments (optional) =
Table 1 - Preliminary
INPUTS
To Measure A
To Measure B
Description
1
tempN =
temperature during
measurement (should be
held constant)
2
relative humidityN =
%
%
relative humidity during
measurement (if not
known, enter -1)
3
mat =
composition of the thin
film layer
4
test structure
=
test structure being
measured
5
design
length
=
μm
design length (needed
for test structure
identification purposes
only)
6
which?
which test structure on
the test chip where
"first" corresponds to
the topmost test
structure in the column
or array that has the
specified length?
7
orient =
orientation of the test
structure on the chip
8
=
×
×
magnification
9
alignN
=
alignment ensured?
10
levelN
=
data leveled?
11
μm
μm
certified value of
physical step height
standard used for calibration
12
μm
μm
certified one sigma
uncertainty of the
certified physical step
height standard used for
calibration
13
6aveN=
μm
μm
maximum of two uncalibrated
values (beforeand after)
where before
is the standard
deviation of six measurements
taken across the
physical step height
standard before the data
session and after
is the standard
deviation of six
measurements
taken across the
physical step height
standard after the data
session
14
=
μm
μm
uncalibrated average
of the six calibration
measurements used to
calculate
6ave
15
6sameN=
μm
μm
maximum of two uncalibrated
values (same1
and
same2)
where
same1
is the standard
deviation of six
measurements
taken on the physical
step height standard at
the same location before
the data session and
same2
is the standard
deviation of six
measurements
taken at this same
location after the data
session
16
=
μm
μm
uncalibrated average
of the six calibration
measurements used to
calculate
6same
17
N
=
μm
μm
uncalibrated drift in
the calibration data
(i.e., the uncalibrated
positive difference
between the average of
the six measurements taken
before the data session
at the same location on
the physical step height
standard and the average of
the six
measurements taken after
the data session at this
same location)
18
the
z-calibration
factor (for the given
magnification)
19
in
=
%
%
if applicable,
the maximum relative
deviation from linearity over the
instrument's total scan
range, as quoted by
the instrument
manufacturer (typically
less than 3 %)
20
%
%
step height relative repeatability standard
deviation obtained from step
height test structures
fabricated in a process
similar to that used to
fabricate the sample
21
μm
anchor etch depth
22
μm
range of the anchor etch
depth (as provided by
the processing facility)
23
μm
estimated value for the
dimension J
(if known); otherwise
input 0.0 μm
24
μm
estimated value for the
combined standard
uncertainty of Jest
(if Jest
is known and inputted);
otherwise input 0.0 μm
25
μm
uncalibrated surface
roughness of platX
measured as the smallest
of all the values
obtained for
splatXt.
(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
splatXt,
splatYt1,
splatYt2,
and
splatZt
in which case
sroughX
=
sroughY
=
sroughZ.)
26
μm
uncalibrated surface
roughness of platY
measured as the smallest
of all the values obtained for
splatYt1
and
splatYt2.
(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
splatXt,
splatYt1,
splatYt2,
and
splatZt
in which case
sroughX
=
sroughY
=
sroughZ.)
27
μm
uncalibrated surface
roughness of platZ
measured as the smallest
of all the values obtained for
splatZt.
(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
splatXt,
splatYt1,
splatYt2,
and
splatZt
in which case
sroughX
=
sroughY
=
sroughZ.)
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
28
34
40
46
29
35
41
47
30
36
42
48
31
37
43
49
32
38
44
50
33
39
45
51
Note 1:
The platform height
measurements are
platXt, platYt1,
platYt2, and platZt.
Note
2: The
standard deviations of the
platform height measurements are
splatXt,
splatYt1,
splatYt2,
and splatZt.
Note 9:
N= AVE (Na, Nb,
Nc)
Note 10:
uLstepA
=
SQRT[splatXave2-(calzA
sroughX)2+splatY1ave2-(calzAsroughY)2]
Note 11:
uLstepB
=
SQRT[splatY2ave2-(calzBsroughY)2+splatZave2-(calzB
sroughZ)2]
Note 12:
uWstepN = σWstepN
=
STDEV(Na,
Nb, Nc)
Note 13:
ucertN = |σcertNN
/ certN| Note 14:
ucalN = |σ6aveNN
/z6aveN|
Note 15:
urepeat(shs)N = |σ6sameNN
/ z6sameN|
Note 16:
udriftN = |(zdriftNcalzN) N
/ [2(1.732) certN]|
Note 17:
ulinearN = |zlinNN
/ (1.732)| Note 18:
urepeat(samp)N
=
σrepeat(samp)N
|N|
Note 19:
ucSHN =
SQRT(uLstepN2+uWstepN2+ucertN2+ucalN2+urepeat(shs)N2+udriftN2
+ulinearN2+ urepeat(samp)N2)
(Each
of the uncertainty components is
obtained using a Type B
analysis, except for uWstepN,
ucalN, urepeat(shs)N,
and urepeat(samp)N which use a Type A analysis.)
Table 3c - Calibrated
OUTPUTS
(in
μm)
64
C =
ucC
=
65
J =
ucJ
=
66
aa
=
ucaa
=
67
ab
=
ucab
=
68
a
=
uca
=
Note 20:
C = A + B
and ucC
= SQRT(ucSHA2
+ ucSHB2)
Note 21:
J = B
- H
and ucJ
= SQRT(ucSHB2
+ ucH2)
where
ucH =
ΔH
/ 6
Note 22:
aa
=
A
+
H
and ucaa= SQRT(ucSHA2
+ ucH2)
Note 23:
ab
=
C
-
Jest and ucab= SQRT(ucC2
+ ucJest2)
Note 24:
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.
However, there may be instances,
e.g., if the anchor etch depth
is large and unknown, where
ab
would be the better choice. Note 25:
Where ucH
and ucJest
are Type B
components.
Ua
= 2uca
= μm
(expanded uncertainty)
3uca
= μm
a
- Ua
= μm
(a lower bound for
a)
a + Ua
= μm
(an upper bound for
a)
Report the results as follows: Since it can be assumed that the
estimated values of the
uncertainty
components are
either approximately uniformly
or Gaussianly distributed with
approximate combined
standard
uncertainty
uca,
the thickness is believed to
lie in the interval
a
±
uca
(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.
2.
The values for tempN
should be between 19.4
and 21.6,
inclusive.
3.
The
values for relative
humidityN
(if known)
should be between 0 %
and 60 %, inclusive.
4.
The value for the design
length should be greater
than
0
μm
and less than or equal
to 1000
μm.
5.
the magnifications
appropriately greater
than 2.5×?
6a.
6b.
7a.
7b.
8.
9.
10.
11.
N
- 0.150 μm)/calzN
and (certN
+ 0.150 μm)/calzN
and not equal to 0.0
μm.
12.
N
should be between 0.000
μm and 0.100 μm,
inclusive.
13.
N
should be between 0.900
and 1.100, but not equal
to 1.000.
14.
15.
σrepeat(samp)N
should be between 0.0 %
and 10.0 %, inclusive.
16.
ΔH,
Jest,
and ucJest
should be greater than
or equal to 0.0 μm and
less than 0.50
μm.
17.
18.
19.
20.
platYt2, and
platZt) should be
between
-2.500 μm and
2.500 μm.
