Data
analysis sheet for thickness
measurements in a
surface-micromachining MEMS process using
an optomechanical technique for
use with the MEMS 5-in-1 (RM 8097).
a)
b)
Figure T.3.a.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]
NIST
SP 260-177, "Standard Reference
Materials: User's Guide for RM
8096 and 8097: The MEMS 5-in-1, 2013
Edition" [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
or C.
The platforms are assumed to be
reflective with no secondary fringe
effect.
If secondary fringes may be an
issue, a higher magnification
objective (e.g., a 50× objective) is used
with an appropriate field of view
converter, if applicable.
date (optional) =
/
/
comments (optional) =
Table 1 - Preliminary
INPUTS
To Measure:
Description
A
B (optional)
C
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
certified value of
physical step height
standard used for calibration
12
μm
certified one sigma
uncertainty of the
certified physical step
height standard used for
calibration
13
6aveNμm
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
uncalibrated average
of the six calibration
measurements used to
calculate
6ave
15
6sameN 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
uncalibrated average
of the six calibration
measurements used to
calculate
6same
17
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
range of the anchor etch
depth (if known);
otherwise input 0.0 μm
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 known);
otherwise input 0.0 μm
25
μm
uncalibrated surface
roughness of platX
measured as the smallest
of all the values
obtained for
splatXt1and
splatXt2.
(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
splatXt1,
splatXt2,
splatYt1,
splatYt2,
splatZt1,
and
splatZt2
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
splatXt1,
splatXt2,
splatYt1,
splatYt2,
splatZt1,
and
splatZt2
in which case
sroughX
=
sroughY
=
sroughZ.)
27
μm
uncalibrated surface
roughness of platZ
measured as the smallest
of all the values obtained for
splatZt1
and splatZt2.
(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
splatXt1,
splatXt2,
splatYt1,
splatYt2,
splatZt1,
and
splatZt2
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, B,
or C).
Table 2 -
MINIMUM HEIGHT
MEASUREMENTS
Uncalibrated
PLATFORM INPUTS
(in
μm) used to find A typically
with a stylus
profilometer
28
Fate of
A
To
force the selection of
ai
(as calculated using
A and H) to be the
thickness, input a
positive number. To
disregard
ai
as a possible thickness,
input a negative number.
To let the software
determine the thickness
by the smallest
uncertainty value, input
zero.
29
35
30
36
31
37
32
38
33
39
34
40
Note 1:
The platform height
measurements are
platXt1 and
platYt1.
Note
2: The
standard deviations of the
platform height measurements are
splatXt1
and
splatYt1.
Table 3 -
DELTA HEIGHT
MEASUREMENTS
Uncalibrated
PLATFORM INPUTS
(in
μm) used to find
B typically
with an optical
interferometer
41
Fate of
B
To
force the selection of
aii
(as calculated using
A, B, and
Jest) to be the
thickness, input a
positive number. To
disregard
aii
as a possible thickness,
input a negative number.
To let the software
determine the thickness
by the smallest
uncertainty value, input
zero.
42
48
43
49
44
50
45
51
46
52
47
53
Note 3:
The platform height
measurements are
platYt2 and platZt1. Note
4: The
standard deviations of the
platform height measurements are
splatYt2
and
splatZt1.
Table 4 -
MAXIMUM HEIGHT
MEASUREMENTS
Uncalibrated
PLATFORM INPUTS
(in
μm) used to find
C typically
with an optical
interferometer
54
Fate of
C
To
force the selection of
aiii
(as calculated using
C and Jest) to be the
thickness, input a
positive number. To
disregard
aiii
as
a possible thickness, input a negative number.
To let the software
determine the thickness
by the smallest
uncertainty value, input
zero.
55
61
56
62
57
63
58
64
59
65
60
66
Note 5:
The platform height
measurements are
platXt2 and
platZt2. Note
6: The
standard deviations of the
platform height measurements are
splatXt2
and
splatZt2.
Note 16:
N= AVE (Na, Nb,
Nc)
Note 17:
uLstepA
=
SQRT[splatX1ave2-(calzA
sroughX)2+splatY1ave2-(calzAsroughY)2]
Note 18:
uLstepB
=
SQRT[splatY2ave2-(calzBsroughY)2+splatZ1ave2-(calzB
sroughZ)2] Note 19:
uLstepC
=
SQRT[splatZ2ave2-(calzCsroughZ)2+splatX2ave2-(calzC
sroughX)2]
Note 20:
uWstepN = σWstepN
=
STDEV(Na,
Nb, Nc)
Note 21:
ucertN = |σcertNN
/ certN| Note
22:
ucalN = |σ6aveNN
/z6aveN|
Note 23:
urepeat(shs)N = |σ6sameNN
/ z6sameN|
Note 24:
udriftN = |(zdriftNcalzN) N
/ [2(1.732) certN]|
Note 25:
ulinearN = |zlinNN
/ (1.732)| Note
26:
urepeat(samp)N
=
σrepeat(samp)N
|N|
Note 27:
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 5c - Calibrated
OUTPUTS
(in
μm)
85
Ccalc =
ucCcalc
=
86
J =
ucJ
=
87
ai
=
ucai
=
88
aii
=
ucaii
=
89
aiii
=
ucaiii
=
90
a
=
uca
=
Note 28:
Ccalc = A + B
and ucCcalc
= SQRT(ucSHA2
+ ucSHB2)
Note 29:
J = B
- H
and ucJ
= SQRT(ucSHB2
+ ucH2)
where
ucH =
ΔH
/ 6
Note 30:
ai
=
A
+
H
and ucai= SQRT(ucSHA2
+ ucH2)
Note 31:
aii
=
Ccalc
-
Jest and ucaii= SQRT(ucCcalc2
+ ucJest2) Note
32:
aiii
=
C
-
Jest and ucaiii= SQRT(ucSHC2
+ ucJest2)
Note 33:
Where ucH
and ucJest
are Type B
components. Note
34:
The
thickness of the suspended
layer,
a,
is the value specified for
ai,
aii,
or
aiii, whichever has the smallest
combined standard uncertainty
value, unless Fate of A, Fate of B, and/or
Fate of C
was predetermined in Tables
2, 3, and/or 4.
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: If it is assumed that the
estimated values of the
uncertainty
components are
approximately 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.
6c.
Alignment has not been
ensured for the
measurement of C.
7a.
7b.
7c.
Data has not been
leveled for the
measurement of C.
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.
Fate of Fate ofFate of
17.
18.
Only one of the three
values for
Fate of A,
Fate of B, and
Fate of C can be
positive.
19.
All three values for
Fate ofA,
Fate of B,
and
Fate of C cannot be
less than zero.
