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SEMI MF1390-1104 © SEMI 2004 7 RELATED INFORMATION 1 MEASUREMENT ERRORS DUE TO DIFFERENCES IN DIAMETER AND THICKNESS BETWEEN A REPRESEN TATIVE WAFER AND A WAFER UNDER TEST NOTICE : This rel ated information is not an of …

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SEMI MF1390-1104 © SEMI 2004 6
13.13.1 Record sample standard deviation and other
statistical parameters as agreed upon between the
parties to the test.
14 Report
14.1 Report the following information:
14.1.1 Date, time, and temperature of test,
14.1.2 Identification of operator,
14.1.3 Location (laboratory) of test,
14.1.4 Identification of measuring instruments, inclu-
ding wafer-holding device diameter, data point spacing,
sensor size, and gravitation-correction method,
14.1.5 Lot identification, including nominal diameter,
nominal center-point thickness, and nominal edge
exclusion (EE) specified.
14.1.6 Description of sampling plan, if any, and
14.1.7 Warp of each wafer measured.
14.2 For referee tests also include in the report the
standard deviation of each set of wafer measurements
and such other statistical parameters as have been
agreed to by the parties to the test.
15 Precision
15.1 Twenty-three 200 mm diameter, single-side
polished silicon wafers were employed in a round-robin
experiment. These wafers represented three different
manufacturing processes. All three subsets were bare
on the front surface. Two subsets were bare on the
back surface and one subset had oxide on the back
surface.
15.2 Eight laboratories measured warp. Warp value
ranges for these three subsets are shown in Table 1.
Each of the twenty-three wafers was measured three
times in succession (in three cassette-to-cassette
“passes”), on a single day on automatic measurement
systems in accordance with this test method.
15.3 All measurement data were acquired with 3 mm
nominal edge exclusion.
15.4 The number of laboratories, samples, and
determinations in this study met the minimum
requirements for determining precision prescribed in
ASTM Practice E 691.
15.5 The ranges of 95% confidence interval, within
which two measurements are considered statistically to
be the same, for within-laboratory repeatability (r) and
between-laboratory reproducibility (R) are shown in
Table 1.
15.6 Figure 2 contains plots of the 95% confidence
intervals for repeatability (r) and reproducibility (R)
against mean value of warp.
15.7 For more details, refer to the Research Report.
4
Table 1 Summary Warp Measurement Statistics
Parameter Warp
Smallest 4.30
Mean, m
Largest 31.25
Smallest 0.184
r, m
Largest 0.695
Smallest 1.112
R, m
Largest 2.097
Figure 2
Warp Repeatability & Reproducibility
16 Bias
16.1 Bias — No standards exist against which the bias
of this test method can be evaluated.
17 Keywords
non-contact measurement; semiconductor; shape;
silicon; wafers; warp
4 Available on request from SEMI Headquarters, Publications
Department, San Jose, CA, Fax: 408-943-7015. Request International
Standards Research Report F01-1016, ASTM Interlaboratory Round
Robin Experiment on Measuring Warp on Silicon Wafers by
Automated Noncontact Scanning and Measuring Flatness, Thickness
and Thickness Variation of Silicon Wafers by Automated Noncontact
Scanning.
Mean Warp,
m
r and R, m
D
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A
W
R
T
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E
G
M
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5 1015202530
0.0
0.5
1.0
1.5
2.0
2.5
Repeatability
Reproducibility
SEMI MF1390-1104 © SEMI 2004 7
RELATED INFORMATION 1
MEASUREMENT ERRORS DUE TO DIFFERENCES IN DIAMETER AND
THICKNESS BETWEEN A REPRESENTATIVE WAFER AND A WAFER
UNDER TEST
NOTICE: This related information is not an official part of SEMI MF1390. This related information was approved
for publication by full letter ballot on April 22, 2004.
R1-1 The sag, or deflection induced by gravity at the
edge of a wafer supported at its center, in m, has been
estimated
3
as:
2
4
2
48
32
)103(
t
KD
Et
kgdD
S
(R1-1)
where:
S =
deflection , in m,
k = geometrical constant (=0.5854),
g = gravitational constant (980 cm/s
2
),
d = density of silicon (2.329 g/cm
3
),
E =
Young’s modulus (~1.610
12
dyne/cm
2
,
D = nominal wafer diameter, in mm, and
t =
nominal wafer thickness, in m.
K, the constant of proportionality is therefore equal to
7.83 10
3
m
3
/mm
4
. Table R1-1 gives estimated
values of sag in micrometers for 100 mm through 300
mm diameter wafers with thickness and diameter as
specified in SEMI M1.
Table R1-1. Estimated Sag, in
m, of Wafers of
Nominal Diameter and Thickness
Diameter,
mm
Thickness,
m
SEMI M1 Reference Estimated Sag,
m
300 775 SEMI M1.15 105.6
200 725 SEMI M1.9 23.8
150 675 SEMI M1.8 8.7
150 625 SEMI M1.13 10.1
125 625 SEMI M1.7 4.9
100 525 SEMI M1.5 2.8
R1-2 For small variations about the nominal values of
diameter and thickness, the relative change of the
gravity effect is 4 times the relative change of the
diameter and 2 times the relative change of thickness:
2
3
4
t
Kd
d
S
(R1-2)
and
3
4
2
t
Kd
t
S
(R1-3)
Therefore the relative changes are as follows:
d
d
S
S
4 (R1-4)
and
t
t
S
S
2 (R1-5)
R1-3 Table R1-2 gives examples of worst-case gravity
effect errors (in micrometers), for 100 mm through 300
mm diameter wafers with thickness and diameter toler-
ances as specified in SEMI M1.
SEMI MF1390-0704 © SEMI 2004 8
Table R1-2 Examples of Gravity Effect Errors
NOTICE: SEMI makes no warranties or representations
as to the suitability of the standards set forth herein for any
particular application. The determination of the suitability
of the standard is solely the responsibility of the user.
Users are cautioned to refer to manufacturer's instructions,
product labels, product data sheets, and other relevant
literature, respecting any materials or equipment
mentioned herein. These standards are subject to change
without notice.
By publication of this standard, Semiconductor Equipment
and Materials International (SEMI) takes no position
respecting the validity of any patent rights or copyrights
asserted in connection with any items mentioned in this
standard. Users of this standard are expressly advised that
determination of any such patent rights or copyrights, and
the risk of infringement of such rights are entirely their
own responsibility.
300 mm Diameter Wafers
Actual Diameter, mm
299.8 300.0 300.2
Gravity Effect Errors,
m
755 3.90 5.67 5.96
775
1.68
0.00 0.28
Actual
Thickness,
m
795
6.84 5.25 4.98
200 mm Diameter Wafers
Actual Diameter, mm
199.8 300.0 200.2
Gravity Effect Errors,
m
705 0.77 1.37 1.47
725
0.57
0.00 0.10
Actual
Thickness,
m
745
0.52 1.26 1.17
150 mm Diameter Wafers
Actual Diameter, mm
149.8 150.0 150.2
Gravity Effect Errors,
m
655 0.49 0.54 0.59
675
0.05
0.00 0.05
Actual
Thickness,
m
695
0.54 0.49 0.45
150 mm Diameter Wafers
Actual Diameter, mm
149.8 150.0 150.2
Gravity Effect Errors,
m
610
0.45
0.51 0.56
625
0.05
0.00 0.05
Actual
Thickness,
m
640
0.52 0.47 0.42
125 mm Diameter Wafers
Actual Diameter, mm
124.5 125.0 125.5
Gravity Effect Errors,
m
605 0.25 0.33 0.41
625
0.08
0.00 0.08
Actual
Thickness,
m
645
0.37 0.30 0.22
100 mm Diameter Wafers
Actual Diameter, mm
99.5 100.0 100.5
Gravity Effect Errors,
m
505 0.17 0.23 0.29
525
0.06
0.00 0.06
Actual
Thickness,
m
545
0.26 0.20 0.15
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