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SEMI MF1451-1104 © SEMI 2004 1 SEMI MF1451-1104 TEST METHOD FOR MEASURING SO RI ON SILICON WAFERS BY AUTOMATED NON-CO NTACT SCANNING This test method was technically approved by th e Global Silicon Wafer Committee and is…

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SEMI MF1392-1103 © SEMI 2003 20
RELATED INFORMATION 3
NUMERICAL CONSTANTS
NOTICE: This related information is not an official part of SEMI MF1392. It was developed during the original
development of the document. This related information was approved for publication by full letter ballot on July 12,
2003.
R3-1.1 The numerical constants given in the equations
in this test method are lumped constants. This appendix
provides details as to the composition of these lumped
constants and the values of the individual constants
used in deriving them. Table R3-1 gives the lumped
constants, their formulas, and their values. The units in
this table include any necessary unit conversions. If
there is no entry for a given equation, either there is no
lumped constant in the equation or the constant is
strictly numeric (for example, as for unit conversion).
Table R3-2 gives the values of the individual constants
used in this test method. The built-in potential, φ, may
vary from about 0.5 to about 0.8 V; the constant value
assumed is an approximation to this parameter.
Table R3-1 Lumped Constants
Equation Formula Value (Note 1)
(13), (17), (18)
φ
0.6 [V]
(14) (19a)
K
Si
ε
0
10359 [pF·µm/cm
2
]
(16)
K
Si
ε
0
/q 6.466 × 10
14
[(F·µm
−2
)/(C·cm
3
)]
(19b)
2/K
Si
ε
0
q 1.2050 × 10
−7
[(cm·F)/(C·pF
2
)]
NOTE 1: The units are given in brackets; the symbol C indicates
coulombs and the symbol F indicates farads.
Table R3-2 Values of Individual Constants
Constant Symbol Value (Note 1)
Built-in potential
φ
0.6 [V]
Permittivity of free space
ε
0
8.8542 × 10
−14
[F/cm]
Dielectric constant of silicon K
Si
11.7
Electronic charge q
1.6022 × 10
−19
[C]
NOTE 1: The units are given in brackets; the symbol C indicates
coulombs and the symbol F indicates farads.
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forth herein for any particular application. The
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herein. These standards are subject to change without
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f
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SEMI MF1451-1104 © SEMI 2004 1
SEMI MF1451-1104
TEST METHOD FOR MEASURING SORI ON SILICON WAFERS BY
AUTOMATED NON-CONTACT SCANNING
This test method was technically approved by the Global Silicon Wafer Committee and is the direct
responsibility of the North American Silicon Wafer Committee. Current edition approved for publication by
the North American Regional Standards Committee on August 16, 2004. Initially available at
www.semi.org
September 2004; to be published November 2004. Original edition published by ASTM International as
ASTM F 1451-92. Last previous edition SEMI MF1451-0704.
1 Purpose
1.1 Sori can significantly affect the yield of
semiconductor device processing.
1.2 Knowledge of this characteristic can help the
producer and consumer determine if the dimensional
characteristics of a specimen wafer satisfy given
geometrical requirements.
1.3 Changes in wafer sori during processing can
adversely affect subsequent handling and processing
steps. These changes can also provide an important
process monitoring function.
1.4 This test method is suitable for measuring the sori
of wafers used in semiconductor device processing in
the as-sliced, lapped, etched, polished, epitaxial or other
layer condition and for monitoring thermal and
mechanical effects on the sori of wafers during device
processing.
2 Scope
2.1 This test method covers a non-contacting,
nondestructive procedure to determine the sori of clean,
dry semiconductor wafers.
2.2 This test method employs a two-probe system that
examines both external surfaces of the wafer
simultaneously.
2.3 The test method is applicable to wafers 50 mm or
larger in diameter, and approximately 100 m and
larger in thickness, independent of thickness variation
and surface finish, and of gravitationally induced wafer
distortion.
2.4 This test method is not intended to measure the
flatness of either exposed silicon surface. Sori is a
measure of the distortion of the front surface of the
wafer.
2.5 This test method measures sori of a wafer corrected
for mechanical forces applied during the test.
Therefore, the procedure described gives the
unconstrained value of sori.
NOTE 1: This sori is indicated by the acronym “GFLYFER”
in Appendix 2, Shape Decision Tree, of SEMI M1.
2.6 This test method includes several methods for
canceling gravity-induced deflection which could
otherwise alter the shape of the wafer.
1
NOTE 2: One of these methods, the Representative Wafer
Inversion Method, is covered by a patent held by ADE
Corporation, 80 Wilson Way, Westwood, MA 02090-1806.
NOTICE: This standard does not purport to address
safety issues, if any, associated with its use. It is the
responsibility of the user of this standard to establish
appropriate safety and health practices and determine
the applicability of regulatory or other limitations prior
to use.
3 Limitations
3.1 Any relative motion along the probe measuring axis
between the probes and the wafer holding device during
scanning will produce error in the measurement data.
Vibration of the test specimen relative to the probe-
measuring axis will introduce error. Such errors are
minimized by system signature analysis and correction
algorithms. Internal system monitoring may also be
used to correct non-repetitive and repetitive system
mechanical translations. Failure to provide such correc-
tions may cause errors.
3.2 If a measured wafer differs substantially in
diameter, thickness, fiducials, or crystal orientation
from that used for the gravitational compensation
procedure, the results may be incorrect. Estimates of
the errors in gravity induced deflection for differences
in diameter and thickness are shown in Related
Information 1. If the crystal orientation of the sample
to be measured differs from the crystal orientation of
the gravity-compensation wafer, then the measured sori
value may differ from the actual sori value by up to
15%. Error tables for fiducial variation have not been
generated.
3.3 Different methods for implementing gravitational
compensation may give different results. Varying
1 Poduje, N., “Eliminating Gravitational Effect in Wafer Shape
Measurements,” NIST/ASTM/SEMI/SEMATECH Technology Confe-
rence, Dallas, TX. Technology for Advanced Materials/Process
Characterization, February 1, 1990.
SEMI MF1451-1104 © SEMI 2004 2
levels of completeness of implementing a method may
also give different results.
3.4 Mechanical variations in wafer holding devices
between systems may introduce measurement
differences. This test method allows the use of a
variety of wafer holding devices (see Section 7.1.4.1);
results obtained with different geometrical
configurations of wafer holding device on the same test
samples may differ.
3.5 Most equipment systems capable of this
measurement have a definite range of wafer thickness
combined with sori (dynamic range) that can be
accommodated without readjustment. If the sample
moves outside this dynamic range during either
calibration or measurement, results may be in error. An
over-range signal can be used to alert the operator and
measurement data examiners to this event.
3.6 The quantity of data points and their spacing may
affect the measurement results. This test method does
not specify the data point spacing (see Section 7.1.4.2);
results obtained with different data point spacings on
the same test samples may differ.
4 Referenced Standards
4.1 SEMI Standards
SEMI M1 — Specifications for Polished
Monocrystalline Silicon Wafers
SEMI MF1241 — Terminology of Silicon Technology
SEMI MF1530 — Test Method for Measuring Flatness,
Thickness, and Thickness Variation on Silicon Wafers
by Automated Non-contact Scanning
4.2 ASTM Standard
D 4356 — Practice for Establishing Consistent Test
Method Tolerances
2
NOTICE: Unless otherwise indicated, all documents
cited shall be the latest published versions.
5 Terminology
5.1 Definitions
5.1.1 mechanical signature, of an instrument — that
component of a measurement that is introduced by the
instrument and that is systematic, repeatable, and
quantifiable.
2 Available from ASTM International, 100 Barr Harbor Drive, West
Conshohocken, PA 19428, Tel: 610-832-9500, Fax: 610-832-9555,
Website
http://www.astm.org. Appears in Volume 14.02 of Annual
Book of ASTM Standards.
5.1.2 median surface, of a semiconductor wafer — the
locus of points equidistant from the front and back
surfaces of the wafer.
5.1.3 reference plane, of a semiconductor wafer — a
plane from which deviations of a specified surface of
the wafer are measured.
5.1.4 reference plane deviation (RPD) — the distance
from a point on a reference plane to the corresponding
point on a wafer surface.
5.1.4.1 Discussion — The front surface of a dome-
shaped wafer is considered to have positive RPD at its
center; the front surface of a bowl-shaped wafer is
considered to have negative RPD at its center.
5.1.5 sori, of a semiconductor wafer — the algebraic
difference between the most positive and the most
negative deviations of the front surface of a wafer that
is not chucked from a reference plane that is a least
squares fit to the front surface.
5.1.5.1 Discussion — The front surface may contain
regions with upward or downward curvature or both;
under some conditions the front surface may be flat.
5.1.6 thickness, of a semiconductor wafer — the
distance through the wafer between corresponding
points on the front and back surfaces.
5.2 Definitions of other terms related to silicon material
technology can be found in SEMI MF1241.
6 Summary of Test Method
6.1 A calibration procedure is performed to set the
instrument's scale factor and other constants. If the
representative wafer inversion method is used for
gravity correction, the calibration procedure also
determines the mechanical signature of the instrument
and the effect of gravity on the wafer.
6.2 The wafer is supported by a small-area chuck with
front surface up.
6.3 Both external surfaces are simultaneously scanned
along a prescribed pattern by an opposed pair of probes
to obtain a set of values of the distances between each
surface and the nearest probe. In each case, both
members of the pair of distances is taken at the same
value of the x and y coordinates.
6.4 The paired displacement values are used to
construct the median surface.
6.5 A correction for gravity effects on the median
surface is made either by subtracting a gravity
correction obtained (1) from measurements on a
representative wafer or (2) from theoretical
considerations or by repeating the scan with the wafer
inverted.