semi合集-English.pdf - 第7380页
SEMI MF1451-1104 © SEMI 2004 4 9 Suitability of Measuring Equipment 9.1 Determine the suitability of the measuring equipment with the use of a reference wafer and its reference sori value in acco rdance with the procedur…
SEMI MF1451-1104 © SEMI 2004 3
6.6 One half the thickness at each point is added to the
corrected median surface to construct the corrected
front surface.
6.7 A least-squares reference plane is constructed from
the corrected front surface.
6.8 The reference plane deviation (RPD) is calculated at
each measured pair of points.
6.9 Sori is reported as the algebraic difference between
the most positive RPD and the most negative RPD.
7 Apparatus
7.1 Measuring Equipment, consisting of wafer holding
device, multiple-axis transport mechanism, probe
assembly with indicator, and system
controller/computer, including data processor and
suitable software.
7.1.1 The equipment shall be direct reading with all
necessary calculations performed internally and
automatically as outlined in Section 11.2.
7.1.2 The equipment shall be equipped with an over-
range signal.
7.1.3 Instrument data reporting resolution shall be 100
nm or smaller.
7.1.4 The measuring equipment contains the following
subsystems:
7.1.4.1 Wafer-holding device, for example a chuck
whose face is perpendicular to the measurement axis,
and on which the wafer is placed for the measurement
scan. The nature and size of the wafer holding device
shall be agreed upon between the parties to the test.
7.1.4.2 Multiple-axis transport mechanism, which
provides a means for moving the wafer-holding device,
or the probe assembly, perpendicularly to the
measurement axis in a controlled fashion in several
directions. This motion must permit data gathering
over a prescribed scan pattern covering the entire fixed
quality area. Data point spacing to be used shall be
agreed upon between the parties to the test.
7.1.4.3 Probe assembly with paired non-contacting
displacement-sensing probes, probe supports, and
indicator unit (see Figure 1).
7.1.4.3.1 The probes shall be capable of independent
measurement of the distances a and b between the
probed site on each surface of the sample wafer and the
nearest probe surface.
Figure 1
Schematic View of Wafer, Probes, and Fixture
7.1.4.3.2 The probes shall be mounted above and
below the wafer in a manner so that the probed site on
one surface of the wafer is opposite the probed site on
the other.
7.1.4.3.3 The common axis of these probes is the
measurement axis.
7.1.4.3.4 The probe separation D shall be kept constant
during calibration and measurement.
7.1.4.3.5 Displacement resolution shall be 100 nm or
smaller.
7.1.4.3.6 The probe sensor size shall be 4 mm by 4
mm, or other value to be agreed upon between the
parties to the test.
7.1.4.3.7 Measuring equipment employing either the
Representative Wafer Inversion Method or the Sample
Wafer Inversion Method for gravity compensation must
provide precise positioning in both measurement
orientations so that measurements are taken at identical
locations for each orientation of the sample.
8 Materials
8.1 Set-up Masters — suitable to accomplish
calibration and standardization as recommended by the
equipment manufacturer.
8.2 Reference Wafer — with a reference sori value 20
m that is used to determine the level of agreement
between the sori value obtained by the measuring
equipment under test and the reference sori value (see
Section 9).
8.3 Representative Wafer — required only if the
Representative Wafer Inversion Method is used for the
gravity correction. A representative wafer shall be
identical in nominal diameter, nominal thickness,
fiducials, composition and crystalline orientation to
those being measured. Its sori need not be known.
SEMI MF1451-1104 © SEMI 2004 4
9 Suitability of Measuring Equipment
9.1 Determine the suitability of the measuring
equipment with the use of a reference wafer and its
reference sori value in accordance with the procedures
of Sub-section 9.2, or by performance of a statistically-
based instrument repeatability study to ascertain
whether the equipment is operating within the
manufacturer's stated specification for repeatability.
9.1.1 The reference sori value is the average of a
number of values obtained for that wafer over a number
of “passes” (repeat measurements). The reference
wafer is measured on the measuring equipment under
test and its reference sori value is compared against the
measured sori value. The acceptable level of the
agreement between the reference and measured sori
values is to be agreed upon by the parties to the test.
9.2 Procedure
9.2.1 Select a reference wafer of appropriate criteria,
together with its associated reference sori value.
9.2.2 Measure the reference wafer on the measuring
equipment under test to obtain a sample sori value.
9.2.3 Subtract the two sori values to obtain the
difference:
samplereferencesori
SoriSori
(1)
9.2.4 The metric to be used to determine acceptability
is difference,
sori.
Accept the measuring equipment as
suitable for use if this difference is less than a value that
is agreed upon between the parties to the test.
NOTE 3: If the measuring equipment is to be used to
measure other parameters, such as flatness and thickness
variation in addition to sori, the reference and sample sori
values may be included in the reference and sample data sets
specified in SEMI MF1530, but this is not necessary if only
sori measurements are to be made.
10 Sampling
10.1 This test method is nondestructive and may be
used on either 100% of the wafers in a lot or on a
sampling basis.
10.1.1 If samples are to be taken, procedures for
selecting the sample from each lot of wafers to be tested
shall be agreed upon between the parties to the test, as
shall the definition of what constitutes a lot.
11 Calibration and Standardization
11.1 Calibrate the measuring equipment in accordance
with the manufacturer's instructions.
11.2 When using the Representative Wafer Inversion
Method for correcting the gravity-induced deflection,
determine z
gravity
, the deflection due to gravity and
machine effects on the representative wafer, in
accordance with Section 12 and Section 13 through
paragraph 13.7.
12 Procedure
12.1 Prepare the apparatus for measurement of wafers,
including selection of diameter, peripheral fiducials,
scan area and data display/output functions. Also select
the gravitational correction method from one of the
following:
Reference Wafer Inversion Method (see Note 2),
Sample Wafer Inversion Method, or
Theoretical Modeling Method.
12.2 Select the fixed quality area (FQA) by specifying
the nominal edge exclusion (EE).
12.3 Introduce the test specimen into the measurement
mechanism with the front surface upward and initiate
the measurement sequence to determine and record the
distances between each probe and the nearest wafer
surface in pairs, a and b, at each measurement position.
Proceed directly to Section 13 unless (1) the Sample
Wafer Inversion Method is being used to correct for
effects of distortion due to gravity or (2) a
representative wafer is being measured to obtain the
gravity correction for use in the Representative Wafer
Inversion Method (see Note 2).
12.4 Repeat Section 12.2 with the wafer inverted (front
surface downward).
13 Calculations
13.1 The following calculations are performed
automatically within the instrument. An outline of the
calculation structures is provided here to indicate the
nature of the procedure.
13.2 Determine the displacements (distances) between
each probe and the nearest surface of the wafer (in
pairs) at intervals along the scan pattern.
NOTE 4: From Figure 1, note that the distance between
Probe A and the nearest surface of the wafer is displacement
value a and the distance between Probe B and the nearest
surface of the wafer is displacement value b.
13.3 Set the origin of the z-axis at the midpoint between
the two probes, A and B.
13.4 Find the distance, z
m
, of the median surface from
the z-axis origin at each point. From Figure 1,
22
t
a
D
z
m
(2)
SEMI MF1451-1104 © SEMI 2004 5
and
22
t
b
D
z
m
(3)
Therefore,
m
z
t
b
Dt
a
D
2
2222
(4)
and
2
ab
z
m
(5)
where
D = distance between Probes A and B,
a = distance between Probe A and the nearest
(top) wafer surface,
b = distance between Probe B and the nearest
(bottom) wafer surface, and
t = wafer thickness.
13.5 For measurements in the normal orientation (front
surface up), call the position of the median surface z
nor
.
13.6 For measurements in the inverse orientation (back
surface up), call the position of the median surface z
inv
.
13.7 For measurements on representative wafers or on
sample wafers when the Sample Wafer Inversion
Method is being used, determine the gravitational
correction to the median surface as follows:
2
invnor
gravity
zz
z
(6)
NOTE 5: This cancels the effect of the representative wafer's
shape while retaining the effect of gravity.
13.8 Determine the gravity compensated median
surface as follows:
13.8.1 Representative Wafer Inversion Method —
Subtract z
gravity
from z
nor
to produce z
com
at each
measurement point.
NOTE 6: The Representative Wafer Inversion Method deals
not only with first-order gravitational effects, but also with
other effects that may influence the measured value, such as
wafer-periphery effects, some machine-specific signature, etc.
13.8.2 Sample Wafer Inversion Method — Subtract
z
gravity
from z
nor
to produce z
com
at each measurement
point. Note that this is equivalent to taking the
difference between the normal and inverted
measurement values at each point:
22
invnorinvnor
norgravitynorcom
zzzz
zzzz
(7)
13.8.3 Theoretical Modeling Method — Apply
gravitational correction developed from a theoretical
model. Although a rigorous model is not known to
exist, approximate corrections have been calculated
3
(see Related Information 1).
13.9 Determine the thickness of the wafer at each point
from the following equation:
)( baDt
(8)
where the terms are defined after Equation (5).
13.10 Add one half the thickness to the gravity
compensated median surface z value at each point to
yield the gravity-compensated front surface:
2
t
zz
comfcom
(9)
13.11 Construct a reference plane that is a least-squares
fit to the gravity-compensated front surface data at all
the points of the of the scan pattern. The reference
plane is of the form:
RRRref
cybxaz
(10)
where a
R
, b
R
, and c
R
are constants selected so that
yx
RRRfcom
cybxayxz
,
2
)](),([ (11)
is minimized over the FQA (see Section 12.2).
13.12 Subtract the z-value of the reference plane (z
ref
)
from the compensated z-value, z
com
, at all the points of
the scan pattern to yield the reference plane deviation
(RPD) at each point:
reffcom
zzRPD
(12)
13.13 Calculate the sori of the wafer as the difference
between the maximum (most positive) and minimum
(most negative) RPD:
minmax
sori RPDRPD
(13)
13.14 Record the calculated sori value.
13.15 For referee or other measurements where the
wafer is measured more than once, calculate the
maximum, minimum, sample standard deviation,
average, and range of all measurements on the sample.
3 Application Note: “Gravitational Sag in Silicon Wafers,” ADE
Corporation, 80 Wilson Way, Westwood, MA 02090-1806, Nov. 20,
1991.