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SEMI MF1618-1104 © SEMI 2004 8 made, and t he amount of information desi red about the uni formity of the thin film. The square cell s in this plan are not necessarily the shape or s ize of the sampling area for the meas…

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SEMI MF1618-1104 © SEMI 2004 7
A1-3 Concentric Circle Plans
2
A1-3.1 The concentric circle plans are designed so that
each measurement location samples approximately an
equal area of the specimen surface. Because these are
circular plans on a circular wafer, ideally they give
equal representation to all portions of the wafer’s
surface. This approximation to equal-area sampling
breaks down for the outermost circle if the size of the
edge exclusion is less then half the radial separation
between the inner circles for the spacing being used. In
this case, the measurements on the outer circle
represent a smaller area of silicon than do the
measurements on the inner circles. Moreover, if the
actual sampling area of the measurement being used is
larger than the value estimated in Section A1-1.1.1,
measurements on the outer circle may be partially
influenced by thin film properties in the excluded
region even though the resulting values are attributed to
the fixed quality area of the film.
A1-3.2
The concentric circle sampling plans utilize a
measurement at the wafer center and points on a
number of concentric circles designated 1, 2, 3, ... n, the
number of circles being chosen by the user according to
wafer diameter, estimated sampling area for the
measurement being made, and the amount of
information desired about the uniformity of the thin
film.
A1-3.2.1
On each circle, the measurements are
separated by equal angular intervals. Eight
measurements are made on the first circle, 16 are made
on the second circle, etc. In general, the number of
measurements is eight times the circle number. For the
first circle, measurements are separated by rotations of
45°, for the second circle, by 22.5°, and so forth,
regardless of the radial value of the measurement or the
wafer diameter.
A1-3.2.2
The radial values for the concentric circles are
determined as follows. Inspect Table A1-1 for the
number of total measurements that are made as a
function of the number of circles used and decide on the
number of circles according to the amount of
information needed for the film uniformity and the time
required for the test instrument to take that many
measurements. Call the chosen number of circles, N
C
.
Divide the value of the outermost radius, R
o
,
determined in Section A1-1.1, by N
C
. This gives the
radial increment between the circles. The center of the
measurement tool or measurement spot is to be placed
at the location given by this radial increment value.
2 Keenan, W. A., Johnson, W. M., and Smith, A. K., “Production
Monitoring of 200 mm Wafer Processing” in Emerging
Semiconductor Technology, ASTM International STP 960, edited by
D. C. Gupta and P. H. Langer (ASTM International, West
Conshohocken, PA, 1986) pp. 598–614.
Figure A1-2 illustrates measurement locations for three-
circle and four-circle sampling plans.
NOTE 3: If the incursion of the orientation flat(s) precludes
taking valid measurements near the flat in conjunction with
the chosen edge exclusion, the parties to the test may choose
to exclude specified measurement locations if the test
instrument permits or to replace specified sites with sites at a
distance from the flat that is equal to the distance specified
with respect to the circular perimeter of the wafer. It must be
remembered, however, that either such choice may have an
adverse impact on the interpretation of any two-dimensional
contour map.
Table A1-1 Number of Measurement Sites for
Various Numbers of Concentric Circles
Number of
circles
3 4 5 6 7 8
Number of
sites
49 81 121 169 225 289
A1-3.2.3 For consistency, place the wafer on the
instrument stage with the primary flat, or notch, facing
the operator. If another convention becomes necessary,
so note it on the report. Measurements are made
starting at the center of the wafer then proceeding
around the first, then the second, then the third circle,
and so forth. For all circles, make sure that the first
measurement is made at the same angular orientation;
the positive x-axis or the positive y-axis, as defined in
the wafer coordinate system specified in SEMI M20, is
recommended. The choice should have no bearing on
the data or its analysis. However, if data is to be
presented as a time-series plot, note on the plot the
position of the first point on each circle as well as
whether the measurements proceed in a clockwise or
counterclockwise fashion on the wafer surface.
A1-3.3
Calculate the uniformity based on the difference
between the maximum and minimum measured values,
HLV(%), and on the standard deviation as a percent of
the mean of all measurements, SUP(%) as detailed in
Section 9.3.
A1-4 Cartesian Sampling Plans
A1-4.1 Cartesian sampling plans sample equal areas in
the interior of the wafer surface, but fail to sample
portions of the wafer near its perimeter. They may not
provide sufficient information about the outermost
portion of the fixed quality area for a given application.
See Figure A1-3 for an illustration in the case of a 37-
point Cartesian sampling plan.
A1-4.2
These plans have a grid of equal-sized cells,
equally spaced about the center of the wafer. A
measurement is made in the center of each cell. The
number of rows and columns in the grid, always an odd
number, is chosen according to wafer diameter,
estimated sampling area for the measurement being
SEMI MF1618-1104 © SEMI 2004 8
made, and the amount of information desired about the uniformity of the thin film. The square cells in this plan are
not necessarily the shape or size of the sampling area for the measurement being used. In general, make sure that
the sampling area for the measurement is smaller than the dimensions of the square.
(a) Three-circle Case (b) Four-circle Case
NOTE: The radius R
o
is given by Equation A1-1 for Method A and by Equation A1-2 for Method B.
Figure A1-2
Illustrations of Concentric Circle Sampling Plans
NOTE: The radius R
o
as discussed in A1-1.1 is not shown in this figure.
Figure A1-3
Illustration of the Cartesian Measurement Site Plan for the Case of Seven Rows by Seven Columns
SEMI MF1618-1104 © SEMI 2004 9
Table A1-2 Approximate Number of Measurement
Sites for Various Numbers of Rows and Columns in
a Cartesian Sampling Plan
Number of
rows and
columns
7 9 11 13 15 17
Number of
sites
37 69 97 137 177 225
A1-4.3 The size of the cells, and the separation of the
measurement sites along the x- and y-axes, is
determined by the number of rows and columns into
which the wafer surface is partitioned. Use Table A1-2
as a guide to the approximate number of measurement
sites for various numbers of rows and columns of cells.
To calculate the dimensions of the square cells, divide
the outermost radius, R
o
, determined in Section A1.1,
by N, the desired number of rows and columns. The
exact number of sites that will be measured is governed
by the number of cells near the wafer perimeter that
need to be excluded because the center of the cell, that
is, the center of the measurement spot, does not fall
within the radius R
o
.
A1-4.4 Use test instrument software to establish the
coordinates of the center of all cells as determined from
the ratio R
o
/N
C
, calculated in Section A1-4.3. Disallow
measurement sites near the wafer perimeter such that
the radial distance to the center of the cell, that is, the
center of the measurement spot, is larger than R
o
. This
follows the same rationale for allowed measurement
sites as is used with the concentric circle plans.
A1-4.5
Take measurements at all sites allowed in
accordance with Table A1-2. The measurement
sequence, whether starting from the center point and
moving outward or starting from one edge a row or
column at a time, is to be decided by the parties to the
test.
A1-4.6
Calculate the uniformity based on the difference
between the maximum and minimum measured values,
HLV(%), and on the standard deviation as a percent of
the mean of all measurements, SUP(%), as detailed in
Section 9.3.
A1-5 Single-Diameter Sampling Plan
A1-5.1 This plan uses a very high density of
measurements along a diameter and includes a
measurement at the wafer center. It is shown
schematically in Figure A1-4 for the diameter being
parallel to a major wafer flat. However, in the case of
notched wafers, the notch would replace the flat in the
figure. It is also possible, by agreement of the parties to
the test, to make the measurements along a diameter at
a specified angle with respect to the fiducial axis as
long as such an angle is then stated in the report.
A1-5.2
Choose a value, N
M
, for the number of
measurements, where N
M
is at least 25. The separation
between measurement sites is given by 2R
o
/(N
M
1),
where R
o
is determined as in Section A1-1.1.
2R
o
/(N
M
–1)
NOTE: The radius R
o
is given by Equation A1-1 for Method
A and by Equation A1-2 for Method B.
Figure A1-4
Illustration of Single-Diameter, High-Density
Measurement Site Plan
A1-5.2.2 Compare the site separation, 2R
o
/(N
M
1),
with the estimated measurement sampling area or spot
size. If the interval is smaller than this value, little
additional information may be obtained by choosing so
large a value for N
M
; it may be appropriate to reduce N
M
so that the new calculated site separation is equal to or
greater than the measurement sampling area.
A1-5.3
Establish the coordinates for all measurement
sites using the site interval value just calculated and the
wafer center as the reference point. Take
measurements at all sites.
A1-5.4
Calculate the uniformity based on the difference
between the maximum and minimum measured values,
HLV(%), and on the standard deviation as a percent of
the mean of all measurements, SUP(%), as detailed in
Section 9.3.