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SEMI MF1618-1104 © SEMI 2004 9 Table A1-2 Approximate Nu mber of Measurement Sites for Various Numbers of Row s and Columns in a Cartesian Sampling Plan Number of rows and columns 7 9 11 13 15 17 Number of sites 37 69 97…

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

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

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

, 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

A1-4.4 Use test instrument software to establish the

coordinates of the center of all cells as determined from

the ratio R

, 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

. 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

, for the number of

measurements, where N

is at least 25. The separation

between measurement sites is given by 2R

/(N

 1),

where R

is determined as in Section A1-1.1.

/(N

–1)

NOTE: The radius R

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

/(N

 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

; it may be appropriate to reduce N

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.

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