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SEMI M21-0304 © SEMI 1992, 2004 1 SEMI M21-0304 GUIDE FOR ASSIGNING ADDRESS ES TO RECTANGULAR ELEMENTS IN A CARTESIAN ARRAY This guide was technically approved b y the Global Silicon Wafer Com mittee and is the direct re…

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SEMI M20-1104 © SEMI 1991, 2004 4
RELATED INFORMATION 1
APPLICATIONS OF THE WAFER COORDINATE SYSTEM
NOTICE: This related information is not an official part of SEMI M20. It was developed during the original
development of the document. This related information was approved for publication by full letter ballot
procedures.
R1-1 SEMI E5, in Stream 12 — Wafer Mapping, delineates how a coordinate system for reporting position data
may be communicated. The origin of this coordinate system, which is specified by the equipment when generating
the wafer map, may be the site at any of the four corners of the array or at the array center. In addition, the stream
provides for transmission of an arbitrary number of reference points to relate the map coordinate system to the
physical wafer. The wafer coordinate system may be used to establish the locations of these reference points and of
the origin of the map coordinate system.
R1-2 SEMI M17 defines a polar array of 1000 elements which can be used to identify the locations on a wafer of
extended defects such as slip. This array is consistent with the wafer coordinate system.
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 mentioned herein. These standards are subject to change without notice.
The user’s attention is called to the possibility that compliance with this standard may require use of copyrighted
material or of an invention covered by patent rights. By publication of this standard, SEMI takes no position
respecting the validity of any patent rights or copyrights asserted in connection with any item 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.
Copyright by SEMI® (Semiconductor Equipment and Materials
International), 3081 Zanker Road, San Jose, CA 95134. Reproduction
of the contents in whole or in part is forbidden without express written
consent of SEMI.
SEMI M21-0304 © SEMI 1992, 2004 1
SEMI M21-0304
GUIDE FOR ASSIGNING ADDRESSES TO RECTANGULAR ELEMENTS
IN A CARTESIAN ARRAY
This guide was technically approved by the Global Silicon Wafer Committee and is the direct responsibility
of the North American Silicon Wafer Committee. Current edition approved by the North American Regional
Standards Committee on October 16, 2003. Initially available at www.semi.org February 2004; to be
published March 2004. Originally published in 1992; last published September 1998.
1 Purpose
1.1 It is frequently very useful to have a standardized
method for labeling elements in an array on a silicon
wafer surface.
1.2 This guide defines an element addressing conven-
tion for locating and uniquely identifying rectangular
elements in a Cartesian array.
1.3 Such arrays are useful in locating sites for site
flatness characterization, defect mapping, determination
of parametric distributions, etc. on unpatterned
semiconductor wafers.
2 Scope
2.1 This guide covers procedures for assigning
addresses that can be used to locate and identify
rectangular elements in a Cartesian array. The array
may be regular or tiled in one direction.
2.2 Relating the position of the array to the wafer
surface is outside the scope of this guide, but it may be
established through use of the wafer coordinate system
defined in SEMI M20.
2.3 This guide covers procedures for assigning a
unique identification (address) for each element in the
array. An example of the results obtained by following
this procedure are given in Related Information 1.
2.4 The element addressing convention in this guide
provides an orderly progression along perpendicular
directions with addresses of adjacent elements in any
direction differing by 1. Consequently, distances may
be calculated in a unified way.
2.5 For complex patterns, more than one array on a
wafer may be defined and related to the same
coordinate axes.
2.6 The element addressing convention in this guide is
consistent with that of the polar array specified in SEMI
M17. In addition, element addresses can be readily
transformed to addresses in other types of addressing
conventions for Cartesian arrays as described in Related
Information 2.
NOTICE: This standard does not purport to address
safety issues, if any, associated with its use. It is the
responsibility of the users of this standard to establish
appropriate safety and health practices and determine
the applicability of regulatory or other limitations prior
to use.
3 Referenced Standards
3.1 SEMI Standards
SEMI M1 — Specifications for Polished
Monocrystalline Silicon Wafers
SEMI M2 — Specification for Silicon Epitaxial Wafers
SEMI M11 — Specification for Silicon Epitaxial
Wafers for Advanced Applications
SEMI M17 — Guide for a Universal Wafer Grid
SEMI M20 — Practice for Establishing a Wafer
Coordinate System
SEMI MF1241 — Terminology of Silicon Technology
NOTICE: Unless otherwise indicated, all documents
cited shall be the latest published versions.
4 Terminology
4.1 Many terms used in silicon wafer technology are
defined in SEMI MF1241.
4.2 Definitions of additional terms may be found in
SEMI M1, SEMI M2, or SEMI M11.
5 Array Element Layout
5.1 The array is constructed from m vertical columns
and n horizontal rows of identical elements of
dimension a horizontally and b vertically. The number
of elements in different rows and columns may vary to
suit the application.
5.2 The address of an element is given by two numbers
separated by a comma: (i,j). The first number, i,
indicates the column and the second, j, the row.
5.3 The longest row and the longest column are used in
identifying the Starting Element, which is assigned the
address (0,0).
SEMI M21-0304 © SEMI 1992, 2004 2
5.4 The array may have a tiled appearance, either with
one or more rows offset relative to the row containing
the Starting Element (row tiling) or with one or more
columns offset relative to the column containing the
Starting Element (column tiling).
5.4.1 For row tiling, the offset, t
r
, is a fraction (p
r
/q
r
) of
the horizontal element dimension, a, where p
r
and q
r
are
small whole numbers.
5.4.2 For column tiling, the offset, t
c
, is a fraction
(p
c
/q
c
) of the vertical element dimension, b, where p
c
and q
c
are small whole numbers.
5.4.3 In either case, the offset may be constant or it
may vary from row to row or column to column. When
the offset is constant, the array pattern is repeated every
q
r
rows or q
c
columns.
6 Element Addresses
6.1 Define the array center as the intersection of the
vertical and horizontal array centerlines, found as
follows:
6.1.1 If the array is regular (not tiled):
6.1.1.1 Count the number of elements, m, in the longest
row.
6.1.1.2 If m is even, start at the leftmost element, count
m/2 elements to the right, and construct a line along the
right vertical boundary of this element. This line is the
vertical array centerline (see Figure 1a).
6.1.1.3 If m is odd, start at the leftmost element, count
the integer of m/2 elements to the right, continue to the
next element to the right, and construct a line through
the center of this element. This line is the vertical array
centerline (see Figure 1b).
6.1.1.4 Count the number of elements, n, in the longest
column.
6.1.1.5 If n is even, start at the topmost element, count
down n/2 elements, and construct a line along the
bottom horizontal boundary of this element. This line is
the horizontal array centerline (see Figure 1c).
6.1.1.6 If n is odd, start at the topmost element, count
down the integer of n/2 elements, continue down to the
next element, and construct a line through the center of
this element. This line is the horizontal array centerline
(see Figure 1d).
6.1.2 If the columns of the array are tiled (see Figure
2a):
6.1.2.1 Count the number of columns, m, in the widest
part of the array from left to right.
6.1.2.2 If m is even, start at the leftmost column, count
m/2 columns to the right, and construct a line along the
right vertical boundary of this column. This line is the
vertical array centerline.
6.1.2.3 If m is odd, start at the leftmost column, count
the integer of m/2 columns to the right, continue to the
next column to the right, and construct a line through
the center of this column. This line is the vertical array
centerline.
6.1.2.4 Count the number of elements, n
′
, in the
column which contains or is immediately to the right of
the vertical array centerline, depending on whether m is
odd or even, respectively.
NOTE 1: The number, n
′
, is usually equal to but may be less
than n.
6.1.2.5 If n
′
is even, start at the topmost element, count
down n
′
/2 elements, and construct a line along the
bottom horizontal boundary of this element. This line is
the horizontal array centerline.
6.1.2.6 If n
′
is odd, start at the topmost element, count
down the integer of n
′
/2 elements, continue down to the
next element, and construct a line through the center of
this element. This line is the horizontal array centerline.
6.1.3 If the rows of the array are tiled (see Figure 2b):
6.1.3.1 Count the number of rows, n, in the widest part
of the array from top to bottom.
6.1.3.2 If n is even, start at the topmost row, count
down n/2 rows, and construct a line along the bottom
horizontal boundary of this row. This line is the
horizontal array centerline (see Figure 1c).
6.1.3.3 If n is odd, start at the topmost row, count down
the integer of n/2 rows, continue down to the next row,
and construct a line through the center of this row. This
line is the horizontal array centerline (see Figure 1d).
6.1.3.4 Count the number of elements, m
′
, in the row
which contains or is immediately above the vertical
array centerline, depending on whether n is odd or
even, respectively.
NOTE 2: The number, m
′
, is usually equal to but may be less
than m.
6.1.3.5 If m
′
is even, start at the leftmost element,
count m
′
/2 elements to the right, and construct a line
along the right vertical boundary of this element. This
line is the vertical array centerline.
6.1.3.6 If m
′
is odd, start at the leftmost element, count
the integer of m
′
/2 elements to the right, continue to the
next element to the right, and construct a line through
the center of this element. This line is the vertical array
centerline.