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SEMI M32-0998 © SEMI 1998, 2004 2 5.2.5 quality level — The ma xi mum d efe ct l eve l agreed upon by the user and the supplier. 5.2.6 supplier risk — The risk of rejecting material that is within the user specifications…
SEMI M32-0998 © SEMI 1998, 2004 1
SEMI M32-0998 (Reapproved 0704)
GUIDE TO STATISTICAL SPECIFICATIONS
This guide was technically reapproved by the Global Silicon Wafer Committee and is the direct responsibility
of the North American Silicon Wafer Committee. Current edition reapproved by the North American
Regional Standards Committee on March 14, 2004. Initially available at www.semi.org May 2004; to be
published July 2004. Originally published September 1998.
1 Purpose
1.1 Specifications are based on requirements
negotiated between trading partners. This document
describes an explicit specification form that defines the
risk level as a part of parametric specifications. This
approach uses process capability information to focus
quality improvement efforts, reduce sampling, and
maintain low risks. It is based on the fundamental belief
that specifications should facilitate the movement
toward processed-in quality instead of inspected-in
quality.
1.2 It is important for users and suppliers to
acknowledge and mutually agree on quality levels so
the methods employed will satisfy their expectations.
Statistical specifications provide a convenient way to
do this.
1.3 Statistical specifications are designed to facilitate
the movement toward processed-in quality. They are
most appropriate for processes that have been
statistically characterized. This means the shape of the
statistical distribution that created the product is known,
or can be approximated to the satisfaction of the user
and the supplier. It also implies that the statistical
control of the process and the measurement systems are
defined to the level that is necessary to meet the current
needs.
2 Scope
2.1 This guide may be used when changing or adding
specifications to SEMI M18.
2.2 Statistical specifications apply to all processes that
have been statistically characterized. Solutions are
given for two product distribution shapes (normal &
lognormal), and the advantages of these solutions are
explained. Appendix 3 shows the statistically
characterized shape for many common silicon wafer
processes.
2.3 This guide applies to processes related to the
production and use of silicon wafers. It may also be
applied to the production and use of other materials.
2.4 This approach implies that the quality level shipped
is the same as the quality level produced.
2.5 This methodology can be an effective tool for
driving quality improvement.
2.6 This procedure can be coupled with other
techniques for centering the mean and reducing the
variation within the process distribution as deemed
necessary by the user and supplier.
2.7 Appendix 4 further explains the rationale for this
approach.
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 Limitations
3.1 Outlier effects are beyond the scope of this
document.
4 Referenced Standard
4.1 SEMI Standard
SEMI M18 — Format for Silicon Wafer Specification
Form for Order Entry
NOTICE: Unless otherwise indicated, all documents
cited shall be the latest published versions.
5 Terminology
5.1 Abbreviations and Acronyms
5.1.1 Cpk — process capability index
5.1.2 ppm — parts per million
5.2 Definitions
5.2.1 capability based sampling — any method that
uses the process capability as a factor in determining
the required sampling.
5.2.2 ECPK — process capability index on a non-
normal process which is corrected for non-normality.
5.2.3 error — the difference between the quality level
committed to a user and the level that could be
received.
5.2.4 process capability index (Cpk) — the smaller of
(upper spec limit - mean) ÷ 3 sigma, or (mean - lower
spec limit) ÷ 3 sigma.
SEMI M32-0998 © SEMI 1998, 2004 2
5.2.5 quality level — The maximum defect level
agreed upon by the user and the supplier.
5.2.6 supplier risk — The risk of rejecting material that
is within the user specifications.
5.2.7 user risk — The risk of accepting material that is
outside the user specifications.
6 Solutions
6.1 The following are examples of statistical
specifications for normal and lognormal distributions.
6.1.1 Normal — The normal distribution describes
processes that target a specific value and have
symmetric random variation about that value. The first
portion of the normal statistical specification is the
familiar tolerance. It uses an upper specification limit
(USL) and a lower specification limit (LSL), or the
target plus and/or minus a value. The second portion,
after the @ sign below, is a measure of the quality
level, in ppm.
LSL to USL @ yy ppm, o
r
Target ± xx @ yy ppm
6.1.2 Lognormal — The lognormal function describes
many of the one-sided distributions that are
encountered in the silicon industry. It applies to those
parameters such as flatness and warp that are bounded
by zero. For lognormal processes, the value of a
parameter could be specified as:
≤ xx @ yy ppm
6.2 More details, and examples of use, are shown in
Appendix 1 for normal applications and Appendix 2 for
lognormal applications.
6.3 For process distributions not following normal or
lognormal forms, Pearson or other distributions may be
used.
SEMI M32-0998 © SEMI 1998, 2004 3
APPENDIX 1
USING STATISTICAL SPECIFICATIONS FOR NORMAL PROCESSES
NOTICE: This appendix was approved as an official part of SEMI M32 by full letter ballot procedure.
A1-1 Statistical Specification Format for
Normal Distributions
A1-1.1 The normal distribution is quite well-known. It
describes processes that target a specific value and have
symmetric random variation about that value. Below
are examples of statistical specifications for normal
processes. The first portion is the familiar tolerance,
and the second portion is a measure of the quality level.
LSL to USL @ yy ppm, o
r
Target ± xx @ yy ppm
Other standard tolerance definitions could be
substituted, or other definitions of the quality level such
as Cpk, Z-value, or percent could be used.
A1-1.2 Adding the quality level removes the potential
for misunderstanding and makes the specification more
meaningful.
A1-2 Example of Use
A1-2.1 Functionally, statistical specifications are
similar to conventional tolerances, except that the
quality level is stated rather than just implied. They can
be directly substituted for tolerances or other forms of
specifications. Statistical specifications are especially
useful for focusing quality improvement efforts,
achieving ship-to-stock relationships, promoting
processed in quality, and reducing after the fact
inspection. In this environment they could be used as
follows:
A1-2.1.1 Through audits and capability reporting a
particular parameter is targeted for improvement or
chosen as a ship-to-stock candidate.
A1-2.1.2 The control methods, distribution shape, and
statistical specification are agreed upon. The tolerance
and quality level defined in the statistical specification
completely define the needed process capability.
A1-2.1.3 Once it is shown that the required capability
is consistently exceeded then reduced inspection
sampling can be implemented without increasing the
risk to the customer or supplier. In this way the process
controls can gradually become the guarantee for
quality, and after the fact inspection can be gradually
reduced to the level that is needed for outgoing quality
reporting.
A1-3 Discussion
A1-3.1 Statistical specifications remove ambiguity,
allow small risks, and promote the movement toward
better process controls and less after the fact inspection.
The quality level (i.e., the yy portion) is often
misunderstood. Some people say they want ppm level
quality but introduce methods that allow 50,000 to
200,000 ppm in error. This causes confusion.
A1-3.2 Many people have the misconception that
tolerances are goal posts that require 100% of the
material to fall inside. Processes are usually described
by statistical distributions, so specifications have little
meaning if a quality level is not defined. For many
years, 99.73% (i.e., ± 3 sigma) was considered to be
satisfactory. “Within tolerance” was understood to
mean within tolerance with a 99.73% confidence, or a
0.27% quality level. Later the 99.73% process was
defined as “cruel”. 0.27% was no longer an acceptable
quality level, and process drift was understood to cause
even higher reject rates. This led to the demand for
better process capabilities (i.e., higher Cpk’s), which
demanded corresponding improvements in process
characterization and control methodologies. At the
same time other users tightened their tolerances to the
point that led to over-control. Either extreme can cause
a mismatch between expectations and capabilities if the
risks are not carefully evaluated.
A1-3.3 Capability-based sampling is perhaps the only
way to rigorously transfer from inspection-based
quality to process control-based quality, without
incurring high risks. Statistical specifications create the
environment for this to work. Once the specification is
clearly defined, it can be clearly achieved. The details
of capability based sampling are beyond the scope of
this document, but the basic concept is easy to
understand. If a process is very capable and controlled,
then the system can be relied upon to create the
necessary quality level with less after the fact
inspection. This is good for both sides. Users get more
reliable quality, and suppliers get the information
needed to focus quality improvement efforts and direct
resources at the most critical processes.