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SEMI M32-0998 © SEMI 1998, 2004 8 APPENDIX 4 RATIONALE FOR STATISTI CAL SPECIFICATIONS NOTICE : This appendix was approved as an official part of SEMI M32 b y full let ter ballot proced ure. A4-1 Introduction A4-1.1 The …

SEMI M32-0998 © SEMI 1998, 2004 7

APPENDIX 3

CURRENT STATISTICAL CHARACTERIZATION OF SILICON

PROCESS PARAMETERS

NOTICE: This appendix was approved as an official part of SEMI M32 by full letter ballot procedure.

A3-1 Statistical Characterization of Silicon Process Parameters

A3-1.1 The following table describes the statistical characterization on a number of silicon wafer processes. The

comments column indicates the level of characterization that has been achieved. “Characterized” means that the

process should, under usual conditions, display the distribution shape shown. “Conditional” means that there are

conditions that might need to be considered before deciding if the shape shown is satisfactory. The chi-square

goodness of fit test was used to characterize the distribution shapes. Actual chi-square goodness of fit values will

typically be proprietary information that is shared only between a given supplier and user.

Table A3-1 Characterization of Silicon Processes

Process or Parameter

Description

Distribution

Shape

Comments

Diameter Normal Characterized

Flatness/Global (GBIR, GF3R, GF3D, GFLR, or GFLD) Lognormal Characterized

Flatness/Site (SF3R, SF3D, SFLR, SFLD, SFQR, SFQD, SBIR,

or SBID)

Lognormal Characterized

Oxygen Concentration Normal Conditional — Non-normalities are mostly

attributed to measurement error, so the

normal distribution is usually satisfactory.

Shape, Bow (Reference SEMI M1, Figure A2-1.) Normal Characterized

Shape, Warp, or Sori (Reference SEMI M1, Figure A2-1.) Lognormal Characterized

Thickness (Polished or EPI) Normal Characterized

SEMI M32-0998 © SEMI 1998, 2004 8

APPENDIX 4

RATIONALE FOR STATISTICAL SPECIFICATIONS

NOTICE: This appendix was approved as an official part of SEMI M32 by full letter ballot procedure.

A4-1 Introduction

A4-1.1 The purpose of a specification is either to

define acceptance criteria or to assist in quality

improvement planning. The basic intent is to quantify

user need so suppliers can accommodate that need.

Developing a clear link between user needs and the

control methods used on the production floor is one of

the most critical steps for creating a Total Quality

Management (TQM) environment. Following are some

key background concepts that allow the reader to

understand the conclusions drawn in this document.

A4-1.2 For most manufacturing processes there is no

such thing as “zero defects”. Processes are described by

statistical probability distributions, and the tails of these

functions can go all the way to infinity. For many years,

99.73% (i.e., ± 3 sigma) was used as the basis for

tolerances. “Within tolerance” was understood to mean

within tolerance with a 99.73% confidence, or a 0.27%

quality level. When users requested better levels, then

new standards such as 33 ppm or 3.4 ppm were made.

In any case, this quality level needs to be agreed upon

for a specification method to have meaning. It can be

measured in terms of ppm, Z, Cpk (which is equal to Z

divided by 3), or percent. Z tables or Cpk tables can be

obtained which provide this information.

A4-1.3 Errors in the 10% or higher range can be

generated if a percentile specification is based on the

central portion of the distribution. An example of such a

specification is “50% ≤ 1.2 microns”. These errors are

not obvious and require careful statistical analysis

based upon real process variation. Multiple percentile

specifications are also difficult to apply. Paragraph A4-

3 provides more details on these issues.

A4-1.4 Conversely, if specifications get too far out on

the tail, they tend to become abstract and are not used

as the primary factor driving quality improvements.

This is especially true for non-normal processes where

the tail of the distribution goes out much farther than

expected from a normal distribution. Figure A4-1

shows where a 3.4 ppm specification would be on a

lognormal process. Users usually will not allow that

much tolerance. However, if the specification is

tightened while the process capability remains the

same, then the consequence is a degradation in the

quality level.

1000

2000

3000

0.0 1.0 2.0 2.9 3.9 4.8 5.8 6.7 7.7 8.6 9.6

10 5

Figure A4-1

Lognormal Tolerance for 3.4 ppm Quality Level

A4-1.5 The mean and sigma specification is another

proposed approach. Intuitively, this seems promising,

but it has many of the same problems as multiple

percentile specifications. More details are given in

Paragraph A4-4.

A4-1.6 Errors in the 5% to 10% range can also be

generated if process distributions are assumed to be

normal when they are not. Knowing the actual

distribution shape is a key factor that opens up a

tremendous amount of knowledge. Figure A4-2 shows

an example of real data that illustrates a lognormal

process. In the past, this was considered to be difficult

because non-normal distributions were only supported

by high-level statistical software. Now even

spreadsheets have them. It should also be noted that

once the process characterization has been done, the

shape of the distribution typically does not change, so

this knowledge can be shared throughout the industry.

Regularly monitoring the process by overlaying the

distribution on the process histogram or cumulative

frequency plot is extremely valuable to confirm that the

process is not taking on unnatural bimodal or outlier

effects. One-sided distributions such as flatness and

warp are so well-characterized by the lognormal

distribution that “goodness-of-fit” results are very close

to 100%. Again, the error gets larger as the point-of

interest moves toward the “center” of the distribution,

but the major concern is the length of the tail. The

lognormal distribution in Figure A4-2 (the curve with a

solid line which is clearly not symmetrical) has a tail

that extends much farther to the right than the normal

distribution which is shown with a dashed line. This

effect, and the impact, is shown in more detail in

Appendix 2.

SEMI M32-0998 © SEMI 1998, 2004 9

500

1000

1500

2000

2500

0.0 1.0 2.0 2.9 3.9 4.8 5.8 6.7

Figure A4-2

Normal vs. Lognormal Shape

A4-1.7 Statistical specifications quantify the quality

level so it is not an abstract assumption left to

conjecture. This allows both the user and supplier to

optimize their control systems to that level. Capability

based sampling is one example. Simply put, this means

to use process capability information to help define the

sampling plan for a process. A detailed discussion of

this subject is beyond the scope of this document, but

the basic concept is easy to understand. If a process is

very capable and controlled it does not need as much

sampling as one that is not. Implementing this strategy

is a big step ahead of standard sampling theory. It might

be the only way to rigorously transfer from inspection

based quality to process control based quality, without

incurring high risks. Statistical specifications create the

environment which facilitates this improved strategy.

Hopefully, the quality levels would be defined in ppm,

but any level agreed upon by both the user and the

supplier would work.

A4-2 Tolerance Specifications

LSL to USL, or Target ± xx

A4-2.1 The main problem with a conventional

tolerance is that many people perceive it as a goal post

that requires 100% of the material to fall inside. This

document has shown in detail that this is simply a

wrong perception. Stating the quality level in the

specification, instead of just implying it, corrects this

problem.

A4-2.2 Another common misconception is that

tolerances and tail probabilities divert attention away

from centering the process. Of course, centering is

important. Considering the impact of poor quality on all

customers, it is clear that a well centered process is far

more efficient than one that is not. It is also generally

true that the suitability of the product is not

significantly different immediately on one side of a

tolerance line compared to the other. However, there

are a number of issues that warrant discussion.

A4-2.2.1 First, centering is usually not difficult, so it

usually does not need a major emphasis. Those who are

experienced in quality improvement techniques would

certainly not forget to center the process. Simply

monitoring the mean trend gives an excellent measure

of centering, and it keeps the focus on the process

rather than the specification. Industry carries a long

history where specifications prevented the attainment of

good process control. Many of the issues have been

explained earlier in this document. To summarize,

process controls are the only way to truly maintain a

centered process, and these controls can only work if

there is enough tolerance in the specification to

accommodate the sensitivity limitations of the control

methods.

A4-2.2.2 The second issue is that it might not be

possible to center. This is clearly the case in one-sided

processes that are bounded by zero. Optimizing

multiple parameters might also dictate that some

parameters get worse.

A4-2.2.3 The final, and most important, issue is the

challenge of teaching statistical methods to the factory

population. It is very easy to teach averages and

centering since they tend to be well understood already.

It is not as easy to teach sigma and the fact that sigma

trends must be thoroughly understood before much of

anything can be said about averages. Confirming that

the R or S chart is controlled before studying the Xbar

chart and doing an F-test before doing a t-test are just

two examples. These are very important concepts that

must be fully understood in order to apply statistical

methods. Over-stressing centering de-emphasizes sigma

and creates an environment where it is not appreciated.

Thinking in terms of sigma is the most important

concept that most people will learn about process

control methods. It deserves a major emphasis.

A4-2.2.4 Of course, centering would be a concern if

mixing and matching of lots is the control method, but

this can be easily spotted in the statistical

characterization process. The fact that some of the

alternatives to tolerances are much more likely to cause

this practice will be further explained in Paragraphs A4-

3 and A4-4.

A4-3 Multiple Distributional Percentile

Specifications

≤

A, %

≤

B, and % ≤ C

A4-3.1 Errors in the 10% or higher range can be

generated if a specification in the central portion of the

distribution is used. An example of such a specification

is “50% ≤ 1.2 microns”.