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SEMI E89-1104 E © SEMI 1999, 2004 3 independent of the value of the measurand, it is more appropriate to use it dir ectly rather than CV. 5.3.6 effect  change in the expected value of a given response due to the change …

SEMI E89-1104

3.2 This guide does not address those aspects of

measurement uncertainty associated with change in the

object being measured, either spatially or temporally.

3.3 This guide does not address determination of

measurement capability in the case of destructive

measurements on samples, or when the MS alters the

object being measured as a result of making the

measurement.

3.4 This guide does not apply to inter-laboratory

experiments designed to measure inter-laboratory

precision of test methods.

4 Referenced Standards

4.1 ISO Standards

ANSI/ISO Z540-2 — Guide to the Expression of

Uncertainty in Measurement

ANSI/ISO/ASQC A3534-1 — Statistics – Vocabulary

and Symbols – Part 1: Probability and General

Statistical Terms.

ISO 3534-3 — Statistics – Vocabulary and Symbols –

Part 3: Design of Experiments.

ISO 5725-2 — Accuracy (trueness and precision) of

measurement methods and results – Part 2: Basic

method for the determination of repeatability and

reproducibility of a standard measurement method.

ISO 9000 — Quality management systems –

Fundamentals and vocabulary, 2000.

NOTICE: Unless otherwise indicated, all documents

cited shall be the latest published versions.

5 Terminology

5.1 Terminology in this section that is not directly used

in this guide, is likely to be encountered while

conducting an MSA.

5.2 Definitions of many other terms related to

metrology and statistics can be found in VIM,

ANSI/ISO/ASQC A3534-1, and ISO 3534-3.

5.3 Definitions

5.3.1 accuracy — closeness of agreement between a

test result or the mean of a group of test results made on

an object and its true value.

2 ISO Central Secretariat, 1, rue de Varembé, Case postale 56, CH-

1211 Genève 20, Switzerland, web site:

www.iso.ch; ISO standards

are available in the United States through the American National

Standards Institute, web site:

www.ansi.org, and in most other

countries through the ISO member body.

3 International Vocabulary of Basic and General Terms in

Metrology, Second Edition [VIM] (ISO, Genève, 1993).

5.3.1.1 Discussion — Accuracy depends on both the

precision and bias of the measurement process. Since

random components of error (resulting in imprecision)

and systematic components of error (resulting in bias)

cannot be completely separated in routine use, the

reported accuracy must be interpreted as a combination

of these two elements.

5.3.2 bias — difference between the population mean

of the test results from a measurement process and the

true (accepted reference) value of the property being

measured.

5.3.2.1 Discussion — Bias is a systematic component

of measurement uncertainty. One or more systematic

error components may contribute to the bias. The true

value and the population mean are both unknown. The

true value may be estimated with the use of a consensus

value. If sufficient measurements are made to

adequately mitigate the effects of measurement

variability, the population mean may be estimated from

the sample mean





(1)

where:

x = sample mean,

n = number of measurements, and

= i

measurement value.

5.3.3 calibration — set of operations that establish the

relationship between values of quantities indicated by a

measurement system (MS) and the corresponding

values assigned to reference materials.

5.3.3.1 Discussion — The purpose of calibration is to

reduce or eliminate bias in the MS.

5.3.4 certified reference material (CRM) — reference

material, one or more of whose property values are

certified by a technically valid procedure, accompanied

by or traceable to a certificate or other documentation

issued by a certifying body.

5.3.5 coefficient of variation (CV) — population

standard deviation expressed as a percentage of the

mean value.

5.3.5.1 Discussion — CV can be estimated from the

sample standard deviation, s, and the sample mean,

,x of a distribution as follows:

100

CV (2)

CV is an appropriate measure of variability only when

the sample standard deviation is proportional to the

mean; otherwise it varies with the value of the

measurand. If the sample standard deviation is

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independent of the value of the measurand, it is more

appropriate to use it directly rather than CV.

5.3.6 effect  change in the expected value of a given

response due to the change of a given factor from one

level to another. It is a measure of influence that a

particular variable level has on the output variable.

5.3.6.1 fixed effect — variable for which estimates of

the mean are obtained for each level.

5.3.6.2 random effect — variable for which estimates of

the mean are not obtained for each level; rather the

variable is treated as a variance component.

5.3.7 factor — predictor variable whose level is

changed with the intent of assessing its effect on the

response variable (in a designed experiment) [adapted

from ISO 3534-3].

5.3.7.1 crossed factor(s) — two factors are crossed

when every level of one factor appears with every level

of the second factor.

5.3.7.2 fixed factor — factor that has either all of its

levels represented in an experiment or levels selected

by a nonrandom process.

5.3.7.3 nested factor(s) — factor that has a different set

of levels appearing within each level of a second factor.

Factor B is nested in factor A when randomization of

the levels of factor B is restricted to specific levels of

factor A.

5.3.7.4 random factor — factor that has randomly

sampled levels from a population of levels.

5.3.8 gage — alternate spelling of gauge.

5.3.9 gauge — instrument used to assign a value to a

quantitative or qualitative characteristic of a physical

entity or phenomenon.

5.3.10 interaction — effect for which the apparent

influence of one factor on the response variable

depends upon one or more other factors [ISO 3534-3].

5.3.11 level  value of a factor (in a designed

experiment) [adapted from ISO 3534-3]. Also called

“setting of a variable.”

5.3.12 linearity — absence of changes in variability or

bias as measurements are made at different points

within the measurement range.

5.3.12.1 Discussion — Traditional definitions of

linearity ignore the fact that variability can change over

the measurement range, as well as bias. The

assumption of constant variability over the

measurement range should be verified during the MS

analysis.

5.3.13 lower specification limit (LSL) — value of an

attribute below which a product is said to be

nonconforming.

5.3.14

matching tolerance (



) — difference in bias for

any two measurement systems (MSs) of the same kind

made under the conditions of reproducibility.

5.3.15 measurand — particular attribute of a phenome-

non, body or substance subject to measurement. [VIM]

5.3.16 measurement resolution, of a gauge — smallest

difference in measurand that can be meaningfully

distinguished by the gauge.

5.3.17 measurement subsystem  any set of entities,

processes, or conditions that share a common purpose

in the measurement.

5.3.17.1 Discussion — A measurement subsystem may

contain one or more of its own subsystems. For

example, a wafer handling mechanism may be further

composed of wafer loading and wafer positioning

subsystems.

5.3.18 measurement system (MS) — all entities,

procedures, and conditions that can influence the test

result obtained with a given measurement process.

5.3.18.1 Discussion — The MS may include, but is not

limited to, the gauge, operators, setup mechanics,

wafers, locations on a wafer, environmental conditions,

software used by the gauge, measurement method, etc.

The MS may be comprised of measurement

subsystems.

5.3.19 measurement system analysis (MSA) —

procedure in which relevant sources of bias and

variability associated with a measurement system (MS)

are estimated.

NOTE 2: MSA is also sometimes called gauge (or gage)

repeatability and reproducibility (GRR or GR&R).

5.3.20 nested design — experimental design in which

different levels of one factor appear in each level of a

second factor.

5.3.21 population standard deviation (



) — square root

of the population variance.

5.3.22 population variance (



) — measure of

dispersion associated with a population distribution.

5.3.22.1 Discussion — For continuous distributions, the

population variance is the second central moment.

5.3.23 precision — general estimator of the variability

of a measurement process about the mean value of the

test results obtained.

5.3.23.1 Discussion — Precision is a random

component of measurement uncertainty. Unless the

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measurement process is in a state of statistical control,

the precision of the process has no meaning. Since the

precision is poorer for greater dispersion of the test

results, specific measures of variability (such as

repeatability and reproducibility) are actually direct

measures of the imprecision of the measurement

process.

5.3.24 precision-to-tolerance (P/T) ratio — ratio of the

precision of a measurement system (MS) to the

tolerance (i.e., absolute magnitude of the full range of

the product specification).

5.3.24.1 Discussion — If the variability associated with

the measurement of a parameter by an MS is very small

compared with the width of the specification range, the

probability of obtaining a test result outside the

specification limits when the value of the parameter

actually lies within the specification limits (or

conversely) is quite small. On the other hand, if the

ratio is too large, the probability of obtaining a false test

result is much greater.

5.3.25 predictor variable — variable that can contribute

to the explanation of the outcome of a designed

experiment. Also called “input variable,” “descriptor

variable,” and “explanatory variable.”

5.3.25.1 Discussion — The term “independent variable”

is not recommended as a synonym due to potential

confusion with independence.

5.3.26 product standard deviation (



Product

) 

population standard deviation associated with the

distribution of values of all possible realizations of a

property of an entity manufactured under specified

conditions.

5.3.26.1 Discussion — The product variability may be

estimated by taking a representative sample from the

population and calculating its sample standard deviation

Product

) taking suitable account of MS variation (see

Section 10.2).

5.3.27 reference material — material or substance, one

or more of whose property values are sufficiently

homogeneous and well established to be used for the

calibration of a MS, for the assessment of a measure-

ment method or for assigning values to materials.

5.3.28 repeatability (



) — variability associated with

repeated measurements taken under repeatability

conditions.

5.3.29 repeatability conditions — test conditions

involving acquisition of a series of test results with the

same test protocol and MS setup in the same laboratory

by the same operator on the same equipment in the

shortest practical period of time on the same test wafer

without explicit recalibration.

5.3.29.1 Discussion — The acquisition of test data

under repeatability conditions is intended to avoid

influences of long-term drift, operator or MS

differences, material variability, and the like.

Recalibration of the MS is expected to cause

discontinuous differences in test results. However, if

recalibration is required by the test protocol or is

internal to the MS, it is considered to be an allowable

variation in determination of repeatability.

5.3.30 reproducibility (



) — variability associated

with the measurement system (MS) when

measurements are made under different (but typical)

conditions.

5.3.30.1 Discussion — Changes associated with

subsystems or test conditions are potential sources of

variation to be estimated. Repeatability is one source of

variation. Other relevant sources of variability may

include time, operator, setup procedure, wafer (of like

variety), measurement location, test instrumentation,

environmental conditions, etc. Although the total

number of contributors to the variance can be

exceedingly large, one typically focuses on a subset that

accounts for a significant portion of the expected MS

variability. For clarity, the selected subset should be

reported together with the reproducibility. If q different

conditions introduce variability into the measurement

independently from one another, the variances add

directly

1 qR



 K

(3)

and they may be separated by the use of judiciously

designed experiments.

5.3.31 response variable — variable representing the

outcome of a designed experiment. Also called “output

variable.”

5.3.31.1 Discussion — The term “dependent variable”

is not recommended as a synonym due to potential

confusion with independence.

5.3.32 root sum of squares (RSS) difference — square

root of the difference of the squares of two numbers.

5.3.33 root sum of squares (RSS) sum — square root of

the sums of the squares of two or more numbers.

5.3.34 sample standard deviation (s)  square root of

the sample variance.

5.3.35 sample variance (s

) — measure of dispersion

given by the average squared deviation from the mean

for a set of numbers.

5.3.35.1 Discussion — If x

is an individual

measurement,

x is the average across all

measurements, and n is the number of measurements,

then