Background Statement for SEMI Draft Document #5225A
New Standard: Test Method for Determining the Counting Efficiency
of Liquid-borne Particle Counters for which the Minimum Detectable
Particle Size is between 30nm and 100nm
Notice: This background statement is not part of the balloted item. It is provided solely to assist the recipient in
reaching an informed decision based on the rationale of the activity that preceded the creation of this Document.
Notice: Recipients of this Document are invited to submit, with their comments, notification of any relevant
patented technology or copyrighted items of which they are aware and to provide supporting documentation. In this
context, “patented technology” is defined as technology for which a patent has issued or has been applied for. In the
latter case, only publicly available information on the contents of the patent application is to be provided.
Background Statement
In semiconductor industry, a wide variety of liquid-borne particle counters has been used. Recently, controlled
particle size has been shifting to below 100 nm, however, the difference of measurement value between liquid-borne
particle counters is becoming actual, especially in case of the measurement particle size to 100 nm or less. The main
reason depends on that the counting efficiency test method for smaller particles than 100 nm sizes has not been
standardized. By standardization of this test method, it is expected that the difference of counting efficiency between
various particle counters in a market will become small.
This document was voted at the cycles 1 in 2012 and was rejected by appropriate notice about the erroneous
descriptions in the measurement procedure of background particles. Japan Liquid Particle Counter Task Force
corrected about the procedure of the background particles measurement, and some unsuitable equations and terms.
Moreover, NA UPW Filter Performance TF proposed to clarify the range of object particle size. As result of the
discussion in Japan Liquid Chemicals Committee, the title and the purpose were changed so that the range of object
particle size should be limited between 30 nm to 100 nm.
This ballot is distributed to the Liquid Chemicals Committee with intercommittee ballot to the Gases Committee.
The voting results of this ballot will be reviewed by the Liquid Particle Counter Task Force (date is TBD), and will
be adjudicated by the Japan Liquid Chemicals Committee at their meeting scheduled on Friday, July 20, 2012 at
SEMI Japan, Tokyo, Japan.
If you have any questions on this ballot, please contact the following Task Force leaders or SEMI Staff:
Liquid Particle Counter Task Force co-leaders:
Kaoru Kondo (RION) at kkondo@rion.co.jp
Kazutoshi Kato (PMS) at kkato@pmeasuring.com
SEMI Staff
Naoko Tejima (SEMI Japan) at ntejima@semi.org
Semiconductor Equipment and Materials International
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DRAFT
SEMI Draft Document 5225A
New Standard: Test Method for Determining the Counting Efficiency
of Liquid-borne Particle Counters for which the Minimum Detectable
Particle Size is between 30nm and 100nm
1 Purpose
1.1 This document is to provide a test sequence for determining the counting efficiency of liquid-borne particle
counters for which the minimum detectable particle size is between 30nm and 100 nm.
2 Scope
2.1 This document covers the counting efficiency test system for liquid-borne particle counters by using the
quantified particle number concentration sample.
2.2 This document defines the test conditions for the counting efficiency test of liquid-borne particle counters.
2.3 The following areas are to be addressed in this document:

Mass concentration of original polystyrene latex (PSL) particle suspension

Factor for calculating the dilution ratio such as fluid, flow rate, pressure, volume, PSL particle number
concentration, etc.

Type of an equipment under test (EUT) liquid-borne particle counter

Type of PSL particles

Description of the test report
NOTICE: SEMI Standards and Safety Guidelines do not purport to address all safety issues associated with their
use. It is the responsibility of the users of the Documents to establish appropriate safety and health practices, and
determine the applicability of regulatory or other limitations prior to use.
3 Limitations
3.1 This test method is limited to testing the counting efficiency by measuring mono-dispersed PSL particles.
However, actual particle size distribution is mostly poly-dispersed and the size distribution varies. So, there may be a
certain level of difference between this test result and actual measurement data.
3.2 This test method is not in opposition to the concepts for the test method of the counting efficiency defined by
ISO21501-2. Rather, it may become a test method effective in the performance check of the reference instrument for
which is requested by ISO 21501-2.
3.3 In this standard practice, in order to enable actual practice, the particle number concentration of test PSL
particles suspension is obtained from a mean size and mass concentration which a manufacturer defines. More exact
number concentration may be obtained by consideration of the size distribution, and precision mass measurement. At
least, it has been experienced that the number concentration obtained from the mean size and mass concentration
from a manufacturer is properly reasonable in case of the over 50 nm PSL particles.
4 Referenced Standards and Documents
4.1 SEMI Standards
SEMI F63 ― Guide for Ultrapure Water Used in Semiconductor Processing
SEMI F104 ― Particle Test Method Guidelines for Evaluation of Components Used in Ultrapure Water and Liquid
Chemical Distribution Systems
This is a Draft Document of the SEMI International Standards program. No material on this page is to be construed as an official or adopted Standard or Safety Guideline.
Permission is granted to reproduce and/or distribute this document, in whole or in part, only within the scope of SEMI International Standards committee (document
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DRAFT
4.2 ISO Standards1
ISO 21501-2 ― Determination of particle size distribution - Single particle light interaction methods - Part2: Light
scattering liquid-borne particle counter
ISO 14644-1 ― Cleanrooms and associated controlled environments - Part 1: Classification of air cleanliness
NOTICE: Unless otherwise indicated, all documents cited shall be the latest published versions.
5 Terminology
5.1 Abbreviations and Acronyms
5.1.1 CV ― coefficient of variation
5.1.2 EUT ― equipment under test.
NOTE 1: The meaning in this document is a particle counter tested.
5.1.3 FC ― flow controller
5.1.4 1st (First) Sample ― primary dilution PSL particle suspension
5.1.5 FM ― flow meter
5.1.6 LPC ― liquid-borne particle counter
5.1.7 PSL ― polystyrene latex
5.1.8 UPW ― ultrapure water
5.2 Definitions
5.2.1 background ― the number counts of LPC when supplying UPW.
5.2.2 coincidence loss ― counting loss of particles which occurs if two or more particles exist simultaneously
within a particle detection area or signal processing time.
5.2.3 minimum detectable particle size ― smallest particle size that LPC can show as threshold.
NOTE 2: The below terms are defined in ISO 21501-2.

size resolution

counting efficiency

false count rate

minimum detectable particle size
6 Apparatus and Reagent Materials
6.1 EUT
6.1.1 EUT is LPC which uses a light scattering principle for the particle detection method.
6.1.2 The minimum detectable particle size of the EUT should be between 30 nm and 100 nm.
6.1.3 It is recommended that EUT is within the term of validity of the calibration certificate by the manufacturer.
6.2 UPW
6.2.1 Use the UPW with the resistivity more than 17 MΩ cm.
6.2.2 Temperature of the UPW shall be adjusted to 25 ± 5 ℃.
6.2.3 Refer to SEMI F63 for the other qualities of the UPW.
1
International Organization for Standardization, ISO Central Secretariat, 1 rue de Varembé, Case postale 56, CH-1211 Geneva 20, Switzerland;
Telephone: 41.22.749.01.11, Fax: 41.22.733.34.30, http://www.iso.ch
This is a Draft Document of the SEMI International Standards program. No material on this page is to be construed as an official or adopted Standard or Safety Guideline.
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6.2.4 Operating pressure downstream of the EUT should be > 100 kPa (gauge pressure) during testing. The limit of
this pressure value is not required when it is confirmed that FC and FM can operate normally.
6.3 Particle Injection Device
6.3.1 Use a particle injection device that can inject a particle at constant flow rate without pulsations.
6.3.2 The accuracy of an injection flow rate and the pressure range of use shall be specified.
6.4 PSL Particle
6.4.1 Use the mono-disperse PSL particles, that is traceable to an international standard of length, and where the
standard uncertainly of the mean particle size is equal to or less than ± 2.5 %.
6.4.2 Since a width of size distribution of test PSL particles affects the uncertainty of measurement results (See §A4
in Appendix 1), the test PSL particles by which the standard deviation of particle size distribution is disclosed shall
be used.
6.4.3 Main suspension material is UPW. Any materials, such as high concentration surfactant which may influence
the size distribution of PSL particles should not be included.
6.5 Test Environment
6.5.1 The recommended cleanliness of the test environment is greater than ISO Class 7 defined in ISO 14644-1.
6.5.2 Temperature of the test environment shall be adjusted to 25±5 ℃.
7 Procedure
7.1 Test Circuit
7.1.1 For this test method, use the schematic shown in Figure 1.
7.1.2 The typical test system should consist of a pre-filter, flow controllers (FC) and meters (FM), particle injection
device, equipment under test (EUT), a resistivity sensor, a thermometer and tubing connecting them. However, when
the performance of UPW supplied to the test circuit has been clarified, pre-filter, resistivity sensor, thermometer, and
pressure gage are not necessarily required in this test system.
7.1.3 The pore size of a pre-filter or the specification of supplying UPW shall be smaller than the evaluated particle
size. However, the quality of UPW may be unable to be controlled only by performance specification of a pre-filter.
Checking by background test is important for the control of cleanliness factor of UPW. Also, the specification of a
pre-filter, and its installation should be considered suitably by the result of the background test.
7.1.4 Use a flow meter of an allowable error to be less than 5 % full scale and of appropriate range. More correct
flow rate can be obtained by measuring the volume of the fluid by a graduated cylinder or measuring the mass of the
fluid by a weighting scale, in the given time measured by a stopwatch. It is also the preferred approach to calibrate
the flow meter by the above method.
7.1.5 Outline of the Procedure of Figure 1.
7.1.5.1 UPW is supplied by a constant flow rate and the flow rate shall be controlled by the sum of the sample flow
rate (U2) of a particle counter and the bypass flow rate (U3).
7.1.5.2 The pressure of UPW in the test system shall be within the operating pressure range of the EUT, and shall be
below the discharge pressure of the injection pump.
7.1.5.3 The diluted PSL test particles by the procedure of Figure 2 are continuously injected into UPW with a
constant flow rate by the injection pump.
7.1.6 For the dilution method of original PSL particle suspension, use the schematic shown in Figure 2.
This is a Draft Document of the SEMI International Standards program. No material on this page is to be construed as an official or adopted Standard or Safety Guideline.
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DRAFT
Document Number: 5225A
Date: 2/6/2016
EUT(LPC
Under test)
U0 (UPW flow rate)
FM & FC
U2 (Sample
flow rate)
Pump
FM & FC
U1 (Injection
flow rate)
LETTER (YELLOW) BALLOT
N2 (Number concentration
of sample)
UPW
N (Measurement value)
U3 (Bypass flow rate)
Injection Sample
N1 (Number concentration
of injection sample)
Figure 1
Schematic Test Setup
Micro pipette
V0 (instillation the volume)
V0 (Sampling the volume)
The original suspension
of PSL particles
V1 (The volume of UPW)
CM (Mass concentration)
Figure 2
Schematic Procedure of the Dilution of the Original PSL Particle Suspension
7.2 Setting the Value of Parameter
7.2.1 The PSL particle number concentration (N2) introduced to EUT shall be less than the maximum particle
number concentration (NL) of the EUT, since the concentration should not make the significant coincidence loss.
Also if the number concentration is too low, the statistical error of measured value becomes large. Therefore, the
concentration should be adjusted so that the measured value for 1 min. exceeds at least 1000.
7.2.2 Set the following each flow rate and volume. Accuracy of the each equipment shall be clarified.
7.2.2.1 Sampling volume of the original suspension of PSL particles (V0)
7.2.2.2 Volume of the UPW for diluting the original suspension of PSL particles (V1)
7.2.2.3 Injection flow rate of the diluted PSL particles (U1)
7.2.2.4 Bypass UPW flow rate (U3)
7.2.3 N2 is defined by the following equation (1), and N0 means the number concentration of original suspension of
PSL particles (see §7.3) and U2 means the rated flow rate of the particle counter. In fact, U0 + U1 can be measured by
U2 + U3.
N2  N0
V0
U1
V

V
U
 0 1   0 U1 
(1)
This is a Draft Document of the SEMI International Standards program. No material on this page is to be construed as an official or adopted Standard or Safety Guideline.
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DRAFT
7.2.4 Example of Setting Each Parameter ― In case that the mean size of PSL test particles is 61 nm, the mass
concentration is 1 % (the number concentration of the PSL particles corresponds to 7.8 × 10 13 #/mL ) and the
maximum measurable number concentration of EUT is 24000 #/mL, following setting values are recommended.
 V0
: 1 µL
 V1
: 1000 mL
 U0
: 1000 mL/min
 U1
: 50 µL/min
 U2
: 20 mL/min
 N2 = 7.8×1013×(0.001/(1000+0.001))×(0.05/(1000+0.05))
= 3900 #/mL
NOTE 3: When the EUT has a bypass flow system in its inside, it should be taken care for the actual sample flow rate setting.
7.3 Preparing 1st Test Sample (Primary Dilution PSL Particle Suspension )
7.3.1 The number concentration of original PSL suspension (N0) is found from the specified mass concentration
(CM) of a PSL particle original suspension by the following equation (2). In case of PSL particles, the shape of
particle can be assumed spherical and the number-mean-size (D0) can be used as typical particle size.
N0 
C M 0
V p p
Vp 
(2)
 D03
(3)
6
Where, Vp is the volume of the PSL particle, ρp is the density of the particle and ρ0 is the density of original PSL
suspension. Actual ρ0 can be treated as almost same as the density of UPW (See Equation (A1-14))in Appendix 1).
NOTE 4: CM is a ratio of the mass of the containing total solid to the mass of original particle solution.
7.3.2 The volume of V0 is determined by the sampling which used micro-pipette.
NOTE 5: The accuracy of micro-pipette should be clarified.
NOTE 6: Contamination of micro-pipette should be fully eliminated.
7.3.3 The sampled original suspension of PSL particle is dropped into UPW of known volume (V1)
NOTE 7: Cleanliness of the UPW and the pod should be enough.
7.3.4 The number concentration of 1st test sample means the number concentration of injection sample (N1). N1 is
shown as following equation (4).
N1  N 0
V0
V 0  V1
(4)
7.4 Test-line Background
7.4.1 This test is required before injecting test PSL particles (see Figure 1)
7.4.2 Set up the EUT into the test circuit
7.4.3 U1, U2 and U3 shall be set to the same conditions as the test.
7.4.3.1 The injection sample shall be UPW.
7.4.3.2 The supply pressure shall be less than the specification of EUT.
7.4.4 The measurement shall be continued for more than 10 minutes, in the state where measured value is stabilized,
7.4.4.1 Record the measured number of particles in at least 1 min. intervals.
This is a Draft Document of the SEMI International Standards program. No material on this page is to be construed as an official or adopted Standard or Safety Guideline.
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7.4.4.2 The required level of the background particle number concentration is less than 1/100 of the particle number
concentration introduced to EUT (N2).
7.4.4.3 The evaluation is performed by the average of 5 times measurements.
7.5 Test
7.5.1 The injection sample is changed from UPW to the 1st sample (PSL particle suspension) prepared by §7.3.
7.5.2 Each flow rate is set as the value fixed by §7.2.
7.5.3 Start measurement.
7.5.3.1 It shall be checked that the unevenness of the number concentration of a sample does not influence a test
result. The evaluation of the unevenness of number concentration is possible by a coefficient of variation (CV). In
this test, CV shall be less than 10 %. The value of CV is obtained by the following equation (5).
CV 

 100
N ave
(5)
where, σ is the standard deviation of measured data and Nave is the average of measured data (N).
7.5.3.2 Following is an example of recommendation of a measurement procedure.
7.5.3.2.1 For stabilizing the number concentration of particles, over 5 times at 1 min. measurement as blank
measurement should be done.
7.5.3.2.2 During the blank measurement, it is desirable to check that the fluctuation of measurement value is
decreasing, since CV value is evaluated at 7.5.3.2.4.
7.5.3.2.3 After the blank measurement, 1 min. measurement is recorded 5 times.
7.5.3.2.4 CV value of 5 times measurement shall be less than 10 %.
7.5.3.2.5 Check of the error by large particles. Certain errors of the number concentration of PSL particle
suspension may generate by containing large particles in original suspension of PSL particles.

When the number of particles that is over 3 times of a mean size of the test PSL particle is over 0.5 % of the
total number of measurement particles, it should be checked for contamination of a test flow circuit or
mixing of air bubbles.

When it is clear that the contamination of the flow circuit or air bubbles are the cause, it is possible to obtain
the counting efficiency except for the number of large particles.

Large particles may have been contained in the original PSL solution if it depends on neither a test flow
circuit nor air bubbles.

In this case, about 14 % or larger error may have generated in the conversion of mass concentration to
number concentration, and this effect should be considered in evaluating the uncertainty of the counting
efficiency (See §A5 in Appendix 1).
7.5.3.2.6 Record the average and the standard deviation of the measurement data.
7.5.4 Procedure After the Test
7.5.4.1 Stop the injection pump.
7.5.4.2 The injection sample is changed from 1st sample to UPW.
7.5.4.3 UPW should be run through until the measured particle concentration becomes less than 1 % of the test
particle concentration.
7.5.4.4 It is possible to remove EUT from the test system.
7.5.5 If the test of different particle sizes should be needed, it shall return to §7.2 and reset the adequate parameters.
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DRAFT
8 Report and Evaluation
8.1 Include each parameter of the test systems such as the specification (type, nominal size and certified mean size,
standard deviation, the name of manufacturer and lot number) of PSL particles, the each flow rate and each volume.
8.2 Include the calculated values, such as number concentration of injected sample, the number concentration of the
sample injected into UPW, the number concentration of the sample introduced into LPC and the counting efficiency.
8.3 The counting efficiency is obtained from the following equation.
counting efficiency
%  
N ave
 100
N2
(6)
Where, Nave is the average of plural measurement data (N) which is obtained in §7.5.3.
8.4 Example of the format of data records is shown in Table 1.
8.5 Refer to Appendix 1, when uncertainty of measurement data should be evaluated and shown.
8.6 When testing plural sizes of PSL particles, it is useful to add Table 2 and Figure 3 shown as an example to Table
1.
Table 1 Example of the Test Report Format
Test Condition
Data of EUT
Flow Rate
Temperature
Type
Manufacturer
Serial #
Sample
(mL/min)
Injection of Particle
Suspension
(mL/min)
UPW
(mL/min)
UPW
(℃)
Environment
(℃)
##-###
XXX Co.
$$$
20
0.05
1000
23
25
Test data
Background Number of
Particles
(#/mL)
Introduced Number of
Particles
(#/mL)
Measurement Number of
Particles
(#/mL)
Measurement Size
Range of EUT
(nm)
Counting
Efficiency
(%)
15
3800
290
≧ 50
7.6
Data of PSL Particle
Type
Manufacturer
Lot. #
Nominal Size
(nm)
Certified Mean Size
(nm)
Standard
Deviation
(nm)
**-***
YYY Co.
$$$$
60
61
2
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DRAFT
Document Number: 5225A
Date: 2/6/2016
Test PSL Particle Size
(nm)
Counting Efficiency
(%)
Measurement Size Range
of EUT (nm)
55
25
over 50
61
53
over 50
70
79
over 50
80
85
over 50
100
93
over 50
123
105
over 50
152
115
over 50
202
113
over 50
LETTER (YELLOW) BALLOT
Table 2 Example of the Test Report Format for Plural PSL Particle Testing
Counting efficiency (%)
1000
100
10
Measurement value of
PSL particles
1
10
100
1000
Size (nm)
Figure 3
Example of the Test Report Graph Format for Plural PSL Particles Testing
9 Summary of Test Method
9.1 This test method describes that test equipment and procedures for determining the counting efficiency of liquidborne particle counter for which the measurable particle size is between 30 nm and 100 nm. The number
concentration of PSL particles is controlled by a quantitative dilution method.
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APPENDIX 1
Uncertainty of Counting Efficiency of a Liquid-borne Particle Counter
determined by a dilution method
NOTICE: The material in this Appendix is an official part of SEMI [designation number] and was approved by full
letter ballot procedures on [A&R approval date].
A1-1 Basics on Measurement Uncertainty
A1-1.1 In this Appendix, a recommended procedure is described for evaluating the uncertainty of a test result of the
counting efficiency of a liquid-borne particle counter. The test method is obtained by the technique. The general idea
of this procedure follows “Guide to the Expression of Uncertainty in Measurement,” which is briefly summarized as
follows
Step 1 ― Identify the relationship between the measurand (quantity intended to be measured), y, and the input
quantities, xi (i = 1, 2, ..., N):
y  f ( x1 , x2 ,  , xN ) .
(A1-1)
This functional relationship is called the mathematical model of measurement.
NOTE 8: Input quantity is a quantity whose value is used to determine the result of measurement, or a quantity that can otherwise
affect a measurement result.
NOTE 9: Although the quantities, Y and Xi, and their estimates, y and xi, are represented by different symbols in the GUM, we
use the same symbols here, as far as there is no fear of confusion.
Step 2 ― Evaluate the standard uncertainty u(xi) of the input quantity xi either by Type A or Type B evaluation of
uncertainty.
NOTE 10: If the estimate of a quantity xi is obtained from xi  q , where q is the mean of a series of observations,
qk (k  1,2,....., n) , then the standard uncertainty of xi is evaluated as
u ( xi ) 
s
.
(A1 -2)
n
n
Here s is the experimental standard deviation of qk given by s =
 (q
k
 q ) 2 (n  1) , or some other estimate of the standard
k 1
deviation based on an experiment conducted separately from the measurement of xi. Uncertainty evaluation based on such
statistical analysis of series of observations is called type A evaluation of uncertainty.
NOTE 11: Method of evaluation of uncertainty by means other than the statistical analysis of series of observations is called type
B evaluation. Type B evaluation is conducted on the basis of available information such as data given in calibration certificates,
instrument specifications, handbooks, and data obtained in the past.
Step 3 ― Combine the standard uncertainties of all xi’s to obtain the combined standard uncertainty of the
measurement result, uc(y), according to the following ”law of propagation of uncertainty”
uc ( y) 
 f


u ( xi ) 
xi

i 1 
N

2
.
(A1-3)
NOTE 12: Equation (A1-3) applies to cases where there are no correlations between input quantities. When the correlations are
not negligible, terms containing correlation coefficients should be added to the right hand side of Equation (A1-3). In the present
standard, we consider only cases where correlations are negligible.
NOTE 13: When the mathematical model (A1-1) takes the form
y  C  x1 p1  x2 p1    x N pN ,
(A1-4)
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where c, p1, p2, ... are constants, Equation (A1-3) is equivalent to the following equation called the law of propagation of relative
uncertainty,
N
 u ( xi ) 
 pi


xi 

i 1

uc ( y)

y
2
(A1-5)
Step 4 ― When necessary, the expanded uncertainty U is calculated according to the following equation:
U  k  uc ( y )
(A1-6)
where k is the coverage factor. In this standard, k = 2 is consistently used for simplicity.
NOTE 14: If the probability distribution characterized by y and uc(y) is a normal distribution, then the interval y  U with k = 2
encompasses approximately 95 % of the distribution.
A1-2 Uncertainty of Counting Efficiency of a Liquid-borne Particle Counter
A1-2.1 The counting efficiency of a liquid-borne particle counter, , is determined from Equation (6) of the main
text, which is cited here again as

N
,
N2
(A1-7)
Applying Equation (A1-5) to (A1-7), we obtain the relative uncertainty of  as
u c ( )

2
 u ( N )   u ( N 2 ) 
 
 
 N   N 2 
,
2
(A1-8)
where u(N2) is evaluated according to the procedure described in sections §A1-3 -§A1-5 below. The uncertainty
u(N) in Equation (A1-8) is evaluated as follows.
A1-2.2 Let Ni (i = 1, 2, ..., n) denote the values of the particle number concentration of the challenge suspension
obtained by the EUT in n repeated measurements. The measurement result N represents the mean of Ni. The
uncertainty u(N) is then calculated as
u( N ) 
s
n ,
(A1-9)
where s is the experimental standard deviation of the data set {Ni}.
A1-3 Uncertainty u(N2): The Case in which Test PSL Particles can be Assumed to be
Monodisperse
A1-3.1 If the particle size of the test PSL particles, Dp, is uniform, as is assumed in the main body of the present
document, the particle number concentration of the challenge suspension, N2, can be determined from equations (1),
(2), and (3) as
N2 
6C M  0
Dp 3  p
r1r2
,
(A1-10)
where r1 and r2 represent, respectively, the dilution ratios when the primary and secondary diluted suspensions are
prepared, and are defined by
r1 
r2 
V0
,
V0  V1
U1
U1

.
U 0  U1 U 2  U 3
(A1-11)
(A1-12)
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In Equation (A1-12) it is assumed that U0+U1 is inferred from U2+U3 (see ¶7.2.3). The relative standard uncertainty
of N2 can be obtained by applying Equation (A1-5) to (A1-10) as
2
2
 u (C M )   u (  0 )   u (  p )   u ( Dp )   u (r1 )   u (r2 ) 
u( N 2 )
 
  
  
 .
 
 3
 
N2
 C M    0    p   Dp   r1   r2 
2
2
2
2
(A1-13)
Each uncertainty component in the right hand side of this equation is evaluated as follows.
A1-3.2 u(CM)
The uncertainty u(CM) is determined based on information provided by the manufacturer of the original suspensions,
if it is available. In case where no such information is available, we first note that u(CM) comes from two major
sources: one associated with impurity particles that may exist in the test suspension, ui(CM); and the other associated
with mass measurements required in determining the value of CM, um(CM). The evaluation of ui(CM) is described in
§A1-5. Regarding um(CM), we cannot evaluate it, unless information is available on how the mass measurements
were conducted in determining CM. However, the accuracy in mass measurement in general, if conducted adequately,
can be expected to be relatively high, and um(CM) may be neglected compared to ui(CM). Hence, in a good
approximation, we may neglect um(CM) in the absence of relevant information on the measurement of CM.
A1-3.3 u( 0)
The density of the original suspension is approximately given by
p  w 

,
 0   w 1  CM
 w 

(A1-14)
where  w is the density of water contained in the suspension. If we assume CM = 0.1 and  p = 1.06 as a
representative case, the second term in the right hand side of (A1-14) amounts only to 0.006, which is negligibly
small. It will hence be sufficient, in practice, to identify  0 with  w, and to let u( 0) given by the bias arising from
this assumption:
u ( 0 )  C M  p  w  .
(A1-15)
A1-3.4 u( p)
The uncertainty u( p) may be provided by the manufacturer of the original PSL suspensions. If not, it may be
inferred from existing literature. For example, reference 2 gives u( p) = 6.4 × 10−4 g/cm3 for 100 nm PSL particles
with  p = 1.065 g/cm3.
A1-3.5 u(Dp)
The uncertainty u(D p) is provided by the manufacturer of test PSL particle suspensions.
A1-3.6 u(r1)
From Equations (A1-3) and (A1-11), we have
u (r1 ) 
V12 u 2 (V0 )  V0 2 u 2 (V1 )
(V0  V1 ) 2
.
(A1-16)
Uncertainties u(V0) and u(V1) are associated with measurement of the suspension volumes. Evaluation of them is
rather straightforward, and is not described in detail here.
A1-3.7 u(r2)
From equations (A1-3) and (A1-12), we have
2
Ehara K., Takahata K., Koike M., Aerosol Sci. Technol., 40 (2006): pp. 521–535.
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(U 2  U 3 ) 2 u 2 (U1 )  U 12 (u 2 (U 2 )  u 2 (U 3 ))
u (r2 ) 
(U 2  U 3 ) 2
.
(A1-17)
Evaluation of u(U1), u(U2), and u(U3) is rather straightforward, and not described in detail here.
dN/dDp
NPSL pPSL(Dp) (PSL particles)
Ni pi(Dp) (Impurity particles)
Dp
Figure A1-1
Schematic Size Distributions of PSL and Impurity Particles
A1-4 Uncertainty u(N2): The case in which Test PSL Particles have a Finite Width in Size
Distribution
A1-4.1 If the size of test PSL particles is not strictly uniform, but has a distribution described by a probability
density function pPSL(Dp) (see Figure A1-1), equation (A.10) must be replaced with
N2 
6C M  0
 Dp 3  p
r1r2
,
(A1-18)
3
where Dp is the third moment of pPSL(Dp) defined by

Dp 3  Dp 3 pPSL ( Dp ) dDp .
NOTE 15: Note that the function pPSL(Dp) is normalized so that it satisfies
(A1-19)
p
PSL ( Dp )dDp
 1 . This applies also to the
impurity particle size distribution introduced in A1-5, pi(Dp).
In equation (A1-18), p is still assumed to be uniform, but this is expected to be a reasonable assumption 2. The
following replacement is then required in equation (A1-13).
3
u ( Dp )

Dp
u ( Dp 3 )
Dp 3
(A1-20)
3
3
A1-4.2 Note that, in general, Dp (the 3rd power of the number average diameter) is not equal to Dp . The third
3
moment, Dp , as well as its uncertainty, can be obtained from the mobility analysis of aerosolized particles3, or
3
3
may be obtained by any other relevant means. If Dp is used in place of Dp in equation (A1-18), their difference
needs to be taken into account in evaluating u(N2).
3
Ehara K, Mulholland G. W., and Hagwood R. C., Aerosol Sci. Technol., 32 (2000); pp. 434-452.
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A1-5 The Effect of Impurity Particles
A1-5.1 If impurity particles are contained in the test suspension, they affect  and hence uc(). The size distribution
of particle number concentration in this case can be depicted schematically as in Figure A1-1, where NPSL×pPSL(Dp)
and Ni×pi(Dp) represent the size distributions of the number concentration of PSL particles and impurity particles,
respectively in the original suspension. If the impurities are existent in the original suspension before the value of
CM is determined, they can affect both N2 and N. If they get mixed after CM is determined, such as in the dilution
processes or in the stage of the counting efficiency test, they affect only N. For simplicity, we assume that Ni << NPSL
(see ¶7.5.3.5.) In this case, the effect on N2 of the impurities that are present before CM is determined is significant
and needs to be considered. For further simplicity, we assume that the impurity particles have the same density as
the PSL particles, p. Now CM can be expressed as
C M  C PSL  Ci ,
(A1-21)
where CPSL and Ci represent the mass concentrations of PSL and impurity particles, respectively, in the original
suspension, and their ratio is given by


3
N i Dp pi ( Dp )dDp
Ci

C PSL N PSL Dp 3 p PSL ( Dp )dDp
(A1-22)
This ratio ought to be reasonably small for the counting efficiency test to be meaningful. Even if Ni << NPSL, Ci/CPSL
may not be negligible, and hence Ni and pi(Dp) need to be carefully examined. Note that if we substitute CPSL in CM
in equation (A1-10), we obtain the "true" concentration N2 (because the impurity particle concentration in the
challenge suspension is assumed negligibly small.) The relative error in CM is given by
C M | C M  C PSL | Ci


.
CM
CM
CM
This bias needs to be considered as a part of the uncertainty of CM, and we have
ui (C M ) Ci

.
CM
CM
In practice, it may be difficult to accurately determine Ci/CM, and an approximate estimate would be required (see
Example below.)
NOTE 16: Impurity particle is defined here as either a particle whose size is not in the main peak of pPSL(Dp), or a
particle that gets mixed after CM is determined. It can be a PSL particle.
A1-5.2 Example of the evaluation of ui(CM)
If it is observed that in the challenge suspension there are no particles whose sizes are larger than three times a
representative PSL size, DPSL, and that Ni/NPSL is smaller than 0.005, we have
Ci CPSL  0.005  33  0.14 .
A rough but conservative estimate of ui(CM) is given by
ui(CM)/CM = 0.14.
A1-6 Referenced Standards and Documents
International Organization for Standardization (1993). Guide to the Expression of Uncertainty in Measurement,
Geneva, Switzerland.
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NOTICE: Semiconductor Equipment and Materials International (SEMI) makes no warranties or representations as
to the suitability of the Standards and Safety Guidelines set forth herein for any particular application. The
determination of the suitability of the Standard or Safety Guideline 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 or equipment mentioned herein. Standards and Safety Guidelines are subject to change
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