Background Statement for SEMI Draft Document 5804
Revision of SEMI M53-0310
PRACTICE FOR CALIBRATING SCANNING SURFACE INSPECTION
SYSTEMS USING CERTIFIED DEPOSITIONS OF MONODISPERSE
REFERENCE SPHERES ON UNPATTERNED SEMICONDUCTOR
WAFER SURFACES
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.
This standard is due for 5-year review as required by SEMI Standards Regulations. The International Advanced
Automated Surface Inspection Task Force’s review resulted in changes summarized below.
(¶ 2.5), Appendix 1: Deleted. Single-point calibration was not recommended and is not generally practiced.
New NOTE 1: (follows renumbered ¶ 2.5): Acknowledges use of DUV-stable deposition materials while
maintaining continuity with LSE sizing.
NOTE 1: Now NOTE 2: Updated current minimum practical deposition sizes to 20-25 nm.
(¶ 3.6): Clarified the utility of monotonic response curves.
(NOTE 3): Eliminated.
(NOTE 8): Mentions automated size peak extraction that many SSISs now have; simplified wording.
(¶ 9.15): M52 Table III, row 5.3, states FWHM < 5%, which would imply σ1<FWHM / 2.355=2.1%.
(¶¶10.1, R1-6): M52 Table III, row 5.3, states expanded uncertainly at 95% conf < 3%.
Editorial: (¶ 1.3): Missing “.”; 4.1 updated title of SEMI M52; 7.1.2 Ref to NOTE 2 to NOTE 3; 7.1.3 Ref to
NOTE 3 eliminated; (¶ 2.6): Renumbered 2.5, reference to Appendix 2 changed to Appendix 1; 8.5.2 corrected
reference to the table in M52.
Notice: Additions are indicated by underline and deletions are strikethrough.
Review and Adjudication Information
Task Force Review
Int’l Automated Advanced Surface Inspection TF
Group:
October 6, 2015
Date:
Time & Timezone:
Location:
City, State/Country:
Leader(s):
3:00-4:00 PM CET
Messe Dresden
Dresden, Germany
Kurt Haller (KLA-Tencor)
Standards Staff:
Kevin Nguyen, [email protected]
Committee Adjudication
Silicon Wafer Europe TC Chapter
October 7, 2015
2:00-3:30 PM CET
Messe Dresden
Dresden, Germany
Peter Wagner (Self)
Fritz Passek (Siltronic)
Kevin Nguyen, [email protected]
This meeting’s details are subject to change, and additional review sessions may be scheduled if necessary. Contact the task
force leaders or Standards staff for confirmation.
Telephone and web information will be distributed to interested parties as the meeting date approaches. If you will not be able to
attend these meetings in person but would like to participate by telephone/web, please contact Standards staff.
Check www.semi.org/standards on calendar of event for the latest meeting schedule.
Semiconductor Equipment and Materials International
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DRAFT
Document Number: 5804
Date: 7/14/2017
Revision of SEMI M53-0319
PRACTICE FOR CALIBRATING SCANNING SURFACE INSPECTION
SYSTEMS USING CERTIFIED DEPOSITIONS OF MONODISPERSE
REFERENCE SPHERES ON UNPATTERNED SEMICONDUCTOR
WAFER SURFACES
Notice: Additions are indicated by underline and deletions are strikethrough.
1 Purpose
1.1 This practice describes calibration of scanning surface inspection system (SSIS) dark field detector channels so
that the SSIS will accurately size PSL (polystyrene latex) spheres deposited on unpatterned polished, epitaxial, or
filmed semiconductor wafer surfaces.
1.2 The purpose of this calibration is to ensure that different SSISs of a given manufacturer and model will assign
the same light scattering equivalent (LSE) diameter to a specific localized light scatterer (LLS).
1.3 This practice defines the use of LSE diameters, as defined in SEMI M59, as a means of reporting real surface
defects whose identity, true size, and morphology are unknown.
1.4 This practice provides a basis for quantifying SSIS performance as used in related standards concerned with
parameters such as sensitivity, repeatability, and capture rate.
2 Scope
2.1 This practice covers:
2.1.1 Requirements for the surface and other characteristics of the semiconductor substrates on which the reference
spheres are deposited to form reference wafers (see ¶ 8.1),
2.1.2 Selection of appropriate certified depositions of reference spheres for SSIS calibration, including size
distribution requirements to be met by the reference sphere depositions, but not the deposition method (see ¶ 8.3),
2.1.3 Generation of calibration curves using model-predicted scatter data that have response curve oscillations and
are thus not monotonic, and
2.1.4 Generation of monotonic calibration curves using model-predicted scatter data.
2.2 Although it was developed primarily for use in calibration of SSISs to be used for detection of localized light
scatterers (LLSs) on polished silicon wafers with geometrical characteristics as specified in SEMI M1, this practice
can be applied to SSISs to be used for detection of LLSs on other unpatterned semiconductor surfaces, provided that
suitable reference wafers are employed.
2.3 This practice does not in any way attempt to define the manner in which LSE values are used to define the true
size of LLSs other than PSL spheres (see ¶ 3.1).
2.4 This practice supports requirements listed in SEMI M52.
2.5 Appendix 1 describes a method that may be used to determine the index of refraction of reference spheres that
are not PSL.
NOTE 1: Repeated exposure to deep UV (DUV) illumination is known to alter the light scattering response of PSL sphere
depositions. Therefore, manufacturers and end-users of DUV SSISs generally use monodisperse depositions of DUV-stable
materials, silica (SiO2) for example, for long-term periodic calibration of SSISs. To maintain continuity with LSE sizing, the
light scattering intensity of such materials are usually assigned to the diameter of hypothetical PSL sphere depositions that would
produce the same intensity, rather than their actual physical diameters. As such, wafers with deposited spheres of any material in
this practice serve as “light scattering intensity reference wafers” rather than “size standards.”
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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SEMI Draft Document 5804
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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 LLSs are normally assigned only LSE sizes, not physical diameters, because the response of an SSIS to an LLS
depends on the SSIS optical system characteristics as well as the size, shape, orientation and composition of the LLS.
The LSE size assigned to a particular LLS by an SSIS calibrated against PSL spheres may be different from that
assigned to the same LLS by another similarly calibrated SSIS of a different model, because different SSISs have
different optical system characteristics.
3.2 Reference spheres as sold in bulk may have specified characteristics (mean diameter uncertainty, diameter
distribution, spread between mean and modal diameter) that differ significantly from the characteristics of the
resulting deposition due to the transfer function of the deposition system. For this reason the practice is limited to
the use of reference sphere depositions that are appropriately characterized in accordance with SEMI M58 and
properly certified (see § 8).
3.3 The largest reference sphere diameter that can be used in this practice depends on individual SSIS
characteristics, but is often limited to a diameter of about ten times the light source wavelength.
3.4 The smallest reference sphere diameter that can be used in this practice is determined by the sensitivity of the
SSIS under calibration.
NOTE 2: At the time of development of this edition of the practice, the smallest practical deposited reference spheres have
physical diameters approaching 20-25 nm, but as IC technology evolves to smaller and smaller critical dimensions, it is expected
that depositions of smaller diameter reference spheres will become available.
3.5 The SSIS signal is not necessarily monotonic with the diameter of a PSL sphere, especially for those having
diameters approaching the wavelength of the light. As a result, the response curve (RC) determined by this practice
may not provide a unique determination of LSE diameter for all LLS.
3.6 If a monotonic response curve is used and if the usable signal range of the detector channel under calibration
extends into a region where there are oscillations in the physical response curve, then LSE size assigned to a PSL
sphere in the region is not necessarily accurate. Nevertheless, this practice ensures an SSIS assigns reproducible
LSE size to an LLS of any size, shape, and material composition.
3.7 Background Contamination
3.7.1 Both the deposition process and calibration procedures must be carried out in a Class 4 or better environment
as defined in ISO 14644-1.
3.7.2 The presence of contamination with LSE sizes near that of the nominal reference sphere diameter on the
reference wafer may skew the results. This condition may result in a large error or poor sizing accuracy.
3.7.3 High levels of contamination on the reference wafer or wafers may overload the SSIS or obscure the peak of
the deposited reference sphere diameter distribution. This condition may also result in a large error or poor
equivalent sizing accuracy.
3.7.4 For these reasons, both the deposition process and calibration procedures must be carried out in a clean
environment, and the reference wafers must be handled in such a way as to avoid contamination between deposition
process and calibration.
3.8 If the surface roughness of the reference wafer or wafers is excessive, the peak of the reference sphere diameter
distribution may be obscured or distorted.
3.9 If the SSIS being calibrated is not operating in a stable condition, the calibration may not be appropriate for
subsequent use of the system. System stability can be evaluated by making repeated calibrations, in accordance with
this practice, over suitable time periods.
4 Referenced Standards and Documents
4.1 SEMI Standards
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
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SEMI M12 — Specification for Serial Alphanumeric Marking of the Front Surface of Wafers
SEMI M20 — Practice for Establishing a Wafer Coordinate System
SEMI M50 — Test Method for Determining Capture Rate and False Count Rate for Surface Scanning Inspection
Systems by the Overlay Method
SEMI M52 — Guide for Specifying Scanning Surface Inspection Systems for Silicon Wafers for the 130 nm to 11
nm Technology Generations
SEMI M58 — Test Method for Evaluating DMA Based Particle Deposition Systems and Processes
SEMI M59 — Terminology for Silicon Technology
4.2 ISO Standard1
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 Acronyms, definitions, and symbols used in silicon technology may be found in SEMI M59.
5.2 Other acronyms used only in this standard are as follows:
5.2.1 GNF — Gain-nonlinearity function
5.2.2 MPRC — Monotonic predicted response curve
5.2.3 MRC — Monotonic response curve
5.2.4 PRC — Predicted response curve
5.2.5 RC — Response curve
5.3 Other terms used only in this standard are as follows:
5.3.1 gain-nonlinearity function (GNF) — the relationship between the actual SSIS response and the modelpredicted SSIS response, given as a function with two or more independent and adjustable parameters. The GNF
should be independent of the reference sphere material, because it is a relationship between the SSIS detector
response and the amount of light predicted to be incident upon the detector.
5.3.2 LSE sphere sizing uncertainty — an estimate of the relative uncertainty in the diameter reported by an SSIS
for a PSL sphere having any diameter in the calibration range, determined by combining contributions from the
calibration diameter errors and the certified deposition uncertainty.
5.3.3 monotonic predicted response curve (MPRC) — a predicted response curve derived from a PRC and modified
to be monotonic. A subscript appended to the MPRC (e.g., MPRCsilica or MPRCPSL), indicates the sphere material for
which the MPRC applies.
5.3.4 monotonic response curve (MRC) — the monotonic relation between the actual SSIS signal and sphere
diameter, which differs from the RCPSL by being derived from the MPRC rather than the PRCPSL. A subscript
appended to the MRC (e.g., MRCsilica or MRCPSL), indicates the sphere material for which the MRC applies.
5.3.5 predicted response curve (PRC) — the model-predicted relation between scattered light intensity (or SSIS
signal response) and sphere diameter that is used to analyze scanner response near various sphere diameters. The
PRC depends upon sphere material and scanner design and is in general non-linear. It may contain regions with
response curve oscillations that make the response-diameter relationship multi-valued. A subscript appended to the
PRC (e.g., PRCsilica or PRCPSL), indicates the sphere material for which the PRC is calculated.
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.
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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SEMI M1 — Specifications for Polished Single Crystal Silicon Wafers
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5.3.6 response curve (RC) — the relation between actual SSIS signal and sphere diameter. A subscript appended to
the RC (e.g., RCsilica or RCPSL), indicates the sphere material for which the RC applies. The RC depends on scanner
design and is in general non-linear. It may contain regions with response curve oscillations that make the responsediameter relationship multi-valued.
5.3.7 response curve oscillations — peaks and valleys in the response curve, which prevent the response curve from
being monotonic.
6 Summary of Practice
6.1 The SSIS being calibrated is set up with machine conditions identical with those to be used in examining wafers.
6.2 Reference wafers with appropriate certified depositions are scanned by the SSIS.
6.3 The peak of the reference sphere diameter distribution deposited on each reference wafer is assigned to the peak
value of the SSIS signal units.
6.4 A predicted response curve is determined for each reference sphere material and for PSL using its index of
refraction and the appropriate parameters for the measurement conditions.
6.5 The actual SSIS signals and the predicted responses are used to determine the gain-nonlinearity function (GNF).
6.6 The PRCPSL and the GNF are used to determine the response curve for PSL (RCPSL), which may have response
curve oscillations.
6.6.1 Discussion — If PSL spheres were used as reference spheres, a graph of the RCPSL will lie very close to, but
may not exactly match, a graph of the recorded signal versus reference sphere diameter. If another sphere material
were used, a graph of the RCPSL will not match a graph of recorded signal versus reference sphere diameter. That is,
an SSIS calibrated to assign LSE diameters to LLSs will not correctly size non-PSL reference spheres.
6.7 The expanded PSL sphere sizing uncertainty is determined and compared to the requirements of SEMI M52.
6.8 A monotonic predicted response curve (MPRCPSL) may be generated from the PRCPSL to remove response curve
oscillations.
6.9 The MPRCPSL and the GNF may be used to determine the monotonic response curve (MRCPSL), which does not
have response curve oscillations.
6.10 A separate RCPSL and MRCPSL are developed for each detector channel.
6.11 Either the RCPSL or the MRCPSL is used to determine and report the LSE diameter.
7 Apparatus
7.1 Scanning Surface Inspection System — Designed to detect, size, and map localized light scatterers (LLSs) on
unpatterned semiconductor wafers, that has the following capabilities:
7.1.1 Scans the entire fixed quality area of the surface of a wafer with a laser beam,
7.1.2 Detects localized light scatterers as laser-light scattering events (see Note 3),
7.1.3 Has a user definable sensitivity threshold used to distinguish between background noise and real LLSs,
7.1.4 Can create a histogram of SSIS signals (i.e., number of laser light scattering events as a function of raw SSIS
signal) for any given region on the wafer,
7.1.5 Can either evaluate the histogram peak or output a data set file that can be imported to a spreadsheet or other
application program that can be used to generate the histogram peak,
7.1.6 Can either accept a user-provided calibration curve for each detector channel or can automatically perform the
steps given in § 9 below,
7.1.7 Is sufficiently repeatable for the intended application, and
7.1.8 Handles wafers in a Class 4 or better clean environment as defined in ISO 14644-1.
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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NOTE 3: The amplitude of the LSE signal into a single detector, as measured for any combination of incident beam direction
and collection optics, does not by itself convey topographic information, for example, whether the LLS is a pit or a particle. It
does not allow the observer to deduce the size or origin of the scatterer without other detailed knowledge, such as its index of
refraction and shape.
8 Reference Wafers
8.1 Substrates — Use bare semiconductor wafers with a native oxide (or other filmed) surface of the type intended
to be tested with the SSIS to be calibrated as substrates for the certified depositions of the reference spheres. This is
particularly important because SSIS response is affected by the optical properties of the substrate. Bare silicon wafer
surfaces have different optical properties than wafers with film layers or wafers of different material. The wafers
must meet the dimensional requirements of SEMI M1 for the appropriate nominal wafer diameter. Wafers nominally
200 mm in diameter and smaller shall be laser marked in accordance with SEMI M12, and wafers nominally
300 mm in diameter shall be laser marked in accordance with ¶¶ 6.5.1.4–6.5.1.4.9 of SEMI M1, including the
optional alphanumeric mark described in ¶ 6.5.1.4.1 of SEMI M1.
8.2 Certified Depositions — The deposition property value that must be certified is the peak sphere diameter. The
diameter distribution on the wafer and the reference sphere material must be specified. The diameter distribution is
determined by the deposition process, and the reference sphere material affects its index of refraction.
8.3 Range and Number of Calibration Diameters — Choose the diameters of the reference spheres for the certified
depositions so that the measurement range for the intended application is significantly covered. Use spheres of size
ranging from less than the largest measurable size down to a size greater than that with an estimated capture rate of
95% and spaced approximately evenly on a logarithmic scale. The minimum and maximum sphere sizes do not need
to be at the extremes of the required calibration range, since this practice allows for extrapolation. Do not exceed the
signal range of the SSIS detector channel being calibrated. The number of certified depositions should be at least 4
more than the number of adjustable parameters used for the GNF. A reference wafer may contain one or more
certified depositions.
NOTE 4: The useful signal range is limited on the small signal side by the background noise or the inherent resolution of the
instrument and on the large signal side by saturation of the detector and/or the related electronics. The small signal limit is
usually defined as the smallest LSE sphere diameter than can be measured with a capture rate of at least 95%.
8.3.1 The index of refraction of the reference spheres may not be the same as that of the bulk material. In the case
of PSL spheres, industry practice is to use the index of refraction of bulk polystyrene, given by:
n  A
B
2

C
4
(1)
where A = 1.5663, B = 0.00785 µm2, C = 0.000334 µm4, and is the wavelength of light. A method suitable for
determining the index of refraction of non-PSL spheres is described in Appendix 2.
NOTE 5: The above coefficients have been shown to be valid over the wavelength range 0.42 <  (um) < 0.62. Some state-ofthe-art SSIS may use excitation at shorter wavelengths. However, good sizing correlation has been observed using this equation
at shorter wavelengths.
NOTE 6: Best results are typically achieved when using the number, the sizes of reference spheres, and the extent of allowable
extrapolation recommended by the SSIS manufacturer.
8.4 Background Contamination
8.4.1 Handle and store reference wafers with great care to avoid contamination and damage.
8.4.2 Establish that the unimodal peaks in the SSIS LLS histogram generated from the reference sphere depositions
are well defined and well above the background level over all the response curve except near the low signal
threshold. Also verify that each unimodal curve extends to less than 50% of its peak value on both sides of the peak
within a diameter range of ±2.5% of the reference sphere diameter at the peak of the distribution. Do not use
depositions that fail either of these criteria.
NOTE 7: The RC depends on scanner design and is in general non-linear. It may contain regions with response curve oscillations
that make the response-diameter relationship multi-valued.
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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8.5.1 For each certified deposition on a reference wafer provide:
8.5.2 The deposition peak diameter and the uncertainty in accordance with the requirements of Row 5.3 of Table 3
of SEMI M52.
8.5.3 The maximum possible value of the deposition diameter distribution full width at half maximum (FWHM)
expressed as a percentage of peak diameter.
8.5.4 The approximate particle count of each certified deposition.
8.5.5 The approximate location of each certified deposition on the reference wafer by the x- and y-coordinates (as
specified in SEMI M20) of the center of the deposition area or by a map or drawing of the wafer.
8.5.6 Identification of the deposition system used for the deposition by model and serial number.
8.5.7 The date of production.
8.5.8 Wafer identification.
8.5.9 Name and address of the reference wafer manufacturer.
8.5.10 Identification of the deposited reference spheres by material, supplier, lot number and model.
9 Procedure
9.1 Obtain the required number of suitable reference wafers with certified depositions (see ¶ 8.3) to cover each
established signal range.
9.2 Set up the SSIS in accordance with the manufacturer’s instructions for the wafer diameter, sizes of reference
spheres, and other machine conditions to be used during the calibration procedure. Ensure that machine conditions
are identical with those to be used in examining wafers with the calibrated SSIS.
9.3 Ensure that the SSIS is operating properly for the selected machine conditions.
9.4 Load the first reference wafer into the SSIS.
9.5 Scan the wafer.
9.6 Generate a data set file of the distribution of localized light scatterers as a function of reported SSIS signal.
9.7 Repeat ¶¶ 9.2–9.6 for each of the remaining certified depositions.
9.8 Determine the peak of the reference sphere diameter distribution for each of the certified depositions used for
the calibration.
NOTE 8: Many SSISs now feature automated determination of the peak of sphere diameter distributions. For SSISs where the
determination is manual, users should carefully note histogram aspects such as scaling and non-uniform bin widths which may
bias peak position.
9.9 For each reference sphere material and for PSL, create a PRC using the SSIS detector channel geometry, source
wavelength, source polarization and appropriate material constants over the range from less than the minimum
certified deposition diameter to greater than the maximum certified deposition diameter with a recommended
diameter spacing of approximately the illumination wavelength divided by 50 in order to accurately predict RC
oscillations. Calculate the PRC using the Bobbert-Vlieger model provided in the Modeled Integrated Scatter Tool
(MIST) program.2 Alternatively, use another program suggested by the instrument manufacturer, provided that it can
be shown to have as good or better results. Record the PRC values for each certified deposition by interpolating the
PRC for the reference sphere material at its certified diameter.
2 This program can be downloaded without charge from the website of the National Institute of Standards and Technology:
http://physics.nist.gov/scatmech
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8.5 Data to Accompany Reference Wafers — The following information must accompany each reference wafer.
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9.10 Obtain the GNF by adjusting the independent parameters for a best fit to the SSIS signals found in ¶ 9.8 versus
the corresponding PRC values obtained in ¶ 9.9. Typically the curve is a smooth straight line on a log-log graph, so
use the following form:
GNF =  (predicted response) 
(2)
This function has two adjustable parameters ( and ). Alternatively, use another function form, provided that the
number of adjustable parameters is small, it is monotonic, and it describes a typical non-linearity for the type of
detector used.
9.11 Create an RC for each reference sphere material by applying the GNF determined in ¶ 9.10 to the PRC for that
material. Graph the RCs (as curves) and the peak SSIS signals determined in ¶ 9.8 (as points) against diameter on a
log-log scale.
9.12 Determine the calibration diameter error between the points and the curve for the corresponding reference
sphere material shown in the graph created in ¶ 9.11.
9.13 If a monotonic response is to be used for large particles, create the MPRC PSL from the PRCPSL using the
method specified by the SSIS manufacturer. If a non-monotonic response is to be used for large particles, go to
¶ 9.16.
9.14 Create an MRCPSL by applying the GNF determined in ¶ 9.14 to the MPRCPSL.
9.15 Determine the expanded PSL sphere sizing uncertainty by:
2
2
U PSL  2  1   2 / N  M ,
(3)
9.16 where 1 is the relative standard uncertainty in the peak reference sphere diameters for the certified depositions,
2 is the standard deviation of the relative calibration diameter error (determined in ¶ 9.12), N is the number of
certified depositions, and M is the number of independent parameters in the GNF. SEMI M52 requires that 1 be
less than 2.1%; in the absence of specific values for 1, the maximum value accepted by SEMI M52 can be used.
9.16 Repeat the procedure of ¶¶ 9.2–9.14 for all of the SSIS detector channels being calibrated.
9.17 Related Information 1 presents an example of this procedure based on one detector channel of a commercially
available SSIS.
10 Interpretation of Results
10.1 The expanded reference sphere sizing uncertainty found for each detector channel in ¶ 9.15 should be less than
3% in order to meet the requirements of SEMI M52.
10.2 If the decision has been made to allow the response to be non-monotonic for large particles, then use the RCPSL
to establish the LSE size of LLSs.
10.3 If the decision has been made to use the monotonic response for large particles, then use the MRC PSL to
establish the LSE size of LLSs.
11 Report
11.1 Report the following information:
11.1.1 Operator identification;
11.1.2 Date and location of measurement;
11.1.3 Manufacturer, model, serial number, and software version of the SSIS;
11.1.4 Reference wafer characteristics as outlined in the certificates accompanying the reference wafers (see § 8);
11.1.5 Histogram for each data set and the assigned peak value of the distribution of reported diameters together
with the certified peak diameter of the PSL sphere distributions used to generate the histogram; and
11.1.6 The GNF, the RCPSL, and the associated certified reference sphere diameters. If a monotonic response is to
be used for large particles, also report the MRCPSL.
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APPENDIX 1
APPENDIX 1REFERENCE SPHERE INDEX DETERMINATION
NOTICE: The material in this appendix is an official part of SEMI M53 and was approved by full letter ballot
procedures on January 2, 2009.
A1-1 This appendix describes a method for determining the index of refraction of non-PSL reference spheres. It
requires an SSIS, but it does not require that the SSIS be of the same design as that for which the reference spheres
will be used to calibrate.
A1-2 Obtain two sets of reference wafers with certified depositions (see ¶ 8.2), one with PSL spheres and the other
with reference spheres of unknown index (the “unknown reference spheres”).
A1-3 Follow ¶¶ 9.1–9.10 using the PSL spheres. For the index of refraction of the PSL spheres, use
n  A
B

2

C
(A2-1)
4
where A = 1.5663, B = 0.00785 µm2, and C = 0.000334 µm4. Report the GNF.
A1-4 Repeat the measurement steps (¶¶ 9.2–9.6) for the unknown reference spheres, to obtain the signal Si for each
unknown reference sphere i.
A1-5 Estimate the anticipated minimum and maximum possible indices for the unknown reference spheres.
A1-6 For each index n ranging from the minimum to the maximum with a small step n, create a PRCn as per ¶ 9.9.
Record the PRCn values for each unknown reference sphere i and for each index n, PRCni.
A1-7 For each index n and each unknown reference sphere i, calculate the GNF error from
Eni  GNF(PRCni )  Si
(A2-2)
A1-7.1 For each index n, calculate the sum of squares GNF error from
Fn   Eni
2
(A2-3)
i
A1-8 Plot Fn versus n. If there is no minimum, go back to ¶ 1.4, starting over with a new range of possible indices.
A1-9 Find the best value of n by fitting the data close to the minimum to a parabola and finding the minimum. Use
the best value of n for the index of the reference spheres at the operating wavelength of the SSIS.
A1-10 Follow steps ¶¶ 9.9–9.17 of the standard using the data from the reference spheres instead of the PSL
spheres and report the calibration diameter errors and the GNF.
A1-11 If the index of refraction, nbulk, for the bulk form of the material is known at the operating wavelength of the
SSIS, then an effective medium void fraction may be estimated from
(nbulk  n)(nbulk  n)(2nbulk  1)
2
x
(nbulk  1)(2nbulk  n 2 )
2
2
(A2-4)
A1-12 If both the effective medium void fraction and the wavelength dependence nbulk() of the index of refraction
of the bulk material are known, then the index of refraction of the reference spheres at other wavelengths  can be
estimated from:
n( )  nbulk ( )
1  2[nbulk ( )]2 ( x  1)  2 x
1  x  [nbulk ( )]2 ( x  2)
(A2-5)
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RELATED INFORMATION 1
EXAMPLE OF MULTI-POINT CALIBRATION WITH FIT TO MODELPREDICTED DATA
NOTICE: This related information is not an official part of SEMI M53 and was derived from the Automated Wafer
Surface Inspection Task Force. This related information was approved for publication by full letter ballot on January
2, 2009.
R1-1 This related information provides an example of the procedure described in § 9. In all of this related
information, the reference spheres were PSL; subscripts on PRC, RC, MPRC, and MRC have been omitted and are
assumed to be PSL.
R1-2 Data were obtained on one detector channel of a commercially available SSIS. Column 1 of Table R1-1 lists
the certified diameters that were used in the calibration procedure. Column 2 of the table lists the measured peak
signals for each of the certified diameters. These signals have been multiplied by an unknown and arbitrary constant.
The peak signals range from Smin = 0.1254 to Smax = 373.2.
R1-3 The predicted response curve (PRC) was calculated using the Modeled Integrated Scatter Tool (MIST)
program.3 The parameters used for the model are given in Table R1-2. The PRC is shown in Figure R1-1. The
model-predicted response for each certified diameter is given in the third column of Table R1-1.
R1-4 Figure R1-2 shows a graph of the measured response values (second column of Table R1-1) versus the modelpredicted response values (third column of Table R1-1). On a log-log scale, it appears to be a straight line, so that
the GNF is chosen to be:
GNF =  (predicted response)
(R1-1)
A best fit to the data yields the two adjustable parameters  = 1.18  10 and  = 1.046. The best fit curve is also
shown in Figure R1-2.
4
R1-5 The RC was developed by applying the function of Equation R1-1 to the signal values of the PRC. The RC is
shown in Figure R1-3. The signals for the certified depositions are shown as points.
R1-6 The calibration diameter error is shown in the fourth column in Table R1-1. These deviations represent the
estimated errors in the measured diameters. The maximum value of this deviation is 1.5% and the standard deviation
is 0.6%. Since there are 14 calibration points and 2 degrees of freedom to the GNF, the expanded PSL sphere sizing
uncertainty is:
U PSL  2 (1.5%) 2  (0.6%) 2 / 14  2  0.9% .
(R1-2)
R1-7 Since this value is below 3%, the calibration meets the requirements of SEMI M52. An MPRC
was generated from the PRC by the following procedure: (A) The PRC was re-evaluated with diameters spaced by
2% over the range 30 nm to 1 µm. (B) For each diameter on the re-evaluated PRC, a straight line was fit (on a loglog graph) to points having diameters within 25% of the given diameter. (C) The MPRC at each diameter was then
given by evaluating the straight line at that diameter. The MPRC is shown with the PRC in Figure R1-1. In order to
demonstrate the procedure, the method for creating an MPRC was adopted in lieu of one provided by the
manufacturer, and the range of particle sizes were extended.
R1-8 The MRC generated by applying the GNF to the MPRC is shown in Figure R1-3 with the RC. This MRC can
be used to size particles throughout the diameter range shown, since it is monotonic.
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
development) activity. All other reproduction and/or distribution without the prior written consent of SEMI is prohibited.
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Certified Diameter (nm)
Measured Response (arb. units) Predicted Response (arb. units)
Calibration Diameter Error
61.7
0.1254
1.746 
75.1
0.4305
5.593  105
0.4%
0.9855
1.225 
104
0.6%
104
0.0%
85.9
105
0.2%
86.4
0.9855
1.267 
100.1
2.333
2.937  104
0.3%
100.7
2.385
3.036  104
0.5%
105.3
3.104
3.894 
104
0.5%
126.6
8.553
1.038 
103
0.8%
153.5
23.37
2.583  103
0.2%
158.0
25.87
2.922 
103
0.4%
185.1
50.42
5.344 
103
0.6%
204.0
69.27
7.244  103
0.6%
199.3
1.959 
102
0.8%
373.2
3.750 
102
1.1%
292.7
363.5
Table R1-2 Parameters Used in MIST
Parameter
Value
Model
Bobbert_Vlieger_BRDF_Model
Wavelength
488 nm
Refractive index of substrate
4.368 + 0.040i
Refractive index of substrate oxide
1.7387
Refractive index of PSL sphere
1.605
Thickness of substrate oxide:
1.6 nm
Incident angle
70°
Incident polarization
p (electric field in plane of incidence)
Collection geometry
All polar angles between 25° and 70°.
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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Table R1-1 Example of Data for Calibration Procedure
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0
10
Predicted Response (arb. units)
-1
10
-2
10
-3
10
-4
10
-5
10
Predicted Response Curve
Monotonic Predicted Response Curve
-6
10
600
700
800
900
1000
500
400
300
200
60
70
80
90
100
50
40
30
-7
10
PSL Sphere Diameter (nm)
Figure R1-1
Predicted Response Curve (PRC) Calculated from MIST
and the Monotonic Predicted Response Curve (MPRC)
Measured Response (arb. units)
1000
100
10
1
Measurement
Gain-Nonlinearity Function
0.1
-5
10
-4
10
-3
10
-2
10
-1
10
Predicted Response (arb. units)
Figure R1-2
Measured Response Values as a Function of Model-Predicted Response Values (points)
and the Gain-Nonlinearity Function (line)
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4
10
3
Response Curve (arb. units)
10
2
10
1
10
0
10
-1
10
Measurement
Response Curve
Monotonic Response Curve
-2
10
600
500
400
300
200
70
80
90
100
60
50
40
30
-3
10
Certified PSL Sphere Diameter (nm)
Figure R1-3
Response Curve (RC) and the Monotonic Response Curve (MRC)
NOTICE: SEMI makes no warranties or representations as to the suitability of the standard(s) set forth herein for
any particular application. The determination of the suitability of the standard(s) 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. These standards are subject to change
without notice.
By publication of this standard, Semiconductor Equipment and Materials International (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.
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