Fine ceramics (advanced ceramics, advanced technical ceramics) -- Ultraviolet photoluminescence image test method for analysing polytypes of boron- and nitrogen-doped SiC crystals

This document specifies a test method for determining the polytypes and their ratios in silicon carbide (SiC) wafers or bulk crystals using ultraviolet photoluminescence (UVPL) imaging. The range of SiC is limited to semiconductor SiC doped with nitrogen and boron to have a deep acceptor level and a shallow donor level, respectively. The SiC wafers or bulk crystals discussed in this document typically show electrical resistivities ranging from 10−3 ohm · cm to 10−2 ohm · cm, applicable to power electronic devices. This method is applicable to the SiC-crystal 4H, 6H and 15R polytypes that contain boron and nitrogen as acceptor and donor, respectively, at concentrations that produce donor-acceptor pairs (DAPs) to generate UVPL. In 4H-SiC the boron and nitrogen concentrations typically range from 1016 cm−3 to 1018 cm−3. Semi-insulating SiC is not of concern because it usually contains minimal boron and nitrogen; therefore deep level cannot be achieved.

Céramiques techniques -- Méthode d'imagerie de photoluminescence ultraviolette pour l'analyse des polytypes dans les cristaux de SiC dopés à l'azote et au bore

General Information

Status
Published
Publication Date
16-Feb-2021
Current Stage
5060 - Close of voting Proof returned by Secretariat
Start Date
12-Jan-2021
Completion Date
11-Jan-2021
Ref Project

Buy Standard

Standard
ISO 21820:2021 - Fine ceramics (advanced ceramics, advanced technical ceramics) -- Ultraviolet photoluminescence image test method for analysing polytypes of boron- and nitrogen-doped SiC crystals
English language
27 pages
sale 15% off
Preview
sale 15% off
Preview
Draft
ISO/FDIS 21820:Version 14-nov-2020 - Fine ceramics (advanced ceramics, advanced technical ceramics) -- Ultraviolet photoluminescence image test method for analysing polytypes of boron- and nitrogen-doped SiC crystals
English language
27 pages
sale 15% off
Preview
sale 15% off
Preview

Standards Content (sample)

INTERNATIONAL ISO
STANDARD 21820
First edition
2021-02
Fine ceramics (advanced ceramics,
advanced technical ceramics) —
Ultraviolet photoluminescence image
test method for analysing polytypes
of boron- and nitrogen-doped SiC
crystals
Céramiques techniques — Méthode d'imagerie de photoluminescence
ultraviolette pour l'analyse des polytypes dans les cristaux de SiC
dopés à l'azote et au bore
Reference number
ISO 21820:2021(E)
ISO 2021
---------------------- Page: 1 ----------------------
ISO 21820:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 21820:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols .......................................................................................................................................................................................................................... 2

5 Principle ........................................................................................................................................................................................................................ 2

6 Apparatus ..................................................................................................................................................................................................................... 2

7 Sampling ........................................................................................................................................................................................................................ 3

8 Procedure..................................................................................................................................................................................................................... 3

8.1 Cleaning of SiC wafer surface ..................................................................................................................................................... 3

8.2 Optical setup ............................................................................................................................................................................................. 3

8.3 Measurement ............................................................................................................................................................................................ 4

9 Expression of results ........................................................................................................................................................................................ 6

9.1 Expression of boundaries of polytypes in CIE 1931 colour space .............................................................. 6

9.2 Transformation of the UVPL image to CIE 1931 colour space with polytype boundaries .... 6

9.3 Determination of polytype ............................................................................................................................................................ 7

10 Test report ................................................................................................................................................................................................................... 7

Annex A (informative) Determination of polytypes ............................................................................................................................. 9

Annex B (informative) Determination of polytypes ..........................................................................................................................17

Annex C (informative) Penetration depth of SiC ....................................................................................................................................25

Annex D (informative) Calibration ......................................................................................................................................................................26

Bibliography .............................................................................................................................................................................................................................27

© ISO 2021 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 21820:2021(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/

iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 206, Fine ceramics.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2021 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 21820:2021(E)
Introduction

Silicon carbide (SiC), which has a close-packed crystal structure, is a promising wide-bandgap (WBG)

material applicable to laser diodes (LDs), light-emitting diodes (LEDs) and electronic power devices.

Polytype inclusion generated during SiC growth is a common problem. During crystal growth, many

types of SiC-stacking can occur within the bulk of a single sample. These different stacking-order types

are called “polytypes.” Polytypes have identical close-packed planes but differ in the stacking sequence

on the axis that is perpendicular to these planes.

SiC has more than 200 known polytypes, but most polytypes are rare, except types 2H, 4H, 6H, 15R and

3C. For example, 4H-SiC is the material used for power production in devices because of its excellent

physical properties. These SiC polytypes have the same density and Gibbs-free energy but different

electronic band structures. The different band structures cause different wavelengths of luminescence

induced by incident ultraviolet (UV) light.

SiC can be grown using several crystal-growth techniques, such as physical vapor transport (PVT),

chemical vapor deposition (CVD) and top-seeded solution growth (TSSG). Polytype inclusion in bulk SiC

is one of the drawbacks during production.

Therefore, a rapid test method to discriminate between polytypes would be useful for the development

and mass production of SiC crystals.

This document specifies a test method to evaluate the polytypes and their SiC ratios by UV-induced

photoluminescence using non-contact and full-field measurement techniques.
© ISO 2021 – All rights reserved v
---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 21820:2021(E)
Fine ceramics (advanced ceramics, advanced technical
ceramics) — Ultraviolet photoluminescence image test
method for analysing polytypes of boron- and nitrogen-
doped SiC crystals
1 Scope

This document specifies a test method for determining the polytypes and their ratios in silicon carbide

(SiC) wafers or bulk crystals using ultraviolet photoluminescence (UVPL) imaging. The range of SiC is

limited to semiconductor SiC doped with nitrogen and boron to have a deep acceptor level and a shallow

donor level, respectively. The SiC wafers or bulk crystals discussed in this document typically show

−3 −2

electrical resistivities ranging from 10 ohm · cm to 10 ohm · cm, applicable to power electronic

devices.

This method is applicable to the SiC-crystal 4H, 6H and 15R polytypes that contain boron and nitrogen

as acceptor and donor, respectively, at concentrations that produce donor-acceptor pairs (DAPs) to

16 −3

generate UVPL. In 4H-SiC the boron and nitrogen concentrations typically range from 10 cm to

18 −3

10 cm . Semi-insulating SiC is not of concern because it usually contains minimal boron and nitrogen;

therefore deep level cannot be achieved.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories

3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
ultraviolet photoluminescence
UVPL

wavelength shifting to a longer wavelength by the interaction of photons with matter

3.2
donor-acceptor pair
DAP

state of a solid in which an electron-hole is created when a photon or other energy is absorbed

3.3
DAP recombination energy
photon energy emitted by the recombination of the donor-acceptor pair (3.2)
© ISO 2021 – All rights reserved 1
---------------------- Page: 6 ----------------------
ISO 21820:2021(E)
3.4
ultraviolet photoluminescence image test method

method to identify the polytypes and their ratios using the donor-acceptor pair recombination energy

(3.3) of materials as the ultraviolet photoluminescence (3.1) colour
4 Symbols
Symbol Designation Unit
C velocity of light 299 792 458 m/s
E bandgap energy eV
(or DAP recombination energy)
−34
H Planck’s constant 6,626 070 04 × 10 J·s
I intensity of the light source W/cm
T temperature K
λ wavelength nm
ρ resistivity Ω.cm
ω angular velocity radian/s
5 Principle

When UV light illuminates a material having DAP recombination energy in the visible-light range, the

material will emit a specific colour depending on the DAP recombination energy. Thus, the polytypes of

SiC can be identified by their luminescence colour because different SiC polytypes have their own DAP

recombination energy. The polytype area in CIE 1931 colour space is mapped and transformed from the

UVPL image; subsequently, the polytype ratios are calculated.
6 Apparatus

6.1 Stage. The experiment should be performed in a non-vibrational state or on an anti-vibration table

to prevent noise caused by vibration.

6.2 Digital camera. This should be a charge-coupled device (CCD) camera with an ISO rating of

(500 ± 100), (f/#) of f/1,8–f/3,2 and zero exposure compensation. The shutter speed should be 1/30

to 1/50 and the white balance should be 6 500 K. These are the standard conditions for the UVPL image

test, but they can be varied.

The purpose and function of a CCD camera is to produce an image similar to the object recognized by

the human eye. This is achieved by synthesizing the image consisting of the artificial fine shapes and

colours. It should be noted that the CCD camera is neither a spectra analyser nor a spectra recorder.

Before evaluating the polytype, the CCD camera should be calibrated. The UVPL image captured by

the CCD camera should be significantly expanded and carefully checked. If any artificial pattern is

observed, the CCD camera should be replaced with another.

6.3 Lens. This is used to focus the incident UV beam onto the specimens. The position and focal length

of the lens should be selected for the beam to spread over every sample with uniform intensity.

6.4 Light source. The wavelength (λ) of the UV light source (UVLS) should be 180 nm to 365 nm in

the nonvisible range and monochromatic range. The intensity of the light source should be 600 mW/

cm or above. The working distance between the sample and the light source should be approximately

(10~30) cm. In reflectance mode, adjust the angle (0~360)° between the direction of the light source

and the direction normal to the sample to prevent the UV source from being incident directly on the

CCD camera and measure only the luminescence beam. In transmission mode, the luminescence beam

2 © ISO 2021 – All rights reserved
---------------------- Page: 7 ----------------------
ISO 21820:2021(E)

produced by the sample should be measured using the CCD camera after having been transmitted

through the sample.

6.5 Filter. UVLSs can emit a visible beam as well as a UV beam. If the visible beam is incident on the

CCD camera, it can disturb the data measurements. Therefore, a bandpass filter that passes only UV

beams should be positioned in front of the UVLS.
7 Sampling

7.1 The UVPL technique can be applied to SiC samples grown by various techniques. The necessary

condition is to have boron and nitrogen dopant at concentrations that are sufficient to emit the

luminescence of the DA pair at an effectively high intensity.

7.2 The flat surface of a sample should be polished finely to improve the measurement accuracy by

preventing the UV beam from being scattered for the beam to remain incident directly on the digital camera.

7.3 Should there be any treatment (e.g. polishing) before the test, it shall be recorded in the test report.

8 Procedure
8.1 Cleaning of SiC wafer surface

The samples should be handled in a clean environment, such as a clean-booth or clean-room. The clean

surface of a wafer should be maintained. Wiping with a soft tissue soaked with a volatile solvent, such

as acetone or ethanol, can render the sample surface free of foreign contaminations, such as dust,

other particles, metals, organic compounds, inorganic compounds or moisture. However, if the surface

contamination remains and thereby influences the measurements, the sample surface should be wet

cleaned in a clean environment, using ultra-high-purity water and chemicals, such as H SO : H O : H O,

2 4 2 2 2
NH OH: H O : H O, HCl: H O : H O or other suitable chemicals.
4 2 2 2 2 2 2

Figure 1 shows examples of polytype shapes. Typically, they have clear and sharp lines revealing the

grain boundaries.

Figure 1 — Crystal grains in UVPL image (clear lines of grain boundary expressing crystal shapes)

8.2 Optical setup
8.2.1 The optical setup should be constructed as shown in Figure 2 a).

8.2.2 The experiment should be performed in a darkroom or with a blackout curtain to prevent

extraneous light, which can disturb the UVPL beam.
© ISO 2021 – All rights reserved 3
---------------------- Page: 8 ----------------------
ISO 21820:2021(E)

8.2.3 The experiment should be performed in a non-vibrational state or on an anti-vibration table to

prevent noise caused by vibration.

8.2.4 Beam expanders (BEs) should be positioned adjacent to the UVLS to expand the beam.

8.2.5 Optical bandpass filters (BF ) are positioned after the BE to filter light except in the UV range.

The transmittance distribution along the wavelength of BF when it passes only the intended UV light is

shown in Figure 2 b).

8.2.6 Support for the sample (SiC) should be positioned such that the UV beam is not incident directly

on the CCD camera.

8.2.7 The normal axes of the CCD camera and the SiC sample should coincide to maximize the UVPL

intensity.

8.2.8 The photoluminescent beam emitted from the SiC sample incident on the CCD camera should

be filtered by a bandpass filter (BF ) to filter the reflected or scattered UV beam from the SiC sample

for only PL light to be incident on the CCD camera. The transmittance distribution along the wavelength

when it filters UV-range light is shown in Figure 2 c).
8.2.9 The image taken by the CCD camera should be transformed into colour space.
8.3 Measurement
8.3.1 Calibration is necessary before measurement. See Annex D.

8.3.2 The UV beam emitted by the UVLS passing through BE and BF then irradiates the SiC sample.

8.3.3 Take pictures of the UVPL image using the CCD camera and save the images in RGB format.

8.3.4 Transform the RGB images to the CIE 1931 colour space.
4 © ISO 2021 – All rights reserved
---------------------- Page: 9 ----------------------
ISO 21820:2021(E)

8.3.5 The polytype can be determined by the position of the colour point when it is plotted on the

colour space.
a) Schematic of a UVPL imaging system
b) Transmittance distribution of BF c) Transmittance distribution of BF
1 2
Key
A expanded UV beam
B UV induced PL beam
C UV LED
UVL ultraviolet light source
BF bandpass filter
BE beam expander
SiC silicon carbide
CC CCD camera
DAQ data acquisition
X wavelength, nm
Y transmittance
Figure 2 — Optical setup for UVPL measurement
© ISO 2021 – All rights reserved 5
---------------------- Page: 10 ----------------------
ISO 21820:2021(E)
9 Expression of results
9.1 Expression of boundaries of polytypes in CIE 1931 colour space

The polytype boundaries are defined in the CIE 1931 colour space as shown in Figure 3. The dotted

lines are the polytype lines. When the temperature of a SiC sample is near 0 K, the transformed points

from the UVPL image are positioned near the edge of the colour space; as the temperature increases, the

colour points approach the centre of the colour space (1/3,1/3,1/3). The black lines in Figure 3 represent

the boundary lines, which are between polytype lines and help to determine the major polytypes.

Figure 3 — Polytype lines (dotted lines) and boundary lines (dashed lines) of polytypes in

CIE 1913 colour space

The detailed procedure for producing the polytype lines and boundaries is described in Annex A.

Annex B shows the boundary points table of each polytype in the CIE 1931 colour space. The specific

polytype regions are defined as the inner regions of polygons made by connecting these boundary

points, as shown in Figures B.1 to B.3.
9.2 Transformation of the UVPL image to CIE 1931 colour space with polytype
boundaries

The UVPL colour data should be transformed to the CIE 1931 colour space using the polytype boundaries

to identify the polytype.

Each polytype has a different DAP recombination energy, which indicates that each polytype has a

different colour. Therefore, when a UVPL image is transformed into the CIE 1931 colour space, each

polytype colour has a different position in the colour space.
6 © ISO 2021 – All rights reserved
---------------------- Page: 11 ----------------------
ISO 21820:2021(E)
9.3 Determination of polytype

9.3.1 After the transformation of the UVPL image to the colour space, the SiC polytype should be

determined.

If the SiC sample is a perfect single crystal, colour points transformed from the image to colour space

should be on one of the red lines only, thus allowing the polytype to be easily determined. However,

there can be a mixture of polytypes in the sample. In that case, colour points can be distributed around

the polytype line.

9.3.2 The polytype can be determined quantitatively. That is, if the colour points are distributed on

only one polytype region, that would be the desired polytype.

9.3.3 If the colour points are distributed widely across several polytype regions, the number of colour

points on each polytype region should be counted and the ratio of polytype region should be calculated

as follows:
100 % = 4H (%) + 6H (%) + 15R (%) + other polytypes (%)

If the 4H (6H, 15R) SiC surface is significantly contaminated, the UVPL image of the contaminated

region can exhibit a different colour from those of the 4H (6H, 15R) SiC. It may then be identified as one

of the other polytypes. Therefore, the measured ratio of 4H, 6H and 15R is the minimum value.

When the total ratio of the 4H, 6H and 15R polytype is less than 100 %, the following issues should be

taken into account.

If a UVPL image has ambiguous shapes accompanied by an unclear boundary or if a region with

characteristic patterns changes its position and area for each measurement, then the sample surface

may be significantly contaminated.

The sample surface should be cleaned following a wet cleaning process using H SO : H O : H O, NH OH:

2 4 2 2 2 4
H O : H O, HCl: H O : H O or other suitable chemicals.
2 2 2 2 2 2
10 Test report

The test report shall be in accordance with the reporting provisions of ISO/IEC 17025 and shall contain

the following information, if available:
a) the name of the testing establishment;
b) the date of the test, report identification and number, operator, signatory;

c) a description of the SiC wafers (material manufacturer, growth method, and conditions);

d) the results obtained, including the UVPL images:
1) image of SiC under illumination in the visible range;
2) UVPL image, image size and format;
3) CIE 1931 colour space and range;
4) penetration depth (see Annex C);
5) CCD camera name;
e) the polytype results determined according to the ranges in colour space;
f) comments about the test or test results;
© ISO 2021 – All rights reserved 7
---------------------- Page: 12 ----------------------
ISO 21820:2021(E)
g) a reference to this document (i.e. ISO 21820:2021).
8 © ISO 2021 – All rights reserved
---------------------- Page: 13 ----------------------
ISO 21820:2021(E)
Annex A
(informative)
Determination of polytypes
A.1 Determination of coordinates of each polytype at 0 K in colour space

Each polytype has an intrinsic DAP recombination energy so that it emits a monochromatic

photoluminescent beam at zero Kelvin when it is illuminated by UV light. The DAP recombination

energy of each polytype is different; this can be used as a criterion for polytype determination.

Table A.1 shows the wavelength of the polytypes measured by a PL spectrometer and the corresponding

DAP recombination energy calculated by applying Planck’s relation (Formula A.1).
Table A.1 — Relation between polytype, DAP recombination energy and wavelength.
DAP recombination energy Wavelength
Polytype
eV nm
4H-SiC 2,295 9 540
6H-SiC 2,032 5 610
15R-SiC 2,006 2 618
Eh==ν (A.1)
where
E is the energy;
h is Planck’s constant;
ν is the frequency of light;
c is the velocity of light;
λ is the wavelength of light.

These DAP recombination energies or wavelengths can be converted into colour space as one-

colour points.

The total intensities of red, green and blue are denoted as X, Y and Z and can be calculated using

Formulae (A.2) to (A.4). Figure A.1 depicts the conversion of monochromatic light into colour space as

colour points. Figure A.1 a) shows the normalized spectral density distribution of the tristimuli, M()λ ,

defined in CIE 1931 and ISO/CIE 11664-3. Figure A.1 b) depicts the monochromatic light intensity

distribution, x()λ , that has the form of a delta function for each polytype as shown in the last row of

Table A.1. Figure A.1 c) depicts the final intensities of X, Y and Z calculated with Formulae (A.2) to (A.4).

The normalized X, Y and Z coordinates are denoted as x, y and z and can be calculated using Formulae

(A.5) to (A.7).
850
XM= λλxdλ (A.2)
() ()
450
© ISO 2021 – All rights reserved 9
---------------------- Page: 14 ----------------------
ISO 21820:2021(E)
850
YM= ()λλyd() λ (A.3)
450
850
ZM= λλzdλ (A.4)
() ()
450
x= (A.5)
XY++Z
y= (A.6)
XY++Z
z= =−1 xy− (A.7)
XY++Z
where
λ is the wavelength of light;

x λ is the monochromatic light intensity distribution of red light where the wavelength is λ;

y()λ is the monochromatic light intensity distribution of green light where the wavelength is λ;

z()λ is the monochromatic light intensity distribution of blue light where the wavelength is λ;

X is the normalized total intensity of red light;
Y is the normalized total intensity of green light;
Z is the normalized total intensity of blue light.
10 © ISO 2021 – All rights reserved
---------------------- Page: 15 ----------------------
ISO 21820:2021(E)
Key
I intensity
W wavelength (nm)
A normalized spectral distribution of tristimulus
B delta functional distribution of photoluminescence
C intensities of XYZ
Figure A.1 — Conversion from monochromatic light to RGB

4H-SiC, 6H-SiC, 15R-SiC and 3C-SiC are plotted as dots at the edge of the colour space. The monochromatic

light is always placed at the edge of the colour space. The dot at the centre corresponds to the white

point because the RGB coordinates of white are (1/3,1/3,1/3).

The monochromatic wavelengths of 15R-SiC and 3C-SiC are closely adjacent to 770 nm and 780 nm

when they are converted into the colour space wherein they overlap, as can be seen in Figure A.2.

© ISO 2021 – All rights reserved 11
---------------------- Page: 16 ----------------------
ISO 21820:2021(E)
Key
W white
Figure A.2 — Polytype colour points in colour space
A.2 Determination of lines of each polytype at various temperatures

At extremely low temperatures, the PL beam is so monochromatic that it has the form of a delta function.

However, as the temperature increases, it assumes the form of a Gaussian distribution.

This property of the PL beam enables it to be modelled as the Gaussian function M(λ) in Formula (A.8),

in which its shape changes as the shape parameter β changes.

When β in Formula (A.8) decreases to zero, M(λ) becomes a delta function, as in Formula (A.9), and the

maximum value and full width half maximum (FWHM) of M(λ) are as shown in Formulae (A.10) and (A.11).

λλ−
−()
M()λ = e (A.8)
β π
limM λδ=−λλ (A.9)
() ()
β→0
λ −λ
−()
11 1
M λ ==ee = (A.10)
ββππ β π
λβ=22ln2 (A.11)
FWHM
where
12 © ISO 2021 – All rights reserved
---------------------- Page: 17 ----------------------
ISO 21820:2021(E)
λ is the centre point of the Gaussian function;
λ is the FWHM of function M(λ);
FWHM
e is exponential function;
ln is natural logarithm function.

β in Formula (A.8) increases as temperature increases, though the relation between them differs

depending on the material. Using this characteristic, the polytype lines are calculated as follows.

The coordinate in the colour space of each polytype at 0 K is calculated and plotted first. These colour

points are all plotted at the edge of the colour space. As the temperature increases, β increases so that

the maximum height of the PL distribution decreases, as in Formula (A.10), and its width increases,

according to Formula (A.11).

Finally, the distribution becomes uniform as β goes to infinity, as shown in Figure A.3.

Key
W wavelength (nm)
I intensity
Figure A.3 — Gaussian distribution depending on temperature

The polytype lines can be calculated using a Gaussian distribution at various temperatures in

Formula (A.8). Figure A.4 shows the procedure, which almost replicates that in Figure A.1, except for

Figure A.4 b), which is extended to various shape parameter β values as in Figure A.3. Figure A.4 c)

shows the results. Although Figure A.3 c) plots only every individual point at the edge of the colour

...

FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 21820
ISO/TC 206
Fine ceramics (advanced ceramics,
Secretariat: JISC
advanced technical ceramics) —
Voting begins on:
2020­11­16 Ultraviolet photoluminescence image
test method for analysing polytypes
Voting terminates on:
2021­01­11
of boron- and nitrogen-doped SiC
crystals
Céramiques techniques — Méthode d'imagerie de photoluminescence
ultraviolette pour l'analyse des polytypes dans les cristaux de SiC
dopés à l'azote et au bore
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO­
ISO/FDIS 21820:2020(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN­
DARDS TO WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS. ISO 2020
---------------------- Page: 1 ----------------------
ISO/FDIS 21820:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH­1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/FDIS 21820:2020(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols .......................................................................................................................................................................................................................... 2

5 Principle ........................................................................................................................................................................................................................ 2

6 Apparatus ..................................................................................................................................................................................................................... 2

7 Sampling ........................................................................................................................................................................................................................ 3

8 Procedure..................................................................................................................................................................................................................... 3

8.1 Cleaning of SiC wafer surface ..................................................................................................................................................... 3

8.2 Optical setup ............................................................................................................................................................................................. 3

8.3 Measurement ............................................................................................................................................................................................ 4

9 Expression of results ........................................................................................................................................................................................ 6

9.1 Expression of boundaries of polytypes in CIE 1931 colour space .............................................................. 6

9.2 Transformation of the UVPL image to CIE 1931 colour space with polytype boundaries .... 6

9.3 Determination of polytype ............................................................................................................................................................ 7

10 Test report ................................................................................................................................................................................................................... 7

Annex A (informative) Determination of polytypes ............................................................................................................................. 9

Annex B (informative) Determination of polytypes ..........................................................................................................................17

Annex C (informative) Penetration depth of SiC ....................................................................................................................................25

Annex D (informative) Calibration ......................................................................................................................................................................26

Bibliography .............................................................................................................................................................................................................................27

© ISO 2020 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO/FDIS 21820:2020(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non­governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/

iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 206, Fine ceramics.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2020 – All rights reserved
---------------------- Page: 4 ----------------------
ISO/FDIS 21820:2020(E)
Introduction

Silicon carbide (SiC), which has a close-packed crystal structure, is a promising wide-bandgap (WBG)

material applicable to laser diodes (LDs), light­emitting diodes (LEDs) and electronic power devices.

Polytype inclusion generated during SiC growth is a common problem. During crystal growth, many

types of SiC-stacking can occur within the bulk of a single sample. These different stacking-order types

are called “polytypes.” Polytypes have identical close-packed planes but differ in the stacking sequence

on the axis that is perpendicular to these planes.

SiC has more than 200 known polytypes, but most polytypes are rare, except types 2H, 4H, 6H, 15R and

3C. For example, 4H-SiC is the material used for power production in devices because of its excellent

physical properties. These SiC polytypes have the same density and Gibbs-free energy but different

electronic band structures. The different band structures cause different wavelengths of luminescence

induced by incident ultraviolet (UV) light.

SiC can be grown using several crystal-growth techniques, such as physical vapor transport (PVT),

chemical vapor deposition (CVD) and top-seeded solution growth (TSSG). Polytype inclusion in bulk SiC

is one of the drawbacks during production.

Therefore, a rapid test method to discriminate between polytypes would be useful for the development

and mass production of SiC crystals.

This document specifies a test method to evaluate the polytypes and their SiC ratios by UV-induced

photoluminescence using non-contact and full-field measurement techniques.
© ISO 2020 – All rights reserved v
---------------------- Page: 5 ----------------------
FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 21820:2020(E)
Fine ceramics (advanced ceramics, advanced technical
ceramics) — Ultraviolet photoluminescence image test
method for analysing polytypes of boron- and nitrogen-
doped SiC crystals
1 Scope

This document specifies a test method for determining the polytypes and their ratios in silicon carbide

(SiC) wafers or bulk crystals using ultraviolet photoluminescence (UVPL) imaging. The range of SiC is

limited to semiconductor SiC doped with nitrogen and boron to have a deep acceptor level and a shallow

donor level, respectively. The SiC wafers or bulk crystals discussed in this document typically show

−3 −2

electrical resistivities ranging from 10 ohm · cm to 10 ohm · cm, applicable to power electronic

devices.

This method is applicable to the SiC-crystal 4H, 6H and 15R polytypes that contain boron and nitrogen

as acceptor and donor, respectively, at concentrations that produce donor-acceptor pairs (DAPs) to

16 −3

generate UVPL. In 4H-SiC the boron and nitrogen concentrations typically range from 10 cm to

18 −3

10 cm . Semi-insulating SiC is not of concern because it usually contains minimal boron and nitrogen;

therefore deep level cannot be achieved.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories

3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
ultraviolet photoluminescence
UVPL

wavelength shifting to a longer wavelength by the interaction of photons with matter

3.2
donor-acceptor pair
DAP

state of a solid in which an electron-hole is created when a photon or other energy is absorbed

3.3
DAP recombination energy
photon energy emitted by the recombination of the donor-acceptor pair (3.2)
© ISO 2020 – All rights reserved 1
---------------------- Page: 6 ----------------------
ISO/FDIS 21820:2020(E)
3.4
ultraviolet photoluminescence image test method

method to identify the polytypes and their ratios using the donor-acceptor pair recombination energy

(3.3) of materials as the ultraviolet photoluminescence (3.1) colour
4 Symbols
Symbol Designation Unit
C velocity of light 299 792 458 m/s
E bandgap energy eV
(or DAP recombination energy)
−34
H Planck’s constant 6,626 070 04 × 10 J·s
I intensity of the light source W/cm
T temperature K
λ wavelength nm
ρ resistivity Ω.cm
ω angular velocity radian/s
5 Principle

When UV light illuminates a material having DAP recombination energy in the visible-light range, the

material will emit a specific colour depending on the DAP recombination energy. Thus, the polytypes of

SiC can be identified by their luminescence colour because different SiC polytypes have their own DAP

recombination energy. The polytype area in CIE 1931 colour space is mapped and transformed from the

UVPL image; subsequently, the polytype ratios are calculated.
6 Apparatus

6.1 Stage. The experiment should be performed in a non-vibrational state or on an anti-vibration table

to prevent noise caused by vibration.

6.2 Digital camera. This should be a charge­coupled device (CCD) camera with an ISO rating of

(500 ± 100), (f/#) of f/1,8–f/3,2 and zero exposure compensation. The shutter speed should be 1/30

to 1/50 and the white balance should be 6 500 K. These are the standard conditions for the UVPL image

test, but they can be varied.

The purpose and function of a CCD camera is to produce an image similar to the object recognized by

the human eye. This is achieved by synthesizing the image consisting of the artificial fine shapes and

colours. It should be noted that the CCD camera is neither a spectra analyser nor a spectra recorder.

Before evaluating the polytype, the CCD camera should be calibrated. The UVPL image captured by

the CCD camera should be significantly expanded and carefully checked. If any artificial pattern is

observed, the CCD camera should be replaced with another.

6.3 Lens. This is used to focus the incident UV beam onto the specimens. The position and focal length

of the lens should be selected for the beam to spread over every sample with uniform intensity.

6.4 Light source. The wavelength (λ) of the UV light source (UVLS) should be 180 nm to 365 nm in

the nonvisible range and monochromatic range. The intensity of the light source should be 600 mW/

cm or above. The working distance between the sample and the light source should be approximately

(10~30) cm. In reflectance mode, adjust the angle (0~360)° between the direction of the light source

and the direction normal to the sample to prevent the UV source from being incident directly on the

CCD camera and measure only the luminescence beam. In transmission mode, the luminescence beam

2 © ISO 2020 – All rights reserved
---------------------- Page: 7 ----------------------
ISO/FDIS 21820:2020(E)

produced by the sample should be measured using the CCD camera after having been transmitted

through the sample.

6.5 Filter. UVLSs can emit a visible beam as well as a UV beam. If the visible beam is incident on the

CCD camera, it can disturb the data measurements. Therefore, a bandpass filter that passes only UV

beams should be positioned in front of the UVLS.
7 Sampling

7.1 The UVPL technique can be applied to SiC samples grown by various techniques. The necessary

condition is to have boron and nitrogen dopant at concentrations that are sufficient to emit the

luminescence of the DA pair at an effectively high intensity.

7.2 The flat surface of a sample should be polished finely to improve the measurement accuracy by

preventing the UV beam from being scattered for the beam to remain incident directly on the digital camera.

7.3 Should there be any treatment (e.g. polishing) before the test, it shall be recorded in the test report.

8 Procedure
8.1 Cleaning of SiC wafer surface

The samples should be handled in a clean environment, such as a clean­booth or clean­room. The clean

surface of a wafer should be maintained. Wiping with a soft tissue soaked with a volatile solvent, such

as acetone or ethanol, can render the sample surface free of foreign contaminations, such as dust,

other particles, metals, organic compounds, inorganic compounds or moisture. However, if the surface

contamination remains and thereby influences the measurements, the sample surface should be wet

cleaned in a clean environment, using ultra-high-purity water and chemicals, such as H SO : H O : H O,

2 4 2 2 2
NH OH: H O : H O, HCl: H O : H O or other suitable chemicals.
4 2 2 2 2 2 2

Figure 1 shows examples of polytype shapes. Typically, they have clear and sharp lines revealing the

grain boundaries.

Figure 1 — Crystal grains in UVPL image (clear lines of grain boundary expressing crystal shapes)

8.2 Optical setup
8.2.1 The optical setup should be constructed as shown in Figure 2 a).

8.2.2 The experiment should be performed in a darkroom or with a blackout curtain to prevent

extraneous light, which can disturb the UVPL beam.
© ISO 2020 – All rights reserved 3
---------------------- Page: 8 ----------------------
ISO/FDIS 21820:2020(E)

8.2.3 The experiment should be performed in a non-vibrational state or on an anti-vibration table to

prevent noise caused by vibration.

8.2.4 Beam expanders (BEs) should be positioned adjacent to the UVLS to expand the beam.

8.2.5 Optical bandpass filters (BF ) are positioned after the BE to filter light except in the UV range.

The transmittance distribution along the wavelength of BF when it passes only the intended UV light is

shown in Figure 2 b).

8.2.6 Support for the sample (SiC) should be positioned such that the UV beam is not incident directly

on the CCD camera.

8.2.7 The normal axes of the CCD camera and the SiC sample should coincide to maximize the UVPL

intensity.

8.2.8 The photoluminescent beam emitted from the SiC sample incident on the CCD camera should

be filtered by a bandpass filter (BF ) to filter the reflected or scattered UV beam from the SiC sample

for only PL light to be incident on the CCD camera. The transmittance distribution along the wavelength

when it filters UV-range light is shown in Figure 2 c).
8.2.9 The image taken by the CCD camera should be transformed into colour space.
8.3 Measurement
8.3.1 Calibration is necessary before measurement. See Annex D.

8.3.2 The UV beam emitted by the UVLS passing through BE and BF then irradiates the SiC sample.

8.3.3 Take pictures of the UVPL image using the CCD camera and save the images in RGB format.

8.3.4 Transform the RGB images to the CIE 1931 colour space.
4 © ISO 2020 – All rights reserved
---------------------- Page: 9 ----------------------
ISO/FDIS 21820:2020(E)

8.3.5 The polytype can be determined by the position of the colour point when it is plotted on the

colour space.
a) Schematic of a UVPL imaging system
b) Transmittance distribution of BF c) Transmittance distribution of BF
1 2
Key
A expanded UV beam
B UV induced PL beam
C UV LED
UVL ultraviolet light source
BF bandpass filter
BE beam expander
SiC silicon carbide
CC CCD camera
DAQ data acquisition
X wavelength, nm
Y transmittance
Figure 2 — Optical setup for UVPL measurement
© ISO 2020 – All rights reserved 5
---------------------- Page: 10 ----------------------
ISO/FDIS 21820:2020(E)
9 Expression of results
9.1 Expression of boundaries of polytypes in CIE 1931 colour space

The polytype boundaries are defined in the CIE 1931 colour space as shown in Figure 3. The dotted

lines are the polytype lines. When the temperature of a SiC sample is near 0 K, the transformed points

from the UVPL image are positioned near the edge of the colour space; as the temperature increases, the

colour points approach the centre of the colour space (1/3,1/3,1/3). The black lines in Figure 3 represent

the boundary lines, which are between polytype lines and help to determine the major polytypes.

Figure 3 — Polytype lines (dotted lines) and boundary lines (dashed lines) of polytypes in

CIE 1913 colour space

The detailed procedure for producing the polytype lines and boundaries is described in Annex A.

Annex B shows the boundary points table of each polytype in the CIE 1931 colour space. The specific

polytype regions are defined as the inner regions of polygons made by connecting these boundary

points, as shown in Figures B.1 to B.3.
9.2 Transformation of the UVPL image to CIE 1931 colour space with polytype
boundaries

The UVPL colour data should be transformed to the CIE 1931 colour space using the polytype boundaries

to identify the polytype.

Each polytype has a different DAP recombination energy, which indicates that each polytype has a

different colour. Therefore, when a UVPL image is transformed into the CIE 1931 colour space, each

polytype colour has a different position in the colour space.
6 © ISO 2020 – All rights reserved
---------------------- Page: 11 ----------------------
ISO/FDIS 21820:2020(E)
9.3 Determination of polytype

9.3.1 After the transformation of the UVPL image to the colour space, the SiC polytype should be

determined.

If the SiC sample is a perfect single crystal, colour points transformed from the image to colour space

should be on one of the red lines only, thus allowing the polytype to be easily determined. However,

there can be a mixture of polytypes in the sample. In that case, colour points can be distributed around

the polytype line.

9.3.2 The polytype can be determined quantitatively. That is, if the colour points are distributed on

only one polytype region, that would be the desired polytype.

9.3.3 If the colour points are distributed widely across several polytype regions, the number of colour

points on each polytype region should be counted and the ratio of polytype region should be calculated

as follows:
100 % = 4H (%) + 6H (%) + 15R (%) + other polytypes (%)

If the 4H (6H, 15R) SiC surface is significantly contaminated, the UVPL image of the contaminated

region can exhibit a different colour from those of the 4H (6H, 15R) SiC. It may then be identified as one

of the other polytypes. Therefore, the measured ratio of 4H, 6H and 15R is the minimum value.

When the total ratio of the 4H, 6H and 15R polytype is less than 100 %, the following issues should be

taken into account.

If a UVPL image has ambiguous shapes accompanied by an unclear boundary or if a region with

characteristic patterns changes its position and area for each measurement, then the sample surface

may be significantly contaminated.

The sample surface should be cleaned following a wet cleaning process using H SO : H O : H O, NH OH:

2 4 2 2 2 4
H O : H O, HCl: H O : H O or other suitable chemicals.
2 2 2 2 2 2
10 Test report

The test report shall be in accordance with the reporting provisions of ISO/IEC 17025 and shall contain

the following information, if available:
a) the name of the testing establishment;
b) the date of the test, report identification and number, operator, signatory;

c) a description of the SiC wafers (material manufacturer, growth method, and conditions);

d) the results obtained, including the UVPL images:
1) image of SiC under illumination in the visible range;
2) UVPL image, image size and format;
3) CIE 1931 colour space and range;
4) penetration depth (see Annex C);
5) CCD camera name;
e) the polytype results determined according to the ranges in colour space;
f) comments about the test or test results;
© ISO 2020 – All rights reserved 7
---------------------- Page: 12 ----------------------
ISO/FDIS 21820:2020(E)
g) a reference to this document (i.e. ISO 21820:—).
8 © ISO 2020 – All rights reserved
---------------------- Page: 13 ----------------------
ISO/FDIS 21820:2020(E)
Annex A
(informative)
Determination of polytypes
A.1 Determination of coordinates of each polytype at 0 K in colour space

Each polytype has an intrinsic DAP recombination energy so that it emits a monochromatic

photoluminescent beam at zero Kelvin when it is illuminated by UV light. The DAP recombination

energy of each polytype is different; this can be used as a criterion for polytype determination.

Table A.1 shows the wavelength of the polytypes measured by a PL spectrometer and the corresponding

DAP recombination energy calculated by applying Planck’s relation (Formula A.1).
Table A.1 — Relation between polytype, DAP recombination energy and wavelength.
DAP recombination energy Wavelength
Polytype
eV nm
4H­SiC 2,295 9 540
6H­SiC 2,032 5 610
15R-SiC 2,006 2 618
Eh==ν (A.1)
where
E is the energy;
h is Planck’s constant;
ν is the frequency of light;
c is the velocity of light;
λ is the wavelength of light.

These DAP recombination energies or wavelengths can be converted into colour space as one­

colour points.

The total intensities of red, green and blue are denoted as X, Y and Z and can be calculated using

Formulae (A.2) to (A.4). Figure A.1 depicts the conversion of monochromatic light into colour space as

colour points. Figure A.1 a) shows the normalized spectral density distribution of the tristimuli, M()λ ,

defined in CIE 1931 and ISO 11664-3. Figure A.1 b) depicts the monochromatic light intensity

distribution, x()λ , that has the form of a delta function for each polytype as shown in the last row of

Table A.1. Figure A.1 c) depicts the final intensities of X, Y and Z calculated with Formulae (A.2) to (A.4).

The normalized X, Y and Z coordinates are denoted as x, y and z and can be calculated using Formulae

(A.5) to (A.7).
850
XM= λλxdλ (A.2)
() ()
450
© ISO 2020 – All rights reserved 9
---------------------- Page: 14 ----------------------
ISO/FDIS 21820:2020(E)
850
YM= ()λλyd() λ (A.3)
450
850
ZM= λλzdλ (A.4)
() ()
450
x= (A.5)
XY++Z
y= (A.6)
XY++Z
z= =−1 xy− (A.7)
XY++Z
where
λ is the wavelength of light;

x λ is the monochromatic light intensity distribution of red light where the wavelength is λ;

y()λ is the monochromatic light intensity distribution of green light where the wavelength is λ;

z()λ is the monochromatic light intensity distribution of blue light where the wavelength is λ;

X is the normalized total intensity of red light;
Y is the normalized total intensity of green light;
Z is the normalized total intensity of blue light.
10 © ISO 2020 – All rights reserved
---------------------- Page: 15 ----------------------
ISO/FDIS 21820:2020(E)
Key
I intensity
W wavelength (nm)
A normalized spectral distribution of tristimulus
B delta functional distribution of photoluminescence
C intensities of XYZ
Figure A.1 — Conversion from monochromatic light to RGB

4H-SiC, 6H-SiC, 15R-SiC and 3C-SiC are plotted as dots at the edge of the colour space. The monochromatic

light is always placed at the edge of the colour space. The dot at the centre corresponds to the white

point because the RGB coordinates of white are (1/3,1/3,1/3).

The monochromatic wavelengths of 15R-SiC and 3C-SiC are closely adjacent to 770 nm and 780 nm

when they are converted into the colour space wherein they overlap, as can be seen in Figure A.2.

© ISO 2020 – All rights reserved 11
---------------------- Page: 16 ----------------------
ISO/FDIS 21820:2020(E)
Key
W white
Figure A.2 — Polytype colour points in colour space
A.2 Determination of lines of each polytype at various temperatures

At extremely low temperatures, the PL beam is so monochromatic that it has the form of a delta function.

However, as the temperature increases, it assumes the form of a Gaussian distribution.

This property of the PL beam enables it to be modelled as the Gaussian function M(λ) in Formula (A.8),

in which its shape changes as the shape parameter β changes.

When β in Formula (A.8) decreases to zero, M(λ) becomes a delta function, as in Formula (A.9), and the

maximum value and full width half maximum (FWHM) of M(λ) are as shown in Formulae (A.10) and (A.11).

λλ−
−()
M()λ = e (A.8)
β À
limM λδ=−λλ (A.9)
() ()
β→0
λ −λ
−()
11 1
M λ ==ee = (A.10)
ββÀÀ β À
λβ=22ln2 (A.11)
FWHM
where
12 © ISO 2020 – All rights reserved
---------------------- Page: 17 ----------------------
ISO/FDIS 21820:2020(E)
λ is the centre point of the Gaussian function;
λ is the FWHM of function M(λ);
FWHM
e is exponential function;
ln is natural logarithm function.

β in Formula (A.8) increases as temperature increases, though the relation between them differs

depending on the material. Using this characteristic, the polytype lines are calculated as follows.

The coordinate in the colour space of each polytype at 0 K is calculated and plotted first. These colour

points are all plotted at the edge of the colour space. As the temperature increases, β increases so that

the maximum height of the PL distribution decreases, as
...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.