IEC TS 62607-6-7:2023

Nanomanufacturing - Key control characteristics - Part 6-7: Graphene - Sheet resistance: van der Pauw method

IEC TS 62607-6-7:2023 establishes a method to determine the key control characteristics sheet resistance RS [measured in ohm per square (Ω/sq)], by the van der Pauw method, vdP.
The sheet resistance RS is derived by measurements of four-terminal electrical resistance performed on four electrical contacts placed on the boundary of the planar sample and calculated with a mathematical expression involving the two resistance measurements.
The measurement range for RS of the graphene samples with the method described in this document goes from 10−2 Ω/sq to 104 Ω/sq.
The method is applicable for CVD graphene provided it is transferred to quartz substrates or other insulating materials (quartz, SiO2 on Si), as well as graphene grown from silicon carbide.
The method is complementary to the in-line four-point-probe method (4PP, IEC 62607-6-8) for what concerns the measurement of the sheet resistance and can be applied when it is possible to reliably place contacts on the sample boundary, avoiding the sample being scratched by the 4PP.
The outcome of the van der Pauw method is independent of the contact position provided the sample is uniform, which is typically not true for graphene at this stage. This document considers the case of samples with non-strictly uniform conductivity distribution and suggests a way to consider the sample inhomogeneity as a component of the uncertainty on RS.

General Information

• Status: Published
• Publication Date: 06-Jun-2023
• ICS: 07.120 - Nanotechnologies
• Technical Committee: TC 113 - Nanotechnology for electrotechnical products and systems
• Drafting Committee: WG 8 - TC 113/WG 8
• Current Stage: PPUB - Publication issued
• Start Date: 12-Jul-2023
• Completion Date: 07-Jun-2023

Standards Content (Sample)

IEC TS 62607-6-7
®

Edition 1.0 2023-06
TECHNICAL
SPECIFICATION

colour
inside


Nanomanufacturing – Key control characteristics –
Part 6-7: Graphene – Sheet resistance: van der Pauw method

IEC TS 62607-6-7:2023-06(en)

---------------------- Page: 1 ----------------------
THIS PUBLICATION IS COPYRIGHT PROTECTED
Copyright © 2023 IEC, Geneva, Switzerland

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from
either IEC or IEC's member National Committee in the country of the requester. If you have any questions about IEC
copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or
your local IEC member National Committee for further information.


IEC Secretariat Tel.: [phone]
3, rue de Varembé [e-mail]
CH-1211 Geneva 20 www.iec.ch
Switzerland

About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.

About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigendum or an amendment might have been published.

IEC publications search - webstore.iec.ch/advsearchform IEC Products & Services Portal - products.iec.ch
The advanced search enables to find IEC publications by a Discover our powerful search engine and read freely all the
variety of criteria (reference number, text, technical publications previews. With a subscription you will always have
committee, …). It also gives information on projects, replaced access to up to date content tailored to your needs.
and withdrawn publications.

Electropedia - www.electropedia.org
IEC Just Published - webstore.iec.ch/justpublished
The world's leading online dictionary on electrotechnology,
Stay up to date on all new IEC publications. Just Published
containing more than 22 300 terminological entries in English
details all new publications released. Available online and once
and French, with equivalent terms in 19 additional languages.
a month by email.
Also known as the International Electrotechnical Vocabulary

(IEV) online.
IEC Customer Service Centre - webstore.iec.ch/csc

If you wish to give us your feedback on this publication or need
further assistance, please contact the Customer Service
Centre: [e-mail].

---------------------- Page: 2 ----------------------
IEC TS 62607-6-7

®


Edition 1.0 2023-06




TECHNICAL



SPECIFICATION








colour

inside










Nanomanufacturing – Key control characteristics –

Part 6-7: Graphene – Sheet resistance: van der Pauw method


























INTERNATIONAL

ELECTROTECHNICAL


COMMISSION





ICS  07.120 ISBN 978-2-8322-7114-8




  Warning! Make sure that you obtained this publication from an authorized distributor.


® Registered trademark of the International Electrotechnical Commission

---------------------- Page: 3 ----------------------
– 2 – IEC TS 62607-6-7:2023  IEC 2023
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
3.1 General terms . 8
3.5 Key control characteristics measured in accordance with this standard . 9
3.6 Terms related to the measurement method . 10
4 General . 11
4.1 Measurement principle . 11
4.2 Non-uniform samples . 11
4.3 Sample preparation method . 11
4.4 Description of measurement equipment . 11
4.5 Ambient conditions during measurement . 12
4.6 Related standards . 12
5 Measurement procedure . 13
5.1 Calibration of measurement equipment . 13
5.2 Detailed protocol of the measurement procedure . 13
5.3 Settings and precautions for the measurement of R . 14
ij,kl
5.4 Four-terminal resistance measurement accuracy . 15
6 Data analysis and interpretation of results . 16
6.1 General . 16
6.1.1 Calculation of R . 16
S
6.1.2 Further corrections . 16
6.1.3 Expression of uncertainty on R . 16
S
6.2 One measurement configuration . 17
6.3 Multiple measurement configurations . 18
7 Results to be reported . 18
7.1 Cover sheet . 18
7.2 Sample identification . 18
7.3 Measurement conditions . 18
7.4 Measurement results . 18
Annex A (informative) Effects of ambient conditions on graphene resistance
measurements . 20
A.1 General . 20
A.2 Temperature (T) . 20
A.3 Relative humidity (RH) . 20
Annex B (informative) Experimental example . 21
B.1 Sample . 21
B.2 Ambient conditions. 21
B.3 Instrumentation . 21
B.4 Sampling plan . 22
B.5 Measurement procedure . 23
B.6 Results . 23

---------------------- Page: 4 ----------------------
IEC TS 62607-6-7:2023  IEC 2023 – 3 –
Annex C (informative) Other standards related to the measurement of sheet
resistance . 25
Bibliography . 26

Figure 1 – Schematic view of a van der Pauw measurement setup, and a detail of

typical spring-mounted probe . 12
Figure 2 – Schematic view of a typical vdP measurement setup and measurement
sequence . 14
Figure 3 – Schematic representation of a possible sampling plan representation for the
vdP method . 19
Figure B.1 – CVD graphene on quartz . 21
Figure B.2 – Schematic lateral view of the multi-terminal fixture . 22
Figure B.3 – Sampling plan used for the present example . 22

Table 1 – Example of measurable values for R , and the corresponding measurement
S
settings and type-B uncertainty, when using a current source Keithley 2602B System
SourceMeter® and a HP 34420 Nano Volt / Micro Ohm Meter (1y calibration
specifications) . 15
Table B.1 – Measured values for R (p) and R (p) using a current source
AB,CD BC,DA

Keithley 2602B and a voltmeter HP 34461 (1y stability specifications) . 23
Table B.2 – Measured values for R (p) and corresponding uncertainty values using a
S
current source Keithley 2602B and a voltmeter HP 34461 (1y stability specifications) . 23
Table B.3 – Summary of the uncertainty contributions to R . 24
S

---------------------- Page: 5 ----------------------
– 4 – IEC TS 62607-6-7:2023  IEC 2023
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________

NANOMANUFACTURING –
KEY CONTROL CHARACTERISTICS –

Part 6-7: Graphene – Sheet resistance: van der Pauw method

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and
in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports,
Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their
preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with
may participate in this preparatory work. International, governmental and non-governmental organizations liaising
with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for
Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence between
any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) IEC draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). IEC takes no position concerning the evidence, validity or applicability of any claimed patent rights in
respect thereof. As of the date of publication of this document, IEC had not received notice of (a) patent(s), which
may be required to implement this document. However, implementers are cautioned that this may not represent
the latest information, which may be obtained from the patent database available at https://patents.iec.ch. IEC
shall not be held responsible for identifying any or all such patent rights.
IEC TS 62607-6-7 has been prepared by IEC technical committee 113: Nanotechnology for
electrotechnical products and systems. It is a Technical Specification.
The text of this Technical Specification is based on the following documents:
Draft Report on voting
113/682/DTS 113/713/RVDTS

Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this Technical Specification is English.

---------------------- Page: 6 ----------------------
IEC TS 62607-6-7:2023  IEC 2023 – 5 –
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/publications.
A list of all parts of the IEC TS 62607 series, published under the general title
Nanomanufacturing – Key control characteristics, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.

IMPORTANT – The "colour inside" logo on the cover page of this document indicates
that it contains colours which are considered to be useful for the correct understanding
of its contents. Users should therefore print this document using a colour printer.

---------------------- Page: 7 ----------------------
– 6 – IEC TS 62607-6-7:2023  IEC 2023
INTRODUCTION
Graphene is a single layer of carbon atoms arranged in a honeycomb lattice. Graphene has
shown many outstanding properties, among which is a high electrical conductivity. Nowadays
2 2
graphene can be easily grown and transferred on large area (cm to even m ) and even roll-to-
roll supports using chemical vapour deposition (CVD) techniques. This is already enabling its
commercial applications in electrotechnical products.
Electrical conductivity of graphene samples can depend on many factors: structural quality,
contamination, coupling with the physical support used for a given application to name a few.
On practical grounds, sheet resistance is a quantity which can be used as global measure of
the local conductivity of a sample with finite geometrical dimensions. In order to check the
reproducibility of the electrical properties of graphene, the sheet resistance is clearly a key
control characteristic for this material.
1
The van der Pauw method [1] allows the measurement of the sheet resistance of samples of
arbitrary shape, with isotropic conductivity and uniform carrier density by performing a pair of
four-terminal resistance measurements with electrical contacts placed at arbitrary positions on
the sample's perimeter. The method is fast (it takes a few minutes) and easy to implement,
since many commercial fixtures are available.
The four-terminal resistance measurements required to apply the method allow to minimize the
effect of the contact resistance that appears between graphene and the measurement probes.
The van der Pauw method does not provide any spatial resolution in principle, but
considerations about real samples' conductivity uniformity can be made.
In this document it is explained how to specifically apply the van der Pauw method on chemical
vapour deposited graphene on rigid insulating support and perform a reliable estimation of the
sample sheet resistance also considering the non-ideal nature of commercial graphene.


___________
1
 Numbers in square brackets refer to the Bibliography.

---------------------- Page: 8 ----------------------
IEC TS 62607-6-7:2023  IEC 2023 – 7 –
NANOMANUFACTURING –
KEY CONTROL CHARACTERISTICS –

Part 6-7: Graphene – Sheet resistance: van der Pauw method



1 Scope
This part of IEC TS 62607 establishes a method to determine the key control characteristics
• sheet resistance R [measured in ohm per square (Ω/sq)],
S
by the
• van der Pauw method, vdP.
The sheet resistance R is derived by measurements of four-terminal electrical resistance
S
performed on four electrical contacts placed on the boundary of the planar sample and
calculated with a mathematical expression involving the two resistance measurements.
• The measurement range for R of the graphene samples with the method described in this
S
−2 4
document goes from 10 Ω/sq to 10 Ω/sq.
• The method is applicable for CVD graphene provided it is transferred to quartz substrates
or other insulating materials (quartz, SiO on Si), as well as graphene grown from silicon
2
carbide.
• The method is complementary to the in-line four-point-probe method (4PP, IEC 62607-6-8)
for what concerns the measurement of the sheet resistance and can be applied when it is
possible to reliably place contacts on the sample boundary, avoiding the sample being
scratched by the 4PP.
• The outcome of the van der Pauw method is independent of the contact position provided
the sample is uniform, which is typically not true for graphene at this stage. This document
considers the case of samples with non-strictly uniform conductivity distribution and
suggests a way to consider the sample inhomogeneity as a component of the uncertainty
on R .
S
2 Normative references
There are no normative references in this document.
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:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp

---------------------- Page: 9 ----------------------
– 8 – IEC TS 62607-6-7:2023  IEC 2023
3.1 General terms
3.1.1
graphene
graphene layer
single-layer graphene
monolayer graphene
single layer of carbon atoms with each atom bound to three neighbours in a honeycomb
structure
Note 1 to entry: It is an important building block of many carbon nano-objects.
Note 2 to entry: As graphene is a single layer, it is also sometimes called monolayer graphene or single-layer
graphene and abbreviated as 1LG to distinguish it from bilayer graphene (2LG) and few-layer graphene (FLG).
Note 3 to entry: Graphene has edges and can have defects and grain boundaries where the bonding is disrupted.
[SOURCE: ISO/TS 80004-13:2017, 3.1.2.1]
3.1.2
bilayer graphene
2LG
two-dimensional material consisting of two well-defined stacked graphene layers
Note 1 to entry: If the stacking registry is known, it can be specified separately, for example, as "Bernal stacked
bilayer graphene".
[SOURCE: ISO/TS 80004-13:2017, 3.1.2.6]
3.1.3
few-layer graphene
FLG
two-dimensional material consisting of three to ten well-defined stacked graphene layers
[SOURCE: ISO/TS 80004-13:2017, 3.1.2.10]
3.2
key control characteristic
KCC
product characteristic which can affect safety or compliance with regulations, fit, function,
performance, quality, reliability or subsequent processing of the final product
Note 1 to entry: The measurement of a key control characteristic is described in a standardized measurement
procedure with known accuracy and precision.
Note 2 to entry: It is possible to define more than one measurement method for a key control characteristic if the
correlation of the results is well-defined and known.
[SOURCE: IEC TS 62565-1:2023, 3.1]

---------------------- Page: 10 ----------------------
IEC TS 62607-6-7:2023  IEC 2023 – 9 –
3.3
blank detail specification
BDS
structured generic specification providing a comprehensive set of key control characteristics
which are needed to describe a specific product without assigning specific values or attributes
Note 1 to entry: Examples of nano-enabled products are: nanocomposites and nano-subassemblies.
Note 2 to entry: Blank detail specifications are intended to be used by industrial users to prepare their detail
specifications used in bilateral procurement contracts. A blank detail specification facilitates the comparison and
benchmarking of different materials. Furthermore, a standardized format makes procurement more efficient and more
error robust.
[SOURCE: IEC TS 62565-1:2023, 3.2]
3.4
detail specification
DS
specification based on a blank detail specification with assigned values and attributes
Note 1 to entry: The characteristics listed in the detail specification are usually a subset of the key control
characteristics listed in the relevant blank detail specification. The industrial partners define only those
characteristics which are required for the intended application.
Note 2 to entry: Detail specifications are defined by the industrial partners. Standards development organizations
will be involved only if there is a general need for a detail specification in an industrial sector.
Note 3 to entry: The industrial partners may define additional key control characteristics if they are not listed in the
blank detail specification.
[SOURCE: IEC TS 62565-1:2023, 3.3]
3.5 Key control characteristics measured in accordance with this standard
3.5.1
sheet resistance
R
S
electrical resistance of a conductor with a square shape (width equal to length) and thickness
significantly smaller than the lateral dimensions (thickness much less than width and length)
Note 1 to entry: There is no definition of the unit ohm per square (Ω/sq) in the International System of units (SI).
Nevertheless, R is a normalized quantity, in which the symbol represents the SI ohm. So there is no ambiguity
S
to the SI, provided the measurements are performed with
concerning the traceability of measurements of R
S
calibrated instrumentation.
[SOURCE: IEC TS 61836:2007, 3.4.79, modified – The entry has been adapted to this
document.]

---------------------- Page: 11 ----------------------
– 10 – IEC TS 62607-6-7:2023  IEC 2023
3.5.2
drift mobility
µ
quotient of the modulus of the mean velocity of the charge carriers in the
direction of an electric field by the modulus of the field strength
2
Note 1 to entry: The SI unit of mobility is cm /V s.
Note 2 to entry: The drift mobility is here considered to be the fundamental, intrinsic (local) property. The Hall and
field effect mobility are then the extrinsic (sample) electrical measurements, carried out to determine the intrinsic
mobility.
Note 3 to entry: The drift mobility for electrons and holes can be very different, depending on the residual doping
and scattering mechanisms for the given sample.
[SOURCE: IEC 60500-521:2002, 521-02-58, modified – The entry has been adapted to this
document.]
3.6 Terms related to the measurement method
3.6.1
four-point probe method
4PP
method to measure electrical sheet resistance of thin films that uses separate pairs of current-
carrying and voltage-sensing electrodes
Note 1 to entry: The method is local with a characteristic length scale defined by the probe distance, and generally
requires the resistivity variations to be on a much larger scale than the probe spacing. Depending on the positions
of the sample-probe contact of the four probe contacts with the surface, different geometrical factors need to be used
to extract the sheet resistance.
[SOURCE: ISO/TS 80004-13:2017, 3.3.3.1, modified – The entry has been adapted to this
document.]
3.6.2
in-line four-point probe method
type of four-point probe measurement where four-point electrodes are aligned in a row
Note 1 to entry: In this method, four probes contact the test sample in a linear arrangement. A voltage drop is
measured between the two inner probes while a current source supplies current through the outer probes.
Note 2 to entry: The distance between the probes needs to be small compared to the lateral dimensions of the
sample so that edge effects on the electric field in the sample can be neglected.
Note 3 to entry: The resistance of the sample can be calculated by Ohm's law. Geometrical factors can be used for
corrections if the sample is too small or if the measurement is performed close to the edges of the sample.
[SOURCE: IEC TS 62607-6-9:2022, 3.2.3, modified – Note 2 to entry has been deleted.]
3.6.3
van der Pauw method
vdP
type of four probe measurement for samples of arbitrary shape
Note 1 to entry: The van der Pauw method requires four probes placed arbitrarily around the perimeter of the
sample, in contrast to the linear four-point probe which is placed on the top of the sample.
Note 2 to entry: The van der Pauw method provides an average sheet resistivity of the sample.
[SOURCE: IEC TS 62607-6-9:2022, 3.2.4, modified – Notes 1 and 4 to entry have been deleted.]

---------------------- Page: 12 ----------------------
IEC TS 62607-6-7:2023  IEC 2023 – 11 –
4 General
4.1 Measurement principle
The measurement principle of the vdP method for the assessment of the sheet resistance R
S
of graphene films is based on the measurement of two four-terminal resistances, or
transresistances, performed on four contacts on the sample boundary. A mathematical theorem,
derived from conformal mapping theory, relates the transresistance of the sample measured in
two different configurations with its sheet resistance R [1]. The problem is practically solved
S
with an explicit formula that has as input the two measured four-terminal resistances and as
. The method is not sensitive to the sample shape and contacts positioning in principle;
output R
S
corrections for real cases exist.
4.2 Non-uniform samples
The van der Pauw method assumes homogeneous samples with uniform conductivity
distribution. If these conditions are met, any measurement performed with the contacts in
arbitrary positions along the sample's boundary should be identical within the measurement
uncertainty. If the sample is not uniform the result of a single vdP measurement can
substantially depend on the contacts position [2]. Since commercial graphene samples can be
far from having a uniform conductivity, it is possible that the user is in this second scenario.
This document gives indications to take into consideration this variability in the measurements
of R which can be larger than the electrical measurements uncertainty itself and to provide a
S
consistent expression of uncertainty on .
R
S
4.3 Sample preparation method
The sample is measured as it is delivered by the supplier. No special sample preparation is
required. An insulating, planar material shall support the graphene. The sample shall be stored
at the ambient conditions of 4.5 prior to the measurements.
4.4 Description of measurement equipment
Th
...