ASTM F76-08(2016)e1

Standard Test Methods for Measuring Resistivity and Hall Coefficient and Determining Hall Mobility in Single-Crystal Semiconductors (Withdrawn 2023)

SIGNIFICANCE AND USE
4.1 In order to choose the proper material for producing semiconductor devices, knowledge of material properties such as resistivity, Hall coefficient, and Hall mobility is useful. Under certain conditions, as outlined in the Appendix, other useful quantities for materials specification, including the charge carrier density and the drift mobility, can be inferred.
SCOPE
1.1 These test methods cover two procedures for measuring the resistivity and Hall coefficient of single-crystal semiconductor specimens. These test methods differ most substantially in their test specimen requirements.  
1.1.1 Test Method A, van der Pauw (1) 2—This test method requires a singly connected test specimen (without any isolated holes), homogeneous in thickness, but of  arbitrary shape. The contacts must be sufficiently small and located at the periphery of the specimen. The measurement is most easily interpreted for an isotropic semiconductor whose conduction is dominated by a single type of carrier.  
1.1.2 Test Method B, Parallelepiped or Bridge-Type—This test method requires a specimen homogeneous in thickness and of specified  shape. Contact requirements are specified for both the parallelepiped and bridge geometries. These test specimen geometries are desirable for anisotropic semiconductors for which the measured parameters depend on the direction of current flow. The test method is also most easily interpreted when conduction is dominated by a single type of carrier.  
1.2 These test methods do not provide procedures for shaping, cleaning, or contacting specimens; however, a procedure for verifying contact quality is given.  
Note 1: Practice F418 covers the preparation of gallium arsenide phosphide specimens.  
1.3 The method in Practice F418 does not provide an interpretation of the results in terms of basic semiconductor properties (for example, majority and minority carrier mobilities and densities). Some general guidance, applicable to certain semiconductors and temperature ranges, is provided in the Appendix. For the most part, however, the interpretation is left to the user.  
1.4 Interlaboratory tests of these test methods (Section 19) have been conducted only over a limited range of resistivities and for the semiconductors, germanium, silicon, and gallium arsenide. However, the method is applicable to other semiconductors provided suitable specimen preparation and contacting procedures are known. The resistivity range over which the method is applicable is limited by the test specimen geometry and instrumentation sensitivity.  
1.5 The values stated in acceptable metric units are to be regarded as the standard. The values given in parentheses are for information only. (See also 3.1.4.)  
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.  
1.7 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
WITHDRAWN RATIONALE
These test methods covered two procedures for measuring the resistivity and Hall coefficient of single-crystal semiconductor specimens.
Formerly under the jurisdiction of Committee F01 on Electronics, these test methods were withdrawn in November 2023. This standard is being withdrawn without replacement because Committee F01 was disbanded.

General Information

• Status: Withdrawn
• Publication Date: 30-Apr-2016
• Withdrawal Date: 28-Nov-2023
• ICS: 29.045 - Semiconducting materials
• Technical Committee: F01 - Electronics
• Drafting Committee: F01.15 - Compound Semiconductors

Relations

• Replaces: ASTM F76-08(2016) - Standard Test Methods for Measuring Resistivity and Hall Coefficient and Determining Hall Mobility in Single-Crystal Semiconductors
• Effective Date: 01-May-2016
• Refers: ASTM E2554-18 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
• Effective Date: 01-Apr-2018
• Refers: ASTM E2554-18e1 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
• Effective Date: 01-Apr-2018
• Refers: ASTM E2554-13 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
• Effective Date: 01-Apr-2013
• Refers: ASTM E2554-07 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method in a Single Laboratory Using a Control Sample Program
• Effective Date: 01-May-2007
• Refers: ASTM D1125-95(2005) - Standard Test Methods for Electrical Conductivity and Resistivity of Water
• Effective Date: 01-Apr-2005
• Refers: ASTM F43-99 - Standard Test Methods for Resistivity of Semiconductor Materials (Withdrawn 2003)
• Effective Date: 10-Dec-1999
• Refers: ASTM D1125-95(1999) - Standard Test Methods for Electrical Conductivity and Resistivity of Water
• Effective Date: 10-Jun-1999
• Refers: ASTM F418-77(1996)e1 - Standard Practice for Preparation of Samples of the Constant Composition Region of Epitaxial Gallium Arsenide Phosphide for Hall Effect Measurements
• Effective Date: 27-May-1977
• Refers: ASTM F418-77(2002) - Standard Practice for Preparation of Samples of the Constant Composition Region of Epitaxial Gallium Arsenide Phosphide for Hall Effect Measurements (Withdrawn 2008)
• Effective Date: 27-May-1977

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
´1
Designation: F76 − 08 (Reapproved 2016)
Standard Test Methods for
Measuring Resistivity and Hall Coefficient and Determining
Hall Mobility in Single-Crystal Semiconductors
ThisstandardisissuedunderthefixeddesignationF76;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginal
adoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscript
epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—In 10.5.1, second sentence, (0.5 T) was corrected editorially to (0.5 mT) in May 2017.
1. Scope 1.4 Interlaboratory tests of these test methods (Section 19)
have been conducted only over a limited range of resistivities
1.1 These test methods cover two procedures for measuring
and for the semiconductors, germanium, silicon, and gallium
the resistivity and Hall coefficient of single-crystal semicon-
arsenide. However, the method is applicable to other semicon-
ductor specimens. These test methods differ most substantially
ductors provided suitable specimen preparation and contacting
in their test specimen requirements.
2 procedures are known. The resistivity range over which the
1.1.1 Test Method A, van der Pauw (1) —This test method
method is applicable is limited by the test specimen geometry
requiresasinglyconnectedtestspecimen(withoutanyisolated
and instrumentation sensitivity.
holes), homogeneous in thickness, but of arbitrary shape. The
contacts must be sufficiently small and located at the periphery 1.5 The values stated in acceptable metric units are to be
of the specimen. The measurement is most easily interpreted regarded as the standard. The values given in parentheses are
for an isotropic semiconductor whose conduction is dominated for information only. (See also 3.1.4.)
by a single type of carrier.
1.6 This standard does not purport to address all of the
1.1.2 Test Method B, Parallelepiped or Bridge-Type—This
safety concerns, if any, associated with its use. It is the
testmethodrequiresaspecimenhomogeneousinthicknessand
responsibility of the user of this standard to establish appro-
of specified shape. Contact requirements are specified for both
priate safety and health practices and determine the applica-
the parallelepiped and bridge geometries. These test specimen
bility of regulatory limitations prior to use.
geometries are desirable for anisotropic semiconductors for
1.7 This international standard was developed in accor-
which the measured parameters depend on the direction of
dance with internationally recognized principles on standard-
current flow. The test method is also most easily interpreted
ization established in the Decision on Principles for the
when conduction is dominated by a single type of carrier.
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
1.2 These test methods do not provide procedures for
Barriers to Trade (TBT) Committee.
shaping, cleaning, or contacting specimens; however, a proce-
dure for verifying contact quality is given.
2. Referenced Documents
NOTE 1—Practice F418 covers the preparation of gallium arsenide
2.1 ASTM Standards:
phosphide specimens.
D1125Test Methods for Electrical Conductivity and Resis-
1.3 The method in Practice F418 does not provide an
tivity of Water
interpretation of the results in terms of basic semiconductor
E2554Practice for Estimating and Monitoring the Uncer-
properties (for example, majority and minority carrier mobili-
tainty of Test Results of a Test Method Using Control
ties and densities). Some general guidance, applicable to
Chart Techniques
certain semiconductors and temperature ranges, is provided in
F26Test Methods for Determining the Orientation of a
theAppendix. For the most part, however, the interpretation is
Semiconductive Single Crystal (Withdrawn 2003)
left to the user.
F43Test Methods for Resistivity of Semiconductor Materi-
als (Withdrawn 2003)
These test methods are under the jurisdiction of ASTM Committee F01 on
Electronics and are the direct responsibility of Subcommittee F01.15 on Compound
Semiconductors. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved May 1, 2016. Published May 2016. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1967. Last previous edition approved in 2008 as F76–08. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/F0076-08R16E01. the ASTM website.
2 4
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof The last approved version of this historical standard is referenced on
these test methods. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
F76 − 08 (2016)
F47Test Method for Crystallographic Perfection of Silicon useful quantities for materials specification, including the
by Preferential Etch Techniques charge carrier density and the drift mobility, can be inferred.
F418Practice for Preparation of Samples of the Constant
Composition Region of Epitaxial GalliumArsenide Phos- 5. Interferences
phide for Hall Effect Measurements (Withdrawn 2008)
5.1 In making resistivity and Hall-effect measurements,
2.2 SEMI Standard:
spurious results can arise from a number of sources.
C1Specifications for Reagents
5.1.1 Photoconductive and photovoltaic effects can seri-
ously influence the observed resistivity, particularly with high-
3. Terminology
resistivity material. Therefore, all determinations should be
3.1 Definitions:
made in a dark chamber unless experience shows that the
3.1.1 Hall coeffıcient—the ratio of the Hall electric field
results are insensitive to ambient illumination.
(due to the Hall voltage) to the product of the current density
5.1.2 Minority-carrierinjectionduringthemeasurementcan
and the magnetic flux density (see X1.4).
also seriously influence the observed resistivity. This interfer-
ence is indicated if the contacts to the test specimen do not
3.1.2 Hall mobility—the ratio of the magnitude of the Hall
have linear current-versus-voltage characteristics in the range
coefficient to the resistivity; it is readily interpreted only in a
used in the measurement procedure. These effects can also be
system with carriers of one charge type. (See X1.5)
detected by repeating the measurements over several decades
3.1.3 resistivity—of a material, is the ratio of the potential
of current. In the absence of injection, no change in resistivity
gradient parallel to the current in the material to the current
should be observed. It is recommended that the current used in
density. For the purposes of this method, the resistivity shall
the measurements be as low as possible for the required
always be determined for the case of zero magnetic flux. (See
precision.
X1.2.)
5.1.3 Semiconductors have a significant temperature coeffi-
3.1.4 units—in these test methods SI units are not always
cient of resistivity. Consequently, the temperature of the
used.Forthesetestmethods,itisconvenienttomeasurelength
specimenshouldbeknownatthetimeofmeasurementandthe
in centimetres and to measure magnetic flux density in gauss.
current used should be small to avoid resistive heating.
This choice of units requires that magnetic flux density be
Resistive heating can be detected by a change in readings as a
−2
expressed in V·s·cm where:
function of time starting immediately after the current is
22 8
1 V·s·cm 5 10 gauss
applied and any circuit time constants have settled.
5.1.4 Spurious currents can be introduced in the testing
The units employed and the factors relating them are sum-
circuit when the equipment is located near high-frequency
marized in Table 1.
generators.Ifequipmentislocatednearsuchsources,adequate
shielding must be provided.
4. Significance and Use
5.1.5 Surface leakage can be a serious problem when
4.1 In order to choose the proper material for producing
measurements are made on high-resistivity specimens. Surface
semiconductor devices, knowledge of material properties such
effectscanoftenbeobservedasadifferenceinmeasuredvalue
as resistivity, Hall coefficient, and Hall mobility is useful.
of resistivity or Hall coefficient when the surface condition of
Under certain conditions, as outlined in the Appendix, other
the specimen is changed (2, 3).
5.1.6 Inmeasuringhigh-resistivitysamples,particularatten-
tion should be paid to possible leakage paths in other parts of
5 the circuit such as switches, connectors, wires, cables, and the
AvailablefromSemiconductorEquipmentandMaterialsInstitute,625EllisSt.,
Suite 212, Mountain View, CA 94043.
TABLE 1 Units of Measurement
Units of
A
Quantity Symbol SI Unit Factor
B
Measurement
Resistivity ρΩ ·m 10 Ω ·cm
−3 −6 −3
Charge carrier concentration n, p m 10 cm
Charge e, q C1 C
2 −1 −1 4 2 −1 −1
Drift mobility, Hall mobility µ,µ m ·V ·s 10 cm ·V ·s
H
3 −1 6 3 −1
Hall coefficient R m ·C 10 cm ·C
H
−1 −2 −1
Electric field E V·m 10 V·cm
Magnetic flux density B T10 gauss
−2 −4 −2
Current density J A·m 10 A·cm
Length L, t, w, d m10 cm
a, b, c
Potential difference V V1 V
A
The factors relate SI units to the units of measurement as in the following example:
1 Ω ·m=10 Ω ·cm
B −2
This system is not a consistent set of units. In order to obtain a consistent set, the magnetic flux density must be expressed in V · s · cm . The proper conversion factor
is:
−2 8
1·V·s·cm =10 gauss
´1
F76 − 08 (2016)
like which may shunt some of the current around the sample. procedure is described for determining resistivity and Hall
Since high values of lead capacitance may lengthen the time coefficientusingdirectcurrenttechniques.TheHallmobilityis
requiredformakingmeasurementsonhigh-resistivitysamples, calculated from the measured values.
connecting cable should be as short as practicable.
7. Apparatus
5.1.7 Inhomogeneities of the carrier density, mobility, or of
the magnetic flux will cause the measurements to be inaccu-
7.1 For Measurement of Specimen Thickness—Micrometer,
rate. At best, the method will enable determination only of an
dial gage, microscope (with small depth of field and calibrated
undefined average resistivity or Hall coefficient. At worst, the
vertical-axis adjustment), or calibrated electronic thickness
measurements may be completely erroneous (2, 3, 4).
gage capable of measuring the specimen thickness to 61%.
5.1.8 Thermomagnetic effects with the exception of the
7.2 Magnet—A calibrated magnet capable of providing a
Ettingshausen effect can be eliminated by averaging of the
magnetic flux density uniform to 61.0% over the area in
measured transverse voltages as is specified in the measure-
which the test specimen is to be located. It must be possible to
ment procedure (Sections 11 and 17). In general, the error due
reverse the direction of the magnetic flux (either electrically or
to the Ettingshausen effect is small and can be neglected,
by rotation of the magnet) or to rotate the test specimen 180°
particularly if the sample is in good thermal contact with its
aboutitsaxisparalleltothecurrentflow.Apparatus,suchasan
surroundings (2, 3, 4).
auxiliary Hall probe or nuclear magnetic resonance system,
5.1.9 For materials which are anisotropic, especially semi-
should be available for measuring the flux density to an
conductors with noncubic crystal structures, Hall measure-
accuracy of 61.0% at the specimen position. If an electro-
ments are affected by the orientation of the current and
magnetisused,provisionmustbemadeformonitoringtheflux
magneticfieldwithrespecttothecrystalaxes(Appendix,Note
density during the measurements. Flux densities between 1000
X1.1). Errors can result if the magnetic field is not within the
and10000gaussarefrequentlyused;conditionsgoverningthe
low-field limit (Appendix, Note X1.1).
choiceoffluxdensityarediscussedmorefullyelsewhere (2, 3,
5.1.10 Spuriousvoltages,whichmayoccurinthemeasuring
4).
circuit, for example, thermal voltages, can be detected by
7.3 Instrumentation:
measuring the voltage across the specimen with no current
7.3.1 Current Source, capable of maintaining current
flowing or with the voltage leads shorted at the sample
through the specimen constant to 60.5% during the measure-
position.Ifthereisameasurablevoltage,themeasuringcircuit
ment.Thismayconsisteitherofapowersupplyorabattery,in
should be checked carefully and modified so that these effects
series with a resistance greater than 200×the total specimen
are eliminated.
resistance (including contact resistance). The current source is
5.1.11 An erroneous Hall coefficient will be measured if the
accurateto 60.5%onallrangesusedinthemeasurement.The
current and transverse electric field axes are not precisely
magnitude of current required is less than that associated with
perpendicular to the magnetic flux.The Hall coefficient will be
−1
an electric field of 1 V·cm in the specimen.
at an extremum with respect to rotation if the specimen is
7.3.2 Electrometer or Voltmeter, with which voltage mea-
properly positioned (see 7.4.4 or 13.4.4).
surements can be made to an accuracy of 60.5%.The current
5.2 In addition to these interferences the following must be
drawn by the measuring instrument during the resistivity and
noted for van der Pauw specimens.
Hall voltage measurements shall be less than 0.1% of the
5.2.1 Errors may result in voltage measurements due to
specimen current, that is, the input resistance of the electrom-
contacts of finite size. Some of these errors are discussed in
eter (or voltmeter) must be 1000×greater than the resistance
references (1, 5, 6).
of the specimen.
5.2.2 Errorsmaybeintroducedifthecontactsarenotplaced
7.3.3 Switching Facilities, used for reversal of current flow
on the specimen periphery (7).
and for connecting in turn the required pairs of potential leads
5.3 In addition to the interferences described in 5.1, the
to the voltage-measuring device.
following must be noted for parallelepiped and bridge-type
7.3.3.1 Representative Circuit, used for accomplishing the
specimens.
required switching is shown in Fig. 1.
5.3.1 It is essential that in the case of parallelepiped or
7.3.3.2 Unity-Gain Amplifiers, used for high-resistivity
bridge-type specimens the Hall-coefficient measurements be
semiconductors, with input impedance greater than 1000×the
made on side contacts far enough removed from the end
specimen resistance are located as close to the specimen as
contacts that shorting effects can be neglected (2, 3). The
possibletominimizecurrentleakageandcircuitti
...

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´1
Designation: F76 − 08 (Reapproved 2016)
Standard Test Methods for
Measuring Resistivity and Hall Coefficient and Determining
Hall Mobility in Single-Crystal Semiconductors
This standard is issued under the fixed designation F76; the number immediately following the designation indicates the year of original
adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript
epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—In 10.5.1, second sentence, (0.5 T) was corrected editorially to (0.5 mT) in May 2017.
1. Scope 1.4 Interlaboratory tests of these test methods (Section 19)
have been conducted only over a limited range of resistivities
1.1 These test methods cover two procedures for measuring
and for the semiconductors, germanium, silicon, and gallium
the resistivity and Hall coefficient of single-crystal semicon-
arsenide. However, the method is applicable to other semicon-
ductor specimens. These test methods differ most substantially
ductors provided suitable specimen preparation and contacting
in their test specimen requirements.
2 procedures are known. The resistivity range over which the
1.1.1 Test Method A, van der Pauw (1) —This test method
method is applicable is limited by the test specimen geometry
requires a singly connected test specimen (without any isolated
and instrumentation sensitivity.
holes), homogeneous in thickness, but of arbitrary shape. The
contacts must be sufficiently small and located at the periphery 1.5 The values stated in acceptable metric units are to be
of the specimen. The measurement is most easily interpreted regarded as the standard. The values given in parentheses are
for an isotropic semiconductor whose conduction is dominated for information only. (See also 3.1.4.)
by a single type of carrier.
1.6 This standard does not purport to address all of the
1.1.2 Test Method B, Parallelepiped or Bridge-Type—This
safety concerns, if any, associated with its use. It is the
test method requires a specimen homogeneous in thickness and
responsibility of the user of this standard to establish appro-
of specified shape. Contact requirements are specified for both
priate safety and health practices and determine the applica-
the parallelepiped and bridge geometries. These test specimen
bility of regulatory limitations prior to use.
geometries are desirable for anisotropic semiconductors for
1.7 This international standard was developed in accor-
which the measured parameters depend on the direction of
dance with internationally recognized principles on standard-
current flow. The test method is also most easily interpreted
ization established in the Decision on Principles for the
when conduction is dominated by a single type of carrier.
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
1.2 These test methods do not provide procedures for
Barriers to Trade (TBT) Committee.
shaping, cleaning, or contacting specimens; however, a proce-
dure for verifying contact quality is given.
2. Referenced Documents
NOTE 1—Practice F418 covers the preparation of gallium arsenide
2.1 ASTM Standards:
phosphide specimens.
D1125 Test Methods for Electrical Conductivity and Resis-
1.3 The method in Practice F418 does not provide an
tivity of Water
interpretation of the results in terms of basic semiconductor
E2554 Practice for Estimating and Monitoring the Uncer-
properties (for example, majority and minority carrier mobili-
tainty of Test Results of a Test Method Using Control
ties and densities). Some general guidance, applicable to
Chart Techniques
certain semiconductors and temperature ranges, is provided in
F26 Test Methods for Determining the Orientation of a
the Appendix. For the most part, however, the interpretation is
Semiconductive Single Crystal (Withdrawn 2003)
left to the user.
F43 Test Methods for Resistivity of Semiconductor Materi-
als (Withdrawn 2003)
These test methods are under the jurisdiction of ASTM Committee F01 on
Electronics and are the direct responsibility of Subcommittee F01.15 on Compound
Semiconductors. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved May 1, 2016. Published May 2016. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1967. Last previous edition approved in 2008 as F76 – 08. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/F0076-08R16E01. the ASTM website.
2 4
The boldface numbers in parentheses refer to the list of references at the end of The last approved version of this historical standard is referenced on
these test methods. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
F76 − 08 (2016)
F47 Test Method for Crystallographic Perfection of Silicon useful quantities for materials specification, including the
by Preferential Etch Techniques charge carrier density and the drift mobility, can be inferred.
F418 Practice for Preparation of Samples of the Constant
Composition Region of Epitaxial Gallium Arsenide Phos-
5. Interferences
phide for Hall Effect Measurements (Withdrawn 2008)
5.1 In making resistivity and Hall-effect measurements,
2.2 SEMI Standard:
spurious results can arise from a number of sources.
C1 Specifications for Reagents
5.1.1 Photoconductive and photovoltaic effects can seri-
ously influence the observed resistivity, particularly with high-
3. Terminology
resistivity material. Therefore, all determinations should be
3.1 Definitions:
made in a dark chamber unless experience shows that the
3.1.1 Hall coeffıcient—the ratio of the Hall electric field
results are insensitive to ambient illumination.
(due to the Hall voltage) to the product of the current density
5.1.2 Minority-carrier injection during the measurement can
and the magnetic flux density (see X1.4).
also seriously influence the observed resistivity. This interfer-
ence is indicated if the contacts to the test specimen do not
3.1.2 Hall mobility—the ratio of the magnitude of the Hall
have linear current-versus-voltage characteristics in the range
coefficient to the resistivity; it is readily interpreted only in a
used in the measurement procedure. These effects can also be
system with carriers of one charge type. (See X1.5)
detected by repeating the measurements over several decades
3.1.3 resistivity—of a material, is the ratio of the potential
of current. In the absence of injection, no change in resistivity
gradient parallel to the current in the material to the current
should be observed. It is recommended that the current used in
density. For the purposes of this method, the resistivity shall
the measurements be as low as possible for the required
always be determined for the case of zero magnetic flux. (See
precision.
X1.2.)
5.1.3 Semiconductors have a significant temperature coeffi-
3.1.4 units—in these test methods SI units are not always
cient of resistivity. Consequently, the temperature of the
used. For these test methods, it is convenient to measure length
specimen should be known at the time of measurement and the
in centimetres and to measure magnetic flux density in gauss.
current used should be small to avoid resistive heating.
This choice of units requires that magnetic flux density be
Resistive heating can be detected by a change in readings as a
−2
expressed in V·s·cm where:
function of time starting immediately after the current is
22 8
1 V·s·cm 5 10 gauss
applied and any circuit time constants have settled.
5.1.4 Spurious currents can be introduced in the testing
The units employed and the factors relating them are sum-
circuit when the equipment is located near high-frequency
marized in Table 1.
generators. If equipment is located near such sources, adequate
shielding must be provided.
4. Significance and Use
5.1.5 Surface leakage can be a serious problem when
4.1 In order to choose the proper material for producing
measurements are made on high-resistivity specimens. Surface
semiconductor devices, knowledge of material properties such
effects can often be observed as a difference in measured value
as resistivity, Hall coefficient, and Hall mobility is useful.
of resistivity or Hall coefficient when the surface condition of
Under certain conditions, as outlined in the Appendix, other
the specimen is changed (2, 3).
5.1.6 In measuring high-resistivity samples, particular atten-
tion should be paid to possible leakage paths in other parts of
the circuit such as switches, connectors, wires, cables, and the
Available from Semiconductor Equipment and Materials Institute, 625 Ellis St.,
Suite 212, Mountain View, CA 94043.
TABLE 1 Units of Measurement
Units of
A
Quantity Symbol SI Unit Factor
B
Measurement
Resistivity ρ Ω · m 10 Ω · cm
− 3 − 6 − 3
Charge carrier concentration n, p m 10 cm
Charge e, q C 1 C
2 − 1 − 1 4 2 − 1 − 1
Drift mobility, Hall mobility µ,µ m · V · s 10 cm · V ·s
H
3 − 1 6 3 − 1
Hall coefficient R m · C 10 cm · C
H
− 1 − 2 − 1
Electric field E V · m 10 V · cm
Magnetic flux density B T 10 gauss
− 2 − 4 − 2
Current density J A · m 10 A · cm
Length L, t, w, d m 10 cm
a, b, c
Potential difference V V 1 V
A
The factors relate SI units to the units of measurement as in the following example:
1 Ω · m = 10 Ω · cm
B − 2
This system is not a consistent set of units. In order to obtain a consistent set, the magnetic flux density must be expressed in V · s · cm . The proper conversion factor
is:
− 2 8
1 · V · s · cm = 10 gauss
´1
F76 − 08 (2016)
like which may shunt some of the current around the sample. procedure is described for determining resistivity and Hall
Since high values of lead capacitance may lengthen the time coefficient using direct current techniques. The Hall mobility is
required for making measurements on high-resistivity samples, calculated from the measured values.
connecting cable should be as short as practicable.
7. Apparatus
5.1.7 Inhomogeneities of the carrier density, mobility, or of
the magnetic flux will cause the measurements to be inaccu-
7.1 For Measurement of Specimen Thickness—Micrometer,
rate. At best, the method will enable determination only of an
dial gage, microscope (with small depth of field and calibrated
undefined average resistivity or Hall coefficient. At worst, the
vertical-axis adjustment), or calibrated electronic thickness
measurements may be completely erroneous (2, 3, 4).
gage capable of measuring the specimen thickness to 61 %.
5.1.8 Thermomagnetic effects with the exception of the
7.2 Magnet—A calibrated magnet capable of providing a
Ettingshausen effect can be eliminated by averaging of the
magnetic flux density uniform to 61.0 % over the area in
measured transverse voltages as is specified in the measure-
which the test specimen is to be located. It must be possible to
ment procedure (Sections 11 and 17). In general, the error due
reverse the direction of the magnetic flux (either electrically or
to the Ettingshausen effect is small and can be neglected,
by rotation of the magnet) or to rotate the test specimen 180°
particularly if the sample is in good thermal contact with its
about its axis parallel to the current flow. Apparatus, such as an
surroundings (2, 3, 4).
auxiliary Hall probe or nuclear magnetic resonance system,
5.1.9 For materials which are anisotropic, especially semi-
should be available for measuring the flux density to an
conductors with noncubic crystal structures, Hall measure-
accuracy of 61.0 % at the specimen position. If an electro-
ments are affected by the orientation of the current and
magnet is used, provision must be made for monitoring the flux
magnetic field with respect to the crystal axes (Appendix, Note
density during the measurements. Flux densities between 1000
X1.1). Errors can result if the magnetic field is not within the
and 10 000 gauss are frequently used; conditions governing the
low-field limit (Appendix, Note X1.1).
choice of flux density are discussed more fully elsewhere (2, 3,
5.1.10 Spurious voltages, which may occur in the measuring
4).
circuit, for example, thermal voltages, can be detected by
7.3 Instrumentation:
measuring the voltage across the specimen with no current
7.3.1 Current Source, capable of maintaining current
flowing or with the voltage leads shorted at the sample
through the specimen constant to 60.5 % during the measure-
position. If there is a measurable voltage, the measuring circuit
ment. This may consist either of a power supply or a battery, in
should be checked carefully and modified so that these effects
series with a resistance greater than 200 × the total specimen
are eliminated.
resistance (including contact resistance). The current source is
5.1.11 An erroneous Hall coefficient will be measured if the
accurate to 60.5 % on all ranges used in the measurement. The
current and transverse electric field axes are not precisely
magnitude of current required is less than that associated with
perpendicular to the magnetic flux. The Hall coefficient will be
−1
an electric field of 1 V·cm in the specimen.
at an extremum with respect to rotation if the specimen is
7.3.2 Electrometer or Voltmeter, with which voltage mea-
properly positioned (see 7.4.4 or 13.4.4).
surements can be made to an accuracy of 60.5 %. The current
5.2 In addition to these interferences the following must be
drawn by the measuring instrument during the resistivity and
noted for van der Pauw specimens.
Hall voltage measurements shall be less than 0.1 % of the
5.2.1 Errors may result in voltage measurements due to
specimen current, that is, the input resistance of the electrom-
contacts of finite size. Some of these errors are discussed in
eter (or voltmeter) must be 1000 × greater than the resistance
references (1, 5, 6).
of the specimen.
5.2.2 Errors may be introduced if the contacts are not placed
7.3.3 Switching Facilities, used for reversal of current flow
on the specimen periphery (7).
and for connecting in turn the required pairs of potential leads
5.3 In addition to the interferences described in 5.1, the
to the voltage-measuring device.
following must be noted for parallelepiped and bridge-type
7.3.3.1 Representative Circuit, used for accomplishing the
specimens.
required switching is shown in Fig. 1.
5.3.1 It is essential that in the case of parallelepiped or
7.3.3.2 Unity-Gain Amplifiers, used for high-resistivity
bridge-type specimens the Hall-coefficient measurements be
semiconductors, with input impedance greater than 1000 × the
made on side contacts far
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