ASTM F76-08(2016)
(Test Method)Standard Test Methods for Measuring Resistivity and Hall Coefficient and Determining Hall Mobility in Single-Crystal Semiconductors
Standard Test Methods for Measuring Resistivity and Hall Coefficient and Determining Hall Mobility in Single-Crystal Semiconductors
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.
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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.
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.
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
which the measured parameters depend on the direction of
2. Referenced Documents
current flow. The test method is also most easily interpreted
when conduction is dominated by a single type of carrier.
2.1 ASTM Standards:
1.2 These test methods do not provide procedures for D1125Test Methods for Electrical Conductivity and Resis-
shaping, cleaning, or contacting specimens; however, a proce- tivity of Water
dure for verifying contact quality is given.
E2554Practice for Estimating and Monitoring the Uncer-
tainty of Test Results of a Test Method Using Control
NOTE 1—Practice F418 covers the preparation of gallium arsenide
Chart Techniques
phosphide specimens.
F26Test Methods for Determining the Orientation of a
1.3 The method in Practice F418 does not provide an
Semiconductive Single Crystal (Withdrawn 2003)
interpretation of the results in terms of basic semiconductor
F43Test Methods for Resistivity of Semiconductor Materi-
properties (for example, majority and minority carrier mobili- 4
als (Withdrawn 2003)
ties and densities). Some general guidance, applicable to
F47Test Method for Crystallographic Perfection of Silicon
certain semiconductors and temperature ranges, is provided in
by Preferential Etch Techniques
theAppendix. For the most part, however, the interpretation is
F418Practice for Preparation of Samples of the Constant
left to the user.
Composition Region of Epitaxial GalliumArsenide Phos-
phide for Hall Effect Measurements (Withdrawn 2008)
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 service@astm.org. 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/F0076-08R16. 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
F76 − 08 (2016)
2.2 SEMI Standard: 5.1.1 Photoconductive and photovoltaic effects can seri-
C1Specifications for Reagents ously influence the observed resistivity, particularly with high-
resistivity material. Therefore, all determinations should be
3. Terminology
made in a dark chamber unless experience shows that the
results are insensitive to ambient illumination.
3.1 Definitions:
5.1.2 Minority-carrierinjectionduringthemeasurementcan
3.1.1 Hall coeffıcient—the ratio of the Hall electric field
(due to the Hall voltage) to the product of the current density also seriously influence the observed resistivity. This interfer-
ence is indicated if the contacts to the test specimen do not
and the magnetic flux density (see X1.4).
have linear current-versus-voltage characteristics in the range
3.1.2 Hall mobility—the ratio of the magnitude of the Hall
used in the measurement procedure. These effects can also be
coefficient to the resistivity; it is readily interpreted only in a
detected by repeating the measurements over several decades
system with carriers of one charge type. (See X1.5)
of current. In the absence of injection, no change in resistivity
3.1.3 resistivity—of a material, is the ratio of the potential
should be observed. It is recommended that the current used in
gradient parallel to the current in the material to the current
the measurements be as low as possible for the required
density. For the purposes of this method, the resistivity shall
precision.
always be determined for the case of zero magnetic flux. (See
5.1.3 Semiconductors have a significant temperature coeffi-
X1.2.)
cient of resistivity. Consequently, the temperature of the
3.1.4 units—in these test methods SI units are not always
specimenshouldbeknownatthetimeofmeasurementandthe
used.Forthesetestmethods,itisconvenienttomeasurelength
current used should be small to avoid resistive heating.
in centimetres and to measure magnetic flux density in gauss.
Resistive heating can be detected by a change in readings as a
This choice of units requires that magnetic flux density be
function of time starting immediately after the current is
−2
expressed in V·s·cm where:
applied and any circuit time constants have settled.
22 8
5.1.4 Spurious currents can be introduced in the testing
1 V·s·cm 5 10 gauss
circuit when the equipment is located near high-frequency
The units employed and the factors relating them are sum-
generators.Ifequipmentislocatednearsuchsources,adequate
marized in Table 1.
shielding must be provided.
5.1.5 Surface leakage can be a serious problem when
4. Significance and Use
measurements are made on high-resistivity specimens. Surface
4.1 In order to choose the proper material for producing
effectscanoftenbeobservedasadifferenceinmeasuredvalue
semiconductor devices, knowledge of material properties such
of resistivity or Hall coefficient when the surface condition of
as resistivity, Hall coefficient, and Hall mobility is useful.
the specimen is changed (2, 3).
Under certain conditions, as outlined in the Appendix, other
5.1.6 Inmeasuringhigh-resistivitysamples,particularatten-
useful quantities for materials specification, including the
tion should be paid to possible leakage paths in other parts of
charge carrier density and the drift mobility, can be inferred.
the circuit such as switches, connectors, wires, cables, and the
like which may shunt some of the current around the sample.
5. Interferences
Since high values of lead capacitance may lengthen the time
5.1 In making resistivity and Hall-effect measurements,
requiredformakingmeasurementsonhigh-resistivitysamples,
spurious results can arise from a number of sources.
connecting cable should be as short as practicable.
5.1.7 Inhomogeneities of the carrier density, mobility, or of
the magnetic flux will cause the measurements to be inaccu-
AvailablefromSemiconductorEquipmentandMaterialsInstitute,625EllisSt.,
rate. At best, the method will enable determination only of an
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
F76 − 08 (2016)
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
measuring the voltage across the specimen with no current 7.3 Instrumentation:
flowing or with the voltage leads shorted at the sample
7.3.1 Current Source, capable of maintaining current
position.Ifthereisameasurablevoltage,themeasuringcircuit
through the specimen constant to 60.5% during the measure-
should be checked carefully and modified so that these effects
ment.Thismayconsisteitherofapowersupplyorabattery,in
are eliminated.
series with a resistance greater than 200×the total specimen
5.1.11 An erroneous Hall coefficient will be measured if the
resistance (including contact resistance). The current source is
current and transverse electric field axes are not precisely
accurateto 60.5%onallrangesusedinthemeasurement.The
perpendicular to the magnetic flux.The Hall coefficient will be
magnitude of current required is less than that associated with
−1
at an extremum with respect to rotation if the specimen is
an electric field of 1 V·cm in the specimen.
properly positioned (see 7.4.4 or 13.4.4).
7.3.2 Electrometer or Voltmeter, with which voltage mea-
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
on the specimen periphery (7). 7.3.3 Switching Facilities, used for reversal of current flow
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
possibletominimizecurrentleakageandcircuittime-constants
specimen geometries described in 15.3.1 and 15.3.2 are de-
(8, 9). Triaxial cable is used between the specimen and the
signedsothatthereductioninHallvoltageduetothisshorting
amplifiers with the guard shield driven by the respective
effect is less than 1%.
amplifieroutput.Thisminimizescurrentleakageinthecabling.
TEST METHOD A—FOR VAN DER PAUW
The current leakage through the insulation must be less than
SPECIMENS
0.1%ofthespecimencurrent.Currentleakageinthespecimen
holdermustbepreventedbyutilizingasuitablehigh-resistivity
6. Summary of Test Method
insulator such as boron nitride or beryllium oxide.
6.1 Inthistestmethod,specificationsforavanderPauw (1)
7.3.3.3 Representative Circuit, used for measuring high-
test specimen and procedures for testing it are covered. A
resistance specimens is shown in Fig. 2. Sixteen single-pole,
procedure is described for determ
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: F76 − 08 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.
1. 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) —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.
2. Referenced Documents
2.1 ASTM Standards:
D1125 Test Methods for Electrical Conductivity and Resistivity of Water
E2554 Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
F26 Test Methods for Determining the Orientation of a Semiconductive Single Crystal (Withdrawn 2003)
F43 Test Methods for Resistivity of Semiconductor Materials (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.
Current edition approved June 15, 2008May 1, 2016. Published August 2008May 2016. Originally approved in 1967. Last previous edition approved in 20022008 as
F76 – 86F76 – 08.(02). DOI: 10.1520/F0076-08.10.1520/F0076-08R16.
The boldface numbers in parentheses refer to the list of references at the end of these test methods.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F76 − 08 (2016)
F47 Test Method for Crystallographic Perfection of Silicon by Preferential Etch Techniques
F418 Practice for Preparation of Samples of the Constant Composition Region of Epitaxial Gallium Arsenide Phosphide for Hall
Effect Measurements (Withdrawn 2008)
2.2 SEMI Standard:
C1 Specifications for Reagents
3. Terminology
3.1 Definitions:
3.1.1 Hall coeffıcient—the ratio of the Hall electric field (due to the Hall voltage) to the product of the current density and the
magnetic flux density (see X1.4).
3.1.2 Hall mobility—the ratio of the magnitude of the Hall coefficient to the resistivity; it is readily interpreted only in a system
with carriers of one charge type. (See X1.5)
3.1.3 resistivity—of a material, is the ratio of the potential gradient parallel to the current in the material to the current density.
For the purposes of this method, the resistivity shall always be determined for the case of zero magnetic flux. (See X1.2.)
3.1.4 units—in these test methods SI units are not always used. For these test methods, it is convenient to measure length in
centimetres and to measure magnetic flux density in gauss. This choice of units requires that magnetic flux density be expressed
−2
in V·s·cm where:
22 8
1 V·s·cm 5 10 gauss
The units employed and the factors relating them are summarized in Table 1.
4. 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.
5. Interferences
5.1 In making resistivity and Hall-effect measurements, spurious results can arise from a number of sources.
5.1.1 Photoconductive and photovoltaic effects can seriously influence the observed resistivity, particularly with high-resistivity
material. Therefore, all determinations should be made in a dark chamber unless experience shows that the results are insensitive
to ambient illumination.
5.1.2 Minority-carrier injection during the measurement can also seriously influence the observed resistivity. This interference
is indicated if the contacts to the test specimen do not have linear current-versus-voltage characteristics in the range used in the
measurement procedure. These effects can also be detected by repeating the measurements over several decades of current. In the
absence of injection, no change in resistivity should be observed. It is recommended that the current used in the measurements be
as low as possible for the required precision.
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
F76 − 08 (2016)
5.1.3 Semiconductors have a significant temperature coefficient of resistivity. Consequently, the temperature of the specimen
should be known at the time of measurement and the current used should be small to avoid resistive heating. Resistive heating can
be detected by a change in readings as a function of time starting immediately after the current is applied and any circuit time
constants have settled.
5.1.4 Spurious currents can be introduced in the testing circuit when the equipment is located near high-frequency generators.
If equipment is located near such sources, adequate shielding must be provided.
5.1.5 Surface leakage can be a serious problem when measurements are made on high-resistivity specimens. Surface effects can
often be observed as a difference in measured value of resistivity or Hall coefficient when the surface condition of the specimen
is changed (2, 3).
5.1.6 In measuring high-resistivity samples, particular attention should be paid to possible leakage paths in other parts of the
circuit such as switches, connectors, wires, cables, and the like which may shunt some of the current around the sample. Since high
values of lead capacitance may lengthen the time required for making measurements on high-resistivity samples, connecting cable
should be as short as practicable.
5.1.7 Inhomogeneities of the carrier density, mobility, or of the magnetic flux will cause the measurements to be inaccurate. At
best, the method will enable determination only of an undefined average resistivity or Hall coefficient. At worst, the measurements
may be completely erroneous (2, 3, 4).
5.1.8 Thermomagnetic effects with the exception of the Ettingshausen effect can be eliminated by averaging of the measured
transverse voltages as is specified in the measurement procedure (Sections 11 and 17). In general, the error due to the Ettingshausen
effect is small and can be neglected, particularly if the sample is in good thermal contact with its surroundings (2, 3, 4).
5.1.9 For materials which are anisotropic, especially semiconductors with noncubic crystal structures, Hall measurements are
affected by the orientation of the current and magnetic field with respect to the crystal axes (Appendix, Note X1.1). Errors can
result if the magnetic field is not within the low-field limit (Appendix, Note X1.1).
5.1.10 Spurious voltages, which may occur in the measuring circuit, for example, thermal voltages, can be detected by
measuring the voltage across the specimen with no current flowing or with the voltage leads shorted at the sample position. If there
is a measurable voltage, the measuring circuit should be checked carefully and modified so that these effects are eliminated.
5.1.11 An erroneous Hall coefficient will be measured if the current and transverse electric field axes are not precisely
perpendicular to the magnetic flux. The Hall coefficient will be at an extremum with respect to rotation if the specimen is properly
positioned (see 7.4.4 or 13.4.4).
5.2 In addition to these interferences the following must be noted for van der Pauw specimens.
5.2.1 Errors may result in voltage measurements due to contacts of finite size. Some of these errors are discussed in references
(1, 5, 6).
5.2.2 Errors may be introduced if the contacts are not placed on the specimen periphery (7).
5.3 In addition to the interferences described in 5.1, the following must be noted for parallelepiped and bridge-type specimens.
5.3.1 It is essential that in the case of parallelepiped or bridge-type specimens the Hall-coefficient measurements be made on
side contacts far enough removed from the end contacts that shorting effects can be neglected (2, 3). The specimen geometries
described in 15.3.1 and 15.3.2 are designed so that the reduction in Hall voltage due to this shorting effect is less than 1 %.
TEST METHOD A—FOR VAN DER PAUW SPECIMENS
6. Summary of Test Method
6.1 In this test method, specifications for a van der Pauw (1) test specimen and procedures for testing it are covered. A procedure
is described for determining resistivity and Hall coefficient using direct current techniques. The Hall mobility is calculated from
the measured values.
7. Apparatus
7.1 For Measurement of Specimen Thickness—Micrometer, dial gage, microscope (with small depth of field and calibrated
vertical-axis adjustment), or calibrated electronic thickness gage capable of measuring the specimen thickness to 61 %.
7.2 Magnet—A calibrated magnet capable of providing a magnetic flux density uniform to 61.0 % over the area in which the
test specimen is to be located. It must be possible to reverse the direction of the magnetic flux (either electrically or by rotation
of the magnet) or to rotate the test specimen 180° about its axis parallel to the current flow. Apparatus, such as an auxiliary Hall
probe or nuclear magnetic resonance system, should be available for measuring the flux density to an accuracy of 61.0 % at the
specimen position. If an electromagnet is used, provision must be made for monitoring the flux density during the measurements.
Flux densities between 1000 and 10 000 gauss are frequently used; conditions governing the choice of flux density are discussed
more fully elsewhere (2, 3, 4).
7.3 Instrumentation:
7.3.1 Current Source, capable of maintaining current through the specimen constant to 60.5 % during the measurement. This
may consist either of a power supply or a battery, in series with a resistance greater than 200 × the total specimen resistance
F76 − 08 (2016)
(including contact resistance). The current source is accurate to 60.5 % on all ranges used in the measurement. The magnitude
−1
of current required is less than that associated with an electric field of 1 V·cm in the specimen.
7.3.2 Electrometer or Voltmeter, with which voltage measurements can be made to an accuracy of 60.5 %. The current drawn
by the measuring instrument during the resistivity and Hall voltage measurements shall be less than 0.1 % of the specimen current,
that is, the input resistance of the electrometer (or voltmeter) must be 1000 × greater than the resistance of the specimen.
7.3.3 Switching Facilities, used for reversal of current
...
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