ASTM F76-86(2002)
(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
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) -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—TypeThis 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 F 418 covers the preparation of gallium arsenide phosphide specimens.
1.3 The method in Practice F 418 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:F 76–86 (Reapproved 2002)
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope arsenide. However, the method is applicable to other semicon-
ductors provided suitable specimen preparation and contacting
1.1 These test methods cover two procedures for measuring
procedures are known. The resistivity range over which the
the resistivity and Hall coefficient of single-crystal semicon-
method is applicable is limited by the test specimen geometry
ductor specimens. These test methods differ most substantially
and instrumentation sensitivity.
in their test specimen requirements.
2 1.5 The values stated in acceptable metric units are to be
1.1.1 Test Method A, van der Pauw (1) —Thistestmethod
regarded as the standard. The values given in parentheses are
requiresasinglyconnectedtestspecimen(withoutanyisolated
for information only. (See also 3.1.4.)
holes), homogeneous in thickness, but of arbitrary shape. The
1.6 This standard does not purport to address all of the
contacts must be sufficiently small and located at the periphery
safety concerns, if any, associated with its use. It is the
of the specimen. The measurement is most easily interpreted
responsibility of the user of this standard to establish appro-
for an isotropic semiconductor whose conduction is dominated
priate safety and health practices and determine the applica-
by a single type of carrier.
bility of regulatory limitations prior to use.
1.1.2 Test Method B, Parallelepiped or Bridge-Type—This
testmethodrequiresaspecimenhomogeneousinthicknessand
2. Referenced Documents
of specified shape. Contact requirements are specified for both
2.1 ASTM Standards:
the parallelepiped and bridge geometries. These test specimen
D1125 Test Methods for Electrical Conductivity and Re-
geometries are desirable for anisotropic semiconductors for
sistivity of Water
which the measured parameters depend on the direction of
E177 Practice for Use of the Terms Precision and Bias in
current flow. The test method is also most easily interpreted
ASTM Test Methods
when conduction is dominated by a single type of carrier.
F26 Test Methods for Determining the Orientation of a
1.2 These test methods do not provide procedures for
Semiconductive Single Crystal
shaping, cleaning, or contacting specimens; however, a proce-
F43 Test Methods for Resistivity of Semiconductor Mate-
dure for verifying contact quality is given.
rials
NOTE 1—Practice F418 covers the preparation of gallium arsenide
F47 TestMethodforCrystallographicPerfectionofSilicon
phosphide specimens.
by Preferential Etch Techniques
1.3 The method in Practice F418 does not provide an
F418 Practice for Preparation of Samples of the Constant
interpretation of the results in terms of basic semiconductor
Composition Region of Epitaxial Gallium Arsenide Phos-
properties (for example, majority and minority carrier mobili-
phide for Hall Effect Measurements
ties and densities). Some general guidance, applicable to
2.2 SEMI Standard:
certain semiconductors and temperature ranges, is provided in
C1 Specifications for Reagents
theAppendix. For the most part, however, the interpretation is
3. Terminology
left to the user.
1.4 Interlaboratory tests of these test methods (Section 19)
3.1 Definitions:
have been conducted only over a limited range of resistivities 3.1.1 Hall coeffıcient—the ratio of the Hall electric field
and for the semiconductors, germanium, silicon, and gallium
(due to the Hall voltage) to the product of the current density
and the magnetic flux density (see X1.4).
These test methods are under the jurisdiction of ASTM Committee F01 on
Electronics and are the direct responsibility of Subcommittee F01.15 on Compound For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Semiconductors. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved May 10, 2002. Published December 1986. Originally Standards volume information, refer to the standard’s Document Summary page on
published as F76–67T. Last previous edition F76–84. the ASTM website.
2 4
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof AvailablefromSemiconductorEquipmentandMaterialsInstitute,625EllisSt.,
these test methods. Suite 212, Mountain View, CA 94043.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
F 76–86 (2002)
3.1.2 Hall mobility—the ratio of the magnitude of the Hall should be observed. It is recommended that the current used in
coefficient to the resistivity; it is readily interpreted only in a the measurements be as low as possible for the required
system with carriers of one charge type. (See X1.5) precision.
3.1.3 resistivity—of a material, is the ratio of the potential 5.1.3 Semiconductors have a significant temperature coeffi-
gradient parallel to the current in the material to the current cient of resistivity. Consequently, the temperature of the
density. For the purposes of this method, the resistivity shall specimenshouldbeknownatthetimeofmeasurementandthe
always be determined for the case of zero magnetic flux. (See current used should be small to avoid resistive heating.
X1.2.) Resistive heating can be detected by a change in readings as a
3.1.4 units—in these test methods SI units are not always function of time starting immediately after the current is
used.Forthesetestmethods,itisconvenienttomeasurelength applied and any circuit time constants have settled.
in centimetres and to measure magnetic flux density in gauss. 5.1.4 Spurious currents can be introduced in the testing
This choice of units requires that magnetic flux density be circuit when the equipment is located near high-frequency
−2
expressed in V·s·cm where: generators.Ifequipmentislocatednearsuchsources,adequate
shielding must be provided.
22 8
1V·s·cm 510 gauss
5.1.5 Surface leakage can be a serious problem when
The units employed and the factors relating them are
measurements are made on high-resistivity specimens. Surface
summarized in Table 1.
effectscanoftenbeobservedasadifferenceinmeasuredvalue
of resistivity or Hall coefficient when the surface condition of
4. Significance and Use
the specimen is changed (2, 3).
4.1 In order to choose the proper material for producing
5.1.6 Inmeasuringhigh-resistivitysamples,particularatten-
semiconductor devices, knowledge of material properties such
tion should be paid to possible leakage paths in other parts of
as resistivity, Hall coefficient, and Hall mobility is useful.
the circuit such as switches, connectors, wires, cables, and the
Under certain conditions, as outlined in the Appendix, other
like which may shunt some of the current around the sample.
useful quantities for materials specification, including the
Since high values of lead capacitance may lengthen the time
charge carrier density and the drift mobility, can be inferred.
requiredformakingmeasurementsonhigh-resistivitysamples,
connecting cable should be as short as practicable.
5. Interferences
5.1.7 Inhomogeneities of the carrier density, mobility, or of
5.1 In making resistivity and Hall-effect measurements, the magnetic flux will cause the measurements to be inaccu-
spurious results can arise from a number of sources. rate. At best, the method will enable determination only of an
5.1.1 Photoconductive and photovoltaic effects can seri- undefined average resistivity or Hall coefficient. At worst, the
ously influence the observed resistivity, particularly with high- measurements may be completely erroneous (2, 3, 4).
resistivity material. Therefore, all determinations should be 5.1.8 Thermomagnetic effects with the exception of the
made in a dark chamber unless experience shows that the Ettingshausen effect can be eliminated by averaging of the
results are insensitive to ambient illumination. measured transverse voltages as is specified in the measure-
ment procedure (Sections 11 and 17). In general, the error due
5.1.2 Minority-carrierinjectionduringthemeasurementcan
also seriously influence the observed resistivity. This interfer- to the Ettingshausen effect is small and can be neglected,
particularly if the sample is in good thermal contact with its
ence is indicated if the contacts to the test specimen do not
have linear current-versus-voltage characteristics in the range surroundings (2, 3, 4).
used in the measurement procedure. These effects can also be 5.1.9 For materials which are anisotropic, especially semi-
detected by repeating the measurements over several decades conductors with noncubic crystal structures, Hall measure-
of current. In the absence of injection, no change in resistivity ments are affected by the orientation of the current and
TABLE 1 Units of Measurement
Units of
A
Quantity Symbol SI Unit Factor
B
Measurement
Resistivity rV ·m 10 V ·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 V ·m=10 V ·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
F 76–86 (2002)
magneticfieldwithrespecttothecrystalaxes(Appendix,Note and10000gaussarefrequentlyused;conditionsgoverningthe
X1.1). Errors can result if the magnetic field is not within the choiceoffluxdensityarediscussedmorefullyelsewhere(2,3,
low-field limit (Appendix, Note X1.1).
4).
5.1.10 Spuriousvoltages,whichmayoccurinthemeasuring
7.3 Instrumentation:
circuit, for example, thermal voltages, can be detected by
7.3.1 Current Source, capable of maintaining current
measuring the voltage across the specimen with no current
through the specimen constant to 60.5% during the measure-
flowing or with the voltage leads shorted at the sample
ment.Thismayconsisteitherofapowersupplyorabattery,in
position.Ifthereisameasurablevoltage,themeasuringcircuit
series with a resistance greater than 200 3the total specimen
should be checked carefully and modified so that these effects
resistance (including contact resistance). The current source is
are eliminated.
accurateto 60.5%onallrangesusedinthemeasurement.The
5.1.11 An erroneous Hall coefficient will be measured if the
magnitude of current required is less than that associated with
current and transverse electric field axes are not precisely
−1
an electric field of 1 V·cm in the specimen.
perpendicular to the magnetic flux.The Hall coefficient will be
7.3.2 Electrometer or Voltmeter, with which voltage mea-
at an extremum with respect to rotation if the specimen is
surements can be made to an accuracy of 60.5%.The current
properly positioned (see 7.4.4 or 13.4.4).
drawn by the measuring instrument during the resistivity and
5.2 In addition to these interferences the following must be
Hall voltage measurements shall be less than 0.1% of the
noted for van der Pauw specimens.
specimen current, that is, the input resistance of the electrom-
5.2.1 Errors may result in voltage measurements due to
eter (or voltmeter) must be 1000 3greater than the resistance
contacts of finite size. Some of these errors are discussed in
of the specimen.
references (1, 5, 6).
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,withinputimpedancegreaterthan1000 3the
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.
The current leakage through the insulation must be less than
TEST METHOD A—FOR VAN DER PAUW
0.1%ofthespecimencurrent.Currentleakageinthespecimen
SPECIMENS
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 determining resistivity and Hall single-throw, normally open, guarded reed relays are used to
coefficientusingdirectcurrenttechniques.TheHallmobilityis connect the current source and differential voltmeter to the
calculated from the measured values. appropriate specimen points. The relay closures necessary to
accomplish the same switching achieved in the circuit of Fig.
7. Apparatus
1 are listed in the table of Fig. 2.
7.1 For Measurement of Specimen Thickness—Micrometer,
7.3.4 Transistor Curve Tracer, can be used for checking the
dial gage, microscope (with small depth of field and calibrated
linearity of contacts to low-resistivity material.
vertical-axis adjustment), or calibrated electronic thickness
7.3.5 Allinstrumentsmustbemaintainedwithintheirspeci-
gage capable of measuring the specimen thickness to 61%.
fications through periodic calibrations.
7.2 Magnet—A calibrated magnet capable of providing a
7.4 Specimen Holder:
magnetic flux density uniform to 61.0% over the area in
7.4.1 Container, if low
...
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