ASTM F76-86(1996)e1

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

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.

General Information

• Status: Historical
• Publication Date: 30-Oct-1986
• Technical Committee: F01 - Electronics
• Drafting Committee: F01.15 - Compound Semiconductors

Relations

• Replaced By: ASTM F76-86(2002) - Standard Test Methods for Measuring Resistivity and Hall Coefficient and Determining Hall Mobility in Single-Crystal Semiconductors
• Effective Date: 31-Oct-1986

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
e1
Designation: F 76 – 86 (Reapproved 1996)
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 F 76; 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 (e) indicates an editorial change since the last revision or reapproval.
e NOTE—Keywords were added editorially in February 1997.
1. Scope and for the semiconductors, germanium, silicon, and gallium
arsenide. However, the method is applicable to other semicon-
1.1 These test methods cover two procedures for measuring
ductors provided suitable specimen preparation and contacting
the resistivity and Hall coefficient of single-crystal semicon-
procedures are known. The resistivity range over which the
ductor specimens. These test methods differ most substantially
method is applicable is limited by the test specimen geometry
in their test specimen requirements.
and instrumentation sensitivity.
1.1.1 Test Method A, van der Pauw (1) —This test method
1.5 The values stated in acceptable metric units are to be
requires a singly connected test specimen (without any isolated
regarded as the standard. The values given in parentheses are
holes), homogeneous in thickness, but of arbitrary shape. The
for information only. (See also 3.1.4.)
contacts must be sufficiently small and located at the periphery
1.6 This standard does not purport to address all of the
of the specimen. The measurement is most easily interpreted
safety concerns, if any, associated with its use. It is the
for an isotropic semiconductor whose conduction is dominated
responsibility of the user of this standard to establish appro-
by a single type of carrier.
priate safety and health practices and determine the applica-
1.1.2 Test Method B, Parallelepiped or Bridge-Type—This
bility of regulatory limitations prior to use.
test method requires a specimen homogeneous in thickness and
of specified shape. Contact requirements are specified for both
2. Referenced Documents
the parallelepiped and bridge geometries. These test specimen
2.1 ASTM Standards:
geometries are desirable for anisotropic semiconductors for
D 1125 Test Methods for Electrical Conductivity and Re-
which the measured parameters depend on the direction of
sistivity of Water
current flow. The test method is also most easily interpreted
E 177 Practice for Use of the Terms Precision and Bias in
when conduction is dominated by a single type of carrier.
ASTM Test Methods
1.2 These test methods do not provide procedures for
F 26 Test Methods for Determining the Orientation of a
shaping, cleaning, or contacting specimens; however, a proce-
Semiconductive Single Crystal
dure for verifying contact quality is given.
F 43 Test Methods for Resistivity of Semiconductor Mate-
NOTE 1—Practice F 418 covers the preparation of gallium arsenide
rials
phosphide specimens.
F 47 Test Method for Crystallographic Perfection of Silicon
1.3 The method in Practice F 418 does not provide an
by Preferential Etch Techniques
interpretation of the results in terms of basic semiconductor
F 418 Practice for Preparation of Samples of the Constant
properties (for example, majority and minority carrier mobili-
Composition Region of Epitaxial Gallium Arsenide Phos-
ties and densities). Some general guidance, applicable to
phide for Hall Effect Measurements
certain semiconductors and temperature ranges, is provided in
2.2 SEMI Standard:
the Appendix. For the most part, however, the interpretation is
C1 Specifications for Reagents
left to the user.
3. Terminology
1.4 Interlaboratory tests of these test methods (Section 19)
have been conducted only over a limited range of resistivities 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
These test methods are under the jurisdiction of ASTM Committee F-1 on
Electronics and are the direct responsibility of Subcommittee F01.15 on Gallium
Arsenide. Annual Book of ASTM Standards, Vol 11.01.
Current edition approved Oct. 31, 1986. Published December 1986. Originally Annual Book of ASTM Standards, Vol 14.02.
published as F 76 – 67T. Last previous edition F 76 – 84. Annual Book of ASTM Standards, Vol 10.05.
2 6
The boldface numbers in parentheses refer to the list of references at the end of Available from Semiconductor Equipment and Materials Institute, 625 Ellis St.,
these test methods. Suite 212, Mountain View, CA 94043.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
F76
and the magnetic flux density (see X1.4). should be observed. It is recommended that the current used in
3.1.2 Hall mobility—the ratio of the magnitude of the Hall the measurements be as low as possible for the required
coefficient to the resistivity; it is readily interpreted only in a precision.
system with carriers of one charge type. (See X1.5)
5.1.3 Semiconductors have a significant temperature coeffi-
3.1.3 resistivity—of a material, is the ratio of the potential
cient of resistivity. Consequently, the temperature of the
gradient parallel to the current in the material to the current
specimen should be known at the time of measurement and the
density. For the purposes of this method, the resistivity shall
current used should be small to avoid resistive heating.
always be determined for the case of zero magnetic flux. (See
Resistive heating can be detected by a change in readings as a
X1.2.)
function of time starting immediately after the current is
3.1.4 units—in these test methods SI units are not always
applied and any circuit time constants have settled.
used. For these test methods, it is convenient to measure length
5.1.4 Spurious currents can be introduced in the testing
in centimetres and to measure magnetic flux density in gauss.
circuit when the equipment is located near high-frequency
This choice of units requires that magnetic flux density be
generators. If equipment is located near such sources, adequate
−2
expressed in V·s·cm where:
shielding must be provided.
22 8
5.1.5 Surface leakage can be a serious problem when
1 V·s·cm 5 10 gauss
measurements are made on high-resistivity specimens. Surface
The units employed and the factors relating them are
effects can often be observed as a difference in measured value
summarized in Table 1.
of resistivity or Hall coefficient when the surface condition of
the specimen is changed (2, 3).
4. Significance and Use
5.1.6 In measuring high-resistivity samples, particular atten-
4.1 In order to choose the proper material for producing
tion should be paid to possible leakage paths in other parts of
semiconductor devices, knowledge of material properties such
the circuit such as switches, connectors, wires, cables, and the
as resistivity, Hall coefficient, and Hall mobility is useful.
like which may shunt some of the current around the sample.
Under certain conditions, as outlined in the Appendix, other
Since high values of lead capacitance may lengthen the time
useful quantities for materials specification, including the
required for making measurements on high-resistivity samples,
charge carrier density and the drift mobility, can be inferred.
connecting cable should be as short as practicable.
5. Interferences
5.1.7 Inhomogeneities of the carrier density, mobility, or of
the magnetic flux will cause the measurements to be inaccu-
5.1 In making resistivity and Hall-effect measurements,
rate. At best, the method will enable determination only of an
spurious results can arise from a number of sources.
undefined average resistivity or Hall coefficient. At worst, the
5.1.1 Photoconductive and photovoltaic effects can seri-
measurements may be completely erroneous (2, 3, 4).
ously influence the observed resistivity, particularly with high-
5.1.8 Thermomagnetic effects with the exception of the
resistivity material. Therefore, all determinations should be
Ettingshausen effect can be eliminated by averaging of the
made in a dark chamber unless experience shows that the
measured transverse voltages as is specified in the measure-
results are insensitive to ambient illumination.
ment procedure (Sections 11 and 17). In general, the error due
5.1.2 Minority-carrier injection during the measurement can
to the Ettingshausen effect is small and can be neglected,
also seriously influence the observed resistivity. This interfer-
particularly if the sample is in good thermal contact with its
ence is indicated if the contacts to the test specimen do not
surroundings (2, 3, 4).
have linear current-versus-voltage characteristics in the range
5.1.9 For materials which are anisotropic, especially semi-
used in the measurement procedure. These effects can also be
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 5 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 5 10 gauss
F76
magnetic field with respect to the crystal axes (Appendix, Note and 10 000 gauss are frequently used; conditions governing the
X1.1). Errors can result if the magnetic field is not within the choice of flux density are discussed more fully elsewhere (2, 3,
low-field limit (Appendix, Note X1.1). 4).
5.1.10 Spurious voltages, which may occur in the measuring
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. This may consist either of a power supply or a battery, in
position. If there is a measurable voltage, the measuring circuit
series with a resistance greater than 200 3 the total specimen
should be checked carefully and modified so that these effects
resistance (including contact resistance). The current source is
are eliminated.
accurate to 60.5 % on all ranges used in the measurement. The
5.1.11 An erroneous Hall coefficient will be measured if the
magnitude of current required is less than that associated with
−1
current and transverse electric field axes are not precisely
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 3 greater than the resistance
contacts of finite size. Some of these errors are discussed in
of the specimen.
references (1, 5, 6).
7.3.3 Switching Facilities, used for reversal of current flow
5.2.2 Errors may be introduced if the contacts are not placed
and for connecting in turn the required pairs of potential leads
on the specimen periphery (7).
to the voltage-measuring device.
5.3 In addition to the interferences described in 5.1, the
7.3.3.1 Representative Circuit, used for accomplishing the
following must be noted for parallelepiped and bridge-type
required switching is shown in Fig. 1.
specimens.
7.3.3.2 Unity-Gain Amplifiers, used for high-resistivity
5.3.1 It is essential that in the case of parallelepiped or
semiconductors, with input impedance greater than 1000 3 the
bridge-type specimens the Hall-coefficient measurements be
specimen resistance are located as close to the specimen as
made on side contacts far enough removed from the end
possible to minimize current leakage and circuit time-constants
contacts that shorting effects can be neglected (2, 3). The
(8, 9). Triaxial cable is used between the specimen and the
specimen geometries described in 15.3.1 and 15.3.2 are de-
amplifiers with the guard shield driven by the respective
signed so that the reduction in Hall voltage due to this shorting
amplifier output. This minimizes current leakage in the cabling.
effect is less than 1 %.
The current leakage through the insulation must be less than
TEST METHOD A—FOR VAN DER PAUW 0.1 % of the specimen current. Current leakage in the specimen
SPECIMENS
holder must be prevented by utilizing a suitable high-resistivity
insulator such as boron nitride or beryllium oxide.
6. Summary of Test Method
7.3.3.3 Representative Circuit, used for measuring high-
6.1 In this test method, specifications for a van der Pauw (1)
resistance specimens is shown in Fig. 2. Sixteen single-pole,
test specimen and procedures for testing it are covered. A
single-throw, normally open, guarded reed relays are used to
procedure is described for determining resistivity and Hall
connect the current source and differential voltmeter to the
coefficient using direct current techniques. The Hall mobility is
appropriate specimen points. The relay closures necessary to
calculated from the measured values.
accomplish the same switching achieved in the circuit of Fig.
1 are listed in the table of Fig. 2.
7. Apparatus
7.3.4 Transistor Curve Tracer, can be used for checking the
7.1 For Measurement of Specimen Thickness—Micrometer,
linearity of contacts to low-resistivity material.
dial gage, microscope (with small depth of field and calibrated
7.3.5 All instruments must be maintained within their speci-
vertical-axis adjustment), or calibrated electronic thickness
fications through peri
...