1、Designation: F76 08 (Reapproved 2016)1Standard Test Methods forMeasuring Resistivity and Hall Coefficient and DeterminingHall Mobility in Single-Crystal Semiconductors1This standard is issued under the fixed designation F76; the number immediately following the designation indicates the year of orig
2、inaladoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.Asuperscriptepsilon () indicates an editorial change since the last revision or reapproval.1NOTEIn 10.5.1, second sentence, (0.5 T) was corrected editorially to (0.5 mT) i
3、n May 2017.1. Scope1.1 These test methods cover two procedures for measuringthe resistivity and Hall coefficient of single-crystal semicon-ductor specimens. These test methods differ most substantiallyin their test specimen requirements.1.1.1 Test Method A, van der Pauw (1)2This test methodrequires
4、a singly connected test specimen (without any isolatedholes), homogeneous in thickness, but of arbitrary shape. Thecontacts must be sufficiently small and located at the peripheryof the specimen. The measurement is most easily interpretedfor an isotropic semiconductor whose conduction is dominatedby
5、 a single type of carrier.1.1.2 Test Method B, Parallelepiped or Bridge-TypeThistest method requires a specimen homogeneous in thickness andof specified shape. Contact requirements are specified for boththe parallelepiped and bridge geometries. These test specimengeometries are desirable for anisotr
6、opic semiconductors forwhich the measured parameters depend on the direction ofcurrent flow. The test method is also most easily interpretedwhen conduction is dominated by a single type of carrier.1.2 These test methods do not provide procedures forshaping, cleaning, or contacting specimens; however
7、, a proce-dure for verifying contact quality is given.NOTE 1Practice F418 covers the preparation of gallium arsenidephosphide specimens.1.3 The method in Practice F418 does not provide aninterpretation of the results in terms of basic semiconductorproperties (for example, majority and minority carri
8、er mobili-ties and densities). Some general guidance, applicable tocertain semiconductors and temperature ranges, is provided inthe Appendix. For the most part, however, the interpretation isleft to the user.1.4 Interlaboratory tests of these test methods (Section 19)have been conducted only over a
9、limited range of resistivitiesand for the semiconductors, germanium, silicon, and galliumarsenide. However, the method is applicable to other semicon-ductors provided suitable specimen preparation and contactingprocedures are known. The resistivity range over which themethod is applicable is limited
10、 by the test specimen geometryand instrumentation sensitivity.1.5 The values stated in acceptable metric units are to beregarded as the standard. The values given in parentheses arefor information only. (See also 3.1.4.)1.6 This standard does not purport to address all of thesafety concerns, if any,
11、 associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.7 This international standard was developed in accor-dance with internationally recognized pr
12、inciples on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:3D1125 Test Methods for Electr
13、ical Conductivity and Resis-tivity of WaterE2554 Practice for Estimating and Monitoring the Uncer-tainty of Test Results of a Test Method Using ControlChart TechniquesF26 Test Methods for Determining the Orientation of aSemiconductive Single Crystal (Withdrawn 2003)4F43 Test Methods for Resistivity
14、of Semiconductor Materi-als (Withdrawn 2003)41These test methods are under the jurisdiction of ASTM Committee F01 onElectronics and are the direct responsibility of Subcommittee F01.15 on CompoundSemiconductors.Current edition approved May 1, 2016. Published May 2016. Originallyapproved in 1967. Las
15、t previous edition approved in 2008 as F76 08. DOI:10.1520/F0076-08R16E01.2The boldface numbers in parentheses refer to the list of references at the end ofthese test methods.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For
16、 Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4The last approved version of this historical standard is referenced onwww.astm.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. Un
17、ited StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barrie
18、rs to Trade (TBT) Committee.1F47 Test Method for Crystallographic Perfection of Siliconby Preferential Etch Techniques4F418 Practice for Preparation of Samples of the ConstantComposition Region of Epitaxial Gallium Arsenide Phos-phide for Hall Effect Measurements (Withdrawn 2008)42.2 SEMI Standard:C
19、1 Specifications for Reagents53. Terminology3.1 Definitions:3.1.1 Hall coeffcientthe ratio of the Hall electric field(due to the Hall voltage) to the product of the current densityand the magnetic flux density (see X1.4).3.1.2 Hall mobilitythe ratio of the magnitude of the Hallcoefficient to the res
20、istivity; it is readily interpreted only in asystem with carriers of one charge type. (See X1.5)3.1.3 resistivityof a material, is the ratio of the potentialgradient parallel to the current in the material to the currentdensity. For the purposes of this method, the resistivity shallalways be determi
21、ned for the case of zero magnetic flux. (SeeX1.2.)3.1.4 unitsin these test methods SI units are not alwaysused. For these test methods, it is convenient to measure lengthin centimetres and to measure magnetic flux density in gauss.This choice of units requires that magnetic flux density beexpressed
22、in Vscm2where:1 Vscm225 108gaussThe units employed and the factors relating them are sum-marized in Table 1.4. Significance and Use4.1 In order to choose the proper material for producingsemiconductor devices, knowledge of material properties suchas resistivity, Hall coefficient, and Hall mobility i
23、s useful.Under certain conditions, as outlined in the Appendix, otheruseful quantities for materials specification, including thecharge carrier density and the drift mobility, can be inferred.5. Interferences5.1 In making resistivity and Hall-effect measurements,spurious results can arise from a num
24、ber of sources.5.1.1 Photoconductive and photovoltaic effects can seri-ously influence the observed resistivity, particularly with high-resistivity material. Therefore, all determinations should bemade in a dark chamber unless experience shows that theresults are insensitive to ambient illumination.
25、5.1.2 Minority-carrier injection during the measurement canalso seriously influence the observed resistivity. This interfer-ence is indicated if the contacts to the test specimen do nothave linear current-versus-voltage characteristics in the rangeused in the measurement procedure. These effects can
26、 also bedetected by repeating the measurements over several decadesof current. In the absence of injection, no change in resistivityshould be observed. It is recommended that the current used inthe measurements be as low as possible for the requiredprecision.5.1.3 Semiconductors have a significant t
27、emperature coeffi-cient of resistivity. Consequently, the temperature of thespecimen should be known at the time of measurement and thecurrent used should be small to avoid resistive heating.Resistive heating can be detected by a change in readings as afunction of time starting immediately after the
28、 current isapplied and any circuit time constants have settled.5.1.4 Spurious currents can be introduced in the testingcircuit when the equipment is located near high-frequencygenerators. If equipment is located near such sources, adequateshielding must be provided.5.1.5 Surface leakage can be a ser
29、ious problem whenmeasurements are made on high-resistivity specimens. Surfaceeffects can often be observed as a difference in measured valueof resistivity or Hall coefficient when the surface condition ofthe specimen is changed (2, 3).5.1.6 In measuring high-resistivity samples, particular atten-tio
30、n should be paid to possible leakage paths in other parts ofthe circuit such as switches, connectors, wires, cables, and the5Available from Semiconductor Equipment and Materials Institute, 625 Ellis St.,Suite 212, Mountain View, CA 94043.TABLE 1 Units of MeasurementQuantity Symbol SI Unit FactorAUni
31、ts ofMeasurementBResistivity m 102 cmCharge carrier concentration n, p m3106cm3Charge e, q C1CDrift mobility, Hall mobility ,Hm2V1s1104cm2V1s1Hall coefficient RHm3C1106cm3C1Electric field E Vm1102Vcm1Magnetic flux density B T104gaussCurrent density J Am2104Acm2Length L, t, w, da, b, cm12cmPotential
32、difference V V1VAThe factors relate SI units to the units of measurement as in the following example:1 m=102 cmBThis 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 cm2. The proper conversion factoris:1Vscm2=108gaussF76
33、 08 (2016)12like which may shunt some of the current around the sample.Since high values of lead capacitance may lengthen the timerequired 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
34、 ofthe magnetic flux will cause the measurements to be inaccu-rate. At best, the method will enable determination only of anundefined average resistivity or Hall coefficient. At worst, themeasurements may be completely erroneous (2, 3, 4).5.1.8 Thermomagnetic effects with the exception of theEttings
35、hausen effect can be eliminated by averaging of themeasured transverse voltages as is specified in the measure-ment procedure (Sections 11 and 17). In general, the error dueto the Ettingshausen effect is small and can be neglected,particularly if the sample is in good thermal contact with itssurroun
36、dings (2, 3, 4).5.1.9 For materials which are anisotropic, especially semi-conductors with noncubic crystal structures, Hall measure-ments are affected by the orientation of the current andmagnetic field with respect to the crystal axes (Appendix, NoteX1.1). Errors can result if the magnetic field i
37、s not within thelow-field limit (Appendix, Note X1.1).5.1.10 Spurious voltages, which may occur in the measuringcircuit, for example, thermal voltages, can be detected bymeasuring the voltage across the specimen with no currentflowing or with the voltage leads shorted at the sampleposition. If there
38、 is a measurable voltage, the measuring circuitshould be checked carefully and modified so that these effectsare eliminated.5.1.11 An erroneous Hall coefficient will be measured if thecurrent and transverse electric field axes are not preciselyperpendicular to the magnetic flux. The Hall coefficient
39、 will beat an extremum with respect to rotation if the specimen isproperly positioned (see 7.4.4 or 13.4.4).5.2 In addition to these interferences the following must benoted for van der Pauw specimens.5.2.1 Errors may result in voltage measurements due tocontacts of finite size. Some of these errors
40、 are discussed inreferences (1, 5, 6).5.2.2 Errors may be introduced if the contacts are not placedon the specimen periphery (7).5.3 In addition to the interferences described in 5.1, thefollowing must be noted for parallelepiped and bridge-typespecimens.5.3.1 It is essential that in the case of par
41、allelepiped orbridge-type specimens the Hall-coefficient measurements bemade on side contacts far enough removed from the endcontacts that shorting effects can be neglected (2, 3). Thespecimen geometries described in 15.3.1 and 15.3.2 are de-signed so that the reduction in Hall voltage due to this s
42、hortingeffect is less than 1 %.TEST METHOD AFOR VAN DER PAUWSPECIMENS6. Summary of Test Method6.1 In this test method, specifications for a van der Pauw (1)test specimen and procedures for testing it are covered. Aprocedure is described for determining resistivity and Hallcoefficient using direct cu
43、rrent techniques. The Hall mobility iscalculated from the measured values.7. Apparatus7.1 For Measurement of Specimen ThicknessMicrometer,dial gage, microscope (with small depth of field and calibratedvertical-axis adjustment), or calibrated electronic thicknessgage capable of measuring the specimen
44、 thickness to 61%.7.2 MagnetA calibrated magnet capable of providing amagnetic flux density uniform to 61.0 % over the area inwhich the test specimen is to be located. It must be possible toreverse the direction of the magnetic flux (either electrically orby rotation of the magnet) or to rotate the
45、test specimen 180about its axis parallel to the current flow.Apparatus, such as anauxiliary Hall probe or nuclear magnetic resonance system,should be available for measuring the flux density to anaccuracy of 61.0 % at the specimen position. If an electro-magnet is used, provision must be made for mo
46、nitoring the fluxdensity during the measurements. Flux densities between 1000and 10 000 gauss are frequently used; conditions governing thechoice of flux density are discussed more fully elsewhere (2, 3,4).7.3 Instrumentation:7.3.1 Current Source, capable of maintaining currentthrough the specimen c
47、onstant to 60.5 % during the measure-ment. This may consist either of a power supply or a battery, inseries with a resistance greater than 200 the total specimenresistance (including contact resistance). The current source isaccurate to 60.5 % on all ranges used in the measurement. Themagnitude of c
48、urrent required is less than that associated withan electric field of 1 Vcm1in the specimen.7.3.2 Electrometer or Voltmeter, with which voltage mea-surements can be made to an accuracy of 60.5 %. The currentdrawn by the measuring instrument during the resistivity andHall voltage measurements shall b
49、e less than 0.1 % of thespecimen current, that is, the input resistance of the electrom-eter (or voltmeter) must be 1000 greater than the resistanceof the specimen.7.3.3 Switching Facilities, used for reversal of current flowand for connecting in turn the required pairs of potential leadsto the voltage-measuring device.7.3.3.1 Representative Circuit, used for accomplishing therequired switching is shown in Fig. 1.7.3.3.2 Unity-Gain Amplifiers, used for high-resistivitysemiconductors, with input impedance greate
