1、Designation: F76 08 (Reapproved 2016)Standard 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 origi
2、naladoption 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.1. Scope1.1 These test methods cover two procedures for measuringthe resistivity
3、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 a singly connected test specimen (without any isolatedholes), homogeneous in thickness, but
4、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 a single type of carrier.1.1.2 Test Method B, Parallelepiped or Bridge-TypeThistest method
5、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 anisotropic semiconductors forwhich the measured parameters depend on the direction ofcurrent flow.
6、 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, a proce-dure for verifying contact quality is given.NOTE 1Practice F418 covers the prepara
7、tion 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 carrier mobili-ties and densities). Some general guidance, applicable tocertain semiconductors an
8、d 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 limited range of resistivitiesand for the semiconductors, germanium, silicon, and galliumars
9、enide. 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 by the test specimen geometryand instrumentation sensitivity.1.5 The values stated in accep
10、table 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, associated with its use. It is theresponsibility of the user of this standard to establish
11、appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3D1125 Test Methods for Electrical Conductivity and Resis-tivity of WaterE2554 Practice for Estimating and Monitoring the Uncer-tainty of Test Re
12、sults of a Test Method Using ControlChart TechniquesF26 Test Methods for Determining the Orientation of aSemiconductive Single Crystal (Withdrawn 2003)4F43 Test Methods for Resistivity of Semiconductor Materi-als (Withdrawn 2003)4F47 Test Method for Crystallographic Perfection of Siliconby Preferent
13、ial Etch Techniques4F418 Practice for Preparation of Samples of the ConstantComposition Region of Epitaxial Gallium Arsenide Phos-phide for Hall Effect Measurements (Withdrawn 2008)41These test methods are under the jurisdiction of ASTM Committee F01 onElectronics and are the direct responsibility o
14、f Subcommittee F01.15 on CompoundSemiconductors.Current edition approved May 1, 2016. Published May 2016. Originallyapproved in 1967. Last previous edition approved in 2008 as F76 08. DOI:10.1520/F0076-08R16.2The boldface numbers in parentheses refer to the list of references at the end ofthese test
15、 methods.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4The last approved version of this historical standa
16、rd is referenced onwww.astm.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States12.2 SEMI Standard:C1 Specifications for Reagents53. Terminology3.1 Definitions:3.1.1 Hall coeffcientthe ratio of the Hall electric field(due to the Hall v
17、oltage) 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 resistivity; it is readily interpreted only in asystem with carriers of one charge type. (See X1.5)3.1.3 resistivityof a material, is the
18、ratio of the potentialgradient parallel to the current in the material to the currentdensity. For the purposes of this method, the resistivity shallalways be determined 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,
19、 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 in Vscm2where:1 Vscm225 108gaussThe units employed and the factors relating them are sum-marized in Table 1.4. Significance and Use4.1
20、In order to choose the proper material for producingsemiconductor devices, knowledge of material properties suchas resistivity, Hall coefficient, and Hall mobility is useful.Under certain conditions, as outlined in the Appendix, otheruseful quantities for materials specification, including thecharge
21、 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 number of sources.5.1.1 Photoconductive and photovoltaic effects can seri-ously influence the observed resistivity, particularly with high
22、-resistivity material. Therefore, all determinations should bemade in a dark chamber unless experience shows that theresults are insensitive to ambient illumination.5.1.2 Minority-carrier injection during the measurement canalso seriously influence the observed resistivity. This interfer-ence is ind
23、icated if the contacts to the test specimen do nothave linear current-versus-voltage characteristics in the rangeused in the measurement procedure. These effects can also bedetected by repeating the measurements over several decadesof current. In the absence of injection, no change in resistivitysho
24、uld 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 temperature coeffi-cient of resistivity. Consequently, the temperature of thespecimen should be known at the time of measurement and the
25、current 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 current isapplied and any circuit time constants have settled.5.1.4 Spurious currents can be introduced in the testingcircuit when the
26、 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 serious problem whenmeasurements are made on high-resistivity specimens. Surfaceeffects can often be observed as a difference in measured
27、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-tion should be paid to possible leakage paths in other parts ofthe circuit such as switches, connectors, wires, cables, and thelike which
28、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 ofthe magnetic flux wi
29、ll cause the measurements to be inaccu-rate. At best, the method will enable determination only of an5Available from Semiconductor Equipment and Materials Institute, 625 Ellis St.,Suite 212, Mountain View, CA 94043.TABLE 1 Units of MeasurementQuantity Symbol SI Unit FactorAUnits ofMeasurementBResist
30、ivity 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 difference V V1VAThe fa
31、ctors 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 08 (2016)2undefined av
32、erage resistivity or Hall coefficient. At worst, themeasurements may be completely erroneous (2, 3, 4).5.1.8 Thermomagnetic effects with the exception of theEttingshausen effect can be eliminated by averaging of themeasured transverse voltages as is specified in the measure-ment procedure (Sections
33、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 itssurroundings (2, 3, 4).5.1.9 For materials which are anisotropic, especially semi-conductors with noncubic crystal structures, Hall measure-men
34、ts 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 is not within thelow-field limit (Appendix, Note X1.1).5.1.10 Spurious voltages, which may occur in the measuringcircuit, for example, th
35、ermal voltages, can be detected bymeasuring the voltage across the specimen with no currentflowing or with the voltage leads shorted at the sampleposition. If there is a measurable voltage, the measuring circuitshould be checked carefully and modified so that these effectsare eliminated.5.1.11 An er
36、roneous Hall coefficient will be measured if thecurrent and transverse electric field axes are not preciselyperpendicular to the magnetic flux. The Hall coefficient 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 int
37、erferences 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 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
38、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 parallelepiped orbridge-type specimens the Hall-coefficient measurements bemade on side contacts far enough removed from the endcontacts th
39、at 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 shortingeffect is less than 1 %.TEST METHOD AFOR VAN DER PAUWSPECIMENS6. Summary of Test Method6.1 In this test method, specifications fo
40、r a van der Pauw (1)test specimen and procedures for testing it are covered. Aprocedure is described for determining resistivity and Hallcoefficient using direct current techniques. The Hall mobility iscalculated from the measured values.7. Apparatus7.1 For Measurement of Specimen ThicknessMicromete
41、r,dial gage, microscope (with small depth of field and calibratedvertical-axis adjustment), or calibrated electronic thicknessgage capable of measuring the specimen thickness to 61%.7.2 MagnetA calibrated magnet capable of providing amagnetic flux density uniform to 61.0 % over the area inwhich the
42、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 test specimen 180about its axis parallel to the current flow.Apparatus, such as anauxiliary Hall probe or nuclear magnetic resonance sys
43、tem,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 monitoring the fluxdensity during the measurements. Flux densities between 1000and 10 000 gauss are frequently used; conditions governing
44、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 constant to 60.5 % during the measure-ment. This may consist either of a power supply or a battery, inseries with a resistance greater th
45、an 200 the total specimenresistance (including contact resistance). The current source isaccurate to 60.5 % on all ranges used in the measurement. Themagnitude of current required is less than that associated withan electric field of 1 Vcm1in the specimen.7.3.2 Electrometer or Voltmeter, with which
46、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 be less than 0.1 % of thespecimen current, that is, the input resistance of the electrom-eter (or voltmeter) must be 1000 greater than th
47、e 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
48、Amplifiers, used for high-resistivitysemiconductors, with input impedance greater than 1000 thespecimen resistance are located as close to the specimen aspossible to minimize current leakage and circuit time-constants(8, 9). Triaxial cable is used between the specimen and theamplifiers with the guar
49、d shield driven by the respectiveamplifier output.This minimizes current leakage in the cabling.The current leakage through the insulation must be less than0.1 % of the specimen current. Current leakage in the specimenholder must be prevented by utilizing a suitable high-resistivityinsulator such as boron nitride or beryllium oxide.7.3.3.3 Representative Circuit, used for measuring high-resistance specimens is shown in Fig. 2. Sixteen single-pole,single-throw, normally open, guarded reed relays are used toconnect
