1、Designation: F390 11Standard Test Method forSheet Resistance of Thin Metallic Films With a CollinearFour-Probe Array1This standard is issued under the fixed designation F390; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the year
2、 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 This test method covers the measurement of the sheetresistance of metallic thin films with a collinear four-probearray
3、. It is intended for use with rectangular metallic filmsbetween 0.01 and 100 m thick, formed by deposition of amaterial or by a thinning process and supported by aninsulating substrate, in the sheet resistance range from 102to104V/h (see 3.1.3).1.2 This test method is suitable for referee measuremen
4、tpurposes as well as for routine acceptance measurements.1.3 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.1.4 This standard does not purport to address the safetyconcerns, if any, associated with its use. It is the responsib
5、ilityof whoever uses this standard to consult and establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E2251 Specification for Liquid-in-Glass ASTM Thermom-eters with Low-Hazard Precision
6、 LiquidsF388 Method for Measurement of Oxide Thickness onSilicon Wafers and Metallization Thickness by Multiple-Beam Interference (Tolansky Method)33. Terminology3.1 Definitions:3.1.1 thin filma film having a thickness much smaller thanany lateral dimension, formed by deposition of a material or bya
7、 thinning process.3.1.2 thin metallic filma thin film composed of a materialor materials with resistivity in the range from 108to103Vcm.3.1.3 sheet resistance, RsV/hin a thin film, the ratio ofthe potential gradient parallel to the current to the product ofthe current density and the film thickness;
8、 in a rectangular thinfilm, the quotient of the resistance, measured along the lengthof the film, divided by the length, l, to width, w, ratio. The ratiol/w is the number of squares.4. Summary of Test Method4.1 A collinear four-probe array is used to determine thesheet resistance by passing a measur
9、ed direct current throughthe specimen between the outer probes and measuring theresulting potential difference between the inner probes. Thesheet resistance is calculated from the measured current andpotential values using correction factors associated with thegeometry of the specimen and the probe
10、spacing.4.2 This test method includes procedures for checking boththe probe assembly and the electrical measuring apparatus.4.2.1 The spacings between the four probe tips are deter-mined from measurements of indentations made by the tips ina suitable surface. This test also is used to determine thec
11、ondition of the tips.4.2.2 The accuracy of the electrical measuring equipment istested by means of an analog circuit containing a knownstandard resistor together with other resistors which simulatethe resistance at the contacts between the probe tips and thefilm surface.5. Apparatus5.1 Probe Assembl
12、y:5.1.1 ProbesThe probe shaft and tip shall be constructedof tungsten carbide, Monel, hardened tool steel, or hard copperand have a conical tip with included angle of 45 to 90.Alternatively, the tip may be formed from a platinum-palladium alloy and resistance welded to the shaft. The tip shallhave a
13、 nominal initial radius of 25 to 50 m. In all cases all of1This test method is under the jurisdiction of ASTM Committee F01 onElectronics and is the direct responsibility of Subcommittee F01.17 on SputterMetallization.Current edition approved June 1, 2011. Published July 2011. Originally approvedin
14、1973 as F390 73 T. Last previous edition approved in 2003 as F390 98(2003).DOI: 10.1520/F0390-11.2For 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 Docum
15、ent Summary page onthe ASTM website.3Withdrawn. The last approved version of this historical standard is referencedon www.astm.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.the four paths from the electrical measurement equipme
16、ntinputs to the film surface must be identical.5.1.2 Probe ForceThe probes shall be uniformly loadedto exert a force sufficient to deform the metal film butinsufficient to puncture the film. A rough guide for loading is aload of 20 g/Mohs (unit of hardness) of the film material oneach probe.5.1.3 Pr
17、obe CharacteristicsThe probes shall be mountedin an insulating fixture such as a sapphire bearing in a methylmethacrylate or hardened polystyrene block in an equallyspaced linear array. The electrical insulation between adjacentprobe points shall be at least 105times greater than the V/I ratioof the
18、 film. The spacing shall be 0.64 to 1.00 mm inclusive(0.025 to 0.040 in. inclusive) as agreed upon between theparties concerned with the test. The precision and reproduc-ibility of the probe spacing shall be established according to theprocedure of 7.1.5.1.4 Probe SupportThe probe support shall allo
19、w theprobes to be lowered perpendicularly onto the surface of thespecimen so that the center of the array is centered on thespecimen within 610 % of the specimen length l and width w.5.2 Electrical Measuring Apparatus:5.2.1 The electrical apparatus shall consist of a suitablevoltmeter, current sourc
20、e, ammeter, and electrical connections(see 7.2).5.2.2 Voltmeter with input impedance 104times the V/Iratio of the film. A vacuum-tube voltmeter, a digital voltmeter,or similar high-impedance input apparatus is suitable.5.2.3 Current Source with current regulation and stabilityof 60.1 % or better. Th
21、e recommended current range is from0.01 to 100 mA.5.2.4 Ammeter capable of reading direct current in therange from 0.01 to 100 mAto an accuracy of 60.1 % or better.5.2.5 The current source and ammeter are connected to theouter probes; the voltmeter is connected to the inner probes.5.3 Specimen Suppo
22、rtA copper block at least 100 mm(approximately 4 in.) in lateral dimensions and at least 40 mm(approximately 1.5 in.) thick, shall be used to support thespecimen and provide a heat sink. It shall contain a hole thatwill accommodate a thermometer (see 5.4) in such a mannerthat the center of the bulb
23、of the thermometer shall be not morethan 10 mm below the central area of the top of the blockwhere the specimen is to be placed.5.4 Thermometer having a range from 8 to 32C andconforming to the requirements for Thermometer 63C asprescribed in Specification E2251.5.5 Vernier Calipers.5.6 Toolmakers M
24、icroscope capable of measuring incre-ments of 2.5 m.6. Test Specimen6.1 The specimen shall consist of a continuous rectangularthin metallic film with a thickness greater than 0.01 m andless than 100 m. Thickness variation shall be less than 610 %of the nominal thickness for thickness from 0.01 m to
25、0.1 m,inclusive; for greater thicknesses, the variation shall be lessthan 65 % of the nominal thickness. The specimen shall beused as prepared by deposition of a material or by a thinningprocess, with no further cleaning or preparation. The testspecimen shall be supported by a substrate consisting o
26、f asuitable insulating material.6.2 GeometryMeasure the length, l, and width, w,ofthespecimen with vernier calipers. Record the values.6.3 Measure the thickness, t, of the film in accordance withMethod F388.7. Suitability of Test Equipment7.1 Probe AssemblyThe probe spacing and tip conditionshall be
27、 established in the following manner. It is recom-mended that this be done immediately prior to a refereemeasurement.7.1.1 Procedure:7.1.1.1 Make a series of indentations on the surface of thespecimen to be tested or other surface of similar hardness withthe four-probe array. Make these indentations
28、 by applying theprobes to the surface using normal point pressures. Lift theprobes and move either the specimen surface or the probes 0.05to 0.10 mm in a direction perpendicular to a line through theprobe tips. Again apply the probes to the specimen surface.Repeat the procedure until a series of ten
29、 indentation sets isobtained.NOTE 1It is recommended that the surface or the probes be movedtwice the usual distance after every second or every third indentation setin order to assist the operator in identifying the indentations belonging toeach set.7.1.1.2 Place the specimen so indented on the sta
30、ge of thetoolmakers microscope so that the Y-axis readings (YAand YBin Fig. 1) do not differ by more than 0.15 mm (0.006 in.). Foreach of the ten indentation sets record the readings A throughH (defined in Fig. 1) on the X-axis of the toolmakersmicroscope and the readings YAand YBon the Y-axis.7.1.2
31、 Calculations:7.1.2.1 For each of the ten sets of measurements calculatethe probe separations, S1j,S2j, and S3jfrom the equations:S1j5 Cj1 Dj!/2 2 Aj1 Bj!/2,S2j5 Ej1 Fj!/2 2 Cj1 Dj!/2, andS3j5 Gj1 Hj!/2 2 Ej1 Fj!/2where the index j is the set number and has a value from 1to 10.7.1.2.2 Calculate the
32、average value for each of the threeseparations using the Sijcalculated above and the equation:Si5S110D (j 5 1105 SijFIG. 1 Measurement Locations for Typical Probe IndentationPatternF390 112where the index i successively takes the values 1, 2, and 3(see 7.1.2.1).7.1.2.3 Calculate the sample standard
33、deviation sifor eachof the three separations using the Sicalculated in 7.1.2.2, the Sijcalculated in 7.1.2.1, and the equation:si5S13D(j 5 110Sij2 Si!2#7.1.2.4 Calculate the average probe spacing Sas follows:S5S13DS11 S21 S3!7.1.2.5 Calculate the probe spacing correction factor Fspasfollows:Fsp5 1 1
34、 1.0821 2 S2/ S!#7.1.3 RequirementsFor the probe assembly to be accept-able it must meet the following requirements:7.1.3.1 Each of the three sets of ten measurements for Sishall have a sample standard deviation siof less than 1 % of Si.7.1.3.2 The average values of the separations ( S1,S2, andS3) s
35、hall not differ by more than 5 % of S.7.1.3.3 The probe indentations shall not puncture the film.7.2 Electrical EquipmentThe suitability and accuracy ofthe electrical equipment shall be established in the followingmanner. It is recommended that this be done immediately priorto a referee measurement.
36、7.2.1 Measure the current through and voltage across astandard resistor whose resistance value is within a factor often of the V/I ratio of the film to be measured. Perform tentimes.7.2.2 Calculate the resistance rifor the ratio of voltage tocurrent for each measurement.7.2.2.1 Calculate the average
37、 resistance r as follows:r 5S110D(j 5 110riwhere:ri= one of the ten values of resistance determined in 7.2.1.7.2.2.2 Calculate the sample standard deviation as follows:sr5S13D(j 5 110ri2 r!2#7.2.3 RequirementsFor the electrical measuring equip-ment to be suitable, it must meet the following requirem
38、ents:7.2.3.1 The value of r must be within 1.0 % of the knownvalue of r.7.2.3.2 The sample standard deviation srmust be less than1.0 % of r.7.2.3.3 The resolution of the equipment must be such thatdifferences in resistance of 0.05 % can be detected.8. Procedure8.1 Connect the voltage measuring appar
39、atus to the twocenter probes.8.2 Connect the current source to the outer two probes.8.3 Equilibrate the specimen at room temperature (2362C) on the heat-sink block. Record the temperature.8.4 Place the test specimen on the mounting block under theprobe with the length parallel to the line of the pro
40、be array towithin6 2. Lower the probe onto the test specimen ensuringthat the center of the probe array is centered on the specimenwithin 610 % of the specimen length l and width w. Establisha current (see 8.5.1) between the outer probes. Record thevoltage and current. Perform ten times.8.5 CautionS
41、purious and inaccurate results can arise froma number of sources.8.5.1 It is recommended that, consistent with the desiredaccuracy, the applied current be as low as possible to reducespecimen heating. In high resistance or very thin films, it maybe desirable to reduce the specimen current to prevent
42、 resis-tance heating. A drifting of the voltage reading may indicate achange in the resistance due to heating.8.5.2 Wear and deformation of the tips in use may makefrequent inspection and replacement necessary.8.5.3 Spurious currents can be introduced into the testspecimen by high-frequency generato
43、rs. If equipment is usednear such sources, adequate shielding should be provided.9. Calculations9.1 Calculate the specimen resistance Rifrom the ratio ofmeasured voltage and current.9.2 Calculate the average specimen resistance Ras follows:R5S110D(j 5 110Ri9.3 Calculate the sample standard deviation
44、 as follows:s 5S13D(j 5 110Ri2 R!2#9.3.1 RequirementFor acceptance of the resistance, thesample standard deviation s shall be less than 1 % of R.9.4 Calculate the ratio of the specimen width w (see 6.2)tothe average probe separation S(see 7.1.2.4). Calculate the ratioof specimen length l to specimen
45、 width w. Determine the lateralcorrection factor c from Table 1 by means of linear interpola-tion.TABLE 1 Lateral Correction Factor, c, for Rectangular Thin Filmsw/ S, /w=1 , /w=2 , /w=3 , /w=41.00 . . 0.9988 0.99941.25 . . 1.2467 1.22481.50 . 1.4788 1.4893 1.48931.75 . 1.7196 1.7238 1.72382.00 . 1.
46、9454 1.9475 1.94752.50 . 2.3532 2.3541 2.35413.00 2.4575 2.7000 2.7005 2.70054.00 3.1137 3.2246 3.2248 3.22485.00 3.5098 3.5749 3.5750 3.57507.50 4.0095 4.0361 4.0362 4.036210.00 4.2209 4.2357 4.2357 4.235715.00 4.3882 4.3947 4.3947 4.394720.00 4.4516 4.4553 4.4553 4.455340.00 4.5190 4.5129 4.5129 4
47、.5129 4.5324 4.5324 4.5324 4.5324F390 1139.5 Calculation the ratio of the film thickness t (see 6.3)tothe average probe separation S(see 7.1.2.4). Find the correla-tion factor F(t/ S) from Table 2 by means of linear interpola-tion.9.6 Calculate the geometrical correction factor F as follows:F 5 c 3
48、Ft/ S! 3 FspwhereFsp= probe spacing correction factor (see 7.1.2.5).9.7 Calculate the sheet resistance Rsas follows:Rs5 R3 F10. Report10.1 For a referee test the report shall include the following:10.1.1 A description of the specimen, including:10.1.1.1 Type of film,10.1.1.2 Specimen identification,
49、10.1.1.3 Color,10.1.1.4 Appearance,10.1.1.5 Source, and10.1.1.6 Previous treatment and tests.10.1.2 Dimensions and data, including:10.1.2.1 Length and width,10.1.2.2 Average values and standard deviations of probespacing,10.1.2.3 Standard resistor value,10.1.2.4 Measured average value and standard deviation ofstandard resistor, and10.1.2.5 Temperature.10.1.3 Measured values of current and voltage.10.1.4 Calculated average value and standard deviation ofresistance.10.1.5 Values of
