1、Designation: F 390 98 (Reapproved 2003)Standard Test Method forSheet Resistance of Thin Metallic Films With a CollinearFour-Probe Array1This standard is issued under the fixed designation F 390; the number immediately following the designation indicates the year oforiginal adoption or, in the case o
2、f revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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
3、collinear four-probearray. 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 suitab
4、le for referee measurementpurposes 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
5、 use. It is the responsibilityof 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:2E 1 Specification for ASTM ThermometersF 388 Method for Mea
6、surement 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 thinning process.3.1.2 thi
7、n metallic filma thin film composed of a materialor materials with resistivity in the range from 108to103Vcm.3.1.3 sheet resistance, Rsin a thin film, the ratio of thepotential gradient parallel to the current to the product of thecurrent density and the film thickness; in a rectangular thinfilm, th
8、e 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 measured direct current throughthe s
9、pecimen 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 spacing.4.2 This test method i
10、ncludes 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 thecondition of the tips.4.2.2 The
11、 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 Assembly:5.1.1 ProbesThe probe shaft
12、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 nominal initial radius of 25
13、to 50 m. In all cases all ofthe four paths from the electrical measurement equipmentinputs to the film surface must be identical.1This test method is under the jurisdiction of ASTM Committee F01 onElectronics and is the direct responsibility of Subcommittee F01.17 on SputteredThin Films.Current edit
14、ion approved May 10, 1998. Published October 1998. Originallypublished as F 390 73 T. Last previous edition F 390 97.2For 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
15、 the standards Document Summary page onthe ASTM website.3Discontinued; see 1992 Annual Book of ASTM Standards, Vol 10.05.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5.1.2 Probe ForceThe probes shall be uniformly loadedto exert a
16、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 Probe CharacteristicsThe probes shall be mountedin an insulating fixture such as a sapphire bearing in a methylme
17、thacrylate 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 film. The spacing shall be 0.64 to 1.00 mm inclusive(0.025 to 0.040 in. inclusive) as agreed upon between thep
18、arties 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 allow theprobes to be lowered perpendicularly onto the surface of thespecimen so that the center of the array is ce
19、ntered 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 source, ammeter, and electrical connections(see 7.2).5.2.2 Voltmeter with input impedance 104times the V/Iratio of t
20、he 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. The recommended current range is from0.01 to 100 mA.5.2.4 Ammeter capable of reading direct current in therange f
21、rom 0.01 to 100 mA to 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 SupportA copper block at least 100 mm(approximately 4 in.) in lateral dimensions and at least 40 mm(approximately 1
22、.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 of the thermometer shall be not morethan 10 mm below the central area of the top of the blockwhere the specime
23、n is to be placed.5.4 Thermometer having a range from 8 to 32C andconforming to the requirements for Thermometer 63C asprescribed in Specification E 1.5.5 Vernier Calipers.5.6 Toolmakers Microscope capable of measuring incre-ments of 2.5 m.6. Test Specimen6.1 The specimen shall consist of a continuo
24、us 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 0.1 m,inclusive; for greater thicknesses, the variation shall be lessthan 65 % of the nominal thickness. The spe
25、cimen 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 of asuitable insulating material.6.2 GeometryMeasure the length, l, and width, w,ofthespecimen with vernier calip
26、ers. Record the values.6.3 Measure the thickness, t, of the film in accordance withMethod F 388.7. Suitability of Test Equipment7.1 Probe AssemblyThe probe spacing and tip conditionshall be established in the following manner. It is recom-mended that this be done immediately prior to a refereemeasur
27、ement.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 by applying theprobes to the surface using normal point pressures. Lift theprobes and move either the specimen
28、 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 indentation sets isobtained.NOTE 1It is recommended that the surface or the probes be movedtwice the usual dis
29、tance 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 stage of thetoolmakers microscope so that the Y-axis readings (YAand YBin Fig. 1) do not differ by more than 0.15
30、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 Calculations:7.1.2.1 For each of the ten sets of measurements calculatethe probe separations, S1j,S2j, and S3j
31、from 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 average value for each of the threeseparations using the Sijcalculated above and the equation:Si5S110D (j 5 110
32、5 Sijwhere the index i successively takes the values 1, 2, and 3(see 7.1.2.1).FIG. 1 Measurement Locations for Typical Probe IndentationPatternF 390 98 (2003)27.1.2.3 Calculate the sample standard deviation sifor eachof the three separations using the Sicalculated in 7.1.2.2, the Sijcalculated in 7.
33、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 1.0821 2 S2/ S!#7.1.3 RequirementsFor the probe assembly to be accept-able it must meet the following
34、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) shall not differ by more than 5 % of S.7.1.3.3 The probe indentations shall not puncture the film.7.2 El
35、ectrical 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.7.2.1 Measure the current through and voltage across astandard resistor whose resistance value is withi
36、n 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 resistance r as follows:r 5S110D(j 5 110riwhere:ri= one of the ten values of resistance determined in
37、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 requirements: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 dev
38、iation 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 apparatus to the twocenter probes.8.2 Connect the current source to the outer two probes.8.3 Equilibrate the
39、 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 probe array towithin6 2. Lower the probe onto the test specimen ensuringthat the center of the probe array
40、 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 CautionSpurious and inaccurate results can arise froma number of sources.8.5.1 It is recommended that, consiste
41、nt 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 resis-tance heating. A drifting of the voltage reading may indicate achange in the resistance due to h
42、eating.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 generators. If equipment is usednear such sources, adequate shielding should be provided.9. Calculations9.1 Cal
43、culate 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 as follows:s 5S13D(j 5 110Ri2 R!2#9.3.1 RequirementFor acceptance of the resistance, thesample standar
44、d 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 width w. Determine the lateralcorrection factor c from Table 1 by means of linear interpola-tion.TABL
45、E 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 . 1.9454 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
46、 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 4.5129 4.5324 4.5324 4.5324 4.5324F 390 98 (2003)39.5 Calculation the ratio of the film thickness t (se
47、e 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 Ft/ S! 3 FspwhereFsp= probe spacing correction factor (see 7.1.2.5).9.7 Calculate the sheet r
48、esistance 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,10.1.1.3 Color,10.1.1.4 Appearance,10.1.1.5 Source, and10.1.1.6 Previous treatment and tests.
49、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 correction factors used.10.1.6 Calculated value of room temperature sheet resis-tance.10.2 Fur
