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Summary

This review is in support of a project to develop a more cost-effective, open-source 4-point probe for use in the PV research community.

A great overview of 4-terminal (kelvin) sensing can be found here.

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• 4 Point Probe
• four point probe measurement
• Solar Panel Parameter Extraction
• four point probe

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• four point probe

Solar Panel Characterization

A simple and efficient solar cell parameter extraction method from a single current-voltage curve

Chunfu Zhang, Jincheng Zhang, Yue Hao, Zhenhua Lin, Chunxiang Zue, "A simple and efficient solar cell parameter extraction method from a single current-voltage curve," Journal of Applied Physics, 110(6), 06504, 2011.

• solar panel electrical characteristics can be modeled with several different models of varying complexity/accuracy
  • Single-diode is simplest
• parameters of models are extracted from I-V tests of the panels at varying illumination levels
  • tests can be wrong since illumination can alter properties
• this paper attempts to simplify tests by solving for the panel parameters as a function of only one test with one illumination level.
• results show acceptable amounts of error for the new functions

Four Point Probe (4PP) operation and use

Measurement of sheet resistivities with the four-point probe

F. M. Smits, "Measurement of sheet resistivities with the four-point probe," Bell System Technical Journal, 37(3), 711-718, 1958.

• describes a formula for calculating sheet resistance based on 4PP measurements
  • ps=C(V/I)
  • C is a correctional factor that depends on the geometry of the sample and the distance b/n probes
    • tables of C's are provided
• describes how to calculate body resistivity of a sample
  • p=(V/I)w(pi/ln2)F(w/s)
    • A table is given to find F(w/s)

Resistivity Measurements on Germanium for Transistors

L. B. Valdes, "Resistivity Measurements on Germanium for Transistors," Proceedings of the IRE, 42(2), 420-427, 1954.

• Describes the base technique to using a 4PP for measuring the surface resistivity of a semiconductor sample
  • Germanium is used as an example, but the article states other semiconductors are equivalent
  • requirements and guidelines for accurate measurements are listed
  • Measurement cases are listed
    • For a semi-infinite sample: p=(V/I)2(pi)s
    • measurement near a boundary: p=p0*F_2(l/s)
      • p0 is from semi-infinite sample
      • a relationship is given for F_2(l/s)
    • other boundary cases are presented, all a variation of equation above
      • parallel to nonconducting boundary
      • " conducting boundary
    • conductivity of a thin sample with a conducting base
    • " with a nonconducting base

Four-point probe measurement of non-uniformities in semiconductor sheet resistivity

L. J. Swartzendruber, "Four-point probe measurement of non-uniformities in semiconductor sheet resistivity," Solid-State Electronics, 7(6), 413-422, 1964.

• 4PP measurement technique produce an average resistivity within the vicinity of the measurement
• 4PP are good at measuring nonuniform resistivities with an effective radius above one and a half the probe spacing
• 4PP is more sensitive when the nonuniformity is centered on the voltage probe, and less when it's centered on the current probe
• square array 4PP are always less sensitive to resistivity fluctuations than equaly spaced inline arrays
• nonuniformity sizes can be easily determined by recording reistivity changes across the nonuniformity
• correction factors for measuring circular samples are given

Four-Point Probe Resistance Measurements Using PtIr-Coated Carbon Nanotube Tips

Shinya Yoshimoto, Yuya Murata, Keisuke Kubo, Kazuhiro Tomita, Kenji Motoyoshi, Takehiko Kimura, Hiroyuki Okino, Rei Hobara, Iwao Matsuda, Shin-ichi Honda, Mitsuhiro Katayama, Shuji Hasegawa, "Four-Point Probe Resistance Measurements Using PtIr-Coated Carbon Nanotube Tips," Nano Letters, 7(4) 956-959, 2007.

• measuring electrical properties of nanoscale materials is tough
  • electrical contacts are difficult to attach
  • contacts can damage the sample and/or the probe
• carbon nanotubes make good probes
  • their resistance can be made more reliable using a conductive coating
  • they cause no electrical/mechanical damage to the sample, even after repeated use
• 2-point method flawed due to difficulty in controlling contact resistance
  • could not measure resistance less than 50kOhm
  • 4-point could measure as low as 2Ohm
• Some stuff about tip construction, not important
• stuff about experimental setup
• the 4PP measurements were performed by running a DC sweep between tips 1 and 4, while measuring the current through tips 1 and 4, and the voltage across tips 2 and 3.
  • a 1e6(A/V) preamplifier was used to detect the current
    • current was as large as 2uA
  • voltage measurement current was less than 0.1pA; negligible
• Tip 3 was shifted to adjust the tip spacing.
  • this changed the measured resistance
    • the resistance changed linearly due to the fact that the measured object is a wire; the current can only travel in a straight line
• the CNT tips did not deform, even after repeated use

Variable-Temperature Micro-Four-Point Probe Method for Surface Electrical Conductivity Measurements in Ultrahigh Vacuum

Takehiro Tanikawa, Iwao Matsuda, Rei Hobaru, Shuji Hasegawa, "Variable-Temperature Micro-Four-Point Probe Method for Surface Electrical Conductivity Measurements in Ultrahigh Vacuum," e-Journal of Surface Science and Nanotechnology, 1, 50-56, 2003.

• To measure the electrical characteristics of surface layers, probes need to be really close together
• This paper describes how to manufacture and use probes with ~um spacing
• Measurements were performed in a temperature-controlled UHV chamber
• An excellent description of electronics is given
  • insulating 16 bit DA/AD converter at 100kHz (haven't been able to find their specific model, but devices with similar capabilities are cheap)
  • Amplifed by a INA114 ($10 on mouser) and OP07 (~$1.50 on mouser)

Microfour-point probe for studying electronic transport through surface states

C. L. Petersen, F. Grey, I Shiraki, S. Hasegawa, "Microfour-point probe for studying electronic transport through surface states," Applied Physics Letters, 77(23), 3782-3784, 2000.

• resistivity of a silicon chip was measured using a microscale 4PP
  • 4PP spacings between 8 and 20um were used
• miscroscale probe spacings were used to measure the resistivity of the surface layers

Direct measurement of surface-state conductance by microscopic four-point probe method

Shuji Hasegawa, Ichiro Shiraki, Takehiro Tanikawa, Christian L. Petersen, Torben M. Hansen, Peter Boggild, Francois Grey, "Direct measurement of surface-state conductance by microscopic four-point probe method," Journal of Physics: Condensed Matter, 14(35), 8379, 2002.

• best description of surface layer conductance yet
• Describes the three paths current from a 4PP follows through a sample
  • describes how these paths are affected by probe spacing
• micro 4PP can measure specific areas of a sample
  • useful if you want to avoid/investigate certain defects
  • useful if you want an extremely detailed conductivity map
• tests were run in a UHV chamber on a silicon substrate to validate
• a deposition of one atomic layer of Ag reduced surface resistance by two orders of magnitude
• an explanation of how probe separation affects sheet resistance measurements is given
• charge carriers have a lower mobility on the surface of a substrate
• the authors account for the influence of atomic stepping on their measurements
  • methods are used to transport steps until they form straight terraces
  • micro 4PP measurements can then be taken in step-free or step-clustered regions
  • steps are shown to increase surface resistance

Micro-four-point probe Hall effect measurement method

Dirch H. Petersen, Ole Hansen, Rong Lin, Peter F Nielsen, "Micro-four-point probe Hall effect measurement method," Journal of Applied Physics, 104(1), 013710, 2008.

• describes a non-destructive way to perform hall-effect measurements on a semiconductor
• uses a 4PP to individually measure carrier sheet density and mobility
• describes 4PP theory
• analysis is restricted to thin films with insulating boundaries
• a magnetic field is applied to the sample, followed by a 4PP measurement
  • magnetic field is generated by a permanent magnet
    • note: could the magnetic bearings in our 3d printer system affect measurements?
  • using some formulas, the carrier mobility and density can be determined from this experiment
• used a CAPRES microRSP-M150 system
• highly doped p-type silicon and germanium samples were tested
• a series of 4PP tests were run at varying distances from the insulating boundary

The Potentials of Infinite Systems of Sources and Numerical Solutions of Problems in Semiconductor Engineering

Arthur Uhlir, "The Potentials of Infinite Systems of Sources and Numerical Solutions of Problems in Semiconductor Engineering," Bell System Technical Journal, 34(1), 105-128, 1955.

• Decribes a lot of math involving the voltage differential due to a plane of semi-infinite point sources
• gives correction factors for resistivity measurements on semiconductor samples of various geometries
• use of 4PP on thin slices is generally satisfactory
  • can be innacurate if one side has a conductive coating, corrections provided
  • goes over work by Valdes for calculating resistivity of samples
• some calculations are included for square pattern 4PP
• some calculations for 2PP are included
• calculations are given for measuring resistivity of filaments

Relationship between the correction factor of the four-point probe value and the selection of potential and current electrodes

R. Rymaszewski, "Relationship between the correction factor of the four-point probe value and the selection of potential and current electrodes," Journal of Physics E: Scientific Instruments, 2(2), 170, 1969.

• may not be relevant
  • much of the article was spent discussing effects of sample geometries on a square configuration 4PP
• it did reference an additional article that relates to inline 4PPs

Correction factors for 4-probe electrical measurements with finite size electrodes and material anisotropy: a finite element study

E. J. Zimney, G. H. B. Dommett, R. S. Ruoff, D. A. Dikin, "Correction factors for 4-probe electrical measurements with finite size electrodes and material anisotropy: a finite element study," Measurement Science and Technology, 18(7), 2067, 2007.

• getting accurate resistivity measurements is hard because you need to put in enough current for the voltage drop to be meaureable
• This paper studies 4PP with large electrode that span the sample's surface
• finite element analysis is used to determine correction factors
• assumes linear I-V curve and homogeneous resistivity
• studies anisotropic reistivity measurements with a 4PP (useful for perovskites!)
• matlab is used to perform FE calculations
• studies effect of interface resistance on the measured voltage
• the effect of electrode size is studied
  • for thin samples, electrode size is mostly irrelevant
• anisotropic properties lead to a change in the thicknes of material being measured
• large electrodes effect the measurement

Geometrical Correction Factor for Semiconductor Resistivity Measurements by Four-Point Probe Method

Masato Yamashita, Masahiro Agu, "Geometrical Correction Factor for Semiconductor Resistivity Measurements by Four-Point Probe Method," Japanese Journal of Applied Physics, 23(1-11), 1499-1504, 1984.

• designed for rectangular specimens
• uses conformal transformation and poisson's method to determin correction factors
• Gives correction factors as a function of sample size and thickness
  • Math is over me, but his results may be useful

Measurement of the Sheet Resistivity of a Square Wafer with a Square Four‐Point Probe

Frank Keywell, George Dorosheski, "Measurement of the Sheet Resistivity of a Square Wafer with a Square Four‐Point Probe," Review of Scientific Instruments, 31(8), 833-837, 1960.

• provides correction factor calculations for a square probe on a square sample
  • uses the infinite sheet of dipoles method

Accurate microfour-point probe sheet resistance measurements on small samples

Sune Thorsteinsson, Fei Wang, Dirch H. Petersen, Torben Mikael Hansen, Daniel Kjaer, Rong Lin, Jang-Yong Kim, Peter F. Nielsen, Ole Hansen, "Accurate microfour-point probe sheet resistance measurements on small samples," The Review of Scientific Instruments, 80(5), 053902, 2009.

• Links several articles referring to correction factors
• reviews sheet resistance theory
• use of dual configuration probes is discussed
  • this measurement style reduces the effect of boundaries for circular samples
• discusses formulas for measuring the sheet resistance of small (a few times the probe pin pitch) samples
  • also discusses proper measurement techniques for such samples
  • discusses use of dual configuration M4PPs to ease measurement
    • in some cases correction factors are unecessary

Four‐Point Probe Correction Factors for Use in Measuring Large Diameter Doped Semiconductor Wafers

David S. Perloff, "Four‐Point Probe Correction Factors for Use in Measuring Large Diameter Doped Semiconductor Wafers," Journal of The Electrochemical Society, 123(11), 1745-1750, 1976.

• when probe separation is small compared to the radius of a circular sample, correction factors are easier to calculate
  • equations are given
  • the measurements are orientation independent for this case
• used automat4ed tester for large samples
  • the device used is extremely dated

Empirical method of calibrating a 4-point microarray for measuring thin-film-sheet resistance (*)

R. Rymazewski, "Empirical method of calibrating a 4-point microarray for measuring thin-film-sheet resistance," Electronics Letters, 3(2), 57-58, 1967.

• Looking for article

Reduction of positional errors in a four-point probe resistance measurement

D. C. Worledge, "Reduction of positional errors in a four-point probe resistance measurement," Applied Physics Letters, 84(10), 1695-1697, 2004.

• cites article that claims resistance errors are dominated by positional errors
• there are three permutations of +/-I and +/-V mappings on the probes that provide useful information
• by utilizing more measurements, some errors can be canceled out
  • formulas are given to achieve this
  • the crappier the probe, the greater the improvement

An algorithm for computing linear four-point probe thickness correction factors

Robert A. Weller, "An algorithm for computing linear four-point probe thickness correction factors," Review of Scientific Instruments, 72(9), 3580-3586, 2001.

• Confirms the foundational work by Valdes in computing correction factors
• Combines various other works into a single formula for computing correction factors
  • different forms of varying accuracy and computational expense are given
• a permutation of the formula is given for samples with a conducting substrate
• loses accuracy as t/s -> 0

Sheet resistivity measurements on rectangular surfaces–general solution for four point probe conversion factors (*)

M. A. Logan, "Sheet resistivity measurements on rectangular surfaces-general solution for four point probe conversion factors," Bell System Technical Journal, The, 46(10), 2277-2322, 1967.

• Looking for article

Four Point Probe standards

ASTM F1529-97

Standard Test Method for Sheet Resistance Uniformity Evaluation by In-Line Four-Point Probe with the Dual-Configuration Procedure

PDF

Description

Has been withdrawn, no replacement

• for measuring sheet resistance and its variation
• designed for circular silicon wafers of any size
  • other shapes can be measured, but correction factors need to be included
• may give misleading results if the silicon is formed on an insulator
• can measure from 10mOhms for metal films to 25kOhms for silicon films
• in-line 4PP takes resistivity measurements at multiple locations
  • measurements are taken with current going both directions to eliminate thermoelectric effects
  • before the probe is raised, another measurement is taken, but with the role of each probe changed
  • measurements should be performed in the dark unless the material is light insensitive
  • if minority carrier injection is an issue, run at lower current
  • low current also reduces resistive changes due to heating
  • device should be vibration isolated
  • lightly doped semiconductors can cause erroneous readings
• recommendations are given for various probe types
• a microscope and hot plate is recommended
• constant-current source must be able to produce enough current to drop 5 to 20mV across the specimen
  • currents between 1e-6 and 1e-2A are required if Rsheet is between 1 and 20kOhm
  • output must be stable to 0.01% or better
• ripple and noise must be less than 0.1% of dc level
• standard resistor should be b/n 2.5 to 25 times the sheet resistance
  • know value of standard resistor to 4 sig figs
• voltmeter should read b/n 1 and 100mV, and resolve to 0.01% or better
  • input impedance should be 1e9
• make sure the probe doesn't destroy the sample when you first build it
• some testing procedures are detailed
• sheet resistance calculations are detailed

ASTM F84-02

Standard Test Method for Measuring Resistivity of Silicon Wafers With an In-Line Four-Point Probe

PDF ('98 version)

Description

has been withdrawn, no replacement

• Watch out for voltmeters that emit small currents for auto testing
  • for sheet resistivities over 1000 Ohm-cm, these currents ca cause erroneous measurments
  • can be accounted for by using forward and reverse measurements

ASTM F81 (*)

Test Method for Measuring Radial Resistivity Variation on Silicon Slices

Link

Looking for article

Has been withdrawn, no replacement

ASTM F374 (*)

Test Method for Sheet Resistance of Silicon Epitaxial, Diffused, Polysilicon, and Ion-Implanted Layers Using an In-Line Four-Point Probe

Link

Looking for article

ASTM F1241 (*)

Terminology of Silicon Technology

Link

Looking for article

Four Point Probe designs

a description of the electronics used for measurents is given in this paper.

An AC Bridge for Semiconductor Resistivity Measurements Using a Four-Point Probe

M. A. Logan, "An AC bridge for semiconductor resistivity measurements using a four-point probe," Bell System Technical Journal, The, 40(3), 885-919, 1961.

• describes a measurement circuit that measures the ratio between voltage and current of a 4PP, and thus the resistivity
  • 60's era analog magic
  • built-in calibration
• describes a system that's entirely grounded, ac operated, and devoid of meters save for an ac null detector
  • constant current source is unnecessary
  • independent of frequency
• precision amplifiers are necessary
• describes steps that need to be taken for various resistivity levels
• goes into the effect of constriction resistance
• is sensitive to probe contact resistance
• thermal noise and parasitic probe capacitance is accounted for

Commercial Review