Resistivity Measurements of Semiconductor
Materials Using the 4200A-SCS ParameterAnalyzer and a Four-Point Collinear Probe––APPLICATION NOTE

Resistivity Measurements of Semiconductor Materials Using the4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe

APPLICATION NOTEIntroduction

The Four-Point Collinear Probe Method

Electrical resistivity is a basic material property that quantifies

The most common way of measuring the resistivity of aa material’s opposition to current flow; it is the reciprocal

semiconductor material is by using a four-point collinearof conductivity. The resistivity of a material depends uponprobe. This technique involves bringing four equally spaced

several factors, including the material doping, processing,probes in contact with a material of unknown resistance. Theand environmental factors such as temperature and humidity.

probe array is placed in the center of the material, as shown

The resistivity of the material can affect the characteristics

in Figure 1.

of a device of which it’s made, such as the series resistance,
threshold voltage, capacitance, and other parameters.

HILO

Source current
from 1 to 4

Determining the resistivity of a material is common in bothresearch and fabrication environments. There are manyHImethods for determining the resistivity of a material, but theVMeasure voltage
between 2 and 3

LOtechnique may vary depending upon the type of material,
magnitude of the resistance, shape, and thickness of the4-Point
Collinear Probematerial. One of the most common ways of measuring
the resistivity of some thin, flat materials, such as

1

semiconductors or conductive coatings, uses a four-point
collinear probe. The four-point probe technique involves

234Semiconductor Wafer

bringing four equally spaced probes in contact with a materialof unknown resistance. A DC current is forced between theouter two probes, and a voltmeter measures the voltage
difference between the inner two probes. The resistivity isFigure 1. Four-point probe resistivity test circuit

calculated from geometric factors, the source current, andThe two outer probes are used for sourcing current and thethe voltage measurement. The instrumentation used for thistwo inner probes are used for measuring the resulting voltage

test includes a DC current source, a sensitive voltmeter, and adrop across the surface of the sample. The volume resistivity

four-point collinear probe.

is calculated as follows:

To simplify measurements, the 4200A-SCS Parameter
Analyzer comes with a project that contains tests for making
resistivity measurements using a four-point collinear probe.
The 4200A-SCS can be used for a wide range of material
resistances including very high resistance semiconductormaterials because of its high input impedance (>1016 ohms).
This application note explains how to use the 4200A-SCS
with a four-point collinear probe to make resistivity
measurements on semiconductor materials.

ρ=where: ρπ		V______××t×k
ln 2		 I
= volume resistivity (Ω-cm)

V = the measured voltage (volts)I= the source current (amperes)t= the sample thickness (cm)k* = a correction factor based on the ratio of theprobe to wafer diameter and on the ratio ofwafer thickness to probe separation* The correction factors can be found in standard four-point probe
resistivity test procedures such as SEMI MF84-02—Test Method
for Measuring Resistivity of Silicon Wafers with an In-Line FourPoint Probe.

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Resistivity Measurements of Semiconductor Materials Using the4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe

APPLICATION NOTE

For some materials such as thin films and coatings, theNotice that the current flows through all the resistances in thesheet resistance, or surface resistivity, is determined instead,first and fourth set of leads and probes, as well as throughwhich does not take the thickness into account. The sheet

the semiconductor material. However, the voltage is only

resistance (σ) is calculated as follows:

measured between probes 2 and 3. Given that between		π V		 Vσ = ____ ___ k = 4.532 ___ k		 ln2 I		I

voltage drop due to RS2 will be measured by the voltmeter. All

where:

not be measured.

probes 2 and 3, the current only flows through RS2, only thethe other unwanted lead (RL) and contact (RC) resistances willσ = the sheet resistance (Ω/square or just Ω)
Note that the units for sheet resistance are expressed interms of Ω/square in order to distinguish this number from themeasured resistance (V/I).

Using the 4200A-SCS to Make
Four-Point Probe Collinear Probe
MeasurementsThe 4200A-SCS comes with a project that is alreadyUsing the Kelvin Technique to Eliminate Lead andContact Resistanceconfigured for automating four-point probe resistivity

Using four probes eliminates measurement errors due toProject, can be found in the Project Library in the Selectthe probe resistance, the spreading resistance under eachview by selecting the Materials filter. This project has twoprobe, and the contact resistance between each metal

tests: one measures the resistivity using a single test current

probe and the semiconductor material. Figure 2 is anotherand the other measures the resistivity as a function of ameasurements. The project, Four-Point Probe Resistivity

representation of the four-point collinear probe setup thatcurrent sweep. These two tests, Four-Point Probe Resistivity

shows some of the circuit resistances.

Measurement (4-pt-collinear) and Four-Point Probe
Resistivity Sweep (4-pt-resistivity-sweep), can also be foundSource Current

HIHI
R L1

R L2

in the Test Library and can be added to a project. A screen

LOcapture of the Four-Point Probe Resistivity Measurement testLOVR L3

R L4

R L = Lead ResistanceR C = Contact ResistanceR S = Sample ResistanceV = Measured Voltage Between
Probes 2 And 3
Only the voltage drop due to RS2 ismeasured by the voltmeter.

1RCRC12R S132VR S2RC34RC4R S3Figure 2. Test setup showing circuit resistances

The RL terms represent the test lead resistance. RCrepresents the contact resistance between the metal probe
and the semiconductor material. The contact resistancecan be several hundred to a thousand times higher than theresistance of the sample material, which is represented by RS.

is shown in Figure 3.
The projects and tests included with the 4200A-SCS areconfigured to use either three or four SMUs (Source Measure
Units). When using three SMUs, all three SMUs are set
to Current Bias (voltmeter mode). However, one SMU willsource current (pin 1 of probe) and the other two (pins 2 and3 of probe) will be used to measure the voltage difference
between the two inner probes. An example of how this isset up with the 4200A-SCS is shown in Figure 4. One SMU(SMU1) and the GNDU (ground unit) are used to source
current between the outer two probes. The other SMUs
(SMU2 and SMU3) are used to measure the voltage drop
between the two inner probes.
When configuring the tests, enter an appropriate test current
for SMU1. This will depend on the resistivity of the sample.
For higher resistance samples, additional Interval time mayneed to be added in the Test Settings pane to ensure asettled reading.

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Resistivity Measurements of Semiconductor Materials Using the4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe

APPLICATION NOTEFigure 3. Screen Capture of Four-Point Probe Resistivity Measurement Test in the Clarius software

Using the Formulator,
calculate the voltage
difference between
SMU2 and SMU3.
SMU1: Set toCurrent Bias (VMU)– Set current levelto have about a
10mV drop between
SMU2 and SMU3.

SMU2: Set toCurrent Bias (VMU)– Use as high impedance voltmeter,and set current to0A on 1nA range.

SMU3: Set toCurrent Bias (VMU)– Use as high impedance voltmeter,and set current to0A on 1nA range.

GNDU: Common
connection for all
SMUs. Or, this canbe SMU4 set toCommon.

Force HI

Force HI

Force HI

Force HI

Figure 4. SMU Instrument Designation for Four-Point Collinear Probe Measurement

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Resistivity Measurements of Semiconductor Materials Using the4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe

APPLICATION NOTE

Figure 5. Formulator dialog box with resistivity calculations in the Four Point Probe Resistivity Project.
The Formulator in the Test Settings pane includes
equations to derive the resistivity as shown in Figure 5.
The voltage difference between SMU2 and SMU3 isSources of Error and Measurement
Considerations

calculated: VDIFF=SMU2V-SMU3V. The sheet resistivity

For successful resistivity measurements, potential sources of(ohms/square) is derived from SMU1 current and voltage

errors need to be considered.

difference calculation, SHEET_RHO=4.532*(VDIFF/SMU1I).
To determine the volume resistivity (ohms-cm), multiply theElectrostatic Interference

sheet resistivity by the thickness of the sample in centimeters

Electrostatic interference occurs when an electrically(cm). If necessary, a correction factor can also be applied tocharged object is brought near an uncharged object. Usually,the formula.

the effects of the interference are not noticeable because

After the test is configured, lower the probe head so the pins
are in contact with the sample. Execute the test by selecting
Run at the top of the screen. The resistivity measurements
will appear in the Sheet in the Analyze view.

the charge dissipates rapidly at low resistance levels.
However, high resistance materials do not allow the charge
to decay quickly and unstable measurements may result.
The erroneous readings may be due to either DC or AC
electrostatic fields.
To minimize the effects of these fields, an electrostatic
shield can be built to enclose the sensitive circuitry. Theshield is made from a conductive material and is always
connected to the low impedance (FORCE LO) terminal of theSMU instrument.

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Resistivity Measurements of Semiconductor Materials Using the4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe

APPLICATION NOTE

The cabling in the circuit must also be shielded. Low noise

Carrier Injection

shielded triax cables are supplied with the 4200A-SCS.

To prevent minority/majority carrier injection from influencing

Leakage Current

resistivity measurements, the voltage difference between
the two voltage sensing terminals should be kept at less

For high resistance samples, leakage current may degrade

than 100mV, ideally 25mV, since the thermal voltage, kt/q, ismeasurements. The leakage current is due to the insulation

approximately 26mV. The test current should be kept as low

resistance of the cables, probes, and test fixturing. Leakage

as possible without affecting the measurement precision.

current may be minimized by using good quality insulators, byreducing humidity, and by using guarding.

Conclusion

A guard is a conductor connected to a low impedance point

The 4200A-SCS Parameter Analyzer is an ideal tool forin the circuit that is nearly at the same potential as the highmeasuring resistivity of semiconductor materials using a four-impedance lead being guarded. The inner shield of the triax

point collinear probe. The built-in resistivity project and tests

connector of the 4200A-SCS is the guard terminal. This guard

are configurable and include the necessary calculations.

should be run from the 4200A-SCS to as close as possible tothe sample. Using triax cabling and fixturing will ensure thatthe high impedance terminal of the sample is guarded. Theguard connection will also reduce measurement time since
the cable capacitance will no longer affect the time constantof the ­measurement.

Light
Currents generated by photoconductive effects can degrade
measurements, especially on high resistance samples. To

Bibliography
ASTM, F76-86. Standard Method for Measuring Hall Mobilityand Hall Coefficient in Extrinsic Semiconductor SingleCrystals. Annual Bk. ASTM Stds., 1999: 10.05.
SEMI MF84-02: Test Method for Measuring Resistivityof Silicon Wafers With an In-Line Four-Point Probe. Last
published by ASTM International as ASTM F 84-02.

prevent this, the sample should be placed in a dark chamber.

van der Pauw, L. J. A Method of Measuring SpecificTemperature

Rec. Repts., 1958: 13 1.

Thermoelectric voltages may also affect measurement

Schroder, Dieter K. Semiconductor Material and Device

accuracy. Temperature gradients may result if the sample

Characterization. John Wiley & Sons, Inc., 1998.

Resistivity and Hall Effects of Discs of Arbitrary Shape. Phips

temperature is not uniform. Thermoelectric voltages may
also be generated from sample heating caused by theLow Level Measurements, Keithley Instruments, Inc.,

source current. Heating from the source current will more

Cleveland, Ohio, 2014.

likely affect low resistance samples, because a higher test
current is needed to make the voltage measurements easier.
Temperature fluctuations in the laboratory environment
may also affect measurements. Because semiconductors
have a relatively large temperature coefficient, temperature
variations in the laboratory may need to be compensated forby using correction factors.

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Resistivity Measurements of Semiconductor Materials Using the4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe

APPLICATION NOTE

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