TECHNIQUES FOR MEASURINGRESISTIVITY FOR MATERIALSCHARACTERIZATION––
4200A-SCS PARAMATER ANALYZER APPLICATIONS GUIDETECHNIQUES FOR MEASURING RESISTIVITY FOR
MATERIALS CHARACTERIZATION APPLICATIONS GUIDE
Which Kelvin method is right for your resistivity measurements? The two application notes in this materials
characterization applications guide offer tips and techniques for choosing between the Four-Point Collinear
Probe or van Der Pauw methods based on the type, shape, and thickness of your material and themagnitude of its resistance.

CONTENTS
Resistivity Measurements of Semiconductor Materials
Using the 4200A-SCS Parameter Analyzer and a
Four-Point Collinear Probe........................................... 3
van der Pauw and Hall Voltage Measurements with
the4200A-SCS Parameter Analyzer.............................. 8

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Resistivity Measurements of Semiconductor
Materials Using the 4200A-SCS Parameter Analyzer
and a Four-Point Collinear Probe
Introduction
Electrical resistivity is a basic material property that quantifies

The Four-Point Collinear
Probe Method

a material’s opposition to current flow; it is the reciprocal

The most common way of measuring the resistivity of aof conductivity. The resistivity of a material depends upon
several factors, including the material doping, processing,and environmental factors such as temperature and humidity.
The resistivity of the material can affect the characteristics
of a device of which it’s made, such as the series resistance,
threshold voltage, capacitance, and other parameters.

semiconductor material is by using a four-point collinear
probe. This technique involves bringing four equally spaced
probes in contact with a material of unknown resistance. The
probe array is placed in the center of the material, as shownin Figure 1.
HI

Determining the resistivity of a material is common in bothLO

Source current
from 1 to 4

research and fabrication environments. There are manymethods for determining the resistivity of a material, but theHItechnique may vary depending upon the type of material,V

Measure voltage
between 2 and 3

LO

magnitude of the resistance, shape, and thickness of thematerial. One of the most common ways of measuring
4-Point
Collinear Probethe resistivity of some thin, flat materials, such as
semiconductors or conductive coatings, uses a four-point1

collinear probe. The four-point probe technique involves
bringing four equally spaced probes in contact with a material

2

3

4

Semiconductor Waferof 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 is
calculated from geometric factors, the source current, andthe voltage measurement. The instrumentation used for thistest includes a DC current source, a sensitive voltmeter, and afour-point collinear probe.
To simplify measurements, the 4200A-SCS Parameter

Figure 1. Four-point probe resistivity test circuit

The two outer probes are used for sourcing current and thetwo inner probes are used for measuring the resulting voltage
drop across the surface of the sample. The volume resistivity
is calculated as follows:

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: ρ

π		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 of
wafer 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

APPLICATIONS GUIDEFor some materials such as thin films and coatings, theNotice that the current flows through all the resistances in the

sheet 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: σ = the sheet resistance (Ω/square or just Ω)

not be measured.

probes 2 and 3, the current only flows through RS2, only theNote 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 Kelvin Technique to Eliminate Lead andContact Resistancethe other unwanted lead (RL) and contact (RC) resistances will

Using the 4200A-SCS
to Make Four-Point Probe
Collinear Probe Measurements
The 4200A-SCS comes with a project that is alreadyUsing four probes eliminates measurement errors due toconfigured for automating four-point probe resistivity

the probe resistance, the spreading resistance under eachmeasurements. The project, Four-Point Probe Resistivity

probe, and the contact resistance between each metal

Project, can be found in the Project Library in the Selectprobe and the semiconductor material. Figure 2 is anotherview by selecting the Materials filter. This project has two

representation of the four-point collinear probe setup thattests: one measures the resistivity using a single test current

shows some of the circuit resistances.

and the other measures the resistivity as a function of acurrent sweep. These two tests, Four-Point Probe Resistivity

Source Current

HI

HI
R L1

R L2

Measurement (4-pt-collinear) and Four-Point Probe

LO

Resistivity Sweep (4-pt-resistivity-sweep), can also be found

LO

V

R 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.

1

RC

RC

1

2

3

2

R S1

V
R S2

RC
3

4

RC
4

R S3

Figure 2. Test setup showing circuit resistances

The RL terms represent the test lead resistance. RC

in the Test Library and can be added to a project. A screen
capture of the Four-Point Probe Resistivity Measurement test
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 and
3 of probe) will be used to measure the voltage difference
between the two inner probes. An example of how this is
set up with the 4200A-SCS is shown in Figure 4. One SMU

represents the contact resistance between the metal probe(SMU1) and the GNDU (ground unit) are used to source

and the semiconductor material. The contact resistancecurrent between the outer two probes. The other SMUs

can be several hundred to a thousand times higher than the(SMU2 and SMU3) are used to measure the voltage drop

resistance of the sample material, which is represented by RS.

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

APPLICATIONS GUIDE

Figure 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 to
0A on 1nA range.

SMU3: Set toCurrent Bias (VMU)– Use as high impedance voltmeter,and set current to
0A 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

APPLICATIONS GUIDE

Figure 5. Formulator dialog box with resistivity calculations in the Four Point Probe Resistivity Project.

The voltage difference between SMU2 and SMU3 is

Sources of Error and
Measurement Considerations

calculated: VDIFF=SMU2V-SMU3V. The sheet resistivity

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

sources of errors need to be considered.

The Formulator in the Test Settings pane includes
equations to derive the resistivity as shown in Figure 5.

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. The
shield is made from a conductive material and is always
connected to the low impedance (FORCE LO) terminal of the
SMU instrument.
The cabling in the circuit must also be shielded. Low noise
shielded triax cables are supplied with the 4200A-SCS.

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

APPLICATIONS GUIDE

Leakage Current

Carrier Injection

For high resistance samples, leakage current may degrade

To prevent minority/majority carrier injection from influencing

measurements. The leakage current is due to the insulation

resistivity measurements, the voltage difference between

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

the two voltage sensing terminals should be kept at lesscurrent may be minimized by using good quality insulators, bythan 100mV, ideally 25mV, since the thermal voltage, kt/q, isreducing humidity, and by using guarding.

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

A guard is a conductor connected to a low impedance pointin the circuit that is nearly at the same potential as the highas possible without affecting the measurement precision.

impedance lead being guarded. The inner shield of the triax

Conclusion

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

The 4200A-SCS Parameter Analyzer is an ideal tool forshould be run from the 4200A-SCS to as close as possible tomeasuring resistivity of semiconductor materials using a four-

the sample. Using triax cabling and fixturing will ensure thatpoint collinear probe. The built-in resistivity project and tests

the high impedance terminal of the sample is guarded. The

are configurable and include the necessary calculations.

guard 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

Bibliography
ASTM, F76-86. Standard Method for Measuring Hall Mobilityand Hall Coefficient in Extrinsic Semiconductor Single
Crystals. Annual Bk. ASTM Stds., 1999: 10.05.

measurements, especially on high resistance samples. To

SEMI MF84-02: Test Method for Measuring Resistivity

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

of Silicon Wafers With an In-Line Four-Point Probe. Last

Temperature
Thermoelectric voltages may also affect measurement
accuracy. Temperature gradients may result if the sample
temperature is not uniform. Thermoelectric voltages may
also be generated from sample heating caused by thesource current. Heating from the source current will more
likely affect low resistance samples, because a higher test

published by ASTM International as ASTM F 84-02.
van der Pauw, L. J. A Method of Measuring SpecificResistivity and Hall Effects of Discs of Arbitrary Shape. Phips
Rec. Repts., 1958: 13 1.
Schroder, Dieter K. Semiconductor Material and Device
Characterization. John Wiley & Sons, Inc., 1998.

current is needed to make the voltage measurements easier.

Low Level Measurements, Keithley Instruments, Inc.,

Temperature fluctuations in the laboratory environment

Cleveland, Ohio, 2014.

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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van der Pauw and Hall Voltage Measurementswith the 4200A-SCS Parameter Analyzer
Introduction
Semiconductor material research and device testing often

van der Pauw Resistivity
Measurement Method

involve determining the resistivity and Hall mobility of a

The van der Pauw method involves applying a current

sample. The resistivity of semiconductor material is primarily
dependent on the bulk doping. In a device, the resistivity
can affect the capacitance, the series resistance, and the­threshold voltage.

and meas­uring voltage using four small contacts on thecircumference of a flat, arbitrarily shaped sample of uniform
thickness. This method is particularly useful for measuring
very small samples because geometric spacing of the

The resistivity of the semiconductor material is often

contacts is unimportant. Effects due to a sample’s size,

determined using a four-point probe technique. With a four-which is the approximate probe spacing, are irrelevant.

probe, or Kelvin, technique, two of the probes are used toUsing this method, the resistivity can be derived from a totalsource current and the other two probes are used to measure
voltage. Using four probes eliminates measurement errors
due to the probe resistance, the spreading resistance undereach probe, and the contact resist­ance between each metalof eight measurements that are made around the peripheryof the sample with the configurations shown in Figure 1.
Once all the voltage measurements are taken, two values

probe and the semiconductor material. Because a highof resistivity, ρA and ρB, are derived as follows:

impedance voltmeter draws little current, the voltage dropsπ		(V1 – V2 + V3 – V4)
ρA = ____ fAts _____________________
		ln 2		
4I

across the probe resistance, spreading resist­ance, andcontact resistance are very small.
One common Kelvin technique for determining the resistivityπ		(V5 – V6 + V7 – V8)
ρB = ____ fBts _____________________
		ln 2		
4Iof a semiconductor material is the van der Pauw (VDP)

where: ρA and ρB are volume resistivities in ohm-cm;

method. The 4200A-SCS Parameter Analyzer includes a

ts is the sample thickness in cm;

project for making van der Pauw measurements. Because of
its high input impedance (>1016Ω) and accurate low current
sourcing, the 4200A-SCS with preamps is ideal for highV1–V8 represents the voltages measured by the voltmeter;
I is the current through the sample in amperes;

resistance samples. This application note explains how to

fA and fB are geometrical factors based on sample symmetry.

make resist­ivity measurements of semiconductor materials

They are related to the two resistance ratios QA and QB asusing the 4200A-SCS and the van der Pauw method.

shown in the following equations (fA = fB = 1 for perfect symmetry).
V5

1

2

4

3

V3

1

2

1

2

1

2

4

3

4

3

4

3

V7

V1
V6
1

2

4

3
V2

Figure 1. van der Pauw Resistivity Conventions

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V4

1

2

1

2

1

2

4

3

4

3

4

3

V8

van der Pauw and Hall Voltage Measurementswith the 4200A-SCS Parameter Analyzer

APPLICATIONS GUIDEQA and QB are calculated using the measured voltages

The 4200A-SCS with four SMU instruments and four preamps

as follows:(for high resistance measurements) is an ideal solution for		V
1 – V2
QA = _________
		V3 – V4

meas­uring van der Pauw resistivity, and should enablemeasurements of resistances greater than 1012Ω. Since each
SMU instrument can be configured as a current source or as

		V
5 – V6
QB = _________
		V7 – V8

a voltmeter, no external switching is required, thus eliminatingleakage and offsets errors caused by mechanical switches.
This removes the need for additional instruments andAlso, Q and f are related as follows:
Q – 1		 _______f		_______=
arc coshQ + 1		 0.693		

(

e0.693/f_______
2)

programming.
For high resistance materials, a current source that can

A plot of this function is shown in Figure 2. The value of f can

output very small current with a high output impedance

be found from this plot once Q has been calculated.

is necessary. A differential electrometer with high input

Once ρA and ρB are known, the average resistivity (ρAVG) canbe determined as follows:

sample. On the lowest current source ranges (1pA and 10pA)of the 4200A-SCS, the input resistance of the voltmeterρA + ρB
ρAVG = _________
		 2

is >1016Ω.

Using the 4200A-SCS to
Measure Resistivity with thevan der Pauw Method

1.0
0.9

Each terminal of the sample is connected to one SMU

0.8

f

impedance is required to minimize loading effects on the

instrument, so a 4200A-SCS with four SMU instruments isrequired. The van der Pauw Project, which has four tests,

0.7

is in the Projects Library and can be found by selecting theMaterials box from the Select pane. A screen capture of the0.6

van der Pauw project is shown in Figure 3.

0.5

Each test has a different measurement setup. A diagramof how the four SMU instruments are configured in the

0.4

1

10

100

Q
Figure 2. Plot of f vs. Q

four tests is shown in Figure 4. For each test, three of the
SMU instruments are configured as a current bias and a
voltmeter (VMU). One of these SMU instruments applies thetest current and the other two SMU instruments are usedas high impedance voltmeters with a test current of zero

Test Equipment

amps on a low current range (typically 1nA range). The fourth

The electrical measurements for determining van dercalculated between the two SMU instruments set up as highPauw resistivity require a current source and a voltmeter.

impedance voltmeters. This measurement setup is duplicatedTo automate measurements, one might typically use aaround the sample, with each of the four SMU instruments

programmable switch to switch the current source and thechanging functions in each of the four tests. The test current

voltmeter to all sides of the sample. However, the 4200A-SCS

and voltage differences between the terminals from theis more efficient than this.

four tests are used to calculate the resistivity in the subsite

SMU instrument is set to common. The voltage difference iscalc sheet.

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Figure 3. van der Pauw Project

Test Name:
i4-v12

Test Name:
i2-v34
CommonCurrent Bias (+)

SMU1

SMU2

CommonCurrent Bias (–)

SMU1

SMU2

Voltmeter

Voltmeter

Voltmeter

SMU1

SMU2

SMU1

V12

2

1

2

1

2

1

2

4

3

4

3

4

3

4

3

SMU4

SMU3

V34

Voltmeter

SMU4

SMU3

V34

Voltmeter

Voltmeter

SMU4

SMU3

Current Bias (+)

CommonVoltmeter

CommonVoltmeter

Common

SMU1

SMU2

SMU1

SMU2

1

Voltmeter

2

4

V41

3
SMU3

Current Bias (+)

SMU4

Voltmeter

Current Bias (+)

SMU2

2

1

4

3

4
SMU3

Current Bias (–)

Voltmeter

SMU1

1

Figure 4. SMU Instrument Configurations for van der Pauw Measurements

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SMU4

SMU3

Current Bias (–)

CommonTest Name:
i1-v23

Test Name:
i3-v41

SMU4

SMU2

V12

1

Voltmeter

V41

Voltmeter

SMU4

CommonCurrent Bias (–)

2
3

V23
SMU3

Voltmeter

Voltmeter

SMU1

SMU4

Common

SMU2
1

2

4

3

V23
SMU3

Voltmetervan der Pauw and Hall Voltage Measurementswith the 4200A-SCS Parameter Analyzer

APPLICATIONS GUIDE

Test Configurations for Measuring
van der Pauw Resistivity

are averaged using the AVG function with an equation, such

In each of the four tests, one SMU instrument is configured

located on the Test Settings pane, the average voltage (V23)

as the current source using the current list sweep function,is selected so that it is sent to the subsite data sheet, where it

two SMU instruments are configured as voltmeters, and one

will be used in the resistivity calculation. The magnitude of theis configured as a common. Here is the configuration for thecurrent source must also be sent to the subsite data sheet, so

i1-v23 test:

click that check box (I1) as well.

Terminal 1 – SMU1: Set to a two-point Current List Sweep.

This same procedure is repeated in all four tests so that

Enter both the positive and negative values of the appropriate

all sides of the sample are measured, as shown previously

source current. Enter the Compliance level and use the Bestin Figure 1. The average voltages from each test are thenFixed source range. Averaging voltage measurements (fromused to calculate the resist­ivity on the subsite Calc sheet.

SMU2 and SMU3) taken at both a positive and negative test

A diagram showing how the SMUs are set up in each test is

current will correct for voltage offsets in the circuit.

shown in Figure 4.

Terminal 2 – SMU2: Set to Current Bias (VMU) with a test

Adjusting the Source Current

current of 0A. Set the appropriate compliance voltage, andThe source current value will need to be modified according

check the Measure Voltage box (VB). Even though 0A will
be output, select an appropriate current source range. The
input impedance of the voltmeter is directly related to thecurrent source range. The lower the current source range is,the higher the input impedance will be. However, the lower
the current source range, the slower the measurement timeas V23=AVG(ABSV23). In the Output Values d­ ialog box

to the expected sample resistance. Adjust the current so thatthe voltage difference will not exceed 25mV (approximately).
In each of the four tests (i2-v34, i3-v41, i4-v12, i1-v23), enter
both polarities of the test current. The same magnitude must
be used for each test.

will be. For most applications, the 1nA range may be used.

Determining the Settling Time

However, for very high resistance measurements, use a lower

For high resistance samples, it will be necessary tocurrent range.
Terminal 3 – SMU3: Set up the same as Terminal B.
Terminal 4 – SMU4: Set the Operation Mode to Common.
In this test, the current is sourced between Terminals 1 and
4 (SMU1 to SMU4). SMU2 will measure the voltage fromdetermine the settling time of the measurement. This canbe accomplished by sourcing current into two terminals of
the sample and measuring the voltage difference between
the other two terminals. The settling time can be determinedby graphing the voltage difference versus the time of themeasurement.

Terminal 2 to Terminal 4. SMU3 will measure the voltage from

Using the 4200A-SCS, the voltage versus time graph can

Terminal 3 to Terminal 4.

easily be created by copying and pasting one of the tests

The Formulator calculates the voltage difference between
SMU2 and SMU3 for both the positive and negative test
current. This can be done using an equation such as
V23DIFF=V2-V3. The absolute values of these numbers(from both the positive and negative test current) aretaken using the ABS function with an equation such as
V23ABS=ABS(V23DIFF). The two voltage difference values

described previously. In the Test Settings pane, take a few
hundred or so readings with a sweep time of one second.
Make sure that the Timestamp box is selected. After thereadings are done, plot the voltage difference versus timeon the graph. (You can choose the parameters to graph byusing Graph Settings.) The settling time is determined fromthe graph. A timing graph of a very high resistance material isshown in Figure 5.

WWW.TEK.COM | 11van der Pauw and Hall Voltage Measurementswith the 4200A-SCS Parameter Analyzer

Figure 5. Voltage vs. Time Graph of Very High Resistance Sample

Figure 6. Subsite Data “Calc” Sheet with Resistivity Displayed

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van der Pauw and Hall Voltage Measurementswith the 4200A-SCS Parameter Analyzer

Determine the settling time by visually inspecting the voltage
difference vs. time graph. Once the settling time has been
determined, use this time as the Sweep Delay (in the Test
Settings pane) for the four resistivity measurement tests
listed previously. This settling time procedure will need to berepeated for different materials; however, it is not necessary
for low resistance materials since they have a short

APPLICATIONS GUIDEHall Voltage Measurements
Hall effect measurements are important to semiconductormaterial characterization because from the Hall voltage,
the conductivity type, carrier density, and mobility can bederived. With an applied magnetic field, the Hall voltage canbe measured using the configurations shown in Figure 7.

settling time.

Calculating the Resistivity
To view the calculated resistivity in the subsite level, selectthe subsite plan in the Project Tree. The Output Values

V(voltage differences and test current) will appear on the data

1

2

4

3

V

1

2

4

3

sheet at the subsite level. The resistivity is calculated on the
Calc sheet from the cell references on the Data sheet. The
thickness, coefficients, and correction factors are also input
on the Calc sheet for the resistivity equation.

Figure 7. Hall Voltage Measurement Configurations

With a positive magnetic field, B, apply a current between

These values can be updated in the Calc sheet in theterminals 1 and 3, and measure the voltage drop (V2–4+)

subsite level. Select the subsite “vdp-test.” Go to thebetween terminals 2 and 4. Reverse the current and measure

Subsite Data tab. It contains the output values of the voltage

the voltage drop (V4–2+). Next, apply current between terminals

differences and the test current. From the Calc Sheet tab,2 and 4, and measure the voltage drop (V1–3+) between

the thickness can be adjusted. The default thickness is 1cm.

terminals 1 and 3. Reverse the current and measure theIf necessary, a correction factor can also be applied to thevoltage (V3–1+) again.

resistivity equation.

Reverse the magnetic field, B, and repeat the procedure

Running the Projectagain, measuring the four voltages: (V2–4–), (V4–2–), (V1–3–),

The van der Pauw Project (vdp-resistivity) must be run atand (V3–1–).

the subsite level. Make sure that all boxes in the Project are

From the eight Hall voltage measurements, the average Hall

checked and select the vdp-test subsite. Execute the projectby using the Run button. Each time the test is run, the subsite
data is updated. The voltage differences from each of the four
tests (i2-v34, i3-v41, i4-v12, i1-v23) will appear in the Subsite
Data “vdp-device” sheet. The resistivity will appear in theSubsite Data “Calc” sheet as shown in Figure 6.

coefficient can be calculated as follows:
		t____________________________________s (V4–2+ – V2–4+ + V2–4– – V4–2–)
RHC =
		
4BI
		t____________________________________s (V3–1+ – V1–3+ + V1–3– – V3–1–)
RHD =
		
4BI
where: RHC and RHD are Hall coefficients in cm3/C;
ts is the sample thickness in cm;
V represents the voltages measured by the voltmeter;
I is the current through the sample in amperes;
B is the magnetic flux in Vs/cm2 (1 Vs/cm2 = 108 gauss)
Once RHC and RHD have been calculated, the average Hall
coefficient (RHAVG) can be determined as follows:

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van der Pauw and Hall Voltage Measurementswith the 4200A-SCS Parameter Analyzer

		R
HC + RHDRHAVG = ____________
		2resistance of the cables, probes, and test fixturing. Leakage

From the resistivity (ρAVG) and the Hall coefficient (RHAVG), thereducing humidity, and by using guarding.

mobility (μH) can be calculated:		| RH |
	µH = _____		ρAVG

Using the 4200A-SCS to Measure the Hall Voltage
The setup to measure the Hall voltage is very similar to thesetup for measuring resistivity. The difference is the locationof the current source and voltmeter terminals. Figure 7
illustrates the setup for Hall voltage measurements. (Figure 4
illustrates the setup for resistivity measurements.) If the usersupplied electromagnet has an IEEE-488 interface, a program
can be written in KULT (Keithley User Library Tool) to control
the electromagnet using the 4200A-SCS. This would requirethat the 4200A-SCS have the 4200-COMPILER option.

current may be minimized by using good quality insulators, by

A guard is a conductor connected to a low impedance pointin the circuit that is nearly at the same potential as the highimpedance lead being guarded. The inner shield of the triax
connector of the 4200-SMU is the guard terminal. This guard
should be run from the 4200-SMU to as close as possible tothe sample. Using triax cabling and fixturing will ensure thatthe high impedance terminal of the sample is guarded. The
guard 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

Sources of Error and
Measurement Considerations

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

For successful resistivity measurements, the potential

Thermoelectric voltages may also affect measurement

sources of errors need to be considered.

accuracy. Temperature gradients may result if the sample

Temperaturetemperature is not uniform. Thermoelectric voltages may

Electrostatic Interference

also be generated from sample heating caused by theElectrostatic interference occurs when an electricallysource current. Heating from the source current will morecharged object is brought near an uncharged object. Usually,

likely affect low resistance samples because a higher test

the effects of the interference are not noticeable because

current is needed to make the voltage measurements easier.

the charge dissipates rapidly at low resistance levels.

Temperature fluctuations in the laboratory environment

However, high resistance materials do not allow the charge

may also affect measurements. Since semiconductors

to decay quickly and unstable measurements may result.

have a relatively large temperature coefficient, temperature

The erroneous readings may be due to either DC or AC

variations in the laboratory may need to be compensated forelectrostatic fields.

by using correction factors.

To minimize the effects of these fields, an electrostatic shield

Carrier Injection

can be built to enclose the sensitive circuitry. The shield is

To prevent minority/majority carrier injection from influencing

made from a conductive material and is always connected

resistivity measurements, the voltage difference between theto the low impedance (FORCE LO) terminal of the SMU

two voltage sensing terminals should be kept at less thaninstrument.

100mV, ideally 25mV, given that the thermal voltage, kt/q, is

The cabling in the circuit must also be shielded. Low noise
shielded triax cables are supplied with the 4200A-SCS.

Leakage Current
For high resistance samples, leakage current may degrade
measurements. The leakage current is due to the insulation

14 | WWW.TEK.COM

approximately 26mV. The test current should be kept to as
low as possible without affecting the measurement precision.

van der Pauw and Hall Voltage Measurementswith the 4200A-SCS Parameter Analyzer

APPLICATIONS GUIDE

Bibliography
ASTM, F76-08. Standard Method for Measuring Hall
Mobility and Hall Coefficient in Extrinsic Semiconductor
Single Crystals.
van der Pauw, L. J. A Method of Measuring SpecificResistivity and Hall Effects of Discs of Arbitrary Shape. Philips
Rec. Repts., 1958: 13 1.
Schroder, Dieter K. Semiconductor Material and Device
Characterization. John Wiley & Sons, Inc., 3rd Edition, 2015.
Low Level Measurements, Keithley Instruments, Inc.,
Cleveland, Ohio, 2014.

WWW.TEK.COM | 15

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