Resistivity Measurements of Semiconductor
Materials Using the 4200A-SCS Parameter
Analyzer and a Four-Point Collinear Probe
––
APPLICATION NOTE
Resistivity Measurements of Semiconductor Materials Using the
4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe
APPLICATION NOTE
Introduction
Electrical resistivity is a basic material property that quantifies
a material’s opposition to current flow; it is the reciprocal
of 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.
Determining the resistivity of a material is common in both
research and fabrication environments. There are many
methods for determining the resistivity of a material, but the
technique may vary depending upon the type of material,
magnitude of the resistance, shape, and thickness of the
material. One of the most common ways of measuring
the resistivity of some thin, flat materials, such as
semiconductors or conductive coatings, uses a four-point
collinear probe. The four-point probe technique involves
bringing four equally spaced probes in contact with a material
of unknown resistance. A DC current is forced between the
outer two probes, and a voltmeter measures the voltage
difference between the inner two probes. The resistivity is
calculated from geometric factors, the source current, and
the voltage measurement. The instrumentation used for this
test includes a DC current source, a sensitive voltmeter, and a
four-point collinear probe.
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 semiconductor
materials because of its high input impedance (>10
16
ohms).
This application note explains how to use the 4200A-SCS
with a four-point collinear probe to make resistivity
measurements on semiconductor materials.
The Four-Point Collinear Probe Method
The most common way of measuring the resistivity of a
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 shown
in
Figure 1.
HI
LO
Source current
from 1 to 4
Measure voltage
between 2 and 3
HI
V
LO
4-Point
Collinear Probe
1
2
3
4
Semiconductor Wafer
Figure 1. Four-point probe resistivity test circuit
The two outer probes are used for sourcing current and the
two inner probes are used for measuring the resulting voltage
drop across the surface of the sample. The volume resistivity
is calculated as follows:
ρ
=
where:
ρ
I
t
π
V
____ __
×
×t×k
ln 2
I
= volume resistivity (Ω-cm)
= the source current (amperes)
= the sample thickness (cm)
probe 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 Four-
Point Probe.
V = the measured voltage (volts)
k* = a correction factor based on the ratio of the
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Resistivity Measurements of Semiconductor Materials Using the
4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe
APPLICATION NOTE
For some materials such as thin films and coatings, the
sheet resistance, or surface resistivity, is determined instead,
which does not take the thickness into account. The sheet
resistance (σ) is calculated as follows:
π
V
V
σ
= ____ ___ k = 4.532 ___ k
ln2 I
I
where:
σ
= the sheet resistance (Ω/square or just
Ω)
Note that the units for sheet resistance are expressed in
terms of
Ω/square
in order to distinguish this number from the
measured resistance (V/I).
Notice that the current flows through all the resistances in the
first and fourth set of leads and probes, as well as through
the semiconductor material. However, the voltage is only
measured between probes 2 and 3. Given that between
probes 2 and 3, the current only flows through R
S2
, only the
voltage drop due to R
S2
will be measured by the voltmeter. All
the other unwanted lead (R
L
) and contact (R
C
) resistances will
not be measured.
Using the 4200A-SCS to Make
Four-Point Probe Collinear Probe
Measurements
The 4200A-SCS comes with a project that is already
configured for automating four-point probe resistivity
measurements. The project,
Four-Point Probe Resistivity
Project,
can be found in the Project Library in the Select
view by selecting the Materials filter. This project has two
tests: one measures the resistivity using a single test current
and the other measures the resistivity as a function of a
current sweep. These two tests, Four-Point Probe Resistivity
Measurement (4-pt-collinear) and Four-Point Probe
Resistivity Sweep (4-pt-resistivity-sweep), can also be found
in the Test Library and can be added to a project. A screen
capture of the
Four-Point Probe Resistivity Measurement
test
Using the Kelvin Technique to Eliminate Lead and
Contact Resistance
Using four probes eliminates measurement errors due to
the probe resistance, the spreading resistance under each
probe, and the contact resistance between each metal
probe and the semiconductor material.
Figure 2
is another
representation of the four-point collinear probe setup that
shows some of the circuit resistances.
Source Current
HI
LO
R
L
= Lead Resistance
R
C
= Contact Resistance
R
S
= Sample Resistance
V = Measured Voltage Between
Probes 2 And 3
Only the voltage drop due to R
S2
is
measured by the voltmeter.
3
is shown in
Figure 3.
The projects and tests included with the 4200A-SCS are
configured 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 will
source 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
(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 may
need to be added in the Test Settings pane to ensure a
settled reading.
HI
R
L1
R
L2
V
LO
R
L3
R
L4
R
C
1
1
R
C
2
2
4
V
R
S2
R
C
3
R
C
4
R
S1
R
S3
Figure 2. Test setup showing circuit resistances
The R
L
terms represent the test lead resistance. R
C
represents the contact resistance between the metal probe
and the semiconductor material. The contact resistance
can be several hundred to a thousand times higher than the
resistance of the sample material, which is represented by R
S
.
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Resistivity Measurements of Semiconductor Materials Using the
4200A-SCS Parameter Analyzer and a Four-Point Collinear Probe
APPLICATION NOTE
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 to
Current Bias (VMU)
– Set current level
to have about a
10mV drop between
SMU2 and SMU3.
Force HI
SMU2:
Set to
Current Bias (VMU)
– Use as high impe-
dance voltmeter,
and set current to
0A on 1nA range.
Force HI
SMU3:
Set to
Current Bias (VMU)
– Use as high impe-
dance voltmeter,
and set current to
0A on 1nA range.
Force HI
GNDU:
Common
connection for all
SMUs. Or, this can
be
SMU4
set to
Common.
Force HI
Figure 4. SMU Instrument Designation for Four-Point Collinear Probe Measurement
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Resistivity Measurements of Semiconductor Materials Using the
4200A-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 is
calculated: VDIFF=SMU2V-SMU3V. The sheet resistivity
(ohms/square) is derived from SMU1 current and voltage
difference calculation, SHEET_RHO=4.532*(VDIFF/SMU1I).
To determine the volume resistivity (ohms-cm), multiply the
sheet resistivity by the thickness of the sample in centimeters
(cm). If necessary, a correction factor can also be applied to
the formula.
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.
Sources of Error and Measurement
Considerations
For successful resistivity measurements, potential sources of
errors need to be considered.
Electrostatic Interference
Electrostatic interference occurs when an electrically
charged object is brought near an uncharged object. Usually,
the effects of the interference are not noticeable because
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.
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