MEASUREMENT TECHNIQUES FOR CHARACTERIZING
GRAPHENE, CARBON NANOTUBES, AND
NANO-MATERIALS AND DEVICES
LOW POWER, LOW VOLTAGE, LOW RESISTANCE
Measurement Technique for Hall Voltage and Resistivity Measurements
Nanovoltmeter
Vxx
Vxy = Transversal Voltage,
Hall Voltage with
applied B
Technique for Measuring Resistance
as a Function of Gate Voltage
Circuit to Measure Drain Family of
Curves on a Carbon Nanotube
Vxx = Longitudinal
Voltage
Vxx
= R xx
I
CNT
Source
Drain
V
SiO2
Si Gate
Vxy
Graphene
Nanovoltmeter
Ground Unit
or SMU3
(if required)
Graphene
A
SMU1
Steps V
SMU2
Sweeps V
Measures I
A
SiO2
Silicon
Vgate
DC Current Source
Quantum Hall Effect Measurements
on Graphene
Current vs. Voltage Characteristics
of Carbon Nanotube FET
Resistance vs. Gate Voltage
of Graphene Device
Longitudinal Resistance of a Graphene Layer on a Silicon Substrate as a
Function of Substrate Voltage
25000
23000
Hall Voltage
VXY
21000
Rxx (ohms)
19000
Longitudinal
Voltage
VXX
17000
15000
13000
11000
9000
7000
5000
-25
-20
-15
-10
-5
0
5
10
15
20
25
Vsubstrate (volts)
Avoiding Sources of Error When Measuring Low Power Materials and Devices
Noise: External Noise Sources • Low Frequency Noise • Johnson Noise
Use the Delta Mode Method
to Eliminate Voltage Offsets and Noise
The Delta method consists of alternating the current source
•External Noise Sources = interferences
created by motors, computer screens,
or other electrical equipment
polarity and using a moving average of voltage readings to calculate
the resistance. Averaging reduces the noise bandwidth and therefore
•Control these External Noise Sources by:
VM3
DUT
Voltage
2182A
VM1
VEMF
VM2
HI
6220
δV = linearly changing
thermoelectric
voltages
HI
V
LO
Cable
I
DUT
LO
Test
Current
Test Lead Resistance: Eliminate Lead
Resistance by Using the 4-Wire Method
2-Wire Method
4-Wire Method
I
I
V
––Shielding and filtering.
––Remove or turn-off the noise source.
––When using DC instruments, integrate each
measurement for an integer number of power
line cycles. The line cycle noise will “average
out” when the integration time is equal to an
integration number of power line cycles.
V
R Lead
R Lead
R Lead
R S ample
R Lead
R S ample
Measured Resistance:
V M/I = RSample + 2RLead
Measured Resistance:
VM/I = R Sample
Time
Eliminate Thermoelectric Voltage Effects
Voltmeter
Copper Test Leads
Metal A
V
Copper Test Leads
Metal A
•Construct test circuits using the same materials
for interconnects.
V
Sample
Sample – Metal B
Use the Current Reversal Method to
Eliminate Voltage Offsets (VEMF )
Ways to Reduce Thermoelectric Voltages
Voltmeter
T1 Metal B
T2
Measurement with Positive Polarity
•Minimize temperature gradients within the
test circuit.
Measurement with Negative Polarity
V E MF
V E MF
V M+
I+
V M-
I-
R
R
•Allow the test equipment to warm up.
Current Source
Temperature Gradient
Thermoelectric voltages are generated when dissimilar metals (Metal A
and Metal B) in the circuit are at different temperatures (T1 and T2).
V M+ = VEMF + IR
•Use an offset compensation method.
V M- = VEMF - IR
Voltage Measurement:
VM =
VM + VM
V + IR (VEMF
= EMF
2
2
IR )
= IR
Use Instrumentation with Sufficient Sensitivity
Use Appropriate Current Source
Use a Nanovoltmeter to Measure Voltage Drops
• Current source should be bipolar to perform current
reversals to eliminate voltage offsets and reduce noise.
• When measuring the resistances of conductors or other
low power materials, very small voltages are measured,
typically in the microvolt and nanovolt range.
• Current source should be capable of accurately sourcing very low
currents (<1E-6A) for low level test devices and materials.
• To measure these very small voltage drops, use a
sensitive voltmeter such as a nanovoltmeter.
• Verify the product specifications to make sure the measurement resolution and accuracy
are sufficient to perform the sensitive measurement part of your application.
• The current source should have an adjustable voltage
compliance to limit voltage to a safe level to avoid damage to the
device.
• The current source should have constant output so user knows
the exact value forced to the material – unlike using a voltage
source and a resistor.
© Copyright 2011 Keithley Instruments, Inc.
No. 3107
1.11 7K.CG
A Greater Measure of Confidence