Chapter 4 Thermoelectric property measurements of nanowires
4.2 Nanowires suspension and completion of measurement platform
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4.2 Nanowires suspension and completion of measurement platform
Several methods were used to suspend the nanowire and complete the measurement platform.
Method one
First, the primary measurement platform was immersed in the DI water and put into the ultrasonic cleaner. Then the Si3N4 membrane was broken by the ultrasonic wave to open a window in the primary measurement platform. Next, the nanowire was picked up by a cat–whisker probe tip which manipulated by a micropositioner under the optical microscope. Then the nanowire was suspended on the on the primary measurement platform and deposit the six electrodes by the FIB.
Figure 4.6 Schematic representation of suspend the nanowire and deposit the electrodes by method one. (1)Prepare a primary measurement platform with membrane. (2)Break the membrane by ultrasonic wave. (3)Suspend the wire. (4)Deposit electrode by FIB.
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Figure 4.7 SEM image of a suspended nanowire.
Method two
Put the nanowire on the primary measurement platform. Part of the nanowire was laid on the Si3N4 membrane. The resistance thermometers, current leads and voltage leads would be made by the electron-beam lithography. Two kind of pattern were used in the measurement. Next, the membrane was etched by the ICP or broke by the tip.
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Figure 4.8 Schematic representation of suspend the nanowire and deposit the electrodes by method two. (a) and (b) follow the same procedure but with different pattern. (1)Prepare a primary measurement platform with membrane. (2)Put the wire on the primary measurement platform.
(3)Make the thermometer and electrodes by lift-off process. (4)Remove the membrane.
Figure 4.9 SEM top view image of the suspended nanowire.
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Figure 4.10 SEM tilt view image of the suspended nanowire.
Method three
First, the resistance thermometers, current leads were made by the electron-beam lithography on the primary measurement platform. The Si3N4 membrane can break by the ultrasonic wave, reacting ion, plasma or tungsten tip to open a window. Next, the nanowire was hanged across two resistance thermometers with two ends of the wire attach to the current lead. As two electrodes of the thermometer was also the voltage lead of 4-point probes method, the contacts of the nanowire and thermometer would be covered with a layer of platinum which are deposited by the FIB to make a better contact and also the contact of current leads.
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Figure 4.11 Schematic representation of suspend the nanowire and deposit the electrodes by method three. (1)Make the thermometers on the primary measurement platform by the lift-off process. (2)Break the membrane by ultrasonic wave. (3)Suspend the wire. (4)Deposit a layer of platinum to cover the contact.
Figure 4.12 SEM image of the suspended nanowire.
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4.4 Thermoelectric properties measurement of the nanowire 4.4.1 Resistivity measurement
Four-point probe method was applies to measure the resistivity. Feed an AC current via a pair of current leads into the specimen and measure the root mean square of the voltage difference via a pair of voltage leads. According to V = IR and ρ = RA/ℓ where V, I, R, ρ, A and ℓ are voltage difference, current, resistance, resistivity, cross-section area of the wire and length between a pair of voltage leads respectively, one can get the resistivity of the nanowire.
4.4.2 Seebeck measurement
To get the Seebeck coefficient, temperature gradient is generated by heater across the sample and thermoelectric voltage that is generated by the Seebeck effect is measure. To generate the temperature gradient, the heater is placed at one end of the sample and an AC current with frequency 1ω with magnitude equals to I sin 𝜔𝑡 is applied to the heater. Heater would produce heat because of the Joule heating.
Because heat that produced by the heater is proportional to the square of the current multiplied by the electrical resistance of the wire Q ∝ (𝐼2sin2𝜔𝑡)𝑅 where Q is the heat that produced by the heater and R is the electrical resistance of the sample and sin2𝛼 = (1 − cos 2𝛼 2⁄ ), so the heater would be heated at frequency 2ω. As the heater is heated at frequency 2ω, the temperature fluctuation on the sample would be also at frequency 2ω. As a length of metallic wire or part of the sample is used as the sensor of the thermometer, temperature coefficient of electrical resistance of them are needed to be known at first. As temperature is fluctuated at frequency 2ω, resistance of the sensor would change at frequency 2ω. By apply a DC current to the sensor and measure the change of the voltage difference between the two end of the sensor at frequency 2ω by using lock-in amplifier, it would able to know the resistance change
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of the sensor. Already knowing the temperature coefficient of electrical resistance of the sensor, how much degree different been created between two end of the sample would be known. By knowing the temperature difference and also measuring the thermoelectric voltage of two end of the sample, Seebeck coefficient can be calculated by the formula: S = − △ V △ 𝑇⁄ .
4.4.3 Thermal conductivity measurement
3ω method was applied for the thermal conductivity measurement. The measurement setup is much like the setup of resistivity measurement. The specimen between the two voltage probes should be suspended to allow the temperature fluctuation. Feed an AC current of the form 𝐼0sin 𝜔𝑡 via a pair of current leads into the specimen and lock the V3ω signal via a pair of voltage leads. Theoretical calculation 𝑉3𝜔 ≈ 4𝐼3𝐿𝑅𝑅′⁄𝜋4𝜅𝑆√1 + (2𝜔𝛾)2. By fitting the experimental data to this formula, one can get the thermal conductivity κ and thermal time constant γ of the specimen. Further detail will shoe in the
There are two ways to perform the measurement. In the first, the measurement platform is maintained at fixed temperatures, and then the frequency dependence of V3ω is measured. In this way, we can check the I3 and the 1 √1 + (2𝜔𝛾)⁄ 2 dependencies of V3ω as well as the relation tan 𝜙 = 2𝜔𝛾. In the second way of measurement, the temperature of the measurement platform is slowly increase or decrease, and the working frequency of the lock-in amplifier is changed between a few set values. The maximum working frequency is adjusted by keeping 2ωγ<4.
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Several inner electrode pattern designs are use in the measurement.
Pattern one
For resistivity and thermal conductivity measure, electrodes A and B are current leads. Electrodes C and D are connected to a locking amplifier. For Seebeck measurement, part of the nanowire between the contact of electrode C and E is the high temperature sensor and part of the wire between the contact of electrode D and F is the low temperature sensor. Current via electrode A and B feed into the sensors.
Electrodes C and D is a pair of voltage lead for measuring the voltage difference that is generate by the Seebeck effect.
Figure 4.13 Schematic representation of pattern one
Pattern two
For resistivity and thermal conductivity measure, electrodes A and B are current leads. Electrodes C and D are connected to a locking amplifier to lock the V1ω and V3ω signal. For Seebeck measurement, a length of gold wire vertical to the heater between the contact of electrode G and H is the high temperature sensor of the thermometer Th and a length of gold wire between the contact of electrode I and J is the low temperature sensor of the thermometer Tc. Current via electrode E and F feed into the thermometer Th and Tc. Electrodes C and D is a pair of voltage lead for measuring the voltage difference that is generate by the Seebeck effect.
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Figure 4.14 Schematic representation of pattern two
Pattern three
For resistivity and thermal conductivity measure, electrodes A and B are current leads. Electrodes C and D are connected to a locking amplifier to lock the V1ω and V3ω signal. For Seebeck measurement, current via electrode C and E feed into the thermometer Th and via electrode D and F feed into the thermometer Th. A length of gold wire parallel to the heater between the contact of electrode H and G is the high temperature sensor of the thermometer Th and a length of gold wire between the contact of electrode I and J is the low temperature sensor of the thermometer Tc. Electrodes C and D is a pair of voltage lead for measuring the voltage difference that is generate by the Seebeck effect..
Figure 4.15 Schematic representation of pattern three
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Bi0.62Sb1.38Te2.74 nanowire with diameter 150nm was excited by a constant alternating current about 0.1μA, where it is a sine wave 𝐼0sin 𝜔𝑡 profile with constant frequency f=9.731Hz. The experimental data of resistivity in temperature range 3.5 – 300 K of the nanowire was shown in Figure 4.16. The corresponding voltage signal with less than two degree shift was picked up by the lock-in amplifier (Figure4.17).0 50 100 150 200 250 300
Figure 4.16 The resistivity of the Bi0.6Sb1.4Te3 nanowire with diameter 150nm.
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Figure 4.17 The temperature dependence of the phase angle of V.