Chapter 2 Thermoelectric material
2.2 Figure of merit
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2.2 Figure of merit
Because thermoelectric materials show the thermoelectric effect in a strong and/or convenient form, it can be demonstrate in power generation and refrigeration.
A figure of merit for the thermoelectric device is defined as Z=S2/ρκ where S is the Seebeck coefficient, ρ is the resistivity, and κ is the thermal conductivity. The performance of a thermoelectric material can be judged by the dimensionless
parameter ZT=S2T/ρκ where T is the use temperature. A greater ZT indicates a greater thermodynamic efficiency. A good thermoelectric material should have high Seebeck coefficient, low resistivity and low thermal conductivity.
Figure 2.5 Schematic dependence of electrical conductivity, Seebeck coefficient, power factor, and thermal conductivity on concentration of free carriers.
[6]
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The electrical conductivity is a reflection of the charge carrier concentration and all three parameters which occur in the figure-of-merit are functions of carrier
concentration. The electrical conductivity increases with increase in carrier
concentration while the Seebeck coefficient decreases, with the electrical power factor maximizing at a carrier concentration of around 1025/cm. The electronic contribution to the thermal conductivity λe, which in thermoelectric materials is generally around 1/3 of the total thermal conductivity, also increases with carrier concentration.
Evidently the figure-of-merit optimizes at carrier concentrations which corresponds to semiconductor materials.
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Chapter 3
Synthesis of nanowires
Introduction
This chapter presents how to synthesize nanowires and the analysis result of the nanowire. Stress-induced method was applied to synthesize nanowires. Section 3.1 introduces the acquired equipment and techniques. Section 3.2 shows how to make the target for the pulsed laser deposition system. Section 3.3 show how to deposit BixSb2-xTe3 thin film by pulsed laser deposition system. Section 3.4 shows the annealing process for growing nanowires. Section 3.5 shows the analysis result of the grown nanowires.
Figure 3.1 Schematic representation of the growth of BixSb2-xTe3 nanowires by stress-induce method. (a) Deposit BixSb2-xTe3 thin films on SiO2/Si substrates by using pulsed laser deposition system. (b) Seal the films in a vacuumed quartz tube. (c) Anneal the films at 350~500 ℃ for 5~21 days (d) Completion of BiSxb2-xTe3 nanowires growth.
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3.1 Experimental equipment and techniques X-ray diffraction (XRD)
X-ray diffraction (XRD) is a common technique for analyzing the crystal structure of materials. Now consider a monochromatic X-ray beam with wavelength λ at an incident angle θ is incident in a crystalline material that the spacing between diffracting planes of the material is d. The path difference of the scattered X-ray by two nearby diffracting plane equals to 2d sin 𝜃 . The scattered X-ray interfere constructively when the path difference of the scattered X-ray equals to an integer multiple of the wavelength. This leads to Bragg law nλ = 2d sin 𝜃. By analyzing the X-ray diffraction pattern, we can identify the structure of materials.
Figure 3.2 Scheme for X-ray diffraction.
Energy-dispersive X-ray spectroscopy (EDS or EDX)
Energy-dispersive X-ray spectroscopy (EDS or EDX) is an analytical technique used for the elemental analysis or chemical characterization of a sample. It relies on the investigation of an interaction of some source of X-ray excitation and a sample. Its characterization capabilities are due in large part to the fundamental principle that each element has a unique atomic structure allowing unique set of peaks on its X-ray spectrum To stimulate the emission of characteristic X-rays from a specimen, a high-energy beam of charged particles such as electrons or protons, or a beam of
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X-rays, is focused into the sample being studied. The incident beam may excite an electron in an inner shell, ejecting it from the shell while creating an electron hole where the electron was. An electron from an outer, higher-energy shell then fills the hole, and the difference in energy between the higher-energy shell and the lower energy shell may be released in the form of an X-ray. As the energy of the X-rays are characteristic of the difference in energy between the two shells, and of the atomic structure of the element from which they were emitted, this allows the elemental composition of the specimen to be measured.
Pulsed laser deposition (PLD)
Pulsed laser deposition is a technique for depositing thin film or making nanoparticle. To deposit thin film, a high power pulsed laser is focused in a vacuum chamber and hit the target. The material which is to be deposited then be vaporized from the target and form a thin film on the substrate. Substituting substrate into liquid nitrogen-cooled copper plate and following a similar procedure in background gas then it can get nanoparticle instead of thin film.
Figure 3.3 Pulsed laser deposition system for nanoparticles and thin film fabrication.
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Scanning electron microscope (SEM)
A scanning electron microscope (SEM) is a type of electron microscope that images a sample by scanning it with a beam of electrons. Electron beam is emitted from an electron gun and be focused by condenser lenses to a spot and interacts with the sample. The energy exchange between the electron beam and the sample results in emission of secondary electrons by inelastic scattering and the emission of electromagnetic radiation, the reflection of high-energy electrons by elastic scattering, each of which can be detected by specialized detectors. The signal then is converted into image and display on the monitor.
Transmission electron microscopy (TEM)
Transmission electron microscopy (TEM) is a microscopy technique whereby a beam of electrons is transmitted through an ultra-thin specimen, interacting with the specimen as it passes through. An image is formed from the interaction of the electrons transmitted through the specimen; the image is magnified and focused onto an imaging device, such as a fluorescent screen, on a layer of photographic film, or to be detected by a sensor such as a CCD camera.
Figure 3.4 Exterior view of TEM and cross section of column.
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high-energy electrons. Because the wavelength of high-energy electrons is a few thousandths of a nanometer and the spacing between atoms in a solid is about a hundred times larger, the atoms act as a diffraction grating to the electrons, which are diffracted. That is, some fraction of them will be scattered to particular angles, determined by the crystal structure of the sample, while others continue to pass through the sample without deflection. As a result, the image on the screen of the TEM will be a series of spots—the selected area diffraction pattern, SADP, each spot corresponding to a satisfied diffraction condition of the sample's crystal structure.3.2 Target preparation
To prepare the target of the pulsed laser deposition system, Bi2Te3 and Sb2Te3 powders were mixed by a particular ratio. The mixed powder is sealed into a vacuumed quartz tube The tube with the powder inside was put into the furnace and heated up to 750℃. The melting point of Bi2Te3 and Sb2Te3 are 585℃ and 580℃
respectively Temperature was kept at 750℃ for a few hours to make sure the Bi2Te3
and Sb2Te3 were form into BixSb2-xTe3 compound. The tube containing the melting compound was slowly cool down to room temperature and formed a bulk. The bulk was cut into ingot. The structure and the composition of the ingot were checked by the XRD and EDX respectively.
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Figure 3.5 X-Ray diffraction pattern of Bi0.5Sb1.5Te3 ingot.
Figure 3.6 EDX spectrum of Bi0.5Sb1.5Te3 ingot.
Table 3.1 The weight percentage and atomic percentage of the Bi0.5Sb1.5Te3 ingot.
Element Weight% Atomic%
Bi 14.48 9.24
Sb 28.4 31.09
Te 57.13 59.68
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Figure 3.7 X-Ray diffraction pattern of Bi1.5Sb0.5Te3 ingot.
Figure 3.8 EDX spectrum of Bi1.5Sb0.5Te3 ingot.
Table 3.2 The weight percentage and atomic percentage of the Bi1.5Sb0.5Te3 ingot.
Element Weight% Atomic%
Bi 40.83 29.51
Sb 8.04 9.97
Te 51.23 60.52
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3.3 Film deposition
Cut the silicon (Si) wafer with 300nm silicon oxide (SiO2) into 9~600mm2 rectangular SiO2/Si substrates. Substrates were cleaned by using acetone, isopropyl alcohol and deionized water in ultrasonic bath for 10 minute each, respectively.
Stick the SiO2/Si substrates on the substrate holder and fix the target on the target holder of the pulsed laser deposition system (PLD). The distance between the target and the substrate was 8 cm. Adjust the laser to focus on the surface of the target.
Vacuum the chamber by rotary pump and cryopump to the pressure lower than 5.0×10-7 torr. Use different power and different frequency of the laser to hit the target for a period of time at room temperature. The total thickness of the formed BixSb2-xTe3 films were ranged from few tens of nanometer to few hundreds of nanometers. The composition of the film is confirm by the EDX
Figure 3.9 SEM image of Bi0.5Sb11.5Te3 thin film that deposited for 1 hour. The power and the frequency of the laser are 170mJ and 10Hz respectively.
The rectangular shows the corresponding area of EDX analysis.
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Figure 3.10 EDX spectrum of Bi0.5Sb1.5Te3 film.
Table 3.3 The weight percentage and atomic percentage of the Bi0.5Sb1.5Te3 film.
Element Weight% Atomic%
Bi 15.00 9.59
Sb 27.86 30.57
Te 57.14 59.83
Figure 3.11 AFM analysis shows that the thickness of the film is about 38nm.
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Figure 3.12 SEM image of Bi1.5Sb0.5Te3 thin film that deposited for 5 min. The power and the frequency of the laser are 160mJ and 30Hz respectively.
The rectangular shows the corresponding area of EDX analysis.
Figure 3.13 EDX spectrum of Bi1.5Sb0.5Te3 film.
Table 3.4 The weight percentage and atomic percentage of the Bi1.5Sb0.5Te3 film.
Element Weight% Atomic%
Bi 42.43 30.90
Sb 7.44 9.30
Te 50.13 59.80
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Figure 3.14 AFM analysis shows that the thickness of the film is about 88nm.
3.4 Annealing process
The films were sealed in a vacuumed quartz tube below the pressure of 5×10-6 mbar and anneal them at 350~500 ℃ for 5~21 days. The thermal expansion coefficient of the BixSb2-xTe3 film (~13.4×10-6/ ℃ ), SiO2 (0.5×10-6/ ℃ ) and Si (2.4×10-6/℃) are different. During the annealing process, the substrate restricted the expansion of the film and put the film under compressive stress. The nanowires then grew from the film in order to release the compressive stress. The films were cooled down in air. Scanning electron microscope (SEM) and optical microscope (OM) were used to observe the nanowire.
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Figure 3.15 OM image of the Bi0.5Sb1.5Te3 thin film after annealing at 350 ℃for 21 days.
Figure 3.16 Side view SEM image of Bi0.5Sb1.5Te3 film after annealing at 350 ℃ for 21 days.
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Figure 3.17 OM image of the Bi1.5Sb10.5Te3 thin film after annealing at 490 ℃for 5 days.
Figure 3.18 Side view SEM image of Bi1.5Sb10.5Te3 film after annealing at 490 ℃ for 5 days.
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3.5 Analysis results
In order to analyze a single nanowire by transmission electron microscopy (TEM), the wire was suspended on a measurement platform so that electron beam can penetrate the wire. The wire is divided into three parts. The end close to the heater is defined as top part. The end away from the heater is defined as bottom part. Between the top and the bottom is the middle part. To see if the wire is well crystalized or not and the growth orientation of the nanowire, selected area diffraction (SAD) was taken.
To see the distribution of the bismuth, antimony and telluride in the wire, EDX line-scan profile was taken. To know the ratio between the three element EDX point scan has been done.
Nanowire No.1
Figure 3.19 SEM image of a suspend nanowire No.1 which grown from Bi0.5Sb1.5Te3 film after annealing at 500 ℃for 5 days. The nanowire is 150 nm in diameter. The electrodes had already deposited by the FIB.
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Figure 3.20 TEM image of the nanowire No. 1.
Figure 3.21 Selected area diffraction pattern of the nanowire No. 1.
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Figure 3.22 The scanning TEM image of (a) top (b) middle (c) bottom part of the nanowire No.1. The EDX line-scan profile show that Bismuth, antimony and telluride homogeneously distributed through the nanowire.
(a)
(b)
(c)
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Figure 3.23 EDX point-scan spectrum of the (a) top (b) middle (c) bottom part of the nanowire No.1. The inset shows the corresponding point.
Table 3.5 Weight percentage and atomic percentage of three parts of the nanowire
Element Atomic% Atom number
Top Middle Bottom Top Middle Bottom
Bi 13.13 13.20 12.87 0.62 0.62 0.62
Sb 29.53 28.88 28.79 1.38 1.38 1.38
Te 57.52 57.92 58.34 2.71 2.71 2.80
(a)
(b)
(c)
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Nanowire No.2
Figure 3.24 SEM image of a suspend nanowire No.2 which grown from Bi1.5Sb0.5Te3 film after annealing at 490 ℃for 5 days. The nanowire is 220 nm in diameter.
Figure 3.25 TEM image of the nanowire No. 2.
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Figure 3.26 TEM image of the nanowire No. 2.
Figure 3.27 Selected area diffraction pattern of the nanowire No. 2.
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Figure 3.28 The scanning TEM image of (a) top (b) middle (c) bottom part of the nanowire No.2. The EDX line-scan profile show that Bismuth, antimony and telluride homogeneously distributed through the nanowire.
(a)
(b)
(c)
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Figure 3.29 EDX point-scan spectrum of the (a) top (b) middle (c) bottom part of the nanowire No.2. The inset shows the corresponding point.
Table 3.6 Weight percentage and atomic percentage of three parts of the nanowire
Element Atomic% Atom number
Top Middle Bottom Top Middle Bottom
Bi 37.54 37.34 37.46 1.66 1.66 1.66
Sb 7.64 7.74 7.57 0.34 0.34 0.34
Te 54.83 54.92 54.97 2.43 2.44 2.44
(a)
(b)
(c)
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conductivity, nanowire was suspended on the measurement platform to allow the temperature fluctuation. In order to measure the thermoelectric properties, electrodes, heater and thermometers were fabricated on the measurement platform. Secstion4.1 introduces the acquired equipment and techniques. Section 4.2 shows how to fabricate the measurement platform and suspend a wire on it. Section 4.4 shows how to measure the thermoelectric properties of the nanowire. Section 4.5 shows the measurement result.4.1 Experimental equipment and techniques Photolithography
Photolithography is a process used in microfabrication to selectively remove parts of a thin film or the bulk of a substrate. It uses light to transfer a pattern from a mask to a light-sensitive chemical photoresist on the substrate. A series of chemical treatments then either engraves the exposure pattern into, or enables deposition of a new material in the desired pattern upon, the material underneath the photo resist.
Dry etch
Dry etching refers to the removal of material, typically a masked pattern of semiconductor material, by exposing the material to a bombardment of ions that dislodge portions of the material from the exposed surface. Unlike with many of the wet chemical etchants used in wet etching, the dry etching process typically etches directionally or anisotropically.
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good process control. Etching a (100) silicon surface through a rectangular hole in a masking material creates a pit with flat sloping <111>-oriented sidewalls and a flat<100>-oriented bottom. The <111>-oriented sidewalls have an angle to the surface of the wafer of: tan−1√2 = 54.7°. If the original rectangle was a perfect square, the pit when etched to completion displays a pyramidal shape.
Lift-off process [7]
A polymer resist layer is patterned first by optical or e-beam lithography.
Metallic thin film is then deposited onto the patterned resist layer. A wet chemical solution dissolves the resist layer, which also lifts off the metallic thin film on top of resist layer from the substrate. Only the metallic film deposited through the resist pattern opening onto the substrate remains. In this way, the resist pattern is transferred onto the substrate as a metallic pattern of reverse polarity.
Focused ion beam (FIB)
FIB systems operate in a similar fashion to a scanning electron microscope (SEM) except, rather than a beam of electrons and as the name implies, FIB systems use a finely focused beam of ions (usually gallium) that can be operated at low beam currents for imaging or high beam currents for site specific sputtering or milling. An FIB can used to deposit material via ion beam induced deposition. FIB-assisted chemical vapor deposition occurs when a gas, such as tungsten hexacarbonyl (W(CO)6) is introduced to the vacuum chamber and allowed to chemisorb onto the sample. By scanning an area with the beam, the precursor gas will be decomposed into volatile and non-volatile components; the non-volatile component, such as tungsten, remains on the surface as a deposition.
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Probe station with micropositioner
A probe station can be used to physically acquire signals from the internal nodes of a semiconductor device. The probe station utilizes manipulators which allow the precise positioning of thin needles on the surface of a semiconductor device. Here, the setup is used for manipulating nanowires. The micropositioner is equip with cat-whisker probe tip and fixed on probe station.
Figure 4.1 Set up of probe station with micropositioner for manipulating nanowire.
Four-point probe method
Current is supplied via a pair of current leads generate a voltage drop across the specimen and also across the current leads themselves. To avoid including that in the measurement, a pair of voltage leads is connected to the specimen. The accuracy of the technique comes from the fact that almost no current flows in the sense wires, so the voltage drop V=RI is extremely low.
Figure 4.2 Four-probe configuration for measuring the resistivity of a wire.
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Resistance thermometer is sensor used to measure temperature by correlating the resistance of the resistance thermometer element with temperature. The temperature dependence of electrical resistance of conductors is to a great degree linear and can be described by the approximation below:
ρ(T) = 𝜌0[𝛼0(𝑇 − 𝑇0)] 𝛼0 = 1 𝜌0[𝛿𝜌
𝛿𝑇]
𝑇=𝑇0
ρ0 just corresponds to the specific resistance temperature coefficient at a specified reference value. That of a semiconductor is however exponential:
ρ(T) = 𝑆𝛼𝐵𝑇
where S is defined as the cross sectional area and α and B are coefficients determining the shape of the function and the value of resistivity at a given temperature.
3ω method for thermal conductivity measurement [8]
In this method, either the specimen itself serves as a heater and at the same time a temperature sensor, if it is electrically conductive and with a temperature-dependent electric resistance. Feeding an ac electric current of the form 𝐼0sin 𝜔𝑡 into the specimen creates a temperature fluctuation on it at the frequency 2ω, and accordingly a resistance fluctuation at 2ω. This further leads to a voltage fluctuation at 3ω across the specimen.
Consider a uniform rod- or filament-like specimen in a four-probe configuration as for electrical resistance measurement. The two outside probes are used for feeding an electric current, and the two inside ones for measuring the voltage across the specimen. The specimen in between the two voltage probes is suspended to allow the temperature fluctuation. All the probes have to be highly thermal conductive, to heat sink the specimen at these points to the substrate. The specimen has to be maintained
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in a high vacuum and the whole setup is heat shielded to the substrate temperature to minimize the radial heat loss through gas convection and radiation.
Figure 4.3 Illustration of the four-probe configuration for measuring the specific heat and thermal conductivity of a wire.
In such a configuration and with an ac electrical current of the form 𝐼0sin 𝜔𝑡
where Cp, κ, R, and ρ are the specific heat, thermal conductivity, electric resistance and mass density of the specimen at the substrate temperature T0, respectively.
𝑅′= (𝑑𝑅/𝑑𝑇)𝑇0. L is the length of the specimen between voltage contacts, and S the cross section of the specimen. Let ∆(𝑥, 𝑡) denote the temperature variation from T0.
i.e. ∆(𝑥, 𝑡) = 𝑇(𝑥, 𝑡) − 𝑇0, Equation (3-1-1) and (3-1-2) become
𝜕
𝜕𝑡∆(𝑥, 𝑡) − 𝛼 𝜕2
𝜕𝑥2∆(𝑥, 𝑡) − 𝑐 sin2𝜔𝑡 ∙ ∆(𝑥, 𝑡) = 𝑏 sin2𝜔𝑡 (4.3) where 𝛼 = 𝜅/𝜌𝐶𝑝 is the thermal diffusivity and b = 𝐼02𝑅/𝜌𝐶𝑝𝐿𝑆, c = 𝐼02𝑅′/𝜌𝐶𝑝𝐿𝑆 The temperature distribution along the specimen would be:
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characteristic thermal time constant of the specimen for the axial thermal process. ∆0 is only κ dependent. The information of Cp is included in the fluctuation amplitude of the temperature around the dc accumulation.By solving the partial difference equation, the resistance fluctuation can be expressed as term at low frequencies, the 3ω component can be express as
𝑉3𝜔(𝑡) ≈ − 2𝐼03𝐿𝑅𝑅′
𝜋4𝜅𝑆√1 + (2𝜔𝛾)2sin(3𝜔𝑡 − 𝜙) (4.6) The root-mean-square (rms) values of voltage across the specimen contains a 3ω component
𝑉3𝜔 ≈ 4𝐼3𝐿𝑅𝑅′
𝜋4𝜅𝑆√1 + (2𝜔𝛾)2 (4.7) By fitting the experimental data to this formula, we can get the thermal conductivity κ
𝜋4𝜅𝑆√1 + (2𝜔𝛾)2 (4.7) By fitting the experimental data to this formula, we can get the thermal conductivity κ