2. Theorem
2.3 Thermoelectricity
In the three decades from 1821 to 1851, the basic effects were discovered and understood macroscopically, and their applicability to thermometry, power generation, and refrigeration was recognized. The sole lasting contribution in the next 80 years was Altenkirch's derivation of thermoelectric efficiency in 1911. Then in the late 1930s, there began 20 years of progress (figure 2.6) that lead to a microscopic understanding of thermoelectricity and the development of today's materials [35].
The topic of thermal-electric energy conversion phenomena were studied over two century. The thermoelectric effect provides a means by which thermal energy can be converted into electricity can be used for heat pumping or Power generation.
Especially, the solid state cooling and power generation devices which based on thermoelectric effects have been investigated since the Seebeck and Peltier effect were discovered [36, 37].
Figure 2.5 Progress in the figure of merit of thermoelectric materials at room temperature.
Seebeck effect
The Seebeck effect was first presented by Thomas Johann Seebeck in 1821.
This phenomenon related with the generation of a voltage along a conductor when it is subjected to a temperature gradient. Chemical potential cause carriers (electrons or holes) diffuse from the hot side to the cold side, creating an internal electric field that opposes further diffusion. The Seebeck coefficient is defined as the voltage generated per degree of temperature difference between two ends (figure 2.7a).
S V
T δ
= −δ , (2.30)
Peltier effect
The Peltier effect is the reverse of the Seebeck effect and observed in 1834 by Jean Peltier. The Peltier effect describes a phenomenon that carriers carry heat when they flow through a conductor. The heat current IQ is proportional to the current I and the proportionality constant Π is called the Peltier coefficient (figure 2.7b).
IQ = Π •I, (2.31)
Figure 2.6 Definition of the thermaoelectric effects. The conductors A and B are joined at junctions 1 and 2. (a) If these junctions are at different temperature, a Seebeck voltage appears across an opening in one of the conductor. (b) If a current is passed, there is Peltier cooling at one junction and Peltier heating at the other.
A thermoelectric EMF is created in the presence of a temperature difference between two different materials. This usually causes a continuous current to flow in the conductors. The voltage is on the order of hundred and several microvolts per degree in semiconductor and metal, respectively. As two materials are joined together, there will be an excess or deficiency in the energy at the junction. The energy difference make the junction either absorb or emit heat, causing heating or cooling. The Seebeck and the Peltier coefficients are related through the Kelvin relation Π=ST, where T is the absolute temperature. A commercial thermoelectric device is shown in Figure 2.8a, which made of many pairs of p–n legs. P-type and n-type semiconductor elements are welded in the top and bottom sides, such that a current flows through all the elements in series, while the energy they carry leaves the cold or hot side in parallel. The thermoelectric power generator and cooler work in reverse, which shown in Figure 2.8b and 2.8c, respectively. For example, in a power generator the hot side has a higher temperature, electrons and holes are driven to the cold side through diffusion and flow through an external load to do useful work.
N P N P N P N P
(a)
(b)
Loading (c)
Figure 2.7 (a) The actual commercial thermaoelectric device. (b) and (c) are the cooler and power generator, respectively.
The heat energy to electrical power conversion efficiency for a given thermocouple varies with the resistance of the load. Ioffe (1957) showed that the highest efficiency is given by
0.5 figure of merit of the thermocouple. The performance of thermoelectric device depends on the figure of merit (ZT) of the material, given by
S2
ZT σ T
= κ , (2.33)
where S, T, σ and κ are the Seebeck coefficient, absolute temperature, electrical conductivity and thermal conductivity, respectively. From an intuitional view, the reason that the electrical conductivity σ enters Z is due to Joule heating. The thermal conductivity κ appears in the denominator of Z because, in thermoelectric coolers or power generators, the thermoelectric elements also act as the thermal insulation between the hot and the cold sides. The main research issue in thermoelectric materials is to increase power factor (mutilation of Sσ) and decrease thermal conductivity (κ) to cause a large figure of merit.
In the recent two decades, environment-protection concepts lead to renewed activity in the science and technology of alternative energy. The directly usage of solar energy is an important issue. There are two accepted proposes for develop the solid-state energy converter, they are photonic-electric and thermal-electric effects.
The thermal-electric effect related phenomena were observed and studied for a long time. Closely related cooling and power generation mechanisms, thermomagnetic effects and themionic emission, are less well established but may soon have their day.
In bulk materials, the quantities S, σ and κ are inter-related, so that the figure of merit, ZT, is difficult to increase in conventional 3D crystalline systems. For a long time, materials with ZT ~1 were accepted limit of ZT. But the new variable of size gives rise to differences in the density of electronic states, allowing new opportunities to vary S, σ and κ independently. The common picture of dimensional-dependent band structure is shown in figure 2.5. As the dimension decreases from 3D crystalline solids to 2D (quantum wells) to 1D (quantum wires) and finally to OD (quantum dots), new physical phenomena are introduced and new opportunities to vary S, σ and κ independently.
Figure 2.8 Electronic density of states for (a) bulk 3D crystal, (b) 2D quantum well, (c) 1D nanowire and (d) OD quantum dot.
There are three generic approaches have been proposed to date for low-dimensional materials, which described in ref.4. (1) quantum-confinement effects [38]: to enhance density of states near the Fermi energy. Using such effects, a ZT of 0.9 at 300 K and 2.0 at 550 K, using estimated thermal-conductivity values, has been reported [39] in PbSe0.98Te0.02/ PbTe quantum-dot structures. (2) phonon-blocking-electron-transmitting superlattices: These structures utilize the acoustic mismatch between the superlattice components to reduce κL [40-42], thereby potentially eliminating alloy scattering of carriers. (3) thermionic effects in heterostructures. [43] Furthermore, they also report a ZT at 300 K of ~2.4 in p-type Bi2Te3/Sb2Te3 superlattices and a ZT ~1.4 in n-type Bi2Te3/Bi2Te2.83Se0.17
superlattices.
The low-dimensional materials seem owing a lot of different behavior from bulk materials. This gives us the motivation to investigate on electronic and thermodynamic behavior for understanding the fundamentals in nano-physics. In the recent two decades, environment-protection concepts lead to renewed activity in the science and technology of alternative energy. The directly usage of solar energy is an important issue. There are two accepted proposes for develop the solid-state energy converter, they are photonic-electric and thermal-electric effects.
The thermal-electric effect related phenomena were observed and studied for a long time. Closely related cooling and power generation mechanisms, thermomagnetic effects and themionic emission, are less well established but may soon have their day.
Chapter 3
Experimental facilities and measurement methods
Introduction
This chapter introduce equipments for study the samples. Section A of 3.1 gives a bright description of X-ray diffraction (XRD) technique for characterizing the lattice structure of nanowires by the x-ray powder diffraction method. Section B of 3.1 gives the description of Scanning electron microscope (SEM) for determining and observing the geometry dimensions and morphology of samples, respectively.
Section C of 3.1 talks about the sample temperature control system.
The last decays have seen significant developments in thin-film thermal conductivity measurement techniques. However, the characterization of the thermal conductivity of a nanowire remains a challenging task. Usually, thermal conductivity measurements are difficult to make with relatively high accuracy, certainly better than within 5%. Sections of 3.2 descript the methods for us to study the electronic and thermal conductivity. Section A of 3.2 introduces the four-probe method for resistivity measurement. Section B and C of 3.2 gives the detail description for Self-heating 3ω method and Construction of measurement system &
sample holder, respectively.
3.1 Introduction to experimental equipments
3.1.1 X-ray diffraction (XRD)
X-ray diffraction (XRD) is a non-destructive technique that reveals detailed information about the crystallographic structure of natural and manufactured materials.
It’s now a common technique for the study of crystal structures and atomic spacing.
When a monochromatic X-ray beam with wavelength λ is projected onto a crystalline material at an angle θ, diffraction occurs only when the distance traveled by the rays reflected from planes differs by a complete number n of wavelengths when conditions satisfy Bragg's Law (nλ=2d sin θ). This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample.
Conversion of the diffraction peaks to d-spacing allows identification of materials. By varying the angle, the Bragg's Law conditions are satisfied by different d-spacings in polycrystalline materials. Based on the principle of X-ray diffraction, a wealth of structural, physical and chemical information about the material investigated can be obtained. A host of application techniques for various material classes is available, each revealing its own specific details of the sample studied.
The specific wavelengths are characteristic of the target material (Cu, Fe, Mo, Cr). The geometry of an X-ray diffractometer is such that the sample rotates in the path of the collimated X-ray beam at an angle θ while the X-ray detector is mounted on an arm to collect the diffracted X-rays and rotates at an angle of 2θ. The instrument used to maintain the angle and rotate the sample is termed a goniometer. X-ray powder diffraction is the method used for the identification of unknown crystalline materials. In our results, the XRD is performed by the PANalytical X'Pert PRO analysis system.
3.1.2 Scanning electron microscope (SEM)
The scanning electron microscope (SEM) is a type of electron microscope that images the sample surface by scanning it with a high-energy beam of electrons in a raster scan pattern. The electrons interact with the atoms that make up the sample producing signals that contain information about the sample's surface topography, composition and other properties such as electrical conductivity.
The types of signals produced by an SEM include secondary electrons, characteristic x-rays, specimen current and transmitted electrons. These types of signal all require specialized detectors for their detection that are not usually all present on a single machine. The signals result from interactions of the electron beam with atoms at or near the surface of the sample. In the most common or standard detection mode, secondary electron imaging or SEI, the SEM can produce very high-resolution images of a sample surface, revealing details about 1 to 5 nm in size.
Due to the way these images are created, SEM micrographs have a very large depth of field yielding a characteristic three-dimensional appearance useful for understanding the surface structure of a sample. This is exemplified by the micrograph of pollen shown to the right. A wide range of magnifications is possible, from about x 25 (about equivalent to that of a powerful hand-lens) to about x 250,000, about 250 times the magnification limit of the best light microscopes. Characteristic X-rays are emitted when the electron beam removes an inner shell electron from the sample, causing a higher energy electron to fill the shell and release energy. These characteristic x-rays are used to identify the composition and measure the abundance of elements in the sample. The morphology and geometry dimensions of our samples are determined with models Hitachi S-4200 FESEM and Horeba EX-220 energy dispersion spectroscopy.
3.1.3 Magnetic Property Measurement System (MPMS)
The Quantum Design MPMS provides solutions for a unique class of sensitive magnetic measurements in key areas such as high-temperature superconductivity, biochemistry, and magnetic recording media. The modular MPMS design integrates a Superconducting Quantum Interference Device (SQUID) detection system, a precision temperature control unit residing in the bore of a high-field superconducting magnet, and a sophisticated computer operating system. Powerful software controls measurements, making data collection and analysis quick and easy.
3.1.4 Physical Property Measurement System (PPMS)
The Quantum Design PPMS represents a unique concept in laboratory equipment:
an open architecture, variable temperature-field system, designed to perform a variety of automated measurements. Use the PPMS with options designed for it or easily adapt it to your own experiments. Sample environment controls include fields up to
± 5 Tesla and temperature range of 1.8 - 400 K. Its advanced expandable design combines many features in one instrument to make the PPMS the most versatile system of its kind.
3.1.5 Cryostat system
The construction for temperature control system include three main parts, the OXFORD Heliox series 3He refrigerator, sample holder, and control device. The figure below represents a schematic of the. The 3He refrigerator insert can be treated like any sample rod for a variable temperature insert. Once loaded, the insert is cooled from 300K down around 70K using exchange gas. The 3He gas contained in a small dump sitting on top of the insert is then condensed at around 1.5K. Once the
3He pot has reached a stable temperature and condensation is completed, the adsorption pump will start to cool the 3He pot and experimental set-up to below 300 mK. The condensation and the cool down time typically require less than 1 hour.
Meanwhile, a homemade sample holder (Figure 3.1) was mounted together with the commercial heater on the 3He pot. The minimum temperature of this construction is 0.4 K, and in our experience, the temperature of sample can keep at this temperature over 4 hours. Furthermore, the whole temperature control instruments were monitored by a computer through the interface GPIB.
Radiation Shielding
Sample chip
Sample mounting bas
Copper base
Figure 3.1 The sketch of the homemade sample holder with copper base and two layer shields.
3.2 Electronic property measurement methods
3.2.1 Four-probe method
If you wanted to determine the high precise of a resistance, you would probably connect its two leads up to an Ohmmeter and read off the value. This could be a problem, if the resistance you are trying to measure is very small. A voltage source may damage your sample due to the high passing current. Do you know how much current should we use to measure resistance? For this reason, one often determines the resistance of a sample by passing through it a known current I, measuring the resulting voltage drop ΔV, and performing the division to get R = ΔV/I. This might be a direct current, or it might be an alternating current. The constant-current circuit allows us to determine the sample resistance with a very small current eliminating the possibility of damage to the sample, especially for an ultra fine wire.
We now turn to the other issue, the problem of lead resistance. The sample resistance might be so low that the resistance of the leads running to the sample might be significant by comparison. A related problem is that of contact resistance.
Somehow we must connect leads between our sample and the external circuit, and this involves making "contact" to the sample. Contacts are notorious sources of resistance. The situation is illustrated as Figure 3.2a. Let the two contacts to the sample be represented by equivalent resistances RC1 and RC2. The measured voltage drop V = I (RC1 + RS + RC2). How do we know what fraction of the voltage drop V is due to R and how much is due to the contacts? Fact is we have no way of knowing, because we measure their series combination. This is especially a problem if RS is much smaller than RC1 and RC2. Consequently, the resistance of the leads will be in series with the resistance you are trying to measure, so will of course
include to the reading.
The four-probe method is the most common way to separate out the resistivity of conducting materials. This can be seen by looking at the equivalent circuit, shown in the Figure 3.2b. Two of the probes are used for applied current source and the other two probes are used to measure voltage. By separating the current contacts from the voltage contacts we are able to distinguish the sample resistance from that of the contacts and connecting wires. If the voltmeter has an infinite input impedance, no current will flow through the voltage contacts, and the measured voltage drop V is across the portion of the sample that is between the two voltage contacts. Even if R is much smaller than RC1 and RC2, the measured voltage drop is still V = I R.
(a)
Figure 3.2 The sketch for the conditions of leads connection from sample to instruments and the effective circuits. Inset (a) is the 2-probe method. Inset (b) is the 4-probe method.
Using a Lock-in to Measure Resistance
The voltage drop ΔV is measured with an oscilloscope, high sensitive voltmeter, or better yet, with a lock-in amplifier. If you are trying to measure voltages on the order of microvolt, you should consider using a lock-in amplifier. Lock-in amplifiers are ideal for making low-frequency resistance measurements. The basic idea is to replace the direct current source with an oscillator I0sinωt, and to replace the voltmeter with a phase-sensitive-detector. Most lock-in amplifiers combine both of these. The oscillator frequency ω is set to some low value, say 13 Hz. The lock-in is set to use its own internal oscillator as the reference for the PSD. The lock-in is calibrated to read ΔV in RMS-voltage so that the sample resistance R=ΔV/I=(ΔV/ERMS)×RL, where ERMS and RL is the RMS-voltage of the lock-in’s oscillator and a series resistor, respectively. In the circuit above there is an oscilloscope connected to the signal monitor output of the lock-in. It is very important to "look" at what it is that you are measuring; never trust the reading without first viewing the signal. The BNC cable connections are "blown up" on the sample box to show the internal wiring of the box. To be sure, all BNC connectors are connected to the BNC cables as expected.
3.2.2 Self-heating 3ω method
Knowledge of the thermal conductivity of thin films, multilayer thin-film, and wires structures is critical for a wide range of applications in microelectronics, photonics, microelectromechanical systems, and thermoelectric materials [44-47].
Some methods developed for the determination or measurement of thermal conductivity of materials, such as the steady-state technique, the 3ω technique, and the thermal diffusivity measurement. [48] Each of these techniques has its own advantages as well as its inherent limitations, with some techniques more appropriate to specific sample geometry, such as the 3ω technique for individual nanowires. For steady-state method, the thermal conductivity of solids is usually determined by measuring the temperature gradient produced by a steady heat flow in a one-dimensional geometry. Direct measurements of the thermal conductivity, for example, typically require the determination of the heat flux and the temperature drop between two points of the sample. Figure 3.3 shows a typical sample configuration of a bulk system. Unfortunately, these techniques often require large, precisely shaped samples and extreme care to be used successfully. From a practical view, it’s impossible to achieve this setup for thin-film and nanowire system. In order to study thin-film and nanowire system, a technique was developed to measure thermal properties. One important technique is the 3ω method, which take 3rd harmonic signal to measure the thermal and electrical conductivity along longitudinal direction.
The 3ω technique and methods for the measurement of thermal conductivity of nanowires is discussed in detail as follow.
In this method, if the sample is electrically conductive and with a temperature-dependent electric resistance, the specimen itself could serve as a heater as well as a temperature sensor. Feeding an ac electric current of the form I0sinωt
into the specimen creates a temperature fluctuation on it at the frequency 2ω, and
into the specimen creates a temperature fluctuation on it at the frequency 2ω, and