Recent Progress in Nanostructured Thermoelectric Materials

Transcription

1 Recent Progress in Nanostructured Thermoelectric Materials Author: Tian Liu 1 1 Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen,The Netherlands t.liu.4@student.rug.nl Supervisor: Graeme R. Blake 1 1 Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands g.r.blake@rug.nl Abstract. Thermoelectrics have long been recognized as a cost-effective and pollution-free technology due to their ability to convert heat energy directly into electric energy. The research on thermoelectric materials keeps exhibiting rapid improvement and exciting breakthroughs in the past twenty years due to the extensive investigation on nanostructured thermoelectric materials.more than ten percent in efficiency has been gained from changes in structural features on a length scale seven orders smaller than that of the devices. This paper sets out to explore the basic mechanisms of the thermoelectric effect, summarizes the main methodology for improving the energy conversion efficiency, critically analyzes measurement accuracy issues, and proposes thermoelectric systems with novel nanostructures that should exhibit better efficiency. A discussion of structural design in nanostructured thermoelectric materials is aimed at enhancing the thermoelectric figure of merit in practical applications. Keywords: Nanostructured thermoelectric materials, Nanoscience

2 CONTENTS 2 Contents 1 Introduction Thermoelectric Materials Basic Theory for Improving ZT Measurement Accuracy in Thermoelectrics Thermoelectric Materials in Low Dimensional systems Quantum Well Superlattices One Dimensional Nanowires Bulk Nanostructured Thermoelectric Materials Progress in Bulk Nanostructured Thermoelectric Materials A Strategy to Improve ZT in Nanocomposites Conclusion 15 5 Acknowledgement 16 6 Reference Introduction 1.1. Thermoelectric Materials The global demand for fossil fuels, such as coal and oil, is continuing to increase, meanwhile the growing speed of non-renewable energy consumption results in inevitable environmental degradation. The limits of conventional energy and the environmental concerning both point to find new ways of improving the energy utilization rate. Thermoelectric materials have attracted increasing attention both from the energy and environmental aspects over the past few decades due to the promising high efficiency of converting waste heat into electric energy. A schematic diagram of the structure of a typical thermoelectric device is shown in Figure 1. The electrons in the n-type material and the holes in the p-type material

3 CONTENTS 3 Figure 1. A thermoelectric device with n-type and p-type legs electrically in series and thermally in parallel. From Shakouri [1]. all carry heat away from the bottom metal-semiconductor contact, by which the hot side metal-semiconductor junction is cooled[1], and that is the Seebeck effect. Practical devices are fabricated of multiple pairs of p-type and n-type semiconductor legs to obtain both high current densities and low voltages. The conversion efficiency of thermoelectric materials is related to a quantity named the figure of merit (ZT) which is defined by Altenkirch in 1911 as the relation in Eq. (1). ZT = S2 σt κ = S2 σt κ l + κ e (1) S is the Seebeck coefficient, σ and κ are the electrical and thermal conductivity of the materials respectively. Thermal conductivity consists of two contributors (κ): lattice thermal conductivity (κ l ) and electron thermal conductivity (κ e ). The relation between ZT and efficiency of a thermoelectric device is plotted in Figure 2, where a higher ZT value is directly related to a high device efficiency. The first functioning thermoelectric devices were built in the 1950s and 1960s, with ZT around 1.0 and efficiency about 4%-6% [2]. In the 1990s, materials with high ZT values were explored in the form of low-dimensional systems and on the nanoscale [3]. Until now, two different approaches have been investigated to search for high ZT thermoelectric materials over the past two decades: one is finding and using new classes of bulk thermoelectric materials with complex crystal structures, and the other is studying materials in low dimensional systems and bulk structures embedded

4 CONTENTS 4 Figure 2. Thermoelectric energy conversion as a function of ZT when the cold side temperature is 300K. A higher ZT is directly related to a high device efficiency. From Chen [7]. with nanomaterials. Bulk structures embedded with nanomaterials are usually called bulk nanostructured thermoelectric materials [4, 5, 6]. Nanostructured materials and thermoelectrics have been the subject of significant research in recent years [5], and it is a challenging topic combining materials science, nanoscience and physics. Exploring nanostructured thermoelectric materials is not only useful searching for the next generation of thermoelectric materials exceeding ZT=2.4, and it is also an inspiration for other research areas of nanoscience by gaining better material performance from small features [8]. In this review paper, firstly the basic theory and methodology for improving ZT is introduced, including a discussion of measurement accuracy. After that, the performances of thermoelectric materials in low dimensional systems and bulk nanostructured thermoelectric materials are reviewed. Finally, a designed approach for improving ZT in nanocomposites is proposed.

5 CONTENTS Basic Theory for Improving ZT Enhancing the figure of merit (ZT) is the common idea for improving efficiency of thermoelectric materials [9], as explained in Figure 2. From the definition of ZT in Equation (1), three correlated quantities need to be taken into consideration for optimizing the value of ZT, and these three factors are a large Seebeck coefficient (S), a high electrical conductivity (σ) and a low thermal conductivity (κ). These quantities are interconnected by the charge carrier concentration n, as plotted in Figure 3. S 2 σ is defined as the power factor of thermoelectric devices, which denotes the contribution of the Seebeck coefficient and electronic conductivity to ZT. The relation between the Seebeck coefficient and the charge carrier concentration n can be expressed as S = 8π2 σk 2 B 3eh 2 m T( π 3n )2/3 (2) where k B is the Boltzmann constant, e is the carrier charge, h is Plancks constant and m is the effective mass of the charge carrier. Here the charge carriers can be either electrons or holes. According to Drude s model, electrical conductivity can be denoted as σ = neµ where µ is the mobility of the charge carrier. conductivity can be denoted as (3) The electronic component of thermal κ e = LTσ = LTneµ (4) which follows the Wiedemann Franz Law. Decreasing the electronic thermal conductivity results in idecreasing the electrical conductivity, and does not affect ZT much. The lattice component of thermal conductivity can be estimated as κ l = 1 3 Cvl (5) where C is heat capacity of materials, v is the average sound velocity for phonons, and l is the phonon mean free path (mfp). Compared to the electronic thermal conductivity, lattice conductivity contributes to the change of ZT much more significantly. There is a trade-off between the improvement of thermopower and the reduction of thermal conductivity by charge carrier concentration. Typically, good thermoelectric materials

6 CONTENTS 6 Figure 3. Illustration of the variation of the Seebeck coefficient (S), electrical conductivity (σ), power factor (S 2 σ), electronic thermal conductivity (κ e ), and lattice (κ l ) thermal conductivity on the charge carrier concentration n, for a bulk material. From Shakouri [1].. are heavily doped semiconductors with carrier concentration of cm 3 (also in Figure 3) [10, 7]. As we mentioned before, there are mainly two methods for improving ZT. For the first appoach, i.e. complex crystal structures, a basic phonon-glass electroncrystal (PGEC) as a high performance thermoelectric material was proposed by Slack in 1995 [11, 12]. This idea implies that high thermoelectric performance materials behave like glass materials regarding their thermal properties and demonstrate electrical properties as crystalline materials. Materials with ZT>1 have been discovered based on this idea, for example in skutterudites, clathrates and β-zn 4 Sb 3 structures [7]. In particular, a high ZT=1.7 is realized in Ba 0.08 La 0.05 Yb0.04 Co 4 Sb 12, which is a n-type skutterudite structure. [13]. However, materials with higher ZT (even more than 2) are normally prepared by the second approach, i.e. nanostructuring. In the nanostructuring method, the phonon mfp decreases while the power factor S 2 σ is maintained at the same level or becomes even higher than in the original bulk materials. The connection among the above three factors: Seebeck coefficient S, electrical conductivity σ and thermal conductivity κ is weaken by the design of nanostrucures. In most cases, only the lattice thermal conductivity is significantly reduced. Comparing the two approaches, the basic idea for

7 CONTENTS 7 the first one is trying to find an optimized balance point in the tade-off between these three factors, while the second approach changes the manner of this trade-off Measurement Accuracy in Thermoelectrics Nevertheless, before starting the introduction to exciting and high performance nanostructured thermoelectric materials, the author would like to mention that there are serious measurement issues for most thermoelectrics. The measurement issues arise because of the complexity of fabricating devices, measurement uncertainty and materials complications [14]. Moreover, inaccurate carrier concentration measurement can also result in wrong Seebeck factor enhancement [8, 15]. Direct efficiency measurements require nearly as much complexity as building an entire device [14].Therefore the figure of merit is obtained by measuring thermal conductivity κ, Seebeck coefficient S and electrical conductivity separately. Thermal conductivity values κ are normally calculated from thermal diffusivity α, while thermal diffusivity measurement exhibits considerable inaccuracy. The relation between thermal conductivity and thermal diffusivity is defined as α = κ (6) ρc p where ρ is the material density and C p is the specific heat capacity. Furthermore, in this calculation, there is also an approximation that the specific heat capacity constant in the material according to the Dulong Petit Law.. This approximation brings uncertainty to the final result, especially in complex nanosctructured materials. The inaccurate measurement in thermal diffusivity and and the approximation of a constant specific heat results in uncertainty around 15%-20% in thermal conductivity calculation. The error for the Seebeck coefficient is around 5% (it may be up to 10%), and the inaccuracy for electric conductivity measurement is also 2%-3%. The final ZT value therefore exhibits significant uncertainty, which can be up to around 30%. Besides the simple superposition of errors due to measurements and the approximation, the final result can be more inaccurate because it originates from the process of separate measurements. Firstly, the inside grain sizes and shapes of thermoelectric materials are changed by annealing, which occurs after each measurement

8 CONTENTS 8 is performed. Therefore separate measurements do not measure the properties of the exact same sample, and there are slightly difference in each measurement. Secondly, the grains in a ceramic material can align in a preferential direction, and the physical properties can exhibit anisotropy such that the sample exhibits better performance when measured along a particular direction. These preferred directions also add difficulties to the ZT measurements. The final errors of ZT can be up to even 50% in some cases. These measurement inaccuracies are directly linked to the reproducibility of experimental results. Currently, the reproducibility of thermoelectric materials with high performance is poor and many excellent results haven t been proved by a second research group [2]. As Snyder and his coworker mentioned, one should be encouraged by results of ZT exceeding 1.5 but remain wary of the uncertainties involved to avoid pathological optimism [14]. 2. Thermoelectric Materials in Low Dimensional systems The great pioneers Hicks and Dresselhaus proposed a few types of thermoelectric materials in low dimensional systems, including 1D conductors, quantum wells and semimetal-semiconductor transition in quantum-well superlattices in 1993 [3, 16, 17]. Later in 1996, they experimentally realized a ZT of 2.0 in 2D multiple-quantum-well structures (PbTe/Pb 1 x Eu x T e) by Molecular Beam Expitaxy (MBE) [18]. That value of ZT iis still one of the highest reported until now. This excellent research guided the journey toward nanostructured thermoelectric materials in the past twenty years Quantum Well Superlattices The original idea of applying quantum well structures to thermoelectric materials is that an enhancement of the power factor S 2 σ could be realized through quantum confinement. Additionally the lattice thermal conductivity could be significantly reduced by the interface scattering in the direction perpendicular to the quantum wells, especially in atom thick layers. The predicted ZT in 2D as a function of layer thickness is plotted in Figure 4. Based on this idea, high ZT values are realized not only in PbTe/Pb 1 x Eu x Te systems [18], but also in PbTe/PbSe 0.2 Te 0.8 by MBE [19]. In 2001, Venkatasubramanian

9 CONTENTS 9 Figure 4. Calculated ZT as a function of layer thickness a in a quantum well structure for layers parallel to the ab plane (1)and b-c plane (2). The dashed line represents the optimized ZT forbulk Bi 2 Te 3. From Hicks[16] and Chen[7]. and his coworkers reported the highest ZT=2.4 in Bi2Te3/Sb2Te3 (p-type) quantum well superlattices [20]. Further explanation about the increased power factor is proposed by Shakouri. The improvement of power factor is due to sharp features in the electronic density of states of quantum-confined structures (Figure 5(b)). It enables a doping-leveltunable increase in the asymmetry between hot and cold electron transport, leading to a large average transport energy and a carrier concentration (i.e., a large Seebeck coefficient and electrical conductivity) [21]. MBE is not the only frabrication technique in quantum well superlattices for thermoelectric materials. Ohta and his coworkers reported ZT=2.4 in a two-dimensional electron gas in SrTiO 3 /SrTi 0.8 Nb 0.2 O 3 superlattices [22], where this sample was fabricated by pulsed laser deposition (PLD). The quantum well thickness was only nm. One should note that this high value of ZT is calculated from the assumption that electrons are strictly confined in that thin layer [1]. Although high ZT values have been discovered in artificial superlattice structure, there is still a long way to go for practical applications for waste heat power generation, since it is difficult to fabricate large area devices for fitting in practical devices. Moreover the stability of the thin layer needs to be investigated for real applications [11]. Larger area and lower cost techniques than MBE and PLD such as Chemical Vapour

10 CONTENTS 10 Figure 5. Schematic illustration of the density of states (DOS) as a function of energy for: (a) a bulk material (3-D), (b) a quantum well (2-D), (c) a nanowire (1-D) Deposition (CVD) have not been well developed for allowing high quality film growth with atomic precision. Fabrication techniques like CVD need to be improved in the fulture especially for the growth of crystalline chalcogenides, which is necessary for many high-performance thermoelectric materials. Thermal conductivity reduction is found to be the main reason behind the enhanced ZT in superlattices. Studies on the heat-conduction mechanisms in superlattices demonstrate that periodic structures are not necessary for thermal conductivity reduction [23]. To overcome the scaling-up problems and find materials for commercial applications, combining bulk nanomaterials and nanostructures seems to be a reasonable solution, which will be introduced later in this paper One Dimensional Nanowires Theoretical calculations predict a large improvement of ZT in one-dimensional nanowires, even higher than in 2D quantum well superlattices. The reasons for this enhancement are the change of DOS (Figure 5(c)) due to the strong quantum confinement and the reduced lattice thermal conductivity due to the high surface to volume ratio [3]. The thermoelectric figure of merit of a one-dimensional conductor or quantum wire depends strongly on the radius of the wire [3]. Theoretical studies on III- V semiconductor nanowires also indicate that InSb seems to be a promising candidate for a reasonably high figure of merit for nanowires around 10nm thick. Some materials (such as GaAs) show calculated high ZT values with diameters which are experimentally unattainable [24]. However, in experiments InSb nanowires exhibit even lower ZT values

11 CONTENTS 11 than their bulk materials [25, 26]. The unexpected reduction of ZT also arises in Bi 2 Te 3 nanowires [27]. The reason for this unexpected reduction has not been fully understood, but may originate from the impurities in nanowires [28, 29, 30]. Improved ZT values are found for some nanowires in experiments, but in general high ZT materials as 2D quantum well superlattice systems have not yet been fabricated.. For example, silicon nanowires demonstrate a ZT=0.25 [31] for rough silicon nanowires of 50 nm in diameter and 0.6 [32] for rough silicon nanowires of 50 nm in diameter, while the bulk ZT for silicon is only around 0.01[33, 34]. Cylindrical Bi nanowires are predicted to have a significantly improved Seebeck coefficient, because a semimetal-semiconductor transition can occur below a critical wire diameter due to quantum confinement [35]. The critical wire diameter at 77 K is found to be between 39nm and 55nm, and it depends on the crystal orientation of the wire axis [35]. Highquality Bi nanowires are difficult to fabricate and they are often fabricated in porous anodic aluminium oxide (AAO) or quartz (SiO2) templates [30]. Large enhancement in the thermoelectric power of Bi nanowires embedded in porous alumina and porous silica was reported by Heremans [36] in 2002, where the nanowires are with diameters of 9nm and 15nm and the thermoelectric power is enhanced by two or three orders in the temperature range of K. High quality nanowires of these materials are generally quite challenging to synthesize. Moreover, the unexpected reduction of ZT also needs to be investigated to find the mechanisms behind it. 3. Bulk Nanostructured Thermoelectric Materials 3.1. Progress in Bulk Nanostructured Thermoelectric Materials Bulk nanostructured thermoelectric materials[23] are bulk materials embedded with nanoparticles or interfaces with nanometer size. These materials demonstrate improved thermoelectric properties similar to the low dimensional systems, where the lattice thermal conductivity is reduced due to designed phonon scattering. Compared to those thermoelectricswith low dimensions, bulk nanostructured thermoelectric materials can

12 CONTENTS 12 be produced in a form suitable for current thermoelectric device configurations [5]. This type of materials are also called nanostructured composite materials or nanocomposites. In some high performing thermoelectric nanocomposites, the main contribution to improved ZT is the reduction of lattice thermal conductivity. The mfps of phonons typically range from several nanometers up to a few hundred nanometers, while the mfps of carriers are much shorter, only a few nanometers [37]. Therefore, nanocomposites offer the possibility for the effective scattering of phonons with long mfps without hindering charge current conduction. Additionally, the Seebeck coefficient can also be lifted due to electron filtering at grain boundaries in nanocomposites [11]. Furthermore, it is desirable to have nanostructural features on different size scales, ranging from single atomic point defects to nanoscale second phase inclusions to grain boundaries / twin boundaries on the hundreds of nm scale. This helps to scatter phonons over their entire wavelength range. A strategy based on this idea is illustrated later in this paper. There have been three main strategies for bulk thermoelectric nanocomposites, as demonstrated schematically in Figure 6[11]. One strategy is to form thermoelectric nanocomposites with single-phase nanograins, which only involves reduction of the thermal conductivity. The other two stratigies are to form second-phase nanoinclusions (Figure 6 (b), (c)), where a large number of interfaces are formed between the thermoelectric material and the nanoinclusions. The interfaces can be either incoherent or coherent, which corresponds to the second and third strategies respectively. A coherent nanoinclusion demonstrates good lattice matching with the matrix phase due to similar lattice constants, while an incoherent nanoinclusion shows a clear boundary between the matrix phase and the dispersed phase for the embedded nanostructures [11]. The Seebeck coefficient is enhanced for the last two approaches, in addition to the reduction of thermal conductivity. Typical strategies to synthesize nanocomposite thermoelectric materials are the powder metallurgy method and melt metallurgy method, which are inspired by classic metallurgical approaches. The powder metallurgy method is to prepare pre-synthesed nanoparticles by physical or chemical routes with fast powder compaction to avoid grain growth. For example spark plasma sintering is a direct current induced hot pressing

13 CONTENTS 13 Figure 6. Approaches for bulk thermoelectric nanocomposites: (a). nanograined composite, (b). nanoinclusion composite with an incoherent interface, and (c). nanoinclusion composite with a coherent interface[11] technology, and it can create extensive interfaces between the neighbouring nanoparticles and lower the thermal conductivity. The melt metallurgy method usually applies melting and quick cooling to obtain small grain size or even amorphous powders [11, 7, 38]. The improvement of ZT has been investigated in a wide range of bulk nanostructured material families, including Bi 2 Te 3 -based nanocomposites, PbTe-based nanocomposites and SiGe-based nanocomposites. For a detail overview of these three families of bulk nanostructured thermoelectric materials, the reader is referred to the recent review article by Chen et al [7]. In this paper, the author proposes an idea for improving ZT by the detailed design of a more efficient way of scattering phonons, i.e. by adjusting the distribution of the nanosize dots or interfaces along the temperature gradient in practical devices A Strategy to Improve ZT in Nanocomposites Current research in nanostructured composites for thermoelectric materials combines low-dimensional and bulk materials for thermoelectric applications. As we mentioned before, nanocomposites (in Figure 6) contain a high density of second-phase nanoinclusions, and they are powerful tools for improving ZT. For example, Girardin et al. reported PbTe bulk materials with homogeneous distributed PbS nano-size dots that improves ZT into 1.4 at 750K in the PbS(8%)-PbTe materials system by lattice thermal conductivity reduction [38]. Biswas et al reported a figure of merit of 1.7 at 800K in PbTeSrTe (SrTe=0.52mol%) materials doped with 1mol% Na2Te [39]. Also in

14 CONTENTS 14 Na 1 x Pb m Sb y Te m+2 systems, ZT=1.7 at 700 K was reported by Poudeu [40]. These nanostructured thermoelectric systems exhibit better ZT than simple bulk materials mainly due to the scattering of long mfp phonons by nano-scale features. The mean free path of phonons in nanocomposites based on bulk materials is determined by two factors:one is scattering from nanosize particles and grain boundaries of the sample and the other is scattering with other phonons.. Current studies have focused on the first factor and improve ZT by optimizing compositions of the materials that can scatter phonons more effectively. In the second factor, the interaction between phonons can also change the mfp by the Umklapp process. The probability that a phonon undergoes a collision is directly proportional to the number of other phonons present and the number of phonons at high temperature is proportional to k B T/ ω, according to the Bose-Einstein Distribution. Therefore the mfp l in the system is approximately proportional to 1/T. In thermoelectrics, a pronounced gradient of temperature is required, meanwhile phonon mfps increase along the temperature gradient. Therefore it is reasonable to propose a model which varies the nano-size features of thermoelectrics along the temperature gradient and gains better scattering results for phonons over their entire mfp range corresponding to different temperatures. A schematic figure is plotted to illustrate this idea in Figure 7, where an increased trend in size for nanoparticles is demonstrated. The homogeneous size distribution (in Figure 7.a) only obtains an average optimized scattering rate for phonons with different mfps. Our designed system (in Figure 7.b.) can optimize the scattering of phonons over their entire mfp range along the temperature gradient, and therefore it could achieve a higher ZT value in the end. One reasonable way to realize this model is applying ferromagnetic nanoparticles with a wide range of sizes in bulk materials. By applying a magnetic field in the molten state of the bulk matrix, a size distribution can be established. For example, one can control the size distribution of magnetite (Fe 3 O 4 ) nanoparticles embedded in GST (Ge 2 Sb 2 Te 5 ) matrices. There are two shortcomings of this idea. One is that the ferromagnetic nanoparticles need a high melting point, which limits the materials that

15 CONTENTS 15 Figure 7. Schematic pictures of: (a). homogeneous size distribution for nanoparticles in a bulk thermoelectric material compared with (b). increased size distribution along the thermal gradient for nanoparticles in a bulk thermoelectric material. The latter model can scatter phonons over their entire mfp range. can be combined with each other.another difficulty is that the crystal types (or space groups) of the nanoparticles and matrices need to be same or compatible. 4. Conclusion Over the past twenty years, thermoelectric nanomaterials and materials embedded with nanostructures have been extensively investigated and and have shown promising potential promising potentials for waste heat utilization. ZT values of thermoelectric materials have been increased from 1.0 in the 1950s to around 2.4 nowadays. In this paper, an idea of adjusting nano-scale structures along the temperature gradient is proposed. This strategy could be a fruitful way to enhance thermoelectric device performance for practical applications. Measurement accuracy and reproducibility of high-performance thermoelectrics are also critically analyzed. Measurement issues of thermoelectrics are very serious (even with errors around 30%-50%) and worth attracting attention from academia for bridging the gap from high-performance materials to practical devices. Moreover, applying thermoelectric materials with a ZT value exceeding 2.0 in commercial devices is still a challenging topic, especially for materials in

16 CONTENTS 16 low dimensional systems. To solve the measurement inaccuracy and apply the excellent breakthrough of ZT into waste heat utilization, scientists from academia and industry need cooperate together for fabricating practical devices and improving efficiency in an accurate way. 5. Acknowledgement This review paper is finished under the guidance of Dr. Blake. The author thanks him for his supervision and suggestions during very useful discussions. The author also appreciates the workshops given by Prof. Chiechi and Dr. Pchenitchnikov and especially thanks Dr. Kaverzin for his teaching in writing skills. 6. Reference [1] A. Shakouri, Recent Developments in Semiconductor Thermoelectric Physics and Materials, Annual Review of Materials Research, vol. 41, no. 1, pp , [2] L.-D. Zhao, V. P. Dravid, and M. G. Kanatzidis, The panoscopic approach to high performance thermoelectrics, Energy & Environmental Science, vol. 7, no. 1, p. 251, [3] L. D. Hicks and M. S. Dresselhaus, Thermoelectric figure of merit of a one-dimensional conductor, Physical Review B, vol. 47, no. 24, pp , [4] G. J. Snyder and E. S. Toberer, Complex thermoelectric materials, Nature materials, vol. 7, no. 2, pp , [5] a. J. Minnich, M. S. Dresselhaus, Z. F. Ren, and G. Chen, Bulk nanostructured thermoelectric materials: current research and future prospects, Energy Environ Sci, vol. 2, no. 5, pp , [6] M. G. Kanatzidis, Nanostructured thermoelectrics: The new paradigm?, Chemistry of Materials, vol. 22, no. 3, pp , [7] Z. G. Chen, G. Hana, L. Yanga, L. Cheng, and J. Zou, Nanostructured thermoelectric materials: Current research and future challenge, Progress in Natural Science: Materials International, vol. 22, no. 6, pp , [8] C. J. Vineis, A. Shakouri, A. Majumdar, and M. G. Kanatzidis, Nanostructured thermoelectrics: Big efficiency gains from small features, Advanced Materials, vol. 22, no. 36, pp , [9] H. Goldsmid, Thermoelectric refrigeration [10] P. Vaqueiro and A. V. Powell, Recent developments in nanostructured materials for highperformance thermoelectrics, Journal of Materials Chemistry, vol. 20, no. 43, p. 9577, 2010.

17 CONTENTS 17 [11] K. Koumoto and T. Mori, Thermoelectric nanomaterials. Springer, [12] D. M. Rowe, CRC handbook of thermoelectrics. CRC press, [13] X. Shi, J. Yang, J. R. Salvador, M. Chi, J. Y. Cho, H. Wang, S. Bai, J. Yang, W. Zhang, and L. Chen, Multiple-filled skutterudites: high thermoelectric figure of merit through separately optimizing electrical and thermal transports, Journal of the American Chemical Society, vol. 133, no. 20, pp , [14] G. J. Snyder and E. S. Toberer, Complex thermoelectric materials, Nature materials, vol. 7, no. 2, pp , [15] C. J. Vineis, T. C. Harman, S. D. Calawa, M. P. Walsh, R. E. Reeder, R. Singh, and a. Shakouri, Carrier concentration and temperature dependence of the electronic transport properties of epitaxial PbTe and PbTe/PbSe nanodot superlattices, Physical Review B - Condensed Matter and Materials Physics, vol. 77, no. 23, pp , [16] L. D. Hicks and M. S. Dresselhaus, Effect of quantum-well structures on the thermomagnetic figure of merit, Physical Review B, vol. 47, no. 19, pp , [17] L. D. Hicks, T. C. Harman, and M. S. Dresselhaus, Use of quantum-well from nonconventional to obtain a high figure of merit thermoelectric materials, Applied physics letters, vol. 63, no. 7, pp , [18] L. Hicks, T. Harman, X. Sun, and M. Dresselhaus, Experimental study of the effect of quantumwell structures on the\nthermoelectric figure of merit, Fifteenth International Conference on Thermoelectrics. Proceedings ICT 96, vol. 53, no. 16, pp , [19] H. Beyer, J. Nurnus, H. Böttner, a. Lambrecht, T. Roch, and G. Bauer, PbTe based superlattice structures with high thermoelectric efficiency, Applied Physics Letters, vol. 80, no. 7, pp , [20] R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit., Nature, vol. 413, no. 6856, pp , [21] M. Christensen, A. B. Abrahamsen, N. B. Christensen, F. Juranyi, N. H. Andersen, K. Lefmann, J. Andreasson, C. R. H. Bahl, and B. B. Iversen, Avoided crossing of rattler modes in thermoelectric materials., Nature materials, vol. 7, no. 10, pp , [22] H. Ohta, S. Kim, Y. Mune, T. Mizoguchi, K. Nomura, S. Ohta, T. Nomura, Y. Nakanishi, Y. Ikuhara, M. Hirano, H. Hosono, and K. Koumoto, Giant thermoelectric Seebeck coefficient of a two-dimensional electron gas in SrTiO3., Nature materials, vol. 6, no. 2, pp , [23] M. S. Dresselhaus, G. Chen, M. Y. Tang, R. Yang, H. Lee, D. Wang, Z. Ren, J. P. Fleurial, and P. Gogna, New directions for low-dimensional thermoelectric materials, Advanced Materials, vol. 19, no. 8, pp , [24] N. Mingo, Thermoelectric figure of merit and maximum power factor in iii v semiconductor nanowires, Applied Physics Letters, vol. 84, no. 14, pp , [25] F. Zhou, A. L. Moore, M. T. Pettes, Y. Lee, J. H. Seol, Q. L. Ye, L. Rabenberg, and L. Shi, Effect

18 CONTENTS 18 of growth base pressure on the thermoelectric properties of indium antimonide nanowires, Journal of Physics D: Applied Physics, vol. 43, no. 2, p , [26] A. I. Persson, Y. K. Koh, D. G. Cahill, L. Samuelson, and H. Linke, Thermal conductance of inas nanowire composites, Nano letters, vol. 9, no. 12, pp , [27] A. Mavrokefalos, A. L. Moore, M. T. Pettes, L. Shi, W. Wang, and X. Li, Thermoelectric and structural characterizations of individual electrodeposited bismuth telluride nanowires, Journal of Applied Physics, vol. 105, no. 10, p , [28] J. H. Seol, A. L. Moore, S. K. Saha, F. Zhou, L. Shi, Q. L. Ye, R. Scheffler, N. Mingo, and T. Yamada, Measurement and analysis of thermopower and electrical conductivity of an indium antimonide nanowire from a vapor-liquid-solid method, Journal of applied physics, vol. 101, no. 2, p , [29] F. Zhou, J. Seol, A. Moore, L. Shi, Q. Ye, and R. Scheffler, One-dimensional electron transport and thermopower in an individual insb nanowire, Journal of Physics: Condensed Matter, vol. 18, no. 42, p. 9651, [30] J. R. Szczech, J. M. Higgins, and S. Jin, Enhancement of the thermoelectric properties in nanoscale and nanostructured materials, Journal of Materials Chemistry, vol. 21, no. 12, pp , [31] A. I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J.-K. Yu, W. A. Goddard Iii, and J. R. Heath, Silicon nanowires as efficient thermoelectric materials, Nature, vol. 451, no. 7175, pp , [32] A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Enhanced thermoelectric performance of rough silicon nanowires, Nature, vol. 451, no. 7175, pp , [33] L. Weber and E. Gmelin, Transport properties of silicon, Applied Physics A, vol. 53, no. 2, pp , [34] O. Caballero-Calero and M. Martín-González, Thermoelectric nanowires: A brief prospective, Scripta Materialia, vol. 111, pp , [35] Y.-M. Lin, X. Sun, and M. Dresselhaus, Theoretical investigation of thermoelectric transport properties of cylindrical bi nanowires, Physical Review B, vol. 62, no. 7, p. 4610, [36] J. P. Heremans, C. M. Thrush, D. T. Morelli, and M.-C. Wu, Thermoelectric power of bismuth nanocomposites, Physical Review Letters, vol. 88, no. 21, p , [37] D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, Nanoscale thermal transport, Journal of Applied Physics, vol. 93, no. 2, pp , [38] S. N. Girard, J. He, C. Li, S. Moses, G. Wang, C. Uher, V. P. Dravid, and M. G. Kanatzidis, In situ nanostructure generation and evolution within a bulk thermoelectric material to reduce lattice thermal conductivity, Nano Letters, vol. 10, no. 8, pp , [39] K. Biswas, J. He, Q. Zhang, G. Wang, C. Uher, V. P. Dravid, and M. G. Kanatzidis, Strained

19 CONTENTS 19 endotaxial nanostructures with high thermoelectric figure of merit., Nature chemistry, vol. 3, no. 2, pp , [40] P. F. P. Poudeu, J. D Angelo, A. D. Downey, J. L. Short, T. P. Hogan, and M. G. Kanatzidis, High thermoelectric figure of merit and nanostructuring in bulk p-type Na1-xPbmSbyTem+2, Angewandte Chemie - International Edition, vol. 45, no. 23, pp , 2006.