Nanoscale Thermoelectrics

The thermoelectric efficiency of a material depends on its electronic and phononic properties. It is normally given in terms of the dimensionless figure of merit Z T = σ S ² T ∕ κ. The parameters involved in Z T are the electrical conductivity σ, the Seebeck coefficient S, and the thermal conductivity κ. The thermal conductivity has two contributions, κ = κ _e + κ _L , the electron thermal conductivity κ _e and the lattice thermal conductivity κ _L . In this chapter all these parameters will be deduced for metals and semiconductors, starting from the Boltzmann transport equation (BTE). The electrical conductivity, the Seebeck coefficient, and the electronic thermal conductivity will be obtained from the BTE for electrons. Similarly, the lattice or phonon thermal conductivity will be given from the BTE for phonons. The ab initio approaches to obtain both the electronic and phononic transport via the BTE will also be analyzed. All the theoretical studies are based on the relaxation time approximation. The expressions for the relaxation times for electrons and phonons will be discussed. The results will be particularized to nanostructures whenever is possible.

We theoretically investigate nanoscale structures such as nanoparticles embedded in bulk materials as a means of improving the thermoelectric energy conversion efficiency. We focus on the impact of such nanostructures on the electron transport in the host material, and discuss the enhancement of the thermoelectric power factor and thus the figure of merit. Nanostructures embedded in thermoelectric materials can create potential variations at the nanoscale due to the hetero-interfaces, which can alter the transport of charge carriers in the host material to enhance the Seebeck coefficient and the power factor. The energy-dependent electron scattering times induced by nanoparticles are calculated using the partial wave method. Thermoelectric transport properties are then calculated based on the linearized Boltzmann transport theory with the relaxation time approximation for various thermoelectric materials such as ErAs:InGaAs, PbTe, and Mg₂Si. The effects of different kinds of nanoparticles including single-phase ionized metallic nanoparticles and core–shell nanoparticles embedded in semiconductors are investigated in these semiconductors. Finally the electron energy filtering scheme is discussed to further enhance the thermoelectric energy conversion efficiency.

The modeling of the thermal conductivity of composites made up of metallic and non-metallic micro/nanoparticles embedded in a solid matrix is discussed in detail, at both the dilute and non-dilute limits of particle concentrations. By modifying both the thermal conductivity of the matrix and particles, to take into account the strong scattering of the energy carriers with the surface of the nanoparticles, it is shown that the particle size effect shows up on the thermal conductivity of nanocomposites through: (1) the collision cross-section per unit volume of the particles and, (2) the mean distance that the energy carriers can travel inside the particles. The effect of the electron–phonon interactions within metallic particles shows up through the reduction of the thermal conductivity of these particles with respect to its values obtained under the Fourier law approach. The thermal conductivity of composites with metallic particles depend strongly on (1) the relative size of the particles with respect to the intrinsic coupling length, and (2) the ratio between the electron and phonon thermal conductivities. The obtained results have shown that the size dependence of the composite thermal conductivity appears not only through the interfacial thermal resistance but also by means of the electron–phonon coupling. Furthermore, at the non-dilute limit, the interaction among the particles is taken into account through a crowding factor, which is determined by the effective volume of the particles. The proposed crowding factor model is able to capture accurately the effect of the interactions among the particles for concentrations up to the maximum packing fraction of the particles. The predictions of the obtained analytical models are in good agreement with available experimental and numerical data and they can be applied to guide the design and improve the thermal performance of composite materials.

The beneficial effects of nanostructured material systems have provided a significant momentum to accomplish high-efficiency thermoelectric materials for power generation and cooling applications. The quantum size effects have been widely explored in order to shrink the contribution of lattice thermal conductivity of the thermoelectric systems, thereby enhancing the overall figure-of-merit. Modifying the nanoscale level structural features and the creation of additional phonon scattering sites in the form of grain boundary interfaces became the basis for fabrication of nanostructured materials. The requirement of specific physical features in nanostructured thermoelectrics also brought a variety of changes to the fabrication processes. In this chapter, we review some of the prominent techniques for fabrication of such nanostructured material systems. An overview of the concepts and techniques for theoretical modeling of the charge carrier and phonon transport mechanisms in the interfacial regions is presented. Further, the constructive effects of nanostructuring in thermoelectric materials are discussed based on a theoretical approach via Boltzmann transport equation under the relaxation time approximation. The calculations are used to demonstrate the advantages and disadvantages of nanoscale effects in the well-known material systems of Si _x Ge_1−x and Mg₂Si.

The field of nanoscale thermoelectrics has progressed enormously recently because of the strong global demand for pollution-free forms of energy conversion. Rapid development and exciting innovative breakthroughs in the field over the last decades have occurred in large part due to newly emerged nanoscale materials with reduced thermal conductivity, and newly developed physical concepts, which make it possible to modify the thermal conductivity of nanoscale materials. We review recent experimental and theoretical advances in the study of thermal conductivity and thermoelectric property of nanowires. We first present several theoretical and experimental results on the reduction of thermal conductivity and the improvement of the thermoelectric figure of merit, including size effect, roughness effect, isotopically doped impurity, surface and interface phonon scattering. We then discuss coherent phonon resonance in core–shell nanowires and its impact on thermal conductivity. Finally, we highlight the importance of these effects on the figure of merit of nanowires.

Thermoelectric efficiency of nanowires is shown to be enhanced when they have disordered surfaces with long range correlations. To show this effect, one needs to solve Schrödinger equation in a surface disordered waveguide geometry as a model for nanowires and employ the resulting transmission to analyze nanowires as feasible heat engines. Using the linear response theory in determining the efficiency of the possible heat engine device based on silicon nanowires is although useful to point out the overall behavior with respect to the continuous incident electron energy, it says nothing about its performance as a heat engine. A nonlinear response theory is proved to be necessary to find out the specific energies at which the nanowire has greater efficiency at max power as a thermoelectric device. The efficiency at the maximum power shows that some nanowires with specific surface disorder structure is more appropriate to use as a heat engine than the others. The possibility of engineering the transmission of electrons in the nanowires to increase their efficiency maybe an answer to the demand of highly efficient thermoelectric semiconductor materials in future.

Bi and its alloys are important thermoelectric materials for solid-state refrigeration and power generation. An increase in the thermoelectric figure of merit is predicted due to quantum confinement and phonon scattering at interfaces for one-dimensional (1D) nanostructured thermoelectric materials. This chapter addresses recent developments in Bi-based nanostructured thermoelectric materials focused mainly on nanowires, nanotubes, and heterostructures. In addition, current challenges in preparation and measurement of 1D nanostructured thermoelectric materials are discussed.

Bi₈₈Sb₁₂ alloy has been doped with 0, 0.066, 0.66, 1.32, and 3.91 % Sm and prepared under two different fabrication conditions. The first being ball milled for 12 h and hot pressed at 240 °C and the second ball milled for 6 h and hot pressed at 200 °C. The results are in agreement with previously studied Ce and Ho samples prepared under similar conditions. A slight ZT enhancement is seen due to doping which is an effect of an enhanced Seebeck coefficient as a result of a decrease in the carrier concentration. The enhancement does not appear to be caused by the magnetic moments of Ce, Sm, and Ho based on the similar change to the gap size with the widely varying magnetic moments of the dopants. In addition, lattice thermal transport in these materials was investigated experimentally and theoretically where phonon dispersions were obtained from first principle calculations, and semiclassical models were used to calculate phonon lifetimes. We have not observed a strong thermal conductivity dependence on the type of the impurity.

Skutterudite is a new family of compounds identified to be a promising candidate for thermoelectric applications. Since the early 1990s, skutterudite-based materials have undergone substantial technological development, making its way to the next generation of thermoelectric devices for power generation and waste heat recovery. Nanostructuring is one approach that could enable significant improvements in thermoelectric performance by reducing the thermal conductivity while maintaining the electronic properties. In this chapter, we present progress towards realizing the potential of bulk skutterudites utilizing low dimensionality and nanostructures with an emphasis on p-type skutterudites. We summarized the synthetic approaches used to create skutterudite nanocomposites, namely, ball milling, melt spinning, in situ formation, high-pressure torsion, and solvothermal and hydrothermal synthesis. The effect of nanostructuring on the thermal and electron transport is also discussed.

Thermoelectric (TE) generators can directly generate electrical power from waste heat, and thus could be an important part of the solution to future power supply and sustainable energy management. The main obstacle to the widespread use of TEs in diverse industries, e.g., for exhaust heat recovery in automobiles, is the low efficiency of materials in converting heat to electricity. The conversion efficiency of TE materials is quantified by the dimensionless figure of merit, ZT, and the way to enhance ZT is to decrease the lattice thermal conductivity (κ _lat) of the material, while maintaining a high electrical conductivity, i.e., to create a situation in which phonons are scattered but electrons are unaffected. Various concepts have been used in the search for this situation, e.g., the use of rattling of atoms weakly bonded in crystals and nanostructuring of materials. Here we report TE properties of skutterudites filled by group 13 elements, i.e., Ga, In, and Tl. Our group has examined the high-temperature TE properties of various skutterudites filed by group 13 elements, viz., Ga-filled CoSb₃, Tl-filled CoSb₃, and In/Tl double-filled CoSb₃. All systems exhibit relatively high TE figure of merit, especially, Tl_0.1In _x Co₄Sb₁₂ achieves a dramatic reduction of κ _lat, resulting in the ZT = 1.20 at 700 K—very high for a bulk material. We have demonstrated that the reduction of κ _lat in Tl_0.1In _x Co₄Sb₁₂ is due to the effective phonon scattering both by rattling of two atoms: Tl and In and by naturally formed nano-sized In₂O₃ particles (<50 nm). Since the combined approach of double filling and self-formed nanostructures could be applicable to various clathrate compounds, our results suggest a new strategy in the improvement of bulk TE materials.

Thermoelectric materials directly convert thermal energy into electric energy through Seebeck effect. The nanostructured approach for these materials has led to significant improvements in the figure of merit mainly by tailoring the lattice thermal conductivity. In this chapter, we provide an overview of the strategies adopted for phonon scattering and its confinement in the nanostructures with the goal of reducing the thermal conductivity. We discuss the approaches that are being adopted for developing cost-effective thermoelectrics and identify the promise offered by oxide materials. Compared with the alloy-based thermoelectric materials, oxide thermoelectrics have many advantages including abundance of raw materials, low cost, non-toxicity, and thermal stability. Several important oxide thermoelectric candidates are introduced with specific focus on ZnO. Self-assembled nano-composites of ZnO have been shown to exhibit reduction in thermal conductivity by a factor of about three mainly due to the phonon scattering by uniformly distributed nanoprecipitates (ZnAl₂O₄) and large grain boundary area. The effects of nanoscale inclusion in Ca-Co-O system (Ca₃Co₄O₉) and natural superlattices in SrO/SrTiO₃ are also discussed. Several self-assembly techniques are discussed which are promising for fabrication of oxide thermoelectrics.

Using nonequilibrium molecular dynamics simulations and nonequilibrium Green’s function method, we investigate the thermoelectric properties of carbon nanotubes and related one-dimensional structures, which include ultrasmall and larger diameter carbon nanotubes, as well as graphene nanoribbons (GNRs) and carbon nanowires (CNWs). It is found that the transmission function of these one-dimensional carbon nanostructures display a clear stepwise structure that gives the number of electron channels. By optimizing the carrier concentration, characteristic size, and/or operating temperature, these systems could exhibit very high figure of merit. Moreover, their thermoelectric performance can be significantly enhanced via man approaches such as surface design, isotope substitution, isoelectronic impurities, and hydrogen adsorption. It is thus reasonable to expect that carbon nanotubes and related one-dimensional carbon nanostructures may be promising candidates for high-performance thermoelectric materials.

The two-dimensional (2D) graphene with many remarkable physical properties, such as high mechanical robustness, excellent thermal conductivity, extremely high conductance, and giant Seebeck coefficient as well as particular electronic band structures, promises well for potential applications in nanoelectronics, spintronics, photonics, and optoelectronics. The quasi-one-dimensional (1D) graphene nanoribbons (GNRs) and graphene nanojunctions (GNJs), which can be precisely patterned from graphene, are the most elementary building blocks for future nanodevices and nanocircuits. In this chapter, we review the latest advances on graphene, GNRs and GNJs in both theoretical and experimental level, including thermal transport, electronic transport as well as thermoelectric properties. In particular, how to enhance the thermoelectric properties in the 1D graphene-based nanostructures through the geometry-decorated method (antidot lattices, nanopores, edge disorder, defect-engineering, and so on) is presented in detail and some novel results are elucidated clearly. It provides the reader a comprehensive understanding of the recent progress in realistic 1D graphene nanostructures, and will be helpful for designing nanodevices based on graphene in the future.

In this chapter, an overview on silicon nanostructures for thermoelectric applications is presented. After an introduction on the key concepts of thermoelectricity, we show that nanostructuring is one of the most promising solutions for making high efficient thermoelectric devices. In particular, we discuss the use of nanostructured silicon as a good thermoelectric material, due to its abundance, its nontoxicity, and its technological pervasiveness in the society, compared to other materials often proposed in the literature. Furthermore, a top-down process for the reliable fabrication of very complex and large area arrays of silicon nanowires (SiNWs) is shown and discussed. Finally, we show that these networks can be employed for the fabrication of high efficiency thermoelectric generators, and the high reliability and the high tolerance with respect to SiNW width dispersion are demonstrated by means of numerical simulations.

In this chapter, strain effect on the thermoelectric figure of merit is investigated in n-type Si/Ge nanocomposite materials. Strain effect on phonon thermal conductivity in the nanocomposites is computed through a model combining the strain-dependent lattice dynamics and the ballistic phonon BTE. The Seebeck coefficient and electrical conductivity of the Si/Ge nanocomposites are calculated by an analytical model derived from the Boltzmann transport equation (BTE) under the relaxation-time approximation. The effect of strain is incorporated into the BTE through strain-induced energy shift and effective mass variation calculated from the deformation potential theory and a degenerate k ⋅ p method at the zone-boundary X point. Electronic thermal conductivity is computed from electrical conductivity by using the Wiedemann–Franz law. Various strains are applied in the transverse plane of the Si/Ge nanocomposites. Thermoelectric properties including thermal conductivity, electrical conductivity, Seebeck coefficient, and dimensionless figure of merit are computed for Si/Ge nanocomposites under these strain conditions.

The possibility to reduce the thermal conductivity leaving essentially unaltered the electron transport makes semiconducting nanowires ideal materials for the engineering of high-efficiency thermoelectric devices. A simple and appealing route to achieve these goals is bringing together Si and Ge, giving rise to Si_1−x Ge _x alloy nanowires with tunable Ge concentration, core–shell structures and multiple axial junctions, i.e. superlattices. In this chapter we review the most recent progresses in this field.