Ebook: Advances in Thermoelectricity: Foundational Issues, Materials and Nanotechnology

The history of thermoelectricity is largely intertwined with the most significant advances of thermodynamics and condensed-matter physics over the last two centuries. The discovery of the thermoelectric effects (Seebeck, Peltier and Thomson) played a key role in the birth of irreversible thermodynamics, largely acting as a workbench of models and theories —including the experimental validation of the Onsager-Casimir relations. Thermoelectricity has further promoted advances in solid-state physics and chemistry, inspiring research on the relationships between thermal conductivity and crystal structure of materials over the first half of the XX century —which further extended to defect engineering in real crystals. In more recent times, research on thermoelectric materials has promoted and motivated a major research endeavor to clarify factors affecting thermal conductivity in nanostructures, in a more general effort to apply nanotechnology to enhance the performance of thermoelectric materials to be exploited in thermoelectric generators and coolers.

Thermoelectricity is today among the most exciting fields of research for a materials physicist. The challenge of devising materials with exceptional properties (low thermal conductivity, high electrical conductivity, and a large Seebeck coefficient) has triggered a global, interdisciplinary endeavor to exploit scientific creativity. The need for sustainable energy has added a technological momentum. Still, thermoelectricity remains a substantial branch of thermodynamics, and the modes of operation of a thermoelectric system still call for sophisticated theoretical analyses, which have inspired novel developments of irreversible thermodynamics, from the analysis of the efficiency at a finite rate to recent studies on phonon hydrodynamics.

The 207 Course of the International School of Physics “Enrico Fermi” dedicated to Advances in Thermoelectricity: Foundational Issues, Materials, and Nanotechnology encompassed the full complexity of modern thermoelectricity. Its organization aimed at exposing students to all most cogent themes relevant to current research in the field. Twelve lecturers participated in the course, and we gratefully thank both those who provided contributed written papers that are published in this volume and those who just provided their lectures.

Classes began with three series of lectures on the fundamentals of thermodynamics, solid-state physics, and statistical mechanics applied to thermoelectricity —delivered by D. Narducci (“Thermodynamics and thermoelectricity”), G. J. Snyder (“Transport property analysis method for thermoelectric materials: Materials quality factor and the effective mass model”), and R. Rurali (“A primer on phonon transport”). Applications of such concepts to materials were then the subject of the lectures given by M. Martin-Gonzalez (“Past and present of metal chalcogenides, oxides, Heusler compounds and Zintl phases as thermoelectrics: A brief summary”) and K. Koumoto (“Low-dimensional inorganic/organic hybrid thermoelectrics”). Furthermore, Y. Grin and H. Sirringhaus delivered lectures on silicon and silicides and on charge and heat transport in organics. Additional insights into applications of nanoscience to thermoelectricity were provided by G. Benenti (“Theoretical approaches for nanoscale thermoelectric phenomena”), and N. Neophytou (“Electronic transport simulations in complex band structure thermoelectric materials”) while J. P. Heremans contributed highlights on spin thermoelectrics and related topics (“Thermal spin transport and spin in thermoelectrics”). The driving force from advanced technology was covered by the lectures delivered by C. Fanciulli (“Thermoelectric harvesting: Basics on design optimization and applications”) and B. Lorenzi (“Heat conversion in solar thermoelectric harvesters” and “Heat conversion in hybrid solar thermoelectric harvesters”).

The course gathered 51 students from 24 countries and was organized to foster informal and continual interactions among students and lecturers. The lively, participative spirit of the course was one of its major successes. This was also the result of the exceptional organizational framework provided by the Varenna secretary. We wish also to gratefully acknowledge the sponsorships we received from ISC s.r.l., the Italian Thermoelectric Society, Elsevier, and the University of Milano-Bicocca, which enabled the partial or full waiving of registrations fees for students coming from less-developed countries and which concurred to support travel expenses of some of the lecturers coming from non-European countries. Last but not least, we gratefully acknowledge the Italian Physical Society that provided us with the opportunity of organizing this course in the prestigious framework of the “E. Fermi” School of Physics.

Dario Narducci, G. Jeffrey Snyder and Carlo Fanciulli

The aim of this lecture was an analysis of the thermodynamics of thermoelectric phenomena and of thermoelectric generators seen as heat engines. The basic theory of classical irreversible thermodynamics is recalled, and the conversion efficiency of thermoelectric generators is computed thereof under Dirichlet boundary conditions both in the constant-property limit (namely for vanishingly small temperature differences) and by using the concept of thermoelectric compatibility (for large temperature differences).

Thermoelectric semiconducting materials are often evaluated by their figure-of-merit, zT. However, by using zT as the metric for showing improvements, it is not immediately clear whether the improvement is from an enhancement of the inherent material property or from optimization of the carrier concentration. Here, we review the quality factor approach which allows one to separate these two contributions even without Hall measurements. We introduce practical methods that can be used without numerical integration. We discuss the underlying effective mass model behind this method and show how it can be further advanced to study complex band structures using the Seebeck effective mass. We thereby dispel the common misconception that the usefulness of effective band models is limited to single parabolic band materials.

In this paper we give a general and basic introduction to the most important concepts related with phonon transport. We first revise Fourier’s equation and the diffusive transport regime, focusing on the main scattering mechanisms that yield a finite thermal conductivity in insulators: anharmonic phonon-phonon scattering, impurity scattering, and boundary scattering. Next we focus on transport regimes beyond Fourier, namely ballistic transport and phonon hydrodynamics.

The development of high–figure-of-merit (zT) thermoelectric materials has become a need to fight environmental problems such as global warming, climate change and to save scarce non-renewable energy, such as oil. In the XXI century, the improvement in the knowledge of how nanostructuration alters and improves the properties, improvements in the band structure calculations, etc. are helping to obtain materials with much higher zTs. This review tries to give a short overview of the state of the art of metal chalcogenides, oxides, Heusler compounds and Zintl phases.

Energy harvesting is one of the ways explored nowadays to face the problem associated to electrical power needs. Typical powers involved are limited but the main advantage offered by the harvesting approach is the capability to achieve a localized power generation enabling a reduction in losses due to power distribution. Thermoelectric technology represents one of the solution for energy harvesting allowing the direct conversion of a collected or wasted heat into electrical power. This short lecture wants to provide the basic concepts associated to the thermoelectric harvesting. The work discusses the ideas associated to the optimization of a thermoelectric device and the design of a thermoelectric system for electrical power production. The discussion focuses the attention on the different critical aspects a researcher has to face in order to produce an operating system able to match the constrains of a target application. To conclude, a description of some reference cases is reported introducing the reader to the technological impact, actual and possible, of an old technology living a renewed interest promoted by a new environment based on new paradigms for power generation and distribution, and widespread diffusion of low-power electronic devices.

Flexible thermoelectric (TE) devices for maintenance-free and long-lasting power source that makes use of the body heat, industrial waste heat and even solar heat have been of growing interest. Low-dimensional nanomaterials, such as 2D TMDCs (transition metal dichalcogenides) and 1D CNTs (carbon nanotubes), are the best-known candidate materials for high-performance flexible TE devices. TiS₂/organics hybrid superlattice materials and CNTs-based nanocomposites will be focused and their interesting structures, TE properties, and manufacturing processes are demonstrated and discussed. Some examples of device applications of the low-D nanomaterials are also presented.

We focus on the theoretical approaches aimed to analyze thermoelectric properties at the nanoscale. We discuss several relevant theoretical approaches for different set-ups of nano-devices providing estimations of the thermoelectric parameters in the linear and non-linear regime, in particular the thermoelectric figure of merit and the power-efficiency trade-off. Moreover, we analyze the role of not only electronic, but also of vibrational degrees of freedom. First, nanoscale thermoelectric phenomena are considered in the quantum coherent regime using the Landauer-BÂĺuttiker method and focusing on effects of energy filtering. Then, we analyze the effects of many-body couplings between nanostructure degrees of freedom, such as electron-electron and electron-vibration interactions, which can strongly affect the thermoelectric conversion. In particular, we discuss the enhancement of the thermoelectric figure of merit in the Coulomb blockade regime for a quantum dot model starting from the master equation for charge state probabilities and the tunneling rates through the electrodes. Finally, within the non-equilibrium Green function formalism, we quantify the reduction of the thermoelectric performance in simple models of molecular junctions due to the effects of the electron-vibration coupling and phonon transport at room temperature.

Thermoelectric materials convert heat through temperature gradients into electricity, and vice versa provide cooling capabilities once a potential difference is applied across them. The realization of complex band structure materials and their alloys, as well as nanostructured materials, have revived the field of thermoelectric from decades of moderate activity, as they allow possibilities to largely improved performance. Theory and simulation of electro-thermal transport properties of materials have also been rapidly advancing. A variety of simulation software and techniques has been developed, or are in the process of being developed to improve the accuracy of these calculations. The most common simulations for the thermoelectric properties of complex materials employ ab initio techniques (DFT) for the dispersion of materials, which are then used within the Boltzmann Transport Equation (BTE) formalism to extract the thermoelectric coefficients. In the majority of studies, the solutions to the BTE assume the constant relaxation time approximation, despite the fact that we know that the scattering mechanisms are not only energy, but momentum, and band dependent. This is due to the vast computational costs in treating energy-dependent scattering mechanisms properly. This paper introduces the BTE formalism, and explains the numerical implementation of the energy-dependent relaxation time approximation.

Solar thermoelectric generators (STEGs) are two steps energy harvesting systems that convert solar power into electricity. Even if the first generation of this kind of systems was developed in the first half of the twentieth century the interest around this technology has been intermittent. Only in recent years the progress of the thermoelectric material efficiency stimulated a renewed interest on STEGs as a viable alternative to harness solar energy. In this paper the basic aspects of STEG technology, along with the analysis of its efficiency, and the state of the art of this field are discussed.

Hybrid thermoelectric-photovoltaic (HTEPV) generators can be seen as an evolution of STEGs. In their structure the opto-thermal converter is constituted by a solar cells. The intention is to implement thermoelectric materials to recover the high fraction of heat losses occurring in solar cell, adding an extra output power to the system. HTEPV have been already shown to be able to enhance the efficiency of solar cells, even if researchers are still trying to make this approach good enough to become reality. In this paper we will analyse the layout and the achievable efficiency of this hybrid devices, highlighting the challenges and the strong points of this approach.

This paper reviews the principles that govern the combined transport of spin, heat, and charge, both from a macroscopic point of view (the Onsager relations) and microscopically (transport by spin-polarized electrons and magnons). The extensive thermodynamic quantity associated with spin transport is the magnetization; its Onsager-conjugate force is in general the derivative of the free energy with respect to the magnetization. The spin-angular momentum is uniquely associated with the magnetization, so that the words “spin” and “magnetization” are used interchangeably. Spins are carried in one of the following two ways: 1) by spin-polarized free electrons in magnetic metals and doped semiconductors, or 2) by spin waves (magnons) that reside on localized electrons on unfilled d- or f-shells of transition metal or rare-earth elements. The paper covers both cases in separate sections. In both cases, it is possible to define a spin chemical potential whose gradient is the more practical conjugate force to spin transport. The paper further describes the anomalous Hall, spin Hall, and inverse spin Hall effects in magnetic and non-magnetic solids with strong spin-orbit coupling because these effects are used to generate and measure spin fluxes. Spin transport across interfaces is described next, and includes spin pumping and spin transfer torque. The final section then puts all these concepts together to describe the spin-Seebeck, spin-Peltier, and magnon-drag effects, which exist in ferromagnetic, antiferromagnetic, and even paramagnetic solids. Magnon-drag, in particular, is a high-temperature effect that boosts the thermopower of metals by an order of magnitude and that of semiconductors by a factor of 2 or 3 above the electronic diffusion thermopower. This is the only example where a spin-driven effect is larger than a charge-driven effect. Magnon drag leads a simple binary paramagnetic semiconductor, MnTe, to have zT ≥ 1 without any optimization. This shows how adding spin as an additional design parameter in thermoelectrics research is a new and promising approach toward the quest for high-zT materials.