Atomic substitution in alloys can efficiently scatter phonons, thereby reducing the thermal conductivity in crystalline solids to the "alloy limit." Using In0.53Ga0.47As containing ErAs nanoparticles, we demonstrate thermal conductivity reduction by almost a factor of 2 below the alloy limit and a corresponding increase in the thermoelectric figure of merit by a factor of 2. A theoretical model suggests that while point defects in alloys efficiently scatter short-wavelength phonons, the ErAs nanoparticles provide an additional scattering mechanism for the mid-to-long-wavelength phonons.

An approximate analytical solution is proposed to estimate the phonon scattering cross section of polydispersed spherical nanoparticles. Using perturbation of the Hamiltonian due to differences in mass and bond stiffness between a host medium and a spherical nanoparticle, an analytical solution is obtained for the scattering cross section in the Rayleigh limit when the size parameter approaches zero. In the geometrical scattering limit, when the size parameter approaches infinity, the van de Hulst approximation for anomalous diffraction is used to estimate the scattering cross section as a function of acoustic impedance mismatch between the host medium and the spherical nanoparticle. Finally, these two limiting cases are bridged by a simple expression to estimate the scattering cross section for intermediate values of the size parameter. Using this, the scattering cross section for a polydispersed distribution of spherical nanoparticles was also estimated as a function of the parameters defining the statistical size distribution.

In this review, we discuss some of the representative strategies of phonon engineering by categorizing them into the methods affecting each component of phonon thermal conductivity, i.e., specific heat, phonon group velocity, and mean free path. In terms of specific heat, a large unit cell is beneficial in that it can minimize the fraction of thermal energy that can be transported since most of the energy is stored in the optical branches. In an artificial structure such as the superlattice, phonon bandgaps can be created through constructive interference by Bragg reflection, which reduces phonon group velocity.We further categorize the mean free path, i.e., scattering processes, into grain boundary scattering, impurity scattering, and phonon-phonon scattering. Rough-surfaced grains, nano-sized grains, and coated grains are discussed for enhancement of the grain boundary scattering. Alloy atoms, vacancies, nanoparticles, and nano-sized holes are treated as impurities, which limit the phonon mean free path. Lone pair electrons and acoustical-to-optical scattering are suggested for manipulating phonon-phonon scattering. We also briefly mention the limitation and temperature range in which the Wiedemann-Franz law is valid in order to achieve a better estimation of electronic thermal conductivity. This paper provides an organized view of phonon engineering so that this concept can be implemented synergistically with power factor enhancement approaches for design of thermoelectric materials. Fig. 1 Strategies of phonon engineering categorized into methods affecting each component of phonon thermal conductivity, i.e., specific heat, phonon group velocity, and scattering processes. Some of the figures are from the literature. 71,80 Fig. 3 Thermal conductivity of the (SrTiO 3 ) m /(CaTiO 3 ) n superlattice versus period thickness. 23 A TEM figure shows the interface quality of the superlattice. Also, a phonon dispersion curve showing phonon bandgaps is presented.

Pure lead-free SnTe has limited thermoelectric potentials because of the low Seebeck coefficients and the relatively large thermal conductivity. In this study, we provide experimental evidence and theoretical understanding that alloying SnTe with Ca greatly improves the transport properties leading to ZT of 1.35 at 873 K, the highest ZT value so far reported for singly doped SnTe materials. The introduction of Ca (0–9%) in SnTe induces multiple effects: (1) Ca replaces Sn and reduces the hole concentration due to Sn vacancies, (2) the energy gap increases, limiting the bipolar transport, (3) several bands with larger effective masses become active in transport, and (4) the lattice thermal conductivity is reduced by about 70% due to the contribution of concomitant scattering terms associated with the alloy disorder and the presence of nanoscale precipitates. An efficiency of ∼10% (for ΔT = 400 K) was predicted for high-temperature thermoelectric power generation using SnTe-based p- and n-type materials.

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