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We assess the impact of the scattering physics assumptions on the thermoelectric properties of five Co-based p-type half-Heusler alloys by considering full energy-dependent scattering times, versus the commonly employed constant scattering time. For this, we employ DFT bandstructures and a full numerical scheme that uses Fermi's Golden Rule to extract the momentum relaxation times of each state at every energy, momentum, and band. We consider electron-phonon scattering (acoustic and optical), as well as ionized impurity scattering, and evaluate the qualitative and quantitative differences in the power factors of the materials compared to the case where the constant scattering time is employed. We show that the thermoelectric power factors extracted from the two different methods differ in terms of: i) their ranking between materials, ii) the carrier density where the peak power factor appears, and iii) their trends with temperature. We further show that the constant relaxation time approximation smoothens out the richness in the bandstructure features, thus limiting the possibilities of exploring this richness for material design and optimization. These details are more properly captured under full energy/momentum-dependent scattering time considerations. Finally, by mapping the conductivities extracted within the two schemes, we provide appropriate density-dependent constant relaxation times that could be employed as a fast first-order approximation for extracting charge transport properties in the half-Heuslers we consider.
Localised surface plasmons create a non-equilibrium high-energy electron gas in nanostructures that can be injected into other media in energy harvesting applications. Here, we derive the rate of this localised-surface-plasmon mediated generation of hot electrons in nanorods and the rate of injecting them into other media by considering quantum mechanical motion of the electron gas. Specifically, we use the single-electron wave function of a particle in a cylindrical potential well and the electric field enhancement factor of an elongated ellipsoid to derive the energy distribution of electrons after plasmon excitation. We compare the performance of nanorods with equivolume nanoparticles of other shapes such as nanospheres and nanopallets and report that nanorods exhibit significantly better performance over a broad spectrum. We present a comprehensive theoretical analysis of how different parameters contribute to efficiency of hot-electron harvesting in nanorods and reveal that increasing the aspect ratio can increase the hot-electron generation and injection, but the volume shows an inverse dependency when efficiency per unit volume is considered. Further, the electron thermalisation time shows much less influence on the injection rate. Our derivations and results provide the much needed theoretical insight for optimization of hot-electron harvesting process in highly adaptable metallic nanorods.
Producing high band and valley degeneracy through aligning of conducting electronic bands is an effective strategy to improve the thermoelectric performance of complex bandstructure materials. Half-Heuslers, an emerging thermoelectric material group, has complex bandstructures with multiple bands that can be aligned through band engineering approaches, giving us an opportunity to improve their power factor. Theoretical calculations to identify the outcome of band engineering usually employ detailed density functional theory for bandstructure calculations, but the transport calculations are kept simplistic using the constant relaxation time approximation due to the complications involved with detailed scattering physics. In this work, going beyond the constant relaxation time approximation, we perform an investigation of the benefits of band alignment in improving the thermoelectric power factor under different density of states dependent scattering scenarios. As a test case we consider the Co-based p-type half-Heuslers TiCoSb, NbCoSn and ZrCoSb. First, using simplified effective mass models combined with Boltzmann transport, we investigate the conditions of band alignment that are beneficial to the thermoelectric power factor under three different carrier scattering scenarios: i) the usual constant relaxation time approximation, ii) intra-band scattering restricted to the current valley with the scattering rates proportional to the density of states as dictated by Fermi's Golden Rule, and iii) both intra-and inter-band scattering across all available valleys, with the rates determined by the total density of states at the relevant energies. We demonstrate that the band-alignment outcome differs significantly depending on the scattering details. Next, using the density functional theory calculated bandstructures of the half-Heuslers we study their power factor behavior under strain induced band alignment. We show that strain can improve the power factor of half-Heuslers, but the outcome heavily depends on the curvatures of the bands involved, the specifics of the carrier scattering mechanisms and the initial band separation. Importantly, we also demonstrate that band alignment is not always beneficial to the power factor. In addition, we show that the bandstructure itself can undergo changes as the bands are aligned in practice, which further affect the band alignment optimization. Our work illustrates the importance of going beyond the constant relaxation time approximation, as well as understanding how the bandstructure of each material behaves when considering band alignment. arXiv:1905.07951v1 [cond-mat.mtrl-sci]
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