Band alignment and scattering considerations for enhancing the thermoelectric power factor of complex materials: The case of Co-based half-Heuslers

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. 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.Comment: 18 pages, 15 figure

DFT study of undoped and As-doped Si nanowires approaching the bulk limit

The electronic properties of pure and As-doped Si nanowires with radii up to 9.53 nm are studied using large scale density functional theory (DFT) calculations. We show that, for the undoped nanowires, the DFT bandgap reduces with increasing diameter and converges to its bulk value, a trend in agreement with experimental data. Moreover, we show that the atoms closest to the surface of the nanowire contribute less to the states near the band edges, when compared with atoms close to the centre; this is shown to be due to differences in Si-Si atomic distances, as well as surface passivation effects. When considering As-doped Si nanowires we show that dopant placement within the nanowire plays an important role in deciding electronic properties. We show that a low velocity band is introduced by As doping, in the gap, but close to the conduction band edge. The dopant location affects the curvature of this band, with the curvature reducing when the dopant is placed closer to the center. We also show that asymmetry of dopant location with the nanowire leads to splitting of the valence band edge.Comment: 9 pages, 9 figures, submitted to Phys. Rev.

Material descriptors for the discovery of efficient thermoelectrics

The predictive performance screening of novel compounds can significantly promote the discovery of efficient, cheap, and nontoxic thermoelectric (TE) materials. Large efforts to implement machine-learning techniques coupled to materials databases are currently being undertaken, but the adopted computational methods can dramatically affect the outcome. With regards to electronic transport and power factor (PF) calculations, the most widely adopted and computationally efficient method is the constant relaxation time approximation (CRT). This work goes beyond the CRT and adopts the proper, full energy and momentum dependencies of electron–phonon and ionized impurity scattering to compute the electronic transport and perform PF optimization for a group of half-Heusler alloys. Then, the material parameters that determine the optimal PF based on this more advanced treatment are identified. This enables the development of a set of significantly improved descriptors that can be used in material screening studies, which offer deeper insights into the underlying nature of high-performance TE materials. We have identified nvεr/Do2mcond as the most useful and generic descriptor, a combination of the number of valleys, the dielectric constant, the conductivity effective mass, and the deformation potential for the dominant electron–phonon process. The proposed descriptors can accelerate the discovery of new efficient and environment-friendly TE materials in a much more accurate and reliable manner, and some predictions for very high-performance materials are presented

Impact of the scattering physics on the power factor of complex thermoelectric materials

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 vs the commonly employed constant scattering time. For this, we employ density functional theory band structures 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 band structure 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

Hot Electron Engineering in Nano Structures

When electromagnetic radiation is applied to a nanoparticle, scattering,  absorption, and transmission of this radiation can take place. The absorbed radiation (photons) will increase the kinetic and potential energy of electrons inside the particle, pushing them into excited states. These excited electrons with high energy are not in thermal equilibrium with the lattice of the nanoparticle <br>    and hence are referred to as hot electrons.     <br>      Hot electrons are injected into the surrounding media if their energies are high enough to cross over the energy barrier at the interface between the nanoparticles and the surroundings. This results in generation of a photocurrent, which is  found useful in many opto electronic applications. Therefore, hot electron generation and injection is a field of high scientific interest.     <br>      Localized surface plasmons (LSPs) generated in metallic nanoparticles via optical excitation create an enhanced electric field inside the nanoparticle, aiding the hot electron generation process. In smaller metallic nanoparticles, absorption is much more dominant than scattering and a larger proportion of excited electrons <br>    end up in higher energy levels, making them ideal for hot electron injection related applications.     <br>      As the particle dimensions are reduced to nanoscale and become comparable to the wavelength of the electron wave function, the energy levels of electrons  become highly discreet and geometrically dependent. The efficiency and magnitude of the hot electron injection process depends on the energy spectrum of the electrons, which is determined based on the shape and size of the nanoparticle.  In this thesis, the shape and size dependent hot electron generation and injection behaviour of metallic nanoparticles, considering the quantized motion of the conduction electrons, are studied. The results of this study are used to design a hot electron based all-optical direction-switching device, which is extremely useful in nanoscale electronic circuitry.     <br>      The shape and size dependence of the electron energy levels cause the dielectric function of the nanoparticle to be geometry dependent as the dimensions of the particle are reduced. When analysing hot electron generation and other optical properties of nanoparticles, the dielectric function is a key input. Therefore, it is important to obtain a realistic dielectric function based on electron excitations <br> at different frequencies, considering the shape as well as the size of the particle by following a quantum-mechanical approach. Therefore, as a final part of this research, the quantum confinement effects on the frequency-dependent dielectric function of metallic nanoparticles and its influence on hot electron generation are studied.     <br>      This thesis is organized as follows. An introduction to hot electrons in nanoparticles and the objectives of this research are presented in Chapter 1, followed by a literature review of the mathematical techniques used to model hot electron generation and injection in Chapter 2. Chapters 3 and 4 present theoretical analyses of shape- and size-dependent hot electron behaviour and design guidelines for nanorods and nanotubes, respectively. A design of a novel all-optical hot electron based current-direction-switching device (CDSD) is presented in Chapter 5, while Chapter 6 discusses the effects of quantum confinement on the permittivity of a nanoparticle and how it effects hot electron generation. Chapter 7 presents a summary of contributions and suggestions for future research

Theoretical analysis of hot electron dynamics in nanorods

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Design of all-optical, hot-electron current-direction-switching device based on geometrical asymmetry

We propose a nano-scale current-direction-switching device(CDSD) that operates based on the novel phenomenon of geometrical asymmetry between two hot-electron generating plasmonic nanostructures. The proposed device is easy to fabricate and economical to develop compared to most other existing designs. It also has the ability to function without external wiring in nano or molecular circuitry since it is powered and controlled optically. We consider a such CDSD made of two dissimilar nanorods separated by a thin but finite potential barrier and theoretically derive the frequency-dependent electron/current flow rate. Our analysis takes in to account the quantum dynamics of electrons inside the nanorods under a periodic optical perturbation that are confined by nanorod boundaries, modelled as finite cylindrical potential wells. The influence of design parameters, such as geometric difference between the two nanorods, their volumes and the barrier width on quality parameters such as frequency-sensitivity of the current flow direction, magnitude of the current flow, positive to negative current ratio, and the energy conversion efficiency is discussed by considering a device made of Ag/TiO(2)/Ag. Theoretical insight and design guidelines presented here are useful for customizing our proposed CDSD for applications such as self-powered logic gates, power supplies, and sensors