The fragility of thermoelectric power factor in cross-plane superlattices in the presence of nonidealities : a quantum transport simulation approach

Energy filtering has been put forth as a promising method for achieving large thermoelectric power factors in thermoelectric materials through Seebeck coefficient improvement. Materials with embedded potential barriers, such as cross-plane superlattices, provide energy filtering, in addition to low thermal conductivity, and could potentially achieve high figure of merit. Although there exist many theoretical works demonstrating Seebeck coefficient and power factor gains in idealized structures, experimental support has been scant. In most cases, the electrical conductivity is drastically reduced due to the presence of barriers. In this work, using quantum-mechanical simulations based on the nonequilibrium Green’s function method, we show that, although power factor improvements can theoretically be observed in optimized superlattices (as pointed out in previous studies), different types of deviations from the ideal potential profiles of the barriers degrade the performance, some nonidealities being so significant as to negate all power factor gains. Specifically, the effect of tunneling due to thin barriers could be especially detrimental to the Seebeck coefficient and power factor. Our results could partially explain why significant power factor improvements in superlattices and other energy-filtering nanostructures mainly fail to be realized, despite theoretical predictions

On the Lorenz number of multiband materials

There are many exotic scenarios where the Lorenz number of the Wiedemann-Franz law is known to deviate from expected values. However, in conventional semiconductor systems, it is assumed to vary between the values of ∼1.49×10−8WΩK−2 for nondegenerate semiconductors and ∼2.45×10−8WΩK−2 for degenerate semiconductors or metals. Knowledge of the Lorenz number is important in many situations, such as in the design of thermoelectric materials and in the experimental determination of the lattice thermal conductivity. Here, we show that, even in the simple case of two- and three-band semiconductors, it is possible to obtain substantial deviations of a factor of 2 (or in the case of a bipolar system with a Fermi level near the midgap, even orders of magnitude) from expectation. In addition to identifying the sources of deviation in unipolar and bipolar two-band systems, a number of analytical expressions useful for quantifying the size of the effect are derived. As representative case studies, a three-band model of the materials of lead telluride (PbTe) and tin sellenide (SnSe), which are important thermoelectric materials, is also developed and the size of possible Lorenz number variations in these materials explored. Thus, the consequence of multiband effects on the Lorenz number of real systems is demonstrated

On the effectiveness of the thermoelectric energy filtering mechanism in low-dimensional superlattices and nano-composites

Electron energy filtering has been suggested as a promising way to improve the power factor and enhance the ZT figure of merit of thermoelectric materials. In this work, we explore the effect that reduced dimensionality has on the success of the energy-filtering mechanism for power factor enhancement. We use the quantum mechanical non-equilibrium Green's function method for electron transport including electron-phonon scattering to explore 1D and 2D superlattice/nanocomposite systems. We find that, given identical material parameters, 1D channels utilize energy filtering more effectively than 2D as they: (i) allow one to achieve the maximal power factor for smaller well sizes/smaller grains which are needed to maximize the phonon scattering, (ii) take better advantage of a lower thermal conductivity in the barrier/boundary materials compared to the well/grain materials in both: enhancing the Seebeck coefficient; and in producing a system which is robust against detrimental random deviations from the optimal barrier design. In certain cases, we find that the relative advantage can be as high as a factor of 3. We determine that energy-filtering is most effective when the average energy of carrier flow varies the most between the wells and the barriers along the channel, an event which occurs when the energy of the carrier flow in the host material is low, and when the energy relaxation mean-free-path of carriers is short. Although the ultimate reason for these aspects, which cause a 1D system to see greater relative improvement than a 2D, is the 1D system's van Hove singularity in the density-of-states, the insights obtained are general and inform energy-filtering design beyond dimensional considerations

The influence of non-idealities on the thermoelectric power factor of nanostructured superlattices

Cross-plane superlattices composed of nanoscale layers of alternating potential wells and barriers have attracted great attention for their potential to provide thermoelectric power factor improvements and higher ZT figure of merit. Previous theoretical works have shown that the presence of optimized potential barriers could provide improvements to the Seebeck coefficient through carrier energy filtering, which improves the power factor by up to 40%. However, experimental corroboration of this prediction has been extremely scant. In this work, we employ quantum mechanical electronic transport simulations to outline the detrimental effects of random variation, imperfections, and non-optimal barrier shapes in a superlattice geometry on these predicted power factor improvements. Thus, we aim to assess either the robustness or the fragility of these theoretical gains in the face of the types of variation one would find in real material systems. We show that these power factor improvements are relatively robust against: overly thick barriers, diffusion of barriers into the body of the wells, and random fluctuations in barrier spacing and width. However, notably, we discover that extremely thin barriers and random fluctuation in barrier heights by as little as 10% is sufficient to entirely destroy any power factor benefits of the optimized geometry. Our results could provide performance optimization routes for nanostructured thermoelectrics and elucidate the reasons why significant power factor improvements are not commonly realized in superlattices, despite theoretical predictions

Random site dilution properties of frustrated magnets on a hierarchical lattice

We present a method to analyze magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal couplings of the original Hamiltonian. The two-dimensional model presented here possesses a macroscopic entropy at zero temperature in the large size limit, very close to the Pauling estimate for spin-ice on pyrochlore lattice, and a crossover towards a paramagnetic phase. The disorder due to dilution is taken into account by considering a replicated version of the recursion equations between partition functions at different lattice sizes. An analysis at first order in replica number allows for a systematic reorganization of the disorder configurations, leading to a recurrence scheme. This method is numerically implemented to evaluate the thermodynamical quantities such as specific heat and susceptibility in an external field.Comment: 26 pages, 11 figure

Theoretical model for the Seebeck coefficient in superlattice materials with energy relaxation

We present an analytical model for the Seebeck coefficient S of superlattice materials that explicitly takes into account the energy relaxation due to electron-optical phonon (e-ph) scattering. In such materials, the Seebeck coefficient is not only determined by the bulk Seebeck values of the materials but, in addition, is dependent on the energy relaxation process of charge carriers as they propagate from the less-conductive barrier region into the more-conductive well region. We calculate S as a function of the well size d, where carrier energy becomes increasingly relaxed within the well for d>λE, where λE is the energy relaxation length. We validate the model against more advanced quantum transport simulations based on the nonequilibrium Green’s function (NEGF) method and also with an experiment, and we find very good agreement. In the case in which no energy relaxation is taken into account, the results deviate substantially from the NEGF results. The model also yields accurate results with only a small deviation (up to ∼3%) when varying the optical phonon energy ℏω or the e-ph coupling strength D0, physical parameters that would determine λE. As a first order approximation, the model is valid for nanocomposite materials, and it could prove useful in the identification of material combinations and in the estimation of ideal sizes in the design of nanoengineered thermoelectric materials with enhanced power factor performanc