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We present a new method for predicting effective thermal conductivity (κ eff ) in materials, informed by ab initio material property simulations. Using the Boltzmann transport equation in a Self-Adjoint Angular Flux formulation, we performed simulations in silicon at room temperatures over length scales varying from 10 nm to 10 µm and report temperature distributions, spectral heat flux and thermal conductivity. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. In this method, a closure term is introduced to the transport equation which acts as a redistribution kernel for the total energy bath of the system. This term is an effective indicator of the degree of disorder between the spectral phonon radiance and the angular phonon intensity of the transport system. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations.

reducing the thermal conductivity. However, porosity also is detrimental to the thermoelectric power factor in the numerator of ZT. In this manuscript we derive strategies to recoup electrical performance in nanoporous Si by fine tuning the carrier concentration and through judicious design of the of pore size and shape so as to provide energy selective electron filtering. A semiclassical Boltzmann transport equation is used to model Si thermoelectric power factor. This model reveals three key results: The largest enhancement in Seebeck coefficient happens for cubic pores with characteristic length around 0.85 nm.For the best energy filtering threshold, nanoporous Si is needed to be doped to higher carrier concentration compared to bulk Si. We show that in a n-type thermoelectric the highest practical filtering threshold that can be provided by a dispersion of spherical nanopores with characteristic length around 16 nm giving a theoretical maximum power factor as high as 89% of the maximum power factor that can be obtained in bulk Si at room temperature.

Engineering materials to include nanoscale porosity or other nanoscale structures has become a well-established strategy for enhancing the thermoelectric performance of dielectrics. However, the approach is only considered beneficial for materials where the intrinsic phonon mean-free path is much longer than that of the charge carriers. As such, the approach would not be expected to provide significant performance gains in polycrystalline semiconducting alloys, such as SixGe1-x, where mass disorder and grains provide strong phonon scattering. In this manuscript, we demonstrate that the addition of nanoscale porosity to even ultrafine-grained Si0.8Ge0.2 may be worthwhile. The semiclassical Boltzmann transport equation was used to model electrical and phonon transport in polycrystalline Si0.8Ge0.2 containing prismatic pores perpendicular to the transport current. The models are free of tuning parameters and were validated against experimental data. The models reveal that a combination of pores and grain boundaries suppresses phonon conductivity to a magnitude comparable with the electronic thermal conductivity. In this regime, ZT can be further enhanced by reducing carrier concentration to the electrical and electronic thermal conductivity and simultaneously increasing thermopower. Although increases in ZT are modest, the optimal carrier concentration is significantly lowered, meaning semiconductors need not be so strongly supersaturated with dopants.