In this paper, thermoelectric properties of nanoporous silicon are modeled and studied by using a computational approach. The computational approach combines a quantum non-equilibrium Green's function (NEGF) coupled with the Poisson equation for electrical transport analysis, a phonon Boltzmann transport equation (BTE) for phonon thermal transport analysis and the Wiedemann-Franz law for calculating the electronic thermal conductivity. By solving the NEGF/Poisson equations self-consistently using a finite difference method, the electrical conductivity σ and Seebeck coefficient S of the material are numerically computed. The BTE is solved by using a finite volume method to obtain the phonon thermal conductivity kp and the Wiedemann-Franz law is used to obtain the electronic thermal conductivity ke. The figure of merit of nanoporous silicon is calculated by ZT=S2σT/(kp+ke). The effects of doping density, porosity, temperature, and nanopore size on thermoelectric properties of nanoporous silicon are investigated. It is confirmed that nanoporous silicon has significantly higher thermoelectric energy conversion efficiency than its nonporous counterpart. Specifically, this study shows that, with a n-type doping density of 1020 cm–3, a porosity of 36% and nanopore size of 3 nm × 3 nm, the figure of merit ZT can reach 0.32 at 600 K. The results also show that the degradation of electrical conductivity of nanoporous Si due to the inclusion of nanopores is compensated by the large reduction in the phonon thermal conductivity and increase of absolute value of the Seebeck coefficient, resulting in a significantly improved ZT.
In this paper, the effect of strain on the thermoelectric figure of merit is investigated in n-type Ge nanowire-Si host nanocomposite materials. The Seebeck coefficient and electrical conductivity of the Si–Ge nanocomposites are calculated using an analytical model derived from the Boltzmann transport equation (BTE) under the relaxation-time approximation. The effect of strain is incorporated into the BTE through the strain induced energy shift and effective mass variation calculated from the deformation potential theory and a degenerate k·p method at the zone-boundary X point. The effect of strain on the phonon thermal conductivity in the nanocomposites is computed with a model combining the strain dependent lattice dynamics and the ballistic phonon BTE. The electronic thermal conductivity is computed from the electrical conductivity using the Wiedemann-Franz law. Normal and shear strains are applied in the transverse plane of the Si–Ge nanocomposites. Thermoelectric properties, including the electrical conductivity, thermal conductivity, Seebeck coefficient, and dimensionless figure of merit, are computed for Si–Ge nanocomposites under these strain conditions.
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