The thermoelectric properties of n type nanoscale three dimensional (3D) Si phononic crystals (PnCs) with spherical pores are studied. Density functional theory and Boltzmann transport equation under the relaxation time approximation are applied to study the electronic transport coefficients, electrical conductivity, Seebeck coefficient and electronic thermal conductivity. We found that the electronic transport coefficients in 3D Si PnC at room temperature (300 K) change very little compared with that of Si, for example, electrical conductivity and electronic thermal conductivity is decreased by 0.26 to 0.41 and 0.39 to 0.55 depending on carrier concentration, respectively, and the Seebeck coefficient is similar to that of bulk Si. However, the lattice thermal conductivity of 3D Si PnCs with spherical pores is decreased by a factor of 500 calculated by molecular dynamics methods, leading to the ZT of 0.76, which is about 30 times of that of porous Si. This work indicates that 3D Si PnC is a promising candidate for high efficiency thermoelectric materials.
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