Thermoelectric properties of nanoscale three dimensional Si phononic crystals

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) is reduced slightly compared with that of bulk Si, for example, electrical conductivity and electronic thermal conductivity is decreased by 22-39% and 30-43% 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 500 times calculated by molecular dynamics methods, leading to the ZT = 0.66 at carrier concentration around 2.66 × 10¹⁹ cm^-3, which is about 26 times of that of porous Si. This work suggests that 3D Si PnC is a promising candidate for high efficiency thermoelectric materials.