  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.
