success, the thermal conductivities in these materials reached values well below the amorphous limit which is $1-2$ W/mK at room temperature [@Kearney18], and thus, cannot be further reduced easily. Therefore, further benefits to $ZT$ can only be achieved from the enhancement of the $PF$. In the majority of cases, however, nanostucturing degrades the electrical conductivity and the $PF$ as well. In addition, the adverse interdependence of the electrical conductivity and Seebeck coefficient does not allow flexibility in $PF$ improvements.

The importance of retaining high $PF$s has recently become more appreciated in nanostructured TE materials. Reference [@Zhao14], in particular, emphasizes the importance of matrix/inclusion band alignment to retain the original conductivity of the material and to avoid degradation in the $PF$. Large $PF$ improvements were also demonstrated in highly doped nanocrystalline Si [@Neo13ntech], especially in the presence of nanovoids [@Lorenzi14]. While the impact of nanostructuring on the thermal conductivity can be more clearly understood as a general increase in phonon scattering, the same cannot be assumed for the $PF$. Due to the complexity in geometry, theoretical works to date (by us and others) focus on one type of nanostructured feature at a time, i.e. only superlattices (SLs) [@Thes16JEM], only nanocrystalline boundaries 