of conductance $G$, Seebeck coefficient $S$, and power factor $PF$, for key structure examples as shown in Fig. 1. The blue bar indicates the pristine channel (Fig. 1a), the red bars the SL barrier channels (Fig. 1b), the magenta bars the SL+NI barrier channel (Fig. 1c), the light green bar the SL well channel (Fig. 1d), and the green bar the SL+NI well structure (Fig. 1e). Column-wise, the three different groups are results for AP scattering only, OP scattering only, and AOP scattering. Notice that the $PF$ in the SL case is higher than that of the pristine channel by $23\%$ under elastic AP scattering conditions only. This is retained when NIs are inserted. ](Figure_3.png "fig:"){width="8.4cm" height="14cm"}\

![image](Figure_4.png){width="\textwidth"}

Results and discussion
======================

In the basis of the above observations, we will explain the $PF$ behavior in these nanostructures. It turns out that the dominance of elastic or inelastic scattering processes has a significant effect in the $PF$ [@Kim11; @Thes16JEM], since relaxation lowers $\langle E ( x ) \rangle$ and degrades the Seebeck coefficient. Therefore, for each one of the five geometries shown in Fig. 1, we consider AP scattering alone, OP scattering alone, and finally both AOP scattering combined. We 