begin by presenting in Figs. 3(a)-(c) some key simulation results for those basic structures with respect to the electronic conductivity, Seebeck coefficient, and $PF$, respectively. In the case of the SL barrier structures, we align the Fermi level with $V_{\text{SL}}$ at $0.05$ eV for optimal performance, whereas in the other cases with the band edge $E_{\text{C}}$. The different bars correspond to the geometries of Fig. 1 as follows: i) blue bars-pristine structure, ii) red bars-SL barrier structure, iii) magenta bars-SL barriers plus NIs structure, iv) light green bars-SL wells structure, and v) green bars-SL wells with NIs structure. The three different column groups show the corresponding values for AP scattering, OP scattering, and AOP scattering, respectively.

**Elastic scattering improves the optimal PF:** We first focus on AP (elastic) scattering conditions, where the results for $G$, $S$, and $PF$ are shown in the first column group of Fig. 3. We compare how each quantity changes with respect to the pristine material (blue bars) for each nanostructured geometry. Interestingly, by raising $E_{\text{F}}$ high in the bands, the conductance $G$ (first column, first row, red bar) is increased by $55\%$, despite the introduction of the SL barriers (we discuss the reasons behind this 