then add NIs with diameter $d=3$ nm each in between those boundaries as indicated in Fig. 1(c). In these structures, the Fermi level is placed at $E_{\text{F}} = V_{\text{SL}} = 0.05$ eV, so that the carriers are allowed easily to flow over the SL barriers. The NIs are modeled as potential barriers of cylindrical shape in rectangular arrangements within the matrix material, and their number density and barrier heights are varied, as discussed in the text below. The choice of the SL and NI sizes are such as to minimize the influence of quantum tunneling, which becomes strong and detrimental for the $PF$ for feature sizes below $3$ nm [@Thes15JAP]. We also consider nanostructured geometries where the potential barriers are replaced with potential wells (Figs. 1(d)-(e)). Finally, we also consider the situation in which the NIs are replaced by voids (not shown). The NEGF approach is ideal for such geometries as they can be described precisely when the Hamiltonian of the system is constructed.

![\[fig2\] (Colour online) Average energy of the current flow $\langle E ( x ) \rangle$ as defined in Eq. (\[eq14\]) along the channel length with (a) SL barriers, (b) SL barriers and NI barriers, and (c) 