scattering are taken into account, i.e., elastic and inelastic scattering, respectively. In this situation, $\langle E ( x ) \rangle$ is indicated by the dashed-black line. Clearly, electrons absorb optical phonons, overpass the potential barriers and then they relax into the wells by emitting optical phonons. The solid-red line shows $\langle E ( x ) \rangle$ under purely acoustic phonon (AP) scattering-limited conditions. In this case scattering is elastic, and the energy of the current is constant along the channel. The dashed-dotted-magenta line shows the optical phonon (OP) scattering-limited transport case, where the energy of the current flow is now slightly lower and the degree of energy relaxation slightly larger compared to the AOP case. Note that we do not compare the two cases on equal basis as the scattering rates for the OP case and AOP case are different, i.e. the OP scattering strength is halved in the AOP case, so relaxation is weaker.

Figure 2(b) shows $\langle E ( x ) \rangle$ in the case where NIs are placed in between the SL barriers (dashed line barriers). The horizontal dashed-green line shows again that under acoustic (elastic) scattering conditions $\langle E ( x ) \rangle$ remains constant along 