which is responsible for this $PF$ improvement. The physical origin for this behavior lies in the fact that the charge carriers propagate on average at higher energies, which allow higher group velocities, and thus higher mobility. This is evident in Fig. 4(a), which shows the transmission versus energy of the pristine material (solid-blue line) and of the SL material (dashed-red line), extracted at every $x$-point as $Tr(x) = \left( h / e^2 \right) \left( I(x) /(f_1 - f_2) \right)$. Note that $I(x)$ is constant in the case of AP which makes the $Tr(x)$ constant, but not in the case of OP and AOP. In the semiclassical Boltzmann transport formalism, the transmission is related to the transport distribution function (TD) $\Xi ( E )$ via $Tr_n (E) = \left( W / L \right) 2\pi\hbar \Xi_n (E)$, where $\Xi_n(E) = g_n(E) \upsilon_n^2 (E) \tau_n (E)$ is the TD function per subband $n$ [@NeoNanoLett; @Neo11PRB; @Mahan96PNAS; @Scheidemantel03]. In the usual case where $\tau_n (E) \propto 1/g_n(E)$, then $\Xi_n(E) \propto \upsilon_n^2 (E) \propto 2 E / m^\star$, which is linear in energy as we also observe within NEGF in Fig. 4(a). In the case of the SL, the transmission opens up for energies above 