From the numerical point of view, the convergence of the self-consistent calculation is quite a difficult task, due to the presence of localized charges. In particular, this is particularly challenging for longer ribbons, which contain a larger number of dopants. To solve this problem, we adopted an enhanced convergence scheme with respect to Reference , based on a progressive approach to the final characteristic. In detail, we chose the starting potential profile for the self-consistent calculations in the following way. For the gate potential for which the convergence was found to be easier (in our simulations, VGS=0.5 V) we used the flat band potential as a guess starting point. Then, the potential profile obtained at the end of the self-consistent simulation was used as a guess potential profile in the calculation performed for the successive gate potential value we considered. We repeated this procedure scanning the entire range of considered gate potentials a few times, alternatively moving for increasing and decreasing values of VGS. At the same time, the error threshold adopted for the termination of the self-consistent calculations was progressively reduced to increase the accuracy of the solution. Finally, we considered that the convergence was achieved once the difference between the ID(VGS) transfer characteristics obtained from successive scans of the domain became negligible.