We compare three-dimensional electrostatics of semiconductor structures with graphene-like lattices of quantum dots and antidots formed in the plane of the two dimensional electron gas. With lattice constant fixed, the shape of the potential may be tuned so that both lattices have minband spectrum where the second Dirac feature is pronounced and not overlaid by the other states. We show that the lattice of quantum dots is more sensitive to fabrication imperfections, because sources of the disorder are located directly above the electronic channels. Thus the lattices of antidots should be preferred semiconductor artificial graphene candidates.
