A strain-free superlattice of inversion domains along the hexagonal axis of SiC is investigated by theoretical calculations. The induced polarization causes a zigzag shape in the band edges, leading to spatial separation of photoexcited carriers and to an effective band gap narrowing tunable over a wide range by the geometry and on a smaller scale by the intensity of the excitation. Calculations on the SiC surface indicate that preparation of such a superlattice might be possible in atomic layer epitaxy with properly chosen sources and temperatures.