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The two-dimensional material C3N has a honeycomb structure similar to graphene, but its heterogeneity of carbon and nitrogen elements makes it multifunctional. By performing a first-principles study, we find that edge morphology induces interesting electronic transport properties in step-like heterojunction devices composed of width-variable zigzag C3N nanoribbons. As long as the right part has an edge of all-carbon morphology, negative differential resistance and rectification effects will occur. If both edges are not of all-carbon morphology due to the presence of N atoms, a forward-conducting and reverse-blocking rectifier diode behavior will appear. These phenomena originate from the peculiar electronic structure of the zigzag C3N nanoribbons. The number of energy bands crossing the Fermi level gradually decreases from 2 to 0 as the number of all-carbon edges decreases, realizing a transition from metal …