A semiconductor structure includes a substrate and a conductive carrier-tunneling layer over and contacting the substrate. The conductive carrier-tunneling layer includes first group-III nitride (III-nitride) layers having a first bandgap, wherein the first III-nitride layers have a thickness less than about 5 nm; and second III-nitride layers having a second bandgap lower than the first bandgap, wherein the first III-nitride layers and the second III-nitride layers are stacked in an alternating pattern. The semiconductor structure is free from a III-nitride layer between the substrate and the conductive carrier-tunneling layer. The semiconductor structure further includes an active layer over the conductive carrier-tunneling layer.