A III-N device includes a III-N layer structure including a III-N channel layer, a III-N barrier layer over the III-N channel layer, and a graded III-N layer over the III-N barrier layer having a first side adjacent to the III-N barrier layer and a second side opposite the first side; a first power electrode and a second power electrode; and a gate between the first and second power electrodes, the gate being over the III-N layer structure. A composition of the graded III-N layer is graded so the bandgap of the graded III-N layer adjacent to the first side is greater than the bandgap of the graded III-N layer adjacent to the second side. A region of the graded III-N layer is (i) between the gate and the second power electrode, and (ii) electrically connected to the first power electrode and electrically isolated from the second power electrode.