A transistor includes a III-N layer structure comprising a III-N channel layer between a III-N barrier layer and a p-type III-N layer. The transistor further includes a source, a drain, and a gate between the source and the drain, the gate being over the III-N layer structure. The p-type III-N layer includes a first portion that is at least partially in a device access region between the gate and the drain, and the first portion of the p-type III-N layer is electrically connected to the source and electrically isolated from the drain. When the transistor is biased in the off state, the p-type layer can cause channel charge in the device access region to deplete as the drain voltage increases, thereby leading to higher breakdown voltages.