A semiconductor device includes a semiconductor material and trenches extending into the semiconductor material from a first main surface of the semiconductor material to form mesas of semiconductor material between the trenches. The device also includes a field plate in the trenches, a body region in the mesas, a source region in contact with the body region in the mesas, and a gate electrode on the first main surface of the semiconductor material and defining a lateral channel region in each of the body regions under the gate electrodes. A drain region is at the opposing main surface of the semiconductor material. The gate electrodes adjacent opposing sides of the same field plate have the same alignment with respect to that field plate. The device can be a MOSFET or HEMT. Corresponding methods of manufacture are also provided.