A MESFET includes a silicon carbide layer, spaced apart source and drain regions in the silicon carbide layer, a channel region positioned within the silicon carbide layer between the source and drain regions and doped with implanted dopants, and a gate contact on the silicon carbide layer. Methods of forming a MESFET include providing a layer of silicon carbide, forming spaced apart source and drain regions in the silicon carbide layer, implanting impurity atoms to form a channel region between the source and drain regions, annealing the implanted impurity atoms, and forming a gate contact on the silicon carbide layer.