A transistor device comprising: source and drain conductors connected by a semiconductor channel provided by a layer of semiconductor material formed over the source and drain conductors; and a gate conductor capacitively coupled to the semiconductor channel via a gate dielectric; wherein at least one of the source and drain conductors comprises a multilayer structure in at least one region thereof, the multilayer structure comprising a lower layer and an upper layer, the material of the lower layer being better than the material of the upper layer at injecting charge into the semiconductor material; and the material of the upper layer exhibiting better electrical conductivity than the material of the lower layer.