A transistor device is fabricated by growing an epitaxial layer of semiconductor material on a semiconductor layer and forming an opening extending through the epitaxial layer at a position where a gate is to be located. This opening provides, from the epitaxial layer, a source epitaxial region on one side of the opening and a drain epitaxial region on an opposite side of the opening. The source epitaxial region and a first portion of the semiconductor layer underlying the source epitaxial region are then converted into a transistor source region. Additionally, the drain epitaxial region and a second portion of the semiconductor layer underlying the drain epitaxial region are converted into a transistor drain region. A third portion of the semiconductor layer between the transistor source and drain regions forms a transistor channel region. A transistor gate electrode is then formed in the opening above the transistor channel region.