A transistor device includes a semiconductor mesa region between first and second trenches in a semiconductor body, a body region of a first conductivity type and a source region of a second conductivity type in the semiconductor mesa region, a drift region of the second conductivity type in the semiconductor body, and a gate electrode adjacent the body region in the first trench, and dielectrically insulated from the body region by a gate dielectric. The body region separates the source region from the drift region and extends to the surface of the semiconductor mesa region adjacent the source region. The body region comprises a surface region which adjoins the surface of the semiconductor mesa region and the first trench. The surface region has a higher doping concentration than a section of the body region that separates the source region from the drift region.