Field effect transistor including a downward-protruding gate electrode and methods for forming the same

A field effect transistor contains a semiconductor material layer including a source-side doped well, a source region, and a drain region. A shallow trench isolation structure is embedded in the semiconductor material layer and extends between the source region and the drain region. Agate dielectric layer overlies the semiconductor material layer. A horizontally-extending portion of a gate electrode overlies the gate dielectric layer, and at least one downward-protruding portion of the gate electrode extends downward from a bottom surface of the horizontally-extending portion into an upper region of the shallow trench isolation structure. The gate electrode is vertically spaced from a bottom surface of the shallow trench isolation structure modifies electrical field in a semiconductor channel to reduce hot carrier injection.