A device includes a trench extending into a semiconductor region and having a first conductivity type, and a conductive field plate in the trench. A first dielectric layer separates a bottom and sidewalls of the field plate from the semiconductor region. A main gate is disposed in the trench and overlapping the field plate. A second dielectric layer is disposed between and separating the main gate and the field plate from each other. A Doped Drain (DD) region of the first conductivity type is under the second dielectric layer and having an edge portion overlapping the DD region. A body region includes a first portion at a same level as a portion of the main gate, and a second portion contacting the DD region, wherein the body region is of a second conductivity type opposite the first conductivity type. A MOS-containing device is at a surface of the semiconductor region.