A vertically oriented self terminating semiconductor device such as a discrete trench MOS device (10, 38) that includes a cylindrical drift region (18) that extend downward from a surface region to a substrate (11) and a dielectric region (20) that exponentially tapers outward from the cylindrical drift region as the drift region approaches the substrate. A field plate electrode (12) is disposed on the dielectric region. Alternatively, the gate electrode (40, 46) may be disposed on the dielectric region, optionally with an underlying field plate electrode (48).