A Schottky rectifier includes MOS-filled trenches and an anode electrode at a face of a semiconductor substrate and an optimally nonuniformly doped drift region therein which in combination provide high blocking voltage capability with low reverse-biased leakage current and low forward voltage drop. The nonuniformly doped drift region contains a concentration of first conductivity type dopants therein which increases monotonically in a direction away from a Schottky rectifying junction formed between the anode electrode and the drift region. A profile of the doping concentration in the drift region is preferably a linear or step graded profile with a concentration of less than about 5.times.10.sup.16 cm.sup.-3 (e.g., 1.times.10.sup.16 cm.sup.-3) at the Schottky rectifying junction and a concentration of about ten times greater (e.g., 3.times.10.sup.17 cm.sup.-3) at a junction between the drift region and a cathode region. The thickness of the insulating regions (e.g., SiO.sub.2) in the MOS-filled trenches is also greater than about 1000 .ANG. to simultaneously inhibit field crowding and increase the breakdown voltage of the device. The nonuniformly doped drift region is preferably formed by epitaxial growth from the cathode region and doped in-situ.