A new semiconductor rectifier structure. In general, a MOS-transistor-like structure is located above a JFET-like deeper structure. The present application teaches ways to combine and optimize these two structures in a merged device so that the resulting combined structure achieves both a low forward voltage and a high reverse breakdown voltage in a relatively small area. In one class of innovative implementations, an insulated (or partially insulated) trench is used to define a vertical channel in a body region along the sidewall of a trench, so that majority carriers from a “source” region (typically n+) can flow through the channel. An added “pocket” diffusion, of the same conductivity type as the body region (p-type in this example), provides an intermediate region around the bottom of the trench. This intermediate diffusion, and an additional deep region of the same conductivity type, define a deep JFET-like device which is in series with the MOS channel portion of the diode. This advantageously permits the MOS channel portion to be reasonably short, and to have a reasonably low threshold voltage, since the high-voltage withstand characteristics are defined by the deep JFET-like device.