A method of making a semiconductor device includes providing an insulating layer containing a plurality of openings, forming a first semiconductor layer in the plurality of openings in the insulating layer and over the insulating layer, and removing a first portion of the first semiconductor layer, such that first conductivity type second portions of the first semiconductor layer remain in lower portions of the plurality of openings in the insulating layer, and upper portions of the plurality of openings in the insulating layer remain unfilled. The method also includes forming a second semiconductor layer in the upper portions of the plurality of openings in the insulating layer and over the insulating layer, and removing a first portion of the second semiconductor layer located over the insulating layer. The second conductivity type second portions of the second semiconductor layer remain in upper portions of the plurality of openings in the insulating layer to form a plurality of pillar shaped diodes in the plurality of openings.