An integrated circuit including vertically oriented diode structures between conductors and methods of fabricating the same are provided. Two-terminal devices such as passive element memory cells can include a diode steering element in series with an antifuse and/or other state change element. The devices are formed using pillar structures at the intersections of upper and lower sets of conductors. The height of the pillar structures are reduced by forming part of the diode for each pillar in a rail stack with one of the conductors. A diode in one embodiment can include a first diode component of a first conductivity type and a second diode component of a second conductivity type. A portion of one of the diode components is divided into first and second portions with one on the portions being formed in the rail stack where it is shared with other diodes formed using pillars at the rail stack.