Silicon nitride antifuses can be advantageously used in memory arrays employing diode-antifuse cells. Silicon nitride antifuses can be ruptured faster and at a lower breakdown field than antifuses formed of other materials, such as silicon dioxide. Examples are given of monolithic three dimensional memory arrays using silicon nitride antifuses with memory cells disposed in rail-stacks and pillars, and including PN and Schottky diodes. Pairing a silicon nitride antifuse with a low-density, high-resistivity conductor gives even better device performance.