A method is described for forming a nonvolatile one-time-programmable memory cell having reduced programming voltage. A contiguous p-i-n diode is paired with a dielectric rupture antifuse formed of a high-dielectric-constant material, having a dielectric constant greater than about 8. In preferred embodiments, the high-dielectric-constant material is formed by atomic layer deposition. The diode is preferably formed of deposited low-defect semiconductor material, crystallized in contact with a silicide. A monolithic three dimensional memory array of such cells can be formed in stacked memory levels above the wafer substrate.