A memory cell according to the present invention comprises a bottom conductor, a doped semiconductor pillar, and a top conductor. The memory cell does not include a dielectric rupture antifuse separating the doped semiconductor pillar from either conductor, or within the semiconductor pillar. The memory cell is formed in a high-impedance state, in which little or no current flows between the conductors on application of a read voltage. Application of a programming voltage programs the cell, converting the memory cell from its initial high-impedance state to a low-impedance state. A monolithic three dimensional memory array of such cells can be formed, comprising multiple memory levels, the levels monolithically formed above one another.