A low-cost memory cell array includes multiple, vertically-stacked layers of memory cells. In one form, each memory cell is characterized by a small cross-sectional area and a read current less than 6.3 microamperes. The resulting memory array has a slow access time and is well-suited for digital media storage, where access time requirements are low and the dramatic cost reductions associated with the disclosed memory arrays are particularly attractive. In another form, each memory cell includes an antifuse layer and diode components, wherein at least one diode component is heavily doped (to a dopant concentration greater than 1019/cm3), and wherein the read current is large (up to 500 mA).