A one-time programmable unit memory cell includes a vertically oriented fuse and an diode in series. Within the vertically oriented fuse, the current flow is substantially vertical, i.e. perpendicular to the plane of the substrate. Also, the vertically oriented fuse is placed between top and bottom conductors. This vertical placement of the elements helps to increase density of memory devices built using these unit cells. Also, vertically oriented fuses consume very little lateral area, which helps the density even further. The unit memory cell has two states, an initial state and a written (programmed) state. In the initial state, a resistance of the cell is finite because the vertically oriented fuse is left intact. In the written state, the resistance is infinite because the fuse is blown open. The cell may be programmed by applying a critical voltage across the cell enough to cause the fuse to become open. The states are detected by applying a read voltage across the memory cell. If the is not programmed, then a measurable amount flows. Otherwise, no current flows due to the open circuit. A cross-point memory array may be formed with unit memory cells formed at each cross point. With addition of read and write circuitry, the memory array maybe used as memory. However, multiple arrays may be stacked to form high density memory devices.