An ovonic phase-change semiconductor memory device having a reduced area of contact between electrodes of chalcogenide memories, and methods of programming the same are disclosed. Such memory devices include a lower electrode including non-parallel sidewalls. An insulative material overlies the lower electrode such that an upper surface of the lower electrode is exposed. In one embodiment, the insulative material and lower electrode may have a co-planar upper surface. In another embodiment, an upper surface of the lower electrode is within a recess in the insulative material. A chalcogenide material and an upper electrode are formed over the upper surface of the lower electrode. This allows the memory cells to be made smaller and allows the overall power requirements for the memory cell to be minimized.