The invention provides for a nonvolatile memory cell comprising a heater layer in series with a phase change material, such as a chalcogenide. Phase change is achieved in chalcogenide memories by thermal means. Concentrating thermal energy in a relatively small volume assists this phase change. In the present invention, a layer in a pillar-shaped section of a memory cell is etched laterally, decreasing its cross-section. In this way the cross section of the contact area between the heater layer and the phase change material is reduced. In preferred embodiments, the laterally etched layer is the heater layer or a sacrificial layer. In a preferred embodiment, such a cell can be used in a monolithic three dimensional memory array.