A memory cell device, of the type that includes a memory material switchable between electrical property states by application of energy, includes first and second electrodes, a plug of memory material (such as phase change material) which is in electrical contact with the second electrode, and an electrically conductive film which is supported by a dielectric form and which is in electrical contact with the first electrode and with the memory material plug. The dielectric form is wider near the first electrode, and is narrower near the phase change plug. The area of contact of the conductive film with the phase change plug is defined in part by the geometry of the dielectric form over which the conductive film is formed. Also, methods for making the device include steps of constructing a dielectric form over a first electrode, and forming a conductive film over the dielectric form.