A memory cell device has a bottom electrode and a top electrode, a plug of memory material in contact with the bottom electrode, and a cup-shaped conductive member having a rim that contacts the top electrode and an opening in the bottom that contacts the memory material. Accordingly, the conductive path in the memory cells passes from the top electrode through the conductive cup-shaped member, and through the plug of phase change material to the bottom electrode. Also, methods for making the memory cell device include steps of forming a bottom electrode island including an insulative element and a stop element over a bottom electrode, forming a separation layer surrounding the island, removing the stop element to form a hole over the insulative element in the separation layer, forming a conductive film in the hole and an insulative liner over conductive film, etching to form a cup-shaped conductive film having a rim and to form an opening through the insulative liner and the bottom of the cup-shaped conductive film to the surface of the bottom electrode, forming a plug of phase change memory material in the opening, and forming a top electrode in contact with the rim of the cup-shaped conductive film.