1. A method for making a memory cell device of the type including a memory material element switchable between electrical property states by the application of energy, the method comprising: depositing a first electrical conductor layer on a substrate; depositing a first dielectric material layer over the first electrical conductor layer; depositing a second dielectric material layer over the first dielectric material layer; forming a first hole through the first and second dielectric material layers and the first electrical conductor layer to create a first electrode strip from the first electrical conductor layer, the first hole bounded by a side wall; etching a portion of the side wall defined by the first dielectric material layer to create a recessed region between the first electrode strip and the second dielectric material layer; depositing a third dielectric material into the first hole, the third dielectric material depositing step carried out to create a void at the recessed region, the void opening onto the first electrode strip; forming a second hole through the third and second dielectric materials and through the first electrode strip to (1) create a first electrode from the first electrode strip, and (2) intersect the void so that the void includes a first void portion not aligned with the second hole and a second void portion aligned with the second hole; filling the second void portion and at least a portion of the second hole with a fourth dielectric material leaving at least some of the first void portion open; removing the second dielectric material layer and portions of the third and fourth dielectric materials above the first dielectric material layer to expose the first void portion; applying a memory material into the first void portion to create a memory material element with the memory material element in contact with the first electrode; and applying a second electrode conductor layer over the outer surface of the first dielectric material layer and in electrical contact with the memory material element.