1. A phase change memory device comprising: a memory cell access layer; and a memory cell layer, operably coupled to the memory cell access layer, comprising a phase change memory cell, said memory cell comprising: first and second opposed, spaced apart contact elements, respectively; a phase change element positioned between the first and second contact elements and electrically coupling the first and second contact elements to one another; the phase change element having a width, a length and a thickness, the length measured between the first and second contact elements and the width measured perpendicular to the length; each of the length, the thickness and the width being less than a minimum lithographic feature size used to form the phase change memory cell; and the first and second contact elements and the phase change element therebetween defining a memory cell arrangement extending generally parallel to the memory cell access layer.