A fin-type programmable memory cell includes a bottom electrode electrically coupled to an access device, a top electrode, and an L-shaped memory material element electrically coupled to the bottom and top electrodes. A memory array includes an array of such memory cells, electrically coupled to an array of access devices. Method for making a memory cell, includes: forming a dielectric support layer over a bottom electrode, the dielectric support layer having an upper surface; forming a cavity through the dielectric support layer, exposing a surface of the bottom electrode and defining a dielectric support structure having a sidewall; forming a film of memory material over the dielectric support structure and in the cavity; depositing a dielectric spacer layer over the memory material film; forming a dielectric sidewall spacer from the dielectric spacer layer and a memory material structure having a generally horizontal portion underlying the dielectric sidewall spacer and a generally vertical portion between the dielectric sidewall spacer and the sidewall of the dielectric support structure; forming a dielectric fill; planarizing the dielectric fill to expose upper ends of the vertical portion of the memory material structure; depositing a top electrode material over the planarized dielectric fill; and forming a top electrode from the top electrode material and a memory material element from the memory material structure.