1. A memory cell, comprising: a bottom electrode; a top electrode comprising a material that is electrically conductive and configured to provide ions of the material under applied bias; a switching layer comprising a second material that is electrically resistive and at least in part permeable to the ions of the material of the top electrode, wherein a subset of the ions migrate into the switching layer in response to application of a program voltage to the memory cell and form a conductive filament through at least a portion of the switching layer; and a tunneling layer positioned between the switching layer and the bottom electrode that is electrically resistive and less permeable to the ions of the material of the top electrode relative to the switching layer, wherein the tunneling layer facilitates a tunneling current between the conductive filament and the bottom electrode.