1. A memory cell comprising: a semiconductor pillar comprising: a heavily doped bottom region of a first conductivity type; a heavily doped top region of a second conductivity type; and a lightly doped or intrinsic middle region interposed between and contacting the top and bottom regions, wherein the middle region comprises a first proportion of germanium, and either the top region or the bottom region comprises no germanium or comprises a second proportion of germanium less than the first proportion; and a reversible state-change element coupled to the semiconductor pillar, the reversible state-change element comprising a layer of a resistivity-switching metal oxide or nitride compound selected from the group consisting of NiO, Nb 2 O 5 , TiO 2 , HfO 2 , Al 2 O 3 , CoO, MgO x , CrO 2 , VO, BN, and AlN.