Provided are nonvolatile memory assemblies each including a resistive switching layer and current steering element. The steering element may be a transistor connected in series with the switching layer. Resistance control provided by the steering element allows using switching layers requiring low switching voltages and currents. Memory assemblies including such switching layers are easier to embed into integrated circuit chips having other low voltage components, such as logic and digital signal processing components, than, for example, flash memory requiring much higher switching voltages. In some embodiments, provided nonvolatile memory assemblies operate at switching voltages less than about 3.0V and corresponding currents less than 50 microamperes. A memory element may include a metal rich hafnium oxide disposed between a titanium nitride electrode and doped polysilicon electrode. One electrode may be connected to a drain or source of the transistor, while another electrode is connected to a signal line.