Control elements that can be suitable for nonvolatile memory device applications are disclosed. The control element can have low leakage currents at low voltages to reduce sneak current paths for non selected devices, and high leakage currents at high voltages to minimize voltage drops during device switching. The control element can be based on multilayer dielectric stacks. The control element can include a zirconium oxide-strontium-titanium oxide-zirconium oxide multilayer stack. The zirconium oxide can be replaced by at least one of hafnium oxide, aluminum oxide, magnesium oxide, or one of the lanthanide oxides.