A method of fabricating a resistive random access memory (ReRAM) cell may include forming a set of nanolaminate structures over an electrode, such that each structure includes at least one first element oxide layer and at least one second element oxide layer. The overall set is operable as a resistive switching layer in a ReRAM cell. In this set, an average atomic ratio of the first element to the second element is different in at least two nanolaminate structures. This ratio may be less in nanolaminate structures that are closer to electrodes than in the middle nanolaminate structures. Alternatively, this ratio may increase from one end of the set to another. The first element may be less electronegative than the second elements. The first element may be hafnium, while the second element may be one of zirconium, aluminum, titanium, tantalum, or silicon.