A three-dimensional array read/write (R/W) memory elements is formed across multiple layers of planes positioned at different distances above a semiconductor substrate. It is preferable to operate the R/W elements with low current and high resistive states. The resistance of these resistive states depends also on the dimension of the R/W elements and is predetermined by the process technology. A sheet electrode in series with the R/W element and a method of forming it provide another degree of freedom to adjust the resistance of the R/W memory element. The thickness of the sheet electrode is adjusted to obtain a reduced cross-sectional contact in the circuit path from the word line to the bit line. This allows the R/W memory element to have a much increased resistance and therefore to operate with much reduced currents. The sheet electrode is formed with little increase in cell size.