We use single-walled carbon nanotube (CNT) crossbar electrodes to probe sub-5 nm memory domains of thin AlOx films. Both metallic and semiconducting CNTs effectively switch AlOx bits between memory states with high and low resistance. The low-resistance state scales linearly with CNT series resistance down to ∼10 MΩ, at which point the ON-state resistance of the AlOx filament becomes the limiting factor. Dependence of switching behavior on the number of cross-points suggests a single channel to dominate the overall characteristics in multi-crossbar devices. We demonstrate ON/OFF ratios up to 5 × 10(5) and programming currents of 1 to 100 nA with few-volt set/reset voltages. Remarkably low reset currents enable a switching power of 10-100 nW and estimated switching energy as low as 0.1-10 fJ per bit. These results are essential for understanding the ultimate scaling limits of resistive random access memory at single-nanometer bit dimensions.