Non-volatile multi-bit memory with programmable capacitance is disclosed. Illustrative data memory units include a substrate including a source region and a drain region. A first insulating layer is over the substrate. A first solid electrolyte cell is over the insulating layer and has a capacitance that is controllable between at least two states and is proximate the source region. A second solid electrolyte cell is over the insulating layer and has a capacitance or resistance that is controllable between at least two states and is proximate the drain region. An insulating element isolates the first solid electrolyte cell from the second solid electrolyte cell. A first anode is electrically coupled to the first solid electrolyte cell. The first solid electrolyte cell is between the anode and the insulating layer. A second anode is electrically coupled to the second solid electrolyte cell. The second solid electrolyte cell is between the anode and the insulating layer. A gate contact layer is over the substrate and between the source region and drain region and in electrical connection with the first anode and the second anode. The gate contact layer is electrically coupled to a voltage source.