The invention provides a memory device for storing electrical charge, which has, as memory elements, tube elements applied on an electrode layer and connect-connected thereto. The tube elements are provided with a dielectric coating, a filling material for filling the space between the tube elements being provided. A counter-electrode connected to the filling material is formed such that an electrical capacitor for storing electrical charge is formed between the electrode layer and the counter-electrode. The tube elements advantageously comprise carbon nanotubes, as a result of which the capacitance of the capacitor on account of a drastic increase in the area of the capacitor electrode surface.