Capacitor structures having first electrodes at least partially embedded within a second electrode, and fabrication methods are presented. The methods include, for instance: providing the first electrodes at least partially within an insulator layer, the first electrodes comprising exposed portions; covering exposed portions of the first electrodes with a dielectric material; and forming the second electrode at least partially around the dielectric covered portions of the first electrodes, the second electrode being physically separated from the first electrodes by the dielectric material. In one embodiment, a method further includes exposing further portions of the first electrodes; and providing a contact structure in electrical contact with the further exposed portions of the first electrodes. In another embodiment, some of the first electrodes are aligned substantially parallel to a first direction and other of the first electrodes are aligned substantially parallel to a second direction, the first and second directions being different directions.