A high surface area capacitor structure includes a storage electrode with recesses. An upper surface of the storage electrode has a maze-like appearance. Low elevation regions of a hemispherical grain polysilicon layer may remain on the upper surface of the storage electrode. The storage electrode or portions thereof may be lined or coated with dielectric material. The dielectric material may space a cell electrode of the high surface area capacitor structure apart from the storage electrode. One or both of the storage electrode and the cell electrode may be formed from polysilicon. Intermediate structures, which include mask material over contiguous low elevation regions of a layer of hemispherical grain polysilicon, which may have a maze-like appearance, and apertures located laterally between the low elevation regions of the layer of hemispherical grain polysilicon, are also disclosed.