An anode (14, 208, 410) and/or cathode (12, 212, 420) of a capacitor has a large surface area. The high surface area of the anode is provided by forming the anode from a thin, electrically conductive layer (16) formed from metal particles (18) or an electrically conductive metallic sponge (416). These materials provide a porous structure with a large surface area of high accessibility. The particles are preferably directional or non-directional sponge particles of a metal, such as titanium. The conductive layer hasa dielectric film (36, 236, 414) on its surface, formed by anodizing the particle surfaces. The dielectric film has a combination of high dielectric constant and high dielectric strength. The cathode (12, 212, 420) of the capacitor is either a conventional solid material or, more preferably, has a large surface provided by forming the surface from a sponge or particles analogously to the anode. The high dielectric strengths obtainable from the capacitor allow for extreme miniaturization, making the capacitor particularly suited for integrated circuit applications.