Implantable defibrillators are implanted into the chests of patients prone to suffering ventricular fibrillation, a potentially fatal heart condition. A critical component in these devices is an aluminum electrolytic capacitor, which stores and delivers life-saving bursts of electric charge to a fibrillating heart. To reduce capacitor size, manufacturers have developed special aluminum foils, such as core-etched and tunnel-etched aluminum foils. Unfortunately, core-etched foils don't work well in multiple-anode capacitors, and tunnel-etched foils are brittle and tend to break when making some common types of capacitors. Accordingly, the inventors devised a new foil structure having perforations and cavities. In an exemplary embodiment, each perforation and cavity has a cross-sectional area, with the perforations having a larger, for example, 2 to 100 times larger, average cross-sectional area than the cavities. Other embodiments of the invention include foil assemblies, capacitors, and implantable defibrillators that benefit from properties of the new foil structure.