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 capacitors, which stores and delivers one or more life-saving bursts of electric charge to a fibrillating heart. To reduce the size of these devices, capacitor manufacturers have developed special aluminum foils, for example core-etched and tunnel-etched aluminum foils. Unfortunately, core-etched foils don't work well in multiple-anode capacitors, and tunnel-etched foils are quite brittle and tend to break when making some common types of capacitors. Accordingly, the inventors devised a new foil structure having one or more perforations and one or more cavities with a depth less than the foil thickness. 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.