Device structures for a metal-insulator-metal (MIM) capacitor, as well as methods of fabricating a device structure for a MIM capacitor. An active device level is formed on a substrate, a local interconnect level is formed on the active device level, and a metal-insulator-metal capacitor is formed in a via opening with a sidewall extending through the local interconnect level and the active device level to a given depth in the substrate. The metal-insulator-metal capacitor includes a first plate on the sidewall, a second plate, and an interplate dielectric between the first plate and the second plate.