The capacitor has a capacitor dielectric formed, in particular, as a high-.quadrature.-dielectrical or ferroelectrical layer. A barrier layer is formed of a compound of a transition element with phosphorus, sulfur or arsenic. The barrier layer is underneath the capacitor dielectric. The barrier layer is oxygen-impermeable and thus prevents the oxidation of deep structures during high-temperature processes, in particular during the production of the capacitor dielectric.