An integrated circuit has an isolation capacitor structure that reduces the risk of breakdown from high electric fields at the edge of the top metal plate of the capacitor. The capacitor structure includes a bottom metal plate above a substrate. A first dielectric layer of a first dielectric material is formed between the bottom metal plate and the top metal plate. The capacitor structure also includes a thin narrow ring formed of a second dielectric material located under a portion of the top metal plate. The second dielectric material has a higher dielectric constant than the first dielectric material. The thin narrow ring follows the shape of the edge of the top metal plate with a portion of the ring underneath the top metal plate and a portion outside the edge of the top metal plate to thereby be located at a place of the maximum electric field.