A 3D-capacitor structure that is based on a trench network etched from a top face of a substrate to form an array of separated pillars. The 3D-capacitor structure includes a double capacitor layer stack that extends continuously on top faces of the pillars at the substrate top face, on trench sidewalls and also on a trench bottom. The trench network is modified locally for contacting a second electrode of the double capacitor layer stack while ensuring that no unwanted short-circuit may occur between the second electrode and a third electrode of the double capacitor layer stack. The 3D-capacitor structure provides an improved trade-off between high capacitor density and certainty of no unwanted short-circuit.