3D-capacitor structure comprising: - a substrate; - a trench network extending from a top face (S 100) of the substrate down to a trench bottom (S 101) along a depth direction which is perpendicular to the substrate top face, the trench network forming a regular array of separated first pillars which are located apart from each other and each surrounded by a closed-loop trench pattern parallel to the substrate top face; - a double capacitor layer stack extending continuously as one single piece on top faces of the pillars at the substrate top face (S 100), on trench sidewalls which are parallel to the depth direction, and also on the trench bottom (S 101), said double capacitor layer stack comprising from the substrate: a first electrode, a first insulating layer, a second electrode, a second insulating layer and a third electrode; and - at least one contact pad located above the substrate top face (S 100) along the depth direction, and arranged for contacting electrically the second electrode, characterized in that the following features are met: /i/ there is provided at least one second pillar, called a contact-supporting pillar, by providing additional substrate portions for bridging between neighboring first pillars which are next to the contact-supporting pillar, so that said additional substrate portions together with the neighboring pillars form a closed-loop trench separation which surrounds the contact-supporting pillar and has a flat top (FT 13) contained in the substrate top face (S 100); /ii/ the first electrode, the first insulating layer and the second electrode extend continuously across the flat top (FT 13) of the closed-loop trench separation and within a separated closed-loop trench portion which is located between the contact-supporting pillar and the closed-loop trench separation, and also within other trench portions which are located outside said closed-loop trench separation; /iii/ the flat top (FT 13) of the closed-loop trench separation is devoid of the third electrode at least along a closed-loop strip which is contained in said flat top and surrounds the separated closed-loop trench portion and the contact-supporting pillar, so that a portion of the third electrode contained within the separated closed-loop trench portion is isolated from another portion of the third electrode which is outside the closed-loop strip; and /iv/ the contact pad is in electrical contact with the second electrode at least above part of the contact-supporting pillar. - a substrate; - a trench network extending from a top face (S 100) of the substrate down to a trench bottom (S 101) along a depth direction which is perpendicular to the substrate top face, the trench network forming a regular array of separated first pillars which are located apart from each other and each surrounded by a closed-loop trench pattern parallel to the substrate top face; - a double capacitor layer stack extending continuously as one single piece on top faces of the pillars at the substrate top face (S 100), on trench sidewalls which are parallel to the depth direction, and also on the trench bottom (S 101), said double capacitor layer stack comprising from the substrate: a first electrode, a first insulating layer, a second electrode, a second insulating layer and a third electrode; and - at least one contact pad located above the substrate top face (S 100) along the depth direction, and arranged for contacting electrically the second electrode, /i/ there is provided at least one second pillar, called a contact-supporting pillar, by providing additional substrate portions for bridging between neighboring first pillars which are next to the contact-supporting pillar, so that said additional substrate portions together with the neighboring pillars form a closed-loop trench separation which surrounds the contact-supporting pillar and has a flat top (FT 13) contained in the substrate top face (S 100); /ii/ the first electrode, the first insulating layer and the second electrode extend continuously across the flat top (FT 13) of the closed-loop trench separation and within a separated closed-loop trench portion which is located between the contact-supporting pillar and the closed-loop trench separation, and also within other trench portions which are located outside said closed-loop trench separation; /iii/ the flat top (FT 13) of the closed-loop trench separation is devoid of the third electrode at least along a closed-loop strip which is contained in said flat top and surrounds the separated closed-loop trench portion and the contact-supporting pillar, so that a portion of the third electrode contained within the separated closed-loop trench portion is isolated from another portion of the third electrode which is outside the closed-loop strip; and /iv/ the contact pad is in electrical contact with the second electrode at least above part of the contact-supporting pillar.