The invention relates to a device, such as an electro-luminescent display device, comprising a substrate, first electrodes which are arranged over the substrate, second electrodes which are arranged over the first electrodes and at least one electrically insulating structure which separates two of the second electrodes and is arranged over at least one of the first electrodes. The insulating structure comprises an opening which extends from the top surface of the structure to the first electrode beneath the structure. The invention further relates to a method of manufacturing such a device. In one preferred embodiment, this method involves the use of sacrificial structures with which openings are obtained the upper parts of which extend along the entire length of the respective insulating structures.