A cathode-electrolyte-anode unit for an electrochemical functional device, in particular a high-temperature fuel cell. The unit has a multi-layer solid-state electrolyte arranged between a porous anode and a porous cathode. The solid-state electrolyte is produced by a vapor deposition process and has a sandwich-type structure consisting of at least one first layer with a lower oxygen content, and at least one second layer with a higher oxygen content. The individual layers have substantially the same composition, with the exception of oxygen.