Disclosed are a new Mercury-free flat light source structure capable of enhancing and adjusting brightness, maintaining stable and uniform discharge, and improving luminous efficiency, and a large flat light source apparatus using the same Mercury-free flat light source structure as a unit cell capable of adjusting the brightness and causing local discharges in selected areas, and a driving method thereof.The flat light source structure according to the present invention includes an upper substrate made of a light transmitting material; a lower substrate separated from the upper substrate by a distance; a barrier rib for maintaining the distance, thereby defining a discharge space filled with a discharge gas with a predetermined pressure; a phosphor coated on at least one of the inner surfaces of the upper substrate and the lower substrate, respectively; a pair of main electrodes disposed at predetermined positions on the surface of the upper or lower substrate and applied with a predetermined driving voltage, frequency and duty ratio to excite the phosphor by plasma generated due to electric field induced in the discharge space; an auxiliary electrode formed at a predetermined position on the lower and/or upper substrate(s) to have a parallel component which is parallel with any one of the main electrodes when viewing the discharge space from the upper substrate and a perpendicular component which traverses the electrodes across the pair of main electrodes.