NOVELTY - The device has an electrolyte layer (13) formed between a negative electrode (11) e.g. lithium metal negative electrode, and an air electrode (12). The air electrode has a set of portions including a set of discharge over-voltages different in each portion in a direction from the negative electrode to the air electrode. One of the discharge over-voltages of the portion of the air electrode closest to the negative electrode is lower than the other discharge over-voltages of the other portions, where the negative electrode is made of a metal.    USE - Battery device e.g. air battery such as button-type air battery, for an electronic device e.g. battery pack, vehicle or electrically driven vehicle such as hybrid car, electric vehicle, electric bike, electric bicycle and railway vehicle, electric power system such as smart grid and household energy management system (HEMS) (all claimed). Can also be used for metal-air battery, and for cellular phone, mobile device, robot, computer i.e. personal computer, vehicular device i.e. in-vehicle device, and appliance i.e. household electric appliance.    ADVANTAGE - The battery device lowers the former over-voltage of the former portion of the air electrode closest to the negative electrode than the latter discharge over-voltages of the latter portions so as to effectively prevent a surface of the air electrode from being covered with a discharge product, thus preventing a void from being clogged by the discharge product that blocks or inhibits flow of oxygen into or from the air electrode, and hence maintaining diffusion of oxygen to inside of the air electrode for a prolonged time during a discharging process so as to improve discharge capacity of the device. The batter device improves performance of the electronic device.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method for manufacturing a battery device.    DESCRIPTION OF DRAWING(S) - The drawing shows a cross-sectional view of an air battery.    Negative electrode (11)    Air electrode (12)    Electrolyte layer (13)    Current collector (14)