A lead frame has a die stage for mounting a semiconductor chip whose electrodes are electrically connected with leads via bonding wires, wherein they are enclosed in a molded resin, thus producing a semiconductor device. The outline of the die stage is shaped so as to be smaller than the outline of the semiconductor chip, and a plurality of cutouts are formed in the peripheral portion of the die stage so as to reduce the overall area of the die stage and to enhance the adhesion between the die stage and molded resin. The length L2 of each cutout ranges from (L1×0.05) to (L1×0.20) where L1 denotes the length of each side of the die stage, and the overall area S2 of the die stage ranges from (S1×0.10) to (S1×0.40) where S1 denotes the overall area of the semiconductor chip.