Abstract: In a semiconductor device having a radiation plate and a method of boding the radiation plate, a radiation plate is overlaid on a die pad formed at the center portion of a lead frame, the die pad and the radiation plate are clamped from upper and lower sides by clamp members, and then ultrasonic wave are is applied to the interface between the die pad and the radiation plate to bond the radiation plate to the die pad with ultrasonic wave, the depth of scratches formed on the surface of the die pad which are formed by the clamp member are reduced to 15 .mu.m or less at maximum and/or 2.0 .mu.m on the average.