A lead frame comprising a first connecting band, a plurality of external leads extending in one direction from said first connecting band, a substrate support having a rear surface and which serves as a heat sink connected at one side thereof to a free end of one of said external leads, a plurality of support strips, each having a portion of small cross-sectional area and being of a predetermined length and extending in a lengthwise direction between portions of larger cross-sectional areas of the respective strip, the cross sections of said portions of small cross-sectional areas being taken perpendicular to said lengthwise direction of said strips, and one end of said strip is connected to another side of said substrate support opposite to the one side connected to said external leads, and a second connecting band extending parallel to said first connecting band with said substrate support disposed therebetween, and connected to opposite ends of said strips, said strips having a smaller thickness than said substrate support and rear surfaces of said strips being at a higher level than the rear surface of said substrate support.