A semiconductor die is attached to a transistor package by a plurality of resilient clamping members, which are bonded at one end to a top surface of the semiconductor die and at another end to a stable surface, such as an emitter, collector, or base lead frame, of the transistor package. The shape and composition of the clamping members provides a resilient force that causes a bottom surface of the die to make and maintain substantially uniform and constant contact with the die attach area of the transistor package, e.g., a mounting flange or non-conductive substrate. The clamping members are preferably conductive and can conduct current from respective transistor cell locations on the die to the respective lead frames to which the clamping members are bonded.