A bonded structure comprising the physical and electrical connections between an integrated circuit element and substrate using a composite bump comprised of a single polymer body of low Young's Modulus, a conductive barrier metal coating covering the polymer body and a soldering metal coating covering the conductive barrier metal coating. When the bonded structure is formed the composite bump is deformed and the low Young's Modulus of the polymer body allows a very reliable bonded structure with very low bonding force. Due to the low Young's Modulus there is little stress tending to break the solder joint after the bonded structure is formed. The bond is formed using a soldering process so that the soldering metal forms a conductive adhesive between the composite bumps and either the substrate input/output pads or the integrated circuit element input/output pads.