After the metal bumps 52 are connected to the tin-containing layer 70 on the bottom surface of the inner leads 68 using a thermal pressing process, a polymer material 74, such as epoxy, polybenzoxazole or polyimide, can be formed between the semiconductor chip 54 and the tin-containing layer 70 on the bottom surface of the inner leads 68, and enclosing the metal bumps 52.