Disclosed is a package for a semiconductor device including a semiconductor die. The package includes a base member, a side wall, first and second conductive films, and first and second conductive leads. The base member has a conductive main surface including a region that mounts the semiconductor die. The side wall surrounds the region and is made of a dielectric. The side wall includes first and second portions. The first and second conductive films are provided on the first and second portions, respectively and are electrically connected to the semiconductor die. The first and second conductive leads are conductively bonded to the first and second conductive films, respectively. At least one of the first and second portions includes a recess in its back surface facing the base member, and the recess defines a gap between the at least one of the first and second portions below the corresponding conductive film and the base member.