Structures and formation methods of a chip package are provided. The chip package includes a semiconductor die and a package layer partially or completely encapsulating the semiconductor die. The chip package also includes a polymer layer over the semiconductor die and the package layer. The chip package further includes a dielectric layer over the polymer layer. The dielectric layer is substantially made of a semiconductor oxide material. In addition, the chip package includes a conductive feature in the dielectric layer electrically connected to a conductive pad of the semiconductor die.