In accordance with another aspect of the present disclosure, in a method of manufacturing a semiconductor device, a magnetic random access memory (MRAM) cell structure is formed. The MRAM cell structure includes a bottom electrode, a magnetic tunnel junction (MTJ) stack and a top electrode. A first insulating cover layer is formed over the MRAM cell structure. A second insulating cover layer is formed over the first insulating cover layer. A dielectric material is formed to fully cover the second insulating cover layer. A chemical mechanical polishing operation is performed on the dielectric material to expose a part of the second insulating cover layer above the MRAM cell structure and not to expose the first insulating cover layer. An interlayer dielectric (ILD) layer is formed over the second insulating cover layer and the dielectric material. A contact opening is formed in the ILD layer, thereby exposing the second insulating cover layer. A part of the second insulating cover layer and a part of the first insulating cover layer are removed, thereby exposing the top electrode. A conductive layer is formed in the opening contacting the top electrode.