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. An interlayer dielectric (ILD) layer is formed. A contact opening in the ILD layer is formed, 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. The second insulating cover layer has an oxygen getter property.