What is claimed is:1. A semiconductor device including a magnetic random access memory (MRAM) cell, comprising:an MRAM cell structure disposed over a substrate, the MRAM cell structure including a bottom electrode, a magnetic tunnel junction (MTJ) stack and a top electrode;a first insulating layer disposed over the MRAM cell structure;a first interlayer dielectric (ILD) layer disposed over the first insulating layer;a second ILD layer disposed over the first ILD layer; anda conductive contact in contact with the top electrode,wherein a side face of the conductive contact includes a lateral protrusion,wherein the second ILD layer includes a first dielectric layer, a second dielectric layer on the first dielectric layer and a third dielectric layer on the second dielectric layer, andwherein the lateral protrusion protrudes into the first dielectric layer.2. The semiconductor device of claim 1, wherein the lateral protrusion is located below an interface between the first ILD layer and the second ILD layer.3. The semiconductor device of claim 2, wherein the first insulating layer is made of one or more selected from the group consisting of aluminum carbide and aluminum oxycarbide.4. The semiconductor device of claim 3, further comprising a second insulating layer made of a nitride-based insulating material,wherein the second insulating layer covers sidewalls of the MRAM cell structure.5. The semiconductor device of claim 4, wherein the nitride-based insulating material is one or more selected from the group consisting of SiON and SiOCN.6. The semiconductor device of claim 4, wherein the first insulting layer is thinner than the second insulting layer.7. The semiconductor device of claim 1, wherein:the conductive contact passes through the first, second and third dielectric layers.8. The semiconductor device of claim 7, wherein:the first dielectric layer, the second dielectric layer and the third dielectric layer are made of different materials from each other, andone of the first or second dielectric layers includes SiC, SiCN or SiOCN.9. The semiconductor device of claim 7, further comprising a second insulting layer made of a nitride-based insulating material,wherein the insulating layer covers sidewalls of the MRAM cell structure.10. The semiconductor device of claim 9, wherein the nitride-based insulating material is one or more selected from the group consisting of SiON and SiOCN.11. The semiconductor device of claim 9, wherein the first insulting layer is thinner than the second insulting layer.12. The semiconductor device of claim 7, wherein the first insulating layer is made of one or more selected from the group consisting of aluminum carbide and aluminum oxycarbide.13. The semiconductor device of claim 12, wherein a concentration of at least one of Al, O, or C in the first insulating layer in a thickness direction is not uniform.14. A semiconductor device including a magnetic random access memory (MRAM) cell, comprising:an MRAM cell structure disposed over a substrate, the MRAM cell structure including a bottom electrode, a magnetic tunnel junction (MTJ) stack and a top electrode;a first insulating layer disposed over and in contact with sidewalls of the MRAM cell structure;a second insulating layer made of a different material than the first insulating layer and disposed over the first insulating layer;a first interlayer dielectric (ILD) layer disposed over the second insulating layer;a second ILD layer disposed over the first ILD layer; anda conductive contact in contact with the top electrode,wherein a top of the second insulating layer is located above a top of the first insulating layer.15. The semiconductor device of claim 14, wherein the top of the second insulating layer is located above a top of the top electrode.16. The semiconductor device of claim 14, wherein the top of the second insulating layer is located below a top of the top electrode.17. The semiconductor device of claim 14, wherein:the first insulating layer is made of a nitride-based insulating material, andthe second insulating layer is made of one or more selected from the group consisting of aluminum carbide and aluminum oxycarbide.18. A semiconductor device including a magnetic random access memory (MRAM) cell, comprising:an MRAM cell structure disposed over a substrate, the MRAM cell structure including a bottom electrode, a magnetic tunnel junction (MTJ) stack and a top electrode;a first insulating layer disposed over sidewalls of the MRAM cell structure;a second insulating layer made of a different material than the first insulating layer and disposed over the first insulating layer;a first interlayer dielectric (ILD) layer disposed over the second insulating layer;a second ILD layer disposed over the first ILD layer; anda conductive contact in contact with the top electrode,wherein a top of the second insulating layer is located below a top of the first insulating layer.19. The semiconductor device of claim 18, wherein the top of the second insulating layer is located below a top of the top electrode.20. The semiconductor device of claim 18, wherein:the first insulating layer is made of a nitride-based insulating material, andthe second insulating layer is made of one or more selected from the group consisting of aluminum carbide and aluminum oxycarbide.