Multilayer mirrors for the extreme ultraviolet (EUV) are key elements for numerous applications of coherent EUV sources such as new tabletop lasers and free-electron lasers. However the field of applications is limited by the radiation and thermal stability of the multilayers. Taking into account the growing power of EUV sources the stability of the optics becomes crucial. To overcome this problem it is necessary to study the degradation of multilayers and try to increase their temporal and thermal stability. In this paper we report the results of detailed study of structural changes in Sc/Simultilayers when exposed to intense EUV laser pulses. Various types of surface damage such as melting, boiling, shockwave creation and ablation were observed as irradiation fluencies increase. Cross-sectional TEM study revealed that the layer structure was completely destroyed in the upper part of multilayer, but still survived below. The layers adjacent tothe substrate remained intact even through the multilayer surface melted down, though the structure of the layers beneath the molten zone was noticeably changed. The layer structure in this thermally affected zone is similar to that of isothermally annealed samples. All stages of scandium silicide formation such as interdiffusion, solid-state amorphization, silicide crystallization, etc., are present in the thermally affected zone. It indicates a thermal nature of the damage mechanism. The tungsten diffusion barriers were applied to the scandium/silicon interfaces. It was shown that the barriers inhibited interdiffusion and increased the thermal stability of Sc/Si mirrors.