Abstract: The instability at the interface of a moving two-phase fluid represents a significant mechanical challenge within the core component of extreme ultraviolet lithography systems, directly affecting droplet morphological stability and lithographic precision. To investigate the complex interfacial dynamics of droplet induced by cavitation, a model of droplet external surface motion driven by internal cavitation oscillations is developed. This model systematically explores the instability mechanisms and evolution patterns of such phenomena. Under the influence of physical parameters such as surface tension and fluid density, Rayleigh-Taylor instability occurs at the droplet surface, resulting in morphological changes that exhibit distinct mode characteristics. High-precision numerical simulations are conducted using the compressibleInterIsoFoam solver within the open-source platform OpenFOAM to investigate the instability mechanisms and morphological evolution of droplet surface. By introducing the vorticity circulation equation, the distributions of the baroclinic term, tangential acceleration, and surface tension along the droplet surface are presented. From the perspective of vortex generation, the mechanism of droplet surface instability is quantitatively analyzed, demonstrating that the baroclinic term is the dominant factor causing droplet surface instability. Further employing the fast Fourier transform, the dominant modes at different time during droplet surface contraction were analyzed in the frequency domain. The influence of motion parameters, such as droplet radius and oscillation period governed by droplet radius and bubble internal pressure, on the evolution of interface modes are discussed. Numerical results indicate that multiple competing dominant modes frequently exist during moving droplet surface, and the dominant mode presents when droplet contraction begins maintains its leading role throughout the interface contraction process. When droplet surface motion provides sufficient space for perturbation development, new dominant modes emerge at the droplet surface. The interaction between different modes significantly influences the final morphology of the droplet surface structure. This finding holds significant value for understanding the evolution mechanisms of surface in multiphase fluid systems.