Dynamics and Scattering Properties at Integrated nanostructure in Cristalline Surface

We suggest using an analytical method to look into the localization and vibrational scattering at the junction of crystalline surface boundaries and implanted nanostructures. The localized modes' energies in the vicinity of the defect are ascertained, and the propagating and evanescent modes in the bulk material are computed. We demonstrate the presence of acoustical modes caused by inhomogeneity and optical localized modes, respectively. Furthermore, a system model's parameters have a significant impact on the quantity and characteristics of these curves. For atomic sites that make up a minimum representation set in the defect's vicinity, the state densities are determined by taking the mean of the Green functions related to the matching approach. Resonances in the bulk material's subband arise from the interplay between the propagating bulk modes and the localized phonons generated by the integrated nanostructure.