Machine Learning Analysis of Localized Vibrations in Perturbed Square Tellurene and Selenene Lattices

This study investigates the behavior of localized vibrations in one-dimensional (1D) and square two-dimensional (2D) crystal lattices of Tellurium (Te) and Selenium (Se), which have gained significant attention due to their exceptional physical properties and potential applications in advanced technologies. Nanomaterials often contain imperfections that critically influence their electronic and structural characteristics. Localized vibrational states emerge when the mass of an impurity atom is less than that of the host lattice atom, leading to phonon-impurity scattering and enhanced phonon frequencies. These vibrations are typically infrared-active, making them detectable in crystal absorption spectra, which is crucial for defect analysis in nanomaterials. The study explores 1D and 2D nanostructures of Te and Se doped with alkali metals (Li, Na, K) and metallic elements (Ag, Cu, Sn), demonstrating their broad applicability in semiconductor devices, including field-effect transistors, CMOS circuits, photovoltaic solar cells, optoelectronic devices, and piezoelectronic systems. Using Python-based computational methods, we analyze localized vibrations in perturbed square Tellurene and Selenene lattices. Our approach combines Hamiltonian mechanics with force constant models to derive phonon dispersion relations and localized vibrational modes. The results reveal distinct resonance behaviors in both longitudinal and transverse modes, with significant frequency shifts observed when impurity masses deviate from the host lattice mass. This work provides insights into phonon confinement effects and defect-induced vibrational modifications, offering a foundation for optimizing nanostructured materials for next-generation electronic and optoelectronic applications.