Vol. 1, Issue 2, Part A (2019)

This paper presents a unified model for predicting the size- and dimensionality-dependent phonon frequency of semiconductor nanocrystals, incorporating surface dangling bond effects. The model is based on Qi's bond energy model, which introduces variable dangling bonds, and the work of Sun, Liang, and Kumar. The phonon frequency is expressed in terms of size, form, atomic or molecular diameter, and surface constituents' relaxation factor. The model was applied to study phonon frequency size variation in Si, CdSe, and InP nanoparticles, with accuracy verified against experimental data. Calculated phonon frequencies showed a downward trend as diameter decreased, indicating size-dependent vibrations. The decrease was more rapid below 6 nm, and theoretical predictions agreed well with available data, particularly below 5 nm. The model's consistency with experimental data suggests it provides a comprehensive description of size-dependent phonon frequency in nanomaterials by incorporating the relaxation factor as a key parameter. This approach offers a new perspective for understanding the interplay between size, surface structure, and vibrational properties of nanomaterials, essential for advancing their technological applications.