We report a classical molecular-dynamics simulation of models of silicon nanoparticles and bulk silicon, in both the crystalline and the amorphous phase, to investigate their vibrational properties. By using a dynamical-matrix approach and a bond-polarizability model, together with a Raman-decomposition approach [Phys. Rev. B 100, 134309 (2019)], we present a comprehensive analysis of the vibrational spectra. In particular, the dependence of the high-frequency range of the Raman spectra on the nanoparticle size is studied. The results are in good agreement with Raman measurements on crystalline nanoparticles and explain the role of the nanoparticle surface, which is responsible for a shift in the Raman spectrum dependent on the particle size. In the low-frequency range, our Raman calculations reproduce well the Lamb-mode signatures, which obey the selection rules deduced by Duval [Phys. Rev. B 46, 5795 (1992)]. As a result of systematic Raman modeling, we confirm the scaling of the main signatures (ascribed to the Lamb modes with $l=0,2$) with respect to the nanoparticle size. By using the Raman-decomposition approach, we demonstrate that only a thin surface layer several angstroms in thickness contributes to the low-frequency Raman signature regardless of the nanoparticle size in the case of both the amorphous and the crystalline phase. Finally, we study the role of the coordination number of the atoms in the surface layer of a nanoparticle in order to explain the difference between the crystalline and amorphous vibrational spectra. The approach developed provides knowledge necessary for the correct interpretation of Raman spectra of nanoparticles, which opens up the possibility of quantitative control of surface-induced effects that may be relevant to various applications.

• Received 3 February 2020
• Revised 15 May 2020
• Accepted 17 June 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.014067