We report a classical molecular dynamics simulation of silicon nanoparticle and bulk models, both in crystalline and amorphous phases, to investigate their vibrational properties. By using a dynamical matrix approach and bond-polarizability model, together with the Raman decomposition approach [Phys. Rev. B 100, 134309 (2019)], we present a comprehensive analysis of vibrational spectra. In particular, the dependency of the high-frequency range of Raman spectra on the nanoparticle size has been studied. The results are in good agreements with the Raman measurements of crystalline nanoparticles and explain the role of the nanoparticle surface responsible for the shift of the Raman spectra depending 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 main signatures (ascribed to the Lamb modes with $l=0,2$) with respect to nanoparticle size. By using the Raman decomposition approach, we demonstrate that only a thin surface layer of several angstroms thickness contributes to the low-frequency Raman signatures regardless of the nanoparticle size in the case of both amorphous and crystalline phases. Finally, we study the role of the coordination number of atoms in the surface layer of nanoparticles in order to explain the difference between crystalline and amorphous vibrational spectra. The elaborated approach brings the knowledge necessary for the correct interpretation of Raman spectra of nanoparticles, which opens up the possibility for quantitative control of surface-induced effects relevant for various applications.

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使用拉曼光谱的模拟和分解对硅纳米粒子进行振动分析

我们报告了经典的分子动力学模拟的硅纳米粒子和块体模型，无论是结晶相还是非晶相，以研究其振动特性。通过使用动态矩阵方法和键极化率模型，以及拉曼分解方法[Phys。Rev. B 100，134309（2019）]，我们提出了振动光谱的综合分析。特别地，已经研究了拉曼光谱的高频范围对纳米颗粒尺寸的依赖性。结果与晶体纳米粒子的拉曼测量值很好地吻合，并解释了纳米粒子表面的作用，该表面负责拉曼光谱随粒度的变化。在低频范围内，我们的拉曼计算可以很好地再现兰伯模式特征，遵守Duval [Phys。Rev.B 46，5795（1992）。通过系统的拉曼建模，我们确认了主要特征的缩放（归因于Lamb模式$升=0，2$）相对于纳米粒子的尺寸。通过使用拉曼分解方法，我们证明在非晶相和结晶相的情况下，无论纳米粒子的大小如何，只有几埃厚的薄表面层都有助于低频拉曼信号。最后，我们研究了原子在纳米颗粒表面层中的配位数的作用，以解释结晶和非晶振动光谱之间的差异。精心设计的方法带来了正确解释纳米粒子拉曼光谱的必要知识，这为定量控制与各种应用相关的表面诱导效应提供了可能性。