We develop an empirical tight binding approach for the modeling of the electronic states and optical properties of Si nanocrystals embedded in a SiO₂ matrix. To simulate the wide band gap SiO₂ matrix we use the virtual crystal approximation. The tight-binding parameters of the material with the diamond crystal lattice are fitted to the band structure of β-cristobalite. This model of the SiO₂ matrix allows us to reproduce the band structure of real Si nanocrystals embedded in a SiO₂ matrix. In this model, we compute the absorption spectra of the system. The calculations are in an excellent agreement with experimental data. We find that an important part of the high-energy absorption is defined by the spatially indirect, but direct in k-space transitions between holes inside the nanocrystal and electrons in the matrix.

中文翻译：

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SiO2基体中Si纳米晶体的光学性质的紧密结合计算。

我们开发了一种经验紧密结合方法，用于对嵌入SiO ₂基质的Si纳米晶体的电子状态和光学性质进行建模。为了模拟宽带隙SiO ₂矩阵，我们使用虚拟晶体近似。材料与金刚石晶格的紧密结合参数符合β-方石英的能带结构。SiO ₂基质的这种模型使我们能够再现嵌入在SiO ₂基质中的真实Si纳米晶体的能带结构。在此模型中，我们计算系统的吸收光谱。计算结果与实验数据非常吻合。我们发现，高能吸收的重要部分由空间间接定义，但在空间直接纳米晶体内部的空穴与基质中的电子之间的k空间跃迁。