Department of Theoretical Physics, Theory of Nanostructures Laboratory, University of Nizhniy Novgorod, Nizhniy Novgorod 603950, Russia.
J Phys Condens Matter. 2010 Jun 2;22(21):215301. doi: 10.1088/0953-8984/22/21/215301. Epub 2010 Apr 30.
Within the framework of the envelope-function approximation the single-particle and the optical gaps of silicon nanocrystals embedded in amorphous SiO(2), Si(3)N(4), Al(2)O(3) and ZrO(2) dielectric matrices were calculated. We employ the model of an Si quantum dot surrounded by a spherical thin intermediate layer with a radially varying permittivity, separating the nanocrystal and the host dielectric matrix. The latter was modelled by the finite-height potential barriers. It has been shown that both the single-particle and optical gaps of the nanocrystals essentially depend on the surrounding material due to the variation of the band offsets for different matrices, which leads to essential shifts of the size-quantized levels. At the same time, an influence of the polarization fields on the optical gap was found to be weak compared to the variation of the confining potential, because of the mutual cancellation of single- and two-particle polarization contributions, which is known as a 'compensation effect'. As a result, hydrogen-like screened electron-hole Coulomb interactions, in fact, individually contribute to the excitonic correction. It has been revealed that the excitonic corrections have close values for the nanocrystals embedded in all the considered matrices: the dispersion of their values is even considerably less than that of the polarization correction values.
在包络函数近似的框架内，计算了嵌入非晶 SiO2、Si3N4、Al2O3 和 ZrO2 介电矩阵中的硅纳米晶体的单粒子和光学能隙。我们采用了一个被球型薄中间层包围的 Si 量子点的模型，该中间层的介电常数随半径变化，将纳米晶体与主介电矩阵隔开。后者通过有限高度势垒建模。结果表明，由于不同基质的能带偏移变化，纳米晶体的单粒子和光学能隙本质上取决于周围材料，这导致了大小量子化能级的显著移动。同时，发现与限制势的变化相比，极化场对光学能隙的影响较弱，这是由于单粒子和双粒子极化贡献的相互抵消，这被称为“补偿效应”。因此，类氢屏蔽电子-空穴库仑相互作用实际上分别对激子校正有贡献。结果表明，嵌入所有考虑的基质中的纳米晶体的激子校正具有相近的值：它们的值的分散性甚至比极化校正值的分散性还要小。
