镶嵌在介质层中纳米晶的单电子能级的精确求解

Exact Calculation of Single-electron States in Nanocrystal Embedded in Dielectric Layer

假设镶嵌在介质层(如SiO2、SiC)中的纳米晶(如Si、Ge、Sn)为球形量子点,考虑到电子在纳米晶和介质层中的有效质量差异,对镶嵌在介质层中单电子的所有束缚态的能量和波函数进行精确求解,分析了量子点半径、势垒高度、电子有效质量等对能级的影响。计算结果表明,量子限制效应随着量子点半径的减小而急剧增强,不同材料电子的有效质量对电子能级也有重要影响。Sn纳米晶的半径为22nm左右,Ge的半径和Si的半径分别约为10nm和7nm时,能观察到较为明显的量子限制效应。本模型提出的计算方法快速而准确,并适用于任意尺寸、任意势垒和任意材料的球方势阱量子点系统。

The single-electron energies and wave functions in nanocrystal embeded in the dielectric layer were described using a model of spherical quantum dots. The barrier-to-dot electron mass ratio was taken into account due to different electron effective mass in different material. Moreover, the influence of the radius of quantum dots and confinement barrier potential on energy levels was investigated in detail. The simulation results indicates that the energy levels are higher than the realistic ones if ignoring the difference of electron effective mass. The smaller the radius is, the more remarkable the quantum effect is. Quantum confinement effects in Sn nanocrystals are expected at relatively large diameters（22nm）. In comparison, quantum confinement effects in Ge nanoerystals are not expected until the radius is on the order of 10nm and in Si when the radius is 7nm.