纳米量子点能级以及能隙计算和修正

用一个简单模型分析了量子点产生能级的原因，推导出能级与量子点尺寸的表达式。根据量子点表面势垒为有限值的特点以及表面存在衰减波，提出量子点内电子波函数不完全满足驻波条件的观点，在量子点的能级表达式中引入一个修正系数。结合量子点表面衰减波的特征，给出量子点修正系数的计算方法。通过理论计算表明：量子点的能级以及能级之间的能量差（间隙）不但与量子点的尺寸有关，而且与其边界条件有关。特别是对于非光滑的表面，其表面势垒对量子点的能级与能隙影响非常大。

Calculation and correction of Nano-level quantum dots

The relationship between quantum dot and energy level was analyzed using a simple model and the equation about the energy level and quantum dot size was developed in this paper. The electron wave function within quantum dot does not fully meet the Standing wave condition for the existence of surface wave attenuation, so a correction factor expression was introduced the equation about energy level of quantum dot. And the calculation method of the correction factor was introduced in this paper. The theory calculation shows that the gap between energy level of quantum dot is not only related to the quantum dot size but its boundary conditions. The surface potential barrier has an important impact on the energy level of the quantum dot and the energy gap especially for non-smooth surface.