引入反比相关双曲余弦平方势描述超晶格量子阱的电子跃迁

Description of electron transition in superlattice quantum well by ch^(-2)x potential

鉴于"方形"势阱过于简单和理想,引入了反比相关双曲余弦平方势描述超晶格量子阱中的电子运动行为。在量子力学框架内,把电子的Schr dinger方程化为了超几何方程,并以Ga1-xAlxAs-GaAs-Ga1-xAlxAs量子阱为例计算了电子的带内跃迁和带间跃迁。结果表明,能级数目和跃迁能量与阱深、阱宽等系统参数有关,只需适当调节这些参数就可望实现对超晶格量子阱光电特征的调节与控制。

An interaction potential with ch^-2x form is introduced to describe the electron motion in superlattice quantum well, and in the frame of quantum mechanics, Schrodinger equation is transformed to the hypergeometric equation by this potential. The eigenvalue and the eigefunction of the system are calculated, and the distribution and the level number in quantum well are also discussed. As an example, the transition energy between two bands for material Ga1-x A1xAs-GaAs- Ga1-xA1x As is calculated. It shows that the level number and the transition energy are related to the system parameters, such as the potential well depth, width etc. The photo-electric properties of superlattice materials can be controlled and regulated by regulating the system parameters.