非对称量子阱与系统的本征值和本征函数

Non-Symmetry Quantum Well and Eigenvalue and Eigefunction for System

利用薄膜生长技术,通过控制材料的厚度来调整阱宽,控制组分来调整阱深,得到了不同光电特性的超晶格半导体材料。为克服"方形"势阱过于简单和理想的缺点,引入非对称相互作用势来描述组分超晶格量子阱。在量子力学框架内,把电子的Schrodinger方程转化为超几何方程,用系统参数和超几何函数严格地求解了电子的本征值和本征函数,并以Ga1-xAlxAs-GaAs-Ga1-xAlxAs量子阱为例计算了电子的带内跃迁。结果表明,阱内的能级数目和跃迁能量与系统参数有关,适当调节参数可得到不同光电性能的超晶格量子阱。

The well width and depth may be regulated respectively by controlling the material thick and component in the foil growing technique. Therefore the superlattice materials can be obtained with the variable photo-electric properties. In order to improve the squared potentil well which is too single and ideal, the non-symmetry interaction potential was introduced. In the frame of quantum mechanics, the equation to describe the particle motion was reduced to the hypergeometric equatin by this potential. The eigenvalue and the eigenfunction of the system were calculated by using the system parameters and hypergeometric function, and the distribution and number of the level in the quantum well were discussed. As example, the level and the transition of an electron in the single quantum well for Ga1-xAlxAs-GaAs-Ga1-xAlx As were calculated. The result shows that the level number and the transition energy are related to the system parameters of the well, the quantum well material with a variable optical and electric characteristic can be obtained only regulating the parameters of the system.