在有效质量近似下,利用微扰法研究了InAs量子环内类氢杂质基态及低激发态的能级分布。受限势采用抛物形势,在二维平面极坐标下,用薛定谔方程的精确解析解进行计算。数值计算结果显示,电子能级敏感地依赖于量子环半径,能级存在极小值,这是由于限制势采用抛物势的结果。如果减小环的半径,可以增加能级间距。第一激发态类氢杂质能级的简并没有消除,n≥2时简并的能级发生分裂并且间距随半径的增大而增大。电子能级间距还敏感地依赖于角频率并随角频率的增大而增大。第一激发态的简并没有消除,第二激发态的简并被部分地消除。在计算InAs量子环中类氢杂质的基态和低激发态的能级时,角频率改变的影响也是很深刻的。文章结果对研究量子环的光跃迁及光谱结构有重要指导意义。

The distribution of energy levels of the ground state and the low-lying excited states of hydrogenic impurities in InAs quantum ring was investigated by applying the effective mass approximation and the perturbation method.In 2D polar coordinates,the exact solution to the Schrdinger equation was used to calculate the perturbation integral in a parabolic confinement potential.The numerical results show that the energy levels of electron are sensitively dependent on the radius of the quantum ring and a minimum exists on account of the parabolic confinement potential.With decreasing the radius,the energy spacing between energy levels increases.The degenerate energy levels of the first excited state for hydrogenic impurities are not relieved,and when the degenerate energy levels are split and the energy spacing will increase with the increase in the radius.The energy spacing between energy levels of electron is also sensitively dependent on the angular frequency and will increase with the increases in it.The degenerate energy levels of the first excited state are not relieved.The degenerate energy levels of the second excited state are relieved partially.The change in angular frequency will have a profound effect upon the calculation of the energy levels of the ground state and the low-lying excited states of hydrogenic impurities in InAs quantum ring.The conclusions of this paper will provide important guidance to investigating the optical transitions and spectral structures in quantum ring.