引入正弦平方势,在量子力学的框架内,把电子在掺杂超晶格中运动的Schrodinger方程化为Mathieu方程,根据Bloch定理讨论了系统能量分布,并用摄动法求解了方程的低阶不稳定区及其禁带宽度,系统自动呈现出了能带结构,再现了带电粒子同掺杂超晶格相互作用的周期性特征。同时,由于不稳定区的宽度与粒子质量、势阱宽度和深度有关,只需适当调节这些参数,就可以调节带隙宽度,从而改变材料的光电性质。 In the framework of quantum mechanics, the Schrodinger equation of electrons traveling in the doped superlattices is transformed into the Mathieu equation. The energy distribution of the system is discussed according to the Bloch theorem. The perturbation method is used to solve the problem that the low-order The stable region and its band gap, the system automatically presents the band structure, reproduces the periodic characteristics of charged particles interacting with the doped superlattice. At the same time, because the width of the unstable region is related to the particle quality, the width and depth of the potential well, only by properly adjusting these parameters, the width of the bandgap can be adjusted to change the photoelectric properties of the material.