计及量子点厚度下, 分别选取抛物势和高斯势描写盘型量子点中电子的横向束缚势和纵向束缚势, 采用Pekar类型变分法推导出量子点中极化子的基态和第一激发态能量本征值和本征函数, 以此为基础, 构造了一个二能级结构, 并基于二能级体系理论, 讨论了极化子在外电场作用下的量子跃迁问题。结果表明, 高斯束缚势比抛物束缚势更能精准反映量子点中真实的束缚势; 量子点的厚度对极化子的跃迁几率Q所带来的影响有趣且有实际意义,不可忽略; 电声耦合强度α、电场强度F、非对称高斯势的势垒高度V0和束缚范围L等对极化子的基态与第一激发态能量以及量子跃迁的影响显著; 本文的结果有助于探讨利用这些物理量来调控量子点的输运特性和光学性质的途径和方法。

Considering the thickness of the quantum dot, the eigenvalues and eigenfunctions of the polaron ground state and first exited state in a quantum dot were derived by using the Pekar variational method with the harmonic and Gauss potentials as the transverse and longitudinal confinement potentials, respectively. Based on above two states, a two-level system was constructed. Then, the polaron quantum transition affected by an electric field was discussed in terms of the two-level system theory. The results indicate that the Gauss potential reflects the real confining potential more accurately than the parabolic potential; the influence of the thickness of the quantum dot on the transition probability Q of the polaron is interesting and significant, and must not be ignore; the ground and the first excited states’ energies and the corresponding transition probability of the polaron are influenced significantly by some physical quantities, such as the strength α of the electron-phonon coupling, strength F of the electric field, barrier V0 and confinement range L of the asymmetric Gauss potential, suggesting the transport and optical properties of the quantum dot can be manipulated further though those physical quantities.