论文标题:量子点量子阱结构中的束缚极化子
Bound Polaron in Quantum-Dot Quantum Well Structures
论文作者
论文导师 王旭,论文学位 硕士,论文专业 理论物理
论文单位 内蒙古大学,点击次数 1762,论文页数 27页File Size1066K
2006-05-25论文网 http://www.lw23.com/lunwen_831972/
Quantum-dot Quantum well structure;bound polaron;ground state energy;binding energy;electron-phonon interaction
本文采用连续介质模型和有效质量近似，研究了量子点量子阱结构中的束缚极化子。通过第一次幺正变换给出了声子的有效哈密顿量，从而求出杂质的极化势，通过第二次幺正变换后，利用变分方法得到电子的基态能量，分析了电子-声子相互作用对束缚极化子基态结合能的影响。结果显示电子-声子相互作用能对总能量的贡献为负。 我们数值计算了量子点量子阱结构中的自由极化子和束缚极化子的基态能量以及基态结合能。结果表明：束缚极化子的基态能量随着阱宽减小先缓慢而后急剧增加，这是因为在阱宽很小的时候，电子的动能很大。变化范围从负到零再到无穷大。而基态结合能随着阱宽减小而减小，当阱宽比较大的时候这种变化比较大，随着阱宽的减小，变化趋于平缓。自由极化子的基态能量和基态结合能的变化趋势与束缚极化子相类似，但其总能量高于束缚极化子的能量，这主要是由于杂质和电子的库仑相互作用能为负而导致的。
In this paper, the bound polaron in Quantum-dot Quantum well structures is investigated based on the continuous medium model and effective mass approximation, the effective Hamiltonian of the phonon and the polarization potential of the impurity are obtained by the first canonical transformation, the ground state of the electron is worked out by using the variational method after the second canonical transformation, the influence of electron-phonon interaction to the ground state of a bound polaron is also analysed. The result shows that the contribution of the interaction energy is negative to the total energy.The ground state energy and the binding energy of a bound polaron in Quantum-dot Quantum well structure are calculated, and the free polaron is also studied. It is found that the ground state energy of the bound polaron increases gradually firstly and then rapidly with decreasing of the well width, this is because the kinetic energy of the electron becomes too big in a narrow well, especially in the total energy of the electron may change from negative to positive at a certain well width and finally diverges to infinity as the well approach zero. However, the binding energy of the bound polaron decreases remarkably as the well decreases in a wider well in the beginning, and approaches a steady value in a narrower well subsequently. The change tendency of the ground state energy and the binding energy of the free polaron are similar to that of the bound polaron, respectively, but the energy of the free polaron is higher than that of the bound polaron, which is resulted in because of the negative coulomb energy of impurity and electron.
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