论文标题:三角形量子阱中的杂质态和极化子
Binding Energy of Donors and Ground State of a Polaron in Symmetric Triangular Quantum Wells
论文作者
论文导师 梁希侠,论文学位 硕士,论文专业 凝聚态物理
论文单位 内蒙古大学,点击次数 123,论文页数 30页File Size1153k
2005-05-10论文网 http://www.lw23.com/lunwen_457460647/
triangular quantum wells; donor impurity states; binding energy;polaron;ground state energy
本文主要研究了三角形量子阱系统中的类氢杂质态结合能和自由极化子基态能量的问题。我们首先用变分法计算了对称三角形量子阱中的类氢杂质结合能。在计算中,计入了电子有效质量和材料静态介电常数的空间依赖性。数值计算结果表明,杂质结合能不仅依赖于电子有效质量和材料的静态介电常数,而且对没有外加势场时量子阱中电子几率密度的空间分布也很敏感。当杂质位于阱中心时结合能达到最大值。所获结果同方阱和抛物阱中情形比较表明:相同情况下三角阱中的杂质态结合能最大。随后,我们又研究了对称三角阱中的电子—声子相互作用对电子极化子基态能量的影响,用类LLP变分法计算了GaAs/Al_(0.96)Ga_(0.04)As对称三角形量子阱中的自由极化子基态能量。计算中计入了纵光学(LO)声子与电子的相互作用。结果显示,阱宽较小时,极化子能量随阱宽增大而急剧减小;而阱宽较大时,能量的减小却比较缓慢。我们还计算了LO声子对极化子基态能量的贡献与阱宽的函数关系,发现电子与LO声子的相互作用能随阱宽的增加而单调上升。阱宽较小时变化显著,阱宽较大时变化缓慢,最终随着阱宽的增加而趋于三维体材料的极限。研究表明:LO声子对局域电子态能量的影响是不可忽略的。通过比较得知,三角阱中的极化子能量比方阱中的大得多。
In this paper, we have studied the binding energies of donors and the ground state energies of a polaron in a symmetric triangular quantum well. Firstly, hydrogen-like donor impurity states in symmetric triangular quantum wells are investigated by a variational method. Both the effect of the variable effective mass of an electron and the spatially dependent dielectric constant are considered in the calculation. The numerical results show that the binding energy depends on not only the effective mass and dielectric constant but also the spatial distribution of the electron probability density. The binding energies of the donor impurity states get the maximums at the well-center. The results are also compared with those obtained in parabolic and square wells. It is seen that the triangular well support the highest binding energies for the donor impurity states. Then, the effect of the electron-phonon interaction on the electron ground state in a symmetric triangular quantum well has been studied. The ground state energy of an electron in the GaAs/Al0.96Ga0.04As triangular quantum well including the effect of the interaction between the electron and LO phonons has been calculated by using a modified Lee-Low-Pines Variational method. The electron wave function in the triangular well is chosen as the Airy function. The numerical results are given and discussed.
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