【摘要】 考虑电子-空穴气屏蔽的影响,研究了有限深量子阱中电子和空穴的本征能量及其相应的各级本征态.电子-空穴气引起的极化电场由泊松方程给出,而电子和空穴则满足考虑极化电场下的薛定谔方程,因此本文自洽计算了泊松方程与薛定谔方程.数值结果表明,内电场使电子和空穴向相反方向靠近势垒,而电子-空穴气将屏蔽内电场使得电子和空穴向阱中心靠近;势垒、内电场和屏蔽之综合效应将影响电子和空穴的本征能量和本征波函数.本文的方法还可推广到求解任意势中的定态薛定谔方程.更多还原

【Abstract】 Eigenfunctions of the electron and hole and their corresponding eigenvalues in a quantum well with finite barriers under the influence of screening effect induced by the electron-hole gas are investigated.The electron and hole satisfy the Schr dinger equations with a polarized field(described by the Poisson equation) induced by the electron-hole gas.The numerical results are computed by solving self-consistently the Poisson equation and Schrodinger equation. It is shown from the numerical result that the internal electric field makes the electron and hole separate to move towards the barriers,whereas the presence of the electron-hole gas will screen the field and make the carriers move towards the center of the quantum well.The combined effect from barriers,internal electric field and screening may influence the eigenenergies and eigenfunctions of the electron and hole.Moreover,the method used here can be generalized to solve the time-independent Schr dinger equations with arbitrary potentials.更多还原