转移矩阵理论及其在Ⅲ/Ⅴ族半导体量子阱体系中的应用

应用转移矩阵方法求解三种不同量子阱体系中基于单带有效质量模型和包络函数近似下的一维定态薛定谔方程.首先，通过比较Ⅰ型单量子阱GaAlAs/GaAs/GaAlAs体系的解析解和数值解，该方法的精确性得到了验证.其次，与Ⅱ型断代量子阱AlSb/InAs/GaSb/AlSb系统的光致发光谱实验结果比较证实了该方法的适用性.最后，利用该方法推广计算了基于GaAs/GaAlAs材料的Ⅰ型耦合多量子阱体系的子带能级和波函数，说明了方法的通用性和实用性. 关键词： 量子阱 转移矩阵方法 光致发光

Formalism of the transfer matrix and its application to Ⅲ/Ⅴ semicondutor quantum well systems

A formalism of transfer matrix method is presented and used to solve a one-dimensional time-independent Schrdinger equation based on a simple one-band effective mass model and the envelope function approximation. The accuracy of this method is proved by comparing the numerical solution and analytical solution for a GaAs-based type Ⅰ single quantum well system， and its applicability is demonstrated by experimental photoluminescence results of the InAs/GaSb-based type Ⅱ and broken-gap quantum well structures. The formalism is extended to calculating the subband energies and corresponding wavefunctions in the GaAs/GaAlAs-based type Ⅰ coupled multiple quantum well systems, showing that the formalism is universal and practical.