一维有限超晶格的电子态与透射问题的转移矩阵方法研究

采用转移矩阵方法,研究了一维有限超晶格的电子态与透射问题.计算了一维有限超晶格含单个缺陷层或少量缺陷层的透射谱和波函数,以及当电子被束缚在一维有限超晶格中电子的本征值和相应的定态本征函数.给出的方法对于研究电子通过任意排列的一维有限超晶格的输运具有普适性.

Transfer Matrix Method Research for Electronic State and Transport of One Dimensional Finite Superlattices

The Kronig-Penney model is an idealized model for calculating the energy bands in crystalline solids with periodical potentials.The conventional formalism is based on effective mass approximation and Bastard's boundary condition. The paper presents a transfer matrix method by which we can deal with many problems about one dimensional finite superlattices.The wave functions at any two positions inside the superlattice are connected by a product of transfer matrixes.The sequence of the matrixes matches the arrangement of the barriers and wells.No matter how the size and the height of the barriers and wells change,we need only to modify the matrixes corresponding to the barrier and well.It's evident that this kind of manipulation is very convenient for computing.Thus this method in this paper can also be used for studying electronic transmission through the one dimensional finite superlattices with arbitrary arranged barriers and wells. Some questions for the one dimensional finite superlattices are studied by means of transfer matrix method.We calculate transmittance and wave function of the one dimensional finite superlattices with one defect layer and also calculate electronic eigenvalues and its eigenfunctions when electron is bound into the one dimensional finite superlattices. We have observed the sharply resonant transmission associated with one defect layer and obtained its localized wave function.We also get exact eigenvalues and its eigenfunctions in this way.It is found that the ground state wave function has no node,and the nth excited state wave function has n nodes.This is true for all finite superlattices with arbitrary arranged barriers and wells.The evanescent boundary condition outside the superlattices demands that the wave function adds a node when the eigenenergy increases from a lower level to a higher level.The eigenvalues and its eigenfunctions are important to understand the electronical and optical properties of the superlattices.