点击次数：

论文类型：期刊论文

发表时间：2006-01-01

发表刊物：INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING

收录刊物：SCIE、Scopus

卷号：4

期号：1

页面范围：3-18

ISSN号：1543-1649

关键字：quantum mechanics; energy band; wave function; semiconductor

摘要：Based on the Bloch theorem and tight-binding theory, a variational principle is applied to analyze the energy bands of crystals. The stiffness matrix used in the finite element method (FEM) is introduced for the expression of the energy of the unit cell of the crystal, and thus the coordinate transformation technique in FEM is applied in the assembly of the total energy and the stiffness matrix of the crystal. The periodical boundary conditions are given, and the energy bands of the three-dimensional crystal are computed. Using the dynamic substructure model and introducing the dual variables, the energy band analysis of the free vibration of the atomic chain is transformed into symplectic eigenvalue problems. The potential energy and mixed energy are computed by combining segments recursively until the shortest periodical length of the chain is assembled. Finally, the pass-band eigenvalues of the energy bands are calculated using the Wittrick-Williants algorithm. The numerical results are given to illustrate the potential of the theory and algorithm developed.