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Indexed by:期刊论文

Date of Publication:2006-01-01

Journal:INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING

Included Journals:SCIE、Scopus

Volume:4

Issue:1

Page Number:3-18

ISSN No.:1543-1649

Key Words:quantum mechanics; energy band; wave function; semiconductor

Abstract: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.