ALGORITHMIC METHOD FOR ENERGY BANDS STRUCTURE SIMULATION IN CUBIC LATTICES

• Published in: Momento no. 48; pp. 18 - 33
• Main Authors: Héctor Barco, Elisabeth Restrepo, Edilberto Rojas
• Format: Journal Article
• Language: English; Spanish
• Published: Universidad Nacional de Colombia 01-06-2014
• Subjects: BCC; cúbica simple; diferencias finitas; Estructura de bandas; FCC
• ISSN: 0121-4470; 2500-8013

In this work a model for studying energy band structures was implemented. The model is based on the finite differences method, using a 3D array. Initially, the unit cell is gridded with h as step, in order to divide the lattice in smaller parts. Each grid point was well-represent by a wavefunction. The derivative of each grid point is obtained approximately in each direction (x, y and z), carrying out the difference between the neighbor points along the axes. Wavefunctions described by the Bloch functions, the laplacian and the derivatives are included into the Schröringer equation. Then, it is solved by numerical methods in order to obtain the eigenvalues (energies), plotted as a function of the wavevector for building the band structures. For studying its performance the model was applied to the different cubic cells as simple cubic, body centered cubic (BCC) and face centered cubic (FCC) lattices with unitary dimensions.