Simulation of band structure for CrN lattices by using a 3D array of range-limited circularly symmetric attractive potential

Abstract

The band structure obtention is important for establishing the different electrical and thermal properties of materials. Band structure of CrN was carried out by employing a 3D array range-limited spherical symmetric potential. For this purpose, several tools of Mathematics package were used. Initially, the unit cell is gridded in order to obtain small parts. Each grid point was well-represented by a wavefunction. The finite differences of each grid point is obtained approximately in each direction ( x , y and z ), establishing the difference between the neighboring points along the axis. The wavefunctions which are described by the Bloch functions, the Laplacian and the derivatives are included into the Schrödinger equation. Then, the equation is solved in order to obtain the eigenvalues (energies), which are plotted to obtain the band structure in (100), (110) and (111) directions.