Analytical Description for the Implementation of Numerical Models Applied to the Study and Determination of the Bandgap of Semiconductor Materials

• DOI: 10.22533/at.ed.317332305019

• Palavras-chave: Graphene, AsGa, bandgap, Semiconductor, Numerical Models.

• Keywords: Graphene, AsGa, bandgap, Semiconductor, Numerical Models.

• Abstract:

  An analytical description for implementing numerical formalism, such as;Tight Binding Model (TBM) and Density Functional Theory (DFT) was performed to understand the semiconductor properties of graphene and Gallium Arsenide (GaAs). Such numerical models (TBM and DFT) were implemented to solve the time-independent Schroedinger equation, with the application of concepts about the Dirac points and Fermi levels of the graphene structure, in addition to the use of the Bohr-Oppenheimer approximation, which provided basis for considering the effects of minimizing the core-core and electron kinetic energy, in obtaining the “bandgap” of the investigated materials. The Hartree-Fock method was also used to solve the Slater – Koster matrix to evaluate the electron-electron interaction, in the interaction model for each electron with an electron cloud in the DFT. By implementing the models, reduced configurations of the “bandgap” of Graphene and AsGa were obtained.