Aplicação do método dos elementos finitos no estudo da estrutura eletrônica e interação elétron-fônon em pontos quânticos

Abstract

The quantum dots are nanocrystals structures, which allows differents optoeletronics properties from its bulk structure. These properties bring potential uses for applications in electronic devices, they have been intensely researched nowadays. However, the most important íngredient for a systematic study of the optical and transport properties in semiconductors quantum dots is the rigorous determination of its electronic structure and density of probability. In this way, different methods and theoretical models have been used to study its problem. Many of them, have the following limitations: no flexibility in the treatment of boundary conditions; high computational effort; limitations due to the nanocrystal size, and mainly, the resolution for low symmetry quantum systems is very complex or not possible. However, the finite elements method (FEM) is a powerful and flexible theorical tool, which can be applied without the limitations or implementation difficulties that exist in other methods. In this way, it was developed, by means of FEM, a theoretical treatment of the electronic structure several quantum dot geometries (spherical, ellipsoidal, lens, conical and cylindrical), in presence or absence of an externai magnetic field. The Schrõdinger equation was driscreticized by means of the Galerkin's weighted residue method with a non-uniform mesh of triangular elements. In this context the FEM was applied to calculate the electron scattering caused by its interaction with acoustic phonons. It is considered two mechanism of interaction: piezoelectric and the deformation potential coupling. It was found that the nanocrystal geometry shape has a strong influence in the electronic structure and electron-phonon scattering rates. Results show that the physical properties of semiconductor quantum dots can be easily controlled by manipulation of size or geometrical shape. For a specific volume of a quantum dot, the electron energy increases with a symmetry reduction. The magnetic field effects are also strongly modified by the size and shape of the nanocrystal. This is attributed to the interplay of magnetic and spatial confinement effects.