Theoretical study of thermoelectric and optical properties in molecular and quantum systems
In this thesis, we analyze the electronic and optical properties in semiconductor heterostructures with zero dimension, that is, a quantum dot, which has a spherical symmetry based on materials such as CdS, ZnS, CdSe, and ZnTe. The calculations are made under the effective mass approximation, considering the effects of external electric and magnetic fields, the effect of surface donor impurity states, and electron-hole interaction with excitonic contribution. These properties are analyzed using the finite element method to solve the time-independent Schrödinger equation. We also analyze the thermoelectric properties in circuits formed from a single molecule connected between two metallic electrodes. To obtain the results, first, an analytical process is carried out in which a renormalization of the system to be studied is done using the Dyson equation for first neighbors, and the Green’s function formalism. Then the Fisher-Lee relation is used to calculate the probability of transmission. Calculations of the current-voltage characteristic curve and thermoelectric properties (Seebeck coefficient, thermal and electrical conductance, and ZT) are made using the Landauer relation. The first part of this thesis is dedicated to the theoretical details that support the equations and the numerical method used in the calculations, beginning with the section on the Landauer-Buttiker electronic transport theory, the Landauer relation, obtaining the integrals of Landauer for the calculation of thermoelectric properties, a section dedicated to the development of electronic and optical properties in semiconductor heterostructures, where the theory of effective mass is analyzed, the Hamiltonian for systems subjected to external electric and magnetic fields, the theory of optical absorption (linear and nonlinear) and finally a brief description of the finite element method. The main details of each chapter are: Chapter 3: A theoretical analysis of optical properties in a ZnS/CdS/ZnS core/shell/shell spherical quantum dot was carried out within the effective mass approximation. The corresponding Schrödinger equation was solved using the finite element method via the 2D axis-symmetric module of COMSOL-Multiphysics software. Calculations included variations of internal dot radius, the application of electric and magnetic fields (both oriented along the z-direction), as well as the presence of on-center donor impurity. Reported optical properties are the absorption and relative refractive index change coefficients. These quantities are related to transitions between the ground and first excited states, with linearly polarized incident radiation along the z-axis. Chapter 4: A theoretical analysis was conducted to examine the electronic and optical properties of a confined electron and a hole in a type-II core-shell spherical quantum dot composed of CdSe/ZnTe and ZnTe/CdSe. The Schr¨odinger equation for the electron and the hole was numerically solved using COMSOL-Multiphysics software in the 2D axisymmetric module, which employs the finite element method under the effective mass approximation. A Fortran code was utilized to calculate excitonic energy, specifically designed to solve the Coulomb integral. The calculations encompassed variations in the inner radius (R1), as well as variations in the electric (Fz) and magnetic (B) fields along the z-axis. The absorption coefficients were determined for transitions between the hole and electron ground states, considering z-polarized incident radiation. Chapter 5: Taking into consideration the research that has been done on the optical and electrical properties of molecular systems, especially the good thermoelectric energy conversion at a nanometric scale that such systems have presented, here we present a new alternative by using a particular Diphenyl-ether molecule as a functional device. Such a molecular system is modeled as a planar segment coupled to two electrodes in the first-neighbor approximation within a tight-binding Hamiltonian. We study the electrical and thermal properties of Diphenyl-ether molecules, like the electric current, electrical and thermal conductance, Seebeck coefficient, and figure of merit, in the strong and weak coupling regimes, considering different structural configurations and variations with temperature. Chapter 6: A theoretical analysis was performed to investigate the transport properties of the Zinc Porphyrin molecule and its response to thermal fluctuations. The renormalization method was used for this analysis, using the Green’s functions technique through the Dyson equation, focusing on first-neighbor interactions. This study produced various results, including energy-dependent transmission probability, voltage-current characteristic curves, electrical and thermal conductance assessments, Seebeck coefficient, and figure of merit (ZT).