Effect of Spatial Dielectric Function on the Total Energy of Cubic Quantum Dots and Frequency Dependent Dielectric Functions in Binary Semi-Conductors
Kahuthu, Stanley Wambugu
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Spatial and frequency dependent response functions of medium-direct band gap binary semiconductors were studied at both nanoscale and in bulk form using ab initio method. To understand why the total energy and the band gap energy of semiconducting materials at nanoscale, such as quantum dots, vary with the particle sizes, this study has invoked dielectric function of binary semiconductors from spatial dependent point of view. Moreover, this study has addressed the discrepancy between theoretical results and experimental data when studying bulk semiconductors which was attributed to failure of full implementation of dielectric funtion which is frequency dependent. Yester years, failure to implement frequency dependent dielectric functions has been attributed to computational demand which has, in this study, been made possible through the use of High Performing Computation (HPC). At nanoscale, Hermanson0s spatial dependent dielectric function was applied in the Hamiltonian when determining total energy of on-center donor impurity in gallium arsenide Quantum-Dot (QD), where the QD was embedded in a matrix of gallium aluminium arsenide. This was necessitated by the fact that behaviour of semiconductors at nanoscale completely deviate from those of their bulk systems. This was studied using both Bloch functions and atomic-like basis functions; the latter from perturbative point of view. The effect of both room temperature and hydrostatic pressure of one atmosphere, on the total energy, were also studied and implemented using Bloch functions. MatLab computation mathematical tool, version 2015, was used for solving relevant Schrodinger equations and for simulation purposes. In bulk systems, frequency dependent dielectric functions of gallium arsenide (GaAs), indium phosphide (InP) and cadmium telluride (CdTe) were studied under the influence of electromagnetic radiations with wavelengths in the range between infrared and visible light. These materials are candidates for heterojunctions such as those that are used to fabricate solar cells and in laser technology. Quantum en-source package for research in electronic structure, simulation and optimization (ESPRESSO) computer code version 5.2.1 with plane waves self consistent field (PWSCF) computer package was used to determine their ground state electronic properties while Yambo computer code version 4.1.4 and BerkeleyGW version 1.2.0 were used to determine their excitation energies and optical properties. From this study, spatial dependent dielectric function was found to give total energy of quantum dots that is higher than that of commonly used dielectric constant. Atomic-like basis functions resulted to higher energies compared to those obtained using Bloch functions. The combined effects of room temperature and atmospheric pressure were found to increase the total energy. This was more pronounced from dots whose size were more than 2:5nm and 3:5nm for spatial independent and spatial depenedent dielectric functions, respectively. Also, electronic structures and optical absorption got from the solution to Bethe-Salpeter Equation was compared with that based on Random Phase Approximation in the presence of the local field (RPA+LF) using Yambo. From frequency dependent dielectric functions, it was observed that different binary semiconductors are excited differently by electromagnetic radiations at different frequencies. From this observation, frequency dependent dielectric functions invoke full interactions in real systems and when considered, optical absorption spectra was found to predict well the order in which heterojunctions should be arranged in optoelectronic devices for optimal output. This study recommends theoretical study of semiconducting materials from full frequency dependent dielectric functions so that the obtained electrical, electronics and optical properties can compare well with those from experimental data.