Investigation of Structural, Electronic and Optical Properties of Silicon(Si) using DFT and TDDFT

Abstract

Silicon is an indirect band gap semiconductor belonging to group III-V. It is commonly used in light emitting diodes (LED) and many optoelectronic devices fabrications. In this thesis, the structural, electronic and optical properties of silicon are investigated using DFT and TDDFT with the help of Quantum ESPRESSO. A number of convergence test were performed to establish the optimal value of various parameters in the numerical calculations. Firstly, the total minimum energy of Silicon per atom was calculated as a function of cutoff energy and k-points sampling. The results of calculations show that the total minimum energy of Silicon per atom is monotonically decreasing with increasing cutoff energy due to variational principle.However, this trend can not be predicted from increasing the k-point sampling.Secondly, the optimal lattice constants of bulk silicon was calculated using the results obtained from energy convergence test (i.e 50 Ry and 6 x 6 x 6 k-points).The equilibrium lattice constant was 5.43 Angestrom. The obtained result was overestimated as compared to the experimental result. Moreover the band structure and density of states of Silicon have been calculated based on the frame work of density functional theory.The calculated band gap Energy of Silicon is 0.83 eV, which is closer to the experimental value (1.12 eV). Finally the real, and imaginary parts of the dielectric function and the electron energy loss function(EELS) were calculated using TDDFT . Keywords: Silicon, density functional theory, pseudopotentials, plane wave self-consistent field, Quantum Espresso Package,time dependent density functional theory(TDDFT)and, turboEEL