7. Quantum Mechanical Calculation Of OPtical Properties of Silicon-Oxide Nanoparticles Using Born-Mayer Potential

by *Iorngbough I.O., Echi I.M., Onoja A.D. and Tikyaa E.V.
Department of Physics, Joseph Sarwuan Tarka University, Makurdi, Nigeria.

Abstract
In this work, the basic postulates of quantum mechanics are applied to calculate the optical properties of silicon oxide nanoparticle using Born-Mayer potential. The Born-Mayer potential was inputted into the time independent Schrödinger equation and the radial wave function was obtained by solving the equation using Runge-Kutta fourth and fifth order method.. The radial wave functions were then used to evaluate the expectation values of the energy of the system. The energies were used in the calculation of the optical properties such as, absorption coefficient extinction coefficient, real and imaginary dielectric constant and optical conductivity of the system. The accuracy of the theoretical model used for calculating the optical properties of silicon oxide nanoparticles was validated by comparing the results with experimental values using the Tauc plot which was used to determine the energy band gap (Eg) of silicon oxide nanoparticles and its optical properties empirically. The results obtained shows an oscillating radial wave function which decays exponentially in amplitude along the direction of propagation due to the core-shell nature of silicon-oxide nanoparticles The curve of the absorption coefficient shows a band gap value of 9.0 eV which is the theoretical band gap value of silicon oxide nanoparticle. The calculated and experimental curves of the absorption, extinction coefficients and the optical conductivity almost ride on each other and also showed good agreement between the theoretical calculation and experimental data.