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A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrodinger Equation

American Journal of Computational Mathematics 2014年第4期4卷 271-279页

作者： johnson oladele fatokun Department of Mathematical Science and Information Technology Federal University Dutsin-Ma Nigeria

In this paper, the one-dimensional time dependent Schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff Ordinary Differential Equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10?4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

关键词： Schrodinger’s Equation Partial Differential Equations Method of Lines (MOL) Stiff ODE Trapezoidal-Like Integrator

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Preparation and Some Properties of Metal Organic Chemical Vapour Deposited Al-Doped ZnO Thin Films Using Single Solid Precursors

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Journal of Modern Physics 2018年第11期9卷 2073-2089页

作者： Olumide Oluwole Akinwunmi johnson Ayodele O. Ogundeji Adetokunbo Temitope Famojuro Olakunle A. Akinwumi Olusoji O. Ilori Olatomide G. Fadodun Ezekiel oladele Bolarinwa Ajayi Department of Physics and Engineering Physics Obafemi Awolowo University Ile-Ife Nigeria Department of Chemistry Obafemi Awolowo University Ile-Ife Nigeria Department of Electrical and Electronic Obafemi Awolowo University Ile-Ife Nigeria Centre for Energy Research and development Obafemi Awolowo University Ile-Ife Nigeria

Zinc Oxide (ZnO) and Aluminium doped ZnO (AZO) thin films were deposited on soda lime glass by Metal Organic Chemical Vapour deposition technique (MOCVD), using prepared compound mixtures of Zinc Acetate di-hydrate (Zn(CH3COO)2⋅2H2O;ZAD) and Aluminium Acetyl-Acetonate (Al(C5H702)3;AAA) precursors at a temperature of 420°C. Effects of the varying mole percent concentrations of AAA precursor additives on the Al dopant concentrations in ZnO were systematically studied. The observations were made via investigations carried out on the morphological, optical, electrical and compositional properties of the deposited thin films. The thin films morphology was found to be strongly dependent on the varying concentration of AAA in the precursor mixtures. The average optical transmittance of the thin films in the uv-visible region was over 85% except 5 mol.% Al. While the energy band gaps were found to be in range of 3.27 - 3.36 eV. There is a blue-shift of the energy band edge observed between 0 and 5 mol.% AAA, which may be due to Burstein-Moss’ band gap widening effect and an opposing band gap renormalization effect at 10 mol.% AAA along with an extra band gap stabilization effect (Roth’s effect) at 15 mol.% AAA in rather quasi-sinusoidal or anomalous behaviour. The optical transmittance and electrical conductivity of ZnO were enhanced with addition of Al dopants. The RBS confirm the presence of Al, Zn and O, and evidence that Al dopants were successfully incorporated into the ZnO.

关键词： ZnO Thin Film ZnO:Al MOCVD Optical Properties AAA ZAD Electrical Properties FESEM UV-Vis Optoelectronic Properties

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