The Study of Effects of Strain on Band Gap of Perovskite Crystal using LDA and LDA+U Method

Table of contents

List of figures

1 Introduction
1.1 Introduction to pervoskite structure
1.1.1 Introduction to CaTiO
1.1.2 Structure
1.1.3 Formation of band gap
1.2 Scope of present study
1.3 How we approach?

2 Theoritical Background
2.1 General Consideration
2.2 Many-Body Hamiltonian and Born-Oppenheimer Approximation
2.3 Hartree-Fock Method of Self Consistent Fields
2.4 Density Functional Theory
2.4.1 General Consideration
2.4.2 Thomas-Fermi Model
2.4.3 Hohenberg-Kohn Theorem
2.4.4 The Kohn-Sham Formalism
2.5 The Exchange -Correlation Functional
2.5.1 Local Density Approximation
2.5.2 Generalized Gradient Approximation
2.5.3 Solution of the Kohn-Sham equations: Self-consistency iteration procedure
2.6 LDA+U Method

3 Computational Details
3.1 General Consideration
3.1.1 PWscf
3.1.2 Post Processing

4 Results and Discussion
4.1 Convergence Tests
4.1.1 Kinetic energy cut-off(ecutwfc)
4.1.2 K-points grid
4.1.3 Lattice parameter
4.1.4 Band structure
4.2 LDA Method
4.2.1 Calculation of band structure of perovskite CaTiO3 by LDA method
4.2.2 Effect of strain on atomic displacement by LDA method
4.2.3 Effect of strain on indirect band gap by LDA method
4.2.4 Effect of strain on direct band gap by LDA method
4.2.5 Partial density of states of perovskite structure of CaTiO3 by LDA method
4.3 LDA+U Method
4.3.1 Determination of Hubbard potential
4.3.2 Calculation of band structure of perovskite CaTiO3 by LDA+U method
4.3.3 Effect of strain on indirect band gap by LDA+U method
4.3.4 Effect of strain on direct band gap by LDA+U method
4.3.5 Partial density of states of perovskite structure of CaTiO3 by LDA+U method
4.3.6 Comparision of band gap between LDA and LDA+U method

5 Conclusions and Concluding Remarks

References