DENSITY FUNCTIONAL THEORY INVESTIGATIONS OF STRUCTURAL, ELECTRONIC AND OPTICAL PROPERTIES OF III ARSENIDES NURUL NAJWA BINTI ANUA UNIVERSITI TEKNOLOGI MALAYSIA DENSITY FUNCTIONAL THEORY INVESTIGATIONS OF STRUCTURAL, ELECTRONIC AND OPTICAL PROPERTIES OF III ARSENIDES NURUL NAJWA BINTI ANUA A thesis submitted in fulfilment of the requirements for the award of the degree of Master of Science (Physics) Faculty of Science Universiti Teknologi Malaysia AUGUST 2014 A thesis submitted in fulfilment of the requirements for the award of the degree of Master of Science (Physics) iii I specially dedicate this thesis to my beloved parents and my siblings for their continuing support along the way. Without them none of my success would be possible iv ACKNOWLEDGEMENT First of all, in humble way I wish to give all the Praise to Allah, the Almighty God for with His mercy in giving me the strength, and time to complete this work. I would like to express my sincere thanks to my supervisor, Dr Rashid Ahmed for his supervision and my co-supervisor Dr Amiruddin Shaari. I am grateful for their valuable guidance, ideas, opinions and encouragement extended to me. My further appreciation dedicated to my parents and my family in continuing support, patience and the encouragement throughout the duration of this research. Thanks also to all my friends and colleagues for their views and concerns. I also place on record, my sense of gratitude to one and all who directly or indirectly, have lent their helping hand in this venture. v ABSTRACT III arsenide semiconductor materials have attracted considerable attention because of their unique characteristics and unfailing applications as base materials in optoelectronics and many other state of the art technologies. In this study, III arsenide investigations are presented by performing calculations using computational approach framed within the density functional theory. Exchange-correlation energy functional plays a crucial role in the efficiency of density functional theory calculations, more soundly in the calculation of fundamental electronic energy band gap. In this density functional-theory study of III arsenide, the implications of exchange-correlation energy functional and corresponding potential were investigated on the structural, electronic and optical properties of III arsenides. For structural properties, local density approximation, generalized gradient approximation and parameterized generalized gradient approximation were applied. For the calculations of electronic properties, recently developed Tran-Blaha modified Becke-Johnson potential has been implemented additionally. To execute this study, state of the art computational code WIEN2k, based on full potential linearized augmented plane-wave and local orbitals methodology, was applied. III arsenide were simulated to obtain their lattice constant, band gap, dielectric constant, reflectivity, absorption, refraction index and the energy loss values. The results point to parameterized generalized gradient approximation as a more appropriate approximation for the calculations of structural parameters. However, the electronic band structure calculations at the level of modified Becke-Johnson potential showed considerable improvements over the other exchange correlation functionals. Besides this, the reported results related to optical properties within modified Becke-Johnson potential show a good agreement with the experimental measurements in addition to other theoretically results. vi ABSTRAK Bahan semikonduktor III arsenida telah berjaya menarik perhatian yang meluas kerana cirinya yang unik dan kejayaan penggunaannya sebagai bahan asas dalam optoelektronik dan teknologi moden yang lain. Dalam kajian ini, penyelidikan III arsenida dijalankan dengan melakukan pengiraan menggunakan pendekatan pengkomputeran berdasarkan pendekatan teori fungsi ketumpatan. Fungsi bagi tenaga pertukaran korelasi memainkan peranan yang penting dalam ketepatan pengiraan fungsi teori ketumpatan, terutamanya dalam pengiraan asas jurang jalur tenaga elektronik. Dalam teori fungsi ketumpatan kajian III arsenida, implikasi hubungan antara fungsi bagi tenaga pertukaran korelasi dan keupayaan yang sepadan terhadap ciri struktur, elektronik dan optik dalam III arsenida telah diselidiki. Bagi sifat struktur, penghampiran kepadatan tempatan, penghampiran kecerunan teritlak dan penghampiran kecerunan teritlak berparameter telah digunakan. Bagi pengiraan sifat elektronik, keupayaan Becke-Johnson terubahsuai Tran Blaha yang dibangunkan baru-baru ini telah diguna pakai sebagai pelaksana tambahan dalam penyelidikan ini. Untuk melaksanakan kajian ini, kod pengiraan termaju WIEN2k berdasarkan keupayaan penuh dengan satah gelombang lelurus berserta kaedah orbital tempatan, telah digunakan. Simulasi ke atas kumpulan III arsenida telah dilakukan bagi mendapatkan nilai pemalar kekisi, jalur tenaga, pemalar dielektrik, pantulan, penyerapan, indeks biasan dan nilai tenaga yang hilang. Keputusan mendapati penghampiran kecerunan teritlak berparameter adalah pendekatan yang lebih sesuai untuk pengiraan parameter struktur. Walau bagaimanapun pengiraan struktur bagi tenaga elektronik di peringkat Becke-Johnson terubahsuai menunjukkan potensi kemajuan yang agak besar berbanding fungsi-fungsi korelasi pertukaran yang lain. Selain itu laporan keputusan bagi ciri optik dengan menggunakan keupayaan Becke-Johnson terubahsuai menunjukkan keputusan yang memuaskan hasil perbandingan antara nilai eksperimen dengan nilai kiraan teori yang lain. vii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION ii DEDICATION iii ACKNOWLEDGEMENTS iv ABSTRACT v ABSTRAK vi TABLE OF CONTENTS vii LIST OF TABLES ix LIST OF FIGURES x LIST OF ABBREVIATIONS xii LIST OF SYMBOLS xiv 1 INTRODUCTION 1.1 Background 1 1.2 Problem Statement 2 1.3 Objectives 3 1.4 Scope of Study 4 1.5 Significance of Study 5 1.6 Previous Study 6 1.7 III-V Semiconductor 8 1.8 Modeling and Simulation 19 2 COMPUTATIONAL METHOD 2.1 Introduction 10 viii 2.2 Density Functional Theory- a tractable tool to 11 to solve the many body problem 2.3 The Born-Oppenheimer approximation (BO) 13 2.4 Density Functional Theory 14 2.5 The theorems of Hohenberg and Kohn 15 2.6 Kohn-Sham equations 17 2.7 Approximations for the Exchange-Correlation 20 Functional 퐸푥푐[푛] 2.8 Local Density Approximation (LDA) 21 2.9 Generalized Gradient Approximation. (GGA) 22 2.10 Modified Becke-Johnson (mBJ) 25 2.11 The Full Potential Linearized Augmented Plane- 27 Wave L(APW+lo) method 2.12 Previous Works 30 3 METHODOLOGY 3.1 Applications of WIEN2k 31 3.2 Method 32 4 RESULTS AND DISCUSSION 4.1 Structural properties 38 4.2 Electronic Properties 42 4.3 Optical Properties 47 5 SUMMARY AND CONCLUSION 5.1 Summary and Conclusion 73 5.2 Suggestions 75 REFERENCES 77 Appendices 87 ix LIST OF TABLES TABLE NO TITLE PAGE 4.1 The calculated structural properties are compared to 41 the experimental and other theoretical data available in the literature 4.2 The energy bandgap 퐸푔 properties of BAs, AlAs, 42 GaAs and InAs 4.3 The calculated data of static dielectric functions 51 휖1 (0) BAs, AlAs, GaAs and InAs 4.4 The highest calculated imaginary parts 휖2(0)of BAs, 52 AlAs, GaAs and InAs 4.5 The calculated refractive index 푛(0) of BAs, AlAs, 56 GaAs and InAs 4.6 The highest calculated refractive index 푛(휔)of BAs, 57 AlAs, GaAs and InAs 4.7 The highest calculated extinction coefficient k(ω) of 59 BAs, AlAs, GaAs and InAs 4.8 The highest calculated absorption coefficient 63 훼(휔)of BAs, AlAs, GaAs and InAs 4.9 The highest calculated reflectivity 푅(휔)of BAs, 68 AlAs, GaAs and InAs 4.10 The highest calculated energy loss L(ω) of BAs, 71 AlAs, GaAs and InAs x LIST OF FIGURES FIGURE NO. TITLE PAGE 1.1 Computational science is defined as the 9 intersection of the three disciplines, i.e. computer science, mathematics and applied science. 2.1 Flow chart for the nth iteration in the self 19 consistent procedure to solve Hartree-Fock or Kohn-Sham equations. Partitioning of the unit cell into atomic sphere 2.2 27 (I) and interstitial region (II) 3.1 Program flow in WIEN2k 34 4.1 Zincblende crystalline structure 35 4.2 Unit cell structure of BAs in zincblende phase 36 4.3 Unit cell structure of AlAs in zincblende 36 phase 4.4 Unit cell structure of GaAs in zincblende 37 phase 4.5 Unit cell structure of InAs in zincblende 37 phase 4.6 The electronic structure of III arsenides in 44 indirect nature (BAs, AlAs) and direct nature (GaAs, InAs) with various exchange correlation potential have been shown. (a), (b),(c) and (d) shows the calculated band structure with LDA, PBE-GGA, WC-GGA and mBJ+LDA 4.7 Density of states of III arsenides calculated 46 with mBJ+LDA potential xi 4.8 The calculated real 휖1 and imaginary 휖2 parts 49 of BAs dielectric functions calculated with LDA, PBE-GGA, WC-GGA, mBJ+LDA and mBJ+GGA. 4.9 The calculated real 휖1 and imaginary 휖2 parts of AlAs dielectric functions calculated with 49 LDA, PBE-GGA, WC-GGA, mBJ+LDA and mBJ+GGA. 4.10 The calculated real 휖1 and imaginary 휖2 parts 50 of GaAs dielectric functions calculated with LDA, PBE-GGA,WC-GGA, mBJ+LDA and mBJ+GGA 4.11 The calculated real 휖1 and imaginary 휖2 parts 50 of InAs dielectric functions calculated with LDA, PBE-GGA, WC-GGA, mBJ+LDA and mBJ+GGA. 4.12 The calculated refractive index 푛(휔) and 54 extinction coefficient k(ω) spectra of BAs with LDA, PBE-GGA, WC-GGA, mBJ+LDA and mBJ+GGA potential. The calculated refractive index 푛(휔) and 4.13 54 extinction coefficient k(ω) spectra of AlAs with LDA, PBE-GGA WC-GGA, mBJ+LDA and mBJ+GGA potential. 4.14 The calculated refractive index 푛(휔) and 55 extinction coefficient k(ω) spectra of GaAs with LDA, PBE-GGA,WC-GGA, mBJ+LDA and mBJ+GGA potential. 4.15 The calculated refractive index 푛(휔) and 55 extinction coefficient k(ω) spectra of InAs with LDA, PBE-GGA, WC-GGA, mBJ+LDA and mBJ+GGA potential. 4.16 The calculated absorption coefficient 훼(휔) of 61 BAs calculated with LDA, PBE-GGA, WC- GGA, mBJ+LDA and mBJ+GGA potential. xii 4.17 The calculated absorption coefficient 훼(휔) of 61 AlAs calculated with LDA, PBE-GGA, WC- GGA, mBJ+LDA and mBJ+GGA potential.