Theoretical calculations of dilute oxides for application to spintronic and photovoltaic devices.

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(1)University Mohammed V Faculty of sciences -RabatN. 𝑜 d’ordre: 2801. Doctoral Thesis Presented by:. Mourad BOUJNAH Discipline: Physics informatics Specialty: Condensed matter and modelling systems. Theoretical calculations of dilute oxides for application to spintronic and photovoltaic devices Defended,. 31/10/2015. In front of the jury:. President :. Hamid EZ-ZAHRAOUY. PES,. Faculty of sciences, Rabat. Lahoucine BAHMAD. PES,. Faculty of sciences, Rabat. Mohamed BENAISSA. PH,. Faculty of sciences, Rabat. Noureddine BENAYAD. PES,. Faculty of sciences Ain Chock, Casablanca. Abdelilah BENYOUSSEF. PES,. Resident member in Hassan II Academy of. Reviewers:. Sciences and Technologies, Rabat Youssef EL AMRAOUI. PES,. Faculty of sciences, Rabat. Abdallah EL KENZ. PES,. Faculty of sciences, Rabat. Mohamed LOULIDI. PES,. Faculty of sciences, Rabat. Dr,. École normale supérieure, Paris, France. Invited: Ari Paavo SEITSONEN. Faculty of sciences, 4 Avenue Ibn Battouta B.P. 1014 RP, Rabat-Morocco Phone:+212(0) 37 77 18 34/35/38, Fax: +212(0) 37 77 42 61,. http://www.fsr.ac.ma.

(2) University Mohammed V Faculty of sciences -Rabat-. Doctoral Thesis Theoretical calculations of dilute oxides for application to spintronic and photovoltaic devices Supervisors:. Author:. Prof. A. El Kenz. Mourad BOUJNAH. Prof. A. Benyoussef. A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the: Laboratory of magnetism and physics of high energies Departement of physics at 31 October 2015 In front of the jury: President :. Hamid EZ-ZAHRAOUY. PES,. Faculty of sciences, Rabat. Lahoucine BAHMAD. PES,. Faculty of sciences, Rabat. Mohamed BENAISSA. PH,. Faculty of sciences, Rabat. Noureddine BENAYAD. PES,. Faculty of sciences Ain Chock, Casablanca. Abdelilah BENYOUSSEF. PES,. Resident member in Hassan II Academy of. Reviewers:. Sciences and Technologies, Rabat Youssef EL AMRAOUI. PES,. Faculty of sciences, Rabat. Abdallah EL KENZ. PES,. Faculty of sciences, Rabat. Mohamed LOULIDI. PES,. Faculty of sciences, Rabat. Dr,. École normale supérieure, Paris, France. Invited:. Ari Paavo SEITSONEN. Faculty of sciences, 4 Avenue Ibn Battouta B.P. 1014 RP, Rabat-Morocco Phone:+212(0) 37 77 18 34/35/38, Fax: +212(0) 37 77 42 61,. http://www.fsr.ac.ma.

(3) ” Seven Deadly Sins: Wealth without work Pleasure without conscience Science without humanity Knowledge without character Politics without principle Commerce without morality Worship without sacrifice.”. Mahatma Gandhi.

(4) Dedication To My Grand Father and My Grand Mother (God rest her soul) My Father and My Mother for the reason of what i become today, Thank you for your great support and continuous care. My sisters Nada, Rajaa and Meryem. My oncle, my aunt and my cousin for supporting me all the way. To all my friends that i love in near and far.. ii.

(5) Acknowledgements The work presented above was made at the Mohammed V University, Faculty of Sciences, in the Laboratory of Magnetism and Physics of High Energies (LMPHE) under the supervision of Prof. Abdallah El Kenz. I have been working with him since Sept. 2009.. I would like to take this opportunity to express my thanks and gratitude to the many people who have in so many ways helped and supported me throughout my Doctoral studies.. First and foremost, I wish to thank you warmly Prof. Abdallah El Kenz, my supervisor, for your indispensable hand-to-hand education and visionary supervision, for all of the encouragements and supports you gave me, on my research work, on my publication and thesis write-up. I am especially thankful to you for being the one recruited me in the group.. I would like to thank you my co-supervisor of this thesis, Prof.. Abdelilah Benyoussef,. without him this work would not have been possible. He has been an inspiration and a great friends for the past fourth years, providing invaluable insight and constructive criticism to the research i have done.. It has truly been a great pleasure and privilege to work with him on. the many different areas of research, and his enthusiasm and willingness to help has allowed me develop to be a better scientist and more capable person. In addition to physics, Prof. Abdelilah Benyoussef has taught me many things about life, which i think will be very useful to my future career.. Besides my supervisor and co-supervisor, it is a pleasure to thanks the thesis committee for reporting and reviewing my thesis and giving their useful comments.. I would like to thank the president and rapporteur of this thesis Prof. Hamid EZ-Zahraouy from Faculty of Science Rabat.. Also i would like to extend my thanks to Prof. Mohamed Benaissa from Faculty of Science Rabat,for reviewing this thesis.. I would like also to offer my thanks to Prof. Youssef El Amraoui from faculty of Science Rabat, for reviewing this thesis.. I would like to thank Prof. Lahoucine Bahmad from Faculty of Science Rabat,for reviewing my this thesis.. I wish to thank you Prof. Mohammed Loulidi, for your patience in revising my papers and this thesis. Thank you especially for treating me as a friend, enlightening me with you wisdom in academics as well as in life. iii.

(6) I’m holding to express my thanks Prof. Nourredine Benayad from faculty of sciences Ain Chock, Hassan II university, Casablanca for reporting and reviewing this thesis. I owe my deepest gratitude to Dr.. Ari Paavo Seitsonen from CNRS, École Normale. Supérieure, Montrouge/Paris - France, for his kind helps in correcting and revising my papers, solving my problems. thesis.. I encountered during my research and for reporting and reviewing my. You were the first foreign professor i met since Nov.. 2011 exactly in US – Morocco. international Workshop on Nano-Materials and Renewable Energies, Ifrane - Morocco. I would also like to thank two other mentors who i have had the privilege of working closely with during my doctoral studies overseas: Prof. Antonio Ferreira Da Silva of the Federal University of Bahia (UFBa), Salvador, Bahia, Brazil, and Prof. Robel Oleg at Department of Material Science and Engineering, McMaster University, Ontario, Canada. They were both most welcoming and helpful, and provided fresh challenges and inspiration for my research. I would like to thank Prof. P. Blaha and Prof. K. Schawrz at Wien Technical University for the. Wien2k. code and their kind reply.. I would like to extend my sincere gratitude to all my colleagues in LMPHE, Master Physics Informatic and Dr. Hicham Labrim from CNESTEN, for their friendship and for their generous assistance in everything we shared, as the conferences, formations, coffee-breaks,. . . I can’t thank all professors without thanking Prof. A. Maaouni and Prof. A. Belayachi, because they gave me the opportunity to teach the young physics students in Bachelor or in Master whether in informatics (Numerical analysis - Matlab Software) or in physics (Physics of materials and applications, Magnetism and Magnetic materials) I also want to thank the experimentalist colleagues for the confidence they have shown in me and stimulating their interest in our work. There is of course Imane Chaki with whom i spent my time writing my thesis and ate our special lunch in the National Library of Morocco and take a nice break coffee in the cafeteria of our faculty of sciences - Rabat.. Also Houda. Ennaciri whose ability and willingness to understand everything and always willing to exchange ideas. Adil Hadri with whom i started to collaborate with and exchange ideas. At last, my Sincere gratitude goes to my parents, without their encouragement and guidance i would not have pursued a path in my life in general. Special appreciation to my uncle Dr. Mohammed Boujnah who is an engineer in the Agricultural Research Institute, who’s my moral and financial support in my whole life and he is the best example for me. Last, but not least, i would like to thank my best friends, Abdennour Taimour, Amine Amghar, Marouan Lakhal, Ayoub Mahmoudi, Sakina Bouifden and Zineb El Fatouani, for being so supportive of my research for the past 4 years, without them life would not have been as enjoyable as it was with them..

(7) Abstract The main objective of this thesis is to explore the electronic, magnetic, optical and electrical properties of dilute oxides (ZrO and ZnO), such as diluted magnetic oxides (DMO) and transparent conducting oxides layer (TCOs), so as to be able to realize spintronic and photovoltaic applications. Firstly, we investigated Zirconia (ZrO ) based DMO systems, such as the point defect of ZrO and Transition Metal (TM) -doped ZrO using the Korringa, Kohn and Rostoker-Coherent Potential Approximation (KKR-CPA) and the full-potential linearized augmented plane wave method (FP-LAPW) respectively for spintronic application. We found that the magnetic moments are observed in the oxygen interstitial and antisite (O𝑖 , O𝑍 𝑟 ) cases. The corresponding ferromagnetic states are more stable than the spin–glass states.. Afterward, we evaluated the. possibility of long-range magnetic order for TM ions substituting Zr.. Our results show that. ferromagnetism is the ground state in V, Mn, and Fe-doped ZrO have a high value of magnetic moment in Mn-doped ZrO . Moreover, it has been found that the V, Mn, and Fe provide half-metallic properties considered to be the leading cause, responsible for ferromagnetism. Beside that, the FP-LAPW method and Boltzmann’s Transport theory, are employed to theoretically investigate the optical and electrical properties of the point defect of ZrO and vanadium -doped wurtzite ZnO with different concentrations (3.125%, 6.25%, 12.5%, 25%). The formation energetics of point defects is studied before and after optimization of positions. Our results indicate that the oxygen antisite of zirconium has the lowest formation energy and could thus be the acceptor defect responsible for the p-type conductivity of undoped ZrO , we found that the highest value of the electrical conductivity is that for the vacancy and antisite of Zr. Finally, Zn. V . O is the optimized composition of the V doped ZnO, which has the highest. conductivity 3.2 10. Key Words:. 𝑐𝑚−. Ab initio. and transmission coefficient about 93 %.. calculations, FP-LAPW, Magnetic properties, Optical properties,. Diluted Magnetic Oxides, Transparent Conducting Oxides, Spintronic..

(8) Résumé L’objectif principal de cette thèse est d’étudier les propriétés èlectroniques, magnétiques, optiques et électriques des oxydes dilués (ZrO et ZnO), tels que les oxydes magnétiques dilués (DMO) et les oxydes transparent conducteur (TCO) de manière à être en mesure de réaliser des applications en spintronique et photovoltaïque. Tout d’abord, nous avons étudié les systèmes DMO à base de dioxyde de zircone (ZrO ), tels que les défauts ponctuels de ZrO et le dopage par les métaux de transition (TM) en utilisant la méthode Korringa, Kohn et Rostoker avec l’approximation du potentiel cohérent (KKR-CPA) et La méthode des ondes planes augmentées linéarisées (FP-LAPW) respectivement pour application à la spintronique. Nous avons trouvé que les moments magnétiques sont observés dans les cas d’intersite et antisite d’oxygène (O𝑖 , O𝑍𝑟 ). Les états ferromagnétiques correspondants sont plus stables que les états de spin-glass. Ensuite, nous avons évalué la possibilité d’existante de l’ordre magnétique à longue portée pour les ions TM en substitution au zirconium. Nos résultats montrent que le ferromagnétisme est l’état le plus stable dans ZrO dopé par V, Mn, Fe et ont une valeur élevée du moment magnétique dans ZrO dopé par Mn.. En outre, il a été trouvé. que le V, Mn et Fe fournissent des propriétés demi-métallique qui sont considérées comme la principale cause responsable de ferromagnétisme. Par ailleurs, La méthode FP-LAPW et la théorie de Transports de Boltzmann, sont employées pour étudier théoriquement la structure électronique et les propriétés optiques et électriques des défauts ponctuels dans ZrO et de ZnO de strucutre Wurtzite dopé par le vanadium á différentes concentrations (3.125%, 6.25%, 12.5%, 25%) pour l’application photovoltaïque. L’énergie de formation des défauts ponctuels est étudiée avant et après optimisation des positions. Nos résultats indiquent que l’oxygène antisite de zirconium a une énergie de formation très basse et pourrait donc être le défaut responsable de la conductivité de type p de ZrO. non dopé, nous avons constaté que la plus grande valeur de la conductivité électrique est celle des sites vacants et des antisites de zirconium. Finalement, Zn, V , O est la composition. optimisée de ZnO dopé par V, qui a la plus forte conductivité 3,2 10. 𝑐𝑚−. et un coefficient. de transmission d’environ 93 %.. Mots clé. : Calculs. ab initio, FP-LAPW, Les propriétés magnétiques, Les propriétés. optiques, Les oxydes magnétiques dilués, Les oxydes transparent conducteur, Spintronique..

(9) Résumé détaillé La recherche dans le domaine des sciences des matériaux et en particulier des oxydes dilués a pris une ampleur considérable grâce à l’enjeu économique du traitement de l’information et la forte augmentation de l’évolution des activités humaines pour la consommation d’énergie. Dans ce contexte, la recherche sur les oxydes magnétiques dilués (DMO) et les oxydes transparents conducteurs (TCO) des systèmes ont été témoins de divers développements pour répondre à cette évolution pour les deux domaines qui sont l’électronique de spin et la photovoltaïque. En commençant par l’excitation initiale menant à des efforts intensifs de recherche dans des nombreux laboratoires à travers le monde, ce qui donne des résultats intéressants, mais soulevant également de nouvelles questions aussi bien les préoccupations liées à des effets non-intrinsèques et le rôle possible des défauts. Ce scénario a attiré notre attention théorique pour la création de nouveaux modèles d’oxydes dilués.. L’objectif principal de ce travail est d’étudier théoriquement, les propriétés électroniques, magnétiques, optiques et électriques des systèmes d’oxydes dilués, tels que DMO et TCO, en utilisant la théorie fonctionnelle de la densité (DFT) et la théorie de transport de Boltzmann. Cela a conduit aux objectifs spécifiques suivants qui sont divisés en deux parties pour répondre à deux principales questions :. 1. L’effet de défauts et du dopage sur le magnétisme. 2. Le rôle de défauts et dopage sur le comportement des matériaux dans l’application photovoltaïques.. Au cours de cette thèse, une introduction a été donnée à propos de l’histoire et de la motivation de la magnétorésistance géante (GMR) et magnétorésistance tunnel (TMR) pour l’application électronique de spin avec les recherches antérieures des oxydes magnétiques dilués, en outre, nous avons fait la même chose pour les oxydes transparents conducteurs pour l’application photovoltaïque comme il est indiqué dans le chapitre 1.. Avant de commencer les résultats et. les discussions de ces deux principaux domaines (DMO et TCO), nous avons présenté dans le chapitre 2 une brève description des propriétés des matériaux tels que magnétique où nous avons donné plus de détails sur les origines du magnétisme et le mécanisme des interactions d’échange. Après, nous avons expliqué les concepts de base de rayonnement électromagnétique et l’interaction lumineuse avec les solides et nous terminons cette section par une explication des propriétés optiques des métaux et métalloïdes et pour finir ce chapitre nous avons présenté briévement les propriétés électriques des matériaux. Dans le cadre théorique, nous avons décrit la théorie de la fonctionnelle de la densité qui est l’élément essentiel dans ce type de calculs avec.

(10) deux méthodes différentes: la méthode Korringa, Kohn et Rostoker avec l’approximation du potentiel cohérent (KKR-CPA) et la méthode des ondes planes augmentées linéarisées (FP-LAPW) (voir chapitre 3).. La première partie est pour étudier théoriquement les propriétés électroniques et magnétiques des défauts intrinsèques et extrinsèques ponctuelles de la phase cubique de ZrO utilisé dans des dispositifs de spintronique.. Dans le chapitre 4, nous avons utilisé la méthode Korringa, Kohn et Rostoker avec l’approximation du potentiel cohérent (KKR-CPA) pour étudier les propriétés électroniques et magnétiques des différents défauts ponctuels dans ZrO phase cubique. Nous avons discuté en particulier le zirconium en intersite (Zr𝑖 ), le zirconium en antisite (Zr𝑂 ), les lacunes de zirconium (V𝑍𝑟 ), l’oxygène en intersite (O𝑖 ), l’oxygène en antisite (O𝑍𝑟 ), et les lacunes d’oxygène (V𝑂 ). Il a été montrée que la lacune d’oxygène et le zirconium en intersite (V𝑂 , Zr𝑖 ) sont de type n, tandis que les autres défauts ponctuels sont de type p.. Les moments magnétiques sont observés seulement. dans l’oxygène en intersite et antisite (O𝑖 , O𝑍𝑟 ). Les états ferromagnétiques sont plus stables que les états verre de spin après le calcul de la différence entre eux. En outre, en augmentant la concentration des défauts, les interactions ferromagnétiques deviennent plus élevées et la température de Curie augmente aussi. On a constaté que le mécanisme responsable de O𝑖 et O𝑍𝑟 est le double échange en raison des caractères semi-métalliques dans ces défauts intrinsèques.. Dans le chapitre 5, nous avons étudié une nouvelle classe de DMO, pour laquelle peu d’activité expérimentale a été rapporté à ce jour, à savoir, DMO basé sur la phase cristalline de Zr −𝑥 TM𝑥 O (TM = V, Mn, Fe, et Co) à x = 6,25 %, utilisant La méthode des ondes planesaugmentées linéarisées (FP-LAPW). Dans nos calculs, le dioxyde de zirconium couramment appelée zircone est un semi-conducteur de type p et possède une grande largeur de bande interdite. Nous montrons que l’état fondamental ferromagnétique est le plus dominant dans ZrO dopé par V, Mn et Fe et le moment magnétique a une grande valeur dans ZrO dopé par Mn. Cependant, ZrO dopé par Co a un état antiferromagnétique est plus stable que celui ferromagnétique. En outre, il a été trouvé que les métaux de transition V, Mn et Fe fournissent des propriétés semimétalliques considérées comme la cause principale responsable du ferromagnétisme. L’utilisation du potentiel modifié de Becke-Jonhson (mBJ) améliore les résultats obtenus par l’approximation du gradient généralisé (GGA) de la structure électronique au niveau de Fermi.. La deuxième partie a été consacrée pour l’analyse des propriétés électroniques, optiques et électriques des oxydes non dopés et dopés utilisés dans des dispositifs photovoltaïques.. Dans le chapitre 6, et pour compléter l’étude de ce que nous avons fait dans la première partie, nous avons étudié les propriétés électroniques, optiques et électriques pour les défauts ponctuels de c-ZrO dans le calculs ab initio et de la théorie de transport de Boltzmann. Nous avons calculé les énergies de formation des défauts ponctuels avant et après optimisation des.

(11) positions et nous avons trouvé que l’antisite Zr a la plus basse énergie de formation trouvé après optimisation des positions. Cependant, la méthode mBJ améliore la largeur de la bande interdite dans la structure électronique. En outre, le coefficient de transmission de V𝑍𝑟 a une valeur plus élevée avec Zr𝑂 en dessous de 520 nm. Alors, la transmittance de V𝑂 devient plus importante dans le domaine infrarouge. Pour compléter le calcul nous avons étudié les propriétés électriques pour expliquer ce fort coefficient de transmission. Nous avons constaté que la plus grande valeur de la conductivité électrique dans le défaut ponctuel de ZrO sont les lacunes et l’antisite de Zr et leurs valeurs sont 4.3x10. et 4.6x10 (.cm)− , respectivement à basse température.. Pour finir ce travail et spécialement cette partie, nous avons dopé ZnO avec différentes concentrations (3,125 %, 6,25 %, 12,5 %, 25 %) de vanadium en utilisant le code wien2k pour calculer les propriétés électroniques et optiques et la théorie de transport de Boltzmann pour les propriétés électriques. La structure calculée de la bande interdite et la densité d’états (DOS) présentent une largeur de bande de ZnO pur (3.3 eV) plus proche de la valeur expérimental. Ainsi, nos résultats indiquent que la transmittance moyenne dans la région de la longueur d’onde (400 à 1000 nm) était de 93 % en raison du faible coefficient d’absorption dans cette gamme. Nous avons constaté que Zn, V , O est la composition optimisée de ZnO dopé par V, qui a la plus forte conductivité (3.2x10. (.cm)− ) et le coefficient de transmission. La haute transmittance et la. conductivité électrique indiquent que le système hexagonal de ZnO dopé par V a des applications potentielles en énergie solaire..

(12) Contents Dedication. ii. Acknowledgements. iii. Abstract. v. Résumé. vi. Résumé détaillé. vii. Contents. x. Abbreviations. xiii. 1 Introduction 1.1. 1.2. I. 1. Thesis overview and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 1.1.1. Giant magnetoresistance and diluted magnetic oxides. . . . . . . . . . . .. 1. 1.1.2. Transparent conductive oxides . . . . . . . . . . . . . . . . . . . . . . . . .. 3. Objective and Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . .. 6. Background information. 8. 2 Materials properties 2.1. Magnetic properties. 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9. 2.1.1. Origins of magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9. 2.1.2. Exchange interaction mechanisms . . . . . . . . . . . . . . . . . . . . . . .. 12. 2.1.2.1. Direct exchange or double-exchange mechanism . . . . . . . . . .. 14. 2.1.2.2. Indirect exchange or Ruderman, Kittel, Kasuya and Yoshida in-. 2.1.2.3. Kinetic p-d exchange. . . . . . . . . . . . . . . . . . . . . . . . .. 17. 2.1.2.4. Super-exchange mechanism . . . . . . . . . . . . . . . . . . . . .. 17. teraction. 2.2. Optical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18. 2.2.1.1. Electromagnetic radiation . . . . . . . . . . . . . . . . . . . . . .. 18. 2.2.1.2. Light interactions with solids . . . . . . . . . . . . . . . . . . . .. 20. 2.2.1.3. Atomic and electronic interactions . . . . . . . . . . . . . . . . .. 21. 2.2.2. Optical properties of metals . . . . . . . . . . . . . . . . . . . . . . . . . .. 22. 2.2.3. Optical properties of nonmetals . . . . . . . . . . . . . . . . . . . . . . . .. 23. 2.2.3.1. 23. 2.2.1. Refraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x.

(13) Contents. 2.3. xi. 2.2.3.2. Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24. 2.2.3.3. Absorption. 25. 2.2.3.4. Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Electrical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28. 2.3.1. Ohm’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28. 2.3.2. Electrical conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29. 2.3.3. Energy band structures in solids. . . . . . . . . . . . . . . . . . . . . . . .. 30. 2.3.4. Temperature dependence-Metals/Semiconductors . . . . . . . . . . . . . .. 31. 3 Theoretical framework 3.1. 33. Schrödinger equation for many-body problem. . . . . . . . . . . . . . . . . . . . .. Born-Oppenheimer approximation. . . . . . . . . . . . . . . . . . . . . . .. 35. 3.1.2. Slater determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36. 3.2. Hartree-Fock approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37. 3.3. Beyond Hartree-Fock approximation. 3.4. Density functional theory. 3.5. 3.6. . . . . . . . . . . . . . . . . . . . . . . . . .. 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40. 3.4.1. Thomas-Fermi-Dirac theory . . . . . . . . . . . . . . . . . . . . . . . . . .. 41. 3.4.2. Hohenberg and Kohn theories . . . . . . . . . . . . . . . . . . . . . . . . .. 43. 3.4.2.1. First Hohenberg-Kohn theorem . . . . . . . . . . . . . . . . . . .. 43. 3.4.2.2. Second Hohenberg-Kohn theorem. . . . . . . . . . . . . . . . . .. 44. 3.4.3. Kohn-Sham Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45. 3.4.4. Solving Kohn-Sham equations . . . . . . . . . . . . . . . . . . . . . . . . .. 46. Exchange-Correlation functional. 46. . . . . . . . . . . . . . . . . . . . . . . .. 3.4.5.1. Local density approximation. . . . . . . . . . . . . . . . . . . . .. 3.4.5.2. Generalized gradient approximation. 3.4.5.3. Hybrid functional. 3.4.5.4. Modified Becke-Johnson potential. 48. . . . . . . . . . . . . . . . .. 48. . . . . . . . . . . . . . . . . . . . . . . . . . .. 49. Korringa, Kohn and Rostoker method. . . . . . . . . . . . . . . . . .. 50. . . . . . . . . . . . . . . . . . . . . . . . .. 51. 3.5.1. Green’s function method . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52. 3.5.2. Green function method for impurities. . . . . . . . . . . . . . . . . . . . .. 53. 3.5.3. Coherent potential approximation. . . . . . . . . . . . . . . . . . . . . . .. 55. Full potential- linearized augmented plane wave + local orbitals method. . . . . .. 56. 3.6.1. Linearized augmented plan wave basis functions . . . . . . . . . . . . . . .. 56. 3.6.2. Augmented plane wave + local orbitals basis functions . . . . . . . . . . .. 57. 3.6.3. Potential and density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58. 3.6.4. Wien2k. 59. Ab initio. package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. study of electronic and magnetic properties of intrinsic and. extrinsic point defects in cubic ZrO used in spintronic applications. 4. 34. 3.1.1. 3.4.5. II. 28. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Ab initio. in 𝑍𝑟𝑂. calculation of magnetic and electronic properties of Point Defects. 62. 63. 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63. 4.2. Calculation method and crystal structure. 64. 4.3. Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 𝑍𝑟𝑂. of 𝑍𝑟𝑂. . . . . . . . . . . . . . . . . . . . . . .. 65. 4.3.1. Electronic structure of. without and with defects . . . . . . . . . . .. 65. 4.3.2. Magnetic properties. with point defects. 66. . . . . . . . . . . . . . ..

(14) Contents. 4.4. xii. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5 The influence of mBJ functional on ferromagnetism of using FP-LAPW method. 𝑑. TM-doped. 70. 𝑍𝑟𝑂. 71. 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5.2. Calculation method and crystal structure. . . . . . . . . . . . . . . . . . . . . . .. 72. 5.3. Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74. 5.3.1. Electronic and magnetic properties . . . . . . . . . . . . . . . . . . . . . . 5.3.1.1. III. 𝑍𝑟𝑂 . TM-doped 𝑍𝑟𝑂. Undoped. 74. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78. 5.3.1.2 5.4. 71. Electronic, optical and electrical properties of undoped and doped. oxides used in photovoltaic applications. 79. 6 Optical and electrical properties of point defects in cubic ZrO through the modified Becke-Johnson approach 80 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6.2. Models and calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81. 6.3. Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81. 6.3.1. Formation energy of point defects . . . . . . . . . . . . . . . . . . . . . . .. 81. 6.3.2. Electronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83. 6.3.3. Optical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84. 6.3.4. Electrical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88. 6.4. 80. 7 Theoretical calculation of optical and electrical properties of V doped ZnO in solar cells Applications 90 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.2. Computational details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91. 7.3. Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92. 7.3.1. Electronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92. 7.3.2. Optical properties. 7.3.3. Electrical properties. 7.4. 90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99. 8 Conclusions and perspectives. 100. Bibliography. 103. List of Publications. 103. .1. .2. Submitted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 .1.1. Chapters book. .1.2. Articles. Published. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.

(15) Abbreviations DMO TCO GMR MR AMR TMR MOS TM DFT HF MP HEG LDA LSDA PBE GGA LDA+U DMFT mBJ KKR CPA FP-LAPW DOS PDOS VB VBM. Dilute magnetic oxides Transparent conduction oxides Giant magnetoresistance Magneto resistance anisotropic magnetoresistance Tunneling magnetoresistance Metal oxide semiconductors Transition metal Density f unctional theory Hartree-Fock Møller-Plesset Homogeneous electron gaz Local density approximation Local spin density approximation Perdew Burke Ernzerhof Generalized gradient approximation Local density approximation with Hubbard U term Dynamic mean f ield theory modified Becke-Johnson Korringa-Kohn-Rostokere Coherent potential approximation Full potentiel linearized augmented plane wave Density of states Partial density of states Valence band Valence band maximum xiii.

(16) Abbreviations. xiv. CBM FM AFM DLM MFA TC EF BZ RMT GS ITO UV IR. Conduction band minimum Ferromangetic AntiFerromangetic Disordered local moment Mean f ield approximation Curie Temperature Fermi Energy Brillouin Zone Muffin-Tin Radius Ground State Indium tin Oxide Ultraviolet Inf rared.

(17) Chapter 1. Introduction 1.1 Thesis overview and motivation The research on diluted magnetic oxides (DMO) and transparent conductive oxides (TCO) systems have witnessed various developments, starting with the initial excitement leading to intensive research efforts in many laboratories around the world, yielding interesting results but also raising new questions and concerns related to non-intrinsic effects and the possible role of defects.. This scenario has attracted our theoretical attention for the creation of new models. of diluted oxides applicable both on spintronics and photovoltaics. That’ll be presented in two subsections, the first one about giant magnetoresistance (GMR) and diluted magnetic oxides and the second one about transparent conductive oxides.. 1.1.1. Giant magnetoresistance and diluted magnetic oxides. In 1838, the concept of an indivisible quantity of electric charge was first theorized to explain the chemical properties of atoms.. Till 1897 the electron was identified as a particle. [1]. The concept of spin was first proposed by Pauli. However, till 1928, when Dirac derived his relativistic quantum mechanics, electron spin was well explained and known as an intrinsic angular momentum characterized by quantum number s=1/2. Since then, it has been realized. 𝑟𝑑 intrinsic spin properties. However, electron charges. that beside mass and charge, electron has 3. and spins have been considered separately.. The 1. 𝑠𝑡 observation of MagnetoResistance (MR) was made by William Thomson (more. commonly known as Lord Kelvin) in 1857 when he measured the resistance behaviour of Fe/Ni 1.

(18) Introduction. 2. in the presence of magnetic field (known as Anisotropic MagnetoResistance (AMR))[2]. The first generation of magnetic sensors was based on the AMR effect through the magnitude of AMR was only a few percent (5%).. In 1988, Baibich et al.. observed the GMR a huge MR around 50% at low tempera-. ture (Fe/Cr) magnetic superlattice grown by molecular beam epitaxy, which is result of spindependent transmission of the conduction electrons between Fe layer through Cr layers [3, 4]. Since then, exploiting the influence of spins on the mobility of electrons in ferromagnetic materials and/or artificial structures becomes one of the intensely researched area in physics, and has introduced the novel idea termed spintronics [5], which can be possibly utilized in the next generation high-speed, low-cost electronic devices. The perspective of faster and smaller devices is even more interesting when seen as a way to circumvent the predicted upcoming limit in Moore’s law as presented in the Figure 1.1.. Figure 1.1:. Moore’s law is further validated by including non-Intel CPUs and extending the timeline to 2012.. The importance of spintronics today has been illustrated by the 2007 Nobel prize in physics, awarded to Albert Fert and Peter Grünberg for their discovery of the GMR in the late 80’s. It requires a strong interplay between electric and magnetic properties and therefore new materials have to be considered and even designed.. A possible solution that is widely studied is the. relatively new family of ferromagnetic semi-conductors or DMO. GMR is based on the spin dependent scattering effects, which was first proposed to explain the anomalous resistivity trends exhibited by bulk ferromagnetic materials doped with impurities by Mott [6].. After the discovery of GMR many researchers have been interested in a new effect was originally discovered by M. Jullière from University of Rennes, France in Fe/Ge-O/Co junctions.

(19) Introduction. 3. at 4.2 K [7], who is the Tunnel magnetoresistance (TMR). The relative change of resistance was around 14%, and did not attract much attention. Among them, Miyazaki et al. in 1994 found 18% in junctions of iron separated by an amorphous aluminum oxide insulator [8] and Jagadeesh Moodera found 11.8% in junctions with electrodes of CoFe and Co [9]. The highest effects observed to date with aluminum oxide insulators are around 70% at room temperature. Since the year 2000, tunnel barriers of crystalline magnesium oxide (MgO) have been under development. In 2004, Parkin and Yuasa were able to make. 𝐹 𝑒/𝑀 𝑔𝑂/𝐹 𝑒. junctions that reach. over 200% TMR at room temperature [10, 11]. In 2008, effects of up to 600% at room temperature and more than 1100% at 4.2 K were observed in junctions of. 𝐶𝑜𝐹 𝑒𝐵/𝑀 𝑔𝑂/𝐶𝑜𝐹 𝑒𝐵. [12].. In the past decade, intensive research efforts have been carried out by researchers around the globe on exploring the effects of DMO doping with a few percent of a transition-metal cation such as V, Cr, Mn, Fe, Co, Ni and Cu on the physical properties of dilute oxides (DO) such as TiO , SnO , ZnO, Cu O, ZrO . . . as presented in Table 1.1 [13–32].. It has been recently reported that some nonmagnetic materials in bulk state exhibit magnetic behavior at the Nanoscale due to surface and size effects. Thus, bulk samples [33, 34] and thin films [35] of the DMO solid solutions behave as expected when they are well crystallized and stoichiometric. Hence, there is a supposition that the ferromagnetic behaviour of thin-film or nanoparticle samples must be due to ferromagnetic impurity phases present as inclusions [36, 37] or as uncontrolled contamination, introduced, for example, by handling samples with steel tweezers [38, 39]. Since the unoccupied. 𝑑 states are also responsible for the ferromagnetism, therefore,. there is a direct connection between the electrical transport and magnetic properties. Later on, some pioneer research on spin dependent scattering was performed by Fert and Campbell [40]. Even more startling are claims that undoped films of some of these oxides are ferromagnetic, or that they can become magnetic when doped with nonmagnetic cations. Examples here are. ferromagnetism’ was. HfO [41, 42], TiO [42, 43] and ZnO doped with Sc [44]. The term ’d suggested by Coey to cover these cases [45].. 1.1.2. Transparent conductive oxides. Transparent conductive oxides (TCO) were observed for the first time in 1907 by Baedeker [46], who used a primitive vapor deposition system to deposit thin-film CdO that was both optically transparent and electrically conducting. This first TCO was a thin film of CdO prepared by thermally oxidizing a vacuum sputtered film of cadmium metal. While CdO is not widely used.

(20) Introduction. 4. Material. E𝑔 (eV). Doping. Moment (𝜇𝐵 ). T𝐶 (K). Reference. TiO. 3.2. V - 5%. 4.2. >400. Hong et al. (2004) [16]. Co - 7%. 0.3. >300. Matsumoto et al. (2001) [14]. Co - 1-2%. 1.4. >650. Shinde et al. (2003) [22]. Fe - 2%. 2.4. 300. Wang et al. (2003) [15]. Fe - 5%. 1.8. 610. Coey et al. (2004) [30]. Co - 5%. 0.3. 650. Ogale et al. (2003) [19]. V - 15%. 0.5. >350. Saeki et al. (2001) [31]. Mn - 2.2%. 0.16. >300. Sharma et al. (2003) [23]. Fe-5%, Cu-1%. 0.76. 550. Han et al. (2002) [24]. Co - 10%. 2.0. 280-300. Ueda et al. (2001) [17]. SnO. ZnO. 3.5. 3.3. CeO. 3.5. Co - 3%. 6.3. 725. Tiwari et al. (2006) [25]. Cu O. 2.0. Co-5%, Al-0.5 %. 0.2. >300. Kale et al. (2003) [19]. In O. 2.9. Fe - 5%. 1.4. >600. He et al. (2005) [26]. Cr - 2%. 1.5. 900. Philip et al. (2006) [27]. ITO. 3.5. Mn - 5%. 0.8. >400. Philip et al. (2004) [28]. LSTO. –. Co - 1.5%. 2.5. 550. Zhao et al. (2003) [29]. ZrO. 6,1. Mn - 25%. 3.45. 570. Ostanin et al. (2007) [32]. Table 1.1:. Some reports on high T𝐶 - DMOs. today because of toxicity concerns, it remains of theoretical interest because of its high electron mobility apparently due to a low effective electron mass. Later, it was recognized that thin films of ZnO, SnO , In O and their alloys were also TCOs. Doping these oxides resulted in improved electrical conductivity without degrading their optical transmission. Al doped ZnO (AZO) [47], Sn doped In O (ITO) [48] and antimony or fluorine doped SnO (ATO and FTO)[49] are among the most utilized TCO thin films in modern technology which are produced by chemical and physical techniques. In particular, ITO is used extensively because of good optical transparency and low electrical resistivity. Most of the TCO materials are n-type semiconductors, but p-type TCO materials are researched and developed. Such TCO include: ZnO:Mg, ZnO:N, IZO, NiO, NiO:Li, CuAlO , Cu SrO , and CuGaO thin films. At present, these materials have not yet found place in actual applications.. Most optically transparent and electrically conducting oxides are binary or ternary compounds, containing one or two metallic elements, which have transmittance as high as 80% in the.

(21) Introduction. 5. Material. Dopant or multicomponent. SnO. Sb(ATO), As, Nb, Ta, F(FTO). In O. Sn(ITO), Ge, Mo, Ti, Zr, Hf, Nb, Ta, W, Te, F, H. ZnO. Al(AZO), Ga(GZO), B(BZO), In, Y, Sc, V, Si, Ge, Ti, Zr, Hf, F. CdO. In, Sn, Y, F, Sc, Ga, Ti. TiO. Nb, Ta. ZnO-SnO. Zn SnO

(22) , ZnSnO. ZnO-In O. Zn In O , Zn In O. In O -SnO. In

(23) Sn O. CdO-SnO. Cd SnO

(24) , CdSnO. CdO-In O. CdIn O

(25). MgO-In O. MgIn O

(26). GaInO , (Ga,In) O. Sn, Ge. CdSb O. Y. ZnO-In O -SnO. Zn In O5-In

(27) Sn O. CdO-In O -SnO. CdIn O

(28) -Cd SnO

(29). ZnO-CdO-In O -SnO. InGa(ZnO). Table 1.2:. Recently discovered TCO materials for transparent electrodes [50]. visible range, their electrical resistivity could be as low as cient (𝛼) smaller than 10. −

(30) 𝑐𝑚,. with an absorption coeffi-.

(31) cm− in the near-UV and VIS range, and with an optical band gap >3. eV. This remarkable combination of conductivity and transparency is usually impossible in intrinsic stoichiometric oxides; however, it is achieved by producing them with a non-stoichiometric composition or by introducing appropriate dopants.. The current commercial transparent conducting oxide used for most transparent electrode applications is In-Sn-O, or ITO. However, it may not be able to satisfy the demands in the speedy development of future optoelectronic devices since indium, the principle material of ITO, due to its low terrestrial abundance has become very costly. Therefore, the search for a new type of TCO material has become extremely urgent. Indeed, a lot of efforts have been dedicated in search for novel TCOs. Table 1.2 shows various types of new TCO materials discovered during the past decades [50]..

(32) Introduction. 6. The TCOs materials are already widely developed and used in several applications, particularly as transparent electrodes in optoelectronic and photovoltaic devices, flat screens, window defrosters in cars, touch screens, smart windows.. 1.2 Objective and Structure of the thesis In the light of the above, our main objective of this work is to study theoretically by using density functional theory and Boltzmann transport theory, the electronic, magnetic, optical and electrical properties of diluted oxides systems, such as DMO and TCO, so as to be able to realize in spintronic and photovoltaic applications. This led to the following specific objectives which is divided in two part to answer to this two main questions as the papers included in this thesis:. 1. The effect of defects and doping on the magnetism.. 2. The role of defect and doping on the behavior of the materials in photovoltaic applications.. The structure of this thesis is as following:. ∙. Chapter 1 :. This chapter provides an introduction to the research work presented in this. thesis. It describes the research background and explains the motivation for pursuing this work. In addition it provides an overview of the approach taken as well as of the results obtained. Finally, it introduces the structure of the thesis.. ∙. Chapter 2 :. A short description on the origin of magnetism and the exchange interac-. tion mechanisms as double-exchange, super-exchange mechanism, RKKY interaction and Kinetic p-d exchange for magnetic properties. In addition to the basic conception of the optical properties of metals and nonmetals such as refraction, reflection, absorption and transmittance coefficients at the end of this chapter a brief presentation on the electrical properties.. ∙. Chapter 3 :. A description of the DFT and methods such as KKR-CPA and. Wien2k. codes. have performed by addressing the theorems having fundamental leads to the elaboration of this theory.. The necessary approximations to the use of these methods of theoretical. calculations, such as the approximation of the potential for exchange-correlation for the DFT, are also written. implementation of DFT.. This chapter is finished by addressing practical aspects for the.

(33) Introduction. ∙. 7. Chapter 4 :. Using the Korringa–Kohn–Rostoker with the coherent potential approxi-. mation (KKR-CPA) method in connection with the Generalized Gradient Approximation (GGA), we have studied the magnetic and electronic properties of different point defects in cubic ZrO . In particular, we have discussed the zirconium interstitial (Zr𝑖 ), zirconium antisite (Zr𝑂 ), zirconium vacancy (V𝑍𝑟 ), oxygen interstitial (O𝑖 ), oxygen antisite (O𝑍𝑟 ), and oxygen vacancy (V𝑂 ) defects. The magnetic moments was observed only in the oxygen interstitial and antisite (O𝑖 , O𝑍𝑟 ) cases.. ∙. Chapter 5 :. Based on. Wien2k code we have studied the electronic structure, magnetic, and. optical properties in cubic crystalline phase of Zr −𝑥 TM𝑥 O (TM = V, Mn, Fe, and Co) at x=6.25% with the GGA and the modified Becke-Johnson (mBJ) of the exchange-correlation energy and potential for application to spintronic devices.. ∙. Chapter 6 :. We have studied the electronic, optical and electrical properties of point. defects of cubic ZrO by using the. Wien2k code and Boltzmann’s Transport theory.. We have. calculated the formation energy for each defect before and after optimization. Afterward, based on the stable formation energy we have evaluated the DOS, absorption, transmission coefficients and electrical properties with TB-mBJ. We have found that the highest value. of the electrical conductivity is that for the vacancy and antisite of Zr are 4.3 10 and 4.6. 10. ∙. .𝑐𝑚−. Chapter 7 :. respectively at the low temperature. The full-potential linearized augmented plane wave method (FP-LAPW) based. on the density functional theory (DFT) and Boltzmann’s Transport theory, have been employed to theoretically investigate the electronic structure, optical and electrical properties of vanadium -doped wurtzite ZnO with different concentrations (3.125%, 6.25%, 12.5%, 25%) to increase the efficiency of transmittance and electrical conductivity of photovoltaic cells..

(34) Part I. Background information. 8.

(35) Chapter 2. Materials properties 2.1 Magnetic properties An understanding of the mechanism that explains the permanent magnetic behavior of some materials may allow us to alter and tailor the magnetic properties in some cases. Magnetism, the phenomenon by which materials assert an attractive or repulsive force or influence on other materials, has been known for thousands of years.. However, the underlying. principles and mechanisms that explain the magnetic phenomenon are complex and subtle, and their understanding has eluded scientists until relatively recent times.. Many of our modern. technological devices rely on magnetism and magnetic materials; these include electrical power generators and transformers, electric motors, radio, television, telephones, computers, and components of sound and video reproduction systems. Iron, some steels, and the naturally occurring mineral lodestone are well-known examples of materials that exhibit magnetic properties. Not so familiar, however, is the fact that all substances are influenced to one degree or another by the presence of a magnetic field.. 2.1.1. Origins of magnetism. Magnetism occur on the sub atomic level from localised polarisation of the electron clouds of certain atoms arising from unpaired electrons. This causes the charge on the atom to have a net angular momentum. Any flow of charge causes additional physical effects on the surroundings, usually referred to as a magnetic effect. The magnitude of this magnetic or spin moment is dependent on the species of atom [51]. How these spin moments interact with each other is 9.

(36) Chapter 1. Materials properties. 10. critical to how different materials are characterised magnetically. When atoms are brought in proximity to each other there is a probability of an electron jumping from one atom to another, known as the Heisenberg exchange [52]. This interaction probability can indirectly couple the spin moments of the atoms, causing the spin moments to align parallel or anti-parallel. In most materials the spin moments are small and aligned randomly, leading to. paramagnetism. as. shown in figure 2.1 (b) with and without external field.. Figure 2.1: (a) The atomic dipole configuration for a diamagnetic material with and without a magnetic field. In the absence of an external field, no dipoles exist; in the presence of a field, dipoles are induced that are aligned opposite to the field direction. (b) Atomic dipole configuration with and without an external magnetic field for a paramagnetic material.. Diamagnetism is a very weak form of magnetism that is nonpermanent and persists only while an external field is being applied. It is induced by a change in the orbital motion of electrons due to an applied magnetic field.The magnitude of the induced magnetic moment is extremely small, and in a direction opposite to that of the applied field as shown in figure 2.1 (a). Certain metallic materials possess a permanent magnetic moment in the absence of an external field, and manifest very large and permanent magnetizations. These are the characteristics of ferromagnetism, and they are displayed by the transition metals iron (as BCC ferrite), cobalt, nickel, and some of the rare earth metals such as gadolinium (Gd), the spin moments are large, and align in parallel. This is schematically illustrated in figure 2.2. The magnetic moment coupling between adjacent atoms or ions occurs in materials other than those that are ferromagnetic. In one such group, this coupling results in an antiparallel alignment; the alignment of the spin moments of neighboring atoms or ions in exactly opposite directions is termed antiferromagnetism. Manganese oxide (MnO) is one material that displays this behavior as presented in figure 2.3.. In ionic compounds, such as oxides, more complex.

(37) Chapter 1. Materials properties. 11. Schematic illustration of the mutual alignment of atomic dipoles for a ferromagnetic material, which will exist even in the absence of an external magnetic field.. Figure 2.2:. Figure 2.3:. Schematic representation of antiparallel alignment of spin magnetic moments for antiferromagnetic manganese oxide.. forms of magnetic ordering can occur as a result of the crystal structure. One type of magnetic ordering is call ferrimagnetism. A simple representation of the magnetic spins in a ferrimagnetic oxide is shown in figure 2.4. The magnetic structure is composed of two magnetic sublattices (called A and B) separated by oxygens. The exchange interactions are mediated by the oxygen anions. When this happens, the interactions are called indirect or superexchange interactions (will be mentioned later on). The strongest superexchange interactions result in an antiparallel alignment of spins between the A and B sublattice. In ferrimagnets, the magnetic moments of the A and B sublattices are not equal and result in a net magnetic moment. Ferrimagnetism is therefore similar to ferromagnetism. It exhibits all the hallmarks of ferromagnetic behavior-spontaneous magnetization, Curie temperatures, hysteresis, and remanence. However, ferro- and ferrimagnets have very different magnetic ordering. All materials can be classified in terms of their magnetic behavior. The two most common type of magnetism are diamagnetism and paramagnetism, which account for the magnetic properties of most of the periodic table of elements at room temperature. These elements are usually referred to as nonmagnetic, whereas those which are referred to ass magnetic are actually classified.

(38) Chapter 1. Materials properties. Figure 2.4:. 12. Schematic diagram showing the spin magnetic moment configuration for Fe and Fe ions in Fe O

(39). as ferromagnetic. The only other type of magnetism observed in pure elements at room temperature is antiferromagnetism. Finally. magnetic materials can also be classified as ferrogmatic, although this is not observed in any pure element but can also be found in coumpounds, such as the mixed oxides, known as ferrite, from which ferrimagnetism derives its name. the value of magnetic susceptibility falls into a particultar range for each type of material and this is shown in table 2.1 with some examples. The various types of behavior are illustrated in figure 2.5. Type of magnetism. Susceptibility. Diamagnetism. Small and negative. Paramagnetism. Example. −. Au. -2.74 x 10. Cu. -0.77 x 10. Small and positive. 𝛽 -Sn. 00.19 x 10. Small and positive. Pt. 21.04 x 10. Small and positive. Mn. 66.10 x 10. − − − −. Large and positive Ferromagnetism. function of applied field,. Fe. Up to. ∼. 100,000. microsructure dependent Antiferromagnetism. Small and positive. Cr. –. Large and positive Ferrimagnetism. function of applied field,. Ba Ferrite. Up to. ∼. microsructure dependent. Table 2.1:. 2.1.2. Susceptibility at room temperature for each type of magnetic material.. Exchange interaction mechanisms. We choose two groups to explain the exchange interaction mechanism in the magnetic materials.. Diamagnetism and paramagnetism belong to the first group, Where there is there. interaction between the individual moments and each moment acts independently of the others. The second one consists of the magnetic materials most people are familiar with, like iron or nickel. Magnetism occurs in these materials because the magnetic moments couple to one another and form magnetically ordered states..

(40) Chapter 1. Materials properties. Figure 2.5:. 13. A summary of the different type of magnetic behavior. In general the origin of ferromagnetism is always the interplay between the electronic spin degree of freedom, repulsive Coulomb interactions and the Pauli principle. Although this statement is general, it does not give any profound or real understanding of the magnetic order. For most systems, it is necessary to proceed in a partially phenomenological way, by identifying the local spin of the exchange interactions that couple them by comparing the properties of simplified model Hamiltonian with experimental observations. Although ferromagnetism is a well known phenomenon, it can have very different origins which are different to understand.. We will comeback later in this part to the different mechanism. giving rise to ferromagnetism. The ferromagnetism in DMO materials originates from the local magnetic moments of the impurities. The dependence of the energy of the system on the orientation of these local moments is called the exchange interaction. There are several types for the exchange interactions between the magnetic moments that can lead to a long-range ordering of the unpaired spins. The most common exchange interactions are schematically illustrated in figure 2.6. The main purpose of.

(41) Chapter 1. Materials properties. 14. The three types of exchange which are a) superexchange where the magnetic ions interact via the same non-magnetic ion; b) direct exchange in which magnetic ions overlapping their charges; c) indirect exchange where the interaction between the magnetic ions is mediated by charge carriers. Figure 2.6:. this part is to give a detailed explanation of the rules that govern the different mechanisms of exchange interactions in dilute magnetic semiconductors.. 2.1.2.1 Direct exchange or double-exchange mechanism Direct exchange occurs when there is direct overlap of the wave functions of electrons associated with nearest-neighbor magnetic atoms (figure 2.6 b). This interaction can also be understood in terms of the Pauli principle and the Coulomb repulsion, since the Coulomb energy is lowered if the spins of the electrons are parallel because for parallel spin alignment the electrons avoid each other better than antiparallel alignment. An initial simple way of understanding direct exchange is to look at two atoms with one electron each.. When the atoms are very close together the Coulomb interaction is minimal when the. electrons spend most of their time in between the nuclei. Since the electrons are then required to be at the same place in space at the same time, Pauli’s exclusion principle requires that they possess opposite spins. According to Bethe and Slater the electrons spend most of their time in between neighboring atoms when the interatomic distance is small. This gives rise to antiparallel alignment and therefore negative exchange (antiferromagnetic), figure 2.7 (a). If the atoms are far apart the electrons spend their time away from each other in order to minimize the electron-electron repulsion. This gives rise to parallel alignment or positive exchange (ferromagnetism), figure 2.7 (b). Double exchange mechanism [53] is responsible for the stabilization of the ferromagnetism in DMO, when the Fermi energy lies in the majority impurity band of t 𝑔 -symmetry in case of impurity band in the gap as in (Ga,Mn)N. In the figure 2.8 we show a schematic density of states (DOS) representing the t 𝑔 -band of a case of impurity band in the.

(42) Chapter 1. Materials properties. Figure 2.7:. Figure 2.8:. 15. (a) Antiparallel alignment for small interatomic distances (b) Parallel alignment for large interatomic distances.. Schematic diagram of the spin polarized DOS of a transition metal impurity in a wide gap semiconductor.. gap, e.g. for Mn in GaN. If we increase the concentration from a lower value, with a DOS given by the full line, to a larger value corresponding to the broader DOS as given by the dashed line, we transfer spectral-weight from around E𝐹 to lower energies, leading to an energy gain, which stabilizes the FM arrangement since it involves bands of the same spin channel. When the Fermi energy lies within the band, the FM arrangement is more favorable because of a gain in energy coming from a broadening of the t 𝑔 -band. Whereas, in the AFM arrangement bands of same spin channel which are largely separated hybridize forming bonding and anti-bonding states where the lower bonding states are pushed to lower energies and higher antibonding states to higher energies.. 2.1.2.2 Indirect exchange or Ruderman, Kittel, Kasuya and Yoshida interaction The other mechanism of interactions between magnetic atoms involve mediation through charge carriers.. This interaction can manifest itself through Ruderman, Kittel, Kasuya and. Yoshida (RKKY) interaction figure 2.6 (c). The local moments can have either a ferromagnetic direct exchange interaction with band electrons on the same site/or an antiferromagnetic interaction due to hybridization between the local moments and band electrons on neighboring sites. When the coupling is weak, the effect is described by RKKY theory..

(43) Chapter 1. Materials properties. 16. Indirect exchange couples moments over relatively large distances. It is the dominant exchange interaction in metals, where there is little or no direct overlap between neighboring electrons. It therefore acts through an intermediary, which in metals are the conduction electrons (itinerant electrons). This type of exchange is better known as the RKKY interaction. The RKKY exchange coefficient. 𝐽,. oscillates from positive to negative as the separation of the ions changes. and has the damped oscillatory nature shown in figure 2.9. Therefore, depending upon the separation between a pair of ions their magnetic coupling can be ferromagnetic or antiferromagnetic. A magnetic ion induces a spin polarisation in the conduction electrons in its neighbourhood. This spin polarisation in the itinerant electrons is felt by the moments of other magnetic ions within range, leading to an indirect coupling. The interaction is characterised by a coupling coefficient. 𝐽 𝑅𝑖𝑗 ∝ where. 𝑘𝐹. 𝐽,. given by. 𝑠𝑖𝑛 𝑘𝐹 𝑅𝑖𝑗 𝑐𝑜𝑠 𝑘𝐹 𝑅𝑖𝑗 −. 𝑘𝐹 𝑅𝑖𝑗 . 𝑘𝐹 𝑅𝑖𝑗 . is the radius of the conduction electron Fermi surface,. (2.1). 𝑅𝑖𝑗. is the thickness of the. nonmagnetic layer. Hamiltonian which reflects this interaction is:. 𝐻 𝑅𝑖𝑗 . Figure 2.9:. 𝐽 𝑅𝑖𝑗 𝑆𝑖 𝑆𝑗. (2.2). Variation of the indirect exchange coupling constant 𝐽 , of a free electron gas in the neighbourhood of a point magnetic moment at the origin (r=0).. In rare-earth metals, whose magnetic electrons in the 4𝑓 shell are shielded by the 5𝑠 and 5𝑝 electrons, direct exchange is rather weak and insignificant and indirect exchange via the conduction electrons gives rise to magnetic order in these materials..

(44) Chapter 1. Materials properties. 17. 2.1.2.3 Kinetic p-d exchange The kinetic p-d exchange, also called Zener’s p-d exchange, exhibits an energy gain with increased linearly with the impurity concentration, since the effects of different impurities on the shift of the valence band superimpose each other. The reason for this is the same as for the superexchange in the following chapter, i.e. the energy shifts due to hybridization are small and can be treated in first order perturbation theory [54]. The situation is different in the case when the d-states of the magnetic impurity lie below. Schematic diagram of the spin polarized DOS in the case of p-d exchange, when the majority d-level lies below the valence p-band and the minority level above.. Figure 2.10:. the valence p-state, as it is in the case for double exchange, as shown in figure 2.10.. When. the d-states hybridize with the valence band p, they push the majority valence band to higher energies while the minority valence states are pushed to lower energies by the minority d states of the impurity, which is schematically sketched in figure 2.10.. 2.1.2.4 Super-exchange mechanism The antiferromagnetism by super-exchange interaction has been shown for crystals of LaMnO [55]. Goodenough et al. [56] formalized the super-exchange interaction, which resulted in the Goodenough-Kanamori rules. An ion of the transition series metals in a tetragonal crystal field undergoes lifting degeneration 3d electronic levels into two groups separated by the energy of the crystal field. 𝑡 𝑔. .. In the case of an octahedral symmetry, the triplet lowest energy is called. and doublet higher energy e𝑔 . In figure 2.11, contains a diagram which shows the different. ∘. configurations cation-anion-cation at 180 . If the two cations have orbital. 𝑒𝑔. half full pointing. in the direction of the anion, the coupling is direct by the rules of Hund and gives strong antiferromagnetism (case 1 in figure 2.11).. If the two. 𝑒𝑔. orbitals are empty (case 2 in figure.

(45) Chapter 1. Materials properties. 18. 2.11) also gives antiferromagnetism but weak. We can imagine that the cation of the electrons have a non-zero probability of being on the empty orbital. 𝑒𝑔. and that this probability is the. same for both cations. Thus, we find the case 1, but only for a very short time, which is why the interaction is weak. For against, in the case 3 of figure 2.11, a cation has an orbital. 𝑒𝑔. half full. and the other empty. In this case, the electron in question can virtually switch from a cation to another provided that both cations have their parallel spins. This virtual passage gives birth to weak ferromagnetic interaction.. Magnetic order according to the orbital kind of neighboring cations. The angle between two cations is set at 180𝑜 and description of 3d orbitals of the cation and the anion of 2p. Figure 2.11:. 2.2 Optical properties 2.2.1. Basic Concepts. 2.2.1.1 Electromagnetic radiation Like it is considered in the familiar sense, the electromagnetic radiation is wave-like consisting of electric and magnetic field components that are perpendicular to each other and also to the direction of propagation (figure 2.12). Light, heat or radiant energy, radar, radio waves, and x-rays are all forms of electromagnetic radiation..

(46) Chapter 1. Materials properties. 19. Each is characterized primarily by a specific range of wavelengths, and also according to the technique by which it is generated. The electromagnetic spectrum of radiation spans the wide range from. 𝑚. ( 10. −. 𝛾 -rays. 𝑛𝑚),. −. (emitted by radioactive materials) having wavelengths on the order of 10. through x-rays, ultraviolet, visible, infrared, and finally radio waves with wave-. lengths as long as. Figure 2.12:. Figure 2.13:. 𝑚.. This spectrum, on a logarithmic scale, is shown in figure 2.13.. An electromagnetic wave showing electric field and magnetic field H components, and the wavelength 𝛿 .. The spectrum of electromagnetic radiation, including wavelength ranges for the various colors in the visible spectrum.. Visible light lies within a very narrow region of the spectrum, with wavelengths ranging between about 0.4. 𝜇𝑚(. − m) and 0.7. 4 x 10. 𝜇𝑚. The perceived color is determined by wavelength; for. example, radiation having a wavelength of approximately 0.4 appears violet, whereas green and red occur at about 0.5 and 0.65. 𝜇𝑚. respectively. The spectral ranges for the several colors are. included in figure 2.13. White light is simply a mixture of all colors. The ensuing discussion is concerned primarily with this visible radiation, by definition the only radiation to which the eye.

(47) Chapter 1. Materials properties. 20. is sensitive. All electromagnetic radiation traverses a vacuum at the same velocity, that of light—namely, 3. m/s (186,000 miles/s). This velocity. x 10. 𝜖. 𝑐. is related to the electric permittivity of a vacuum. and the magnetic permeability of a vacuum. 𝑐. 𝜇 √. through. 𝜖 𝜇. (2.3). Thus, there is an association between the electromagnetic constant c and these electrical and magnetic constants.. Furthermore, the frequency and the wavelength of the electromagnetic. radiation are a function of velocity according to. 𝑐. 𝜆𝜈. (2.4). Frequency is expressed in terms of hertz (Hz), and 1 Hz=1 cycle per second. Ranges of frequency for the various forms of electromagnetic radiation are also included in the spectrum (figure 2.13). Sometimes it is more convenient to view electromagnetic radiation from a quantum-mechanical perspective, in which the radiation rather than consisting of waves, is composed of groups or packets of energy which are called photons. The energy E of a photon is said to be quantized or can only have specific values, defined by the relationship. 𝐸. where. ℎ. ℎ𝜈. ℎ 𝑐𝜆. (2.5). is a universal constant called Planck’s constant, which has a value of 6.63 x 10. −

(48). 𝐽.𝑠.. Thus, photon energy is proportional to the frequency of the radiation, or inversely proportional to the wavelength. Photon energies are also included in the electromagnetic spectrum (figure 2.13).. 2.2.1.2 Light interactions with solids When light proceeds from one medium into another (e.g., from air into a solid substance), several things happen. Some of the light radiation may be transmitted through the medium, some will be absorbed and some will be reflected at the interface between the two media. The intensity of the beam incident to the surface of the solid medium must equal the sum of the intensities of the transmitted, absorbed and reflected beams, denoted as. 𝐼. 𝐼𝑇 𝐼𝐴 𝐼𝑅. 𝐼𝑇 , 𝐼𝐴. and. 𝐼𝑅. respectively, or. (2.6).

(49) Chapter 1. Materials properties. 21. Radiation intensity, expressed in watts per square meter, corresponds to the energy being trans-. Figure 2.14:. Light interactions with solids.. mitted per unit of time across a unit area that is perpendicular to the direction of propagation. An alternate form of equation 2.6 is. 𝑇 𝐴𝑅. (2.7). where T, A and R represent, respectively, the transmissivity (𝐼𝑇 /𝐼 ), absorptivity (𝐼𝐴 /𝐼 ) and reflectivity (𝐼𝑅 /𝐼 ) or the fractions of incident light that are transmitted, absorbed, and reflected by a material; their sum must equal unity, since all the incident light is either transmitted, absorbed, or reflected. Materials that are capable of transmitting light with relatively little absorption and reflection are transparent-one can see through them. Translucent materials are those through which light is transmitted diffusely; that is, light is scattered within the interior, to the degree that objects are not clearly distinguishable when viewed through a specimen of the material. Materials that are impervious to the transmission of visible light are termed opaque. Bulk metals are opaque throughout the entire visible spectrum; that is, all light radiation is either absorbed or reflected. On the other hand, electrically insulating materials can be made to be transparent. Furthermore, some semiconducting materials are transparent whereas others are opaque.. 2.2.1.3 Atomic and electronic interactions The optical phenomena that occur within solid materials involve interactions between the electromagnetic radiation and atoms, ions and/or electrons. The absorption and emission of electromagnetic radiation may involve electron transitions from one energy state to another.. For the sake of this discussion, consider an isolated atom, the. electron energy diagram for which is represented in figure 2.15. An electron may be excited from.

(50) Chapter 1. Materials properties. 22. an occupied state at energy to a vacant and higher-lying one, denoted by the absorption of a photon of energy. The change in energy experienced by the electron, depends on the radiation frequency as follows:. 𝐸 where, again,. ℎ. ℎ𝜈. (2.8). is Planck’s constant.. For an isolated atom, a schematic illustration of photon absorption by the excitation of an electron from one energy state to another. The energy of the photon ℎ𝜈

(51) must be exactly equal to the difference in energy between the two states (E

(52) -E ). Figure 2.15:. At this point it is important that several concepts be understood. states for the atom are discrete, only specific. 𝐸 ’s. First, since the energy. exist between the energy levels. Thus, only. photons of frequencies corresponding to the possible. 𝐸 ’s. for the atom can be absorbed by. electron transitions. Furthermore, all of a photon’s energy is absorbed in each excitation event. A second important concept is that a stimulated electron cannot remain in an excited state indefinitely. After a short time, it falls or decays back into its ground state or unexcited level with a reemission of electromagnetic radiation.. In any case, there must be a conservation of. energy for absorption and emission electron transitions.. 2.2.2. Optical properties of metals. Metals are opaque because the incident radiation having frequencies within the visible range excites electrons into unoccupied energy states above the Fermi energy, as demonstrated in figure 2.16 (b); as a consequence, the incident radiation is absorbed in accordance with equation 2.8.. All frequencies of visible light are absorbed by metals because of the continuously. available empty electron states, which permit electron transitions as in figure 2.16 (a)..

(53) Chapter 1. Materials properties. 23. (a) Schematic representation of the mechanism of photon absorption for metallic materials in which an electron is excited into a higher-energy unoccupied state. The change in energy of the electron 𝐸 is equal to the energy of the photon. (b) Reemission of a photon of light by the direct transition of an electron from a high to a low energy state. Figure 2.16:. In fact, metals are opaque to all electromagnetic radiation on the low end of the frequency spectrum from radio waves through infrared, the visible, and into about the middle of the ultraviolet radiation. Metals are transparent to high-frequency (x- and. 𝛾. ray) radiation.. Most of the absorbed radiation is reemitted from the surface in the form of visible light of the same wavelength which appears as reflected light; an electron transition accompanying reradiation is shown in figure 2.16 (b). The reflectivity for most metals is between 0.90 and 0.95; some small fraction of the energy from electron decay processes is dissipated as heat. Since metals are opaque and highly reflective, the perceived color is determined by the wavelength distribution of the radiation that is reflected and not absorbed. A bright silvery appearance when exposed to white light indicates that the metal is highly reflective over the entire range of the visible spectrum. In other words, for the reflected beam, the composition of these reemitted photons in terms of frequency and number, is approximately the same as for the incident beam.. 2.2.3. Optical properties of nonmetals. By virtue of their electron energy band structures, nonmetallic materials may be transparent to visible light. Therefore, in addition the refraction, reflection, absorption and transmission phenomena also need to be considered.. 2.2.3.1 Refraction Light that is transmitted into the interior of transparent materials experiences a decrease in velocity, and, as a result, is bent at the interface; this phenomenon is termed refraction. The.