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Vysoké Učení Technické V Brně Brno University of Technology VYSOKÉ UČENÍ TECHNICKÉ V BRNĚ BRNO UNIVERSITY OF TECHNOLOGY FAKULTA ELEKTROTECHNIKY A KOMUNIKAČNÍCH TECHNOLOGIÍ ÚSTAV FYZIKY FACULTY OF ELECTRICAL ENGINEERING AND COMMUNICATION DEPARTMENT OF PHYSICS DIELEKTRICKÉ VLASTNOSTI TENKÝCH VRSTEV OXIDŮ TANTALU A NIOBU DIELECTRIC PROPERTIES OF THIN TANTALUM AND NIOBIUM OXIDE LAYERS DOKTORSKÁ PRÁCE DOCTORAL THESIS AUTOR PRÁCE INES FAISEL ABUETWIRAT, BSc, MSc AUTHOR VEDOUCÍ PRÁCE doc. Ing. KAREL LIEDERMANN, CSc. SUPERVISOR BRNO 2014 Abstract Dielectric relaxation spectroscopy is one of the useful methods in studying the molecu- lar dynamics of materials. Owing to recent developments in instrumentation and advances in measurement technique, it is possible to obtain the dispersion of dielectric permittivity in a wide frequency range and for very different materials. The purpose of my work was to investigate dielectric relaxation spectra and conductiv- ity of oxides of titanium, niobium, tantalum, lanthanum and hafnium for field emission cathodes. The objective of the research was to analyze the frequency and temperature behaviour of these oxides, as well as their conductivity over a wide frequency and tem- perature range, and to attempt to determine the origin of the relaxation. As the original range of oxides has been very broad, focus was paid to tantalum (Ta) and niobium (Nb) oxides only, also with regard to their application in electrolytic capacitors. Electrical, thermal and mechanical (processing) properties of Ta and Nb oxides have already been well established. Little is known, however, about detailed mechanisms of their dielectric relaxation. The results acquired for Ta2O5 show a relaxation peak in the temperature and frequency range available, 187 K – 385 K, 1 Hz – 10 MHz. The loss peak frequency follows the Arrhenius law dependence with the activation energy of 0.048 eV. In conductivity spectra, Ta2O5 film exhibits a steady – state value at low frequencies and a monotonous increase at high frequencies depends on temperature. The observed conductivity fol- lowed a slightly superlinear power law. The results acquired for Nb2O5 show a relaxa- tion peak in a similar temperature and frequency range, 218 K – 373 K, 1 Hz – 1 MHz. The loss peak frequency follows the Arrhenius law dependence with the activation energy of 0.055 eV. Niobium oxide capacitor shows conductivity mechanism similar to tantalum capacitor. Abstract Dielektrická relaxační spektroskopie je jednou z uţitečných metod pro studium mole- kulární dynamiky materiálů. Díky nedávnému pokroku v přístrojové a měřicí technice je dnes moţné získat dielektrické spektrum v širokém frekvenčním intervalu a pro ve- lice rozdílné materiály. Cílem mé práce bylo studium dielektrických relaxačních spekter a vodivosti oxidů titanu, niobu, tantalu, lanthanu a hafnia pro katody pracující na principu studené emise. Cílem výzkumu bylo analyzovat frekvenční a teplotní chování těchto oxidů, včetně jejich vodivosti, v širokém frekvenčním a teplotním rozsahu, a pokusit se stanovit původ relaxačního mechanismu. Vzhledem k tomu, ţe původně zadaný rozsah oxidů byl dosti široký, soustředila se pozornost pouze na oxidy tantalu a niobu, rovněţ s ohle- dem na jejich aplikace v elektrolytických kondenzátorech. Elektrické, tepelné a mechanické (při zpracování) vlastnosti oxidů tantalu a niobu jsou dnes jiţ dobře prozkoumány. K dispozici je však jen málo poznatků o jejich dielektric- kých relaxačních mechanismech. Výsledky získané pro Ta2O5 ukazují existence relaxačního maxima, nacházejícího se v experimentálně dostupném teplotním a frekvenčním intervalu 187 K – 385 K a 1 Hz aţ 10 MHz. Frekvence ztrátového maxima se řídí Arrheniovým zákonem s aktivační energií 0.048 eV. Ve vodivostních spektrech vykazují tenké vrstvy Ta2O5 na nízkých frekvencích ustálenou hodnotu a při vysokých frekvencích monotónní nárůst, který závisí na teplotě. Pozorovanou vodivost lze popsat mocninnou funkcí s exponentem nepatrně větším neţ jedna (tzv. superlineární závislost. Výsledky získané pro Nb2O5 v podobné teplotní a frekvenční oblasti, 218 K – 373 K, 1 Hz – 1 MHz rovněţ ukazují jedno relaxační maximum. Frekvence ztrátového maxima se opět řídí Arrheniovým zákonem s poněkud vyšší aktivační energií 0.055 eV. Niobové kondenzátory vykazují vodivostní mechanismus shodný s kondenzátory tantalovými. Keywords Dielectric spectroscopy, dielectric relaxation, dielectric spectra, electrical conductivity, tantalum oxide, niobium oxide. Klíčová slova Dielektrická spektroskopie, dielektrická relaxace, dielektrická spektra, elektrická vodivost, oxid tantalu, oxid niobu. Abuetwirat, I. F. Dielectric properties of thin tantalum and niobium oxide layer. Brno: Vysoké učení technické v Brně, Fakulta elektrotechniky a komunikačních technologií, 2014, 104 s., Research Advisor: Karel Liedermann, PhD, MEng, Assoc. Prof. Obligatory statutory declaration I declare that I have written my doctoral thesis “Dielectric relaxation properties of thin tantalum and niobium oxide layer” independently, under the guidance of the doctoral thesis supervisor and using the technical literature and other sources of information which are all quoted in the thesis and detailed in the list of literature at the end of the thesis. As the author of the doctoral thesis, I furthermore declare that, as regards the creation of this doctoral thesis, I have not infringed any copyright. In particular, I have not unlawfully encroached on anyone‟s personal and/or ownership rights and I am fully aware of the consequences in the case of breaking Regulation §11 and the following of the Copyright Act No. 121/2000 Coll., and of the rights related to intellectual property right and changes in some Acts (Intellectual Property Act) and formulated in later regulations, inclusive of the possible consequences resulting from the provisions of Criminal Act No. 40/2009 Coll., Section 2, Head VI, Part 4. Brno, November 2014 Ines Faisel Abuetwirat Acknowledgments I would like to thank my advisor, Doc. Ing. Karel Liedermann, CSc. for his help and guidance in completing my research and thesis. I would also like to express my special thanks to Prof. Peter Lunkenheimer of the University of Augsburg, Germany for dielectric relaxation measurements. I would like to thank all my colleagues at Department of Physics for the friendly environment, and for their help, when I needed it most. In particular, I would like to express my deepest thanks to Dr. Tomas Palai-Dany and Dr. Vladimír Holcman. I would like to thank my family for their love, support and encouragement. Finally, I would like to thank my beloved husband, Usama Alshbeni, for everything. Brno, November 2014 Inas Faisel Abuetwirat Dielectric relaxation properties of thin tantalum and niobium oxide layer Contents 1 Background ........................................................................................................... 16 2 Material under study ............................................................................................ 18 2.1 Tantalum (Ta) ................................................................................................... 18 2.2 Niobium (Nb) ................................................................................................... 19 3 Theoretical Foundations ....................................................................................... 21 3.1 Dielectric relaxation spectroscopy – state of the art ........................................ 21 3.1.1 Polarization ........................................................................................... 21 3.1.2 Polarization mechanism ....................................................................... 23 3.1.3 Classification of dielectric materials .................................................... 27 3.1.4 Variation of the dielectric constant in alternating fields ...................... 27 3.1.5 Impedance dielectric spectroscopy ....................................................... 28 3.1.6 Dielectric spectroscopy ........................................................................ 30 3.1.7 Single relaxation time model: the Debye equation .............................. 31 3.1.8 The analysis of dielectric data in terms of relaxation time (frequency) ........................................................................................... 33 3.1.9 The relation between dielectric relaxation and chemical structure ...... 35 3.1.10 Temperature dependence ...................................................................... 36 3.1.11 Time domain dielectric spectroscopy charging /discharging currents and Hamon approximation ..................................................... 38 3.2 Conduction mechanisms .................................................................................. 41 3.2.1 Bulk-limited conduction ....................................................................... 41 3.2.2 Electrode limited process ..................................................................... 43 3.3 Electrolytic capacitor ....................................................................................... 46 3.3.1 Parallel Plate Capacitor ........................................................................ 46 3.3.2 Basic features of electrolytic capacitors ............................................... 46 3.3.3 Construction of tantalum oxide capacitor ............................................ 47 3.3.4 Stability of tantalum oxide capacitor .................................................... 50 3.3.5 Electrical performance ........................................................................
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