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Molecular beam epitaxy of magnetic oxynitride films : construction of a combined growth/analysis system,.. 2012

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Molecular Beam Epitaxy of Magnetic Oxynitride Films Construction of a combined growth/analysis system, development of experimental tools and investigation of two oxynitride systems by Ryan Christopher Wicks B.Sc.H., Queen’s University, 2005 M.Sc., The University of British Columbia, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in The Faculty of Graduate Studies (Physics) The University Of British Columbia (Vancouver) October 2012 © Ryan Christopher Wicks 2012 Abstract The overarching theme of this thesis is the growth and characterization of thin fer- romagnetic oxide films. This is a very broad project, and as a result, this thesis covers a variety of related topics. These include technical aspects, like the design and commissioning of a combined film growth and analysis system (Chapter 2), the devel- opment of an algorithm to build up surface diffraction patterns from single-reflection high-energy electron diffraction images (Chapter 3) and a chapter detailing methods to measure and correct for various non-linearities in the response of electron analyzers used in photo-electron spectroscopy (Chapter 4). An intermediate chapter (Chapter 5) deals with theoretical calculations to determine the effect of substituting pnictogens (nitrogen, phosphorous and arsenic, specifically) for oxygen in EuO. In particular, it is determined which systems are most likely to synthesize without phase separating and how the system reacts to the addition of acceptor sites from the pnictogen. This information motivates the experimental work in Chapter 6 on nitrogen-substituted EuO, which uses a novel growth technique to produce the first example of a mixed valent europium system. Both the development of a novel growth technique and the study of a new type of ferromagnetic semiconductor are important first steps in building future spintronic devices. The final chapter (Chapter 7) details attempts to grow nitrogen-substituted SrO in an attempt to induce ferromagnetic ordering in a normally non-magnetic oxide by spin polarizing the p-states. The results in this last chapter demonstrate that p-state derived magnetism is present in SrO1-xNx. ii Preface Statement of Relative Contributions The design and construction of an MBE chamber and associated XPS analysis cham- ber is discussed in Chapter 2. The MBE chamber was designed by Luc Vanema and Doug Wong, and initially assembled by Doug Wong. I completed assembly of the MBE chamber with Mr. Wong’s assistance. I designed the XPS analysis chamber, with input from Dr. Andrea Damascelli, Mr. Wong and Harold Davis. I assembled the XPS analysis chamber myself, with assistance from Mr. Wong and members of the Quantum Materials Group at UBC. I performed the initial commissioning of both chambers. The cryostat design was initiated by me and has been continued by Riccardo Comin and Pinder Dosanjh. The sample holder was designed by Dr. David Hawthorn, based on a design by Omicron Nanotechnology GmbH. These results have not been published elsewhere. Chapter 3 is part of a larger review paper by Dr. Nicholas Ingle [1], and represents the portion of the work with which I was involved. Specifically, I acquired and analyzed most of the data on RHEED reconstruction and assisted Alex Yuskauskas and Simon Leung with the code and algorithm development. I also assisted Dr. Ingle and Dr. Markus Paul with the manuscript preparation. A version of Chapter 4 has been published in the Review of Scientific Instruments [2]. This work was conducted in the Quantum Materials Group at UBC under the supervision and with the assistance of Dr. Ingle and Dr. Damascelli, and was a significant expansion of work I began during my master’s thesis. I designed the experiment, took the data, analyzed it and prepared the manuscript. The calculations presented in Chapter 5 were performed by myself, with assistance from Dr. Ilya Elfimov and Jason Zhu. The calculations were performed on the UBC dftlap cluster, maintained by Dr. Elfimov, and used the WIEN2k software package [3]. These results have not been published elsewhere. iii Publications Arising from Thesis Work The work presented in Chapter 6 was performed at the University of Cologne in the group of Dr. Liu Hao Tjeng. With assistance from Dr. Simone Altendorf, Dr. Ronny Sutarto, Dr. Damascelli and Dr. Tjeng I grew the films, performed the experiments, analyzed the data and prepared the manuscript. This chapter is a version of a paper published in the journal Applied Physics Letters [4]. I performed all of the work presented in the final chapter on the growth of SrO1−xNx. This work was carried out at UBC, and has not been published elsewhere. Publications Arising from Thesis Work This thesis work has produced the following publications: Chapter 3: N.J.C. Ingle, A. Yuskauskas, R. Wicks, M. Paul, and S. Leung. The structural anal- ysis possibilities of reflection high energy electron diffraction. Journal of Physics D: Applied Physics, 43:133001, 2010. Chapter 4: R.C. Wicks and N.J.C. Ingle. Characterizing the detection system non-linearity, in- ternal inelastic background, and transmission function of an electron spectrometer for use in x-ray photoelectron spectroscopy. Review of Scientific Instruments, 80:053108, 2009. Chapter 6: R. Wicks, S.G. Altendorf, C. Caspers, R. Sutarto, L.H. Tjeng, and A. Damascelli. NO-assisted molecular-beam epitaxial growth of nitrogen substituted EuO. Applied Physics Letters, 100:162405, 2012. S.G. Altendorf, N. Hollmann, R. Sutarto, C. Caspers, R.C. Wicks, Y.- Y. Chin, Z. Hu, H. Kierspel, I.S. Elfimov, H.H. Hsieh, H.-J. Lin, C.T. Chen, and L.H. Tjeng. Spectroscopic observation of strain-assisted Tc enhancement in EuO upon Gd doping. Physical Review B, 85:081201, 2012. iv Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Condensed Matter Systems and Magnetism . . . . . . . . . . . . . . 1 1.1.1 Exchange Interactions and Models of Magnetism . . . . . . . 3 1.1.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . 7 1.2 EuO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 Historical Development of EuO . . . . . . . . . . . . . . . . . 11 1.2.2 Modern Perspectives on EuO . . . . . . . . . . . . . . . . . . 12 1.3 Ligand Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 X-ray Photoelectron Spectroscopy . . . . . . . . . . . . . . . . . . . 21 2 Design and Construction of a Combined MBE Film Growth and Analysis System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Shared Design Elements . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 v Table of Contents 2.3.1 Sample Holders . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.2 Sample Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4 MBE Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.1 RHEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4.2 LEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4.3 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4.4 Future Improvements . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Analysis Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5.1 Chamber Design . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.5.2 Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5.3 X-ray Source . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5.4 Electron Gun . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5.5 Description of Cryostat and In Situ Transport Measurements 38 2.5.6 Future Improvements . . . . . . . . . . . . . . . . . . . . . . 43 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3 The Structural Analysis Possibilities of RHEED . . . . . . . . . . 45 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1.1 RHEED as an In Situ Growth Monitoring Tool . . . . . . . . 49 3.2 RHEED as a Surface Symmetry Tool . . . . . . . . . . . . . . . . . . 51 3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Characterization of an Electron Spectrometer . . . . . . . . . . . . 57 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.4 Internal Analyzer Inelastic Scattering . . . . . . . . . . . . . . . . . 63 4.5 Transmission Function . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5 Calculated Electronic Structure of the Europium Pnictide Family 73 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 vi Table of Contents 6 Absorbate-Controlled Nitrogen Substitution in EuO Thin Films 82 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.2 Growth of EuO1-xNx . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.3 Electronic Structure and Magnetic Properties of EuO1-xNx . . . . . . 89 6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7 The Growth of Magnetic SrO1-xNx . . . . . . . . . . . . . . . . . . . 92 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 7.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.3 Growth on YSZ and MgO . . . . . . . . . . . . . . . . . . . . . . . . 94 7.4 Magnetism in SrO1-xNx . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Appendix Cryostat Thermal Calculations Worksheet . . . . . . . . . . . . . . . . 125 vii List of Tables 5.1 The different ground state energies for the substituted and phase sep- arated options for EuO with 3.125% of the oxygen replaced with ni- trogen, phosphorous, and arsenic . . . . . . . . . . . . . . . . . . . . 78 viii List of Figures 1.1 A plot of various magnetization curves from the Weiss model . . . . . 8 1.2 A decision tree outlining the Kohn-Sham algorithm . . . . . . . . . . 10 1.3 The thermodynamic phase diagram for europium as a function of tem- perature and oxygen concentration . . . . . . . . . . . . . . . . . . . 13 1.4 A schematic of a MBE . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.5 Rocking curve of the (002) diffraction peak Ca1-xSrxCuO2 sample . . 19 1.6 Diagram showing the photoemission process . . . . . . . . . . . . . . 22 2.1 An image of the constructed MBE/analysis system . . . . . . . . . . 25 2.2 Model of sample holder . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3 Model of actuator grabbing sample holder . . . . . . . . . . . . . . . 29 2.4 Schematic layout of the MBE and analysis chamber and transfer routes 30 2.5 Representative RHEED data taken with this system . . . . . . . . . . 32 2.6 Representative LEED data taken with this system . . . . . . . . . . . 33 2.7 Representative XPS spectra of a SrO1-xNx sample . . . . . . . . . . . 37 2.8 Models of various parts of the cryostat . . . . . . . . . . . . . . . . . 40 2.9 Thermal model of the cryostat . . . . . . . . . . . . . . . . . . . . . . 42 3.1 RHEED geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 Example RHEED image . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.3 A RHEED diffraction pattern as a function of time . . . . . . . . . . 50 3.4 A RHEED diffraction pattern as a function of time . . . . . . . . . . 52 3.5 RHEED images from a quasi-3D EuO film on LaAlO3 . . . . . . . . . 53 3.6 Azimuthal scan of a GaAs β(2× 4) reconstructed surface . . . . . . . 54 3.7 Several reciprocal lattice visualization from RHEED data . . . . . . . 56 4.1 A diagram of the experimental setup of an XPS measurement . . . . 60 4.2 Measurements of detector non-linearity . . . . . . . . . . . . . . . . . 62 ix List of Figures 4.3 Raw transmission function data taken with an electron gun . . . . . . 65 4.4 Intermediate transmission function data . . . . . . . . . . . . . . . . 67 4.5 Experimentally determined transmission function at 90, 60 and 30 eV pass energies for medium area mode . . . . . . . . . . . . . . . . . . . 69 4.6 Transmission functions determined for the medium area mode with different electron spot sizes and iris settings . . . . . . . . . . . . . . 69 4.7 Corrected XPS spectra measured on a Au sample for different analyzer configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.1 Spin-resolved DOS for EuO . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 EuO super-cell structure . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3 DOS for EuO with 3.125% pnictogen substitution for oxygen . . . . . 76 5.4 Spatial distribution of above Ef hole density in EuO1-xNx . . . . . . . 80 5.5 Radial distribution of above Ef hole density in EuO1-xNx around the central N site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.1 Increase in nitrogen concentration in the EuO1-xNx films as a function of NO partial pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.2 RHEED spot intensity oscillations for 2− 3% and 16% nitrogen con- centration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3 Valence band XPS spectra of EuO1-xNx as a function of nitrogen con- centration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.4 Magnetization curves for two different EuO1-xNx samples at 10 Gauss 89 7.1 RHEED time series of SrO1-xNx films grown on different substrates. 96 7.2 XPS of the SrO1-xNx films . . . . . . . . . . . . . . . . . . . . . . . . 98 7.3 Detailed XPS spectrum of the nitrogen 1s peak showing a multiplet splitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.4 SQUID magnetization measurements of two SrO1-xNx films grown on MgO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 x List of Abbreviations ARPES - Angle Resolved Photo-Emission Spectroscopy CAE - Constant Analyzer Energy (also FAT) CCD - Charge Coupled Detector CF - Con-Flat® CLS - Canadian Light Source CRR - Constant Retard Ratio (also FRR) CTR - Crystal Truncation Rod CVD - Chemical Vapour Deposition DFT - Density Functional Theory EELS - Electron Energy Loss Spectroscopy Ef - Fermi Level e-beam - electron-beam FAT - Fixed Analyzer Transmission FRR - Fixed Retard Ratio GGA - Generalized Gradient Approximation J - Exchange Parameter or Total Angular Momentum LEED - Low-Energy Electron Diffraction LSDA - Local Spin Density Approximation xi List of Abbreviations LSDA+U - Local Spin Density Approximation + Hubbard U MBE - Molecular Beam Epitaxy MCP - Multi-Channel Plate MIT - Metal-Insulator Transition NSSRC - National Synchrotron Science Research Center OFHC - Oxygen-Free High-Conductivity PLD - Pulsed Laser Deposition PVD - Physical Vapour Deposition QCM - Quartz Crystal Microbalance QMSC - Quantum Materials Spectroscopy Center REIXS - Resonant Inelastic X-ray Scattering RHEED - Reflection High-Energy Electron Diffraction RKKY - Ruderman-Kittel-Kasuya-Yosida STM - Scanning Tunnelling Microscopy SWR - Surface-Wave Resonance Tc - Curie Temperature TEM - Transmission Electron Microscopy TF - Transmission Function TMO - Transition Metal Oxide UBC - University of British Columbia UHV - Ultra High Vacuum YSZ - Yttrium Stabilized Zirconate xii List of Abbreviations XAS - X-ray Absorption Spectroscopy XPS - X-ray Photoelectron Spectroscopy XRR - X-ray Reflectivity xiii Acknowledgements A Ph.D. thesis is a huge undertaking, and I wouldn’t have been able to make it through without assistance from many different sources. First and foremost, I’d like to thank Dr. Andrea Damascelli for supporting me through a somewhat tumultuous Ph.D. When Dr. Ingle left the group, Andrea allowed me to continue on the same research project, despite not having much experience with MBE growth. He even went so far as to send me to Germany to work with Dr. Tjeng’s group, and found the resources to allow me to build my own equipment. I appreciate all the feedback and assistance he has given me over the years. There are many present and former members of the Quantum Materials Group whom I should mention. Dr. Ilya Elfimov and Dr. George Sawatzky have been invaluable sources of information, and I thank them for taking time to talk me through scientific problems I’ve had. Dr. Nicholas Ingle taught me most of what I know about MBE growth and vacuum science. I appreciate the advice he offered me, even if I didn’t always follow it. I’d also like to mention other members of the group who have helped me out over the years: Dr. Jeff Mottershead, Christian Veenstra, Dr. David Fournier, Dr. Giorgio Levy, Dr. Thomas Roth, Riccardo Comin, Jason Zhu, Jonathan Rosen, Dr. Suman Hossain and Bart Ludbrook. Others at UBC whom I’d like to mention are Doug Wong, who is always willing to answer my technical questions and give me a hand, and Pinder Dosanj, for helping me out with the SQUID and anything cryogenic. My committee members also deserve to be mentioned for taking the time to help guide me through my Ph.D. and for reading this for me: Dr. Rob Kiefl, Dr. Fei Zhu and Dr. Mark Halpern. My time working in the group of Dr. Hao Tjeng was very rewarding and gave me the experience I needed to complete my Ph.D. Specifically, I’d like to thank Dr. Tjeng for allowing me to visit his group, for his many valuable insights and for providing a direction for the EuO1-xNx work when I was completely stuck. I’d also like to thank the people I worked with directly while in Cologne: Dr. Simone Altendorf, Dr. Ronny Sutarto, Christian Caspers and Lucie Hamdam. xiv Acknowledgements Finally, I’d like to thank my wife, Marja, and my children, Evan and Tessa, for being awesome. xv Chapter 1 Introduction The work in this thesis focuses on the growth and study of magnetic oxide thin films. Achieving this goal requires the use of several complicated experimental techniques, mastery of a difficult sample preparation technique and a deep understanding of the materials under study through complex theoretical calculations. As a result, only a portion of this thesis deals directly with the materials. The first half focuses entirely on technical aspects: designing a combined molecular beam epitaxy (MBE) growth/analysis system and improving the tools used to characterize films grown by MBE. The materials science begins in the second part of the thesis with a theoretical study of pnictide-doped EuO, and continues with the growth and study of one of these system, EuO1-xNx. The thesis concludes with a growth study of a system that is predicted to exhibit ligand magnetism, thin film SrO1-xNx. The goal of this introduction is to give a non-specialist reader enough information to understand the material presented in the later chapters. Section 1.1 summarizes aspects of the physics of condensed matter systems and their relationship to mag- netism, and introduces a computational method for calculating material properties. Section 1.2 provides an overview of the properties of the material EuO by outlining its historical development and discussing its contemporary significance. Section 1.3 introduces the concept of ligand magnetism, which is important for understanding the signifigance of N-doped SrO. Section 1.4 introduces the technique of MBE and of physical vapour deposition (PVD) in general. Finally, Section 1.5 provides a quick overview of X-ray photoelectron spectroscopy (XPS). 1.1 Condensed Matter Systems and Magnetism It is straightforward to write down a Hamiltonian that describes any solid system consisting of N heavy, positively charged nuclei and many lighter positively charged electrons. This is called the quantum many-body Hamiltonian [5]: 1 1.1. Condensed Matter Systems and Magnetism Ĥ = − h̄ 2 2 ∑ i ∇2−→ Ri Mi − h̄ 2 2 ∑ i ∇2−→ri me − 1 4pi0 ∑ i,j e2Zi |−→Ri −−→rj | + 1 8pi0 ∑ i 6=j e2 |−→ri −−→rj | + 1 8pi0 ∑ i 6=j e2ZiZj |−→Ri −−→Rj| (1.1) where the atomic positions, atomic masses, electron positions, electron masses and number of electrons per atom are given by Ri, Mi, ri, mi and Zi, respectively. The first two terms describe the non-relativistic kinetic energy of the nucleus and the electrons, while the last three terms describe the intra-atomic Coulomb energy, the electron- electron Coulomb energy and the nuclei-nuclei Coulomb energy. For a macroscopic solid, Equation 1.1 represents approximately 1023 coupled terms, and as such, the problem is completely intractable without making some very aggressive assumptions. The first assumption normally made is called the Born-Oppenheimer approxima- tion. This approximation assumes that because the mass of the nucleus is much larger than the mass of the electron, the nucleus can be considered fixed in position. As a result, the nuclei-nuclei interaction becomes a constant, the kinetic energy of the nucleus disappears and the intra-atomic Coulomb reaction can be re-written as an electron interacting with a material-dependent static field. Equation 1.1 becomes: Ĥ = − h̄ 2 2 ∑ i ∇2−→ri me + 1 8pi0 ∑ i 6=j e2 |−→ri −−→rj | + V̂ext (1.2) Ĥ = T̂ + V̂ + V̂ext (1.3) where T̂ is the electron kinetic energy, V̂ is the electron-electron interaction and V̂ext is the potential energy of the electrons in the external field of the nucleus. This equation is universal, and applicable in most situations.1 While the problem has now been greatly simplified, it is still too difficult to solve exactly, since we are still dealing with many coupled terms due to the electron-electron interaction. There are several different ways this problem can be approached. In some sys- 1Conventional superconductivity is one area where the Born-Oppenheimer approximation is too aggressive. The lattice must be allowed to relax to produce the polarons needed to produce Cooper pairs [6]. Likewise, phonons are neglected in the Born-Oppenheimer approximation. 2 1.1. Condensed Matter Systems and Magnetism tems, it is acceptable to simply ignore the electron-electron correlations, or deal with them in a mean-field way and reduce the problem to a relatively simple single elec- tron problem (this is the basis for the tight binding model, Hartree-Fock method and Local Density Approximation (LDA)). However, since in this thesis we are con- cerned with studying magnetic systems, we must include at least some aspect of the electron-electron correlation because, as will be shown later, these correlations are fundamental to producing magnetic ordering. One method of understanding Equa- tion 1.3 is to develop phenomenological model systems that attempt to capture the most relevant aspects of the electron-electron interaction and study them. For in- stance, in the study of magnetic systems, models like the Heisenberg model and the Weiss model build on the concept of exchange and electronic correlation to explain magnetic ordering. Another method for understanding Equation 1.3 that is especially useful for performing practical calculations of material properties on real systems is that of Density Functional Theory (DFT), with approximations derived in the phe- nomenological magnetic models, specifically, the local spin density approximation (LSDA) or LSDA plus Hubbard U (LSDA+U). In the next sub-section, I will briefly discuss exchange and how it is incorporated into various models of magnetic ordering. I will then discuss the basics of DFT and LDA, and how DFT can be extended through LSDA and LSDA+U to study real magnetic systems, so that practical theoretical calculations can be performed. 1.1.1 Exchange Interactions and Models of Magnetism The exchange interaction is a purely quantum mechanical effect that arises from the requirement that the combined wave function of identical fermions must be anti- symmetric under the exchange of any two particles [7, 8]. This effect is most clearly demonstrated in a two-particle system (this derivation loosely follows that found in Blundell, Reference 9). To satisfy the requirements of overall anti-symmetric ex- change, the spatial part of the wave function of a two-particle system that is symmet- ric under exchange of the two particles must have a spin part that is anti-symmetric, or a singlet. Likewise, if the spatial part of the wavefunction is anti-symmetric, then the spin part must be symmetric, or a triplet. The combined wave functions for these states in terms of the single-particle wave functions are given in Equations 1.4 and 1.5: 3 1.1. Condensed Matter Systems and Magnetism |ΨS〉 = 1√ 2 (|ψa(−→r1 )〉 |ψb(−→r2 )〉+ |ψa(−→r2 )〉 |ψb(−→r1 )〉) |χS〉 (1.4) |ΨT 〉 = 1√ 2 (|ψa(−→r1 )〉 |ψb(−→r2 )〉− |ψa(−→r2 )〉 |ψb(−→r1 )〉) |χT 〉 (1.5) where |Ψ〉 is the combined two-particle wave function that satisfies the anti-symmetry requirement for fermions, a and b denote different particles, −→r1 and −→r2 are two position vectors, |ψa(−→r )〉 and |ψb(−→r )〉 are the single-particle wave functions, χ is the spin part of the wave function and T and S correspond to a triplet or a singlet, respectively. The energies for the singlet ground state and triplet ground state, and the energy difference between them are then given by: ES = 〈ΨS | Ĥ |ΨS〉 (1.6) ET = 〈ΨT | Ĥ |ΨT 〉 (1.7) ES − ET = 2 ( 〈ψa(−→r1 ) | 〈ψb(−→r2 ) | Ĥ |ψa(−→r2 )〉 |ψb(−→r1 )〉 ) (1.8) For a two-particle system, the spin part of the Hamiltonian can be written as: Ĥspin = −2(ES − ET )−→S1 · −→S2 = − ( 〈ψa(−→r1 ) | 〈ψb(−→r2 ) | Ĥ |ψa(−→r2 )〉 |ψb(−→r1 )〉 ) −→ S1 · −→S2 = −J −→S1 · −→S2 (1.9) where J is called the exchange integral. If J is positive, then ET is greater than ES, and the triplet state is preferred. If J is negative, then the singlet state is lowest in energy. For this model of two electrons on the same site/nuclei, it can be shown that the triplet state is always lowest in energy, as long as the single particle states are degenerate [10]. This is due to the high Coulomb energy cost associated with forming the singlet state; two electrons in the same state (the symmetric combination) have much more overlap of their electronic densities than two electrons in different states (in an anti-symmetric combination). The larger overlap in electronic densities in the spatially symmetric singlet state leads to a large Coulomb repulsion that raises the 4 1.1. Condensed Matter Systems and Magnetism overall energy of this configuration relative to triplet configurations. The Heisenberg Model The model discussed above is only valid for two electrons on a single site. However, a similar model can be developed that deals with electrons on neighbouring sites in a crystal lattice. This is called the Heisenberg model [7]: Ĥ = − ∑ i,j Jij −→ Si · −→Sj (1.10) This double sum covers the entire lattice in the crystal, and every pair of particles has a unique Jij exchange interaction. The sign of Jij determines whether the ex- change is ferromagnetic (positive) or anti-ferromagnetic (negative). This model can be greatly simplified by assuming that the wavefunctions of the individual electrons do not extend much past their nearest neighbours, and so the exchange integral is 0 for all non-nearest neighbours. Even with this assumption, however, the problem is still complicated due to the difficulty in performing the exchange integral (see, for instance, Slater, Reference 11). It has been used to describe low lying spin wave excitations that explain the Bloch T 3 2 magnetization behaviour seen experimentally in many ferromagnetic systems [10]. Different Types of Exchange There are some general features of the on-site and nearest neighbour exchange inte- grals that hold true for many systems [9]: 1. For electrons on the same site in degenerate levels, the exchange integral is positive and the spins align. This minimizes the Coulomb energy by keeping the electrons apart, and is consistent with the previous example of two electrons on the same site. 2. For electrons on neighbouring sites, the exchange integral due is generally neg- ative, causing neighbouring spins to anti-align (align anti-ferromagnetically). This happens because wave functions on neighbouring sites prefer to form bond- ing orbitals. Since these bonding orbitals are symmetric, the spin part of the wave function must be anti-ferromagnetic to remain antisymmetric overall. 5 1.1. Condensed Matter Systems and Magnetism One limitation of the nearest neighbour Heisenberg model is that it only allows for direct exchange – exchange between two adjacent atoms with partially filled bands (item two above). However, there are many other types of exchange interactions, including superexchange (between two unfilled sites separated by a filled intermedi- ate) [12, 13], indirect/itinerant exchange (mediated by conduction electrons through the RKKY interaction [14–16]), and double exchange (important for mixed valence systems like Fe3O4 and La1-xSrxMnO3). Each of these exchange mechanisms relies on longer range interactions than just nearest neighbour. In fact, direct exchange does not play a role in many magnetic systems, since the overlap between adjacent sites is quite small in orbitals with d- and f- characteristics. Since this thesis deals primarily with ferromagnetic systems, we have to look beyond direct exchange and the nearest neighbour Heisenberg model. The Weiss Model of Ferromagnetism Another approach to understanding magnetism in condensed matter systems is to try to build models that take into account the different types of exchange in approximate ways. The classical model of a ferromagnetic material, the Weiss model of ferromag- netism [17], does this by assuming that every spin in the system feels a magnetic field derived from every other spin in the system. As more spins align, the internal field increases, which increases the overall magnetization of the system. In this section, I will demonstrate the connection between the Heisenberg and Weiss models, and point out some general features of the Weiss model. We begin by looking at the Hamiltonian for a spin in an external magnetic field: ĤB = gµB ∑ j −→ Sj · −→B (1.11) where g is the g-factor, µB is the vacuum permeability and −→ B is the magnetic field. To draw the connection between the Weiss model and the Heisenberg model, we have to reduce the Heisenberg model to the form shown in Equation 1.11. Re-arranging the Heisenberg model (Equation 1.10) gives: Ĥ = ∑ i −→ Si · ( −2 ∑ j Jij −→ Sj ) (1.12) 6 1.1. Condensed Matter Systems and Magnetism Comparing Equation 1.12 with Equation 1.11, we can see that the bracketed por- tion of Equation 1.12 can be re-written as an external field. The following definition of the external field is most useful: −−→ Bmf = −2 gµB 〈 ∑ j Jij −→ Sj〉 (1.13) where −−→ Bmf is the thermally averaged molecular field due to the rest of the system. Substituting the above into Equation 1.10 produces the Weiss model of a ferromagnet in terms of a molecular field: ĤWeiss = gµB ∑ i −→ Si · −−→Bmf (1.14) The Weiss model was developed well before the Heisenberg model, but one can see that there is a direct connection between the two. Since −−→ Bmf has not been restricted to nearest neighbours, it can incorporate a variety of different exchange interactions. However, the assumption we make is that the internal field is the same for every lattice point. This assumption reduces the problem to a paramagnetic system in a field with a strength that depends on the material’s magnetization. Following through with this solution produces magnetization curves like the ones shown in Figure 1.1. While the Weiss model effectively removes any information about the exchange mechanism beyond its general strength and assumes the exchange is the same at every lattice site, it still does a very good job of describing ferromagnetism from a phenomenological standpoint. 1.1.2 Density Functional Theory Now that we have introduced several models that have provided insight into the quantum many-body problem and electron-electron correlations, we will discuss a practical technique that builds on these results to model real systems. Specifically, this short section will briefly introduce the powerful technique of Density Functional Theory (DFT). This section is an introduction to Chapter 5 which uses the DFT formalism with LSDA+U to calculate the electronic structure of pnictide doped EuO. For a more thorough discussion of the technique, refer to References [18, 19]. Dealing with the electron-electron interaction is difficult regardless of the number 7 1.1. Condensed Matter Systems and Magnetism Figure 1.1: A plot of various magnetization curves from the Weiss model. From S. Blundell. Magnetism in Condensed Matter. Oxford Master Series in Condensed Matter Physics. Oxford University Press, England, 2001, used with permission. of particles involved (whether there are 2 or 1023 of them). However, an additional practical problem associated with solving the quantum many-body problem is working with a wave function that depends on the position of every particle in the system; it is much simpler to work with a single function of position that describes the aggregate electron density. People have been trying to find ways to work with electronic densities since the inception of quantum mechanics because they are straightforward functions of position and are also easy to probe experimentally (the first such instance was the Thomas-Fermi model [5]). A valid objection to using density approaches to solve quantum mechanics problems was that essential information about the problem might be lost in going from the full wave function to a simpler density. Hohenberg and Kohn were able to put these approaches onto a stable theoretical footing by proving that for every possible external potential Vext, there is a unique electron density that can be used to describe the ground state energy of the system. All of the information in the ground state wave function that solves the quantum many-body problem is contained in the electronic density ρo( −→r ). They were also able to prove that, assuming the functional describing the system is known, a solution to the quantum many-body problem can be found using variational principles [20]. 8 1.1. Condensed Matter Systems and Magnetism While the Hohenberg-Kohn theorems gave legitimacy to approaches based on densities, they were not useful for practical calculations of electronic structure; it is a proof of existence only. All of the difficulty associated with solving for the kinetic energy and electron-electron interaction is lumped into a general functional which is the same for every system. The system specific portion of the problem is easy to calculate, but the form of this general function is completely unknown, which makes it impossible to use the Hohenberg-Kohn results to directly solve problems. Kohn and Sham were able to reformulate the quantum many-body Hamiltonian (1.3) into a form amenable to a self-consistent solution [21]. They did this by using the concept of density functional and by breaking the Hamiltonian into a non-interacting, single particle problem with a small correlated term, called the exchange-correlation potential (Vxc). The non-interacting problem is initially solved using an appropriate single particle basis (called the Kohn-Sham orbitals). Using this basis, a new po- tential is derived that incorporates the exchange-correlation potential (Vxc) into the original potential (VH). This produces modified Kohn-Sham orbitals, and the process is repeated until the density derived from the Kohn-Sham orbitals stops changing, indicating the ground state density has been reached 2. Figure 1.2 shows a decision tree that describes the Kohn-Sham algorithm. This process is exact, assuming the exchange-correlation potential is known (which, of course, it is not). There are different choices for the exchange-correlation potential, but the most accepted are the local density approximation (LDA), local spin den- sity approximation (LSDA), generalized-gradient approximation (GGA) and hybrid orbitals. Each of these approximate potentials has its own advantages and disadvan- tages. In this thesis, we use the GGA potential. It should be noted that the choice of the Kohn-Sham orbitals is another important parameter for practical calculations. Fortunately, there are many software packages available for performing DFT calcula- tions that make these choices for you. In this thesis, we use WIEN2k [3], but many other possibilities exist. Chapter 5 uses DFT with the LSDA+U approximation to calculate the properties of doped EuO thin films. In the next section, we review some of the research that has been done on EuO, and talk about its potential in future device applications. 2Keep in mind that the Kohn-Sham orbitals have no physical meaning: they do not represent the ground state wave functions of the system. They uniquely describe the density, but the reverse is not true. There are many possible combinations of wave functions that could represent the same density. 9 1.2. EuO Guess ρ0(r) Determine VH and VXC from ρi-1(r) New HKSi Solve HKSi Φi(r) = εi Φi(r) New Φi(r) Construct ρi(r) from Φi(r) Does ρi = ρi-1? ρi is the self- consistent density Input ρi-1(r) No Yes Figure 1.2: This figure depicts a decision tree outlining the Kohn-Sham algorithm. This method allows one to iteratively approach a solution to the quantum many-body problem. Starting with an appropriate choice of basis ρ0( −→r ), the potentials V̂H and V̂xc are derived from their functionals. The resultant Kohn-Sham Hamiltonian is solved, producing the wave function φn. This wave function is then used to produce a new electron density. This process is repeated until the density no longer changes over iterations, indicating the true ground state has been found. 1.2 EuO There has been much interest and study surrounding EuO, both historically and re- cently, albeit for different reasons. In this section, I will begin by summarizing the most interesting and relevant properties of EuO. I will then discuss the historic de- velopment of EuO and our current understanding of ferromagnetism in stoichiometric EuO. Finally, I will discuss the current resurgence of interest in EuO and present some of the modern work that has been done regarding doping and thin film growth. This will provide context for the work of Chapters 5 and 6. Europium monoxide (EuO) is the prototypical ferromagnetic semiconductor [22, 10 1.2. EuO 23] with a room temperature band gap of 1.2 eV [24]. It has a Curie temperature (TC) of 69 K [23], and below the ferromagnetic transition temperature, the band gap is considerably reduced due to an exchange splitting of the bottom of the conduction band by about 0.6 eV [25]. This leads to a nearly 100% spin polarization for charge carriers introduced by doping [26, 27]. The Eu are in a Eu2+ f 7 configuration, which leads to a large magnetic moment of 7 Bohr magnetons. Structurally, EuO synthesizes in a NaCl type structure, with a lattice parameter of 5.142 Å [28]. In metal-rich or electron-doped samples, EuO exhibits a metal-insulator transition with a resistivity jump of 6 and 8 order of magnitude, respectively, as a function of applied magnetic field and temperature [29–31]; this is even higher than what is observed in the colossal magneto-resistance manganites [32, 33]. 1.2.1 Historical Development of EuO EuO was first synthesized in 1956 by Brauer [34], but only received considerable attention after its ferromagnetic nature was discovered in 1961 by Matthias [23]. This discovery generated a great deal of interest at the time, because it settled an ongoing debate about whether a ferromagnetic insulator could exist [35] (EuO was only the second ferromagnetic semiconductor discovered; CrBr3 had been discovered the year before [36]). The reason so many people doubted the existence of a ferromagnetic insulator was that the only exchange interaction understood at the time that led to ferromagnetic exchange was the indirect, RKKY interaction, which required the presence of conduction electrons. The discovery of ferromagnetic insulators made it clear that the picture of exchange at the time was incomplete. Another interesting aspect of EuO’s ferromagnetic behaviour is that it was not well described by the mean-field Weiss model [37, 38]; the low temperature magnetization had the wrong form (T 3 2 rather than e −C T ) and the critical exponent was too large. The Heisenberg model was able to reconcile these differences [39], and as such, EuO is regarded as a prototype 3D Heisenberg ferromagnet (when confined to next nearest neighbour exchange, see the next paragraph). Hints to the nature of the exchange mechanism were found by studying the entire europium chalcogenide family [40]. The europium chalcogenides start with ferromag- netic EuO and begin to become less strongly ferromagnetic (i.e., lower Tc) down the periodic table through EuS and EuSe, eventually ending with antiferromagnetic 11 1.2. EuO EuTe [41]. This progression suggests a competition between ferromagnetic and anti- ferromagnetic exchange is taking place as the orbital overlap is changed. This led Kasuya to formulate the following microscopic model of the various types of exchange [40, 42, 43]. Nearest-Neighbour J1: ˆ A 4f electron is virtually excited to the above Ef (Fermi level) 5d band, where it then interacts with nearest neighbour 4f spin moment. This leads to a ferro- magnetic exchange Next Nearest-Neighbour J2: ˆ Superexchange, where an f- electron is exchanged with another f- electron on neighbouring site through an oxygen. This effect is anti-ferromagnetic and small, since the overlaps are small. ˆ Multiple exchange interactions due to the O 2p electron or hybridized O 2p/Eu 5d electrons jumping to the vacant above Ef orbitals. These interactions can be either ferromagnetic or anti-ferromagnetic, depending on the bond angles. 1.2.2 Modern Perspectives on EuO There are a number of review papers dedicated to progress in understanding the physics of EuO [35, 40, 44, 45]. The current revival of interest in EuO has to do with the search for an appropriate material for building spin-based electronics. Modern microprocessors built with standard semiconductor technology and charge-based elec- tronics are beginning to come up against the physical limits of data processing speed, heat dissipation and limitation set by quantum mechanics. Spin-based electronics could potentially utilize the property of spin to store and process information, result- ing in much faster, cooler processors, and potentially the ability to perform quantum computation. EuO is a prime candidate for use in spintronic devices because it is an intrin- sic ferromagnetic semiconductor (in contrast to the Dilute Magnetic Semiconductors (DMSs), which require doping with magnetic ions to become ferromagnetic [46, 47]), and because it can be incorporated with conventional semiconductor materials (EuO 12 1.2. EuO has been grown successfully on Si, GaN and GaAs [26, 48–50]). However, two primary impediments to incorporating EuO into practical devices need to be overcome; the first is EuO’s chemical reactivity and the second is its low Curie temperature. EuO’s chemical reactivity makes it notoriously difficult to grow. The problem is that the EuO phase is unstable in the presence of oxygen; it will spontaneously react to produce Eu2O3 or Eu3O4, both of which are non-magnetic. The thermodynamic phase diagram is shown in Figure 1.3. The increase in Eu3+ 4f 6 (J=0)) due to over- oxidation quickly kills the magnetic exchange between Eu2+ 4f7, leading to a drastic suppression of Tc [51]. To produce bulk EuO, accurate starting conditions are needed [52–54], and after growth, the samples must be stored under good vacuum to prevent over oxidation. The Eu2O3 and Eu3O4 surfaces do not passivate, so the EuO sample will eventually completely oxidize if left exposed to the atmosphere. Figure 1.3: The thermodynamic phase diagram for europium as a function of temper- ature and oxygen concentration. The shaded area represents the narrow region where stoichiometric EuO will form. From M.W. Shafer, J.B. Tor- rance, and T. Penney. Relationship of crystal growth parameters to the stoichiometry of EuO as determined by I.R. and conductivity measure- ments. Journal of Physics and Chemistry of Solids, 33:2251, 1972, used with permission. One way to get more control over the material growth process is to grow thin films of material, and so a considerable amount of work has been done to prepare thin films of EuO. This method of material preparation allows for much more control over the kinetics of reaction, and makes it easier to produce unstable materials like EuO (see 13 1.2. EuO the next section for a discussion of the film growth technique used in this thesis). Reference 55 provides an overview of the various attempts to grow EuO in thin film form since the original thin film growth in 1967 by Ahn et al. [56]. The most reliable method for growing films of EuO is that of MBE distillation (this is the method used for all the films in this thesis, including SrO). The details of this technique are presented in the next section on MBE, but for our purpose here, it is enough to say that MBE distillation is a reliable enough growth method for repeatable production of EuO films. Coupled with appropriate capping and passivating layers, this technique could make it possible to produce reliable and robust EuO-based devices. The second problem that must be overcome before a practical EuO-based elec- tronic device can be developed is that of raising its Curie temperature to at least the level attainable with liquid nitrogen cooling (77K), and ideally to above room temperature. There are two ways in which an increase in the Curie temperature can be achieved, through applied pressure and doping. Externally applied pressure has been extensively studied as a method to increase the Curie temperature [57–63], reaching a maximum Tc of 200K [58]. Pressure is ef- fective at changing the Curie temperature because by straining the crystal lattice, the overlap between adjacent atomic orbitals can be increased, leading to a modification of the exchange integrals. However, applying the pressures required to cause appre- ciable changes in Curie temperature requires bulky and expensive pressure cells that preclude the use of pressure as a practical method of raising the Curie temperature. One interesting suggestion has been to use epitaxial strain brought about by growing EuO films on dissimiliar materials to raise the Curie temperature. Theoretical studies have shown that this technique could potentially raise the Curie temperature of a sto- ichiometric EuO film to 175K [61]. Unfortunately, early experimental results indicate that epitaxial films of EuO(100) grown on Ni(100) substrates (a 3.1% compressive strain) begin to relax back to their bulk state after 2-3 mono-layers of growth, reach- ing their bulk value after about 30 mono-layers [64]. This leaves chemical doping as the only viable alternative to increasing the Curie temperature of EuO. Chemical doping of EuO has been extensively studied [26, 65–80]. The most promising candidate is gadolinium, which has the same f-electron structure as eu- ropium, but with one extra electron in the 6s shell. The highest reported Tc in Gd doped thin film EuO was 125K, easily accessible with liquid nitrogen, but still a considerable way from room temperature. The mechanism by which the gadolinium 14 1.3. Ligand Magnetism increases the Curie temperature is unclear. It may be a function of electron doping [40, 79, 81], or of chemical pressure [61, 62, 68, 77, 78, 80]. Recently, a combined theoretical and X-ray absorption study by Altendorf et al. was able to show that the high Tc of Gd-doped EuO could only be due to a combination of both electron doping and chemical pressure [82]. Magnetism in EuO is due primarily to the europium f-orbitals, either interacting with each other, or using nearest neighbour oxygen as intermediaries. However, a relatively new area of research is the spin polarization of p-orbitals. Since we study one of these materials in Chapter 7, we will summarize the important theoretical and experimental advances in ligand magnetism in the next section. 1.3 Ligand Magnetism Magnetism due to ligand atoms is an unusual and counter intuitive result. In co- ordination chemisty, the ligand atoms bind to a central metal ion by donating charge. Magnetism is normally associated with these central metal ions which contain d- or f-type orbitals: the transition metals and the rare-earths. This is because un- paired charges in d- and f-orbitals can have high spins, and exhibit large electronic correlations because they are very localized. The localized d- and f-type orbitals in- hibit screening and make it possible for very large on-site Coulomb interaction to be present and strong associated intra-atomic interaction. Ligand atoms, like carbon, oxygen and nitrogen, are characterized by extended s- and p-type orbitals which have lower total spin (when the states are not filled) and large spatial extent of their va- lence electrons in most solids. Since the s- and p- orbitals are more extended, they form wider bands and screen the on-site Coulomb repulsion, which produces weaker intra-atomic interactions. To suggest that ligand atoms like oxygen are non-magnetic is incorrect, however. Consider, for instance, that the lowest energy configuration for two holes on an oxygen is a spin triplet state (this was justified in section 1.1.1). For oxygen, the spin singlet sits 1.47 eV higher in energy [11]. It is fair to question whether this result applies to solids as well. Indeed, a Auger spectroscopy study of Cu2O was able to show that the Hund’s rule exchange parameter (Jh) for two holes on the oxygen site was 1.2 eV [83, 84]. Furthermore, this Hund’s rule exchange parameter is effectively unscreened in most systems (Jh is due to higher order terms in the Slater integral expansion of 15 1.4. Molecular Beam Epitaxy the Coulomb repulsion term; only the first order/monopole term (f0/U) is screened by free charges, the higher multiple parts of the expansion are much more difficult to screen [85]). So introducing holes in an anion p-band is a viable route to magnetism; even through the on-site electronic correlation is heavily reduced due to screening in these systems, the Jh term, which is unaffected by screening, is still large enough to produce magnetism. There have been several recent theoretical and experimental papers either predict- ing or confirming the presence of magnetism due to the spin polarization of unfilled p-orbitals: including bulk systems like the III-V and II-IV semiconductors (BaN, SrN, CaN, CaP, CaAs and CaSb), molecular magnets (Cs4O6, CsO2, RbO2, Rb4O6 and KO2), graphite, graphene, and, most important for the work in this thesis, non- magnetic hosts doped with non-magnetic defects or dopants. We will only briefly cover some of the result of the last class of materials: for more details, please see the comprehensive review by Volnianska and Buguslawski [86]. A part of the reason ligand magnets had not been realized before is simply because the ligand orbitals tend to be filled (no unpaired spins). While there are systems that do have ligand orbitals crossing the Fermi energy (for instance, CrO2 [87, 88]), they are rare. The most straightforward way to introduce a narrow bandwidth ligand state at the Fermi level is to dope or add defects to the system. An example of the latter is oxygen deficient CaO, which is predicted to be a half-metallic ferromagnet [89]. A technologically promising example of a doped ligand magnet is carbon doped ZnO, where Curie temperatures of above 400K have been reported [90]. In this thesis, we deal with the simpler N-doped SrO system, which is predicted to exhibit ferromagnetism by producing holes on the ligand sites [91]. In the next section, I will introduce the technique of MBE, which is used in Chapters 6 and 7 to prepare films EuO1-xNx and SrO1-xNx, respectively. 1.4 Molecular Beam Epitaxy The central theme of this thesis is using MBE growth to prepare novel oxynitride materials for further study. In this section, I will provide a basic introduction to MBE and Physical Vapour Definition (PVD), while contrasting them with other material preparation techniques. I will then motivate the choice of MBE as a growth technique for the materials studied in this thesis, and introduce the details of the technique by 16 1.4. Molecular Beam Epitaxy way of examples that justify that choice. Substrate Heater RHEED Gun Ti Source Sr Source Shutters RHEED Screen       O2 Source Substrate (rotateable) Figure 1.4: A schematic of an MBE, showing features common to most systems. These include shuttered sources, a RHEED gun (with the angle exag- gerated). The heated substrate is normally rotated continuously during growth on production systems to ensure an even deposition of material (for research systems, this is not normally done because the substrates are much smaller). The set up shown in this figure is arranged to grow SrTiO3 by alternating between deposition and Sr and Ti while continually exposing the substrate to oxygen. MBE is a materials preparation technique whereby thermally generated molecular beams (usually generated by Knudsen cells [92] or electron-beam (e-beam) evapora- tors) are evaporated onto heated substrates in an ultra high vacuum environment. Gaseous species can also be introduced to the system through leak valves. Figure 1.4 shows how MBEs are commonly arranged. The technique is closely related to sput- tering and pulsed laser deposition (PLD), since they are all specific types of PVD. All PVD processes are characterized by the transfer of material from a source to a substrate by way of a highly directed beam (due to the long mean free path of the particles in the vacuum environment of the deposition chamber). This is in contrast to chemical vapour deposition (CVD), whereby the material to be deposited onto the surface is transferred from the source to the substrate through a carrier gas [93, 94], or bulk growth, in which precursor materials are mixed in a cell and allowed to react while being subjected to external stimuli (for example, pressure and temperature). 17 1.4. Molecular Beam Epitaxy There are four primary reasons for choosing MBE over another material prepara- tion technique like bulk growth or CVD. These are the ability to produce well-defined surfaces, the ability to grow films with high crystallinity and chemical purity, the abil- ity to control the structure and chemistry of the film in novel ways, and the ability to produce unstable phases. The first advantage that MBE has over competing techniques is its ability to produce a well-defined surface that is of suitable cleanliness and flatness for surface sensitive measurements. To study the surface of a material, the surface cannot be exposed to the atmosphere. For bulk crystals, this limits surface sensitive measure- ments like scanning tunnelling microscopy, photoemission (Chapter 4), and electron diffraction (Chapter 3) to materials that exhibit a natural cleavage plane. Bulk ma- terials can be sputtered or scraped to expose clean surfaces, but these techniques do not produce atomically flat crystal terminations and properties of the surface can be altered by the process [95]. MBE is capable of producing extremely clean sur- faces (i.e., no unwanted adsorbates) due to the ultra high vacuum environment of the growth chamber. For many materials, it is even possible to grow a thin film with an abrupt surface termination. As long as the film is prepared and transferred under UHV conditions, then the surface will remain clean. Good examples of materials that do not present a natural cleavage plane but that have been studied with surface sensitive techniques are SrCuO2 and EuO [55, 96]. The second advantage that MBE has over some other material preparations tech- niques is a high crystalline and chemical purity. The UHV environment ensures that the growth takes place in an environment that is free of possible contaminants. Furthermore, the ability to precisely control and monitor material deposition rates ensures that the stoichiometry of the films can be controlled precisely. Finally, the temperature required for surface diffusion of adsorbed molecules is much lower than that for bulk diffusion. This makes it easier for adsorbates to cluster into step edges or islands and leads to a decrease in the number of defects if the film is grown with a high enough substrate temperature to allow for diffusion (otherwise, the film will be amorphous). Figure 1.5 shows the rocking curve of the (002) diffraction peak of a Ca1-xSrxCuO2 film with an angular FWHM of 0.14°, comparable to the best silicon single crystals [97]. The third reason for choosing MBE growth over other methods is that MBE allows for an unprecedented amount of control over the chemical composition of the film. 18 1.4. Molecular Beam Epitaxy Figure 1.5: Rocking curve of the (002) diffraction peak Ca1-xSrxCuO2 sample. The FWHM of this peak is 0.14°, which is only slightly higher than the instru- ment resolution of 0.03. This sharp peak indicates that the crystallinity of the film is very high, comparable to the best quality silicon single crystals. From D.P. Norton, B.C. Chakoumakos, J.D. Budai, and D.H. Lowndes. Epitaxial growth of single crystal Ca1-xSrxCuO2 thin films by pulsed laser deposition. Applied Physics Letters, 62:1679, 1993, used with permission. Coupled with feedback from tools like Reflection High Energy Electron Diffraction (RHEED), discussed more in Chapter 3, it is even possible to control the composition of each atomic layer [98]. The most extreme examples of this type of control come from the relatively new field of multi-layer oxide heterostructures [99–101]. These new oxide-based materials exhibit exciting physics at the interface, including 2D electron gases, superconductivity and colossal-magnetoresistance, and may lead to new types of electronic devices [102]. While we do not control the film’s composition to this level in this thesis, we do take advantage of the fact that the growth takes place on top of the crystal at the vacuum interface to prepare our films. Specifically, the binary oxide films grown in Chapters 6 and 7 were all prepared using the technique of MBE distillation [25, 51, 103, 104]. This technique makes it possible to grow high- quality, stoichiometric binary oxides by evaporating metal ions onto a hot substrate 19 1.4. Molecular Beam Epitaxy under a low pressure of oxygen. For the particular case of europium, the low oxygen pressure prevents the formation of Eu2O3 and/or Eu3O4, while any unreacted metal is re-evaporated from the hot substrate surface [50, 51, 105]. This growth technique is unique to MBE; if this were attempted with a bulk growth technique, the resultant EuO would have a significant amount of Eu metal incorporated into it due to the low pressure of oxygen. Confining the reaction to the surface/vacuum interface makes it possible to remove the excess, unreacted metal. The final reason for choosing MBE over another growth technique, and perhaps the most compelling is that it is possible to reach out-of-equilibrium phases. These unstable phases can be achieved in several ways. One common technique is grow- ing epitaxially strained films on top of substrates (i.e., a film that is forced into a strained state because it is constrained by the structure of the previous atomic layer). Epitaxial lattice matching is especially interesting in transition metal oxide (TMO) and rare-earth oxide (REO) films because small changes in atomic overlap can have a considerable effect on the electronic properties of the materials due to the highly localized d- and f- orbitals [61]. For instance, the material VO2 undergoes a metal to insulator transition (MIT) at just above room temperature. This temperature of this MIT can be tuned between 300K and 369K by applying epitaxial strain to the VO2 films [106–108]. Another way that MBE allows film growers to reach otherwise inaccessible thermodynamic material phases is the lower temperatures required to grow materials on a surface, as opposed to in bulk. For instance, it is not possible to grow N-doped SrO in bulk because the high temperatures required to obtain suffi- cient material interdiffusion causes the formation of nitrides and nitrates of strontium [109]. However, N-doped SrO can be grown through MBE, presumably due to the lower temperatures required for growth [91] (see also Chapter 7). Despite all of the advantages of MBE, there are several serious drawbacks to the technique as well. The presence of a dissimilar substrate complicates the use of bulk measurements for characterization. It is also a very low yield technique, compared to bulk and CVD growth. It takes a long time to set up for a sample growth, and the sample size is limited to a single wafer per growth (for research, about a sample a day is the maximum throughput). Finally, there are certain types of materials that simply will not grow well in an MBE due to their complicated structures or chemistries. For instance, materials that require a high oxygen pressure to grow in bulk to reach the correct oxidation state are very difficult to grow with MBE [96, 110]. 20 1.5. X-ray Photoelectron Spectroscopy Despite these difficulties, however, the ability to grow clean unstable oxide films with pristine surfaces makes MBE the growth method of choice for this thesis. 1.5 X-ray Photoelectron Spectroscopy The last section on MBE film growth pointed out that one of the difficulties associated with MBE grown films is that conventional tools for structural and chemical analysis are ill-suited for thin films. Chapter 3 deals extensively with the problems associated with structural analysis of thin films, so we will delay our discussion of appropriate structural probes until then. This section introduces the versatile XPS technique for chemical and electronic structure analysis of thin films. The most common tool for performing chemical analysis of thin films is XPS. While other techniques, like Rutherford back-scattering, can produce some of the same information information as XPS, none are as versatile as photo-electron spectroscopy. XPS provides a snapshot of the electronic energy levels of a N-electron system with one electron removed. The process involves photo-exciting an electron from a core level into a state above Ef , where it travels through the vacuum to be detected by an electron spectrometer. A diagram explaining the process is reproduced in Figure 1.6. The short mean free path of electrons in solids ensures that only the top few monolayers of the sample are probed in XPS, electrons from deep inside the sample are scattered before reaching the vacuum. This makes it very sensitive to the surface and top few layers of a material; this is ideal for studying thin films. Another advantage of XPS over other chemical analysis tools, like mass spectroscopy, is that XPS is non- destructive. XPS does have some drawbacks, however. It requires UHV conditions to preserve the surface of the film being studied and to prevent scattering of photo- excited electrons, and the samples being studied must be conducting or they will accumulate charge. Furthermore, it is difficult to extract quantitative information from XPS spectra due to the highly non-linear spectrometer response. This problem is addressed in Chapter 4. The simplest use of XPS is for chemical identification. Individual elements in the film are identified by comparing the measured spectrum with spectra of the atomic elements. This provides a rough picture of the composition of the sample, and is a quick way to identify contaminants, but performing a quantitative analysis of a spectrum to extract exact composition is difficult because of the highly non-linear 21 1.5. X-ray Photoelectron Spectroscopy E Ev EF EB Sample N(E) N(E     ) Valence Band Core Levels Spectrum EF Ekin hν hν φ E 0 V 0 kin Figure 1.6: This figure provides a visual description of the photoemission process. Electrons bound in core levels are excited into states above Ef , where they are able to move through the vacuum and be detected by an elec- tron analyzer. The electron analyzer builds up a spectra by counting electrons as a function of their kinetic energy. Originally from Stefan Hüfner. Photoelectron Spectroscopy : Principles and Applications, vol- ume 82 of Springer Series in Solid-State Sciences. Springer-Verlag, 2nd edition, 1996. ISBN 3540608753, extracted from A. Damascelli. Probing the electronic structure of complex systems by ARPES. Physica Scripta, T109:61, 2004, used with permission. behaviour of most electron spectrometers (this problem is addressed in Chapter 4). However, in certain situations, relative concentrations of material can be extracted. For instance, the cross-section corrected oxygen 1s and nitrogen 1s core level, which are close in energy and in a relatively flat region of the spectrometer response, are used to determine nitrogen concentration of the films grown in Chapters 5 and 7. Chemical bonding information can also be extracted from an XPS spectrum. Dif- ferent types of bonding and co-ordination can cause the core level energies to shift, 22 1.5. X-ray Photoelectron Spectroscopy allowing one to identify different chemical states and structures. This technique is used in Chapter 7 to show that our nitrogen-doped SrO films contain no nitrites (NO–2) or nitrates (NO – 3) of Sr. More subtle effects, due to the interaction of the photo-excited electrons with the perturbed N-1 electron system left behind, can be used to extract additional infor- mation about chemical states and electronic structure. In Chapter 7, we demonstrate that the nitrogen 1s peak exhibits a multiplet splitting. A multiplet splitting is due to the interaction of the unpaired spin left behind by the photoemission process and an unpaired spin at the Fermi level. For SrO1-xNx, this confirms that the nitrogen is truly doping the SrO and forming magnetic moments on the nitrogen sites. 23 Chapter 2 Design and Construction of a Combined MBE Film Growth and Analysis System 2.1 Introduction This chapter describes the construction of a system for growing films of oxides and characterizing them using XPS and transport measurements. Systems like this are necessary because surface science and the study of thin films are two of the most technically difficult areas of condensed matter to study. There are two reasons for this: the surface is easily contaminated, and the surface layers represent a small fraction of the total volume of a sample [113]. Tools like electron spectroscopy, which use the short mean free path of electrons to remove the bulk signal, are very good probes of surface features [111]. However, the samples must be prepared and studied in very clean environments, and generally under UHV, to maintain a clean surface and allow the probe electrons to travel to the detector. The system developed here will combine an MBE for producing extraordinarily clean oxide films and the ability to perform XPS and temperature-dependent transport immediately after growth. While similar systems can be purchased commercially as separate units and joined together, this system is unique because it has been designed to provide a high level of flexibility, mobility and potential for reuse. The design of the MBE chamber had to be as mutable as possible because it will eventually be part of the Resonant Inelastic X-ray Scattering (REIXS) beamline at the Canadian Light Source (CLS). Since this beamline is a multi-user facility, the ability to retool the system to grow a wide variety of materials and to occasionally attach it to the end station were key design goals. Practically, this involved removing some features that are common on larger MBEs used in semiconductor research, 24 2.1. Introduction Figure 2.1: An image of the constructed MBE/analysis system. like liquid nitrogen cooling shrouds (which would make MBE of oxides difficult due to condensation of the process gas) and gate valves to isolate every source (which increase the chamber size, complexity and weight). The net result is a chamber that can be completely repurposed in a little over a week and moved to a new location by two people without any special equipment. The goal in the design of the analysis chamber was characterization of samples, rather than performance of subtle and complex experiments. There are several sys- tems already in use that attach an analysis chamber to an MBE, but in many of these cases the experiments being performed are very complex, like ARPES or STM measurements. These systems produce exciting and important results, but rely on growth recipes to ensure they are producing high-quality samples. By combining a versatile MBE system with an analysis chamber geared towards characterization, I have created a powerful system for developing recipes for high-quality samples. 25 2.2. Shared Design Elements 2.2 Shared Design Elements 2.3 Vacuum As was discussed in Chapter 1, one of the biggest advantages of MBE growth is that it can create very pure films with top layers that are ideally suited for surface sensitive measurements. This presents a problem if the samples have to be transferred between systems, because exposure to even high vacuum conditions (> 10−7 mbar), can reduce the lifetime of the surface to less than a minute.3 Since MBE grown films are generally very thin, one could consider the entire structure to be surface dominated, and the lifetime of the surface is really the lifetime of the sample, especially in systems whose surfaces do not passivate well (like EuO). Therefore, samples prepared by MBE must be immediately transferred under UHV to the analysis chamber for characterization, especially if surface sensitive measurements are to be performed. Practically, this means attaching the two systems together and ensuring that both of them are kept under UHV conditions. For the MBE, this entails pumping with an Austen Scientific Cryo-Plex® 8LP cryopump. A cryopump is a type of entrapment pump that absorbs gas on a cold surface to maintain UHV conditions. The absorbing surface of the pump is kept at low-temperature (around 10K at the cold head) by throttling high-pressure helium gas with a piston. These are closed cycle systems, with the high-pressure gas provided by a compressor [114]. The advantages of this type of pump are that it has the fastest pumping speed of any available pump, and that it is able to pump any gas, including hydrogen and helium. It does require an initial pump down to high vacuum conditions before it can operate, and this initial pump down is achieved with the load lock’s turbopump. For the analysis chamber, the long, thin cryostat would vibrate as a result of the cryopump piston’s motion, making experiments on small samples difficult, so a combination of a Pfieffer TV800 turbomolecular pump backed by a Varian Triscroll roughing pump and a Varian VacIon Plus 300 1680 ion pump powered by a Varian 929-7000 controller are used to pump the chamber. The ion pump is another type of entrapment pump, but rather than condensing gases on a cold surface, it ionizes 3In this case, I have defined the lifetime of the surface to be the time it takes to fully cover the surface with one atomic layer of contamination. The rate of surface coverage can be derived approximately using the ideal gas law and Boltzmann statistics. 26 2.3. Vacuum neutral gas particles, and then accelerates them through a large potential into a tita- nium cathode with a large surface area. Gases are either permanently buried in the cathode, or chemisorbed onto the fresh titanium surface produced by ion bombard- ment [114]. While ion pumps are not as good at pumping noble gases as a cryopump, they produce no vibrations. Care must be taken to ensure that stray magnetic and electric fields from the pump do not affect the experiment. After baking, the base pressures in each chamber were in the low 10−10 to high 10−11 mbar scale, as measured with standard Bayard-Alpert type ion gauges. Both chambers incorporate an SRS RGA100 residual gas analyzer, used for leak checking, as well as checking the composition of the gas load in the chamber and setting MBE growth pressures. 2.3.1 Sample Holders One design requirement of the MBE/analysis chamber was that it be compatible with the sample holders used on the REIXS beamline at the CLS. The sample holders used for this system are variants of a sample plate used in UHV vacuum systems built by Omicron Nanotechnology GmbH. and were redesigned by David Hawthorn. Figure 2.2 is a model of one of the sample holders. Substrates were attached to these sample holders with Cu paste from Tanaka Kikinzoku International. The sample holders were machined from Oxygen-Free, High-Conductivity (OFHC) copper for high thermal conductivity and vacuum compatibility, and the transfer arm tab was made of titanium to reduce the risk of stray magnetic fields near the sample (austenitic stainless steel is susceptible to the formation of martensitic, ferromagnetic domains during cold working [115]). The screws connecting the tab to the sample were made of titanium and ordered from United Titanium Ltd. An additional change from the standard Omicron sample holder design is the wedge running across the front of the sample holder. This element is included so that the sample holders will be compatible with the REIXS endstation cryostat at the CLS. The wedge serves the function of increasing surface area contact/reducing the thermal resistance of the contact between the sample holder and the cryostat. To achieve the high force required to produce good thermal contact, an annealed stainless steel, threaded insert is placed in the front of the sample holder. This stainless steel insert prevents the titanium screw from damaging the threads in the relatively soft copper 27 2.3. Vacuum Figure 2.2: A model of the sample holder. Samples are affixed to the holder using copper paste from Tananka Kikinzoku International. The sample holder is manipulated with a transfer arm that attaches to the titanium lug. For the MBE and LEED sample positions, the sample is held in place by friction. When placed in the cryostat, the 8-32 threaded hole opposite the titanium tab is used to produce a higher force contact between the sample holder and cryostat. A threaded insert is used instead of threading directly into the copper to prevent damage to the relatively soft copper threads during thermal contraction and expansion. of the sample holder, and cold welding of a high-force titanium/titanium contact if a titanium insert is used. Annealing of the stainless steel insert removes any magnetic domains formed during cold working. 2.3.2 Sample Transfer Sample transfer in the MBE analysis chamber is relatively simple. The titanium tab on the sample holder is grabbed by a pincer grip attached to a vacuum transfer arm. The pincers have countersunk grooves that lock around the sample holder tab to prevent it from slipping out of the jaws. Both the pincer grip and transfer arm were purchased from Ferrovac GMBH (Ferrovac Model PGWMS(OM) straight pincer 28 2.3. Vacuum Figure 2.3: Model of actuator grabbing sample holder. The jaws of this Ferrovac Model PGWMS(OM) straight pincer grip are positioned over the tita- nium tab on the sample holder with a dual rotary transfer arm, also from Ferrovac GMBH. The groove in the jaws prevents the sample holder from sliding out of the jaws or rotating. Retrieved from the Fer- rovac Model PGWMS(OM) product page on 27 January 2012 (http: //www.ferrovac.ch/product_desc.cfm?product_id=1722). Used with permission. grip and Ferrovac Model RMDG1000-100 dual rotary transfer arm).4 The arm and sample holder are shown in Figure 2.3 The sample holder can be transferred along the axis of the transfer arm, as well as rotated around this axis. All of the sample transfer positions can be adjusted horizontally and vertically to accept the sample holder. The sample holder is held in place by friction, or by tightening a locking screw in the face of the sample (in the MBE, the sample is held in place by friction, since most of the heat transfer happens through radiation, while on the cryostat, a locking screw is used to improve the thermal contact). The layout of the two chambers is presented in Figure 2.4, showing the various sample positions and the location of the transfer arms. Two, one-meter-long transfer arms provide enough motion to reach every possible sample position in the chamber. The transfer arm on the load lock picks up the sample from a five-position sample carousel and loads them into the LEED sample position. From there, the sample 4The fiberglass reinforced bushing used in the Ferrovac transfer arms has been found to provide smoother motion and more reliable service than other transfer arm designs based on bearings. I would recommend this method of grabbing samples for new designs because it is easy to grab a sample, and once grabbed, it is very difficult to accidentally drop. 29 2.4. MBE Chamber Load Lock Sample Preparation MBE Analysis Chamber Hemispherical       Analyzer RHEED Screen LEED RHEED Gun Growth LEED/ Arm Change MBE Transfer Arm Load Lock Transfer Arm Figure 2.4: This schematic shows the layout of the MBE and analysis chambers, as well as the routes followed to transfer samples. The various growth and transfer positions are represented by coloured dots. The motion degrees of freedom are also indicated. holder is rotated 90° and picked up by a second transfer arm that moves it to the MBE growth position or into the analysis chamber. 2.4 MBE Chamber The MBE chamber is shaped like a horizontally aligned cylinder. The left half of the cylinder (as depicted in Figure 2.4) is where the growth occurs and the right half is where the sample transfer occurs, as well as any LEED measurements. The growth half of the chamber has five 41 2 ” Con-Flat® (CF) ports pointing at a single spot that lies along the axis of the cylinder (the sample growth position). These five ports are reserved for deposition sources and gas feedthroughs. The effusion from these sources can be blocked by a pneumatically driven shutter. The sample growth position was determined by attaching laser diodes to the five deposition ports and observing where the beams intersected. A sample stage is lowered into this sample position to load and unload the sample 30 2.4. MBE Chamber and for growth. The sample holders are loaded into the stage with the face of the sample pointed downwards to expose the sample to the sources and the RHEED beam. The sample stage is connected to the chamber through a MDC Compact Manual Z stage for large vertical movements, a MDC Vacuum V-Planar Dual Axis X-Y stage for small lateral adjustments and a Thermionics RNN differentially pumped rotary seal for rotations around its axis. This sample stage is water cooled and can heat the sample to over 700°C with an oxygen-resistant, resistive ceramic button heater from HeatWave Labs. The heater is controlled by a HeatWave Labs Model 101303-22A power supply controlled by a Watlow Series 96 type K thermocouple temperature controller. The sample stage was designed by Doug Wong of the Department of Physics and Astronomy at UBC. When the sample holder is raised, a STM100/MF QCM can be moved horizontally into the sample growth position with a MDC Vacuum Compact Manual Z stage and was used to measure the rate of material deposition. The LEED half of the MBE chamber has a simpler, unheated sample stage that is connected to a Thermionics EC Series XYZ precision manipulator (EC B600 XYZ) stage and a rotary feed through. The face of the sample holder is aligned so that when the holder is rotated, the sample is facing the LEED. This sample stage sits at the intersection point of the two perpendicular transfer arms and is used to change the direction of sample travel. 2.4.1 RHEED The MBE system uses a STAIB instruments NEK300R3-BRC10 RHEED gun to produce an electron beam, and the kSA 400 RHEED system to measure the diffracted image. The measurement system consists of an 8” CF phosphor screen imaged by a K-30FW 10-bit CCD camera with a 12 mm F/1.4 lens. The RHEED data was recorded and analyzed with the kSA RHEED analysis software. The RHEED gun and viewport ports on the MBE chamber are canted to about 2° below horizontal and aimed at the sample growth position. With this setup, it was possible to measure RHEED diffraction patterns along certain crystal directions, and even measure RHEED intensity oscillations during growth. Figure 2.5 shows representative data taken with this system. However, due to a design error, screw heads and retaining clips were protruding on the sample stage, 31 2.4. MBE Chamber 0 400 800 1200 Growth Time (s) In te ns ity (a) (b) Figure 2.5: Representative RHEED data taken with this system. (a) shows a RHEED diffraction image of an annealed YSZ (001) surface. (b) shows RHEED os- cillations associated with the layer by layer growth of a SrO1-xNx grown on a YSZ substrate. The initial strong oscillations correspond to the growth of SrO, using oxygen donated by the substrate. The weaker oscillations after 700 seconds of growth may be due to the growth of SrO1-xNx. preventing the electron beam from reaching the sample surface in all orientations. As a result, it was not possible to completely characterize the sample surface using techniques like those described in Chapter 3. 2.4.2 LEED The MBE system also features a LEED system from Omicron NanoTechnology GmbH (SPECTALEED model with a M315210 control unit). Figure 2.6 shows the LEED pattern of a cleaved Na2IrO3 taken with this LEED. While the information about the surface structure of the substrates and films that the LEED provided is useful, the device was rarely used in practice in conjunction with MBE grown films. The LEED system takes up to an hour to stabilize once started, and cannot be operated during film growth or annealing due to the high gas pressures in the growth chamber. Rather than let the sample degrade while waiting for the LEED to stabilize, the 32 2.4. MBE Chamber Figure 2.6: Representative LEED data taken with this system. This figure shows the LEED pattern of the surface of a Na2IrO3 cleaved crystal taken at 90 eV kinetic electron energy. (courtesy of Riccardo Comin) LEED measurement was performed after XPS spectra were measured. In most cases, the surface had degraded during the XPS measurement to the point where it was impossible to find a diffraction pattern with LEED. 2.4.3 Sources There are a variety of sources available on this system, each suited for a certain material. For materials with high vapour pressures, two RADAK I vacuum furnaces from Luxel Corporation are available. These low-temperature Knudsen cells are placed inside a custom water-cooled nipple, and can reach a maximum temperature of 1350‰ with the Luxel RADAK Power Controller II controlled by a Eurotherm 2408 type K thermocouple temperature controller. In an oxygen environment, the source should be limited to below 800‰ to prevent damage to the radiation shields. For materials with lower vapour pressures, two high-temperature effusion cells from MBE Komponenten GmbH are available (P/N HTEZ40-1-19-KS-2006998). These high-temperature Knudsen cells come with an integrated cooling shroud and shut- 33 2.4. MBE Chamber ter, and are capable of reaching temperatures of up to 1900‰ (crucible dependent). Each is powered by a TDK-Lambda Genesys Programmable DC Power supply (P/N GEN40-19), controlled by a Eurotherm 2404 type C thermocouple temperature con- troller. For the lowest vapour pressure materials, an EFM3 e-beam evaporator from Omi- cron NanoTechnology is available. This source uses an electron beam to locally heat the material to be evaporated (either in rod form for metals or in a conductive cru- cible) rather than resistively heat the entire crucible. Regardless of the method of evaporation, if a crucible is used, care must be taken in selecting it to ensure there are no unwanted reactions between the material being evaporated and the crucible. These can come in the form of chemical reactions or physical incompatibility. Aluminum is a particularly troublesome material that ex- hibits both these problems. When aluminum is melted in an Al2O3 or W crucible, the highly reactive aluminum tends to reduce the Al2O3 crucible and alloy with the W, leading to crucible failure. Furthermore, if aluminum is allowed to melt, it wets the walls of the crucible container, and when cooled, produces an enormous force on the crucible walls, again leading to crucible failure. The solution, for the particular case of aluminum, is to use a pyrolitic BN crucible, to prevent alloying, and to never let the aluminum solidify once it has been melted. The source either has to be emptied of aluminum, or the crucible needs to be discarded. For the sources discussed here, a combination of pyrolitic BN, Al2O3 and W crucibles were purchased. Precision leak valves are used to introduce gas into the growth chamber. The valves are manually controlled, but are capable of reliably setting the pressure to within ±2 × 10−10 mbar. An Oxford Applied Research TC-50 thermal gas cracker is also available for producing atomic gas species containing more than one element. The gas is flowed over a hot catalytic surface, which causes most binary gases to dis- associate (with the exception of nitrogen, because its bonding energy is too high). In contrast to a plasma gas cracker, which only operates under high vacuum conditions, the thermal gas cracker works best below 10−7 mbar of gas pressure. 2.4.4 Future Improvements While this MBE system lacks some of the extra features found on other systems, like computer controlled shutters and the ability to change sources without venting 34 2.5. Analysis Chamber the entire chamber, it is, overall, a very good system for growing a wide range of different materials. The simplicity of the design and speed at which the entire system can be reconfigured make the system versatile enough to be used at the multi-user REIXS beamline. However, there are several aspects of the MBE system that should be changed. The first recommendation is to remove protruding screws from the base of the MBE sample stage. These screw heads impede the electron beam, and effectively block RHEED diffraction over about half of the available angles. The second recommendation is to replace the heater in the MBE sample stage with a non-inductively wound resistive heater and a DC power supply. The current heater power supply uses 60 Hz AC to deliver power the heater. This causes the RHEED beam profile to blur when power is applied to the heater, decreasing the sharpness of the RHEED diffraction pattern. A non-inductively wound heater driven by a DC power supply would help to eliminate this problem. The Knudsen sources present the same problem, but as they are located further away from the sample and the RHEED beam, they impact the RHEED pattern less. The final change I recommend is to move the LEED into a separate analysis cham- ber. This will make it possible to take LEED images immediately after growth or annealing because the source can be started and reach a stable operating condition while the sample is being prepared in an adjacent chamber. Once the film is ready, it can be transferred to the analysis chamber and the LEED pattern measured immedi- ately. Alternatively, if the MBE sample stage is repaired to allow for diffraction along all directions and the sample positioning is automated, then the methods presented in Chapter 3 can be used to produce LEED-like diffraction images. 2.5 Analysis Chamber The purpose of the analysis chamber is to characterize samples grown in the MBE in situ. Many sample characterization tasks are performed after removing the sample from the chamber and after evaporating a protective capping layer onto the sample surface if the sample is sensitive to air. SQUID and X-ray diffraction are good ex- amples of techniques that can be performed after the sample has been capped and removed from the chamber. However, there are several techniques that are surface sensitive or cannot be performed with a capping layer, which should be done in situ: 35 2.5. Analysis Chamber XPS, UPS, Auger, STM and transport, for instance. Transport is an example of a bulk-sensitive measurement, but for the case of thin films, it is best done in situ since a capping layer would interfere with the measurement. This analysis chamber has been designed to perform temperature-dependent XPS and transport measurements on the films, since these two measurements complement the structural information produce by RHEED diffraction. The construction of this analysis chamber was broken into two stages: the first stage brought the system to the point where it could be used to analyze films grown in the MBE with XPS at room temperature; the second stage will add an open flow cryostat to the system so that temperature-dependent XPS and transport can be performed. By splitting the work in this way, films could be grown earlier than would be possible if the analysis chamber and cryostat were completed as a single unit. The most useful information about film growth comes from the room-temperature XPS (chemical information and core level electronic structure). Temperature-dependent XPS and transport are more important when studying specific material properties: for instance, the metal-insulator transitions in EuO. At the time of this writing, the cryostat is still being assembled and tested. 2.5.1 Chamber Design Since the analysis chamber was to be used to perform electron spectroscopy, one of the first design decisions was whether to use stainless steel or µ-metal. µ-metal chambers are required when performing low-energy electron spectroscopy, like ARPES or UPS, because stray magnetic fields can have a signifigant impact on the electron trajectories. However, they are considerably more expensive than a stainless steel chamber. For this analysis chamber, since we are performing XPS measurements, the average electron energies being measured are on the order of hundreds or thousands of electron volts, and the deflection due to magnetic fields from the environment are not observable. As a result, since the benefits gained from a µ-metal chamber were negligible, the choice was made to make this chamber from stainless steel to reduce overall cost. 36 2.5. Analysis Chamber Binding Energy (eV) 1000 0800 600 400 200 Cu 2p N KLL O KLL O 1s N 1s Sr 3s Cu LMM Sr 2p 1/2 Sr 2p 3/2 Sr 3d Sr 4s Sr 2p 1 2 3 In te ns ity  (1 04  C ou nt s) Figure 2.7: Representative XPS spectra of a SrO1-xNx sample showing a wide scan with the important peaks labelled. 2.5.2 Analyzer The heart of any electron spectroscopy system is the electron analyzer, which mea- sure the kinetic energy of photoexcited electrons. The details of analyzer operation are discussed more throroughly in Chapter 4. This system incorporates a PHOIBOS 100 hemispherical electron analyzer with an HSA3500 plus power supply, made by SPECS GmbH. This analyzer has a 5-channeltron detector, and is capable of mea- suring electron energies from just above 1 eV to 3.5 keV. The best factory-measured resolution of this particular analyzer was 125 meV. This value matches the 12% to 88% width of the Fermi edge of an Ag sample measured at a temperature of 300K using UV photons from a He I line. 2.5.3 X-ray Source This system uses a dual anode, XR 50 X-ray source from SPECS GmbH to produce the X-ray photons to perform XPS. This unmonochromated source has both Al and Mg anodes, which produce 1486 and 1253 eV photons, respectively, from their Kα lines. The Mg anode produces a higher resolution signal than the Al anode, but the Al anode produces higher photon energies, allows one to measure deeper core levels, 37 2.5. Analysis Chamber and produces higher flux. The presence of both anodes allows the user to choose an anode that minimizes the overlap of Auger peaks in with the core level peaks of interest. Since this is an unmonocromated source, it limits the resolution of the entire XPS system. X-ray satellites (photons with slightly higher energy than the characteristic line) must be removed from the signal as well [116]. The sharpest peak measured had a FWHM of 1.246 eV. This was an Ag 3d 1/2 level, measured with Mg Kα radiation at 300 K, and with a pass energy of 20 eV. The spot size illuminated by the x-ray source is approximately 1 cm in diameter. This X-ray source has strict water cooling temperature, pressure and composition requirements, so a PolyScience 600 series (6360T11A120) recirculating chiller is used to cool the device. 2.5.4 Electron Gun The analysis system also includes a SPECS GmbH EQ 22/35 electron gun, powered by a PU-EQ22 electron source power unit. This electron gun is used primarily for calibration (such as measuring the transmission function, see Chapter 4) and for performing simple Auger electron spectroscopy (the spread in beam energy is too large to perform more complicated measurements, like EELS). This source can produce electrons with energies from tens of eV to 5 keV. 2.5.5 Description of Cryostat and In Situ Transport Measurements The second major portion of the analysis chamber design was the cryostat. Its de- sign and construction came after the design and construction of the XPS system because the characterization of the films grown by MBE did not require temperature- dependent XPS or transport measurements; these tools are appropriate for more detailed studies of the sample’s physics, after the sample growth problems have been addressed. As a result, only the design of the cryostat has been completed, and as of this writing, initial commissioning is taking place. This cryostat will be used to perform temperature-dependent XPS and transport measurements, and so stability, precise temperature control and the ability to perform two very different measure- ments on the same sample were key requirements for the cryostat design. Some of the secondary design criteria were fast response and low helium consumption. 38 2.5. Analysis Chamber The cryostat design was dictated by the temperature control requirements of the transport and temperature-dependent XPS measurements, as well as the desire to conserve liquid helium. Transport measurements have very simple temperature con- trol requirements: the measurement should be reliable as long as the temperature sensor and sample are in good thermal contact, and the rate at which the temper- ature of the sample changes is slower than the response time of the temperature sensor and the transport measurement apparatus. Temperature-dependent XPS has stricter temperature control requirements than transport. XPS measurements may take several hours, so stability is very important. This requires the use of heaters and well-tuned controllers to maintain steady control. A final design requirement is low helium consumption, due to the high cost of liquid helium ($1500 per 100 litres at the time of writing). The ideal solution for helium consumption would be to use a closed cycle system (similar to a cryopump); however the vibration would make it difficult to perform XPS on small samples and may produce unreliable contacts for transport measurements. To minimize helium consumption and ensure a fast thermal response to facilitate good temperature control, the thermal mass of the entire system has been made as small as possible, so an efficient heat exchanger has been designed and a radiation shield has been incorporated into the system. Figure 2.8 shows a model of the bottom of the cryostat without its radiation shield. (a) shows the bottom of the cryostat with the radiation shield removed and the lower wires in place. (b) shows the connection of the radiation shield to the cryostat tube. The wires coming from the top of the cryostat are thermally connected to this block to reduce the transfer of heat to the heat exchanger (the wires are not shown in this image). (c) shows a cross-section of the heat exchanger to reveal its internal structure. The liquid helium passes through the central hole of the heat exchanger and fills the reservoir. Boil-off helium gas escapes upwards through the outer holes. The many small holes increase the effective surface area the helium gas can interact with, and improves the thermal transfer. The escaping helium gas also cools the cryostat tube, which in turn pulls heat out of the radiation shield and the wire contacts that connect to it. Rather than wrap wires over spools to remove heat from the wires, the wire coming from the top of the cryostat is broken at the radiation shield and at the heat exchanger. An electrical connection is made through a copper block at each of these points, and that copper block is epoxied into grooves cut into the cryostat body, with sapphire spacers to facilitate heat conduction without shorting the signal to the 39 2.5. Analysis Chamber (a) (b) (c) Figure 2.8: Models of the various parts of the cryostat. Panel (a) shows the heat exchanger, sample holder and the variable thermal contact between them. Panel (b) shows the radiation shield connection to the cryostat tube. Panel (c) shows a cross-section of the heat exchanger. Liquid helium is introduced through the central hole, and the helium gas escapes through the small holes around the periphery. The increased surface area due to the small escape holes improves the heat exchange between the exchanger and the escaping helium gas. The wires have been removed from between the top of the cryostat, the radiation shield and the top of the cryostat heat exchanger to make the image clearer. 40 2.5. Analysis Chamber cryostat. Many of these design elements were suggested by Pinder Dosanjh. Another interesting aspect of this cryostat design is the ability to vary the heat transfer between the reservoir and the sample stage by changing the cross-section of the copper connection between them. This was included in the design as an extra degree of freedom that can easily be changed after the cryostat is assembled. This heat transfer element can be experimentally optimized to provide the ideal trade-off between thermal response of the sample and helium consumption. The orientation of the sample holder determines which experimental tool will be used. To perform XPS, the sample is oriented facing the opening in the radiation shield, so that the X-ray source can be moved close the the surface of the sample and the photoelectrons can escape to reach the analyzer. To perform transport, the sample faces towards the pin holder at the back of the cryostat. This pin holder is moved towards the sample by turning a screw that drives the pin mount along alignment rails. Spring-loaded, non-magnetic, Pogo® pins press into the sample surface, providing a consistent electrical contact. The pins are held in place with epoxy in a pin holder than can be quickly replaced for use with different sample geometries. The pins and pin holder are cooled through a copper braid attached to the sample holder and through the wires connected to the pins. Cryostat Modelling A theoretical model of the cryostat was derived to test development decisions and de- termine approximate operating temperatures and helium flows. Figure 2.9 shows the different components that were modelled, the temperature state variables associated with those components, and the heat flow through the system. Conduction and radi- ation contributions were modelled exactly using Fourier’s law of conduction and the Poisson equation for radiative heat transfer, respectively. Newton’s law of cooling was used to model the heat transfer between the liquid helium and the heat exchanger, but the cooling power of the escaping gaseous helium was not explicitly dealt with; rather, it was assumed that the gas had warmed to ambient temperatures by the time it reached the top of the cryostat, and that the temperature changed linearly along the length of the cryostat tube. A further assumption was that the temperature of the shield was equal to the temperature of the cryostat support tube at the point of contact, and that heat from the radiation shield was carried away by the helium gas and not though conduction. These assumptions removed the difficult problem 41 2.5. Analysis Chamber Tshield Texchanger Tholder Tambient Heat Transfer High Low Radiant Radiant Radiant Heater 2 Heater 1 Variable Conduction Conduction Conduction Conduction Liquid HeCooling Heater and Sensor Wires Figure 2.9: Schematic model of the cryostat components used to develop a thermal model. The different blocks labelled with temperature values represent different components, each with its own state equation, and the arrows represent the heat flow into or out of different components. The colour scale represents the amount of heat flow into or out of the different com- ponents. The black arrows represent variable heat flows from heaters, or from the liquid helium (variable with helium flow). of calculating the heat transfer between the cryostat tube and escaping helium gas. They also mean that any temperatures derived from this model will likely be worst- case scenarios, since the heat flow down the cryostat tube and the temperature of the radiation shield will likely be overestimated. Using this simple model, the operating point of the heat exchanger was determined to be just above the boiling point of liquid helium (4.21 K). The sample holder position temperature was calculated to be above 4.35 K, depending on the size of the thermal junction. The cryostat should be able to maintain these temperatures at a flow of 0.08 L/h of liquid helium. While the lowest operating temperature of the holder did not change drastically with the geometry of the thermal junction, the effect of applied 42 2.6. Conclusions heater power did become more drastic. By changing the width of the solid copper junction from 2 cm to 3 mm, the base temperature of the holder only changes by 0.3 K (4.35 K to 4.65 K). However, for the same geometry, the temperature reached by applying 10 Watts of heater power to the holder goes from 50 K to 160 K for the same amount of helium flow. The equations and the Sage worksheet used to calculate these values have been included in the Appendix. This model only deals with the equilibrium operating values, so some testing needs to be performed to determine if cool down and response time for this system are acceptable. 2.5.6 Future Improvements Overall, the XPS analysis system performed well, but there are several possible im- provements that could be made. The resolution of the system is limited by the X-ray source, and ideally, a monochromatized x-ray source would be fitted to this chamber. Unfortunately, the large size required for the Rowland circle design found on most monochromated x-ray sources makes it impossible to fit on this particular chamber. Another option to improve the resolution would be to fit the chamber with a UV lamp. While this would limit the energy range to a few tens of eV below the Fermi edge, it would be an excellent complement to the core level XPS spectra produced by the existing unmonochromated source. Another design element that has not been discussed but should be improved upon is the rigidity of the frame. The frame for this chamber was made from square aluminum extrusion with a 1.5” width, from 80/20 Inc. This size of extrusion was more than sufficient to support the weight of the chamber. However, to bring the chamber to the height of the MBE, long vertical legs were required. To prevent significant horizontal or torsional oscillations, extra bracing was required. In future designs using 80/20 aluminum extrusion for the frame, I would recommend 2.5” or 4” extrusions, even for small chambers. 2.6 Conclusions Overall, the combined MBE growth and analysis system has performed well. The MBE growth system is properly equipped to grow a wide variety of different materials, 43 2.6. Conclusions and can be configured to do so reasonably quickly. The XPS portion of the analysis system has provided invaluable data about the films grown by MBE, and has also been used by other people in the group to characterize cleavable crystals for other projects. The cryostat is still being assembled and tested. 44 Chapter 3 The Structural Analysis Possibilities of RHEED 3.1 Introduction RHEED systems are found on almost all PVD growth chambers. In this chapter, I will introduce the technique by contrasting it with conventional diffraction tools, and demonstrate why RHEED is such a powerful tool for film growers. I will then show how the limited diffraction data the technique produces is normally used. Finally, I will present a method I helped to develop that allows the full surface diffraction pattern to be reconstructed by combining multiple RHEED diffraction patterns. The primary reason that RHEED is so often used by film growers is that probing a thin film with conventional diffraction tools is very difficult to do. Conventional crystal X-ray diffraction can by used to determine the complete structure of the crys- tal. This requires a reasonably large, homogeneous sample because X-rays interact weakly with matter. This implies that X-ray diffraction primarily probes the bulk of a crystal; surface structures in these crystals are difficult, if not impossible, to resolve because of the small volume (relative to the bulk) that surface features occupy. This limitation in probing surface structures with X-ray diffraction extends to thin films as well; the volume occupied by a thin film is small relative to the bulk substrate, and so the film produces a very weak diffracted signal. One solution to the problem of the weak interaction of the X-rays is to use synchrotron X-ray sources to increase the brilliance of the beam (about 1012 times brighter than conventional lab-based X-ray generation [117]). The increased brightness makes it possible to measure sur- face structures via crystal truncation rods (CTRs) [118] and the full structure of the thin film via conventional diffraction (CTRs will be discussed later in this section in the context of RHEED diffraction). For routine, lab-based analysis of thin films, however, the utility of X-ray diffraction is limited to a small set of lattice parame- 45 3.1. Introduction ters perpendicular to the surface, and reflectometry measurements of thickness and surface roughness with a θ − 2θ X-ray diffractometer. Even in this limited case, the film needs to be very thick to measure a diffraction peak. Getting any structural information from a very thin film is impossible using conventional X-ray diffraction. The root of the problem with X-rays for surface and film diffraction is the weak interaction of X-rays with matter. To probe the surface, a particle that interacts more strongly than a photon needs to be used. An ideal candidate is electrons. The short mean free path of the electrons ensures that only the first few monolayers of the crystal are probed. This characteristic of electrons is what gives photoemission its surface sensitivity [111]. For X-ray diffraction, characteristic radiation from various materials with wavelengths around 1.5 Å [119] are commonly used (the size of a typical C-C bond). To get the same deBroglie wavelength from electrons, we use the equation [10]: λ = 12.3 (EeV ) 1 2 (Å) (3.1) which tells us that electrons with kinetic energies around 70 eV will produce similar deBroglie wavelengths to standard X-ray sources, but with much more surface sen- sitivity than conventional X-rays. Electrons at this energy have a probing depth of approximately 2 − 5 Å, based on the universal curve of the electron mean free path [111, 113]. This indicates that only the first couple of monolayers of the sample will produce any diffraction when using electrons as the probe. There are several well-developed electron diffraction tools that can be used to study thin films, surfaces and interfaces; these include TEM, LEED and RHEED. TEM is a very powerful technique that can be used to study bulk, surface and in- terface structures [99, 120, 121], as well as provide some chemical information [122]. However, it is a destructive technique, and is also very difficult to perform and an- alyze. TEM also requires very expensive and specialized facilities to perform the measurements. LEED is more amenable for day-to-day characterization of surfaces. It is non-destructive and provides immediate qualitative information on the surface symmetry. However, due to the low electron energies used, dynamic multiple scatter- ing events are quite common, which can make the analysis of LEED images difficult [123]. Furthermore, both TEM and LEED can only be performed after film growth, not during, since the sample needs to be placed directly in front of the detector. 46 3.1. Introduction RHEED screen transmitted  e-beam incident  e-beam Ewald sphere reciprocal lattice rods [100] [010] (00) (11) (11) (01) (12) (10)(21) azimuthal rotation Figure 3.1: This image depicts the real-space geometry of a RHEED diffraction mea- surement, with a depiction of the momentum space Ewald sphere con- struction intersecting the CTRs superimposed. RHEED compromises on the amount and quality of the diffraction data to simplify the analysis and to make it possible to perform diffraction measurements during growth. The glancing angle of the electron beam makes it possible to move the electron source and measurement system away from the deposition sources and other growth equipment used in PVD. In the glancing angle geometry, higher electron energies are required to maintain similar scattering wavelengths to a back scatter technique like LEED. For instance, the in-plane DeBroglie wavelength of electrons with 15 keV kinetic energy at a glancing angle of less than 2°s is slightly less than 1 Å. The higher kinetic energies also help to reduce the amount of dynamic and multiple scattering that takes place. Despite the high energy of the electrons (typically 15−30 keV), the large angle of incidence of the beam ensures that the high level of surface sensitivity is retained. The Figure 3.1 demonstrates the geometry of the technique and kinetics of RHEED diffraction. This image makes use of the Ewald sphere construction to demonstrate the diffraction process. A sphere of radious 1 λ is drawn around the tip of the vec- tor representing the momentum of the incoming electrons (the scattering vector). Where this sphere intersects points in the reciprocal lattice, the Bragg condition for diffraction is satisfied, and a gnomic projection of the diffracted spot is formed on the screen. In conventional X-ray diffraction, the crystal is rotated through a variety of different angles, and many diffraction spots are measured. Then the reciprocal lattice 47 3.1. Introduction is reconstructed from these multiple images, and the structure of the crystal is de- termined. In RHEED images, however, the resultant pattern is quite different. Since the electrons only penetrate a short way into the sample, the diffraction patterns are dominated by CTRs [118]. CTRs are characteristic of diffraction from a 2D layer. In a bulk crystal, the diffraction spots represent a point in the reciprocal lattice. The reciprocal lattice is a Fourier transform of the real space lattice positions, and a single point in a Fourier transform is equivalent to a repeated structure in real space. On the surface of the crystal (at the crystal truncation layer) or at an interface between two materials, the unit cell is replicated along its surface, and in two dimensions, each set of scattering planes would form a single point in reciprocal space. In three dimensions, however, there is a sharp discontinuity in real space, which corresponds to an extended feature in reciprocal lattice space.5 In principle, these CTRs only intersect the Ewald sphere at 1 or 2 points per rod. However, in practice, step edges, islands and general disorder on surfaces broaden the diffraction rods, giving the CTRs a finite width that intersects the Ewald sphere over an extended region and produces the observed rods. While surface X-ray diffraction requires huge X-ray fluxes to see these features, the short electron probe depth in RHEED causes the CTR to dominate the image. Conversely, RHEED can image 3D diffraction spots, but these are much harder to resolve than in X-ray diffraction. One exception to this is rough surfaces where the electron beam passes through features on the surface. In this sort of system, diffraction spots are superimposed on the CTRs. Figure 3.2 shows a RHEED diffraction pattern of a particularly good quality YSZ substrate. This image exhibits most of the features encountered in RHEED diffraction, including the spectral (reflected) electron beam spot, the CTRs and the shadow edge (the electron shadow cast by the edge of the sample). Two features that have not been discussed are the Kikuchi lines and the related surface-wave resonance (SWR). The Kikuchi lines are associated with the diffraction of inelastically scattered electrons from the incoming beam of electrons [124]. These inelastically scattered electrons have an isotropic angular distribution, but still produce diffraction based on the Laue condition. In this case, however, rather than produce sharp diffraction 5For instance, the Fourier transform of a delta function is a constant in Fourier space. For the truncation of a crystal, it is more like the Fourier transform of a Heaviside step function or a Fermi function, which produces an extended distribution of intensity. 48 3.1. Introduction shadow edge specular spot Kikuchi lines CTRs SWR Figure 3.2: A good quality RHEED image of an annealed YSZ (001) surface, with the different RHEED features labelled. These features include the specu- larly reflected central electron spot, 2D diffraction rods (crystal truncation rods), the shadow edge (due to the edge of the sample) and Kikuchi lines (due to inelastically scattered electrons). spots, the diffracted electrons form cone shapes with very large radii. The small solid angle that the detector screen covers causes the Kikuchi cones to appear as lines. Kikuchi lines are a signature of a crystallographically pure sample with few defects, and can be understood in terms of diffraction from a point source of electrons located inside the sample. The increase in intensity where the Kikuchi lines and the CTRs cross is called a SWR [125]. It is important to be aware of the SWRs because these features are often incorrectly labelled as 3D diffraction spots. Kikuchi lines are used quite often in TEM to align the sample [126], and, in principle, with special apparatus and analysis, they can provide full 3D diffraction information from a film [1]. 3.1.1 RHEED as an In Situ Growth Monitoring Tool It is true that the diffraction information one obtains from RHEED is limited to diffraction from one set of crystal planes when used with one stationary sample (the next section presents a method for obtaining all the in-plane diffraction patterns by rotating the sample). However, the utility of RHEED comes from its ability to monitor a single diffraction pattern as a function of time. For instance, the lattice 49 3.1. Introduction Growth Time (minutes) D iff ra ct ed  In te ns ity 0 2 4 6 8 Figure 3.3: RHEED time series for a SrCuO2 growth. The vertical axis is the diffrac- tion pattern and the horizontal axis is time. Each vertical cut represents a single RHEED diffraction pattern integrated along the CTRs. The diffrac- tion pattern before the start of growth is that of a SrTiO3 substrate, and the signal after 1 minute shows the diffraction of the film. The change in reciprocal lattice spacing corresponds to a lattice parameter change from 3.905 Å to 1.760 Å. parameter change can be tracked over the course of the growth. Figure 3.3 shows how the RHEED pattern changes as a function of growth time for a SrCuO2 film grown on top of the (001) surface of a SrTiO3 substrate. Each vertical slice of the image represents a single RHEED diffraction pattern integrated perpendicular to the shadow edge and along the CTRs. The diffracted pattern before 1 minute is that of the substrate, and the pattern after 1 minute is the film. The change in reciprocal lattice spacing corresponds to a lattice parameter change from 3.905 Å to 1.760 Å. For this growth, the instantaneous change of lattice parameter suggests that the film immediately relaxed into its bulk phase; there was no epitaxy. This is not surprising given the extreme difference in the lattice parameters. Another way in which information about the mechanism of growth can be ex- tracted from RHEED is to observe the change in structure of the CTRs with time. It is common to observe some structure in the RHEED CTRs, but this has more to do with the topology of the surface than true bulk diffraction. For a flat surface, the CTRs are true rods, without any structure along their length. If the surface has some structure, the electron beam is no longer probing just the 2D surface, it will also produce some 3D diffraction spots due to transmission through surface features. This creates spotty CTRs, and indicates that the surface is becoming rough. By 50 3.2. RHEED as a Surface Symmetry Tool observing the RHEED diffraction pattern during growth, the growth mechanism can be determined. For instance, a well-prepared substrate will produce a diffraction pat- tern characterized by streaky CTRs, indicating a flat surface. As growth progresses, it quickly becomes apparent in what manner the film is growing. If the diffraction pattern immediately becomes spotty, this indicates a Volmer-Weber/island formation type growth mode. If the diffraction pattern remains streaky and then slowly tran- sitions to spots, this indicates a Stranski-Krastanov/layer-then-island growth mode. Finally, if the diffraction pattern remains streaky, the film is growing in a Frank-van der Merwe/layer-by-layer mode [127]. If the film is growing in a Stranski-Krastanov or Frank-van der Merwe mode, there is the possibility of observing RHEED oscillations, which allows the film growth to be monitored at the level of a single atomic layer. The process that leads to RHEED oscillations is depicted in Figure 3.4. At full mono-layer coverage, the intensity of the reflected spectral spot is at a maximum. As material is deposited onto the surface, the reflected signal intensity drops as the surface roughness increases. Finally, as the surface coverage approaches a full mono-layer, the signal intensity recovers, indicating one full mono-layer has formed on the surface. This technique is very useful in monitoring film thickness, and has been used to prepare thin film heterostructures with a precise number of atomic layers [99–101]. 3.2 RHEED as a Surface Symmetry Tool While RHEED is most often used as a growth monitoring tool, the technique still pro- duces viable diffraction information. It is even possible to extract surface structural and symmetry information from it by combining many different diffraction patterns while rotating the sample around its azimuth. In this section, we will discuss how this was achieved at UBC. The simplest way to determine surface structure with RHEED is to collect the diffraction images of the sample along the high-symmetry direction. Figure 3.5 shows the RHEED images of a quasi-3D 1000 Å EuO film grown on LaAlO3 (001) at 0°, 45°and 26.5° with respect to the LaAlO3 [100] direction. If similar diffraction patterns of the substrate with known spacing are measured and used to calibrate the system, then the spacing for the (100), (110), and (120) planes can be determined from these images. 51 3.2. RHEED as a Surface Symmetry Tool Figure 3.4: An explanation of RHEED oscillations. As the atomically flat surface begins to roughen, the amount of diffuse scattering of the electron beam decreases to a minimum corresponding to maximum surface roughness. As the amount of material deposited begins to approach that required for a full mono-layer, diffuse scattering decreases and the RHEED intensity increases to a maximum corresponding to a full mono-layer deposited. From K. Ploog. Microscopical Structuring of Solids by Molecular Beam Epitaxy—Spatially Resolved Materials Synthesis. Angewandte Chemie International Edition in English, 27(5):593, 1988, used with permission. Imaging the high-symmetry directions of the crystal produces quantitative infor- mation about the lattice spacing and the basic in-plane symmetry of the film, but in certain situations it can be more informative to visualize the symmetry of the crystal directly. Braun et al. [129] have developed a simple method for directly viewing the symmetry of the surface from RHEED diffraction data. They begin by measur- ing many RHEED diffraction patterns as a function of azimuthal angle. They then arrange single horizontal slices of the image (taken through the spectral spot) on top of each other and orient them by their azimuthal angle. Ideally, this produces a LEED-like image of the surface symmetry. Figure 3.6 demonstrates the results of this technique on the surface of a GaAs sample with a β(2× 4) reconstruction. The diffraction pattern shown in Figure 3.6 suffers from low signal-to-noise. This is because Braun et al. [129] are only using a single cut of the RHEED diffraction pattern to build up their image. This approach partially mitigates the problem associated with the RHEED pattern being a gnomic projection of the curved Ewald sphere onto a flat screen. If the entire image is integrated, the diffraction spots become broader 52 3.2. RHEED as a Surface Symmetry Tool (a) (c) (b) Figure 3.5: RHEED images from a quasi-3D EuO film on LaAlO3 at (a) 0° to the LaAlO3 pseudo-cubic [100] direction, (b) 45° and (c) 26.5°. Diffraction from the first Laue zone, with the expected lateral spacing, can be seen in (c). the further they are from the center of the screen. At UBC, we have improved the technique presented by Braun et al. [129] by correcting the distortions in the RHEED pattern due to the projection of the image onto a flat screen. This produces a 3D data set that can be integrated perpendicular to the sample surface. By doing so, we produce much higher signal-to-noise data, 53 3.2. RHEED as a Surface Symmetry Tool Figure 3.6: Azimuthal scan of a GaAs β(2× 4) reconstructed surface. The main az- imuths and the surface unit cell are indicated. From W. Braun, H. Moller, and Y.H. Zhang. Reflection high-energy electron diffraction during sub- strate rotation: a new dimension for in situ characterization. Journal of Vacuum Science and Technology B, 16:1507, 1998, used with permission. without unnecessarily broadening the diffraction spots. While this was primarily a data analysis task, the MBE chamber used for this work did require some modification. Specifically, the sample stage was fitted with a stepper motor controlled by a Thermionics SMC stepper motor controller (the sample stage already incorporated a rotary seal that allowed for continuous rotation). This system was controlled by a LabView program that co-ordinated the sample positioning and the capturing of RHEED images from a UNIQ Vision Systems UP-600CL CCD camera and STAIB RHEED system. One difficulty that we encountered with this method of collecting the RHEED data was that small angular misalignments in the sample would cause huge changes in the position of the RHEED image on the screen. Furthermore, the point on the sample surface at which the best RHEED diffraction pattern was found did not always lie on the axis of rotation. As a result, the data acquisition program had to be constantly paused to allow the operator to re-optimize the RHEED diffraction pattern, which 54 3.3. Conclusions caused the RHEED image position to change. The changing image position also required additional analysis to ensure that the projection correction was performed correctly. The data analysis consisted of four steps. In the first pass through the data, the shadow edge of the RHEED image was found by finding the maximum in the vertical gradient of the background. This de- fined the top of the diffracted image. A second pass identified the horizontal position of the straight through beam by locating the straight through beam (when avail- able) or the spectral spot. This corresponded to the horizontal center of the image. Then, with the position of the image well defined, the RHEED diffraction pattern was projected onto the Ewald sphere defined by the electron beam energy. Finally, the different diffraction patterns were combined, and then integrated along the direction perpendicular to the surface [130]. Some representative data are presented in Figure 3.7. It is clear that all of the images in Figure 3.7 have considerably better signal-to- noise ratio than the diffraction data shown in Figure 3.6, with results comparable to a LEED image. Inset (a) produces a very clean image, while insets (b) and (c) have additional streaky features. The streaky features shown in (b) and (c) are actually Kikuchi lines that were incorporated into the image reconstruction. They are absent from (a) because thick heteroepitaxial films tend to have more defects than their bulk counterparts because of the lattice mismatch between film and substrate. This causes the crystallinity of the film to suffer to the point where Kikuchi diffraction is no longer possible. Insets (b) and (c) are both from annealed single crystals, and as such have a higher degree of crystallinity and so they have stronger Kikuchi lines. To prevent these Kikuchi lines from appearing in the reconstructed data, a retarding field analyzer would need to be incorporated into the RHEED system to prevent the inelastically scattered electrons that form the Kikuchi lines from reaching the phosphor screen. 3.3 Conclusions In this section, I have presented details of the RHEED diffraction technique, explained why it is popular in PVD systems, and provided examples of how it is commonly used to monitor film growth. I then presented a method that makes it possible to image the full symmetry of a substrate’s or film’s surface developed by others, and 55 3.3. Conclusions (a) (b) (c) Figure 3.7: A reciprocal lattice visualization from RHEED data of (a) Au deposited on a mica substrate, (b) an O-terminated ZnO (0001) substrate showing a R30°( √ 3 × √3) reconstruction and (c) a SrTiO3 (001) substrate with the reciprocal lattice spacing indicated by the grid. then explained improvements we have made to the technique at UBC that improve the quality and signal-to-noise of the data. Several surface diffraction patterns were presented, which demonstrated that our technique is capable of producing LEED-like surface symmetry data. 56 Chapter 4 Characterization of an Electron Spectrometer 4.1 Introduction X-ray photoelectron spectroscopy (XPS) is a powerful tool for studying the chemical properties of the surface of materials. With it, we can learn about a material’s elec- tronic structure, chemical composition, surface contaminants, and oxidation state by measuring a combination of core level peak positions for chemical state information and relative peak areas for quantitative analysis. This requires a spectrometer that is well calibrated not just for energy position, but also for absolute intensity. From a film grower’s perspective, XPS is an ideal tool to characterize the properties of thin-film based materials because it is surface sensitive and non-destructive. Perhaps most important, XPS can be performed in situ, allowing the characterization of sen- sitive samples which must be handled completely in vacuum to prevent damage or contamination. For instance, films of transition metal or rare-earth oxides may not maintain their as-grown oxidation state when exposed to atmosphere. XPS measure- ments can even be performed mid-growth, which is important for the characterization of thin-film heterostructures. At the heart of any XPS measurement is an electron spectrometer. The most common electron spectrometer in use today is the hemispherical capacitor analyzer, also called the concentric hemisphere analyzer, shown schematically in Figure 4.1. These spectrometers consist of a lens system which focuses and slows down the in- coming electrons, a hemispherical capacitor analyzer that discriminates the electrons as a function of their kinetic energy, and a detection system that counts these discrim- inated electrons. The spectrometer has a large effect on the data that are collected. This is most often discussed in terms of a transmission function T (Ek, Ep) [131–140], which describes the fraction of the total number of photoelectrons which are detected 57 4.1. Introduction after being photo-emitted from a sample with kinetic energy Ek and which then travel through the hemispheres with energy Ep (the so-called pass energy, to which the electrons have been decelerated by the analyzer lens system). Once the trans- mission function has been experimentally determined, it can be divided out from the measured spectra. However, besides the transmission function, there are other ways spectrometers can affect XPS data; these include the sample-analyzer-photon source geometry, in- ternal analyzer inelastic scattering, and detector nonlinearities. Weng et al. have compared the effectiveness of several methods for measuring the transmission func- tions for both an older model spectrometer as well as a more modern one with a two-dimensional detection system [139, 140]. They show that any method of mea- suring the transmission function fails if there are unaccounted for non-linearities in the detection system. Mannella et al. measured the detector non-linearity for a spec- trometer with a two-dimensional detection system and found deviations from linear behavior as large as 40% [141]. Detector non-linearity is a function of the flux inci- dent on the detector, and it cannot be divided out of the spectrum in the same way the transmission function can be. The internal analyzer inelastic background has also been studied by several authors [142–144] and was shown to provide an additive contribution to the spectrum, which can be significant for certain choices of exper- imental parameters such as the pass energy. Since these two effects can both lead to Ek- and Ep-dependent contributions to the photoemission intensity and cannot be simply divided out from the spectrum, they both must be addressed prior to the characterization of the transmission function. The goal of the work described in this chapter is to measure the probability of an electron getting through the electron analyzer and being measured by the detection system as a function of the spectrometer settings, electron kinetic energy and intensity. This is a critical first step in performing quantitative analysis of XPS data using peak area or peak height analysis. Furthermore, if one wants to apply background subtraction based on physical arguments, like the Tourgaard background, the response of the spectrometer must be corrected [136]. In this chapter, we present a method for determining and removing the most im- portant spectrometer-specific contributions from an XPS spectrum. We deal with the various contributions to the final spectrum in the reverse order in which they are applied to the signal as it moves through the spectrometer. We first investigate the 58 4.2. Experimental Details response of the detection system to applied flux. Secondly, we measure the internal analyzer inelastic background. Finally, after taking into account both of these effects, we determine the transmission function of the analyzer and lens system. We find that the transmission function for this spectrometer is strongly affected by changes in the lens mode, iris setting, and source spot size. This highlights the importance of measuring the transmission function in the exact configuration in which the spec- trometer will be used when performing XPS measurements. We also find that the method used here to remove the transmission function can indicate or exclude the presence of other unaccounted for Ek- and Ep-dependent spectrometer contributions to XPS data. 4.2 Experimental Details We use a PHOIBIOS 150 hemispherical electron analyzer produced by SPECS GmbH. This spectrometer relies on a multi-element lens system to provide different types of imaging through a variety of lens modes. A schematic of the analyzer and detection system is shown in Figure 4.1. There is an iris on the front of the lens system, which is used to define the sharpness of the acceptance area of the spectrometer. In this work, the iris is kept in the fully open position, except when noted (an acceptance angle of roughly 12°). The spectrometer’s detection system consists of a multi-channel plate/phosphor screen and a CCD camera from PCO (PixelFly) to record the two- dimensional spectrum. This spectrometer does not have a mesh between the analyzer and the detection system to electrically separate them. A one-dimensional spectrum is obtained by integrating over the direction perpendicular to the energy dispersion to produce a set of data similar to that which would be measured by a series of channeltron detectors. The medium magnification and medium area lens modes are appropriate for gen- eral purpose XPS and will be used exclusively for this work. The medium magnifica- tion mode magnifies a small portion of the sample, and this magnified area is defined by voltages in the lens system. The medium area mode has a higher transmission than the medium magnification mode, and the sharpness of the acceptance area is defined entirely by the iris. XPS spectra from in situ grown amorphous Au films are used to determine the detector nonlinearity, internal analyzer inelastic scattering, and transmission function. 59 4.2. Experimental Details    CCD Camera MCPPhosphour    Screen Hemispherical    Capacitor Electrostatic Lens          System  X-ray Source X-Ray Photon Sample e- e- Detection   System Electron Analyzer Figure 4.1: A diagram of the experimental setup of an XPS measurement. Electrons are photo-excited by an X-ray source, and those with sufficient kinetic en- ergy are collected by the electrostatic lens. The lens focuses the electrons on the entrance slit of the hemispherical capacitor. The potential between the two concentric hemispheres in the capacitor produces an electrostatic field which discriminates the electrons as a function of kinetic energy as they pass between the hemispheres. A multi-channel plate amplifies the electron signal before it impinges on a phosphor screen and is measured by a CCD camera. Base pressure in the analysis chamber was 10−9 mbar, and in all of the measurements, we observed no sample aging with the metallic samples. The X-ray source is an unmonochromated dual anode SPECS XR-50; Al Kα radiation is used to determine the detector nonlinearity and Mg Kα radiation is used to measure the transmission function from XPS data. All spectra are measured at normal incidence to the sample. The X-ray source, sample and analyzer angle are fixed at the standard value of 54.7o. The spot size of the x-ray source is approximately 1 cm in diameter. The remainder of the transmission function data are taken using an electron gun as the source (SPECS EQ 22) and measuring the electrons reflected off the Au sample surface. 60 4.3. Linearity 4.3 Linearity To measure the detector nonlinearity, one would like to expose the two-dimensional detection system to a wide range of known electron fluxes and measure the detector response. The ideal measurement entails exposing the detection system to a source of electrons which produces a uniform distribution of counts over the entire detector. However, the dual requirement of having a wide count rate range and a flat spectrum are difficult to realize in practice. The solution to this problem is to measure the most intense peaks in an XPS spectrum, which results in different electron fluxes on differ- ent regions of the detection system, as the total photocurrent is changed. Therefore, the response of the different regions of the detection system can be determined as a function of “spectral photocurrent”, which is the fraction of the total photocurrent at a certain kinetic energy. Since we use an X-ray source to generate our photocurrent, we must check that the latter is proportional to applied X-ray power and then quantify the relationship between them. To do this, an isolated sample was prepared and the total photocur- rent was measured with an ammeter placed between sample and ground. The total photocurrent was found to respond slightly nonlinearly to the applied X-ray power. Therefore, the measured photocurrents are used as the basis for all the later mea- surements, as opposed to applied X-ray power, so that when studying the detector’s intensity response any deviation from a linear behavior can be ascribed to the detec- tion system. To measure the intensity response of the detection system, a spectrum of the Au 4f peaks is tracked as a function of total incident photocurrent. The Au 4f peak was used because it is a very intense peak that is also close to the Fermi edge, which reduces the background of inelastically scattered electrons. This means that the detector can be exposed to very low and very high count rates in the same exposure. The measurements are taken with a fixed retarding voltage and a pass energy of 100 eV. Using peaks at different kinetic energies did not change the response of the detection system, but reduced the range of counts we were able to sample. In Figure 4.2 a the XPS intensity vs. spectral photocurrent measured at 1398 eV kinetic energy is presented; this particular energy value, as shown in the inset of Figure 4.2 b, corresponds to the maximum of the Au 4f7/2 peak and is where the highest detector count rate is observed. As indicated by the linear fit also shown 61 4.3. Linearity Au 4f 5/2 7/2  Ek (eV) 13 92 13 94 13 96 13 98 14 00 14 02 50 100 150 200 250 0 D et ec to r C ou nt  R at e   c ou nt pi xe l s ec on d ( ) 50 100 150 200 250 0 D et ec to r C ou nt  R at e   c ou nt pi xe l s ec on d ( ) Spectral Photocurrent (a.u.) 0 2 4 6 8 10 12 (a) (b) Spectral Photocurrent (a.u.) 0 2 4 6 8 10 12 Spectral Photocurrent (a.u.) 0 2 4 6 8 10 12 -2 0 2 4 R es id ua ls  (%  D ev ia tio n) 6 -4 Figure 4.2: (a) Linear fit to the XPS intensity measured on a Au sample as a function of spectral photocurrent at 1398 eV kinetic energy [this corresponds to the maximum of the Au 4f7/2 peak as shown in the inset of (b)]; the percentage deviation from this linear fit is presented in the inset of (a). (b) XPS intensity vs. spectral photocurrent at various kinetic energies along the Au 4f peak structure, as identified by the symbols (see inset). The solid lines represent the different contributions of a 3rd order polynomial fit of the data (red - 1st order, blue - 1st and 2nd orders, green - 1st, 2nd and 3rd orders). in Figure 4.2 a, the detector response is approximately linear over the accessible intensity range. However, the inspection of the percentage difference between data and linear fit (inset of Figure 4.2 a) provides evidence for some systematic deviations, 62 4.4. Internal Analyzer Inelastic Scattering particularly pronounced at low fluxes: while over most of the photocurrent range the difference is within ±3%, at the lowest measured flux the difference is about 6%. These deviations, although small, might become significant when analyzing spectral features extending over a wide range of intensities. To characterize in more detail and remove this systematic deviation from purely linear behavior, in Figure 4.2 b the XPS intensity vs. photocurrent is plotted at 10 different kinetic energies along the Au 4f peak structure, together with the results of a 3rd order polynomial fit of the whole dataset. Note that this approach relies on the assumption that the lowest intensity data behave perfectly linearly; however, if the lowest fluxes exhibit deviations from linearity, this will lead to a substantial overestimate of the nonlinearity at large fluxes. Nevertheless, this particular choice of linear response allows us to compare our results to that of Mannella et al. [141]. For our detection system, we find only a small deviation from linearity, one that is at least four times less strong than the Mannella et al. result. We will use this data to correct for the detection system nonlinearity before proceeding to the subsequent steps of our analysis of the spectrometer response. 4.4 Internal Analyzer Inelastic Scattering Next we will characterize the analyzer contribution to XPS spectra deriving from the internal inelastic scattering. The inelastic scattering taking place inside the analyzer plays a complicating role in the analysis of signals at low pass energy and in measure- ments of the transmission function. There can be many sources of internal inelastic scattering, including electrons scattered inside the lens, secondary electrons being liberated from the internal hemisphere by electrons below the pass energy, electrons scattered from the hemisphere exit slit and residual gas. The largest contribution, however, comes from electrons with energies higher than the pass energy that are scattered off of the outer hemisphere [142]. Additionally, since our two-dimensional detection system incorporates a CCD camera, we will also have a constant back- ground in our spectra associated with the camera dark count rate. This effect is unrelated to the analyzer internal inelastic scattering, but because the dark count rate has a similar effect on the spectra, we will deal with both problems at the same time. In this section we will only discuss the method to remove the analyzer internal inelastic background, but with the understanding that this method will also remove the simpler flat background associated with the CCD camera dark count rate. 63 4.5. Transmission Function The method proposed by Battistoni et al. [144] is used here to measure the internal analyzer inelastic background. It involves lowering the pass energy of the spectrometer (and consequently the transmission) so that any structure in the signal transmitted to the detection system drops below the level of the noise. The only contribution left in this case comes from the electrons that are inelastically scattered inside the analyzer [144]. Since this background signal is independent of the transmis- sion function, once it is measured it can be subtracted from other data sets acquired at different pass energies. This internal analyzer scattering is sample dependent, which has been previously verified by several authors [143, 144], as well as dependent on the spectrometer set-up and sample geometry/orientation; therefore it should be re-measured for every new experiment. The contribution from the internal analyzer inelastic background for the SPECS PHOIBIOS 150 hemispherical analyzer was measured by collecting spectra as the pass energy was lowered. We generally measured the same, peak-free spectra for all pass energies below 5 eV, suggesting that we were no longer measuring signals that originated from electrons passing through the lens with no inelastic collisions. Generally, the intensity of the spectra measured below 5 eV pass energy, the internal analyzer inelastic background, increases as the kinetic energy decreases. In everyday XPS analysis, with this particular spectrometer, the analyzer internal inelastic scat- tering will not be a major contributor to the overall signal. For spectra at 100 eV pass energy, its contribution is less than 1% of the total intensity integrated over kinetic energy, and can be neglected. It can, however, become very important for a spectrum taken at low pass energies; for instance, below 20 eV it contributes more than 20% of the integrated intensity and must be taken into account when measuring the transmission function. 4.5 Transmission Function Once the internal inelastic background and detection system nonlinearities are cor- rected, the transmission function can be measured. We will discuss the transmission function for fixed analyzer transmission or constant analyzer energy mode, since it is the mode most often used in XPS. The photoemission intensity, I(Ek), can be written in a simplified form as [111]: 64 4.5. Transmission Function 100 eV 90 eV 80 eV 70 eV 60 eV 50 eV 40 eV 30 eV 20 eV 2 eV Kinetic Energy (eV) 200 400 600 800 1000 1200 1400 In te ns ity   c ou nt s pi xe l s ec on d ( ) 0 50 100 150 200 250 Figure 4.3: Electron gun spectra taken at different pass energies in medium area mode with an open iris, already corrected for intensity nonlinearity. The small structure at 250 eV kinetic energy is an Au Auger peak. The peak that moves as a function of kinetic energy is due to the transmission function. The 2 eV pass energy scan will be used to further correct for the internal analyzer inelastic background to obtain the processed data shown in Figure 4.4. I(Ek) = AB(EK)T (Ek, Ep), (4.1) where A is a term that contains all of the sample and spectrometer factors that remain constant during a given experiment (e.g., geometry of the apparatus, acceptance area, photon flux, and sample chemical concentration), and B(Ek) represents the sample kinetic-energy-dependent contributions (mean free path of photoelectrons inside the sample and photoionization cross-section). Finally, the transmission function of the electron analyzer and lens system, T (Ek, Ep), is the term in Equation 4.1 we are most interested in determining. Weng et al. have studied several different methods for measuring the transmission function of electron spectrometers [139, 140]. Of the variety of different methods that have been proposed, we have chosen to use a method based on the work of Hemminger et al. [138]. This method entails choosing a functional form for the transmission 65 4.5. Transmission Function function and using experimental data to fit this function (albeit in an unusual way). It offers advantages over other methods for a variety of reasons. Firstly, it does not rely on a priori knowledge of the transmission function of another device, or mode of operation of the same device. Secondly, the form of the transmission function can be derived from first principles by considering the transmission of electrons over the potential barrier created by the retarding field of the analyzer, as well as the trajectories of the electrons in this field. Thirdly, and most importantly, the functional form of the transmission function allows one to mathematically isolate the kinetic energy and pass energy-dependent transmission function from the kinetic energy- dependent spectrum (this will be explained more below). The form of the transmission function is presented in Equation 4.2. If one ignores the exponent n, this equation has the quadratic dependence in pass energy and inverse dependence on kinetic energy that is expected for transmission through a retarding field [145]. We must extend this equation so as to account for the deviations from the ideal behavior observed under realistic operational conditions; to do this, an exponent n is added to Ep Ek term (the inverse of the retard ratio term). n is itself a function of Ep Ek , but no constraints are placed on its functional form so that the model has enough freedom to account for higher order terms of the inverse of the retard ratio as well as other deviations from the ideal behavior of the transmission function: T ∝ Ep ( Ep Ek )n . (4.2) To determine the transmission function, n must be mathematically separated from the A and B(Ek) terms. This is done by substituting Equation 4.2 into Equation 4.1 and taking the natural logarithm of both sides, which yields: ln I Ep = lnA+ lnB(Ek) + n ln Ep Ek . (4.3) As explained in more detail below, to experimentally find n we can now plot ln I Ep , where I is the measured photoemission intensity, versus ln Ep Ek and then subtract off the kinetic energy-dependent offsets lnA+ lnB(Ek). Applying the above method of extracting the transmission function involves mea- 66 4.5. Transmission Function ln EpEk -4 -3 -2 -1 0 ln I E p -1.5 -1.0 -0.5 0.0 ln EpEk -4 -3 -2 -1 0 -1.0 0.0 1.0 ln I E p -2.5 -2.0 Figure 4.4: Intermediate transmission function data for medium area mode, including the pass energy dependence of the sensitivity of the detection system. The detection system nonlinearity, internal analyzer inelastic scattering, and lnA+lnB(Ek) offset have been removed. The inset shows the data before offset removal; each black line identifies a dataset characterized by fixed kinetic energy and varying pass energy. suring several spectra at different pass energies in the spectrometer mode of interest. Representative data taken in the medium area lens mode with a focused electron beam reflected off of a flat Au surface are shown in Figure 4.3. The electron gun was set to 1600 eV kinetic energy; in the range of interest, and except for a small Auger structure at 250 eV, this produces a rather featureless spectrum of inelastically scattered electrons (decreasing in intensity for decreasing kinetic energy). Using the electron gun has the advantage of providing higher average intensity than is normally attainable in an XPS spectrum, allowing for faster data collection for an equiva- lent signal-to-noise value. The nonlinearity corrected data in Figure 4.3 exhibit a pass energy-dependent structure beyond a simple scaling of intensity, which moves to higher kinetic energy as the pass energy increases and stems from the pass energy dependence of the transmission function. In order to extract n, once the data have been corrected for both nonlinearity and internal analyzer inelastic scattering, it is convenient to discuss intermediate data obtained from the measured photoemission intensity by plotting ln I Ep versus ln Ep Ek . As emphasized by the black lines in the inset of Figure 4.4, this yields one curve for 67 4.5. Transmission Function each kinetic energy as a function of the 9 measured pass energies (Ep = 2 eV is only used for correcting the internal analyzer scattering), each curve with a different sample dependent offset lnA+lnB(Ek). Most importantly, one should note that each of these fixed kinetic-energy curves represents a portion of the same n = n(ln Ep Ek ) function, albeit on a different range of ln Ep Ek and with a different offset. To extract n(ln Ep Ek ) the offsets are removed, producing the single set of data shown in the main panel of Figure 4.4. Offset removal was done by a least squares minimization of overlapping data sets. During this stage of the data analysis, the importance of the analyzer internal inelastic background becomes apparent. The offset removal procedure, which removes sample-specific information and produces the single line shown in Figure 4.4, does not work at low pass energies if the internal analyzer inelastic background has not been previously removed from the data. This is because the electrons scattered inside the analyzer and the detection system dark count rate are not accounted for in Equation 4.1, and must be removed from the raw spectrum before the transmission function is extracted. Finally, by using Equation 4.2 in combination with the knowledge of n(ln Ep Ek ) as obtained from the data in Figure 4.4, we can calculate the transmission function for medium area mode at pass energies of 90, 60 and 30 eV. The corresponding curves are shown in Figure 4.5 and, as anticipated, appear to explain the pass energy-dependent structure seen in Figure 4.3. Since this spectrometer does not have a grid to electrically separate the hemi- spherical capacitor and the detection system, there is a pass energy dependence on the sensitivity of the detection system. Here, we have dealt with this change in sen- sitivity by taking it as part of the transmission function, although it is actually an artifact of the detection system and not the analyzer. Using this same procedure, we can also study the effect on the transmission func- tion of changing the spectrometer and source parameters (for instance, the size of the area illuminated by the source). Figure 4.6 contrasts the different transmission functions in medium area mode which result from the use of focused and unfocused electron beams, mimicking a change in the X-ray source spot size, as well as the clos- ing of the iris. By varying the spot size on the sample, a large change occurs in the structure of the transmission function. This is most likely due to off-axis electrons being transmitted differently than on-axis ones. By closing down the iris, the off-axis 68 4.5. Transmission Function Kinetic Energy (eV) 200 400 600 800 1000 1200 1400 T ra ns m is si on  F un ct io n (A rb . U ni ts ) 0 20 40 60 80 100 120 140 160 90 eV 60 eV 30 eV Figure 4.5: Experimentally determined transmission function at 90, 60 and 30 eV pass energies for medium area mode. Small Spot, Iris Open Large Spot, Iris Open Large Spot, Iris 20 Large Spot, Iris 10 T ra ns m is si on  F un ct io n (A rb . U ni ts ) Kinetic Energy (eV) 200 400 600 800 1000 1200 1400 0 5 10 15 20 25 Figure 4.6: Transmission functions determined for the medium area mode with dif- ferent electron spot sizes and iris settings. electrons disappear from the spectrum, and we begin to see some of the features from the focused/small spot size spectrum reappearing (the hump at 800 eV kinetic energy, for instance). These results highlight the importance of measuring the transmission function of the spectrometer in the same configuration in which it will be operated during the experiments. 69 4.5. Transmission Function 100 eV MA 100 eV MM 80 eV MA 60 eV MA 40 eV MA Kinetic Energy (eV) 40 0 60 0 80 0 10 00 12 0020 0 Kinetic Energy (eV) 400 600 800 1000 1200200 In te ns ity  ( a. u. ) 0 5 10 15 20 25 30 35 In te ns ity Figure 4.7: XPS spectra measured on a Au sample at different pass energies in medium area (MA) mode and medium magnification (MM) mode; the data have been corrected for analyzer nonlinearity, elastic scattering, and transmission function. The inset shows the raw data. The small differ- ence around 950 eV produces differences in the peak areas of less than 1%. To verify that our procedure removes the transmission function, we have taken spectra of an Au sample in a variety of modes with different transmission functions. The inset of Figure 4.7 shows data taken at four different pass energies in medium area lens mode and one pass energy in medium magnification lens mode. Each spec- trum has a unique transmission function. The application of our procedure for the removal of nonlinearity, inelastic scattering, and analyzer transmission returns the corrected XPS spectra shown in the main panel of Figure 4.7, which are in remark- able agreement with each other. Data taken in the same lens mode at different pass energies demonstrates that the method is self-consistent (since these data are used to calculate their own transmission function), and the data taken in different lens modes demonstrates that the method produces very good agreement when comparing data taken in lens modes with very different transmission characteristics. Using this method of measuring the transmission function has the advantage of providing obvious clues when there are unaccounted for spectrometer contributions to the data. For instance, the internal analyzer inelastic scattering, if left uncorrected, 70 4.6. Conclusions produces structures in the plots of ln I Ep versus ln Ep Ek , which make it impossible to properly remove the kinetic energy-dependent offsets and find the transmission func- tion. Other spectrometer contributions with a functional dependence on Ep and Ek that is different from that of the transmission function would have a similar impact on the analysis. The ability to remove the transmission function with this method effectively indicates that, in the cases studied here, there are no other significant unaccounted for spectrometer contributions dependent on pass and kinetic energy. Spectra taken on different materials were also found to produce equivalent trans- mission functions, but only when the sample size, geometry and position were repro- duced exactly between runs. This sensitivity of the transmission function to changes in sample geometry highlights the need to measure the transmission function sepa- rately for each sample one would like to quantitatively analyze if the samples cannot be placed in the chamber precisely (for instance, cleaved sample that have a different geometry in every experiment). In situations where the samples have a fixed geome- try and can be precisely placed, the same transmission function could be conceivably used for each new sample. This makes this technique well suited to analyzing thin films. There is no measurable change in peak position since the transmission function varies slowly across the width of a typical core level photoemission peak, so measure- ment of the transmission function should not be necessary for analysis based on peak positions. 4.6 Conclusions We have presented a method for characterizing the response of a hemispherical ana- lyzer for acquiring XPS data. This involves measuring the linearity of the detection system, the strength of the analyzer internal inelastic scattering, and the transmis- sion function of the analyzer and lens system. In our particular experimental set-up, we have found that the nonlinearity of the detection system is of the order of a few percent and that contributions from the internal inelastic scattering are negligible at pass energies commonly used in XPS (accounting for less than 1% of the total intensity at 100 eV pass energy). Finally, we have measured the transmission func- tion of the analyzer and lens system and have shown the importance of measuring the transmission function for the specific settings that will be used under operational conditions. We have also found that the presented method can be used to highlight 71 4.6. Conclusions the presence, or lack, of other pass energy-dependent and kinetic energy-dependent spectrometer contributions to the measured XPS data. While this method shows that the transmission function is very sensitive to the size and position of the sample, it is possible to use it when studying films grown with MBE because the substrate size and positioning can be controlled very precisely. 72 Chapter 5 Calculated Electronic Structure of the Europium Pnictide Family 5.1 Introduction As was discussed in the introduction, the use of EuO in practical device applications has been limited by poor sample quality and a low Curie temperature. An addi- tional property that would be beneficial for creating active devices like transistors (as opposed to passive spin filters) is the ability to incorporate complementary dopants into the material. In conventional semiconductor physics, both hole and electron dopants are required to produce active devices capable of amplifying a signal. While demonstrating the possibility of both hole and electron doping is interesting for future device applications, the current focus is on increasing the Tc of these materials. Al- though there have been many studies of electron doping of EuO through substitution of the Eu site, hole doping and substitution on the ligand oxygen site have not been investigated [40]. There are several ways that hole doping of EuO could contribute to an increase in Tc. The first is an increase in conductivity and the associated indirect ferromagnetic exchange [146, 147]. The second mechanism comes from the intrinsic spin polarization of unfilled p-orbitals. This is an active area of study, mostly focused on materials containing unfilled N, C, or O states, and no unfilled d- or f-shells [86]. However, it is reasonable to expect that the same mechanism that produces magnetic coupling in light atoms like N, O, and C would contribute to the exchange in EuO. Both of these results point towards oxygen replacement as a viable route to increasing the Curie temperature of a ferromagnetic semiconductor like EuO. In this chapter, we explore through theoretical calculations the possibility of hole doping EuO through substitution of oxygen with various pnictogens (nitrogen, phos- phorous, and arsenic, in this work). To determine the electronic structure of nitrogen-, 73 5.2. Methods phosphorous-, and arsenic-doped EuO, we begin by performing LSDA+U super-cell calculations. We also calculate the total energies of the substituted and the phase- separated cases to determine which systems will likely hole dope rather than phase- separate, to identify the best candidate for further experimental work. Finally, we determine where the holes actually reside spatially in the most promising material to see whether holes reside on the ligand rather than on the Eu sites. 5.2 Methods The DFT calculations were performed using the WIEN2k software package [3], which is based on the full-potential (linearized) augmented plane wave + local-orbital basis set. To account for exchange and correlation effects, the Generalized Gradient Ap- proximation (GGA) was used [148]. Only ferromagnetic configurations were consid- ered in this study. Since the LSDA or GGA methods alone will produce an incorrect metallic DOS for EuO, the LSDA+U method was used to account for strong cor- relations in the europium 4f shell [149]. The on-site Coulomb repulsion, U, for the europium 4f orbital was chosen to be 8.3 eV and the exchange parameter, Jh, was chosen to be 0.77 eV, based on earlier theoretical and experimental work [61, 150]. The lattice parameter of the EuO unit cell was set to 5.144 Å for all the calculations. To verify that our choice of parameters produces a reasonable solution, the DOS for bulk EuO was calculated and compared with previous experimental and theoretical works. The result, shown in Figure 5.1, reproduced the expected structure, with a gap of 0.7 eV that matches previous calculations and experiments [61, 71]. To perform doping studies, a super-cell made up of a 2 × 2 × 2 grid of rock salt EuO unit cells was used. One of the oxygen sites was substituted for a pnictogen, yielding a doping of 3.125%. The super-cell structure is shown in Figure 5.2, with the red, blue, and green sites representing oxygen, europium, and nitrogen, respectively. The bulk lattice parameter of EuO was maintained for these growths; the systems were allowed to relax around the dopant. The super-cell technique is useful for doping studies like this, but it greatly in- creases the size of the basis set needed for the calculation. To perform these calcu- lations in a reasonable time, the DFTLAP cluster maintained by Dr. Ilya Elfimov was used. Another factor to consider when performing a dopant study using a super- cell calculation is that the location of the dopant site is fixed in the larger unit cell. 74 5.2. Methods  0  1  2  3 -5 -4 -3 -2 -1  0  1  2  3 D O S Energy (eV)   Total DOS Spin Up Spin Down -3  -2  -1 Total Eu DOS Total O DOS  0.7 eV Figure 5.1: EuO DOS calculated with the parameters given in the Methods section. The bottom right inset shows the structure of the EuO unit cell used in this calculation, with red and blue representing oxygen and europium, respectively. This implies an assumption that the doping is evenly spread throughout the mate- rial. In reality, clustering or phase-separation may occur. We address the possibility of phase-separation later in the chapter. Figure 5.2: The bulk structure of the EuO super-cell used to study the electronic structure of the substituted material. The red, blue, and green sites represent oxygen, europium, and the pnictogen, respectively. 75 5.2. M eth o d s D O S Energy (eV) (c)  Total DOS  Eu d DOS  Eu f DOS  As 4p DOS Spin Up Spin Down (b)  Total DOS  Eu d DOS  Eu f DOS  P 3p DOS Spin Up Spin Down (a)  Total DOS  Eu d DOS  Eu f DOS  N 2p DOS Spin Up Spin Down-40 -20 0 20 40 -4 -2 0 2 -4 -2 0 2 -4 -2 0 2 Figure 5.3: DOS for EuO with 3.125% (a) nitrogen, (b) phosphorous, and (c) arsenic substituted for oxygen. The total, Eu d-state, Eu f-state, and pnictide p-state DOSs are given by the black, red, green, and blue lines, respectively. The top side of the graphs shows the spin up states, and the bottom side shows the spin down states. 76 5.3. Results and Discussion 5.3 Results and Discussion Figure 5.3 shows the DOS for EuO1-xPnx, x = 0.03125, where Pn = N, P, and As. In each instance, we find a polarized DOS at the Fermi level, which consists of hybridized europium 4f and pnictide p-states. There is also a decrease in p-state weight at the Fermi level as the atomic number of the pnictide element increases, probably due to the higher binding energy of the unhybridized p-levels. While this is suggestive of hole doping, the distribution of charge in the unit cell above Ef will ultimately determine whether the hole resides on the ligand or Eu site. Before determining the spatial distribution of the states above Ef , however, one should determine whether these materials can even be synthesized. To ascertain whether these materials are stable, we have to determine whether the material prefers to substitute the pnictogen for an oxygen, or is more likely to separate and produce two different materials. To accomplish this, we compared the ground state energies of the pnictogen substituted materials with the ground state energies of a mixture of EuO and EuN, EuP, or EuAs. This type of calculation takes into account the ionic radious of the various elements to determine if the final material will be stable. This is a very rough estimate, and the results should be treated as such. In reality, the free energy and entropy of the system will be what determine whether the system phase separates. However, our DFT calculations are only valid at 0K temperature, and cannot include the finite temperature effects that would drive the system to phase separate. The lattice parameters used for the EuN, EuP, and EuAs structures matched their experimentally measured values (5.020 Å for EuN, 5.756 Å for EuP, and 6.076 Å for EuAs [151]). It should be noted that EuAs actually adopts the N2O2 crystal structure, which is a distortion of the NiAs structure, due to anion-anion pairs [152]. Following Horne et al. [153], we use the EuAs material in our calculations. The results are shown in Table 5.1 and indicate that, of the three pnictogens studied, only the nitrogen is likely to be incorporated into the material (the substituted material has a lower ground state energy than the phase separated material). Since we do not relax the super-cell in our calculations, the ground state energy of the phase separated case will be slightly higher than it would be otherwise, which causes the values in Table 5.1 to be higher as well. We do not expect this to materially affect our result, however, since the P and As cases would stay phase separated with a decrease in the phase separated ground state energy, and we don’t expect the N super-cell to relax 77 5.3. Results and Discussion appreciably because the bulk lattice parameters of EuO and EuN are so similar. Having eliminated phosphorous and arsenic as potential dopants, we can now focus our calculation of the above Ef electron density on the nitrogen case. The distribution of charge above Ef is important because it will determine whether the pnictide impurity will enhance or destroy ferromagnetism. There are three possible ways for the above Ef charge to be arranged: all the weight could be on the N site, the weight could be distributed evenly throughout the crystal, or the weight could reside primarily on the Eu sites. The first instance would be interesting because this is the scenario described by Elfimov et al. [91], where holes localized on substituted nitrogen sites potentially lead to ferromagnetic exchange, even in a non-magnetic oxide. However, the DOSs in Figure 5.3 all have a large amount of Eu 4f weight just above Ef , which makes this possibility unlikely. The second possibility, that the above Ef weight corresponds to molecular orbitals that extend through the material, is interesting because this would facilitate an indirect exchange, which might enhance ferromagnetism. The final possibility is that the majority of the above Ef weight is localized to the Eu 4f states, which implies that the Eu transfers an electron to the pnictide site, producing Eu3+, rather than introducing holes in the material. This is not a desirable result if the only goal is to produce devices based on complementary dopants. However, this result would be interesting because it would represent the first mixed-valent Eu system (over-oxidized EuO1-δ is actually a phase separated mix of EuO and Eu2O3/Eu3O4). Energy Difference/ Super-Cell (eV) Nitrogen -3.8 Phosphorous 0.80 Arsenic 0.88 Table 5.1: The different ground state energies for the substituted and phase separated options for EuO with 3.125% of the oxygen replaced with nitrogen, phos- phorous, or arsenic. The energy difference indicates which option is more stable (negative values indicate substitution while positive values indicate phase-separation). To determine the above Ef charge density, the window of energy considered in the DFT calculation was limited to a range from 0 eV to 0.5 eV. This energy region contains all of the N 2p and Eu 4f above Ef weight, but does not extend high enough 78 5.3. Results and Discussion to include the Eu 5d-states starting at about 0.7 eV. The result of this calculation is visualized in Figure 5.4. This represents a single value of the charge density (roughly 10% of the maximum value), and shows a linear combination of N 2p states forming a spherical charge density around the central nitrogen site, and nearest neighbour Eu orbitals. It is interesting to note that the Eu hole densities occupies a symmetric a1g-like molecular orbital formed by Eu 4f-states mixed with N 2p-states. Figure 5.4 seems to suggest that the hole introduced by the N is located on both the nitrogen and nearest neighbour europium sites, rather than being distributed throughout the unit cell, but this is impossible to confirm using the single isosurface in panel (a). Panel (b) shows the contour plot of a 2D slice of the charge density around the central nitrogen. This perspective shows that a significant part of the charge density is situated on the adjacent Eu sites. To determine how the charge is distributed, the data shown in Figure 5.4, panel (a), was transformed into spherical co-ordinates with the central nitrogen site at the origin to produce a radial charge density and an accumulated charge, which are shown in Figure 5.5. Note that the accumulated charge does not quite reach the expected value of one electron per unit cell in this figure. This is because the integrated region only covered the volume of a sphere that fits inside the unit cell (there would be no overlap between this sphere and a sphere centered around the nitrogen in an adjacent unit cell). This left a small amount of electronic density outside the region of integration. As a consistency check, an integral over the entire unit cell volume produced the expected one electron per unit cell density. The large amount of charge density situated on the nearest neighbour europium sites is a strong indication that charge transfer from europium to nitrogen is occurring in this system. This transfer of electrons from europium to nitrogen (Eu2+ to Eu3+) would most likely manifest as a drop in the Curie temperature if it were due to over-oxidation of EuO [51]. The EuO1-xNx case is slightly different than that of over- oxidized EuO, however. When there is an excess of oxygen, the EuO phase separates to form Eu2O3 and Eu3O4. In this case, the material has not phase separated; rather, the Eu3+ is integrated into the lattice, forming a mixed valent system. This suggests the possibility of a double exchange mechanism in EuO1-xNx. 79 5.3. Results and Discussion 0 1 2 -1 -2 -2 -1 0 1 2 (Å) (Å ) (a) (b) Figure 5.4: The spatial distribution of the DOS in a window just above Ef for EuO1-xNx, with x = 3.125%. In panel (a), the central sphere corresponds to the superposition of several N p-states, while the nearest neighbour density is associated with Eu 4f orbitals. The Eu orbitals with an ap- preciable density are the ones with nodes oriented closest to the central nitrogen. Panel (b) shows a contour plot of the 2D density correspond- ing to a cut through the central nitrogen and four nearest neighbour europium. 80 5.4. Conclusions 0 20 40 60 10 30 50 Distance From Nitrogen (Å) C ha rg e D en si ty  (e /Å ) 0 0.2 0.4 0.6 0.8 1.0 C harge (e) 1 2 3 4 5 70 Figure 5.5: The radial distribution of above Ef hole density (blue line) and the charge (red line) in EuO1-xNx around the central N site . The majority of the charge (70%) sits on the nearest neighbour europium sites, while only about 5% sits on the nitrogen site. The remainder of the density sits outside the region of integration on next nearest neighbour oxygen and europium sites. 5.4 Conclusions In summary, substituting oxygen for a pnictogen species in EuO is most likely not a viable method for introducing holes into EuO. In terms of the structural stability of the material, only nitrogen substitution appeared to be a viable option. Phosphorous and arsenic were more likely to phase separate into different materials. The distri- bution of charge in the unit cell of EuO1-xNx points toward charge transfer from the nearest neighbour europium sites as being the most likely scenario. However, unlike in over-oxidized EuO, the system does not appear to phase separate into materials containing Eu2+ and Eu3+; instead, it may form a mixed-valent system, which sug- gests the possibility of double exchange. This mixed valency could be confirmed with an XPS study of this material. 81 Chapter 6 Absorbate-Controlled Nitrogen Substitution in EuO Thin Films 6.1 Introduction The calculations in the previous chapter make a strong case for proceeding with an experimental study of EuO1-xNx. Even without these theoretical calculations as mo- tivation, combining EuO and EuN would be an interesting project because EuN is a borderline half-metallic ferromagnet. At first glance this might appear surprising, due to the non-magnetic, J = 0 character of its Eu3+ f 6 ions (J in this context refers to total angular momentum, and not the exchange parameter)(this convention will be used for the remainder of the thesis). However, recent band structure calculations seem to indicate that the J = 0 state can be spin polarized, giving rise to ferromag- netism with an unoccupied f band located close to – or even right at – the chemical potential [153–155]. This would lead to the realization of half-metallic ferromagnetic behaviour. Ruck et al. have investigated this possibility in EuN films grown by molecular beam epitaxy (MBE). However, by studying the magnetic properties using X-ray magnetic circular dichroism, they found no evidence for a ferromagnetic state [156]. Their experiment did determine that there was a strong Eu2+ driven polariza- tion of Eu3+ ions, suggesting that at sufficient Eu2+ concentration, EuN may exhibit DMS-like behaviour. Extrapolating from the suggestion made by Ruck et al. (that small amounts of Eu2+ could lead to DMS-like behaviour), we decided to embed small amounts of N into EuO. The polarizing effect of the EuO lattice on non-magnetic Eu3+ f 6 due to nitrogen may lead to the formation of a spin-polarized impurity level, whose filling is directly controlled by the nitrogen concentration. As a result of the narrow bandwidth of the f -derived band, these carriers would be characterized by a large effective mass. In this chapter, we grow thin films of EuO1-xNx in an attempt to realize half- 82 6.2. Growth of EuO1-xNx metallic ferromagnetic behavior associated with nominally non-magnetic Eu3+ ions and the first mixed-valent Eu system. To do this, we develop a novel technique for introducing nitrogen into binary oxide films. After outlining the details of the technique, we demonstrate that our method allows us to control the doping level while producing high-quality films. We also examine the electronic and magnetic properties of the films to determine how the nitrogen affects the properties of EuO. 6.2 Growth of EuO1-xNx Since EuO1-xNx has not been synthesized in thin film form before, we must first determine whether such a system can be grown (two references describe work on a very similar material, but synthesized in bulk form with many Eu metal inclusions [157, 158]). It is widely known that it is difficult to grow pure EuO thin films. EuO is extremely unstable in air, and even in a UHV environment – if it is grown with too much supply of oxygen – it will form Eu2O3 and/or Eu3O4 phases. On the other hand, if it is grown with too little supply of oxygen, Eu metal clusters may form [105]. Both of these situations will deteriorate the extraordinary properties of EuO. These problems can be overcome to successfully grow high-quality EuO thin films via the MBE distillation method, which involves evaporating europium metal onto a hot substrate under a low pressure of oxygen [25, 51, 103, 104]. The low oxygen pressure prevents the formation of Eu2O3 and/or Eu3O4, while any unreacted metal is re-evaporated from the hot substrate surface, thus maintaining the well-proven europium distillation growth technique [51, 105, 159]. This is the approach we have chosen to grow our EuO1-xNx films; however, instead of pure oxygen, we use NO gas, and during the course of the work we discover that the amount of oxygen to be replaced by nitrogen can be tuned. The choice of NO gas both as the oxidizer and as a means of substituting nitrogen in EuO was inspired by earlier NO2-assisted epitaxial growth of Fe3O4, Fe1−δO, and CrO [161, 162]. There, NO2 gas was used because it is a very efficient oxidizer; as a side effect it was found that, in addition to the desired amount of oxygen, nitrogen was also being incorporated into the films. Since the nitrogen concentration in the films was decreasing with increasing NO2 pressure, it was hypothesized that the probability of nitrogen substitution was higher when there was insufficient oxygen to form a stoichiometric material. Since the conditions in MBE distillation are always oxygen 83 6.2. Growth of EuO1-xNx  400 399 398 397 Pressure (10-10 Torr) N itr og en  C on ce nt ra tio n (% ) Binding Energy (eV) In te ns ity 2 6 10 14 18 1 2 3 4 5 6  Figure 6.1: Increase in nitrogen concentration in the EuO1-xNx films as a function of NO partial pressure. These concentrations were measured using the ra- tio of the background-subtracted nitrogen and oxygen 1s core level areas in XPS, corrected for their corresponding photo-ionization cross-sections. The inset shows the increase in the nitrogen 1s core level peak with in- creasing NO pressure, as measured by XPS. The red line is a guide to the eye, based on a fit to the Langmuir adsorption equation [160]. deficient by design, this technique can be used as a general approach to incorporate nitrogen into oxide films. For the case of EuO, since NO2 is far too aggressive an oxidizer, we chose NO gas instead, following the work on nitrogen-substituted SrO by Elfimov et al. [91]. In that work, by keeping the rate of metal evaporation constant and changing the background pressure of NO gas in the UHV growth chamber, the amount of nitrogen taken up by the film could be tuned. The EuO1-xNx samples were grown on yttria stabilized zirconia (YSZ) substrates, whose 5.142 Å lattice constant is very close to that of bulk EuO, 5.144 Å. These substrates, purchased from SurfaceNet GmbH, have a surface normal in the [001] di- rection. The substrates were annealed in the growth chamber for two hours at 600oC in 1× 10−6 Torr of oxygen (the chamber base pressure is in the 10−10 Torr range). This procedure removes surface contaminants, re-oxygenates the substrate, and gives defects on the surface enough mobility to aggregate into step edges, producing an atomically flat surface. After annealing, the substrate temperature was set to 450oC. Europium metal was evaporated from a Knudsen cell at a rate of 8.2 Å per second. 84 6.2. Growth of EuO1-xNx In te ns ity  (A rb . U ni ts ) 4003002001000 Time (s)  2-3 %  16 % Figure 6.2: RHEED spot intensity oscillations for 2-3 % and 16% nitrogen concen- tration, respectively. The inset shows a LEED diffraction pattern for a 13% N-substituted sample. The diffraction pattern is consistent with a (001) EuO surface. The initial three oscillations in the 16% nitrogen substitution case are consistent with a layer-by-layer growth process en- abled by oxygen being donated to the film by the YSZ substrate. The 2-3 % substitution film additionally exhibits RHEED oscillations that con- tinue well past the thickness where oxygen donation from the substrate could have an effect, indicating that these prolonged oscillations are due to sustained layer-by-layer growth of EuO1-xNx. The LEED diffraction pattern indicates that even after 100 minutes of growth, the film remains crystalline. The rate was measured with a quartz crystal monitor. The chamber was backfilled with NO gas through a precision leak valve and the NO partial pressure was mea- sured with an MKS Instruments residual gas analyzer. While Eu evaporation rate and substrate temperature were kept constant for all growths, the amount of NO gas used to oxidize and dope the films was adjusted between growths. The range of gas pressures was between 1× 10−10 and 5× 10−10 Torr. The choice of substrate temper- ature, evaporation rate, and NO pressure range determine whether the conditions are favourable for MBE distillation; approximate starting parameters were chosen based on earlier work [51, 163]. Figure 6.1 demonstrates how the amount of nitrogen incorporated into the EuO1-xNx 85 6.2. Growth of EuO1-xNx films varies by changing the background pressure of the NO gas. The concentration of substituted nitrogen was estimated from the photo-ionization cross-section [164] corrected ratio of nitrogen and oxygen 1s core level peaks measured by X-ray pho- toemission spectroscopy (XPS) [162]. The XPS measurements were performed in situ with monochromatized AlKα radiation and a VSW 150 electron analyzer. As shown in the inset of Figure 6.1, the nitrogen 1s peak grows with the NO pressure (the spectra were normalized to the oxygen 1s peak area, not shown). We note that the non-linear increase of nitrogen concentration in the EuO1-xNx films with increasing NO pressure is very different from the previously reported linear decrease with increasing gas pressure observed in the NO2-assisted growth of Fe3O4, Fe1−δO and CrO [161, 162]. In these latter cases, the metal-to-NO2 gas flux ratio was approximately 1, setting the growth far outside of the MBE distillation regime used here. One could then envision that the NO2 oxidizes first the available Fe or Cr, leav- ing behind an equal number of NO molecules that can react with the remaining metal; since the number of these remaining metal sites is inversely proportional to the initial NO2 pressure, one obtains the observed linear decrease in nitrogen concentration with increasing NO2 pressure. For the present case of NO-assisted growth of EuO, we can conclude that the increase of the N-to-O ratio with increasing NO pressure stems specifically from the MBE distillation conditions, although further research will be needed for the accurate quantitative modeling of the adsorption kinetics under these conditions.6 In addition to providing a method for introducing nitrogen into EuO films, MBE distillation with NO gas also produces films with excellent crystalline quality. All of the films exhibited low-energy electron diffraction (LEED) and reflection high- energy electron diffraction (RHEED) patterns, with well-ordered diffraction spots after growth. The films also exhibited layer-by-layer growth under certain conditions, as indicated by the presence of typical RHEED oscillations (see Figure 6.2 for rep- resentative RHEED data from 2-3% and 16% nitrogen-substituted EuO1-xNx, and 6One concern that should be addressed in a future study is the relative importance of hydrogen inclusion in the films. None of our measurements were sensitive to hydrogen contamination, but the RGA indicates that it is the primary background gas present during growth (the Eu metal Knudsen cell releases a large amount of hydrogen when heated, due in part to the processing needed to purify the metal, but also due to contamination by the hydrocarbon solvents used to remove the protective coating of oil from the metal before introducing it to the chamber). Dr. Rob Kiefl has suggested a future infrared spectroscopy study to determine if there are any hydroxyl bonds present in the material, which would indicate unwanted hydrogen contamination. 86 6.2. Growth of EuO1-xNx      In te ns ity  (N or m al iz ed  C ou nt s) Binding Energy (eV) 2-3 7 13 16 20 Eu2+ 4f 7 O 2pEu3+ 4f 6 15 10 5 0 0 4 8 6 2 N Concentration (%) Figure 6.3: Valence band XPS spectra of EuO1-xNx as a function of nitrogen con- centration. The increase of spectral intensity in the Eu3+ peak, and the corresponding decrease in Eu2+ spectral weight, suggest that nitrogen is being incorporated in its 3− oxidation state, in agreement with previous calculations (Chaper 5). The ratio of the measured peak area of the Eu3+ to the total Eu peak areas agree with the N concentration measured by core level XPS (Figure 6.1). The XPS spectra were normalized to the total number of counts. crystalline LEED data from a 13% substituted sample). The LEED diffraction pat- tern is consistent with the [001] direction of EuO. The 16% substitution level does exhibit three RHEED oscillations only at the beginning of growth, but they quickly disappear. This behavior is seen for all films, regardless of the substitution level; how- ever, the lower pressure growths exhibit RHEED oscillations that continue for several tens of monolayers. The difference between high- and low-pressure regimes is most likely due to a too high concentration of defects in the heavily nitrogen-substituted films; these defects act as nucleation sites, initiating three-dimensional island growth and destroying the two-dimensional, layer-by-layer growth. Initially, however, the growth is primarily controlled by oxygen being donated to the film by the YSZ sub- strate, rather then by the NO gas [51]; this allows the observation of layer-by-layer growth independent of the NO gas pressure. RHEED oscillations that continue be- yond 4-5 monolayers cannot be due to the substrate donating oxygen, because the film is at that point too thick for oxygen from the substrate to diffuse to the surface [51]. Therefore, these additional oscillations must originate from EuO1-xNx growing 87 6.2. Growth of EuO1-xNx in a truly layer-by-layer mode, as in the case of the 2-3% substitution level shown in Figure 6.2. Obtaining a reliable measure of the thickness of these films was not possible. An attempt was made to measure the films’ thickness using X-ray reflectivity (XRR), but no reliable fits could be made to the experimental data, and hence the thickness could not be determined. This was most likely because the small surface area of the samples produced a low signal relative to the noise, but could also have been due to a high degree of surface roughness, either on the film itself or in the capping layer of aluminum. Inferring film thickness from the amount of Eu deposited is not appropri- ate in this case either, since the deposition rate for MBE distillation is determined by a non-linear (and unknown) relationship between the evaporation rate, the substrate temperature, and the NO gas pressure. In principle, the thickness could be extrapo- lated from the RHEED oscillation period and the total growth time. However, this approach would only work for the samples with the lowest N concentrations, as these were the only ones that exhibited sustained RHEED oscillations. Furthermore, pre- vious work by Sutarto et al. showed that the thicknesses derived from the RHEED oscillations do not match the thicknesses from XRR [51, 55]. The only method of approximately determining the film thickness that was avail- able to us was to compare our EuO1-xNx growths to the previous growths of EuO using MBE distillation, by Sutarto et al. [51, 55]. Since their recipes for EuO were used as the basis for our EuO1-xNx growths, and since the two types of films were grown in the same chamber, the growth conditions were equivelant and we are able to use thickness versus pressure data presented in their paper to extract our film thicknesses [51]. We do have to assume that our thicknesses are exactly half, since NO gas has half as much atomic oxygen available as O2. Comparing our results to theirs yields thicknesses ranging from 70 Å up to 300 Å over the entire doping range studied, but we have no way to independently confirm that this comparison of EuO with EuO1-xNx is valid. The thicknesses derived by this method are used in the next section to yield magnetization measurements that produce the expected 7 µB magnetic moment, at least for the thinnest samples (70 Å). At higher levels of nitro- gen substitution, the magnetic moment drops, but whether this is due to a drop in magnetization or to inaccurate thickness measurement is unclear. For future growths, larger substrates should be used to increase the signal in the X-ray reflectivity mea- surements. If thickness measurements are still not possible, the next step would be to 88 6.3. Electronic Structure and Magnetic Properties of EuO1-xNx 8 6 4 2 0 M ag ne tiz at io n (µ B /u ni t c el l) 250200150100500 Temperature (K) N Concentration (%)  2-3  13 Figure 6.4: Magnetization curves for two different EuO1-xNx samples at 10 Gauss. The transition temperature remains unchanged from the EuO value of 69-70K, even at high levels of nitrogen substitution. grow thinner films. This might decrease the amount of surface roughness of the films (the progression from 2D to 3D RHEED diffraction patterns occurs continuously; this would suggest that thinner films would have smoother surfaces).. 6.3 Electronic Structure and Magnetic Properties of EuO1-xNx The results discussed above demonstrate that MBE distillation with NO gas is a suit- able approach for producing high-crystallinity, epitaxial EuO1-xNx films, with tune- able nitrogen-oxygen substitution. To establish the oxidation state of the substituted nitrogen, and to provide a more detailed characterization of the films’ electronic structure, we performed XPS valence band measurements in situ (Figure 6.3). The spectra evolution indicates that as the nitrogen concentration increases, so does the Eu3+ spectral weight, while the Eu2+ intensity decreases. We also note that the oxy- gen 2p intensity does not increase with increasing NO pressure, establishing that the increase of Eu3+ spectral weight is due to the substitution of O2− with N3−, thus with nitrogen being incorporated in its 3- oxidation state. Furthermore, the increase 89 6.3. Electronic Structure and Magnetic Properties of EuO1-xNx in peak area of the Eu3+ peak relative to the total Eu peak area agrees well with the nitrogen concentration measured by core level XPS (Figure 6.1). These results are consistent with the transfer of charge from the europium sites to the nitrogen, in agreement with our previous calculations (Chapter 5) and are also very similar to the spectra of over-oxidized Eu1−δO films [51, 55]. Whereas these XPS results match those from over-oxidized Eu1−δO films, the elec- tronic/magnetic properties of EuO1-xNx are remarkably different. In particular, at variance with the behavior observed for Eu1−δO, where small amounts of Eu3+ lead to a drastic suppression of the ferromagnetism [51], increasing N concentration in EuO1-xNx still produces the expected line shape, suggesting an appreciable preserva- tion of the ferromagnetic phase. Important is that the Tc of about 69 K, as in pure EuO, is observed over a wide range of nitrogen substitution. These magnetization measurements were performed ex situ with a Quantum Designs MPMS-XL7 SQUID magnetometer in a 10 Gauss field (after capping the samples with a thick aluminum layer to protect them from further oxidation when removed from the MBE system), and are shown here in Figure 6.4. For these measurements, the surface of the sample was oriented perpendicular to the field. The increasing amount of nitrogen in the film does appear to decrease the sat- uration magnetization, which seems to suggest that the increasing concentration of Eu3+ is diluting the magnetic Eu2+. However, it is interesting to note that the mag- netization does not drop as quickly as one would expect for over-oxidized Eu1−δO [51]. Furthermore, this drop in overall magnetization is not supported by the only other work dealing with nitrogen-substituted EuO; in that case, the magnetization remained roughly constant, and even increased at the highest nitrogen substitution levels [157, 158]. It is possible that this drop in saturation magnetization is due to an overestimate of the film thickness, arising from the different kinetics of EuO1-xNx growth relative to EuO growth (which we used as a proxy to estimate film thickness). If the film thickness followed a trend similar to that shown for concentration in Figure 6.1, the resultant thickness would be less and the magnetic moment higher. From this data, it is impossible to determine which scenario is the cause of the drop in the overall magnetic moment: inaccurate thickness, or an intrinsic drop in magnetization due to the inclusion of nitrogen. Further research into the growth kinetics of this system is recommended to determine the true origin of the magnetization drop. It is unclear from our data whether the drop in magnetization seen in Figure 6.4 is 90 6.4. Conclusions due to the nitrogen substituting oxygen or if a phase-separated mixture of EuN and EuO is created. We can immediately eliminate the situation where small domains of EuN are evenly distributed throughout the film. Similar to over-oxidized EuO, these small non-magnetic domains spread evenly throughout the crystal would interfere with the magnetic exchange7. Since we do not see the same drastic drop in Tc and magnetization happening here that we would expect for over-oxidized EuO, the only two remaining possibilities are the formation of EuO1-xNx or that the EuN aggre- gates into large domains. To decide between these two possibilities, magnetic force microscopy or scanning SQUID microscopy could be used to identify the individual domains. 6.4 Conclusions In conclusion, by substituting nitrogen for oxygen in EuO, we have made a Eu2+/Eu3+ system that remains ferromagnetic despite the inclusion of Eu3+ 4f 6 sites, something not possible in the more extensively studied Eu1−δO. In addition, EuO1-xNx is also the ideal system for the specific purpose of studying the hopping between the f 7 (J = 7/2) and f 6 (J = 0) levels located in proximity of the chemical potential. In this respect, EuO1-xNx is also better than EuxGd1−xN – in which such f 6/f 7 mixing is also achieved – since in the latter case the 4f 7 levels of Eu and Gd are split in energy by several eVs [163], preventing an efficient hopping within the f band. More generally, the MBE NO-assisted distillation technique described here provides a means to tune the amount of substitution of nitrogen for oxygen in other binary oxides. Two materials of current interest in the field of p-state magnetism that could be grown with this technique are N-doped ZnO and SrO (SrO is dealt with in the next chapter). We recommend further research into the growth kinetics of this system to help explain the non-linear dependence of the nitrogen concentration on the NO gas pressure and to determine how the film thickness depends on the NO gas pressure. We also recommend a scanning magnetization study of these films to determine if they are phase-separating, and if they are not, a future resonant inelastic X-ray scattering (REIXS) to study the magnetic order of these films. 7This dilution induced loss of ferromagnetism is seen in another europium chalcogenide Eu1-xSrxS. In this system, the dilution of the magnetic Eu with non-magnetic Sr causes a gradual drop in Tc up to a critical concentration where the ferromagnet transitions to a paramagnet at high temperature, and a spin glass at low temperature [165, 166] 91 Chapter 7 The Growth of Magnetic SrO1-xNx 7.1 Introduction The discovery of a magnetic semiconductor with a room-temperature Tc would her- ald a major revolution in electronics design and computing. By harnessing the spin degree of freedom of the electron, current limits to increasing computing power could be circumvented, leading to faster, smaller, and more efficient devices. A ferromag- netic semiconductor may even make it possible to build a viable quantum computer. However, intrinsic ferromagnetic semiconductors are very rare, have low Tc values, and tend to be damaged by exposure to the atmosphere [40, 167]. Attempts are being made to improve the Tc values of these materials, but for now, the most promising class of material for a practical ferromagnetic semiconductor is the DMSs. DMSs are generally III-V or II-VI semiconductors that begin to exhibit ferromag- netism when doped with transition metal ions. The enormous amount of research being done on DMSs was motivated by the theoretical work of Dietl et al. [147], which was based on the earlier work of Zener [146]. They predicted that the magnetic dopants would have an effective exchange interaction mediated by conduction band electrons, leading to long-range magnetic ordering of the impurities. Unfortunately, a room-temperature ferromagnetic semiconductor has yet to be reliably synthesized [46, 47], but the problems so far encountered have forced researchers to consider other mechanisms to produce magnetic ordering that have until now been overlooked. One of the new areas of research motivated by research in DMSs is the effect that unpaired charges due to light elements like C, N, and O can have on magnetic systems. This has led to theoretical predictions (and some experimental confirmation) of spin polarization of p-orbitals in systems containing no elements with unfilled d- and f-orbitals. Traditionally, the role of light elements like O, C, and N have been neglected outside of their role as intermediaries for mechanisms like super-exchange (in the case of oxygen). There are two reasons for this. The first is that these light 92 7.2. Experimental elements tend to have their orbitals filled when they form a compound. Second, in the rare cases where the orbitals are not filled, their extended 2p character allows significant screening to occur, reducing the strength of electron-electron interactions that would lead to magnetic ordering. However, this picture is incomplete since it neglects the higher order electron-electron interaction terms that are not screened, including the Hund’s rule interaction, Jh (or equivalently, the F2 Slater integral). In conventional magnetic materials with d- or f-type orbitals, the higher order terms are usually much smaller than the Hubbard U/F1 Slater integral and so don’t contribute to the magnetism. However, in light elements like C, N, and O, Jh can be of the same order of magnitude as the Hubbard U, and can become dominant when U is screened. For a comprehensive review of the recent advances in p-state based magnetism, see [86]. In this chapter, we will investigate one system that has been predicted to exhibit p-orbital based ferromagnetism. Elfimov et al. have explored the effect of hole dop- ing in SrO by substituting nitrogen for oxygen [91]. They were able to theoretically demonstrate that the ground state of this system was ferromagnetic, and have gone so far as to show experimentally that localized magnetic moments are present on the nitrogen sites. The goal of this chapter is to take the previous work of Elfimov et al. to its conclusion by determining whether SrO1-xNx films exhibit long-range magnetic order. We begin by looking at the feasibility of growing SrO1-xNx by MBE on two types of substrates: YSZ and MgO. We determine the structural and chemical prop- erties of the films with a combination of RHEED and XPS measurements. We then present the results of SQUID magnetization measurements of the films’ susceptibility. We also discuss the problems we encountered and how they can be overcome in the future. 7.2 Experimental The film growths and all measurements were performed at UBC. The film growths, as well as all RHEED, LEED, and XPS measurements, were performed in the MBE growth and analysis chamber described in Chapter 2. The Sr was evaporated from a Radak Knudsen cell. The rate of metal evaporation was measured with a Sycon STM100 MF QCM. For most growths, the evaporation rate was set to 0.2 Å per second, which corresponds to a cell temperature between 400 and 550‰. The broad 93 7.3. Growth on YSZ and MgO temperature range is due to an instability in the Sr source, the cause of which is discussed later. The base pressure of the growth chamber with the sources and substrate at 150‰ was 1 × 10−10 mbar, and jumped to 5 × 10−8 mbar when the sources were at growth temperatures (450‰ for the substrate and between 400-550‰ for the Sr source). The majority of the outgassing was due to the Sr source and was primarily hydrogen, as determined by an SRS RGA100 residual gas analyzer. The NO gas was introduced into the chamber through a precision leak valve and its pressure measured with the RGA. The concentration of N and the rate of film growth were controlled by varying the NO gas pressure. It was determined that exposure to the atmosphere for several weeks did not appreciably affect the XPS spectra of the films, so the films were removed from the growth/analysis chamber without a capping layer. All SQUID measurements were taken with a Quantum Design MSPS 1822 SQUID magnetometer. The samples were oriented so that the film surface was perpendicular to the applied field. The YSZ and MgO single crystal substrates were ordered from MTI Corporation. Both crystals were epi-polished by the manufacturer to a surface roughness of less than 10 Å. Samples were affixed to copper sample holders, described in Chapter 2, with copper paste made by Tanaka Kikinzoku International. Both substrates have a cubic FCC structure of CaF2 type for YSZ and rock salt type for MgO. The YSZ substrates have a lattice parameter of 5.125 Å, which is very close to the bulk value of SrO, 5.16 Å [91], and were cut to expose the surface perpendicular to the [100] direction [168]. The YSZ substrates were annealed at 600‰ in 1× 10−6 mbar of O2 for two hours before growth [51]. The MgO substrates have a lattice parameter of 4.216 Å and were cut perpendicular to the [110] direction [169]. The MgO substrates were annealed at 500‰ in 2× 10−7 mbar of O2 for 2 hours before growth [51]. These two substrates were chosen because each one satisfies a different set of growth or experimental criteria: the YSZ substrate was chosen because its lattice parameter is close to the SrO lattice parameter, while the MgO was chosen because it has a less structured magnetic signal. 7.3 Growth on YSZ and MgO MBE distillation with NO gas as the oxidizer, the details of which are covered in chapter 6, is an excellent way to grow films of SrO1-xNx. Sr metal, like Eu metal, is 94 7.3. Growth on YSZ and MgO very reactive, which makes the conventional method of plasma cracking N2 to create atomic nitrogen dopants impractical, due to the high nitrogen pressure required to create the plasma. This is undesirable because the presence of significant N2 species would cause strontium nitrites and nitrates to form in addition to nitrogen-substituted strontium oxide. MBE distillation with NO gas allows for the selective uptake of N radicals by the film while ensuring minimal exposure to N2 species. Additionally, it should be possible to extract the initial growth parameters for SrO1-xNx from the pre- viously discussed EuO1-xNx growths because Sr and Eu have similar vapour pressures, which implies similar growth kinetics for the same NO gas pressures. The best substrate growth temperature for producing flat crystalline films was determined by studying RHEED diffraction patterns before and after growths per- formed at different temperatures. At a substrate temperature of 350‰ the growing films lost their RHEED diffraction patterns immediately after opening the Sr source shutter. This occurred on both YSZ and MgO substrates. This behaviour is consistent with the formation of an amorphous SrO1-xNx film. At 450‰ substrate temperature, the RHEED diffraction for YSZ maintained its rod-like, 2D diffraction pattern for several minutes into the growth, and then slowly transitioned to a spotty 3D pat- tern. The 2D diffraction pattern was accompanied by RHEED oscillations in some growths on YSZ as well (the blue line in Figure 7.1 shows the RHEED time series for a 6% nitrogen-substituted film). This suggests either: a layer-then-island, Stranski- Krastanov growth mode for SrO1-xNx [170], or the growth of SrO in the same mode with oxygen donated by the substrate. The RHEED oscillations on the YSZ sub- strate are very clear for the first five monolayers, then drop off suddenly, similar to what happens with EuO1-xNx [4]. This similiarity between SrO1-xNx and EuO1-xNx films grown on YSZ suggests that the oscillations we observed were likely due to the YSZ substrate donating oxygen to the film up to the point where the oxygen could no longer diffuse through the SrO. SrO1-xNx films grown on MgO substrates did not show any RHEED oscillations, and the transition to a 3D diffraction pattern from the 2D substrate diffraction pattern was slow but started immediately after the shutter was opened (the red line in Figure 7.1). This suggests an island, Volmer-Weber type growth mode on MgO [170]. This is not surprising given the large difference in lattice parameter between MgO and SrO. The sudden drop in reflectivity at the beginning of growth suggests that the strontium metal deposited on the surface was not able to organize into a pristine 2D layer, due to the large lattice mismatch between SrO and 95 7.3. Growth on YSZ and MgO 0 250 500 750 1000 1250 1500 Time (s) In te ns ity  (A rb itr ar y U ni ts ) SrO0.94N0.06 on:  YSZ  MgO Figure 7.1: RHEED time series of SrO1-xNx films grown on different substrates under similar conditions. The blue trace, corresponding to a YSZ substrate, ex- hibits strong oscillations in the signal intensity for the first 5 monolayers, after which point they quickly die out. These oscillations are similar to those seen in the EuO1-xNx growths presented in the last chapter, and are likely caused by the same mechanism: the transfer of oxygen from the YSZ substrate to the deposited Sr metal. The red trace is growth on a MgO substrate. There is an immediate drop in intensity at the beginning of growth, but no oscillations. MgO. This initial layer would have many defects, which would act as nucleation sites for the growth of 3D islands. Subsequent material deposited on this surface would continue to aggregate onto these features, with the film consequently never recovering its initial reflectivity. Due to a limitation of the chamber design (discussed in Chapter 2), LEED patterns could not be taken on these films. The inability to operate the LEED electron gun under high oxygen pressures, coupled with its long turn-on time, made it impractical to study the LEED diffraction patterns immediately after growth. Attempts were made to measure LEED after XPS scans were made, but the long time required to acquire XPS spectra meant that the sample surfaces were too damaged to measure a LEED pattern. After growth, XPS was performed on the films to determine their stoichiometry, doping levels, and electronic structure. Figure 7.2 shows a survey XPS spectrum, covering a wide energy range. The expected Sr and O peaks are present, as well 96 7.3. Growth on YSZ and MgO as a small contribution from the Cu substrate holder. A small N 1s peak can be seen around 400 eV binding energy. The nitrogen concentration in the first few 10’s of monolayers of the sample can be calculated from the ratio of the cross-section corrected area of the N 1s peak to the total N and O 1s peak areas [162, 164]. For the sample shown in Figure 7.2, the nitrogen concentration measured by this technique is 5%. None of the films have a strong C 1s peak at 285 eV, indicating that these films are exceptionally clean (the C 1s peak is so common in XPS that it is often used for energy calibration [116]). The close proximity of the Sr 2p peaks could be masking a very small carbon peak, however8. An interesting feature that is common to all of the films studied is the broad peak at 190 eV, labelled with a red arrow. This feature appears to correspond to a plasmon energy loss peak associated with the adjacent Sr 3d peaks, but a plasmon peak would indicate a metallic film. Our initial hypothesis was that this peak was due to the build up of metallic Sr due to the films being grown outside the distillation regime. To address the possibility that the substrate temperature of 450‰ was too low to support the distillation of Sr metal, the Sr metal desorption from the substrate was studied with XPS. Spectra were measured on a clean MgO substrate, then again after evaporating roughly 15 monolayers of Sr metal onto a room temperature substrate surface. A final XPS measurement was performed after heating the substrate with the layer of metal for 30 minutes at 450‰. The pre-evaporation spectra and post- heating spectra are equivalent, showing no Sr, while the post-evaporation/pre-heating spectrum shows a significant Sr metal signal. These results indicate that desorption of Sr metal is occurring at the growth temperatures, at least from a Sr metal or MgO surface. The above annealing scenario does not match the actual kinetics of growth, how- ever. It is possible that the rate of Sr metal deposition is too high to allow all the un-reacted metal to re-evaporate off the substrate, leading to an excess of metal being trapped in the film. The metallic surface may be due to trapped metallic Sr diffusing to the surface (alkali and alkaline earth metals readily diffuse to the surface of ox- ides; this property makes them good gettering materials [171–175]). To address this possibility, we also attempted to anneal a SrO1-xNx film under conditions equivalent 8As was the case for the EuO1-xNx films, the primary gas present during growth is hydrogen. This raises the possibility of hydrogen contamination or doping, which our XPS measurements are not sensitive to. Infrared spectroscopy measurements should be performed to determine if any hydroxyl bonds are present. 97 7.3. Growth on YSZ and MgO Binding Energy (eV) 1000 0800 600 400 200 Cu 2p N KLL O KLL O 1s N 1s Sr 3s Cu LMM Sr 2p 1/2 Sr 2p 3/2 Sr 3d Sr 4s Sr 2p 1 2 3 In te ns ity  (1 04  C ou nt s) Figure 7.2: A survey scan of a SrO1-xNx film with a 5% nitrogen concentration. The absence of a strong carbon 1s peak at 285 eV indicates a very clean film, although the nearby strontium 2p states may be obscuring the peak if it is small. An interesting feature is the broad peak at 190 eV, labelled with the red arrow. This appears to be a plasmon energy loss peak associated with the adjacent Sr 3d levels, suggesting metallic Sr is present in the film. to a MgO substrate anneal (2 hours at at 500‰ in 2× 10−7 mbar of O2). Even this aggressive anneal cycle was unable to affect the mysterious peak, suggesting that the plasmon peak was not due to metal diffusing from the interior of the sample. A few studies suggest that this plasmon peak is due to a persistent layer of Sr metal that forms on certain SrO surfaces due to an electrostatic effect [174–176]. A modern interpretation would be that a metallic layer forms on the top surface of the SrO film to prevent a polar catastrophe [99]. The large energies and potentials associated with the polar catastrophe prevent the exposed Sr metal from binding its free electrons with any available oxygen; any change in the amount of charge on the surface will create a field inside the film that diverges with film thicknesses. However, this electrostatic divergence only occurs when crystals grow in the [111] direction in rock salt type crystals, which does not correspond to the exposed surface of either substrate. It is possible that the film grows with the [111] surface exposed after 98 7.3. Growth on YSZ and MgO 390 2400 3000 In te ns ity  (c ou nt s) Binding Energy (eV) 415 410 395400405 2500 2600 2700 2800 2900 a b c 1.84 eV2.15 eV a:b = 2.24:1 triplet/singlet area ratio: 3:1 singlet-triplet splitting: 1.6 eV a-b splitting = 1.84 eV Figure 7.3: This figure shows a detailed XPS spectrum of the nitrogen 1s peak for film with 13% nitrogen. The peak position and multiplet splitting are consistent with a nitrogen dopant with a spin 1 2 moment, as opposed to a nitrite (NO–2) or nitrate (NO – 3) species. an amorphous buffer layer is deposited on the substrate. This amorphous layer is almost certainly forming on the MgO substrate, as evidenced by the immediate drop in RHEED intensity, but it is unclear if this is happening with the YSZ substrates. An amorphous buffer layer may be forming after the initial RHEED oscillations due to the substrate. The potential implications of this result deserve more study. One initial avenue of investigation would involve laying down single atomic layers of SrO, and determining both the surface structure and at which thickness the surface of the film becomes metallic (where the potential in the film exceeds the oxidation potential of the Sr). This could be performed easily (with an appropriate chamber set up) using the RHEED reconstruction technique discussed in Chapter 3. Having addressed the origin of the plasmon peak and the potential existence of a metallic over-layer in all the SrO1-xNx films, we move on to the question of how the nitrogen is being incorporated into our films. We know from previous attempts to grow bulk SrO1-xNx that the high temperatures required to achieve sufficient bulk mobility to grow the material also produce nitrites and nitrates of strontium, rather than doped SrO1-xNx [109]. Figure 7.3 shows a detailed scan of the nitrogen 1s peak of a 13% substituted film. There are several interesting aspects of this spectra: the first 99 7.3. Growth on YSZ and MgO is the position of the main peak, and the second is the splitting. The large peak at 394.8 eV binding energy is the nitrogen 1s mainline. This peak position corresponds to a nitride N3– species [116, 172]. Both nitrite and nitrate species have higher binding energies, around 400 eV, depending on the material [116], so with this result, we can exclude the possibility that the films contain nitrites or nitrates. The presence of a nitride species suggests that the extra hole produced by the nitrogen is located on the nitrogen site, which is a necessary condition for the fer- romagnetism described by Elfimov et al. [91]. This is further supported by another interesting aspect of this spectrum: it exhibits a multiplet splitting of the 1s peak (due to the exchange coupling of the hole on the N 1s site with the core hole produced in the photoemission process), which is indicative of a localized charge on the nitrogen site. Following the suggestion in Elfimov et al. [91], we compare our N 1s peak to that of NO gas. We find that the ratio of peak area a to peak area b is 2.23:1, relative to the expected 3:1 for a triplet/singlet multiplet splitting. Furthermore, the splitting between peaks a and b is roughly what is expected for NO gas: 1.84 eV versus 1.6 eV. The additional peak, c, is attributed to a shake-off energy loss peak due to band gap transitions. This is supported by the energy difference between peaks a and c roughly matching the expected band gap in SrO (4.0 eV compared to 5.3 eV [177]). This also suggests that the interior of the film is an insulator or a semiconductor; the plasmon peak previously discussed is due to a metal layer confined to the sample surface. The previous XPS results present a clear picture of how the nitrogen is incorpo- rated into the SrO. Unlike with EuO, the nitrogen appears to be incorporated as a dopant, with an additional hole residing on the system residing on the nitrogen site itself. This is supported by both the energy position of the nitrogen 1s peak and its multiplet splitting. The last important parameter that can be extracted from our XPS spectra is the nitrogen concentration as a function of growth NO gas pressure. Unfortunately, there appears to be no correlation between growth parameters and resultant nitrogen concentrations. The nitrogen concentrations measured with XPS range from 0% (SrO) all the way up to 20%. However, there is no correlation be- tween the growth pressure and these concentrations (the growth parameter was the only intentionally changed parameter). This behaviour was eventually traced to a problem with the Sr evaporator. The evaporation rate of the Sr source depended on the oxygen or NO gas pressure in the growth chamber. Even more problematic was 100 7.4. Magnetism in SrO1-xNx that this effect appeared to be cumulative, and the Sr source temperature had to be raised with each subsequent film growth to maintain the same rate. This was incor- rectly attributed to a decrease in source material available in the effusion cell; it was actually due to an increasingly thick SrO layer forming on top of the pure Sr metal in the chamber. SrO does not form a passivating protective layer, and each subsequent exposure to oxygen during substrate anneal cycles created a slightly thicker layer of oxide between the Sr metal and the vacuum. As this layer became thicker, the Sr metal had to diffuse further and further through the oxide layer to be evaporated from the source, requiring higher and higher temperatures to maintain the same deposition rate. Unfortunately, this property of the Sr source was realized too late to fix; the MBE equipment had been dismantled and shipped to the CLS. If this work were repeated, the Sr metal source could be protected in two ways. The first would be to anneal the substrates in a separate chamber (like the load lock). The largest oxygen exposures occurred during the substrate annealing cycles, and moving this process to a separate chamber would solve the problem. If it were not possible to anneal in a separate chamber, another solution would be to evaporate a large amount of Sr during the annealing. Evaporated Sr metal would coat the adjacent walls and shutter, and act as a getter pump to locally pump the area around the source, preventing contamination of the Sr metal in the crucible. This method has been used successfully by others to protect Sr sources used in oxide MBEs [178]. 7.4 Magnetism in SrO1-xNx Despite encountering some surmountable problems that affect the repeatability of the film growth, our results show that it is possible to grow crystalline, if not epitaxial, nitrogen-doped SrO; we can confirm that the nitrogen forms a nitride 3− species (and exclude the possibility of nitrate or nitrite species forming), and that the hole introduced by the nitrogen resides primarily on the nitrogen site. So far, these results match those of Elfimov et al [91] Our next task is to use SQUID magnetization measurements to determine whether the localized magnetic moments introduced by the nitrogen produce any long-range magnetic order. There are several challenges to performing magnetization measurements on these SrO1-xNx films. Unlike for the previously discussed EuO1-xNx films, we do not have a good proxy for determining film thickness. Small substrate sizes and rough surfaces in 101 7.4. Magnetism in SrO1-xNx the MgO growths contributed to make XRR measurements impractical as a measure of film thickness. As a result, we cannot determine reliable film thicknesses to convert the magnetization data into an intrinsic unit (like the Bohr magneton/unit cell). Furthermore, if a ferromagnetic signal is present in SrO1-xNx, it will be very difficult to detect, unlike with EuO or EuON. This is due to both the lower value of J (1 2 for SrO1-xNx versus 7 2 for EuO) and the smaller number of magnetic moments (only the dopant N sites in SrO1-xNx, as opposed to every Eu site in EuO). For similarly sized films, the magnetic signal associated with ferromagnetic SrO1-xNx would be roughly two orders of magnitude smaller than that for ferromagnetic EuO. Another problem that became immediately apparent was that our post-annealed YSZ substrates appeared to be anti-ferromagnetic. The transition temperature cor- responds to that of absorbed oxygen [179]; we therefore suspect that this signal has something to do with the high mobility of oxygen in the substrate causing a layer of oxygen to form on the top of the sample. We were able to eliminate absorbed oxygen due to a leak in the SQUID system as the reason for this behaviour. Why this peak was not apparent in the previously described EuO1-xNx growth is unclear. There may have been a difference in the quality of the substrate between the two experiments, since they came from different suppliers. An alternative explanation is that the large ferromagnetic signal in EuO1-xNx masks the small anti-ferromagnetic signal. The MgO substrates do not exhibit this behaviour, so we will continue our investigation by focusing on them exclusively. Figure 7.4 shows the SQUID magnetization measurements as a function of tem- perature of two SrO1-xNx films at 4% (blue) and 16% (green) doping levels, as well as fits to these measurements (in a 1000 Gauss field). Unlike with the EuO1-xNx growths, we have no proxy for estimating films thicknesses reliably, and so we have left the magnetization measurements in extrinsic units. The fits were performed using a model that included a ferromagnetic transition on top of a combined paramagnetic and diamagnetic background. In both cases there appears to be a small ferromag- netic transition at at 46 and 44K, respectively. Qualitatively comparing the size of the jump to the previous growths of EuO1-xNx, we find a difference in signal strength that matches our expectation of about two orders of magnitude difference (assuming similiar film thicknesses). It is interesting to note that the 16% doped sample has a weaker ferromagnetic transition than the 4% doped sample. This may be due to clus- tering at higher doping levels. The analysis of this data is hampered by the relative 102 7.4. Magnetism in SrO1-xNx 4      Fits 16 1 2 3 4 5 20 40 60 80 100 120 Temperature (K) M ag ne tiz at io n (E M U )( x1 0- 6 ) 0 N Concentration (%) Figure 7.4: SQUID magnetization measurements as a function of temperature of two SrO1-xNx films grown on MgO in a 1000 Gauss field. The blue curve corresponds to a 4% doped sample and the green curve corresponds to a 16% sample. Both exhibit what appears to be a ferromegnetic tran- sition at 46K for the 4% sample and 44K for the 16% sample. The red lines correspond to fits to the data based on a model that incorporates a ferromagnetic transition on top of a background consisting of a large paramagnetic signal and a small diamagnetic signal. strength of the background compared to the ferromagnetic signal; the fits (shown in red in the figure) are very sensitive to the choice of starting parameters. This problem will be addressed with a new Torlon sample holder that has constant density along its length, which should help to reduce the paramagnetic background. The strength of the background could also be reduced by subtracting off the contribution of the MgO substrate, however, the variability in the straw sample holder signal has made this difficult. It is possible that the transition seen in the SrO1-xNx samples is due to absorbed oxygen. The best measurement to demonstrate whether the system is ferromagnetic of anti-ferromagnetic is a hysteresis curve above and below the transition temperature. While these measurements were attempted, the quality of the data that was obtained was too poor to determine conclusively whether the transition around 45K is due to oxygen or ligand magnetism. 103 7.5. Conclusions 7.5 Conclusions In this chapter, we have shown that it is possible to grow SrO1-xNx films with MBE distillation. We demonstrate that the nitrogen is incorporated as a dopant and pro- duces holes on the nitrogen site. Furthermore, we show that the isolated magnetic moments due to the nitrogen may order ferromagnetically around 45K, validating the theoretical predictions of spin polarization of p-orbitals by Elfimov et al [91]. We recommend that these growths be repeated to address a technical problem associated with obtaining consistent growth behaviour, and to obtain more reliable SQUID mea- surements with a smaller background signal. If these results can be validated with further experimental work, then we will have conclusively demonstrated ferromag- netism due to ligand holes in a normally non-magnetic oxide. 104 Chapter 8 Conclusions This thesis presents work aimed at studying novel magnetic oxynitride thin films. This included technical projects, such as the design and construction of a combined growth and analysis system, developing a method to generate 2D surface diffraction patterns from multiple RHEED images, and presenting a recipe for characterizing the response of an electron spectrometer. The technical work was followed by a theoretical investigation of pnictide-doped EuO, and growth studies of EuO1-xNx and SrO1-xNx. This study of novel ferromagnetic systems, and the development of the tools to prepare and characterize them, is important for both basic research into magnetism and the search for alternatives to DMS materials for spintronic applications. The more technical work has led to several important advances. While the design and construction of the MBE growth/analysis chamber presented in Chapter 2 was more evolutionary than revolutionary, the resultant system was effective, and is cur- rently being used by researchers at UBC and at the CLS. The cryostat designed for this system is the first to incorporate both temperature-dependent XPS and transport into the same system. This cryostat will be very useful to others who want to study the transport properties of materials with easily damaged surfaces. Chapter 3 dealt with extracting 2D surface symmetry data from multiple RHEED images, and is important because it provides film growers with a new technique to extract surface diffraction patterns during growth. While the initial setup is difficult, this technique has advantages over LEED in that the measurements can take place in situ and during growth, and the higher kinetic energies reduce the effect of dynamical scattering on the diffraction pattern. Chapter 4 brought together and extended several techniques for characterizing the response of different parts of an electron spectrometer so that the effect the analyzer has on an acquired spectrum can be measured and removed. This is an important first step in performing quantitative analysis of XPS data. However, we also found that the analyzer’s contribution is very sensitive to small changes in sample position and analyzer settings, to the point where it is almost necessary to remeasure the 105 Chapter 8. Conclusions transmission function for every new sample if the position or size cannot be exactly controlled. For film growers working with well defined substrates, it is possible to measure the transmission function once for a series of film growth experiments. Care must be taken when analyzing XPS data to ensure that the effect of the spectrometer response is minimized. The calculations presented in Chapter 5 investigated the possibility of hole doping the ferromagnetic semiconductor EuO through pnictogen substitution of the oxygen site. The calculations showed that N substitution was the best candidate for an experimental study because it was the most likely to substitute an oxygen rather than phase-separate. However, the distribution of charge above Ef was primarily located on nearest neighbour europium sites, suggesting charge transfer from europium to nitrogen to be the most likely scenario as opposed to doping the system with holes. This does raise the possibility that EuO1-xNx is a mixed valent europium system, and that double exchange could enhance the Curie temperature of the system beyond that of stoichiometric EuO. The previous theoretical calculations motivated the experimental growth study in Chapter 6. EuO1-xNx films were grown with nitrogen substitutions of up to x = 20% using MBE distillation with NO gas. This growth method produced good-quality films that exhibited both RHEED and LEED diffraction patterns, and controllable dopings (although the mechanism that describes the non-linear nitrogen concentration increase as a function of gas pressure is still unclear). Valence band XPS indicated that the amount of Eu3+ increased with increasing nitrogen concentration, consistent with the theoretical calculations in Chapter 5. The saturation magnetization of the films appeared to drop from the expected 7µB with increasing nitrogen concentration, but it is unclear whether this is an intrinsic effect or due to necessary assumptions to determine the film thickness. Most important, however, was that the Curie temper- ature remained unchanged, even at high levels of nitrogen substitution, and that the measured drop was not as severe as it would be in the case of over-oxidized EuO1+δ. Further study of both the kinetics of the growth technique is recommended so that the non-linear nitrogen concentration can be understood and the dependence of film thickness on the growth parameters can be determined. This will allow one to deter- mine whether the saturation magnetization is truly dropping as a result of nitrogen substitution. The final chapter of this thesis dealt with the growth of SrO1-xNx thin films, 106 Chapter 8. Conclusions which were grown using the same technique as the EuO1-xNx films in Chapter 5. While we were unable to reliably control the doping level of the SrO1-xNx films due to a problem with the Sr effusion source, we were able to show that the nitrogen 1s peak appears to exhibit a multiplet splitting. This indicates the presence of local magnetic moments and also shows that the position of the peak precludes the possible formation of nitrates and nitrites of strontium. Furthermore, we were able to identify a possible ferromagnetic transition around 45K in samples grown on MgO substrates. It is recommended that this study be repeated so that consistent doping of the films can be achieved, and with a new SQUID sample holder to reduce the magnetization background. If these results can be repeated, then this system truly exhibits long- range magnetic ordering due exclusively to nitrogen vacancies. The impact of this thesis will be strongest in the fields of p-orbital based mag- netism and DMSs. Our technique of NO-assisted MBE distillation has been shown to produce good-quality films of nitrogen-doped binary oxides. We have already used this technique to grow ferromagnetic SrO1-xNx; we expect that it could be applied with great success to the growth of other N-doped II-VI oxides like MgO, ZnO, and CaO. ZnO1-xNx is an especially attractive candidate for future study. 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Journal of Physics D: Applied Physics, 40:6497, 2007. 124 Cryostat Thermal Calculations Worksheet This appendix contains the contents of the Sage mathematical environment worksheet used to model the cryostat behaviour in Chapter 2. #Define variables and state equations. var(’Th Te Ts d Qh2 Qh1 l ls’) Ta = 297 R = 3.94 + 0.00425/(0.01145 - d) eqShield = 297 - ls/l*(Ta - Te) == Ts eqExchanger = 1.068E-4*(Ta - Te) - 22.2*(Te-4.2) + 3.84E-7*(Ts-Te)/(l-ls) + 2.56E-6*(Th -Te)+ (Th - Te)/R + Qh1 + 9.072E-12*(Ts^4 - Te^4) == 0 eqHolder = 1.125E-11*(Ts^4 - Th^4) + 3.56E-12*(Ta^4 - Th^4) + Qh2 - 2.56E-6 *(Th -Te)- (Th - Te)/R==0 #Define starting values and solve the non-linear state equations. lv = 1 Qh1v = 0 Qh2v = 0 dv = 0.0 lsv = 0.5 S=solve([ eqShield.substitute(l=lv, Qh1=Qh1v, Qh2=Qh2v, d=dv, ls=lsv), eqExchanger.substitute(l=lv,Qh1=Qh1v,Qh2=Qh2v, d=dv, ls=lsv), eqHolder.substitute(l=lv, Qh1=Qh1v, Qh2=Qh2v, d=dv, ls=lsv) ], Ts, Th, Te, solution_dict=True) print S[-2] #Take the real positive solutions and calculate the required flow to maintain 125 Cryostat Thermal Calculations Worksheet # the equilibrium values Tev = (S[-2])[Te] var(’Flow’) eqFlow = Flow == 22.2*(Te-4.2)/50.9*60 print eqFlow.substitute(Te=Tev) 126


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