2 MEDIUM-ENERGY ION SCATTERING STUDIES OF INTERFACES IN ULTRA- THIN OXIDE FILMS by TIAN FENG A Dissertation submitted to the Graduate School-New Brunswick Rutgers, The State University of New Jersey In partial fulfillment of the requirements For the degree of Doctor of Philosophy Graduate Program in Physics and Astronomy Written under the direction of Professor Torgny Gustafsson and approved by New Brunswick, New Jersey October, 2011
3 ABSTRACT OF THE DISSERTATION MEDIUM-ENERGY ION SCATTERING STUDIES OF INTERFACES IN ULTRA- THIN FILM SYSTEMS By TIAN FENG Dissertation Director: Professor Torgny Gustafsson Interfaces in thin film/substrate systems play a central role in the performance of electronic devices in nano/microelectronics. However a detailed microscopic knowledge of the structure and composition of an interface is usually not established. Medium energy ion scattering (MEIS) is a powerful technique in interface analysis by providing depth profiling with sub-nanometer resolution, MEIS been used in this thesis to study two thin film systems. The interface between the two insulating oxides LaAlO 3 /SrTiO 3 has recently been found to exhibit a range of novel electronic properties, as for example a totally unexpected metallic electron mobility (two-dimensional electron gas). The origin of these novel properties is still under debate. An electronic reconstruction model, adopted by many researchers, assumes the interface to be completely abrupt and structurally perfect. MEIS has been used to systematically investigate this interface and provide the depth distributions of four metal atoms present in the overlayer/substrate system. The interface is found to be far from ideal and to exhibit substantial intermixing. ii
4 A doping mechanism based on the atomic reconstruction is tentatively proposed to account for the high mobility at the interface. The thin films of hafnium oxide and silicate have received intensive research as candidates to replace SiO 2 as a gate dielectric in silicon-based electronics. Oxygen interaction with these films under high temperature annealing, a common processing treatment, is a crucial issue. An isotopic labeling technique ( 16 O/ 18 O) in combination with MEIS is used to elucidate this issue. At low temperatures the incorporation involves oxygen exchange, while at higher temperatures an interfacial layer is found to form at the film/si interface. Dependence of the oxygen incorporation on the microstructure of the film and the presence of N is also discussed. iii
5 Acknowledgement This thesis would not have been possible without help from many people I encounter along the long road to the Ph.D. I owe my deepest gratitude to my advisor, Torgny Gustafsson, for his invaluable guidance, support, and extreme patience. He gave me the luxury of conducting research on surface science in a relaxed manner. I would like to gratefully and sincerely thank Eric Garfunkel and Leonard Feldman for all the insightful advices and critical comments to the research projects I have done at Rutgers. I am grateful to the other members of my thesis committee, Robert Bartynski, Matthew Copel, Paul Leath, and Jolie Cizewski for interest in my work and valuable comments. I would like to thank Theodore Madey for his inspiring teaching that made me appreciate how exciting the research on surface science is. I am indebted to Lyudmila Goncharova, a role model of doing decent research, for all the practical and useful advices, not to mention teaching me how to operate the daunting machine. I owe much thanks to Hang Dong Lee, whom I have been working with on many projects, for his excellent physics intuition and optimism when we were in desperate situations. Most of the experimental work and analysis in the chapter of LAO/STO in this thesis would be impossible without his help. I am thankful to Hsu-Chang Lu for so many highly valuable and effective suggestions to fix the machine. I am always impressed by him: who could still recall so much technical details ten years after graduating from this lab? Many thanks to Chien-Lan Hsueh for useful discussions on experiments and valuable advice on my future career path. I owe special thanks to Leszek Wielunski for lending us instruments whenever we need them and for inspiring discussions on every subtle aspects of the ion scattering technique. Thanks to Lei Yu for the knowledge of semiconductor device. I would like to express my gratitude to all the other people in the 2G group: Mateus Dalponte, Ozgür Celik, Dan Mastrogiovanni, Xingguang Zhu, Yi Xu, etc, iv
6 particularly for constructive input about my talks and presentations. I am especially grateful to Can Xu, who helped me a lot during my thesis writing. My colleagues from Bob s group, Quantong Shen, Wenhua Chen, Eric Bersch, Senia Coh, Sylvie Rangan, and Boris Yakshinskiy are always willing to lend us tools and instruments. Bill Schneider and his team at the machine shop made my lab life much easier by machining high-quality parts and by providing useful technical support. Yuri Streltsov fixed all the broken electronics. The staffs in the physics department whom I often bothered, Gwen Chupka, Valerie Cardinale, Helen Posluszny, Shirley Hinds, Nancy Pamula and Kathy DiMeo are extremely helpful. I would also like to thank my fellow graduate students in the physics department, Weihua Zheng, Xinjie Wang, Junyi Li, Chenglin Zhang, Jian Wei, Shitao Lou, Hua Yao, Hao Wang, and Xifan Wu for continued encouragements on my PhD study and for making my time at Rutgers fun. Lastly, but by far not least, I am very thankful to my wife Xin Wang and my parents for being patient and supportive for my pursuit to become a physicist. Tian Feng, May 23, 2011 v
7 Dedication 献给我的父母 vi
8 Table of Contents Abstract.ii Acknowledgement... iv Dedication... vi Table of Contents... vii List of Figures... x List of Tables... xii List of Acronyms... xiii 1 Introduction Brief Description of concepts in the field of Surfaces, Thin Films and Interfaces High Dielectric Constant Gate Oxides Basics of MOSFETs MOSFET Scaling Candidate High-κ Oxides Epitaxial Oxides Summary Medium Energy Ion Scattering Introduction Principles of MEIS Interactions of Medium-Energy Ions and Atoms The Kinematic Factor Scattering Potential, Scattering Cross Section, and Ion Neutralization Shadowing, Channeling, and Blocking Energy Loss and Straggling Energy Loss Rate Ion Stopping Mechanisms Energy Straggling vii
9 2.4 Simulation of the MEIS Energy Spectrum Convolution of Conventional Gaussians Energy Loss Model for Near Surface Scattering The Stopping Power in a Crystal Instrumentation The LaAlO3/SrTiO3 Heterointerface Introduction Material Basics and Heterostructure Growth Possible Explanations of Conducting Interface Polar Discontinuity Oxygen Vacancies Experimental Beam Type Scattering Configurations Results The Helium Random Direction Spectrum Helium Channeling Spectrum Proton Beam Results Summary on Cationic interdiffusion Laser Fluence and Ion Irradiation Discussion La Deficiency in Film Cation site exchange La Doping in the Substrate Conclusions Oxygen Diffusion in Hafnium Oxides and Silicates Introduction viii
10 4.2 Experimental Sample Growth and Preparation Isotopic Labeling Results O incorporation at 763K O incorporation at higher temperatures Discussion Exchange Reactions Growth of Interfacial Silicon Oxide Presence of interfacial nitrogen Conclusions Curriculum Vita ix
11 List of Figures Figure 1.1 Schematic of an n-channel MOSFET Figure 2.1 A two-body elastic collision process Figure 2.2 The kinematic factor versus scattering angle Figure 2.3 Formation of a shadow cone Figure 2.4 Backscattering geometry Figure 2.5 Energy dependence of the electronic stopping power Figure 2.6 Schematic illustration of the deconvolution of an energy spectrum Figure 3.1 Crystal structure of perovskite ABO Figure 3.2 AFM image of STO and LAO surfaces Figure 3.3 Polar catastrophe Figure 3.4 Double alignment scattering configuration Figure 3.5 Planar channeling effects Figure 3.6 Helium random spectrum Figure 3.7 Helium channeling spectrum Figure 3.8 Angular spectrum of LAO and STO Figure 3.9 Proton backscattering spectra Figure 3.10 Unit-cell by unit-cell areal density of La, Al, Sr, Ti Figure 3.11 Proton spectra as a function of total ion dose Figure 3.12 Energy level diagram of LAO/STO Figure 4.1 Channeling spectrum of an as-deposited silicate film x
12 Figure O and 16 O peaks Figure 4.3 Effects of vacuum crystallization anneal Figure 4.4 Oxygen isotopic exchange and incorporation and interfacial SiO x growth Figure O and 18 O isotopic depth distribution Figure 4.6 Oxygen areal densities Figure 4.7 Nitrogen depth distribution Figure 4.8 Arrhenius plot of oxygen incorporation near interface xi
13 List of Tables Table 3.1 Areal densities for La, Sr, and Ti Table 3.2 Schematic illustration of selected site exchange configurations and associated dipole moments Table 4.1 Areal densities of different oxygen isotopes before and after annealing xii
14 List of Acronyms 2DEG AES AFM ALD ARXPS CMOS EELS EOT FWHM HEIS ISS ITRS 2 Dimensional Electron Gas Auger Electron Spectroscopy Atomic Force Microscope Atomic Layer Deposition Angle Resolved X-ray Photoelectron Spectroscopy Complementary Metal Oxide Semiconductor Electron Energy Loss Spectroscopy Effective Oxide Thickness Full Width at Half Maximum High Energy Ion Scattering Ion Scattering Spectroscopy International Technology Roadmap for Semiconductors LAO LaAlO 3 LEED LEIS MBE MCP MEIS MOSFET PDA PLD PSD Low Energy Electron Diffraction Low Energy Ion Scattering Molecular Beam Epitaxy Micro Channel Plate Medium Energy Ion Scattering Metal Oxide Semiconductor Field Effect Transistor Post Deposition Annealing Pulsed Laser Deposition Position Sensitive Detector xiii
15 RBS RHEED SIMS SRIM STEM STM Rutherford Backscattering Spectroscopy Reflection High Energy Electron Diffraction Secondary Ion Mass Spectroscopy Stopping and Range of Ions in Matter Scanning Tunneling Electron Microscope Scanning Tunneling Microscope STO SrTiO 3 TEA TEM UHV VLSI UPS u.c. XPS XRD Toroidal Electrostatic Analyzer Transmission Electron Microscope Ultra High Vacuum Very Large Scale Integrated Circuit Ultraviolet Photoelectron Spectroscopy unit cell X-ray Photoelectron Spectroscopy X-ray Diffraction xiv
16 1 1 Introduction This thesis describes results from experimental studies of depth profiling of ultrathin films. Chapter 1 starts with a brief description of concepts central to the physics of surfaces, thin films, and interfaces. Following this, an introduction and motivation of the two ultra-thin film systems studied in the thesis work. The experimental technique of medium-energy ion scattering (MEIS) is described in detail in chapter 2. Chapters 3 and 4 then describe our results from the two parts of this work. 1.1 Brief Description of concepts in the field of Surfaces, Thin Films and Interfaces Surface science is a sub-discipline of the more general field of solid state physics . Conceptually, solid state physics is the atomic physics of the condensed state of matter. The main goals consist of deriving an atomistic or microscopic description of the macroscopic properties of a solid, such as elasticity, specific heat, optical response, electrical conductivity, and magnetism. The characteristic difference from atomic physics stems from the necessity to describe a vast number of atoms. Condensed matter consists of an assembly of about atoms per cm 3 of volume. In order to make such a large number of atoms accessible to a theoretical description, an infinitely extended solid is assumed in most theoretical models in classic solid-state theory. For instance, much of the understanding of solids comes from study of a special type of solid in which the atoms are located in an ordered array. These crystalline solids are periodic in all three dimensions. The infinite translational symmetry of an idealized
17 2 crystalline solid simplifies the mathematical treatments considerably by application of a number of symmetry operations. Such a description of a solid is a good approximation for deriving macroscopic properties, such as thermal and electrical conductance, that depend on the total number of atoms contained in the solid. This understanding can even be applied in some cases to non-crystalline solids. The surface of a solid can be defined as the region (usually several atomic layers thick) where the properties of the bulk change due to the presence of the surface, or where new properties (associated only with a surface) appear. Mathematically, the introduction of a surface breaks the translational symmetry along the surface normal direction, where the, surface atoms are in an environment with fewer neighbors than in the bulk. Such a reduction in atomic coordination can lead to dangling bonds and/or rebonding driven by minimizing the surface energy, which also gives rise to changes in the atomic structure at the surface, such as relaxation (shifts in the spacings between layers of atoms at the surface), and reconstruction (lateral changes in the surface periodicity relative to the bulk). Other surface-specific effects include new surface-localized electronic states (created at energies lying in the gaps of the bulk energy bands), and surface plasmons (collective oscillations of the conduction electrons in a metal). Therefore understanding the atomic and electronic structure of the surface atoms is of the fundamental interest in surface science. Dynamical and chemical processes at the surface (surface phonons, adsorption, and desorption) are also of fundamental interest. Deposition of a thin solid film on a surface introduces an interface to the system. Such a film is bound by a solid-solid interface and its surface (film-vacuum interface),
18 3 thus its properties are basically determined by the properties of the two interfaces. Again, due the small number of atoms contained in the film, the concepts of bulk solidstate physics cannot be simply applied. Instead the physics of small atomic clusters, which often possess more surface atoms than bulk atoms, may be a useful starting point. Understanding and controlling interfaces has now become of critical importance in micro/nanoelectronics. A detailed microscopic knowledge of the structure and composition of interfaces helps researchers better understand device materials properties, and makes precise control in interface engineering possible. This may, in turn, lead to improvement in device electrical performance. The field of surface and interface science attracts researchers from a wide range of disciplines including physics, chemistry, materials science, and electrical engineering. This interdisciplinarity is a direct result of the importance of this field to so many applications of technological importance. One motivation of historical importance is the goal of understanding heterogeneous catalysis . The greatly increased rate of some reactions during catalysis occurs because at least one of the gaseous participants in the reaction has been chemically modified due to adsorption onto the surface of the solid catalyst. Therefore it is of great scientific (and applied) interest to study the nature of the chemical bonding at the surface and the dependence on surface conditions such as morphology (faceting or planar). Modern semiconductor device technology is another area that would be quite unthinkable without research on semiconductor surfaces and interfaces . As the size of devices continues to shrink, the surface to volume ratio increases, essentially making them surface (or interface) devices. With the increasing
19 4 trend towards greater miniaturization surfaces and interfaces become an increasingly important factor in the functioning of a device. For instance, the preparation techniques such as molecular beam epitaxy (MBE)  for complex multilayer devices and nanostructure, a variety of thin-film deposition techniques such as atomic layer deposition (ALD) , are largely derived from surface science techniques. We now summary some experimental aspects of probing surfaces and interfaces. First, most surface science experiments are performed in an ultra-high vacuum (UHV) environment, because only for pressures in the Torr range or lower can the surface remain atomically clean for the duration of an experiment. Various characterization setups are integrated in a state-of-the-art UHV system for in-situ measurements. Characterization of the surface and thin film then generally proceeds by irradiating the surface with some type of particle (photons, electrons, ions), and then detecting scattered (elastic or inelastic) or newly created particles. There is basically an experimental technique named for each possible pair of in-going and out-going particles. Surface sensitivity can arise in a number of different ways. For instance, electrons with energy in the range of ev have a quite limited travel distance (elastic meanfree-path) in solids before being inelastically scattered, and hence attenuated. Therefore, any process in the solid creating electrons in this energy range can only be detected outside the surface if the event occurred within roughly one mean-free-path length of the surface ( 10 Å). Important techniques in this category include X-ray photoelectron spectroscopy (XPS), and Auger electron spectroscopy (AES). Incident ions or electrons can be of low enough energy that their De Broglie wavelengths are so large
20 5 that elastic interactions (diffraction, hence scattering) with the atoms at the surface may occur. Such techniques include low-energy ion scattering (LEIS), and low-energy electron diffraction (LEED). Another category of surface sensitive techniques utilizes scanning probes, in which very sharp tips of nearly atomic dimensions are scanned across a surface with a positioning capability better than atomic dimensions. For instance, electron tunneling currents can be measured by the scanning tunneling microscope (STM), providing an electron density map of the surface. Atomic scale topography of the surface can be measured using the atomic force microscope (AFM). Note that no single surface science technique can provide all the answers to questions regarding atomic or electronic structure at surface. Almost all reported results in this field come from a combination of complimentary methods. For instance, MEIS cannot provide direct information of the chemical state of surface atoms, which can be done with various electron spectroscopies, such as XPS and ultraviolet photoelectron spectroscopy (UPS). 1.2 High Dielectric Constant Gate Oxides Silicon-based electronics have been the mainstay of the microelectronics industry for several decades, driving technological breakthroughs that affect virtually all aspects of everyday life. The building block of modern microelectronic devices, the metal-oxidesemiconductor-field-effect-transistor (MOSFET), has been made progressively smaller over the past fifty years with the aim of placing more of them on an integrated circuit (IC) chip, and its continued performance improvement is largely responsible for the great success of the personal computer and other microelectrics-based inventions. Miniaturization of the MOSFET is observed to follow Moore s Law of scaling with the
21 6 number of devices on an IC doubled approximately every two years. The International Technology Roadmap for Semiconductors (ITRS) defines how the feature size of design parameter scales this trend can be continued . The miniaturization, however, cannot continue forever because atomic dimensions will be reached which will become a key constraint to continued scaling. This section begins with describing the technological background of the MOSFET, followed by a brief discussion of its scaling. Finally, a set of requirements for an alternative gate oxides is summarized Basics of MOSFETs The heart of a MOSFET is essentially a parallel plate capacitor. Figure 1.1 shows a basic MOSFET structure with a metal layer, an oxide layer, and a semiconductor substrate. The metal and oxide layer are also known as the gate electrode and the gate dielectric, respectively. Conventional MOSFETs use highly doped polycrystalline Si (poly- Si) as the gate electrode, SiO 2 as the gate dielectric, and more lightly doped single crystal Si as the substrate. The source and drain electrodes are highly doped Si regions embedded in the Si substrate. A MOSFET functions as a switching device in most common applications. This is made possible by the field effect: the charge carrier density near the semiconductor-oxide interface can be modulated by a voltage applied to the gate stack. Application of an appropriate gate voltage will induce a high density of minority carriers in the channel region between the source and drain electrodes (inversion mode), which results in a current between these two electrodes driven by a voltage bias across them. This is the on state of the MOSFET. By changing
22 7 the gate voltage, the charge carrier density can be reduced significantly, and the device can be turned off. Figure 1.1 Schematic of an n-channel MOSFET MOSFET Scaling The performance of a MOSFET can be assessed by considering a simple model for the drive current in a MOS structure (using the gradual channel approximation) : (1.1) where is the channel width, the channel length, the channel carrier mobility, the capacitance per unit area (referred to as capacitance from here on unless otherwise noted) associated with the gate oxide when the underlying channel is in the inverted state, and is the threshold voltage (the voltage needed to turn the device on). It can be seen in this simplified approximation that the drain current can be increased by reducing the channel length and/or increasing the gate oxide capacitance. The parallel plate capacitance associated with the MOSFET structure is (1.2)
23 8 where is the dielectric constant (also referred to as the relative permittivity) of the gate oxide (dielectric) material, the permittivity of free space, and the thickness of the oxide. Historically the increase in the capacitance has been accomplished by making the oxide layer thinner. The thickness of this layer has now become as small as 10Å. At this thickness, under the current operating gate voltages, the gate leakage current due to direct tunneling of electrons through the SiO 2 layer becomes too high (the tunneling current increases exponentially with decreasing oxide thickness), so that the static power dissipation increases to unacceptable values. Furthermore, SiO 2 does not exhibit bulk electronic properties when it becomes thinner than about 7Å , which sets an ultimate limit to its usage as the gate oxide. In addition it is becoming increasingly difficult to make and measure accurately such thin films. Finally the reliability of SiO 2 films against electrical breakdown declines in thin films. According to ITRS, as of 2009, the SiO 2 dielectric cannot be made thinner, and it must be replaced by a physically thicker layer of some new material of higher dielectric constant (high-κ), in order to increase the capacitance and to decrease the gate leakage current. It is convenient to define an equivalent oxide thickness of the new gate oxide: (1.3) where 3.9 is the static dielectric constant of SiO 2. The EOT of a high-κ layer is the thickness that an SiO 2 layer would have in order to yield the same capacitance. The objective is to develop high-κ oxides which allow scaling to continue to ever lower values of EOT.
24 9 Note that the introduction of a new gate oxide material usually requires a new metal as the gate electrode material, since poly-si is generally found to be incompatible with the new high-κ material both electrically and thermodynamically . There is also a set of criteria for the gate metal based on the work function. Potential candidates such as Al, Au, Ti, and TiN, have been explored. This area of research is outside the scope of this thesis Candidate High-κ Oxides The reason that silicon has dominated the semiconductor industry for over the past five decades is the incredible advantageous material properties of amorphous, thermally-grown SiO 2 : It is thermodynamically and electrically stable, has very few electronic defects, and excellent electrical isolation properties. Therefore the new gate oxide material should have the same or better electrical and chemical properties: first of all, its κ value must be high enough to be used for a reasonable period of continued scaling; it must be a good insulator with a wide enough bandgap that gives rise to reasonable conduction and valence band offsets to ensure low leakage current; it must have few electrically active defects in the bulk and at the interface with Si; it must have thermal stability on Si against intermixing or diffusion to ensure a sharp interface under high temperature annealing up to Since late 1990s intensive research has been done on potential candidate high-κ gate dielectrics [9-14], including transitional metal oxides and silicates (Ta 2 O 3, TiO 2, ZrO 2, and HfO 2 ), rare-earth metal oxides (Gd 2 O 3, Y 2 O 3, CeO 2, and La 2 O 3 ), and also other oxides (Al 2 O 3 ). Perovskite-type oxides such as SrTiO 3 and LaTiO 3 have also attracted interest as
25 10 alternative gate dielectrics. Hafnium dioxide HfO 2 and its silicate have been the leading candidates. Actually major semiconductor manufacturers have already began to replace SiO 2 by HfO 2 at the 45 nm technical node around HfO 2 has a high dielectric constant and a relatively large bandgap of 5.8 ev, and it has excellent chemical and thermal stability in contact with silicon . One issue with HfO 2 is that it undergoes a phase transition from amorphous to crystalline form when annealed to . At these temperatures HfO 2 films crystallize into a monoclinic phase, from which phonons develop as scattering centers of charge carriers. The crystallization of HfO 2 could lead to the formation of charged defect states in the oxide that shift the threshold voltage . The use of hafnium silicate films has been shown to increase the crystallization temperature while keeping the high dielectric constant . Therefore a remaining issue is how high-temperature annealing affects the composition and structure of the oxide and silicate films in an ambient and/or vacuum environment, and also how oxygen interacts with these high-κ films under these annealing conditions. These are the main motivation of the thesis work in Chapter Epitaxial Oxides An epitaxial system consists of two or more single crystals in contact with a specific crystallographic orientation. Homoepitaxy refers to a crystalline film grown on a substrate of the same material. This technology is used to grow a film which is more pure than the substrate and to fabricate layers having different doping levels. For example, most SiC electronic devices utilize epitaxial SiC for at least part of the active device structure. The primary reasons are that the well-grown SiC epilayers have superior electrical
26 11 properties and are more controllable and reproducible than bulk sublimation-grown SiC wafer material . Heteroepitaxy refers to epitaxy where the crystalline overlayer and substrate are of different materials. This technology is often used to grow crystalline films of materials for which single crystals cannot otherwise be obtained and to fabricate integrated crystalline layers of different materials. For example, high crystalline quality GaN, a compound semiconductor commonly used in light-emitting diodes (LEDs), can be obtained by low temperature metalorganic vapor epitaxial growth using an AlN buffer layer on a sapphire substrate . Heteroepitaxy is widely used in semiconductor fabrication. The integration of alternative channel materials, such as III- Vs, Ge, and graphene on a silicon substrate requires heteroepitaxial deposition of these high crystalline quality p and n channel materials. Ultrathin epitaxial binary metal oxides are attracting a great deal of interest. Such high quality epitaxial films are candidates of alternative gate dielectrics on Si, Ge and GaAs according to ITRS Due to its relatively high dielectric constant, large bandgap, and thermodynamic stability on Si, single crystal Sc 2 O 3 thin films have been considered to replace SiO 2 and have shown an atomically sharp interface in direct contact with Si(111) . Epitaxial oxides, such as Ga 2 O 3 /Gd 2 O 3, have demonstrated good electrical properties  and a smooth interface [22,23] on GaAs, and, with a Si 3 N 4 cap layer, has also shown thermal stability and improved electrical performance on InGaAs . Another class of interesting epitaxial oxides is complex metal oxides, more specifically, ternary perovskite oxides of the ABO 3 form, where at least one of A and B is
27 12 a transition metal. In bulk these complex oxides have been found to exhibit a broad spectrum of intrinsic functionalities. These include electronic properties ranging from superconducting to metallic to semiconducting to insulating, magnetic properties ranging from ferromagnetic to ferrimagnetic to antiferromagnetic to multiferroic to colossal magnetoresistive, dielectric properties ranging from low-k to high-k to ferroelectric to piezoelectric. Novel approaches to synthesize and control these epitaxial oxides on the atomic level , such as molecular beam epitaxy (MBE)  and pulselaser deposition (PLD) , have been developed in the 1970s and 1980s along with other physical vapor deposition techniques. These methods make growth and precise control of thin film heterostructures possible and provide a pathway to fabricate functional materials and devices. As a result of the integration of Si technology and complex oxide materials, new ferroelectric, ferromagnetic, spintronic and high heterostructures can be build on Si platforms. For instance, the perovskite oxide SrTiO 3 has an extremely high dielectric constant ( 2000) that undoubtedly makes it a potential alternative gate oxide candidate. McKee  demonstrated that SrTiO 3 can be grown in perfect registry on a Si substrate, where the heteroepitaxy is established via commensurate and thermodynamically stable SrSi 2 /SrO buffer layers. They also reported capacitors with the electrically equivalent capacitance of a SiO 2 film less than 10Å thick, which has attracted much research work as a promising alternative gate dielectric. Atomic-scale engineering of the type discussed above is not confined to the integration of conventional semiconductors. These epitaxial techniques allow for the
28 13 preparation of heterostructures of perovskite oxides that can be used for a wide range of purposes. An example is the BaTiO 3 /SrTiO 3 superlattice . The perovskites BaTiO 3 and SrTiO 3 are alternately deposited to build up the epitaxial composite. Such superlattices not only are relevant to fundamental science involving size, strain, and the coupling of order parameters, but are also investigated for novel applications including acoustic cavities for terahertz modulators or phonon lasers. Even a single interface can have surprising properties. A two dimensional electron gas (2DEG) has been claimed to exist at the heterointerface between the band insulator/band insulator system of LaAlO 3 /SrTiO 3  and Mott insulator/band insulator system of LaTiO 3 /SrTiO 3 . The mechanism responsible for such behavior is still under debate. Chapter 3 of this thesis focuses on the compositional and structural characterization of the LaAlO 3 /SrTiO 3 heterointerface and attempts to provide a qualitative argument on the origin of 2DEG from the point of view of doping. The major experimental characterization method employed in the thesis work (ion scattering) is a powerful tool in determining the atomic structure of such thin epitaxial layers (Chapter 2 and 3) . Compared to other characterization techniques commonly used in this area, such as transmission electron microscopy (TEM), the ion scattering method is non-destructive, mass-specific, and provides elemental depth profiles with very high resolution. In addition, the data interpretation is straightforward. Ion channeling analysis (Chapter 2) has been used to characterize several key properties of epitaxial layers such as crystallinity of the epitaxial film, disorder at the interface due to lattice-mismatch, and orientation of the epitaxial film with respect to the substrate,
29 14 etc. Further quantitative structural information such as atomic reconstruction and relaxation of the epitaxial layers can be obtained by straightforward interpretation of the angular distribution of backscattering of channeled ions. 1.4 Summary The scaling of complementary metal oxide semiconductor transistors has led to the silicon dioxide layer, used as a gate dielectric, being so thin that its leakage current is too large. Thus it has been necessary to replace the SiO 2 with a physically thicker layer of oxides of higher dielectric constant (high-κ). Hafnium oxide and hafnium silicate have been found to satisfy most of the requirements for an alternative gate oxide and have been made commercially available since However, oxygen incorporation in these Hf-based dielectrics upon annealing, a common processing treatment, is not well understood. Detailed study of oxygen incorporation as a function of annealing temperature, time and film quality will be presented. Complex metal oxide material is of interest because of a wide range of functionalities. The heterostructure LaAlO 3 /SrTiO 3 develops, it has been argued, a two dimensional electron gas at the interface. Ion scattering, a powerful technique to characterize epitaxial layer, is used to investigate the composition and atomic structure of this heterointerface. 1. H. Lüth, Solid Surfaces, Interfaces and Thin Films, 5 ed. (Springer Verlag, 2010). 2. G. A. Somorjai, and Y. Li, Introduction to Surface Chemistry and Catalysis, 2 ed. (John Wiley & Sons, 2010).
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31 n-channel GaAs MOSFETS with Ga 2 O 3 (Gd 2 O 3 ) As gate oxide, Solid-State Electronics 41, 1751 (1997). 22. M. Hong, M. A. Marcus, J. Kwo, J. P. Mannaerts, A. M. Sergent, L. J. Chou, K. C. Hsieh, and K. Y. Cheng, Structural properties of Ga 2 O 3 (Gd 2 O 3 )--GaAs interfaces, presented at the AVS, M. Hong, J. R. Kwo, P.-C. Tsai, Y. Chang, M.-L. Huang, C.-P. Chen, and T.-D. Lin, III V Metal Oxide Semiconductor Field-Effect Transistors with High κ Dielectrics, Japanese Journal of Applied Physics 46 (2007). 24. J. F. Zheng, W. Tsai, T. D. Lin, Y. J. Lee, C. P. Chen, M. Hong, J. Kwo, S. Cui, and T. P. Ma, Ga 2 O 3 (Gd 2 O 3 )/Si 3 N 4 dual-layer gate dielectric for InGaAs enhancement mode metal-oxide-semiconductor field-effect transistor with channel inversion, Applied Physics Letters 91, (2007). 25. R. Ramesh, Schlom, Darrell G, Whither Oxide Electronics, MRS bulletin (2008). 26. D. Dijkkamp, T. Venkatesan, X. D. Wu, S. A. Shaheen, N. Jisrawi, Y. H. Min-Lee, W. L. McLean, and M. Croft, Preparation of Y-Ba-Cu oxide superconductor thin films using pulsed laser evaporation from high T c bulk material, Applied Physics Letters 51, 619 (1987). 27. R. A. McKee, F. J. Walker, and M. F. Chisholm, Crystalline Oxides on Silicon: The First Five Monolayers, Physical Review Letters 81, 3014 (1998). 28. W. Tian, J. C. Jiang, X. Q. Pan, J. H. Haeni, Y. L. Li, L. Q. Chen, D. G. Schlom, J. B. Neaton, K. M. Rabe, and Q. X. Jia, Structural evidence for enhanced polarization in a commensurate short-period BaTiO 3 /SrTiO 3 superlattice, Applied Physics Letters 89, (2006). 29. A. Ohtomo, and H. Y. Hwang, A high-mobility electron gas at the LaAlO 3 /SrTiO 3 heterointerface, Nature 427, 423 (2004). 30. A. Ohtomo, D. A. Muller, J. L. Grazul, and H. Y. Hwang, Artificial chargemodulationin atomic-scale perovskite titanate superlattices, Nature 419, 378 (2002). 31. L. C. Feldman, J. W. Mayer, and S. T. Picraux, Materials analysis by ion channeling: submicron crystallography. (Academic Press, 1982). 16
32 17 2 Medium Energy Ion Scattering 2.1 Introduction Medium-energy ion scattering (MEIS) is a powerful surface science technique for the determination of structure and composition of surfaces and interfaces [1-4]. Basically, light probing ions (usually H + or He + ) with an energy of KeV are incident along a major crystallographic direction in the solid. The backscattering ion intensity is measured as a function of scattering angle and energy. The angular distribution of the ions is a measure of the target geometrical structure and the thermal vibration amplitudes of the surface atoms, while the energy spectra provide information on the composition and its depth dependence of the atoms in the sample. Compared with high-energy (0.5-2 MeV) ion scattering (HEIS), commonly known as Rutherford backscattering (RBS) [5-7], MEIS provides a higher depth resolution. The ions, travelling in the solid, lose energy to electrons and nuclei via various elastic and inelastic interaction processes. Since the total energy loss is proportional to ion path length, the depth resolution of ion scattering technique is directly related to the energy resolution of detection system, where is the energy resolution and is the stopping power (the energy loss per unit length of ion path in solid, more in Section 322.3). In the RBS energy regime, the stopping power of the ions is small. The solid state (surface barrier) detector used in RBS has a relatively poor energy resolution, at best 5 KeV for H + and KeV for He +. These factors result in a poor depth resolution, which makes RBS more suitable for depth profiling method of thicker
33 18 films. In the MEIS energy regime of KeV, the stopping power of H + and He + reaches its maximum for most target materials. High energy resolution ( ) can be realized with a combination of toroidal electrostatic analyzer and a two-dimensional position-sensitive detector (PSD) equipped with microchannel plates (MCP) . Such a high energy resolution is also realized by a sector magnetic spectrometer with one-dimensional PSD and MCP  in a commercialized MEIS system. Under optimal conditions (i.e., appropriate probing ion and primary energy and scattering angle), nearly monolayer resolution 3Å near surface region has been achieved. It should be noted that in MEIS little lateral nanoscale information is obtained because the probing ion beam has a macroscopic size ( ) and is rastered over the sample in order to avoid ion beam-induced damage. It is worth mentioning the other extreme of ion scattering technique, low-energy ion scattering (LEIS) , also known as ion scattering spectroscopy (ISS), which exploits noble gas ions of a few KeV. At this energy regime, the incident ions interact strongly with both the target nuclei and electrons. Ions that travel beyond the outermost layer are mostly neutralized by charge exchange processes and experience multiple scattering events, thus making a quantitative analysis of the backscattered ions from sub-surface layers very difficult. Only (some of) the ions scattered from the outermost layer of the target remain charged and are analyzed by an electrostatic detector. Therefore LEIS is highly surface-specific, but is not very useful for non-destructive depth profiling.
34 Principles of MEIS Interactions of Medium-Energy Ions and Atoms For a fast moving light ion (H + and He + ) of a few hundred KeV, the distance of closest approach between the ion and a target nucleus is greater than the sum of the nuclear radii and less than the sum of the atomic radii. For example, the distance of closest approach for a 130 KeV H + incident head-on to O is 90 fm (determined by setting the Coulomb energy at the turn-around point to the incident energy), while the O nuclear radius is 3 fm and the atomic radii of H + and O is of a few angstroms. Therefore two different kinds of interactions of an ion of such medium-energy with atoms of a solid are needed to be considered. The first one is an elastic nuclear collision, in which both the kinetic energy and momentum of ion and target nucleus are conserved. For small impact parameters, the incident ion undergoes a major change in direction (being backscattered) while the nucleus of the target atom receives considerable recoil energy. Elastic nuclear collision leads to mass specificity (section 2.2.2) and discussions of scattering potential and cross section. The second one is inelastic atomic collision, which is always associated with atomic excitations and/or ionizations. These processes are most probable when the incident ion velocity is close to that of orbital electrons in specific shells. The effects of inelastic collisions on the incident ion are a) limited negligible changes in direction, and b) a slight loss in energy (electronic stopping, section 2.3.1). The latter phenomenon provides depth sensitivity. The treatment of the scattering process in MEIS can be confined to classical, non-relativistic mechanics. A 100 KeV proton has a de Broglie wavelength of order of
35 20 Å, which is much less than an atomic spacing. Since one can safely assume that the scattering potentials do not vary over a distance comparable to the wavelength of the proton, then a classical formalism can be applied. Figure 2.1 A two-body elastic collision process. The scattering angle, initial energy and final energy of the incident ion are all measured in the lab frame The Kinematic Factor The kinetic energy of the elastically backscattered ions from the surface region can be derived by applying conservation of energy and momentum to an elastic twobody collision (Figure 2.1), regardless of the scattering potential. The target atom is assumed to be stationary before the scattering event, justified by the fact that the thermal vibration velocity of target atom is negligible ( 10 5 cm/s) compared with the velocity of incident ion of a few KeV ( 10 8 cm/s). The final energy of an ion (mass ) is equal to the initial energy multiplied by a kinematic factor: (2.1)
36 21 Figure 2.2 The kinematic factor versus scattering angle for proton scattering from various target atoms. where, is the scattering angle in the lab frame, and. This formula holds for, therefore the projectile mass is preferred to be as small as possible in order to probe all elements in material. The lightest ions, protons and helium ions are therefore usually chosen as projectiles. Figure 2.2 shows the dependence of the kinematic factor on the scattering angle for protons incident upon several target masses, illustrating the mechanism through which target atoms with different mass can be distinguished. As large as possible a difference in exit energy, or the difference in, is needed to resolve different target masses. Figure 2.2 shows at the largest scattering angles has a maximum for a given, which results in backscattering geometry in which spectra are always taken at the maximum scattering angle allowed by the experimental setup. Light elements C, N, and O are clearly resolved by proton backscattering at most scattering angles. As the target mass increases,
37 22 however, the difference in exit energy between ions scattered from similar masses becomes less, i.e., the mass resolution becomes worse for heavy target atoms (Si and Al on Figure 2.2). For instance, 100 KeV H + scattering from a 4 unit cell LaAlO 3 film ( 15.2Å thick) on SrTiO 3 substrate is unable to separate the La ( ) and Sr ( ) peaks. The situation is solved with a larger incident mass (He + ions ) with a higher primary energy of 130 KeV, yielding a large enough energy difference between surface La and substrate Sr signals to resolve the two peaks. Ultimately, the mass resolution is limited by the energy resolution of the MEIS experimental setup Scattering Potential, Scattering Cross Section, and Ion Neutralization After obtaining what is on the surface by means of the kinematic factor, the next question is naturally how much is there. Quantitative analysis requires knowledge of scattering the cross section, which in turn is derived from the potential describing the interaction of the ion with the target nucleus. Furthermore, since the detector only detects the positively charged ions scattered from the sample, knowledge of the fraction of exiting ions remaining charged is also required. The cross section σ describes the probability of scattering occurring at a single scattering center. Geometrical interpretation of the cross section is that if the impact parameter of ions is less than the radius of the cross section of the scattering center, i.e., ions are incident within the cross section, the ions will be deflected (scattered) in the collision, otherwise no scattering takes place. For a total of ions incident on a layer of thickness, containing a volume density of randomly distributed scattering centers,
38 23 the number of all scattering events from these centers is, if denotes the fraction of ions remaining positive, the detected scattering events is then (2.2) In our experimental setup, the total number of incident ions is counted as beam dose, or beam current flux, in units of number of ions per second, measured by a Faraday cup placed in front of the sample. For the measured scattering yield, one has to know quantitatively the cross section and ion fraction in order to determine the number of total scattering centers, or the areal density of elements,. The cross section is analytically calculated from the potential the ions experience in the material. Such interactions are the bare Coulomb repulsion by target nuclei if the distance of closest approach is much smaller than the radius of the inner most electron shell, typically the case for ions in the MeV energy range employed in RBS. The differential cross section of such a bare Coulomb potential is the classical Rutherford cross section in the center-of-mass frame. Transformation to the lab frame gives [5,6] (2.3) where, and is the scattering angle in the lab frame. One can estimate the size of this cross section in the MEIS regime. Consider 130 KeV protons scattered from O at a lab angle of 125 o, the Rutherford differential cross section is in the order of (10 barns), according to Equation (2.3); with areal density of Al, a solid angle range of MEIS setup steradians, and, the magnitude for the fraction of scattered protons at 125 o, (Equation (2.2)), is One could also get a feel for the
39 24 fraction of all the ions that are backscattered from the sample, which is in the order of 10-9, by integrating the cross section from 90 o to 180 o. Such small cross sections lead to the single scattering (large angle close nuclear encounter) approximation when treating ion scattering from near surface atoms. Though multiple scattering from near surface atoms is negligible, it might not be the case for scattering processes deeper inside the solid . The incident ions in LEIS energy regime have much higher probability of experiencing multiple scattering due scattering cross sections at least four order larger, which complicates quantitative data analysis in LEIS. The elemental sensitivity of MEIS depends on the atomic number of the target atom, since the scattering cross section varies with. Therefore MEIS is very sensitive to heavy elements. For example, Hf can be detected at cm -2, about 0.1% monolayer level, while in relative terms MEIS sensitivity for lights elements is poorer: the detection limit for C and O is at least cm -2, about 10% of a monolayer. So it would be undesirable to measure these light element peaks superposed on high yield background due to scattering from heavier substrate atoms ( random spectrum ). More accurate measurements of these light elements can be achieved by taking advantage of channeling (section 0). In the MEIS case the use of an unscreened Coulomb potential is inadequate. Consider 130 KeV H + incident on Hf atoms. The inner most electron K shell radii are approximately 720 fm (using the expression with,, and ), while the distance of closest approach is approximately 800 fm (by equating turn-around Coulomb energy to incident energy). Therefore the ions do not see the bare
40 25 Coulomb potential of the target Hf nuclei. Even for the scattering from the medium to light elements, in which case the large angle scattering occurs well inside the K shells, screening has also to be considered because ions must penetrate the electron cloud before experiencing the full Coulomb repulsion of the target nuclei. A variety of screened Coulomb potentials, which take into account the shielding of the nucleus by the atomic electrons, have been derived. These theoretical potentials have been compared to the large range data, obtained from a wide range of energies and incident ion types including even high, to gauge the accuracy of the theoretical models. For the purposes of MEIS, the most accurate are based on quasi-classical statistical Thomas-Fermi model of the atomic potential. The most used approximate solution to this model is the Molière potential . These screened Coulomb potentials (between atoms of charge and ) have the general form (2.4) where is the screening function and is the screening length, the distance scale from the nucleus beyond which screening effects become significant. In the Molière numerical approximation, the screening function is (2.5) where, and. The screening length can have several analytical forms, each tuned so that the form of the screening function agrees with experimental data in the range of interest. For the purpose of MEIS, the commonly used form of screening length is
41 26 (2.6) where, the Bohr radius. For most ion-target combinations, is of the order of. The cross section of the screened Coulomb potential form in Equation (2.4) can now be derived. Since the incident ions do not see the full charge of the target nuclei, equivalent to a slight increase in the incident ion energy, one can assume Rutherford scattering with an effective kinetic energy increase of, which is estimated as the magnitude of the decrease in the potential energy due to screening, which in turn is estimated by the first term in the Taylor expansion of Equation (2.4). Therefore a simple form relating the corrected cross section to the Rutherford value can be shown to be (2.7) The final aspect of the ion-surface interaction necessary to understand in order to determine quantitative elemental information is the fraction of exiting ions remaining positively charged. The charge exchange process is a complex subject which has many aspects depending on the specific type of projectile and primary energy. In the RBS energy regime, the fast-moving projectile is effectively stripped of electrons and travels as an ion through the matter. In the MEIS energy regime, where the velocity of a projectile is comparable to that of its core shell electrons, where is Bohr velocity, the probability that an electron is captured by a moving projectile is much higher than at MeV energies. At even low velocities, as in LEIS, the equilibrium charge
42 27 state of the projectile is a dynamic one, i.e., the projectile charge state fluctuates due to continuous electron capture and loss processes along the trajectory . Therefore the neutralization of a projectile must be carefully accounted for in MEIS and LEIS measurements. Since the underlying mechanisms of charge exchange processes are not yet fully understood, for our MEIS measurements at Rutgers, the charged fraction of an exiting ion can be semi-empirically determined with the use of surface barrier detector, which detects both neutral and charged energetic particles . Busch measured neutralization probability of protons from metal surfaces in good agreement with other experimental data and obtained a semi-empirical fit function for the exit energy dependence of the charged fraction of protons. His and others study show that the charged fraction of protons in the MEIS region primarily depends on the exiting energy, and is almost independent of target materials with at most a 10% variation for different targets. Kitsudo etc.  observed that for He + in the MEIS energy region, the charged fraction has a pronounced dependence on target and increases almost linearly with exiting energy. Particularly, there is a substantial amount ( ) of backscattered doubly charged He 2+ ions. For heavy target atoms measured by an electrostatic energy analyzer this will lead to an additional peak/bump at about one half of the scattered energy of the singly charged He + ions, as we observe in Bi from He + scattering of Bi 2 Se 3. This complicates the interpretation of the energy spectrum. In the case of systems containing several elements where the charged fraction cannot be accurately measured, the results above provide a reasonable estimate. In summary, in order to precisely determine the number of atom on the surface or in a thin film, one must have a
43 28 knowledge of the charged fraction of ions scattered from each of the elements because the ions leaving the surface at different exiting energies. Figure 2.3 Formation of a shadow cone behind an atom directly visible to the incoming ion beam Shadowing, Channeling, and Blocking The surface sensitivity of MEIS can be understood with the concept of shadowing and channeling , which is also of fundamental importance in determining the surface structure of crystalline solids with MEIS. When a monoenergetic and collimated ion beam is aligned along a major crystallographic direction ( a row of atoms ) in a single crystal, the deflections of ions from the first atom along the row leads to the formation of a shadow cone (Figure 2.3), greatly reducing the probability of scattering from deeper atoms along this row. The shadowing effect results in the surface sensitivity of MEIS technique. The radius of the shadow cone at a distance behind the scattering center is derived under the small-angle approximation and a bare Coulomb potential to be (2.8)
44 29 A typical value of, for 100 KeV protons incident along <001> direction on a Si target, is at a distance of behind the first layer of Si atoms. The shadow cone radius will be reduced for screened Coulomb potentials, depending on the ratio between (Equation (2.8)) and the screening length (Equation (2.6)) . In most cases, it is of the value given above. When the ions travel deep inside the crystal and is comparable to the distance to the neighboring atom rows, they start to experience correlated small-angle deflections from those deeper atoms. In turn the steered ions are confined to the spaces or channels between the atom rows and do not make close encounter collisions with the lattice atoms. This is known as channeling. The channeled ions will not hit the bulk atoms except for defects at interstitial and/or lattice sites. Actually as a direct application of the channeling technique, dechanneling measurements of the ion beam is an important means to characterize defects in solids. When thermal vibrations are considered, atoms in sub-surface layers have a probability of entering the channels. As a result the incident ions can be backscattered by the atoms in sub-surface layers, in addition to the ones from the outermost layer. These near surface atoms give rise to the so-called surface peak in the energy spectrum. The total number of atoms visible to the ion beam per row is well described by a universal function of the ratio of the thermal vibration amplitude to the shadow cone radius for any ion-target combination. This relation can be used to predict how many atoms can be seen by probing ions and compared with actual atom content determined by a MEIS measurement. For example, at a Si-terminated 4H-SiC(0001)/oxide interface
45 30 , there are one monolayer of Si atoms directly exposed to the normal incident ion beam and two more monolayers of Si directly underneath the top two C monolayers. Using the lattice constant of bulk terminated SiC, one calculates the radius of the shadow cone from C atoms at Si atoms underneath to be. The thermal vibration amplitude of Si atoms is using the Debye temperature of SiC. According to the universal curve, about 67% of the Si atoms in the C shadow cones are visible to the ion beam, giving a total contribution of Si from the SiC substrate of atoms cm -2. The amount of Si in the amorphous oxide overlayer is then determined by subtracting cm -2 from the total amount of Si measured by the Si surface peak. With the measured amount of O, the oxide layer then turns out to have perfect SiO 2 stoichiometry. In addition, the measured substrate C amount is in good agreement with the theoretical calculation (two open C monolayers), indicating a near perfect interface between the thin oxide layer and the SiC substrate. Outgoing ions, backscattered from near surface layers, may encounter other lattice atoms closer to the surface, leading to more deflections in a similar manner. This blocking effect along specific crystallographic direction gives rise to a non-monotonic scattering angle dependence of the surface peak area and blocking minima in the angular distribution. The position and shape of such blocking dips contain information about the geometrical structure and thermal vibration amplitudes of atoms in the surface region. In a favorable case, when the blocking dip is fully defined by scattering by the second layer, the distance between the first and second layer with respect to the bulk interlayer spacing, the surface relaxation, can be directly determined from the
46 31 angular shift of block dip relative to the bulk blocking direction, using simple trigonometry. In more complicated cases, detailed Monte-Carlo simulations of ion scattering angular yield, based on calculations of many ion trajectories in the binary encounter approximation, are conducted with relative atom positions and surface vibration amplitudes as fitting parameters. These parameters are optimized to give the best possible fit to the experimental angular yields, as judged by a reliability factor [17,18]. This feature of MEIS is very powerful for obtaining surface relaxation and surface reconstruction information and has solved many problems concerning the structural and vibrational properties in metal, semiconductors and oxide surfaces. In a double alignment scattering geometry, where the incident ion beam is aligned with a major crystallographic direction of substrate (channeling), and a detector is aligned with another major index direction (blocking), the probabilities of making close encounters with substrate atoms is very small, thus greatly suppressing the bulk scattering signal. As a result the signals from light elements in thin amorphous overlayers are not overwhelmed by the background bulk signals, yielding more accurate measurements of their contents. Due to their much smaller cross sections it would be difficult to accurately determine the light element contributions in an otherwise (random) scattering geometry. It is worth mentioning that the channeling effect usually plays a dominant role in reducing the background signal (usually more than a 95% reduction), while the blocking effect yields a further reduction of the remaining signal, depending on the crystalline quality of the sample and the incident and outgoing directions of ion beam.
47 Energy Loss and Straggling The energy loss of the probing ion gives MEIS its depth profiling capability, while the energy straggling sets a fundamental limit to the depth profiling resolution Energy Loss Rate When an energetic ion impinges on a solid, the first-order process is the penetration/implantation (forward scattering) into the solid. Large-angle backscattering is a secondary process, because the cross section for such an event is so small, even for an ion at LEIS energies, as seen in section When the ion travels through the solid, it loses energy to target atoms and electrons through a series of collisions. Since these energy loss processes can be assumed to be continuous on a macroscopic scale (though microscopically they are discrete processes of excitation and ionization), one can define the energy loss per unit length or stopping power,. The stopping cross section is also frequently used, where is atomic density of the target. Figure 2.4 Backscattering geometry illustrating the incident angle, exit angle, scattering angle, depth where backscattering occurs, initial energy, and exit energy where the ions leave the surface.
48 33 The energy loss rate is generally a function of energy, but in MEIS one always deals with layers that are thin enough that the ion energy loss rate when traversing these layers can be treated as a constant value until a backscattering event, that is, the amount of energy lost, where is the distant traversed by ion. Considering both the incoming path and outgoing path in the scattering geometry shown in Figure 2.4, one can relate the exiting energy to the depth where the large angle backscattering event occurred, through the energy loss rate: (2.9) where the surface approximation and is used. Since experimental values of the energy loss rate for many ion-target combinations are available (for composite samples, the stopping power is given by Bragg s rule) , the depth information is obtained from the exiting energy, in other words, the energy scale of the energy spectrum is also a depth scale. Because the kinematic factor can be calculated quantitatively, and because both the ion scattering cross section and the energy loss rate are accurately known, one can calculate a theoretical energy spectrum for any given input structure. Vice versa, given an experimental energy spectrum and some general knowledge of the sample, one can reconstruct the sample structure by comparison with theory, i.e., modeling the experimental spectrum with input parameters such as layer thickness and stoichiometry (section 2.4).
49 Ion Stopping Mechanisms This section presents a basic overview of the physics of energy loss (stopping) of light ions in solids. There are two separate stopping mechanisms: nuclear stopping through elastic collisions with target nuclei, and electronic stopping through inelastic collisions with atomic electrons that excite or ionize these electrons. Nuclear collisions involve large discrete energy losses and significant angular deflections of the ion trajectory, while electronic collisions involve much smaller energy losses and negligible deflection of the ion trajectory. Theoretical treatments of these collisions fall into two categories: fast collisions and slow collisions. The criterion separating the two is the velocity of the projectile relative to the mean orbital velocity of the atomic electrons in the outer and inner shell of the target atom. In the RBS regime, the few MeV light projectile has a velocity cm/s, much greater than the orbital velocity of electrons cm/s in common target atoms. In this case, the incident ion is fully stripped of its own electrons and can be viewed as a positive point charge because of the fast speed. The influence of these incident ions on stationary electrons can be treated as a sudden, small external perturbation (the impulse approximation). Bohr derived the following equation (free electron gas model) by including both large momentum transfer within the electronic orbits and small momentum transfer outside the orbits: (2.10) where and are the ion and target atomic numbers, the target atomic density, the electron mass, the ion velocity and the ionization energy of target atoms. The
50 35 electronic stopping power increases with decreasing velocity because the ion spends more time in the vicinity of the atom. Bethe and Bloch extended this theory by including Figure 2.5 Energy dependence of the electronic stopping power for H + and He + ions in Al. The region where nuclear stopping dominates is also indicated. relativistic effect and nonparticipation of strongly bound inner shell electrons, and estimated the transition velocity between the fast and slow collision cases: the Bohr velocity cm/s, corresponding to 25 KeV protons or 100 KeV He + ions. The nuclear stopping in this energy regime is at least three orders of magnitude smaller than the electronic stopping due to the heavy mass of the nuclei compared to that of the electrons (as shown by replacing electron mass by nucleus mass in Equation (2.10)). At ion velocities significantly lower than the Bohr velocity (Lindhard-Scharff region, 8 KeV to 25 KeV for protons), the electronic stopping power is found to be approximately proportional to the velocity. In this region, as velocity of the ion
51 36 decreases, its velocity is comparable to or even less than that of inner shell electrons. In turn these tightly bound electrons play a decreasing role in the stopping process, and the number of target electrons available for excitation decreases. In addition, the probability of the ion capturing electrons (neutralization) becomes large due to the matched velocity, so the net charge of the projectile becomes lower. As a result, the electronic stopping decreases as the ion velocity decreases. The maximum of the electronic stopping power lies in the vicinity of the transition region between these two theoretical approaches, namely the Thomas-Fermi velocity, the MEIS energy regime, making it difficult to obtain stopping parameters exclusively from theory. For this reason, most stopping values used for the purpose of analyzing MEIS energy spectra are found from experimental values (tabulated values of Anderson and Ziegler), or from numerical calculations (the SRIM code ). The high depth resolution of MEIS exploits the maximum electronic stopping at MEIS energies combined with the high energy resolution of the detection system. For completeness, in the LEIS energy regime ( KeV), as the ion velocities ( cm/s) are even smaller than the orbital velocities of the outer shell electrons in the target atoms, few electrons participate in the slowing down of the ions, thus the electronic stopping is expected to be negligible in this regime. The nuclear stopping due to elastic atomic collision dominates in this energy regime. This can be understood by considering a situation in which the ions constantly bump into the solid atoms, suffering many large angle scattering processes. This would occur if the distance of closest approach for the ion-atom interaction were at least of the order of the screening
52 37 radius. Using the Thomas-Fermi model of the atom with the Molière approximation, the upper limit on the incident energy of ion can be found so that the distance of closest approach is greater than the screening length. For He + ions, this energy is 1.3 KeV, right in the LEIS energy region. Because the atomic collisions dominate, in sputtering using incident noble gas ions to clean surfaces this energy region is used, in order to achieve maximum sputtering yield Energy Straggling In the discussions above, we have considered the electronic energy loss to be essentially continuous along the ion path. However, one important aspect of the truly discrete nature of the inelastic ion-atom collisions must be examined. The total energy loss during the ion s trajectory is subject to statistical fluctuations, due to both fluctuations in the size and the number of the discrete energy losses. The resulting broadening of the ion energy distribution as it passes through the solid is called straggling. Energy straggling places a finite limit on the precision with which energy losses, and hence depths, can be resolved. For short travel distances (energy loss less than about 1% of the incident energy) the distribution is an asymmetric Vavilov distribution (section 2.4.2). For larger distances the distribution becomes approximately Gaussian. Meaningful deconvolution of MEIS data can be obtained by using the simple Gaussian form for the energy straggling. In the fast ion regime (fully stripped ions), Bohr derived the following expression for straggling in the free electron model (2.11)
53 38 where is the variance of the energy distribution for ions (atomic number ) travelling through the target (with atomic number and atomic density ) a distance. However, in the MEIS regime, projectile velocities are comparable to the electronic velocities. For this transition region, the local electronic density and the velocity distribution of the electrons must be taken into account. To this end, using the Thomas- Fermi model, Lindhard and Scharff extended Bohr s treatment . Their result is expressed in terms of the Bohr straggling, (2.12) (2.13) where is the Bohr velocity. For any at MEIS regime the straggling is reduced from Bohr s value by about one half. Equation (2.12) provides a suitable starting point for estimating straggling parameters needed for energy spectra simulation. 2.4 Simulation of the MEIS Energy Spectrum One of the strengths of MEIS is its depth profiling capability with sub-nanometer resolution. The elemental depth profiles are extracted from the energy spectrum by analyzing the shape of the signal from different atoms. This section summarizes some key issues concerning the quantitative analysis of MEIS energy spectrum based on the energy loss process discussed in the previous section.
54 Convolution of Conventional Gaussians When penetrating a thin ( ) amorphous film, light ions experience a large number of large impact-parameter collisions with ion cores and electrons (both elastic and inelastic). Since the energy transferred in these processes is much smaller than the energy straggling for the given travel path, it is then valid to neglect the details of the energy transfer during individual encounters and to assume a Gaussian energy loss distribution because of the large number of collision processes. To simulate the energy spectrum the thin film is divided into thin slices ( thick) and the energy loss from each slice is modeled using Gaussian straggling. Considering both the inward and the outward ion path, one obtains the scattering yield by summing up the contributions from every slice: (2.14) where is the thickness of th slice, the scattering cross section is evaluated at depth of beneath surface:, the straggling term includes the Lindhard-Scharff straggling along inward/outward path and the finite energy resolution of detection system where the last two terms depend on the depth according to Equation (2.11) and (2.12), and is the mean exiting energy given by Equation (2.9). Stopping powers have been tabulated (Ziegler) or can be calculated from available software (in our case, SRIM).
55 40 The MEIS simulation program that has been used in this work was developed by Tomoaki Nishimura . Relevant parameters of a tentative layered structure are used as input: thickness, density and composition of each layer as well as the channeling probability of each element if a crystalline structure is considered. The concentration and depth profiles of the different species can be determined from an optimum fit to the experimental energy spectrum by varying these input parameters by trial and error. Figure 2.6 Schematic illustration of the deconvolution of an energy spectrum from neighboring thin layers. Note that for simplicity only five Gaussians are shown. Typically at least 60 layers are needed to model such a 30Å thick film Energy Loss Model for Near Surface Scattering For an ultrathin film ( ), the number of ion-target collisions in the near surface region is necessarily small, therefore the central theorem does not apply and the assumption of Gaussian straggling breaks down. Pezzi et al.  treated the energy loss in this case as a consequence of a series of independent binary encounters with finite cross section, therefore the energy loss follows a Poisson distribution. Naturally the Poisson distribution asymptotically approaches the normal distribution when
56 41 dealing with large number of scattering events, as is the case for a thicker film. In addition, the energy loss due to the excitation and/or ionization in near zero impactparameter collisions is also taken into account. This inelastic energy loss process, combined with the Poisson statistics, gives rise to an asymmetric backscattering peak. The effect of the electronic structure on the peak shape is more remarkable for heavy target atoms (e.g. Hf atoms) in ultrathin film, where the core electrons have large binding energies. Software that implements this model is available on Pezzi s website  The Stopping Power in a Crystal Understanding the electronic stopping is important for extracting reliable values for the depth profiles. The discussions of electronic stopping power so far have assumed a random distribution of target atoms, as for amorphous or polycrystalline structures. Under the double alignment scattering geometry often used in MEIS experiments (section 0), in which both the incoming and the outgoing ion trajectories are aligned with major crystallographic directions of substrate, however, the inelastic energy loss in the single crystal region (substrate) of detected ions is found to be up to three times higher than under random conditions . This can be attributed to the impact parameter dependence of the electronic stopping power. The channeled ions do not sample the entire stopping medium with equal probability; they traverse regions with low electron density in the middle of the channels (resulting in lowered stopping power of channeled ions), and also regions with high density near atomic rows. Under channeling and blocking conditions, the ions that eventually enter the detector have
57 42 experienced two large angle small impact parameter scattering events from the substrate atoms, leading to an increase in the stopping power of detected ions due to the increased electron density. Thus one should be careful when analyzing the depth scale of substrate from a channeling energy spectrum. Fortunately the depth scale of the substrate is of minor concern in this thesis. However one should always keep this issue in mind when dealing with epitaxial films. 2.5 Instrumentation MEIS involves a rather sophisticated/complicated experimental setup, primarily due to the need for very high energy resolution, which requires a stable accelerator and complex detection equipments. Since detailed descriptions of MEIS instrumentation is covered in Hsu-Chang Lu and Brett Busch s thesis, this section focuses on some recent experimental issues regarding energy resolution and quantitative data analysis. A toroidal electrostatic analyzer (TEA) collects and energy-analyzes backscattered ions in a horizontal scattering plane, by applying voltages of opposite polarity to its toroidal plates . The geometrical dimensions of the TEA have been optimized to provide desired energy and angular focusing characteristics of the TEA. A pair of chevron-mounted micro-channel plates (MCP), operated in a pulse saturated mode and enabling single event counting, then amplify the signal from an incident ion, by means of multiple emissions of secondary electrons, to a level ( pc per incident ion) that can be registered by a multi-anode charge-dividing collector, known as 2D position sensitive detector (PSD). The x (angle) position and y (energy) position of the electron cloud are resolved by measuring the divided charge at four electrodes of the PSD. After
58 43 the positions are decoded by a position analyzer, a 2D histogram is accumulated in a memory buffer, from which the data is finally read out by an IBM compatible PC. A GUI (graphic user interface) data acquisition program has been developed using Visual C++ to perform functions such as automated data acquisition, data correction and further analysis. Busch discussed contributions from several factors to the total energy resolution, 160 ev, which was determined by the full width at half maximum (FWHM) of leading edge of the surface peak of a sub-monolayer of Au on Si. After removing the intrinsic contribution due to proton-au interaction (excitation of valence electron, ion energy straggling, etc.), his calculation showed the instrumental contribution was 108 ev. Though this result was quite consistent with the reported value of such 2D detection systems , the breakdown of the instrumental contribution had to be re-examined ten years later after his experiment. The beam energy fluctuation is monitored by a proportional voltage meter connected to the accelerator. This energy spread is now measured to be about 100 ev. The vertical size of the collimating slit located in front of the sample is a very important factor determining the energy resolution since the electric field in the TEA is applied along this direction, corresponding to the energy coordinate in the PSD. The nominal height of the slit and the nominal distance between the slit and sample are 0.1 mm and 50 mm, respectively. These two numbers need to be checked in the future work. The center energy passing through the TEA is determined by the voltage applied to the TEA electrodes, where is in KeV and in KV. The electrode voltage ripple is measured to be about 5 mv, resulting in an almost
59 44 negligible fluctuation on beam energy. Besides applied voltages being made stable, the four voltages applied across the MCP s have been adjusted to yield an optimum pulse height distribution (PHD) of counts to ensure high energy resolution. A direct method to measure the instrumental resolution would be to use a mask with an array of evenly spaced holes placed in front of the channel plates to give a reference for an evenly spaced matrix . We have instead used an indirect method based on measurements on an ultrathin ( ) HfO 2 film. The current instrumental resolution, as a fitting parameter in the spectrum simulation program, is estimated to be about 400 ev for 100 KeV protons and 600 ev for 100 KeV He +. These are preliminary results and more work is ongoing. Still some meaningful points can be made so far. The difference in energy resolution for proton and He + beams might be attributed to different ion-target interactions, especially the straggling from excitations of valence electrons (note that the straggling effect due to ion penetration has been removed as a factor). To determine the energy resolution of the system, a sub-monolayer of high Z elemental sample is preferred because one wants to avoid the complications from the convolution of sub-surface layers and straggling averaging for a layer of unknown stoichiometry. A vacuum-deposited thin Au layer on Si satisfies the above requirements, though one needs to be cautious about the formation of Au clusters on the Si substrate. Such growth could be monitored by low energy electron diffraction (LEED) in the MEIS chamber. Putting aside those measurement details, the aging of MCP s might be the primary cause of the degraded energy resolution, since the MCP has a finite life time
60 45 due to particle irradiation . Replacing them with a new pair of MCP s is a straightforward solution, though it requires a full and careful calibration of the MCP and PSD. The image produced by the detection system is usually slightly distorted because of a coupling capacitance between the two electrically isolated chains of triangular electrodes on PSD. Therefore the calibration step is needed to restore the geometrical information. Nonlinearity in energy is corrected by computing the true exiting energy of ions scattered from the surface atoms based on the kinematic factor Equation (2.1) for a given scattering angle (the angular nonlinearity itself is negligible *Lu s thesis]). Non-uniformity in the MCP efficiency is corrected using a polycrystalline Ta foil as target sample that produces an almost uniform scattering yield. Two more issues remain to be discussed about the experimental parameters in the simulation program. The first one is the solid angle of the MEIS detector. This quantity, together with a normalization constant used in the data acquisition program, can be extracted by comparing with the results of some standard sample (e.g. a graphite sample with a known number of Sb atoms implanted) determined by RBS. The second is the ion dose. The ion dose is indirectly measured by a Faraday cup placed in front the sample . Since the mesh in the Faraday cup is designed in a such a way that the area of the mesh opening is one half that of the whole mesh, this leads to the assumption that the number of ions incident on the sample is the same as the one registered on the mesh, which again needs to be double checked, especially for the case of insulating samples. The Faraday cup is held at -300 V relative to the sample to suppress the secondary electrons from the sample surface. But on insulating surfaces, positive
61 46 charges would easily build up keeping other probing ions from hitting the sample, and obviously making accurate measurements of ion dose difficult. Such charging problems could be solved by either using a conducting paste or electron flooding. 1. J. F. van der Veen, Ion beam crystallography of surfaces and interfaces, Surface Science Reports 5, 199 (1985). 2. R. Tromp, Medium Energy Ion Scattering, in Practical Surface Analysis: Ion and neutral spectroscopy, (Wiley, 1992), pp T. Gustafsson, Medium Energy Ion Scattering for Near Surface Structure and Depth Profiling, in Ion Beams in Nanoscience and Technology, (Springer, 2009), pp M. Copel, Medium-energy ion scattering for analysis of microelectronic materials, IBM Journal of Research and Development 44, 571 (2000). 5. W. K. Chu, J. W. Mayer, and M. A. Nicolet, Backscattering spectrometry. (Academic Press, 1978). 6. T. L. Alford, L. C. Feldman, and J. W. Mayer, Fundamentals of Nanoscale Film Analysis, 2 ed. (Springer, 2010). 7. Y. Wang, and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, 2 ed. (Materials Research Society, 2010). 8. R. M. Tromp, M. Copel, M. C. Reuter, M. H. v. Hoegen, J. Speidell, and R. Koudijs, A new two-dimensional particle detector for a toroidal electrostatic analyzer, Review of Scientific Instruments 62, 2679 (1991). 9. K. Kimura, K. Ohshima, K. Nakajima, Y. Fujii, M. Mannami, and H. J. Gossmann, Monolayer resolution in Rutherford backscattering spectroscopy, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 99, 472 (1995). 10. H. H. Brongersma, M. Draxler, M. de Ridder, and P. Bauer, Surface composition analysis by low-energy ion scattering, Surface Science Reports 62, 63 (2007). 11. L. C. Feldman, J. W. Mayer, and S. T. Picraux, Materials analysis by ion channeling: submicron crystallography. (Academic Press, 1982). 12. G. Molière, Therorie der Streuung schneller geladener Teilchen I. Einzelstreuung am abgeschirmten Coulomb-Feld, Zeitschrift für Naturforschung 2A, 133 (1947). 13. B. W. Busch, Thesis, Rutgers University, Y. Kitsudo, K. Shibuya, T. Nishimura, Y. Hoshino, I. Vickridge, and Y. Kido, Charge exchange of medium energy H and He ions emerging from solid surfaces, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 267, 566 (2009). 15. O. S. Oen, Universal shadow cone expressions for an atom in an ion beam, Surface Science 131, L407 (1983).
62 16. X. Zhu, H. D. Lee, T. Feng, A. C. Ahyi, D. Mastrogiovanni, A. Wan, E. Garfunkel, J. R. Williams, T. Gustafsson, and L. C. Feldman, Structure and stoichiometry of (0001) 4H--SiC/oxide interface, Applied Physics Letters 97, (2010). 17. P. R. Watson, Critical Compilation of Surface Structures Determined by Ion Scattering Methods, Journal of Physical and Chemical Reference Data 19, 85 (1990). 18. T. C. Q. Noakes, P. Bailey, and D. P. Woodruff, MEIS surface structure determination methodology: Application to Ni (100)c(2 2)-O, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms , 1125 (1998) Q. Yang, D. J. O'Connor, and Z. Wang, Empirical formulae for energy loss straggling of ions in matter, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 61, 149 (1991). 21. Y. Kido, and T. Koshikawa, Ion scattering analysis programs for studying surface and interface structures, Journal of Applied Physics 67, 187 (1990). 22. R. P. Pezzi, P. L. Grande, M. Copel, G. Schiwietz, C. Krug, and I. J. R. Baumvol, Advanced ion energy loss models: Applications to subnanometric resolution elemental depth profiling, Surface Science 601, 5559 (2007) P. F. A. Alkemade, W. C. Turkenbrg, and W. F. Van Der Weg, The energy loss of medium-energy He+ ions backscattered from a Cu(100) surface, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 28, 161 (1987). 25. H. C. Lu, Thesis, Rutgers University, J. Ladislas Wiza, Microchannel plate detectors, Nuclear Instruments and Methods 162, 587 (1979). 27. J. B. Zhou, Thesis, Rutgers University,
63 48 3 The LaAlO3/SrTiO3 Heterointerface 3.1 Introduction In early 2004, Ohtomo and Hwang reported that a high-mobility conducting electron system develops at the interface between two perovskite oxides LaAlO 3 (LAO) and SrTiO 3 (STO), despite the fact that both constituent materials are band insulators . This material system has attracted wide-spread interest over the past several years, and the physics responsible for this quasi-two-dimensional electron gas (or electron liquid ) in still under debate. Polar discontinuity, doping with oxygen vacancies in the STO substrate, indiffusion of La into the substrate, and/or lattice distortion have been proposed as possible mechanisms of the formation of the conducting LAO/STO interface. In particular, an electronic reconstruction model associated with the polar discontinuity was proposed in the original paper. In this model the LAO/STO interface is assumed to be completely abrupt and structurally perfect, owing to the ability of precise control of the heterostructure on an atomic level . This assumption has been adopted by many other experimentalists and those who carry out first principles calculations of electronic structure at the LAO/STO interface. However, a few experimental papers [4-6] indicate that this heterointerface might not be as sharp as the others assumed. These results have unfortunately been largely ignored. This is where can MEIS play an important role: as a direct technique to characterize atom profiles in a buried interface, we have carried out MEIS measurements on a series of LAO/STO samples prepared in the pioneering laboratories
64 49 at the University of Augsburg (one 4 unit-cell sample), the University of Tokyo (three 4 unit-cell samples with different laser fluence), and Pacific Northwest National Laboratory (one 7 unit-cell sample). This chapter is organized as follows: sections 3.2 is a brief review of some basics of two constituent materials and also the growth method of such heterostructures is discussed. Section 3.3 summarizes two prevailing proposed explanations of the origin of the mobile electron system based on abrupt interface assumption. Section 3.4 discusses some experimental considerations of ion beam type and energy, along with two scattering geometries employed. Section 3.5 presents MEIS results as well as the interpretation of the depth profiles of the four metal elements. Further discussions on the La atom profile is given in Section Material Basics and Heterostructure Growth The perovskite transition metal oxides have a general formula of ABO 3, where A stands for a large cation of an alkaline-earth, and B for a small cation of a transition metal, a rare-earth metal, or a group-iii metal. ABO 3 compounds can condense into a large diversity of crystal structures, among which are cubic, orthorhombic, tetragonal and monoclinic structures. The unit cell of a cubic perovskite structure is shown in Figure 3.1(a), where an A ion occupies the cubic center, with B ions at the vertices, and O ions in the middle of edges (another equivalent representation of this unit cell is that B ions occupy the cubic center, while A ions are at the vertices, and O ions are at the face centers). The A-site is twelve-fold coordinated, whereas the B-site is six-fold coordinated and surrounded by an octahedron of O ions (BO 6 ) as shown in Figure 3.1(b). Figure 3.1(c)
65 50 shows an instructive description of the perovskite structure. Along the <100> direction the perovskite can be thought of as a stacking of alternating AO and BO 2 atomic layers. This view will be further discussed in next section. Figure 3.1 Crystal structure of perovskite ABO 3. (a) the cubic unit cell, (b) the BO 6 octahedra, and (c) the alternating AO and BO 2 atomic layers. SrTiO 3 is cubic (space group Pm3m) at room temperature with a lattice constant of Å. Intrinsic SrTiO 3 has a relatively large, indirect band gap of 3.25 ev, which can be considered as either a band insulator or a semiconductor. SrTiO 3 can be doped into a metallic or superconducting state depending on the carrier density introduced by oxygen vacancies. A small amount of cationic substitution, such as La for Si or Nb for Ti, can also lead to the insulator-metal transition. SrTiO 3 has a high dielectric constant that makes it a potential candidate for the gate dielectric material in CMOS. As a thoroughly studied complex oxide, SrTiO 3 is a standard substrate for many heteroepitaxial oxides, such as high superconducting YBa 2 Cu 3 O 7-x, colossal magnetoresistance oxides, and ferroelectrics, due to the similarities in structure and lattice constants, in addition to its
66 51 chemical inertness. LaAlO 3 has a rhombohedral structure (space group R3c) at room temperature and undergoes a transition to a cubic perovskite structure at . Since the heteroepitaxial LaAlO 3 film is grown at a relatively lower temperature, the actual structure of the film differs from the cubic only by a small antiphase rotation of its AlO 6 octahedra . This structure can be described as pseudocubic with a lattice constant of Å. The resulting small lattice mismatch of 3% to SrTiO 3, together with a similar thermal expansion coefficient as SrTiO 3, enable the epitaxial growth of LaAlO 3 film on SrTiO 3 substrate. LaAlO 3 is a band insulator with a wide gap of 5.60 ev and is also considered as a candidate for a gate dielectric due to its relatively high value ( ) . The complex oxide LAO/STO heterostructure is grown in an ultrahigh vacuum (UHV) chamber by pulsed laser deposition (PLD)  using a single crystalline LaAlO 3 target on (001)-oriented SrTiO 3 single crystalline substrate. A TiO 2 -terminated substrate surface is obtained by well-established chemical and thermal treatment : buffered HF etching, deionized water rinsing and subsequent annealing in an oxygen environment. The TiO 2 fraction is about 90% on the SrTiO 3 surface after these treatments, as was shown by a more quantitative MEIS study . Atomic force microscopy (AFM) shows the morphology of the TiO 2 -terminated surface (Figure 3.2(a)). The high quality of this surface termination is illustrated by a clear terrace-step structure with a step height of a unit cell. Layer-by-layer growth of perovskite LaAlO 3 film is achieved by ablating from a single-crystal LaAlO 3 target using a KrF excimer laser ( nm, pulse width 25 ns). One of the advantages of PLD over other deposition techniques is that the material transfer, through an ablation plume to the film to be
67 52 grown, presumably keeps the stoichiometry of the target material. Typical deposition conditions are a substrate temperature of, oxygen pressure of mbar, and laser fluence of J/cm 2. The film growth is monitored by in-situ reflection high-energy electron diffraction (RHEED). The oscillations of RHEED intensity during the initial growth of the first unit cells indicate a two-dimensional layer-by-layer growth mode (not shown). Figure 3.2(b) shows an AFM image  of a 5-unit-cell thick LaAlO 3 grown on TiO 2 -terminated SrTiO 3. The original terrace-step structure of the substrate is preserved throughout the film growth, indicating the presence of LaAlO 3 surface with one type of termination. Figure 3.2 AFM image of (a) TiO 2 -terminated SrTiO 3 (001) substrate and (b) 5-unit-cell LaAlO 3 film grown on the substrate. The scan profile (not shown) of the AFM image shows smooth terraces with unitcell steps, and the RMS roughness is estimated to be less than 1 Å. Note that the typical width of the terraces is with a probing depth of 20 Å ( nm. Therefore, in a typical MEIS scattering geometry 5-unit-cell) and a scattering angle of 125, considering the inward and outward path, a very small percentage (less than ) of the ions probe the surface steps. In other words, most ions probe the very smooth terrace region,
68 53 which is important in extracting accurate depth profiling information from the energy spectrum, since spectrum modeling assumes a perfectly flat surface. Any kinds of deviation from such an ideal surface, such as formation of islands, surface roughness, and pin holes, can easily complicate the data interpretation. In this sense the depth profiling information of the LAO/STO heterointerface obtained from MEIS is by far the most reliable compared to results from other systems we have studied (for example a topological insulator Bi 2 Se 3 film on Si). Figure 3.3 The polar catastrophe illustrated for atomically abrupt (001) interfaces between LaAlO 3 and SrTiO 3. The dipole discontinuity at the unreconstructed interface of (a) AlO 2 /LaO/TiO 2 and (b) AlO 2 /SrO/TiO 2 produces a non-negative/non-positive electric field, leading in turn to an electric potential that diverges with thickness. (c) If half an electron is added to the last TiO 2 layer, the resulting interface dipole causes the electric field to oscillate about zero and the potential remains finite. (d) Removing half an electron from the SrO layer in the form of oxygen vacancies can avoid the potential divergence at the AlO 2 /SrO/TiO 2 interface. 3.3 Possible Explanations of Conducting Interface Polar Discontinuity
69 54 A simple elementary electrostatic consideration has been put forward to explain the high conductance at the LAO/STO interface (Error! Reference source not found.). The formal valence states of the atoms involved can be assigned as La 3+, Al 3+, O 2-, Sr 2+, and Ti 4+ ; to first order, only Ti has accessible mixed valence character, allowing for reduction towards Ti 3+. As discussed above, the (001)-orientated perovskite structure ABO 3 can be considered as alternating stacks of AO and BO 2. In the simple ionic limit, SrTiO 3 is a sequence of charge-neutral sheets of (SrO) 0 and (TiO 4 ) 0 (non-polar layers), while LaAlO 3 has alternating -charged sheets of (LaO) 1+ and (AlO 2 ) 1- (polar layers). When joining these two perovskites with atomic abruptness, a polar discontinuity results at the interface. Two interface configurations arise, which can be defined by the layer composition between AlO 2 and TiO 2 at the interface: AlO 2 /LaO/TiO 2 or AlO 2 /SrO/TiO 2. Error! Reference source not found. (a) and Error! Reference source not found. (b) show that if there is no redistribution of charges, the polar discontinuity at an atomically abrupt interface leads to a polar catastrophe, where the electrostatic potential diverges with LaAlO 3 film thickness. The polar catastrophe can be avoided by rearrangement of electric charges. Unlike conventional semiconductor heterostructures with a polar discontinuity where each ion has a fixed valence, in complex oxides compositional roughening (atomic reconstruction) is not the only option for charge rearrangement: mixed valence charge compensation can occur if electrons can be redistributed at lower energy cost than redistributing (moving) ions [4,14]. Such compensation at the AlO 2 /LaO/TiO 2 interface could be realized by a mixed valence state of Ti (half Ti 4+ and half Ti 3+ ) as a result of a net
70 55 transfer of half an electron per two-dimensional unit cell across the interface from the LaO layer to the TiO 2 layer. This produces an interface dipole that causes the electric field to oscillate about zero and the potential remains finite (Figure 3.3 (c)). This electronic reconstruction results in an n-type interface. Indeed, metallic conductivity and Hall transport measurements suggest free electrons at the n-type interface . An analogous p-type AlO 2 /SrO/TiO 2 interface could be achieved by removing half an electron per unit cell from the SrO layer (Figure 3.3 (d)). Since none of the cations can assume higher valence states, the only possible way of compensating is by invoking oxygen vacancies:, where represents the doubly positivecharged vacancy at the oxygen site and the freed electrons. Thus this can be seen as an atomic interface reconstruction. Interestingly, the resistance of the p-type AlO 2 /SrO/TiO 2 interface is three orders of magnitude higher than that of n-type AlO 2 /LaO/TiO 2 interface , showing insulating behavior. This oversimplified polar discontinuity picture assumes no cationic disorder and perfect stoichiometry at the atomically abrupt AlO 2 /LaO/TiO 2 interface and predicts the intrinsic n-type carrier density at the interface to be cm -2 based on the unit cell area of TiO 2 sheet. This picture is consistent with the observed existence of a critical thickness of the LaAlO 3 film to induce the electronic reconstruction in fully oxygenated samples, where oxygen vacancies in the substrate are removed by high oxygen partial pressure during growth and extremely long post-growth oxygen annealing . Thiel el al found the presence of a fourth unit cell of LaAlO 3 abruptly changes the TiO 2 - terminated interface from insulating to conducting. But their measured carrier density is
71 56 only cm -2. It is worth mentioning that these films are indeed fully oxygenated since the films grown at lower oxygen pressure demonstrate a much higher carrier density cm -2 (section 3.3.2) [1,6]. Moreover, a recent X-ray photoemission study of band offsets from the position of the core levels of the cations  indicates an absence of an electric field associated with the polar discontinuity model in samples with one to three unit-cell-thick LaAlO 3 films. Furthermore, no partially reduced Ti 3+ is observed at the interface by photoemission measurements . All these results indicate there must be other mechanisms responsible for the conducting TiO 2 - terminated interface Oxygen Vacancies The free carrier density of 2DEG deduced from Hall measurements was reported to be cm -2 in the original paper, which is later confirmed by other groups [17,18], though it seems remarkably high compared to the conventional two-dimensional electron gas systems (for example, cm -2 for AlGaAs/GaAs). Oxygen vacancies are proposed to be the origin of the high conductivity at the interface. Since the initial SrTiO 3 is insulating and has no oxygen vacancies, they are introduced by the PLD process, whereby the energetic particles from the ablation plume impinging on the surface sputter off oxygen. Kalabukhov et al systematically changed growth and annealing conditions and were able to tune the carrier density from over cm -2 down to cm -2 by adding more oxygen after growth . This study demonstrates that oxygen vacancies exist to a lesser or greater extent, depending on the background pressure of oxygen during film growth and that they affect the conductivity. As for the p-type hole-
72 57 doped interface, the introduction of oxygen vacancies, therefore more electrons, compensates the holes present at the interface, resulting in low conductivity. As described above, the composition of the interface plays an important role in the mechanisms of the conducting interface. As MEIS can determine the film composition, we have used this technique to investigate the abrupt interface assumption, and also if possible to investigate the possible oxygen deficiency in the substrate. 3.4 Experimental Beam Type We have used both proton and helium ions to investigate the LAO/STO system. There are fewer complications in understanding the interaction of protons with a surface than there are for heavier ions, for example, more information is available in literature concerning the charge exchange for protons exiting the surface. It turns out, however, that the proton is not a good choice for the LAO/STO system due to its poor mass resolution for heavy target elements, in this case, particularly the La in the ultrathin LAO film and the Sr in the substrate. Most importantly, the observed La indiffusion and Sr outdiffusion result in more ambiguity in extracting accurate depth profiles using the proton beam (section 3.5.3). Therefore a helium beam was eventually used as the probing ion beam due to its much better mass resolution for heavy elements (section 2.2.2) giving well-separated La and Sr peaks. The helium beam energy was chosen to be KeV, based on two considerations. First, it resolves La and Sr peaks very well even in case of extensive interdiffusion. Second, it provides the best depth resolution given
73 58 the current status of the accelerator. For most materials, the maximum electronic stopping is around KeV for helium , much larger than for protons, yielding a depth resolution of (one unit cell) near the surface. In addition to longer data acquisition time, one drawback of this relatively high energy is that the energy span of a whole energy spectrum (from O to La) is so large that it is impossible for the data acquisition program to include all elements in one data file, because that would exceed the maximum number of energy windows allowed in the program. Thus one has to separately take spectra for light and heavy elements, which sometimes introduces some normalization uncertainty when merging two spectra, which makes the analysis of the light elements such as O and Al difficult. An alternative method is to use a lower energy ( KeV) and/or the proton beam Scattering Configurations In order to fully characterize the LAO/STO heterostructure with MEIS, two scattering geometries were utilized: channeling (double alignment) and random. In the channeling geometry, the ion beam is directed along the surface normal , and the detector is aligned with the  direction of substrate STO, thus the major scattering events occur in (110) plane in which all of A-site, B-site and oxygen atoms of the perovskite structure are visible to the projectile ions (Figure 3.4). Due to the shadowing effect (section 2.2.4) and the nearly matched lattice constants of LAO and STO, the ion beam is highly sensitive to the outermost layers of this heteroepitaxial structure, i.e., this geometry is very useful in determining the composition of the outermost LAO unit cell, with the backscattering signals from substrate bulk greatly suppressed.
74 59 Figure 3.4 Double alignment scattering configuration. For simplicity only one unit cell of LAO is shown. The random scattering geometry allows one to determine the stoichiometry of the epitaxial film and elementary depth profiles through the film, across the buried interface and down to the first unit cells of the substrate. The random scattering is achieved by intentionally aligning the ion beam away from the major crystallographic axes of the substrate, so that it appears to the incident ions that the atoms from both the epitaxial film and the crystalline substrate are positioned in a random fashion. The axes need to be tilted away by angles larger than a critical angle, below which the ions are considered to be effectively channeled . The critical angle is calculated as (3.1) where and are the atomic number of incident ion and target atom, respectively, the primary energy, and the atomic spacing along the axis. The critical angle is for 130 KeV helium ions along a <001> Sr atomic row in SrTiO 3. It was not straightforward to get a real random spectrum. Initially, after tilting the sample away from the beam by about each rotation axes, the resulting spectrum did not display
75 60 Figure 3.5 (a) Energy spectrum of bare STO with channeling effects along with a simulated random energy spectrum. (b) Schematic illustration of the oscillation associated with planar channeling. the plateau feature of substrate elements expected on a random spectrum. Instead it always showed some valley-like features like those indicated in Figure 3.5 (a). Figure 3.5 (a) is an energy spectrum of a bare STO substrate after the same tilting. One should not interpret such features as real (only chemically impossible stoichiometries would result). One possible origin of such features can be oscillations associated with planar channeling [20,21], rather than axial channeling, since these features occur around the depths where such oscillations are expected (Figure 3.5 (b)), where is the  Sr row separation on a (110) plane. Another possibility is the outgoing ions being blocked by some high-index axes. In either case the spectrum shows a strong channeling
76 61 effect most likely due to the high level of crystallinity of the STO substrate. After several trials, a set of large angle tilts was eventually found that produced a real random Figure 3.6 Helium random spectrum with two models. Note that the La peak is far off in the stoichiometric film model. Inset shows the valley region between the La and Sr peaks. spectrum showing pronounced plateaus. 3.5 Results As described above, the threshold thickness to induce a high conducting sheet is 4 unit cell. This section presents both the helium and proton backscattering results from one of the four unit-cell LAO/STO samples, followed by a summary of results from the other four unit-cell samples grown under somewhat different conditions. Comparisons with a slightly thicker LAO film (7 u.c.) and a much thicker film (25 u.c.) are briefly discussed. The 7 unit-cell sample was measured by MEIS and the 25 unit-cell by RBS .
77 The Helium Random Direction Spectrum Figure 3.6 shows a random MEIS spectrum using KeV He + ions, along with two simulations. The two simulations are for: (i) a fully stoichiometric four unit-cell LAO film with an atomically abrupt interface to the TiO 2 -terminated STO substrate; (ii) an offstoichiometric film with an intermixed interface in which optimal agreement with experiment was sought by varying the atom profiles. The abrupt interface simulation clearly does not match the experimental spectrum. The simulated La peak far exceeds the experiment, the low energy tail of La peak and the leading edge of Sr plateau do not fit, and the counts in the valley between La and Sr are not accounted for. By contrast, the optimized intermixing interface model yields much better agreement with experiment. In this model, the LAO film has to have less La to fit the La peak height, some La needs to be incorporated in the first few unit cells of STO substrate to account for the high energy end of the valley, and Sr has to be incorporated in the LAO film to fit the leading edge of the Sr plateau and the low energy end of the valley. The presence of La in STO and Sr in LAO indicates the indiffusion of La and the outdiffusion of Sr across the LAO/STO interface. In our optimized model the La areal density within the four u.c. film is cm -2, and the La density within the first ( u.c.) of the STO is cm -2, giving rise to a total areal density of cm -2 detected in the overlayer and the STO immediately adjacent to the interface. Since the areal density for La in a stoichiometric 4 unit-cell LAO film is cm -2, of La is not accounted for. A discussion about this La deficiency are given in section The
78 63 simulation also yields Sr and Ti areal densities within the LAO film of cm -2 and cm -2, respectively. For this film, a slight maximum in the backscattering intensity can be seen between the La and Sr signals. These counts can technically be fit by incorporating La inside the STO down to below the interface, implying indiffusion. However, it is hard to understand why a maximum should occur instead of a constant or decaying intensity. This will be discussed further in the next section and also in section Figure 3.7 (a) Comparison of He + random (blue circles) and channeling (black circles) spectra for a four u.c. LAO film. Note that the valley counts in channeling spectrum almost drop to zero (inset). (b) Simulation of an abrupt interface model, in which a probability of 50% of being visible to the He + beam is arbitrarily assigned to the Sr and Ti in the top layer of STO.
79 Helium Channeling Spectrum Structural Properties Figure 3.7 (a) shows a channeling spectrum using KeV He + ions under the double alignment scattering geometry, along with a random spectrum. Both of the spectra are taken at the same scattering angle ( suppressed in the channeling spectrum with ). The bulk signal is greatly, indicating very good crystallinity of the STO; the La peak intensity in channeling is of that in the random direction, indicating some deviation from good crystallinity. The absence of dechanneling suggests the LAO/STO system is free of any detectable defects related to La, Sr and Ti atoms, e.g., interstitials and interface disorder. No detectable interstitials has implications for the diffusion mode: these interdiffused cations appear to always occupy lattice sites rather than interstitial sites. The counts in the valley of the channeling spectrum are most likely due to the background noise of the detection electronics, whose level is estimated from the counts at higher energies than the La peak, where there can be no scattering signals from the sample but the system noise. It is then interesting to compare the valley levels from the two spectra. Clearly the valley of the random spectrum is significantly higher than that of the channeling, indicating the counts in the random spectrum are not all due to the background, and there must be another origin for these counts: real La deep indiffusion and/or multiple scatterings (section 3.6.1). If La diffusion is responsible, then the indiffused La atoms must exclusively occupy lattice sites and not interstitial sites, otherwise the valleys of random and channeling spectra would be of the same level.
80 65 No detectable interface disorder suggests good heteroepitaxy, although the bulk lattice constants have a mismatch of 3%. This can be seen more clearly in Figure 3.7 (b), which shows the same channeling spectrum, together with a simulation for an abrupt interface. In this simulation, we have arbitrarily given a 50% probability for the Sr and Ti in the top layer of STO to be visible to the ion beam. The simulated Sr peak has much more intensity and the simulated Sr and Ti peaks are at lower energies than the experiment. These discrepancies indicate the contributions of the interfacial Sr and Ti to the observed Sr and Ti signals. An optimized simulation (not shown) shows that only of Sr and of Ti from the first two unit cells of the STO are visible to the beam. Interestingly, more interfacial Ti than Sr are visible to the beam, which is consistent with the fact that the top La atoms have stronger shadowing effect on subsequent A-site atoms (La and Sr) along the atomic rows than the top Al atoms on B-site atoms (Al and Ti) (Figure 3.4). This observation agrees with the assumption that the interdiffusions all occur at the coordinately equivalent lattice sites: La Sr exchange at the A-site and Figure 3.8 (a) Angular distribution of backscattering intensity of the LAO and STO. (b) Schematic illustration of the blocking dips, from which the longitudinal lattice constant of the LAO can be determined.
81 66 Al Ti exchange at the B-site. As a result of the good heteroepitaxy, one can deduce the longitudinal lattice constant of the four unit-cell LAO film from angular spectrum. The angular spectrum is obtained from the 2D spectrum by summing up data of a given element as a function of the scattering angle . Figure 3.8 (a) shows the angular spectra of La and the STO substrate, and Figure 3.8 (b) illustrates how is determined from simple trigonometry. The blocking dips of the substrate and the epitaxial film show an angular shift of, so the blocking direction in the film is at with respective to the incident beam direction, based on the blocking dip of an ideal cubic structure occurring at ( in and  out). Since the LAO film is laterally strained to the STO substrate, thus on the (110) scattering plane the bulk LAO lattice constant, which is smaller than. Such a compressive strain is expected since the inplane lattice parameter of LAO is stretched to fit the larger lattice constant of STO substrate resulting in the compressed out-of-plane lattice parameter. Also the extracted out-of-plane lattice constant is in very good agreement with direct X-ray diffraction (XRD) measurements  Depth Profiling Information Further atom depth profiles can be obtained by detailed analysis of the channeling spectrum (Figure 3.7 (b)). The experimental Sr and Ti peaks occur at higher energies than those in the simulation for the abrupt interface model, suggesting closer proximity to the surface. Indeed, the experimental energies for Si and Ti agree very well
82 67 with those they would have if they are present at the surface, i.e., and, where is the kinematic factor. This indicates unambiguously outdiffusion of these species to the first LAO unit cell at the surface. Note that the channeling spectrum provides a stronger evidence of the presence of Sr and Ti at the surface than the energies of the leading edges in the random spectrum because of the high sensitivity (up to cm -2 ) of the surface peaks to the content of two species in the outermost unit cell under the double alignment scattering. This is especially useful when they are only 5 at.% in the overlayer, and surface signals from such a small amount are overwhelmed by bulk ones in the random spectrum. A subtle point concerning the interpretation of these Sr and Ti bumps is that the simulation to the channeling spectrum in itself cannot rule out the possibility of the presence of pin holes at the level of in the LAO film that would directly expose the STO substrate to the probing ions. However, typical AFM images (Figure 3.2(b)) clearly show uniformity of the LAO film. The simulation in Figure 3.7 (b) reproduces the La peak more satisfactorily if one were to incorporate a concentration gradient of the La atoms. Such deconvolutions should however not be used to extract depth profiles, since ions inherently see fewer La atoms due to the shadowing effect Proton Beam Results This section presents spectra using H + as incident ions, putting emphasis on the depth profiles of the light elements Al and O. Figure 3.9 (a) shows a random spectrum with all plateaus from the substrate: Sr, Ti and O, along with a simulation for a fully stoichiometric 4 unit-cell film with an abrupt interface. The large overlap of the La and
83 68 Figure 3.9 Proton backscattering spectra. (a) Random spectrum with a simulated spectrum of a four u.c. LAO film with an abrupt interface on STO. (b) Channeling spectrum with an abrupt interface model. Sr peaks makes accurate depth profiling of these heavy atoms difficult using the proton spectra. In addition, the spectrum has some weak channeling features: the Ti plateau beneath the Al peak is not completely horizontal. However, if one manages to subtract the background, the simulated Al peak reproduces the experiment very well. With a slight uncertainty mainly due to the relatively poor counting statistics as a result of low sensitivity to Al, our model shows that the LAO film is almost stoichiometric in Al and the indiffusion of Al, if there is any, could not be deeper than the second unit-cell of the
84 69 STO. The maximum indiffusion depth was estimated by incorporating a substantial amount of indiffused Al to a certain depth in the STO to see if the simulation would yield a good fit to the low energy tail of the Al peak. The presence of a small amount of Al in shallow layers of STO is confirmed by angle-resolved X-ray photoemission spectroscopy (ARXPS) which has comparable sensitivity to all four elements. Oxygen is present in both constituents of the LAO/STO system. The profile of oxygen in the STO substrate close to the interface is of interest, because the oxygen vacancies in this region are by some proposed to be responsible for the conducting interface. The oxygen profile in this region can be extracted from the O plateau in the random spectrum since unlike the channeling case, the protons can actually access these buried O atoms under the random scattering geometry. The O plateau shows a relatively poor counting statistics again due to the intrinsically low sensitivity to O. This leads to a uncertainty in determining the content of buried O atoms. In other words, δ in oxygen-deficient SrTiO 3-δ needs to at least 0.45 for such a deficiency to be detected in our present apparatus. Unfortunately the reported oxygen deficiency level, based on the charge carrier density determined from Hall measurement, is only cm -2, a level of, or δ = 0.05, one order beyond our sensitivity. Analysis of the H + channeling spectrum (Figure 3.9 (b)) yields some useful structural information. The simulation in that figure assumes the four u.c. LAO film is stoichiometric in both Al and O but not in La and makes an abrupt interface with the STO. Again the channeling spectrum shows a good heteroepitaxy of the LAO film (no strong interfacial Sr or Ti peaks). This channeling spectrum also exhibits a Ti peak at
85 70 higher energy than predicted for an abrupt interface model, indicating the Ti presence in the top unit cell of LAO, consistent with the helium spectrum. The fact that the simulated Al peak extends to lower energies than the experimental surface peak is expected since only the Al atoms in the top layers are visible to the proton beam due to the shadowing effect. As for O, the simulated peak agrees very well with experiment. The agreement on the leading edge of the O peak is expected, since all of the O in the top LAO layer of an ideal film are visible to the ion beam. The agreement on the low energy edge cannot provide oxygen occupation information near the interface region, because this part has O contribution from both the LAIO overlayer and the first few unit cells of STO. Figure 3.10 Unit-cell by unit-cell areal density of La, Al, Sr, Ti in the four u.c. LAO and the top few STO u.c. The nominal interface is indicated by a dashed line. Note the intermixing near/at the interface. MEIS loses mass resolution at depth ( u.c.).
86 Summary on Cationic interdiffusion To summarize the depth profiling information of La, Al, Sr and Ti obtained from the random and channeling spectra using both helium ions and protons, one can plot the areal density of each element as a function of depth (Figure 3.10). The areal densities for La, Sr and Ti are obtained from the deconvolution of the optimized simulation to the helium random spectrum. The areal density of stoichiometric La in one unit cell, cm -2, is plotted as a reference. To the first order, Al is considered to be fully stoichiometric in the LAO with no indiffusion, since it is difficult to extract accurate amount of indiffused Al as discussed in the previous section. The lowest unit cell of LAO is closer to being stoichiometric in La than the top three unit cells. This trend is consistent with the observed nearly stoichiometric La in the 7 unit-cell and 25 unit-cell films. The nominal interface is also indicated. The plot illustrates the existence of extensive cationic intermixing (except Al 3+ ) across the LAO/STO interface, and an atomically abrupt interface should not be assumed for this PLD-grown 4 unit-cell LAO/STO sample. More on La indiffusion is given in section Laser Fluence and Ion Irradiation The data presented above were taken from a film grown with an intermediate laser energy density on the LAO crystal target of 1.1 Jcm -2. Similar results of interfacial intermixing were obtained for films grown using low (0.7 Jcm -2 ) and high (1.6 Jcm -2 ) energy densities, as summarized in Table 3.1. With increasing laser fluence, there is a slight increase in the extent of Sr outdiffusion into LAO, as a result of larger energy transfer expected from more energetic ions. However, the other atom profiles are
87 72 nearly the same, suggesting the intermixing process is not strongly affected by laser fluence, at least over the range investigated. It remains to be seen if metastable abrupt interfaces can be formed using thermal growth techniques such as molecular beam epitaxy (MBE), in which the energies of the evaporants are much lower ( ev) than that of the incident ions from the ablation plume in PLD ( ev or higher). Recently, Segal et al  studied MBE-grown LAO/STO samples and could not exclude the possibility of intermixed interfaces in their samples. Another thermal technique, atomic layer deposition (ALD), has recently demonstrated the capability to grow an amorphous LAO film on STO substrate with a conducting interface . It would be also interesting to investigate this interface since ALD growth involves only chemical processes and not the energetic ions employed in the ALD process. Low (0.7 Jcm -2 ) Medium (1.1 Jcm -2 ) High (1.6 Jcm -2 ) La in the LAO La in the first nå of STO 0.26 (n=10å) 0.38 (n=15 Å) 0.39 (n=16å) La total Sr in the LAO Ti in the LAO Table 3.1 Areal densities for La, Sr, and Ti in four u.c. LAO films grown with different laser fluences. The initial motivation to study ion irradiation was to investigate if the incident proton or helium ion beam could possibly induce any damages in sample, even when the ion beam is being rastered across the sample to minimize the potential irradiation damages. Such destructive damage would of course make quantitative analysis of MEIS less reliable. The threshold of beam dose to induce detectable damage is determined by monitoring the resulting spectra while prolonging beam exposure with the beam fixed
88 73 Figure 3.11 Proton spectra as a function of total ion dose for a four u.c. LAO film. on one spot on sample. It was found that the beam dose ( cm -2 ) associated with beam rastering that was used during data acquisition is one order of magnitude below the threshold ( cm -2 ), therefore one should not worry about the irradiation damage when interpreting the spectrum. Quite surprisingly, prolonged ion beam exposure is observed to promote additional La-Sr intermixing at room temperature. Figure 3.11 shows the effect of increased proton beam dose along the  direction in a four u.c. film: the La peak drops, there is an increase in the Sr and Ti peaks, and a transfer of intensity from the region of the La and Sr peaks to the intervening valley. As seen in section 3.5.1, the increased valley level can be interpreted as more La indiffusion into the substrate. Note that another possible reason for the decrease in La peak intensity is La atoms have been sputtered off by the bombardment of the energetic protons. However, the sputtering effect, if there is any, is expected to be very small, because the sputtering yield is almost negligible given the ion/target combination and the primary energy used. This
89 74 conclusion is based on a calculation by SRIM. As described in Chapter 2, more than 99% of proton energy loss in the near-surface region is in the form of electronic excitation and/or ionization of target atoms. These transferred energies could be the source of the indiffusion of La by prolonged proton irradiation. These results also suggest the relative instability of the interface, and may have implications for the role of energetic ions in the laser plume for driving the intermixing. 3.6 Discussion La Deficiency in Film The determination of the La concentration is most accurate since the La peak is isolated from all other peaks. Random spectra using He + as well as protons reveal that the combined La concentration in the four u.c. LAO film and the first of the substrate STO is only 70% of that in a stoichiometric LAO film. Such a La deficiency is observed in all four four-unit-cell samples we have investigated by MEIS and also the 25 u.c. sample investigated by RBS. This section explores a few possible causes of the La deficiency. The deficiency is unlikely to occur during the PLD growth process. One of the commonly assumed advantages of PLD film growth is the ability to preserve the elemental ratio of the target material through the congruent ablation under optimal conditions . The sputtering effect from impinging ablation particles during plasma recondensation, one potential cause of elemental deficiency in PLD growth, is presumably negligible because of the low kinetic energies (10 ev to 50 ev) of the impinging species. Some deviations from this premise were observed in PLD growth of
90 75 homoepitaxial STO  and of Co-doped ZnO films , but none shows such a large deficiency. In fact, both the PLD-grown 7 u.c. and 25 u.c. LAO/STO samples show a La:Al ratio close to unity in the LAO film. Deep indiffusion into the STO substrate might account for the deficiency in the film. As discussed in section 3.5.1, in order to fit the valley between the La peak and Sr peak in the random energy spectra, a certain amount of La has to be incorporated deep inside STO. One can roughly estimate how deep La atoms would penetrate if all of missing La atoms contribute to this process. For simplicity, here a uniform diffusion profile with a height by the flat valley is used. This gives a depth of, a region where the La signal overlaps with the one from the substrate and is well beyond MEIS detection limit. Our data can therefore not confirm or disprove this. However, such an indiffusion seems unphysically deep. One should carefully examine the arguments above. First of all, the uniform diffusion is highly questionable. Instead a graded diffusion profile would make more physical sense. Second, random spectra from other samples show valleys of similar intensity (for example the nonzero counts we observe in front of the Al peak in random spectrum of Bi 2 Se 3 on sapphire with helium ions). As discussed in section , the system noise alone cannot account for the valley counts. Other artifacts such as multiple scatterings can conceivably contribute to these counts. These statements should not affect the conclusion of shallow La indiffusion, because shallow indiffusion only accounts for the low energy tail of La peak and high energy end of the valley. Actually the shallow indiffusion is confirmed by other characterization techniques , such as STEM/EELS and ARXPS, which reveal that La
91 76 concentration is significantly lower than that expected for an fully stoichiometric four u.c. LAO, and a clear presence of La extending a few unit cells into the STO. It has been argued that desorption of La atoms might be the main reason of the deficiency . Considering the long exposure times to the ambient when the samples have been transported for different characterizations this may conceivably be a factor. However, the heterointerface of the 4 unit-cell samples investigated by MEIS all show similar transport results as the published ones Cation site exchange MEIS depth profiling for the four cations in the LAO/STO system agrees with the proposed site exchange (La Sr and Al Ti) mechanism for cation interdiffusion. This section briefly discusses how charges are redistributed under these site exchanges and the consequences on interface dipole and total energy. Figure 3.12 Energy level diagram of LAO/STO extracted from core-level and valence-band XPS spectra. Compensating charge carriers are expected to appear due to the site exchange of cations. Replacement of an Al 3+ ion by a Ti 4+ ion (Ti Al ) inside the LAO is expected to result in the appearance of a compensating electron, while replacement of a Ti 4+ by an Al 3+ (Al Ti ) inside the STO results in a compensating hole. Similarly substitutional Sr 2+ at a
92 77 La 3+ site (Sr La ) in the LAO is expected to result in the appearance of a compensating hole and substitutional La 3+ at a Sr 2+ site (La Sr ) in the STO a compensating electron. However, analysis of the electronic states in the vicinity of the band edges suggests that to the first order, no such electron-hole pairs need to be considered for the purpose of charge redistribution . This could be understood by examining the band diagram of the interface determined by X-ray photoemission spectroscopy (XPS) . Band offsets are shown in Figure 3.12 and no band bending is detected. Since the conduction band (CB) edge in the STO is lower than that in the LAO, the electron compensating the Ti 4+ impurity in the LAO will be strongly polarized towards the interface. Similarly, since the valence band (VB) edge in STO is lower than that in LAO (holes less bound on VB edge in STO), the hole compensating the Al 3+ in STO is strongly polarized towards the interface. Thus, the electron and hole remain in the vicinity of the interface, and the system becomes more energetically stable when they recombine. In other words, Al Ti site exchange can be considered as an exchange of Al 3+ and Ti 4+ ions, which takes place without the formation of charge carriers. The same arguments apply to La Sr site exchange: as long as these substitutional impurities are close to the interface and the bottom of the CB of STO is higher than the top of the VB of LAO, these compensating electrons and holes tend to recombine. Therefore it is a good approximation to consider only the formal valence charges of the exchanged cations, without contributions from compensating charge carriers, in an attempt to obtain a simple picture of the charge redistribution associated with cation site exchanges .
93 78 AlO 2 3 LaO 3 AlO 2 2 LaO 2 AlO 2 1 LaO 1 TiO 2 1 SrO 1 TiO 2 2 SrO 2 Dipole Ideal Al 3 Ti 1 Al 1 Ti 1 La 1 Sr 1 La 1 Al 1 Sr 1 Ti 1 Table 3.2 Schematic illustration of selected site exchange configurations and associated dipole moments. The first and second columns indicate the atomic plane and its distance from the interface, respectively. In the ionic limit, the charge redistribution associated with such site exchanges can eliminate the polar catastrophe as illustrated in Table 3.2. This table lists the resulting dipole moments in a supercell in selected site exchange configurations. The subscript number refers to the atomic plane relative to the interface from which the exchanged atom was taken, for example, Al 3 Ti 1 is the exchange of an Al atom in the top AlO 2 layer with an Ti atom in the first TiO 2 layer. For each configuration the column on left refers to the cell that undergoes cation exchanges. The picture here, though simplified, yields some meaningful predictions: there is always an energy gain associated with the Al Ti site exchange, while the La Sr exchange destabilizes the system. A combination of these two exchanges could possibly produce an energetically favorable configuration. Further first principles calculations , which is beyond the scope of this thesis work, confirm the observations above and shows that thermodynamically stable configurations always involve simultaneous
94 79 La Sr and Al Ti exchanges, in other words, an extensively intermixed interface is more stable than an ideal interface structure La Doping in the Substrate As discussed in previous two sections, a significant amount of La atoms diffuse deep into the STO in a site exchange fashion and these substitutional La Sr impurities, as shallow donors, give rise to compensating electrons. Similar Al Ti impurities might give rise to compensating holes, or at least be a source of deep-level traps for donor electrons from La. As our MEIS measurements reveal, there are much more indiffused La than Al in the STO, indicating this interface should be n-type, consistent with XPS results and the fact that such heterointerface is found to be exclusively n-type by other groups working on this system. It is interesting to consider the doping in the LAO: Sr outdiffusion is expected to dope the LAO p-type and Ti to dope LAO n-type. However, the large bandgap of LAO suggests Sr-acceptor (Ti-donor) levels would be too far from the VB (CB) edge to be thermally ionized at ambient temperature, and would thus be deep-level traps for any mobile electron (holes) that are present rather than a source of mobile holes (electrons). Thus, no conductivity of either sign is expected in the LAO. Comparing the measured sheet carrier concentration with the amount of indiffused La 3+ yields some interesting results. MEIS determines the La areal density within the first of STO to be cm -2 (Table 3.1), which exceeds the observed sheet carrier density, cm -2, by a factor of 20. A few factors have to be considered here. First, one La Sr site contributes one donor electron only if the substitutional La impurity is fully ionized, or electrically active. Second, there would be
95 80 some holes from Al Ti sites and such holes would be deep-level traps for the mobile electrons from La Sr. Thus the sheet carrier density from La doping is expected to be less than the La areal density, in qualitative agreement with experiment, though the amount of indiffused La seems slightly excessive. Such excess La indiffusion might form in response to the presence of Sr vacancies that are created as a result of post-annealing LAO/STO in an oxygen ambient in an attempt to remove oxygen vacancies . One should always keep in mind that the all of the results discussed above cannot rule out oxygen vacancy mechanism in which the charge carriers are proposed to be sourced by oxygen vacancies inside the STO. Siemons et al  inferred a much higher local charge density of cm -2 from a single unit cell of LAO by ultraviolet photoemission (UPS). They attributed the large carrier concentration to a thin donor layer of oxygen vacancies and pointed out that due to the large dielectric constant of STO the electrons are not so tightly bound to this donor layer and high mobility could result from in-plane transport remote from the charged donor layer. 3.7 Conclusions With high sensitivity to heavy atoms and excellent depth resolution, our MEIS data unambiguously demonstrate the outdiffusion of substrate Sr atoms and Ti atoms up to the outermost unit cell of the LAO film, and the indiffusion of La atoms from the LAO film into the STO substrate. There is preferential diffusion of La into the STO, which leads to n-type doping of the STO and formation of mobile electrons in the STO. These results call into questions the popular interpretation of conductivity based on an electronic reconstruction to alleviate the polar catastrophe with an atomically abrupt
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99 84 4 Oxygen Diffusion in Hafnium Oxides and Silicates 4.1 Introduction As discussed in Chapter 1, the continued scaling of gate stack in silicon metaloxide-semiconductor field-effect-transistors (MOSFETs) requires the introduction of new materials in complementary-metal-oxide-semiconductor (CMOS) technology. Hafnium oxide and silicates with high-permittivity (high-κ) have been leading candidates of alternative gate dielectric materials and have been intensely investigated [1,2]. At the present 45nm and 32nm technology nodes these materials have already begun to replace silicon oxide . Hafnium-based oxide and silicates have many desirable properties that meet most of the selection criteria to successfully perform as gate dielectrics: they are found to have relatively high dielectric constants (κ>20) , high heats of formation  (therefore they are thermodynamically stable in direct contact with silicon), and relatively large band gaps [6,7]. One of the significant issues with Hf oxides and silicates is high oxygen diffusivity through the film that leads to the formation of an uncontrolled interfacial silicon oxide layer between the gate dielectric layer and the silicon channel during the deposition of the gate dielectric as well as during post-deposition anneal (PDA) [8,9]. Such an interfacial layer is undesirable from the point of view of scaling, since this layer has a low dielectric constant (3.9) and somewhat compromises the benefit of the new high-κ dielectric material by increasing the overall EOT. From the point of view of electrical performance, an ultrathin layer of SiO 2 is actually desirable and intentionally
100 85 grown before the deposition of high-κ oxides in order to minimize Si dangling bonds, traps and any other interface defects that would result in poor electrical characteristics (for example, a threshold voltage shift). In addition, the PDA is a standard thermal process to passivate any defects to improve electrical performance. The annealing ambient may either intentionally be oxygen rich or contain traces of oxygen as in the case of N 2. Therefore, understanding the process of oxygen incorporation during the post-deposition processing of the high-κ gate stack is of critical importance for meeting device performance specifications. Despite enormous research work on this material system, there is no detailed knowledge of the oxygen transport mechanism under annealing conditions. 4.2 Experimental Sample Growth and Preparation HfO 2 films were grown on 1nm SiO 2 /Si(001) at 600K by atomic layer deposition (ALD) by our collaborators at Sematech. ALD is a method of cyclic deposition and oxidation in a layer-by-layer fashion and is designed to produce uniform and conformal films due to self-limiting surface reaction . In our case the starting surface is exposed to a metalorganic precursor tetrakis(ethylmethylamino)hafnium Hf[N(CH 3 )C 2 H 5 ] 4 (TEMAH) which is absorbed as a saturated monolayer. The excess TEMAH is purged from the growth chamber by a nitrogen pulse. A pulse of the oxidation agent (O 3 ) is then introduced which fully oxidizes the adsorbed layer to HfO 2, after which volatile reaction products (alkane) and the excess oxidant are purged by another nitrogen pulse. Such cycles are repeated until the desired thickness is reached. Hf silicate films are grown
101 86 similarly with an additional silica precursor tetramethoxysilane Si(OCH 3 ) 4 (TMOS), and the stoichiometry of the resulting film is controlled by adjusting the relative amounts of TEMAH and TMOS. Nitrogen incorporation in the films is achieved by postgrowth annealing in NH 3 (973K, 60s). Postgrowth oxidation in 18 O 2 (98% isotopically enriched) is conducted in a separate UHV chamber (base pressure 10-9 Torr) at Rutgers. The sample is first briefly annealed at K (monitored by an optical pyrometer and/or a K-type thermocouple) to remove surface carbon and then stabilized at a desired annealing temperature of K, followed by 18 O 2 introduction at a partial pressure of 0.01 Torr for 5-30 minutes. Then it is in-situ transferred to the UHV MEIS analysis chamber to avoid ambient contamination Isotopic Labeling As discussed in Chapter 2, MEIS is a mass-specific technique and provides depth profiles of atoms of different masses in a thin film. Under optimal film thickness and backscattering geometry conditions, sequential oxidation with different isotopes 16 O 2 and 18 O 2 yields an energy spectrum with well-resolved 16 O and 18 O peaks . Careful analysis of the reacted amount of the oxygen isotopes and their depth profiles as functions of reoxidation conditions (temperature, time and pressure) reveals the reaction mechanism and kinetics. There are some subtle points regarding depth profiling with 18 O that deserve to be mentioned. Since the stopping power and straggling of 18 O are not well established, these values must be carefully calibrated against other depth profiling techniques (such
102 87 as TEM and ellipsometry) to yield reliable depth profiling information. From the point of view of peak shape, for the same 18 O and 16 O content and distribution, the 18 O peak should have a higher intensity than the 16 O peak, because of the different scattering cross sections. 4.3 Results Since the size of the probing beam is 0.1 mm 1 mm, our MEIS data represent the averages over such a macroscopic area on the sample, making it hard to distinguish between a compositional gradient and surface and/or interface roughness. A complementary surface roughness characterization technique, atomic force microscopy (AFM), is therefore performed on selected as-deposited and annealed samples. The root-mean-square (rms) roughness of as-deposited films is, and less than for annealed ones, less than or comparable to MEIS depth resolution near the surface. Therefore, the MEIS energy spectrum could be safely interpreted as a depth spectrum. In this study all MEIS energy spectra are obtained with 130 KeV H + at a scattering angle of o under a double alignment scattering geometry, which yields accurate measurements of the amorphous overlayer. Figure 4.1 shows an H + backscattered energy spectrum from a nitrided as-deposited Hf silicate sample. The high energy edges of the Hf, Si, O and C (but not N) peaks indicate all these elements can be found at the surface, while the leading energy of the N peak is lower than it would have been if N was on the surface. This means that the nitrogen is buried. A simulation of this spectrum shows that the outermost layer of this sample is a stoichiometric Hf 0.67 Si 0.33 O 2 film with a thickness of 27Å. Underneath is a thin interfacial silicon nitride (Si x N y ) layer (with no
103 88 oxygen in this layer)with a thickness of 6Å. Note that again the position of the N peak indicates that nitrogen has diffused through the film, and all nitrogen is confined within the interfacial Si x N y layer. Both the Si and O peaks have contributions from both the silicate film and the interfacial layer. Modeling the shape of the Si peak reveals a concentration variation with depth with a Si peak maximum occurring at an energy corresponding to a depth well below the surface. A small C surface peak indicates a tiny amount of hydrocarbon contamination on the sample surface. Figure 4.1 Channeling spectrum of an as-deposited Hf 0.67 Si 0.33 O 2 /SiO x N y /Si(001) film The energy spectrum shown in Figure 4.1 is typical of the samples studied in this thesis. After annealing in 18 O at a certain temperature, the Hf peak of Hf silicate samples usually undergoes little change: its height slightly increases and width decreases slightly with the Hf areal density remaining constant. This small change is mostly likely due to phase segregation of the silicate layer as discussed below. The height of the Hf peak of the Hf oxide sample decreases, corresponding to crystallization of the film after annealing, in which case fewer Hf atoms are visible to the probing ion in the channeling
104 89 direction. While the analysis of the Hf peak could not yield much useful information, the two oxygen isotope peaks and the silicon peak are of more interest when trying to understand the oxygen diffusion mechanism and the interface reaction. Therefore, we will focus the discussion on the analysis of oxygen, nitrogen, and silicon, only mentioning analysis on Hf when necessary. Figure O and 16 O peaks for (a) the HfO 2 /SiO 2 /Si(001) and (b) the Hf 0.67 Si 0.33 O 2 /SiO x N y /Si(001) films as a function of re-oxidation time. (c) Oxygen exchange kinetics in hafnium oxide (black open) and hafnium silicate (blue solid) films O incorporation at 763K This section presents results of 18 O incorporation in an Hf oxide sample and an Hf silicate sample annealed at 763K.
105 90 Figure 4.2 (a) shows the part of the backscattered H + spectrum corresponding to the two oxygen isotopes in this film as reoxidation proceeds. Modeling the energy spectrum of an as-deposited HfO 2 sample gives its depth profile as HfO 2 27 Å /SiO Å/Si(001). In Figure 4.2 (a) the corresponding energy position of the interface at the high-κ film/interfacial layer as well as at the surface are indicated by dashed vertical lines. A pronounced 18 O peak spanning from the outer surface of HfO 2 to the SiO 2 interfacial layer is observed after 10 min. of 18 O 2 exposure (P=0.01Torr, 763K). Concurrent with the development of the 18 O peak, the intensity of the 16 O peak decreases. This observation shows that the development of the 18 O peak is likely not due to 18 O 2 molecular diffusion through the hafnium oxide to the Si interface as is the case in SiO 2 /Si, otherwise there would be no decrease in the 16 O; but rather due to an exchange reaction in the high-k film, i.e., 16 O leaves the surface and 18 O incorporates into the high-κ film. After a longer (40 min.) 18 O 2 exposure there is a larger increase in the 18 O aerial density and further decrease in the 16 O density, however, the total oxygen content (the sum of 16 O and 18 O), as calculated from the oxygen peak area, remains the same. The silicate film Hf 0.67 Si 0.33 O 2 /SiO x N y /Si(001) shows a slightly different 18 O incorporation behavior. Under the same processing conditions the silicate film (Figure 4.2 (b)) shows a noticeably lower 18 O exchange fraction compared to the oxide film in Figure 4.2 (a). Figure 4.2 (c) shows the concentrations of both oxygen isotopes as a function of 18 O 2 exposure time. This figure clearly shows that the exchange rate in the Hf oxide films was faster than for Hf silicates: the oxygen exchange fraction reaches >90%
106 91 Composition Total oxygen O loss ( 18 O gain) Exchange ( atoms/cm 2 ) ( atoms/cm 2 ) fraction f HfO (7.8) 0.50 HfO 2 (crystalline) (5.8) 0.40 Hf 0.67 Si 0.33 O (2.6) 0.20 Hf 0.33 Si 0.67 O 2 14 < 0.5 (0.5) < 0.04 SiO 2 /HfO (1.0) 0.07 Hf 0.67 Si 0.33 O 1.67 N (2.1) 0.20 Table 4.1 Areal densities of different oxygen isotopes before and after annealing in 18 O 2 environment (partial pressure 10-2 Torr) at 763K for 30 min. of its final value in 10 min. for HfO 2, whereas for Hf silicates the exchange is much slower and continues at these experimental conditions, even after 120 min. of 18 O exposure. The saturation of exchange for the Hf oxide is believed to be governed by the onset of the crystallization as discussed below. Note that for both the oxide and the silicate films, the total amount of oxygen remains constant at the annealing temperature of 763K even after a long exposure of 18 O. The 18 O exchange fraction f, defined as ratio of 18 O to the total oxygen ( 16 O + 18 O) areal density in an Hf 1-x Si x O 2-y N y films (excluding any interfacial SiO 2 ), is used to quantify and compare the amount of 18 O incorporated into the high-κ layer. Table 4.1 lists representative exchange fractions for selected as-deposited and crystalline Hf oxide, silicate and silica oxynitride films annealed at 763K for 30 min. Notably the oxygen exchange fraction for the as-deposited film is higher than for the silicate and the recrystallized oxide films. Since the annealing temperature may be sufficient to induce chemical phase separation  in this composition of Hf silicate, the lower O exchange fraction observed likely results from a lower surface area of HfO 2 exposed to oxygen, and/or a suppression of the diffusion through the grain boundaries that are silica
107 92 enriched. Interestingly the nitrogen incorporation in the Hf silicates does not change the exchange fraction significantly (Table 4.1). Figure 4.3 Effects of vacuum crystallization anneal (1073K, 40min.). (a) MEIS energy spectra show additional interfacial SiO x formed in a HfO 2 /SiO 2 /Si(001) film after crystallization anneal. (b) XPS spectra for the Si 2p region confirm the SiO 2 formation (peaks normalized to the Si 0 peak). The dependence of oxygen interactions on microstructure (amorphous and crystalline) of hafnium oxide films at 763K is also investigated. Under the same annealing conditions in 18 O (0.01 Torr, 763K, 30 min.) a crystalline Hf oxide film shows a slightly slower oxygen exchange rate than its amorphous counterpart (Table 4.1) and also shows a 18 O content gradient decreasing from the outermost surface towards the lower (dielectric/si) interface. Crystallization of the oxide film is achieved by high temperature (1023K) annealing in an UHV environment . In addition we note here that crystallization anneals results in the development of an additional 4-5Å of SiO 2 at the interface (not shown). A comparison of the XPS Si 2p peaks for pure HfO 2 films shows that after the 1023K crystallization anneal, the amount of interfacial SiO 2
108 93 increases slightly (Figure 4.3), consistent with our MEIS observations. The origin of this additional interfacial SiO 2 formation will be discussed further below. Note that unless otherwise specified, all discussions that follow concern amorphous films. Figure 4.4 Schematic illustration of oxygen isotopic exchange and incorporation and interfacial SiO x growth in a hafnium silicate film for an as-deposited film, and re-oxidized for 30 min. at 763K, 973K, and 1223K, respectively O incorporation at higher temperatures After annealing at 763K, no changes are observed in the Hf, Si and N peaks (not shown) for both (the amorphous) oxide and the silicate films, implying that there is no additional interfacial SiO 2 growth. This may be explained by inefficient atomic O diffusion through the interfacial (SiO 2 or SiO x N y ) layer under these conditions. However, as annealing temperatures increase above 763K, interfacial silicon oxide growth is observed in addition to the oxygen exchange in the Hf dielectric layer. Figure 4.4
109 94 Figure 4.5 (a) 16 O and (b) 18 O isotopic depth distribution for hafnium silicate films oxidized for 30 min. at 763K-1223K. The horizontal arrows indicate the spread of N during oxidation. schematically shows the evolution of the Si and O peaks for Hf 0.67 Si 0.33 O 2 /SiO x N y /Si(001) films at different temperatures with the same 18 O 2 pressure (0.01 Torr) and annealing time of 30 min. The rise of the Si peak area can be directly associated with SiO x growth and will be analyzed in section The resulting oxygen depth profiles for these films are shown in Figure 4.5. The amount of 18 O exchanged in the Hf silicate layer increases as the temperature goes up, and so does the depth of 18 O and 16 O incorporation. The deeper incorporation of oxygen isotopes leads to the formation of silicon dioxide (or silicon suboxide) beneath the original silicon oxynitride layer. The exact depth of the
110 95 Figure 4.6 Oxygen areal densities in (a) the hafnium silicate layer and (b) the interfacial SiO x N y layer as a function of re-oxidation temperature during 30 min. anneal. SiO x /Si interface and the detailed shape of oxygen distribution in this region cannot be precisely determined with MEIS: first, the energy straggling effect of this buried layer gives an error of on the thickness of the transition region; second, roughness of the SiO x layer contributes to the broadening of the low energy tail of oxygen peaks and further complicates the modeling . More reliable areal density information, however, can be extracted from MEIS energy spectra. In Figure 4.5 we show the comparison of the 18 O to 16 O content in the Hf-containing layer (the oxygen exchange fraction) as well as in the interfacial SiO x N y and SiO x layer. As shown in Figure 4.6 (a), the amount of 18 O
111 96 in the silicate layer increases continuously with the annealing temperature. This is an exchange reaction in that the total oxygen amount in this Hf silicate layer remains a constant at all temperatures. Figure 4.6 (b) shows that up to 763K, there is no apparent oxygen incorporation in the interfacial SiO x N y layer (no net increase in oxygen, no oxidation of the Si substrate, only isotopic exchange in the silicate overlayer). At higher temperatures up to 973K, the oxygen isotopes start to incorporate in the interfacial layer with the 16 O being the predominant isotope. Above 1000K after 30 min annealing the 18 O content at the interface becomes larger than that of 16 O. Assuming that the only source of 18 O is the gas phase 18 O 2, and 16 O is only in the as-deposited films, we can evaluate how much 16 O is leaving the samples during this incorporation process. From integrating the area of the 16 O peak, we find that we initially have 16 O atomic density of atoms/cm 2 in the as-grown Hf silicate film, and that atoms/cm 2 remain in both the silicate and the interfacial layers after 1223K annealing in 18 O 2. Therefore 35% of the 16 O atoms have been removed either via a desorption process from Hf 0.67 Si 0.33 O 2 surface in direct exchange with gas phase 18 O 2, or via a Si 16 O desorption from SiO 2 /Si(001) interface. The remaining 16 O is mostly in the interfacial SiO x N y layer, as if they have been pushed there by the 18 O atoms from Hf 0.67 Si 0.33 O 2 layer. It is interesting to investigate the depth distribution of the interfacial nitrogen upon annealing and compare it with that of the oxygen isotopes at various annealing temperatures (Figure 4.7). The total nitrogen amount in the film decreases by approximately a factor of two over the temperature range studied. In addition, the depth distribution broadens quite appreciably. When the nitrogen is present, the
112 97 Figure 4.7 Nitrogen depth distribution in Hf 0.67 Si 0.33 O 2 /SiO x N y /Si(001) films re-oxidized in 18 O 2 at different temperatures. The mole fraction y is shown on the y-axis. The inset shows the integrated areal density of nitrogen as a function of re-oxidation temperature. oxygen distribution extends deeper than the initial nitrogen distribution. The similarity between the areal densities and profiles of incorporated 18 O (Figure 4.5 (b)) and lost N (Figure 4.7) suggests an exchange reaction as a principle mechanism responsible for nitrogen loss and oxygen incorporation. An Arrhenius plot is a useful tool to analyze the activation energy of the exchange reaction. Figure 4.8 shows the Arrhenius plot of the interface 18 O+ 16 O content for three different samples: one with 45Å of starting SiO 2 , another with 45Å of starting SiO x N y , and a third with 27Å Hf 0.67 Si 0.33 O 2 /6ÅSiO x N y, all oxidized in 18 O 2 under similar conditions. In these ultrathin films oxidation is presumably reaction limited, therefore the interface reaction will be independent of the starting oxide thickness and the increase of 18 O at the interface should linearly depend on both time and pressure. One can see that compared to pure SiO 2, the rate of oxide growth near