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Magnetocapacitance:  A Probe of Spin Dependent Potentials

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Magnetocapacitance: A Probe of Spin Dependent Potentials
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2008

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Capacitance ( jstor )
Capacitors ( jstor )
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Electric potential ( jstor )
Electrodes ( jstor )
Magnetic fields ( jstor )
Magnetism ( jstor )
Magnets ( jstor )
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MAGNETOCAPACITANCE: A PROBE OF SPIN DEPENDENT POTENTIALS By KEVIN T. MCCARTHY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2002

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Copyright 2002 by Kevin T. McCarthy

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To my father, without whom I would have stopped asking questions.

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ACKNOWLEDGMENTS I am truly indebted to many individuals who have contributed to the success of my project. Though I cannot possibly acknowledge all contributors, I would like to express my sincere gratitude toward a few of them. I would especially like to thank Professor Arthur Hebard, my research advisor. His experience and guidance have proved invaluable in my research efforts. His positive, open-minded attitude toward research creates a unique laboratory environment free of criticism and full of encouragement. As many will attest, Dr. Hebard’s optimism is infectious, and generates enthusiastic students who look forward to working in the lab. I would also like to express my appreciation for the assistance of Dr. Stephen Arnason. I was lucky to have such a knowledgeable and competent mentor and friend. I am grateful to Dr. Fred Sharifi, for without his encouragement and prodding, I would never have approached Dr. Hebard in the first place. I am dearly thankful for all of my lab mates and friends who have made my experience at UF wonderful: Jim Cooney, Quentin Hudspeth, Brian Thorndyke, Greg Martin, Marc Soussa, Stephanie Getty, Nikoleta Theodoropoulou, Jeremy Nesbitt, Xu Du, Partha Mitra, and Hidenori Tashiro, to name a few. I am grateful to Professor Richard Woodard for his unbelievable level of availability and willingness to assist students in solving physics problems of any kind (and at any time). He is perhaps the best teacher I have ever met. I would like to thank the McCarthy family (mom, dad, John, Loran, and Mitchell) for their encouragement and positive outlook, which have produced in me the necessary confidence to achieve my goals. Finally, my deepest iv

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appreciation is due my wonderful wife, Jen, for her unconditional love, support, and understanding. I cannot imagine a kinder individual. v

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF FIGURES ......................................................................................................... viii ABSTRACT.........................................................................................................................x CHAPTER 1 INTRODUCTION ...........................................................................................................1 1.1 Motivation................................................................................................................. 2 1.2 Magnetocapacitance.................................................................................................. 3 1.3 Pd and PdFe Alloys................................................................................................... 5 1.4 Benefit to Society...................................................................................................... 6 2 ELECTRON SCREENING IN METALS.......................................................................7 2.1 Screening in General: Definition and Manifestations.............................................. 7 2.2 Thomas-Fermi Screening........................................................................................ 10 2.3 Thomas-Fermi Screening in a Finite Magnetic Field ............................................. 13 2.4 Temperature-Dependent Screening at Finite Magnetic Fields ............................... 17 2.5 Correlations Between Screening Length and Susceptibility................................... 19 2.6 Screening in Ferromagnets ..................................................................................... 21 3 CAPACITANCE............................................................................................................24 3.1 Definition and Uses................................................................................................. 24 3.2 Parallel Plate Model of Capacitance....................................................................... 26 3.3 Screening Effects .................................................................................................... 27 3.4 Complex Impedance of Capacitors......................................................................... 30 4 EXPERIMENTAL TECHNIQUES...............................................................................34 4.1 Sample Growth ....................................................................................................... 34 4.1.1 Substrate Preparation ....................................................................................... 35 4.1.2 DCand RF-Magnetron Sputtering ................................................................. 37 4.1.3 Reactive Ion Beam Sputtering ......................................................................... 40 4.1.4 Thermal Evaporation ....................................................................................... 41 vi

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4.1.5 Plasma Oxidation............................................................................................. 42 4.1.6 Quartz Crystal Thickness Monitor................................................................... 43 4.2 Vacuum Systems..................................................................................................... 44 4.2.1 Turbomolecular Pumps.................................................................................... 44 4.2.2 Diffusion Pumps .............................................................................................. 45 4.2.3 Cryosorption Pumps......................................................................................... 46 4.2.4 Valving, Manifolding, and Rotary Vane Pumps.............................................. 47 4.3 Characterization Tools............................................................................................ 50 4.3.1 Lock-in Amplifier............................................................................................ 50 4.3.2 Impedance Analyzer ........................................................................................ 51 4.3.3 Capacitance Bridge.......................................................................................... 52 4.3.4 QD-6000 Physical Property Measurement System.......................................... 56 4.4 Computer Interfacing and Data Analysis................................................................ 57 5 EXPERIMENTAL RESULTS AND DISCUSSION ....................................................59 5.1 Frequency-Dependent Interface Capacitance of Al-AlO x -Al Tunnel Junctions..... 60 5.1.1 Sample Fabrication .......................................................................................... 61 5.1.2 Impedance Measurements and Analysis.......................................................... 63 5.1.3 Interpretation and Discussion .......................................................................... 68 5.2 Capacitive Response of Si-SiO x -Metal Structures.................................................. 70 5.2.1 Sample Fabrication .......................................................................................... 71 5.2.2 Measurements and Analysis ............................................................................ 74 5.2.3 Results and Discussion .................................................................................... 78 5.3 Magnetocapacitance of Al-AlO x -Gd Capacitor Structures..................................... 79 5.3.1 Sample Fabrication .......................................................................................... 80 5.3.2 Magnetocapacitance Measurements ................................................................ 82 5.3.3 Interpretation and Discussion .......................................................................... 88 5.4 Magnetic Field Dependent Screening in Pd-AlO x -Al Structures ........................... 90 5.4.1 Sample Fabrication .......................................................................................... 91 5.4.2 Magnetocapacitance Measurements and Analyses.......................................... 92 5.4.3 Conclusions...................................................................................................... 98 6 SUMMARY AND FUTURE DIRECTIONS................................................................99 6.1 Summary................................................................................................................. 99 6.2 Proposed Future Directions................................................................................... 101 LIST OF REFERENCES.................................................................................................107 BIOGRAPHICAL SKETCH ...........................................................................................110 vii

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LIST OF FIGURES Figure Page 2-1: Schematic of electrostatic screening at the surface of a metal.......................................10 3-1: Schematic of thin capacitor structure .............................................................................27 4-1: AJA International A320-U-A magnetron sputter gun schematic...................................37 4-2: Schematic showing magnetic field lines in a magnetron sputter gun ............................39 4-3: Diagram of reactive ion beam sputtering (RIBS) geometry...........................................41 4-4: Schematic diagram of thermal evaporation geometry....................................................42 4-5: Diffusion pump diagram.................................................................................................46 4-6: Vacuum system schematic .............................................................................................48 4-7: Rotary vane pump schematic..........................................................................................49 4-8: Capacitance bridge circuit..............................................................................................53 4-9: Schematic of three terminal lead configuration for capacitance measurements ............55 4-10: Schematic of PPMS sample probe ...............................................................................57 5.1: Cross stripe geometry for tunnel junctions.....................................................................62 5.2: Real part of capacitance vs. frequency for Al-AlOx-Al tunnel junction........................64 5-3: Areal admittance versus frequency for aged Al-AlO x -Al tunnel junction .....................65 5-4: Complex capacitance plot for aged Al-AlO x -Al tunnel junction ...................................67 5-5: Diagram showing geometry during ion-milling procedure...........................................72 5-6: Cross section of Si-SiOx-M capacitor structure............................................................73 5-7: Diagram of electrical connections for Si-SiO x -M capacitor structure...........................74 viii

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5-8: Inverse capacitance versus dielectric thickness for Si-SiO x -Ni .....................................75 5-9: Effective additional dielectric thickness (d 0 ) for Si-SiO x -M structures .........................77 5-10: Diagram of Al-AlO x -Gd capacitor structure ................................................................81 5-11: Diagram of electrically contacted Al-AlOx-Gd capacitor structure.............................82 5-12: Change in capacitance versus magnetic field for Al-AlO x (50 )-Gd..........................85 5-13: Capacitance versus temperature at H = 0 T and H = 7 T for Al-AlO x (50 )-Gd ........86 5-14: Magnetization and dM/dT versus temperature for 1000 Gd on Si ...........................87 5-15: Inverse capacitance versus dielectric thickness for Pd-AlO x -Al..................................93 5-16: Magnetocapacitance of Pd-AlOx-Al structure.............................................................94 5-17: Capacitance versus temperature for Pd-AlO x -Al .........................................................97 6-1: Geometry for spin-diffusion length measurement..........................................................103 ix

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MAGNETOCAPACITANCE: A PROBE OF SPIN DEPENDENT POTENTIALS By Kevin T. McCarthy May 2002 Chairman: Arthur F. Hebard Major Department: Physics We have measured the magnetic field dependence of the capacitance of Pd-AlO x -Al thin film structures. The AlO x dielectric is thin enough to ensure that the capacitance is dominated by screening effects in the electrodes. The observed quadratic dependence of capacitance on magnetic field is consistent with a theoretical model that includes the effect of a spin-dependent electrochemical potential on electron screening in the paramagnetic Pd. This spin-dependent electrochemical potential is related to the Zeeman splitting of the narrow d-bands in Pd. The application of a magnetic field increases the screening length, which is consistent with our observed negative magnetocapacitance. x

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CHAPTER 1 INTRODUCTION Capacitance measurements performed on a thin metal-insulator-metal (MIM) thin-film structure are known to reveal more than simply the bulk dielectric properties of the insulator (dielectric) layer. 1-4 Mead 1 first pointed this out over 40 years ago in the context of Ta-Ta 2 O 5 -Au tunnel junctions. He realized that for very thin insulator layers, though the geometrical capacitance diverges, the measured capacitance saturates as it is dominated by electric field penetration into the metallic electrodes. Other workers 5, 6 calculated the magnitude of the effect and incorporated this information into a model of electron tunneling which includes the effect of electric field penetration into the electrodes. This effect is often overlooked today, and as a result, some experimenters overestimate the dielectric thickness of MIM structures determined via capacitance measurements. We are interested in the physics revealed by capacitance measurements on MIM structures in the thickness regime where the capacitance is determined by the interfacial properties of the structure. This dissertation focuses on the mechanisms that govern the capacitance of thin MIM structures, the physical properties revealed by these measurements, and the development and application of magnetic field-dependent capacitance, or magnetocapacitance, as a tool to probe the spin-dependent properties of ferromagnetic and paramagnetic metals and semiconductors. This introductory chapter is intended to motivate our current investigations with recent experimental and theoretical results by other workers. It will also introduce the technique of magnetocapacitance and 1

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2 give justification for its application to various metals, and finally discuss why these measurements are relevant to the condensed matter physics community and to society at large. Chapter 2 gives a theoretical background into electron screening, which is the dominant mechanism behind the observed capacitance saturation in thin MIM structures. Chapter 3 explains the theory behind capacitance both in general as well as in the specific case where the screening contribution is significant. Chapter 4 describes in detail all experimental techniques used in this project and Chapter 5 summarizes our experimental results. Finally, Chapter 6 is concerned largely with the generalization of magnetocapacitance techniques to other novel systems and the future work motivated by our present investigations. 1.1 Motivation The present solid-state electronics industry centers on the charge of the electron. Microscopic devices manipulate the transport of charge with electric fields to store and process information and perform calculations. Electrical signals are generated, detected, and amplified using solid-state devices that are the backbone of today’s technology. Since electrons also have a spin, or magnetic moment, they can be manipulated by magnetic fields as well as electric fields. Recently, magnetoelectronic devices have appeared in various applications including read heads for computer hard drives. These read heads exploit the spin of the electron to detect the local magnetic environment by way of giant magnetoresistance, or GMR. The interplay between spin and charge comprises the core of magnetoelectronics, or “spintronics.” Spintronics is an active field of research with a broad spectrum of experimental and theoretical challenges.

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3 The design and implementation of spintronic devices demand accurate experimental characterization of magnetic metals and semiconductors. Specifically, a detailed understanding of metal-semiconductor and metal-dielectric interfaces is necessary. For example, spin injection from a ferromagnetic metal into a semiconductor depends critically on the physics of the interface. 7, 8 The spin polarization of the tunneling current in magnetic tunnel junctions (MTJ’s) is affected by spin-dependent surface screening in the ferromagnetic electrodes. 9 The magnitude of the magnetoresistance in GMR is determined in part by the quality of the interfaces between ferromagnetic and nonmagnetic layers. 10 The study of these and other interface effects facilitates a better understanding of the relevant physics in these devices. Our goal in this work has been the development of capacitance and magnetocapacitance measurements as tools with which we can probe the interfacial properties of a variety of MIM structures involving paramagnetic and ferromagnetic metals and semiconductors. Since magnetocapacitance measurements are sensitive to spin-dependent potentials, we have employed them in a new way, detecting spin-polarization in metals. In the most general terms, we have set out to understand the origin and manifestations of spin-dependent electrochemical potentials and the fundamental physical properties of materials that these potentials reveal. 1.2 Magnetocapacitance When a MIM capacitor structure is subjected to a magnetic field, the measured capacitance of the structure can (and often does) change. This phenomenon is known as magnetocapacitance. If the capacitance of the structure increases (decreases) as the field is ramped, it exhibits positive (negative) magnetocapacitance. Throughout this

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4 dissertation, mention of the “magnetocapacitance technique” refers to the sweeping of the magnetic field in the region of the sample from zero to some predetermined value while simultaneously measuring the capacitance of the structure. As we will show in this dissertation, the magnetocapacitance technique probes various magnetic properties of the materials comprising an MIM structure. If the thickness (area) of the dielectric spacer decreases as a magnetic field is applied, the capacitance of the structure will increase (decrease) and the structure will exhibit positive (negative) magnetocapacitance. Similar effects exist when the metal layers expand or contract in the presence of an applied field. Magnetocapacitance also reveals changes in the dielectric constant of the insulator layer with applied field. 11 The sensitivity of the dielectric constant to magnetic field could result from magnetic field-dependent loss mechanisms, or magnetic field-dependent structural rearrangement. The aforementioned mechanisms behind magnetocapacitance are small in the structures we have studied when compared with the magnetic field-dependence of the screening lengths of the metal electrodes in our MIM structures. We have used the magnetocapacitance technique to probe the spin-dependent screening lengths of various metals, including Pd and the metallic alloy Pd 1-x Fe x . This information is useful for a variety of reasons. From a fundamental physics standpoint, since the screening length is dependent on the band structure in a metal (as we will show in Chapter 2), a probe of this length is another probe of the Fermi surface, similar to magnetic susceptibility and heat capacity. Since the band structure in the transition metals is exceedingly complicated, 12 many experimental knobs are necessary to fully characterize its complexity. Furthermore, the screening length is so short in most

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5 metals that surface band structure effects likely dominate, and are therefore revealed by magnetocapacitance techniques. Surface-sensitive techniques are important for understanding the physics of the nanometer length scale (nanoscience) as technology pushes devices smaller and smaller. From an applications standpoint, magnetocapacitive devices can be envisioned to detect magnetic moments on the surface of a material, much like magnetoresistive and GMR read heads do for computer hard drives. Similarly, a spin-dependent screening length could perhaps be used to detect non-equilibrium spin-polarization in spin-injection devices, or spin-diffusion lengths in metals and semiconductors. These and other ideas will be discussed throughout this dissertation. 1.3 Pd and PdFe Alloys We chose MIM structures involving Pd and alloys of PdFe because of their interesting magnetic properties. 13-15 Pd has the highest Pauli paramagnetic susceptibility of all the paramagnetic elements. This makes it well suited for magnetocapacitance measurements, as the magnetic field dependence of the screening length tends to be small and also tends to scale with the spin-susceptibility of the material. Pd is said to be nearly ferromagnetic 16 because though ferromagnetic exchange interactions exist between itinerant electrons, the Stoner criterion for ferromagnetism is not quite satisfied. There are sharp features in the density of states near the Fermi energy resulting from the narrow d-bands in Pd; 12 therefore Pd is a good candidate for verifying the sensitivity of magnetocapacitance measurements to band structure. Screening in itinerant ferromagnets involves electrons that are spin-polarized even in the absence of a magnetic field. 9 For this reason, it is useful to measure the capacitance of a MIM structure, in which one of the metals is an itinerant ferromagnet,

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6 while sweeping through the Curie temperature. The evolution of the band structure and the onset of spontaneous spin-polarization as the metal undergoes a ferromagnetic transition may cause a change in the screening length, which would be detectable in the measured capacitance. We have performed preliminary investigations to try to observe this phenomenon in Pd 1-x Fe x alloys, and the results are presented in Chapter 5. These alloys have a concentration-dependent Curie temperature below which they are itinerant ferromagnets. Alloying a Pd film with about 15 atomic % Fe or less yields a film with a Curie temperature below room temperature where it is easily accessible with cryogenic techniques. These and other measurements reveal to what extent the screening length in metals is dependent on magnetic field, band structure, and spin-polarization. 1.4 Benefit to Society These investigations provide valuable insight into the physics of condensed matter systems. A deeper understanding of the far-reaching manifestations of magnetism has been gained, and new dynamics of spin-dependent transport and charge storage have been elucidated. This insight will eventually have direct and/or indirect applications in electronic/spintronic devices. Fundamental research provides both researchers and members of society with intrinsically valuable knowledge and understanding. These will inevitably lead to progress.

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CHAPTER 2 ELECTRON SCREENING IN METALS One of the primary reasons the independent electron approximation works so well at metallic densities is because the electrostatic potential due to individual electrons (and ions, for that matter) is screened over a length scale comparable to the inter-atomic spacing of the metal. 17 This chapter deals with the theory behind electron screening in metals. A general exposition is first given on the idea of screening and its definition, along with manifestations of screening in various experiments. A derivation of the Thomas-Fermi screening length of paramagnetic metals is then given at zero temperature (T = 0) and zero magnetic field (H = 0). Modifications of Thomas-Fermi screening are then presented to account for finite temperature and magnetic field, and similarities between the temperature and field dependence of screening and magnetic susceptibility are discussed. Finally, a model of electron screening in ferromagnets, derived from the Thomas-Fermi model, will be given. 2.1 Screening in General: Definition and Manifestations Screening in this dissertation refers to the shielding of electric fields from penetrating the surface of a metal. Consider an infinite half space of a conducting material for x < 0 and a vacuum for x > 0. Imagine an electric field applied in the negative x direction normal to the surface of the conductor. Since there exists free charge in the conductor, current will flow and a net negative charge will build up near the surface (x = 0) until the electric field is precisely zero deep within the conductor. This configuration of charges is such that it exactly minimizes the total energy of the system. 7

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8 Another, perhaps oversimplified explanation is that charges move until there is no force on them, so as long as an electric field persists inside the metal, negative charges continue to flow to the surface of the conductor. An equilibrium condition is reached only when the electric field is zero deep inside the conductor. The surface charge shields, or “screens,” the bulk of the conductor from the electric field. Because of the Pauli exclusion principle (electrons are fermions!), the surface charge must be distributed over a finite length into the conductor to avoid an infinite charge density at the surface, which would minimize the total energy classically, but cost a great deal of energy quantum mechanically. In other words, it is the gradient of the electrochemical potential that determines the force on an electron, not the gradient of the electrostatic (Coulomb) potential. As we will show, the solution to the screening problem involves a constant electrochemical potential (no force on electrons) while allowing for a spatially varying electrostatic potential. Please note, though the classical solution involves an infinite volume charge density, the areal charge density is finite. In fact, the areal charge density induced at the surface is equivalent in the classical and quantum solutions as long as the “surface” in the quantum case extends into the conductor until the field is essentially zero. The length over which the electric field decays (exponentially) to zero in the limit of small electric fields is known as the screening length. The screening length in metals is an intrinsic property of the material itself. It depends on the carrier concentration and band structure of the metal and has recently been shown to depend on spin. Screening lengths influence electronic behavior in a variety of experiments including but not limited to capacitance measurements, tunneling

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9 spectroscopy, and field gating experiments. We leave a discussion of capacitance measurements to Chapter 3. Tunnel junctions are essentially MIM capacitor structures in which the dielectric layer is extremely thin (~15 in many cases). Because this barrier is so thin and because the tunneling current is dependent on the electric field at the surface of the metal electrodes, an accurate model of electron tunneling must include screening effects to account for the smaller than predicted tunneling current. This amounts to a rescaling of both the insulating barrier height and the effective barrier thickness, and the reader is referred to the literature for details. 5, 6 Electric field gating experiments rely on electric field penetration into the material under study to dope the “gated” material with charge, or to deplete it of charge, depending on the polarity of the field. To accomplish this, a conducting electrode (gate), separated from the material of interest by a thin (~100-1000) insulating layer, is placed either above or below and parallel to the material of interest. The structure resembles a MIM structure, except the material the experimentalist wishes to gate replaces one electrode. Field gating is accomplished by applying a voltage between the gate and the material of interest, and changes in electronic properties of the gated material are observed by simultaneous measurements, typically of conductivity. In these types of experiments, only the region into which the electric field penetrates contributes to the modification of electronic properties. For this reason, it is necessary to know the screening length in the gated material to determine the volume contributing to the measured changes.

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10 E0 x = 0 x 0 MetalVacuum Figure 2-1: Schematic of electrostatic screening at the surface of a metal 2.2 Thomas-Fermi Screening Consider the hypothetical model presented in section 2.1 and shown schematically in figure 2-1 in which there exists a real metal occupying the half space defined by x < 0 and a vacuum occupying the region defined by x > 0. Consider, again, an electric field (of strength E 0 ) applied normal to the interface in the negative x direction on the vacuum side. Let us calculate the induced charge in the metal in terms of the electrostatic potential, , defined with respect to the potential deep inside the metal (), as follows. From elementary theory using Fermi statistics, the number density anywhere within the metal is given by ()x ()0

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11 331()2.exp()()12dknxexk (2.1) The integral runs over all of k-space, (vectors are denoted by boldface type) is the energy of an electron in the state defined by the wave vector k, ()k 1BkT where k B is the Boltzmann constant, and is the electrochemical potential in the metal. The magnitude of the electron charge is given by e (positive quantity) and the factor of 2 is from spin degeneracy. We are under the assumption that the band structure of the metal is unaffected by the broken translational invariance resulting from the boundary at x = 0. We have also assumed that the presence of the electrostatic potential does not alter the electronic states, as we have simply added the electrostatic potential energy, , to the band energy, . We now transform the integral over wave vector into an integral over energy, leading to ()ex ()k (2.2) 0()()()nxdNfex where 1()exp1f (2.3) is the Fermi function and is the density of states, or twice (because of spin degeneracy) the Jacobian of the coordinate transformation. Taking the limit as temperature goes to zero produces a sharp Fermi function, which is equal to zero for and equal to one for . Therefore, at T = 0, equation (2.2) becomes ()N ()ex ()ex , (2.4) ()0()()exnxdN

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12 but this is just (2.5) ()()00()()()()fffffexexnxdNdNndN where the first integral in (2.5) is simply the total carrier concentration (n 0 ) in the absence of an applied electric field, which is exactly cancelled by the positive background of the ions. Note that we have replaced the chemical potential by the Fermi energy () since at T = 0. Therefore, the net charge induced by the electric field is given by f f . (2.6) ()0()()()ffexnxnxndN Now, if we take the limit of small electric fields (ex) and expand the density of states around the Fermi energy, then to first order in the potential, the induced charge density is ()f . (2.7) ()()()fnxNex The induced charge must also satisfy Poisson’s equation, to wit: 02 . (2.8) The total charge density is given by . (2.9) ()()xenx Since the potential and induced charge depend only on x, Poisson’s equation becomes 2220()()()fdxeNdx x . (2.10) For the present geometry, the solution to this equation (inside the metal where x < 0) is a decaying exponential. Requiring the potential to go to zero deep within the metal yields

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13 0()exp,0TFxx x (2.11) where is the electrostatic potential at x = 0 and 0 2201()fTFeN . (2.12) We have thus derived an expression for the Thomas-Fermi screening length, , and we will adhere strictly to this definition, (2.12), for the remainder of this dissertation. We arrived at equation (2.12) by assuming a planar distribution of screening charge (i.e. only dependent on the perpendicular distance from the interface) in response to an applied electric field, whereas it is conventional to assume an embedded (point) charge TF 17 and calculate the resulting screening charge. The result, as shown in the previous equation, is the same. It is trivial to show that this length has the aforementioned interpretation. Combining equation (2.11) with gives the solution for the electric field strength, E 0expTFxEE , (2.13) where 00TFE is the electric field strength at the surface. From equation (2.13) it is clear that the electric field only penetrates the surface of the metal over a length scale given by the Thomas-Fermi screening length, . TF 2.3 Thomas-Fermi Screening in a Finite Magnetic Field We now develop a modified theory of Thomas-Fermi screening which includes the effect of the presence of a magnetic field in the space containing our metal. We

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14 proceed in a straightforward manner building off of our previous assumptions. Consider the identical model given in the previous section (metal occupying the half-space defined by x < 0, electric field applied normally, etc.), except there now exists a magnetic field of strength H throughout all of space in an arbitrary direction. We continue as before, counting the number of electrons in the system, but this time, the conduction band is spin-split because of H. In other words, the energy of the spin-up (-down) electrons is reduced (increased) by the Zeeman energy, , as it is energetically favorable for the magnetic moments of the electrons to align with the magnetic field (the magnetic moment of the electron is given by , the Bohr magneton). We should note that throughout this dissertation, spin-up (-down) refers to electrons that have their magnetic moment aligned parallel (antiparallel) to the magnetic field, H. The spin-dependent volume density of electrons in the metal is now given by BH B 3,31()exp()()12BdknxexHk (2.14) where it is understood that refers to the carrier concentration of spin-up electrons, the determination of which involves the in the argument of the exponential, and receives the and refers to the concentration of spin-down carriers. We assume the magnetic field is weak enough that it does not perturb the band structure of our metal. Note the missing factor of 2 in front of the integral: it came from the spin-degeneracy of the conduction band, which has been lifted by the magnetic field. Note, also, that in the limit of zero magnetic field, as given in equation (2.1) and the Thomas-Fermi screening length is recovered. We again transform to an integral over energy, after which (at T = 0) the concentration becomes ()nx BH( ()nx BH )()()nxnxnx

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15 (),120()()BexHnxdN . (2.15) In finite magnetic field, even at T = 0. This will become evident shortly. f We briefly digress to discuss the magnetic field dependence of the chemical potential. Let us require that the application of a magnetic field does not change the total number of electrons in our system. In this case, the total number density of electrons cannot depend on magnetic field. For this reason, we will require that in the absence of an electric field, as defined in equation (2.5). From equation (2.15), the total number density in the absence of an electric field ( everywhere) is 0()()nxnxn 0 112200()()BBHHnndNdN . (2.16) This can also be expressed as 11220()()()fBBffHHnndNdNdN . (2.17) We now expand the density of states around the Fermi level 212fffffN()N()N'()()N"()() (2.18) and perform the integrations in (2.17), keeping only terms up to linear order in () and up to quadratic order in H. Replacing the first integral with n f 0 , we find 2102()()()()ffBnnnNHN' f . (2.19) Therefore, for the total carrier concentration to be conserved, the sum of the second two terms must vanish. This implies 212()()ffBfN'HN , (2.20) up to quadratic order in H.

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16 We now return to the carrier concentration in the presence of both electric and magnetic fields. Referring to equations (2.15) through (2.17), we find that the total carrier concentration is given by ()()11220()()()()()fBBffexHexHnxnxdNdNdN . (2.21) We again expand the density of states using equation (2.18), replace the first integral by n 0 , perform the other integrations, and keep only terms up to linear order in and e, and up to quadratic order in H. We are left with the following: ()x 2102212()()()()()(()()ffffBfffBnxnxnNN'N"HexNN' )H (2.22) The sum of the last two terms vanishes as in (2.19), and substituting equation (2.20) for the chemical potential yields 22102()()()()()()()fffBfN'nxnxnNN"HexN . (2.23) We define ,,102()()nxnxn (2.24) which gives . (2.25) 0()()()()nxnxnxnxn In this case, the induced charge density is given by . (2.26) ()()()xenxnx Poisson’s equation must be satisfied, to wit: 22221220()()()()1(()()fffBffN"N'dxeNHdxNN )x . (2.27)

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17 We find it convenient to define a band structure parameter, , as 2()()()()()()fffffN"N'N'NNN . (2.28) The solution to equation (2.27) is another decaying exponential, 0()expxx , (2.29) but this time, the screening length is modified from its Thomas-Fermi value as follows: 21222111BTFH . (2.30) With this analysis, we have determined the first non-trivial magnetic field dependent correction to the Thomas-Fermi screening length, which occurs at quadratic order in H. 2.4 Temperature-Dependent Screening at Finite Magnetic Fields We now turn to the effect of temperature on the models presented in the previous sections. We will assume low enough temperature such that the Sommerfeld expansion is applicable to the calculation of the carrier concentration at finite electric and magnetic fields and we will only be interested in the lowest order correction to the results previously obtained. The Sommerfeld expansion applies to integrals of the form , (2.31) ()()gfd where is the Fermi function defined in equation (2.3), and is a function of energy that does not change rapidly for small () perturbations of the energy from the Fermi energy. With these definitions, the Sommerfeld expansion is given by ()f ()g BkT

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18 422()()()()()6BBkTgfdgdkTg'O . (2.32) We will be interested only in terms up through quadratic order in T. To account for finite temperature, we must rewrite (2.15) as ,120()()()BnxdNfexH (2.33) We next apply the Sommerfeld expansion to the total carrier concentration, and performing the same manipulations and assumptions as before, we find that equation (2.22) is modified as follows: 22210222212()()()()()()(6()()()6fffBBfffBBfnxnxnNN'HkTN"exNHkT )N' (2.34) The sum of the last two terms must vanish to conserve particle number in the absence of an electric field. Imposing this condition yields the chemical potential in the presence of a magnetic field at finite temperature to quadratic order in both H and T, to wit: 22212()()6(ffBBfN'HkTN ) . (2.35) Applying this to equation (2.34), and satisfying Poisson’s equation as before yields the following temperature and magnetic field dependent screening length: 22212221116BBTFHkT () . (2.36) Recall that is defined in equation (2.28). Thus we have determined the lowest order corrections to the Thomas-Fermi screening length due to temperature and magnetic field. It is worth noting that the temperature and magnetic field dependences enter equation

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19 (2.36) with the same strength, . 12 It will be shown in the next section that although determines the strength of the temperature dependence of the Pauli paramagnetic susceptibility, a new (band structure) parameter must be introduced to account for the strength of the magnetic field dependence of the same quantity. n fB 2.5 Correlations Between Screening Length and Susceptibility We will now use a formalism similar to the one presented in the context of electron screening in metals but apply it to magnetic susceptibility. Similar treatments of this problem can be found in the literature. 12, 16, 18 We will see how the susceptibility is dependent on two band structure parameters, one of which determines both the magnetic field and temperature dependence () of the screening length. While the screening length depends on the sum of the carrier concentrations of the two spin bands, , the Pauli paramagnetic susceptibility depends on the difference, . Let us first calculate this difference at zero temperature, and then apply the Sommerfeld expansion to reveal the full, temperature dependent result. It is clear from equation (2.15), setting everywhere, that the difference is given by nn nn ()0ex 1122()()BBffHHndNdN (2.37) which, after expanding the density of states in the usual way, and keeping terms up through cubic order in H, is equivalent to 316()()()ffBfBnnNHN'HN"H . (2.38) Plugging in equation (2.20) for the chemical potential yields 2316()()()2()ffBfBfN'nnNHN"HN . (2.39)

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20 The magnitude of the magnetization of the carriers is simply the polarization number density multiplied by the magnetic moment of each individual carrier, explicitly: BnnM H . (2.40) Recalling the definition of the magnetic susceptibility, , as , (2.41) M and combining equations (2.39) through (2.41), it is easy to see that the magnetic susceptibility for our system is 22216()()()13()()ffBfBffN"N'NHNN ) . (2.42) With the conventional definition of the Pauli paramagnetic susceptibility, which is simply the magnetic susceptibility near zero field, , (2.43) 2(PBfN and the introduction of another band structure parameter given by 2()()3()()fffN"N'NN f , (2.44) we can rewrite equation (2.42) as 2161PBH . (2.45) We can modify our calculation to include the effect of temperature (to lowest non-trivial order) by way of the Sommerfeld expansion, using as defined in equation (2.28), and we present only the result: 22216(,)1()6PBHTHkT B . (2.46)

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21 It is clear from this analysis that the strength of the magnetic field dependence () is fundamentally different from the strength of the temperature dependence () in the case of the magnetic susceptibility. This does not hold for our screening length calculation, in which case the dependences entered with the same strength () [cf. equation (2.36)]. 2.6 Screening in Ferromagnets Finally, we present a simple model to capture the essence of screening in ferromagnets with first order corrections to the Thomas-Fermi value arising as a result of exchange interactions. In ferromagnets, the carriers interact via exchange interactions, parameterized by J, in addition to the Coulomb interactions already discussed, which were given by . More specifically, carriers of the majority (minority) spin-band have their energies lowered (raised) by the presence of spin-polarization (). This is known as the exchange interaction in ferromagnets, and it is the origin of ferromagnetism. ()ex nn We make the simple assumption, which falls under the category of mean-field theory, that the spin-up and spin-down bands are split in energy by . This is equivalent to the existence of an effective field in the ferromagnet arising as a result of spin polarization given by ()Jnn (effBJHn )neff (2.47) This is essentially a renormalized magnetization in the ferromagnet, which produces an unphysically large magnetic field. Clearly, our mean-field assumption is similar in nature to the Zeeman splitting previously presented (cf. equation (2.14)) by letting . The difference, which will become clear shortly, is that the magnetic BBHH

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22 field is not externally applied, but built-in and proportional to the spin-polarization. For this reason, the spin-polarization itself must be solved self-consistently in the following way. We again consider the same geometry as before, with a ferromagnet replacing the paramagnetic metal. Equation (2.14) is replaced by 3,31()exp()()12BeffdknxexHk ,, . (2.48) Recalling our definition of H eff , and we can rewrite (2.48) as , (2.49) ()()(),0()()exJnxnxnxdN where we have assumed zero temperature and is the density of states of spin-up and spin-down carriers, respectively. Replacing the density of states with its value at the Fermi energy, and defining ,()N , (2.50) 00,,00()JnnndN equation (2.49) becomes , (2.51) ,,,0()()()()()fnxnexJnxnxN with . (2.52) ,,0()()nxnxn We now solve for the induced carrier polarization, which yields ()()()()()1()()ffffNNnxnxexJNN (2.53)

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23 to first order in J. Combining equations (2.51) through (2.53) yields the full induced carrier concentration, ()()4()()()()()1()()ffffffNNJNNnxnxexJNN . (2.54) Again, we solve Poisson’s equation for this geometry and determine the screening length up to first order in J, to wit: 220()()4()()11()()fffffNNJNNeJNN f . (2.55) We note that this expression is identical to Zhang’s result 9 if we assume his exchange constant, J, is the negative of ours. This expression clearly collapses to the Thomas-Fermi screening length (cf. equation (2.12)) in the limit as . 0J

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CHAPTER 3 CAPACITANCE This dissertation is concerned largely with the application of capacitance measurements to MIM structures which possess very thin (~50) insulator layers. This chapter focuses on the general theory of capacitance, as well as the specific case of MIM structures with thin dielectrics. We first define capacitance and discuss some of its manifestations, giving examples and uses of capacitors. We then calculate the capacitance of a parallel plate capacitor in the thick limit. Next, we discuss the ramifications of making our structures thin, in which case screening effects become important, and finally, we present the electrical response (impedance) of a capacitor structure with a complex capacitance. 3.1 Definition and Uses References made to the capacitance of a structure refer to the ability, or capacity of the structure to store charge. A capacitor structure must consist of (at least) two conducting electrodes separated by an insulator or insulators. It is easiest to consider the static case (dc) in which a constant voltage is applied across the electrodes, or terminals of the capacitor, and the charge, which accumulates on the electrodes, is measured. We require that the capacitor remains charge neutral in this “charging” and, therefore, if one electrode gains a net charge of +Q, the other electrode must accumulate a net charge of -Q. The capacitance of the structure is simply the constant of proportionality between charge, Q, and voltage, V, and can be expressed mathematically as 24

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25 QCV . (3.1) Capacitors are used in a variety of applications due to their interesting and useful electrical properties. The ability of capacitors to store charge (and, hence store electric fields) makes them suitable for the storage of information. Typical random access memory (RAM) in most computers operates by way of an array of metal-oxide-semiconductor capacitors (MOSC) in which the storage of charge is detected by the electric field penetration into the semiconductor electrodes. Each capacitor in the array is either charged or uncharged, and these make up the digital bits, or building blocks of the computer memory. The necessity for faster computers pushes these capacitors in the direction of thinner dielectrics and smaller electrode areas, and these trends give rise to new electrical effects which will be discussed later in this chapter. Capacitors are present in the overwhelming majority of electronic applications, and are suited for this purpose due to their frequency-dependent impedance, which will also be discussed in this chapter. They are used as electrical filters, variable frequency tuners, ac couplers, and a whole host of other applications. The measurement of capacitors can reveal a variety of physical properties. For example, the dielectric properties (dielectric constant, loss, etc.) of the insulator layer in MIM structures are revealed by capacitance measurements. The charge doping density in electric field gating experiments is also determined by measuring the capacitance (and multiplying by the applied voltage) between the gate and material of interest. Capacitance techniques are also used to determine the distribution and density of interface states (charge traps) in metal-insulator-semiconductor structures. Many other examples of the utility of capacitance measurements exist, and some will be presented in detail in this dissertation.

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26 3.2 Parallel Plate Model of Capacitance The parallel plate model of capacitance is simple, but useful. For MIM structures in which the thickness of the insulator layer is on the order of microns and the area of the electrodes is on the order of square millimeters, the deviation of the measured capacitance from the capacitance predicted from the parallel plate model is vanishingly small. The parallel plate model has two major assumptions: the electrodes have an infinite area, and there exists no electric field penetration into the electrodes (). We will show the limitations of this model explicitly in the next section. 0 Consider two very large conducting sheets, each of area A, situated parallel to one another. An insulator of dielectric constant , and thickness d separates them. Let us apply a surface charge density of to one sheet (electrode) and to the other. We know from elementary theory that between the plates, the electric field is given by 0E . (3.2) We have assumed so that we can neglect fringing effects. This assumption is generally true in practice. Since the voltage between the plates is the line integral of the electric field, we find 2d A 0dV . (3.3) The surface charge density is simply the charge (Q) divided by area (A), i.e. QA , so it is obvious from its definition, cf. (3.1), that the capacitance is given by 0gACd . (3.4)

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27 Thus we have formally defined the geometrical capacitance (C), or equivalently, the capacitance assuming a parallel plate model. It is understood that throughout this dissertation, C is as defined in equation (3.4). g g 3.3 Screening Effects For tunnel junctions, in which the dielectric layer is exceedingly thin (~20 ), the parallel plate model breaks down. 1, 2 For this reason, we turn to a more realistic model for the capacitance of parallel plate (MIM) structures in which electric field penetration into the electrodes is taken into account. We will see that the inclusion of field penetration (finite screening length) drastically alters the predictions of the parallel plate model for thin dielectrics. -D0dD+dM1M2Dielectric(0VVElectrostatic PotentialPosition Figure 3-1: Schematic of thin capacitor structure

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28 Consider the same geometry presented in the previous section, shown schematically in figure 3-1. This time, we specify explicitly the positions of the electrodes and the dielectric layer. For the sake of generality, we will assume that the two electrodes are composed of different metals, M 1 and M 2 . One electrode (M 1 ) is placed so that its boundaries are defined (normal to the x-axis) at x = -D, and x = 0. The other electrode (M 2 ) is placed so that its boundaries are defined at x = d, and x = d + D. There is a dielectric medium between the plates with dielectric constant , and the screening lengths in the electrodes are much smaller than their thickness (). We define the potential at x = 0 as . Recall from the previous chapter that the potential in M 1,2D 1 1 is given by 11()exp0xx x (3.5) where is the screening length in M 1 1 . Clearly, it is also true that 22()expxdxVxd (3.6) where V is the potential applied across the entire structure ( VD), is the potential drop across M dD 2 2, and is the screening length in M 2 2 . We can find the electric field strength at the surfaces of each electrode at x = 0 and x = d using (3.7) E The result is independent of which interface we choose as the electric field must be constant for 0 < x < d (there is no free charge in this region and the electrodes appear as infinite planes of charge). Therefore, we have the following relation: 12120xdE . (3.8)

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29 Given the definition of the potential as the line integral of the electric field, we find that the total potential across the entire structure is given by 111dV 2 (3.9) where the first and third terms on the right hand side (RHS) are the potentials due to the electric field penetration into the electrodes, and the second term is the potential across the dielectric due to the presence of a spatially uniform electric field. Using equation (3.8), we can rewrite the full potential in terms of as 1 1121Vd . (3.10) Although the accumulated charge is distributed into the electrodes, we are still free to use equation (3.2) due to the planar geometry (the electric field in the dielectric does not depend on how far from the interface the induced charge resides), in which case the charge divided by the area is given by 0101QAE , (3.11) which leads to 120QQVdCA . (3.12) Thus, the capacitance is modified from its parallel plate, or geometrical value by 0010111,,igiACdCCCd 2 , (3.13) with C defined in equation (3.4), and C is known throughout this dissertation as the interface capacitance. So, we see that accounting for screening effects amounts to an effective dielectric thickness given by g i

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30 , (3.14) 0effdd d so that the capacitance may be written as 0effACd . (3.15) As an equivalent alternative interpretation, one may think of the interface capacitance, , as a capacitance in series with the geometrical capacitance, C. With either interpretation, it is clear that when the dielectric thickness, d, is comparable to d iC g 0 , the interfacial contribution to capacitance is significant. We also note that as the dielectric thickness vanishes, the capacitance no longer diverges, as it would in a simple parallel plate model (cf. equation (3.4)), but instead approaches the interfacial value, . This capacitance saturation is observed, iC 4 and data to this effect will be presented in chapter 5. 3.4 Complex Impedance of Capacitors The electrical impedance of real capacitor structures is frequency dependent and complex. In general, the capacitance itself is frequency dependent and complex, and this fact can be understood in terms of leakage and loss. Leakage is defined to be the conduction of dc current through the insulator region of an MIM capacitor structure with an applied dc voltage. A frequency independent resistor in parallel with the capacitor mathematically represents leakage. A tunnel junction is a leaky capacitor, as it is meant to pass a dc current in the presence of a dc voltage. Loss, on the other hand, is associated with ac processes. It is represented by the complex part of the capacitance and gives rise to frequency-dependent dissipation. There are a variety of loss mechanisms, each of which corresponds to some inelastic process. For example, localized states (charge traps) in the region of the metal-insulator interface in MIM structures charge and discharge in an inelastic way, with particular frequency dependence. Also, rotating dipoles in the

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31 dielectric can contribute to loss as they are damped viscously. Other examples of loss exist, but the important point is that the common thread uniting loss mechanisms and distinguishing loss from leakage is the absence of a dc current associated with loss. Consider a sinusoidal voltage of amplitude V 0 and frequency applied across the terminals of a capacitor of capacitance C. We write the voltage as a complex function of time to simplify the algebra (Vt). Referring to the definition of capacitance given in equation (3.1), we find that the current, or time rate of change of charge on a capacitor is given by 0()expVit ()()()()dQtdVtItCiCVtdtdt . (3.16) Recalling that impedance is defined as the constant of proportionality between complex voltage and complex current (Vt), it is clear from equation (3.16) that the impedance of a capacitor with capacitance C is given by ()()ZIt 1ZiC . (3.17) Let us consider the case of a leaky, lossy capacitor, where the leakage is parameterized by a parallel resistance value, R 0 , and the loss is the imaginary part (C 2 ) of the capacitance, which we define as . (3.18) 12()()()CCiC Recalling that the impedance of a resistor is just the resistance itself, and applying the parallel impedance formula, which can be expressed as 11jjZZ , (3.19) we find that after a little bit of algebra, the complex impedance of a leaky, lossy capacitor is given by

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32 00201202011()(()1()(RRCiRCZRCRC 2)) . (3.20) We can express this in terms of the magnitude and phase of the impedance ( expZZi ), which yields 012220201()1()()RZRCRC (3.21) and 10102()()tan1(RCRC ) , (3.22) where the arctangent is defined between 22 . The parameters Z , , and R 0 are measurable with an impedance analyzer, and from these, the capacitance is calculated by inverting equations (3.21) and (3.22). The inversion is straightforward, and the results are as follows: 1sin()()()CZ , (3.23) and 20cos()1()()CZR . (3.24) Thus we have derived relations for the impedance of a complex capacitor, and we have shown how measurements of the magnitude and phase of the impedance in conjunction with an independent measurement of the dc resistance lead to the determination of the real and imaginary parts of the capacitance. We will describe another method of measuring capacitance using a bridge technique in chapter 4, and we

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33 will show the experimental results obtained using an impedance analyzer and these analyses in chapter 5.

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CHAPTER 4 EXPERIMENTAL TECHNIQUES This chapter presents the details of all experimental techniques applied in the collection of the data to be presented in the next chapter. We first present the specific techniques involved in the preparation and growth of the MIM structures mentioned throughout this dissertation, including expositions on particular growth techniques and on the theory of operation of various vacuum systems. Next, we discuss the characterization tools used in these investigations, including, but not limited to bridge techniques, amplifiers, and cryostats. We then present the details concerning electrical connections, including notes about cabling and proper grounding. Finally, we introduce the various roles computers play in our interfacing, data recording, and data analysis. For additional detail concerning standard vacuum practices and thin-film growth and characterization, the reader is referred to the exhaustive work of Maissel and Glang. 19 4.1 Sample Growth All substrate preparation and sample growth takes place in-house. Careful attention is paid to cleanliness and consistency in an effort to minimize spurious effects and to yield the most reliable and reproducible results. This section details the techniques utilized in the fabrication of our MIM structures. All deposition processes occur in vacuum systems designed specifically for the particular growth technique. Standard vacuum procedures are practiced at all times, and vacuum conditions are maintained 34

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35 throughout all growth processes. Thickness is monitored during growth in all of our vacuum systems with Inficon quartz crystal thickness monitors. 4.1.1 Substrate Preparation All MIM structures in these investigations are grown upon either glass, or Si substrates. For samples grown on glass substrates, the following preparation steps are followed. Glass microscope slides (3” x 1” x 1mm) are cut into 1” x 0.3” x 1mm “coupons.” Cutting is accomplished by first scribing the backside with a diamond scribe in the desired cutting location, and then, upon turning the glass over (scribed side down) onto a rubber surface, pressing with a straight edge precisely opposite the position of the scribe mark. The glass breaks cleanly along the scribed line as the rubber flexes beneath it. Glass coupons are then placed in a Teflon basket to be cleaned. The substrate-containing Teflon basket is placed in a beaker, which contains deionized (DI) water with a small amount of Alconox, a mild detergent. The beaker is placed in an ultrasonicator for 15 minutes to dissolve any oils and remove dirt from the surfaces of the substrates. Substrates are then rinsed with DI water and re-sonicated in pure DI water for another 15 minutes to remove any residual detergent. Substrates are then sequentially sonicated in Acetone, Isopropanol, and Methanol for 15 minutes per solvent with each solvent placed in a separate beaker. The substrates are completely submerged in all cleaning steps involving ultasonication. It is important not to let any solvent (unless it is exceedingly clean) evaporate on the surface of the substrates, as the residual contamination is virtually impossible to remove. For this reason, after the final sonication step, the substrates are rinsed with Methanol, and then immediately blown dry with clean N 2 gas from the boil-off of a liquid nitrogen dewar.

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36 For samples grown on Si substrates, the preparation steps are similar, but markedly different. We start with a 4” diameter, circular, (100) orientation, .022” thick Si wafer. The entire wafer is cleaned using the same steps in the glass substrate cleaning procedure. The polished surface is then coated with S-1813 photoresist so that in the cutting step, Si dust does not attach itself to the substrate surface where it is very difficult to remove. We first apply the resist, and then spin the wafer at 5000 rpm for 30 seconds to evenly coat the wafer. The entire wafer is then hard-baked at 140 for 30 minutes. A coated wafer is attached (with the help of a hot plate) to an 8” diameter Si wafer, bonded by a polymer with a melting point of about 120. The 4” wafer is then cut into precise 1cm C C 2 squares with a dicing saw that completely cuts through the 4” wafer without penetrating the surface of the 8” wafer. Square substrates are removed from the 8” wafer by placing the wafer on a hot plate, which melts the polymer, and utilizing tweezers to carefully pull the substrates away. Residual polymer is removed via sonication in Acetone, but the heating steps tend to cross-link the photoresist, which renders it insoluble in Acetone. For this reason, the final cleaning step involves a Piranha etch, 20 which consists of 50 parts H 2 SO 4 (sulfuric acid) to 1 part H 2 O 2 (hydrogen peroxide), maintained at 120. Substrates are placed in a Teflon basket, and dipped into the etch for 3 min, moving the substrates frequently to avoid bubble formation at the substrate surfaces. Once removed from the Piranha etch, substrates are immediately placed in a beaker of DI water, after which they are individually rinsed with flowing DI water, blown dry with clean N C 2 as before, and placed on a hot plate maintained at 120 for 10 minutes to drive off any residual water. C

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37 4.1.2 DCand RF-Magnetron Sputtering A variety of growth techniques were employed in these investigations. This section deals with the application of magnetron sputtering to the growth of thin, metal films. Sputtering, in general, refers to the deposition of a material under vacuum conditions via bombardment of a target with accelerated ions, which reside in a typically charge neutral plasma. These ions “sputter” the target, and microscopic, sputtered bits of the target material adhere to the substrate, which is placed so that it faces the sputtered side of the target. A quartz crystal thickness monitor is placed near the substrate and provides in-situ thickness information. Magnetron sputtering is a specific type of sputtering in which strong permanent magnets are used to confine the plasma to the volume immediately surrounding the target. The magnets also serve to direct the ions into the target. Shown in figure 4-1 is a schematic of an A320-U-A sputter gun from AJA International. Figure 4-1: AJA International A320-U-A magnetron sputter gun schematic 21

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38 Sputtering depends on the presence of a pure, inert gas, maintained at a precise pressure, usually on the order of 1 mTorr. The sputtering gas serves to provide a plasma from which ions are accelerated to accomplish sputtering. To ensure the proper purity of the sputtering gas, the chamber in which deposition is to occur must be evacuated to a pressure of ~1e-6 Torr or below before the introduction of the gas. During sputtering, a voltage is applied between the ground shield and the target (figure 4-1) to generate a strong electric field. The electric field ionizes the sputtering gas (argon in our applications) in the region of high electric field strength and free electrons accelerate and undergo helical motion in the confining magnetic field.

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39 Figure 4-2: Schematic showing magnetic field lines in a magnetron sputter gun 21 These, in turn, bombard other inert gas molecules, knocking off more electrons, and thus sustaining a plasma. The positively charged ions are drawn toward the target, as only paths along the magnetic field lines are undeflected. Figure 4-2 shows both the orientation of the magnets, and the positions of the magnetic field lines in the AJA sputter gun. The target block is water cooled as the majority of the power dissipated during sputtering is delivered to the target in the form of heat.

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40 This same gun design is used in both dcand rf-magnetron sputtering applications. The terms dc and rf refer to the power supply used to generate the plasma. Conducting targets can be sputtered using dc or rf (13.56 MHz) power supplies, while insulating targets require the use of an rf driving voltage since an insulating target cannot dissipate the charge generated by the flux of ions from a dc source. In both cases, the substrate is located along the axis of the sputter gun facing the target. For example, in figures 4-1 and 4-2, the substrate would be above the gun, with the desired deposition surface downward facing. 4.1.3 Reactive Ion Beam Sputtering Another sputtering technique used in this work, reactive ion beam sputtering (RIBS), involves a reactive gas, as well as an inert sputtering gas. RIBS is typically used to form oxides and nitrides of various metals, with oxygen and nitrogen as the reactive gasses, respectively. The reactive gas combines, or reacts with the sputtered material to form the desired compound or composite. In this technique, an ion gun distinct from the target facilitates sputtering, as shown in figure 4-3. The ion gun generates a collimated beam of ions at a specified energy, and these are directed toward the target. The ions are removed from a plasma, which is generated and sustained via the thermal emission of electrons from a hot cathode inside the gun. The thermally emitted electrons are accelerated through a potential difference, and caused to spiral around magnetic field lines present in the gun, following long paths, and ionizing sputtering gas molecules. In this way, a plasma is generated and sustained. The ions in the plasma are accelerated through a series of grids maintained at the particular potentials required to give a collimated beam of ions at the user-specified energy. The sputtering rate is a function of the beam voltage (energy) and the beam current. A flux of sputtered target material

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41 arrives and adheres to the substrate, and in this way, RIBS is accomplished. Thickness is monitored on a quartz crystal thickness monitor located near the substrate. Reactions between the sputtered material and the reactive gas can occur on the target, in flight between the target and substrate, or on the substrate. Though it is unclear where the relevant reactions occur, many believe they occur at the substrate surface. Figure 4-3: Diagram of reactive ion beam sputtering (RIBS) geometry 4.1.4 Thermal Evaporation Perhaps the simplest deposition method used in this project is thermal evaporation. This technique utilizes a tungsten (W) or tantalum (Ta) filament, or boat to heat and evaporate the desired material. Figure 4-4 diagrams the geometry of a typical thermal evaporation system. Current is sent through the filament, heating it and the evaporant via Joule heating. The flux travels ballistically from the evaporant and condenses onto the substrate (lower) surface. To avoid oxidation, contamination, and

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42 scattering of the flux, the pressure in the vacuum chamber must be maintained at ~1e-5 Torr or below. We typically evaporate at pressures below 1e-6 Torr. Film thickness is measured in-situ using a quartz crystal thickness monitor placed in close proximity to the substrate. Figure 4-4: Schematic diagram of thermal evaporation geometry 4.1.5 Plasma Oxidation Native oxides grown on a variety of metals act as robust, pinhole-free dielectric barriers for tunnel junctions and capacitor structures. Plasma oxidation is one way to accomplish native oxide growth. It involves the use of an electrode, which is biased negatively with a dc voltage relative to the vacuum chamber, in the presence of an oxygen atmosphere maintained at a precise pressure. The rest of the vacuum chamber, including the substrate, is grounded during plasma oxidation. With the electrode biased,

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43 an electric field exists between the electrode and the rest of the chamber. This electric field ionizes nearby oxygen molecules, accelerating electrons and generating a plasma, just as mentioned in the previous sections on sputtering. Oxygen ions strike the film present on the surface of the grounded substrate, thereby oxidizing the film. 4.1.6 Quartz Crystal Thickness Monitor In each of the vacuum deposition systems mentioned in the previous sections, an Inficon quartz crystal thickness monitor is located in close proximity to the substrate and measures the accumulation of material during the deposition process. Each thickness monitor consists of a quartz crystal, oscillator circuit, and controller. The crystal is in the shape of a disk and is about 1 cm in diameter and 1 mm thick. The upper and lower surfaces of the quartz disk are coated with a thin film of gold. When placed in a rigid housing, a spring-loaded contact provides an Ohmic connection to one side of the crystal while the other side of it is exposed to the incoming flux, and grounded to the housing. The gold-coated quartz crystal is essentially a capacitor with extremely sharp resonances, which occur at precise frequencies associated with vibrational modes of the crystal. The oscillator circuit excites the crystal with an ac (~6 MHz) voltage in an attempt to couple electrically to the mechanical modes of the crystal. The circuit sweeps the frequency, and locates a particular resonance, which it detects by way of an impedance measurement. The oscillator locks on to this resonant frequency, and continues to drive the crystal. As deposited (sputtered or evaporated) material arrives at the substrate and thickness monitor, the surface of the crystal obtains additional mass, which decreases the resonant frequency. The oscillator shifts the driving frequency to maintain the resonance condition, and the controller uses the frequency shift to determine the accumulated mass.

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44 Calibrations are made between accumulated mass and film thickness, and in this way, in-situ thickness measurements are made. 4.2 Vacuum Systems This section describes the vacuum practices that are used throughout the MIM fabrication process. We first give a brief introduction into the general theory of operation of all primary pumps used in these investigations. These include turbomolecular, diffusion, and cryosorption pumps. We then discuss the valving and manifolding necessary for the effective operation of a complete vacuum system, including an introduction to rotary vane pumps. 4.2.1 Turbomolecular Pumps Turbomolecular, or turbo pumps efficiently pump gasses at reduced pressures by way of momentum transfer from turbine blades. They require a mechanical backing pump, which maintains the turbo pump exhaust (foreline) at ~100 mTorr. Turbo pumps are capable of ultimate pressures of about 1e-10 Torr. An alternating series of stators and rotors effectively compress the residual chamber gasses in the following way. The rotors, which contain blades of varying pitch, are spun at ~20,000 rpm and impart momentum to the gas molecules. The stators direct the flow of gas toward the foreline, and segregate the pump into many sections, each of which has a successively higher pressure. The turbo pump can, for this reason, be considered a multistage pump. The exhaust gasses flow out the foreline, and through the backing pump, which exhausts to atmospheric pressure. Turbo pumps are capable of pumping continuously at pressures below ~10 mTorr. Above this pressure, they become terribly inefficient, and can even become damaged by short exposures to high (atmospheric) pressures. They are meant to

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45 operate in the molecular regime, characterized by a mean free path for gas molecules on the order of the rotor to stator separation distance, as opposed to the viscous regime. For this reason, a vacuum chamber must first be rough pumped, or roughed (usually by the backing pump) down to as low a pressure as possible (~50 mTorr) before a turbo pump can be used. 4.2.2 Diffusion Pumps Like turbo pumps, diffusion pumps impart momentum to the residual gasses in the chamber in the direction of the foreline. Diffusion pumps also require the use of a backing pump, maintaining the foreline at a reduced pressure. The foreline requirements are not as strict for most diffusion pumps, as they require a pressure of ~500 mTorr or below. Unlike turbo pumps, diffusion pumps impart momentum to the gas molecules by way of a supersonic jet of oil vapor. A schematic diagram of a simple diffusion pump is presented in figure 4-5. Diffusion pump oil (work fluid) is heated in the bottom of the pump. The oil vapor travels up the chimney, and is allowed to escape through precision-machined jets, which are aimed downward and toward the water-cooled outer walls of the pump. Since the pressure is much lower in the throat area than in the chimney, the vapor rapidly expands, and thus its velocity is dramatically increased. As the vapor travels toward the outer wall at supersonic speed, it imparts downward momentum to gas particles that have diffused into the throat of the pump. This produces a pressure differential between the high vacuum intake and the foreline, and a mechanical pump removes the pumped gasses from the foreline. A typical diffusion pump is limited only by the rate of outgassing in the vacuum chamber, as pumping speed, measured in liters per second, is constant below about 1 mTorr.

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46 Figure 4-5: Diffusion pump diagram 19 Diffusion pumps suffer from a problem called back streaming. Back streaming is when diffusion pump oil, though it has a very low vapor pressure at room temperature (~1e-9 Torr), makes its way into the vacuum chamber by traveling backwards through the throat. To minimize this effect, many diffusion pumps are equipped with cold traps. A cold trap consists of a series of baffles in thermal contact with a liquid nitrogen bath (77 K). The trap is located between the diffusion pump and the main chamber. Cold traps reduce the back streaming of diffusion pump oil to a negligible amount. 4.2.3 Cryosorption Pumps Another type of primary vacuum pump, which does not require a backing pump, is the cryosorption, or cryo pump. These pumps consist of a compressor, expansion

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47 chamber, and cold head. A refrigerant (usually He gas) is first compressed, and then cooled to room temperature in the compressor. The refrigerant then passes through the expansion chamber, where it is allowed to expand in such a way that its final temperature is minimized. The refrigerant is then returned to the compressor. The expansion chamber is thermally linked to the cold head, which under typical operating conditions is maintained at ~15 K by the refrigeration process. The cold head consists of a large surface area, porous material, like charcoal, for maximum adsorbant capacity. While maintained at low temperatures, the cold head adsorbs the residual gas in the chamber, and thus cryo pumping is accomplished. Because cryo pumps have no exhaust, they need to be regenerated at a frequency dictated by the gas load and adsorbant capacity. Regeneration requires venting the cold head with warm N 2 gas, maintaining an overpressure until the cold head is at room temperature, and finally pumping on it with a pump capable of an ultimate pressure of 50 mTorr or below. This effectively desorbs the vast majority of molecules, as the heat of adsorbtion is exceedingly small for most gasses. Like turbo pumps and diffusion pumps, cryo pumps require a preliminary roughing of the vacuum chamber to ~50 mTorr before cryo pumping is initiated. 4.2.4 Valving, Manifolding, and Rotary Vane Pumps A typical vacuum system consists of many integrated components. In this subsection, we discuss systems involving both primary and backing pumps. Cryo pumped systems are not detailed here, but many of the same principles can be applied in a straightforward way. A diagram of a generic vacuum system is shown in figure 4-6.

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48 Figure 4-6: Vacuum system schematic This diagram shows the placement of all valves and pumps used in evacuating a typical system. In addition to backing up the primary pump, the backing pump serves to rough the chamber. Evacuation from atmospheric pressure proceeds as follows. With both pumps running and the gate and foreline valves closed, the roughing valve is opened. When the pressure in the chamber is ~50 mTorr, the roughing valve is closed. The foreline valve is then opened to back the primary pump, and finally, the gate valve is opened. It is very important that neither the mouth, nor the foreline of the primary pump are exposed to atmospheric pressure inadvertently, as exposure can damage turbo pump rotors, and can cause oxidation and back streaming of diffusion pump oil. For this reason, any time the gate valve is open, the foreline valve must also be open to maintain the foreline at an acceptable pressure.

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49 Backing pumps for vacuum systems come in a variety of types. The most common backing pump is the rotary vane pump. A schematic of this type of pump is shown in figure 4-7. Figure 4-7: Rotary vane pump schematic 19 A rotary vane pump functions via a cylindrical rotor rotating about an axis that is off-center from a larger diameter cylindrical housing, or stator. The rotor contains multiple spring-loaded vanes, which are in constant contact with the inner diameter of the stator. These vanes provide a seal between the stator and rotor, and as the rotor turns and a vane passes the inlet, gas is drawn into the pump and temporarily resides in the region defined between the inlet and the vane that most recently passed. Once another vane passes the inlet, the gas that was drawn in during the cycle that began when the first vane passed is isolated from the inlet. As the rotor continues to rotate, the first vane eventually passes the exhaust port. The next vane then forces the gas out the exhaust, and thus the

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50 cycle is complete. In this way, pumping is accomplished. A typical rotary vane pump is capable of evacuating a vacuum system to the ~50 mTorr range. 4.3 Characterization Tools This section outlines the various devices used to perform our electrical measurements. Capacitance measurement techniques comprise the core of our experimental characterization tools, and we have applied them liberally to various MIM structures. Capacitance is measured in a variety of ways under a number of conditions. We first introduce some of the building blocks of capacitance measurements, including the lock-in amplifier and impedance analyzer. We then discuss bridge techniques and their advantages over other methods, explaining the theory of operation of a capacitance bridge. Finally, we describe the Quantum Design cryostat system, which we use to control the temperature and magnetic field environment of our samples while simultaneously measuring their capacitance. 4.3.1 Lock-in Amplifier One basic tool that we use in capacitance measurements is a lock-in amplifier. Our lock-in amplifier of choice is the Princeton Applied Research PAR 124A. A lock-in is used to measure the in phase and out of phase voltage components of a small signal at a precise frequency. The measurement utilizes a reference signal at the measurement frequency, and the phase of the unknown voltage is determined with respect to the reference. Lock-ins are especially well suited for measuring extremely small signals that are shrouded in noise. The key element, which makes a lock-in so selective in such a narrow frequency range, is the multiplier. Consider a reference signal, generated by the lock-in, with a voltage versus time given by

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51 , (4.1) 0()cos()refVtVt where V 0 is the amplitude and is the frequency of the reference signal. Consider, also, an incoming signal, defined by its Fourier components as (4.2) ()cos()sin()iiiiVtAtBt i where and represent the amplitudes of the in phase and out of phase components of the incoming signal at a frequency of , and the summation runs over all frequencies present. A lock in multiplies the reference signal by the incoming signal, which yields iA iB i 102()()refVtVtVAoscillatory terms . (4.3) So we see that the product of the two oscillatory signals gives a constant term plus a bunch of oscillatory ones, which average to zero. The time averaged dc voltage (filtered, in practice) gives the amplitude of the incoming signal at the reference frequency via equation (4.3). The lock in also has provisions for phase shifting the reference signal by 2 , and a multiplication of this phase shifted signal by the incoming signal yields the amplitude of the out of phase component at the reference frequency. 4.3.2 Impedance Analyzer The impedance analyzer used in this work is a Solartron model 1260A. It is designed to measure the complex impedance of a sample in the frequency range of to 32MHz. The analyzer has an on-board frequency synthesizer that acts both as the drive signal for the test sample, and the reference signal for the voltage measurement. The 1260A has an output, which drives the sample at the user-specified frequency and amplitude, a current amplifier input to measure the current through the sample, and differential voltage inputs to measure the voltage across the sample. The 1260A 10Hz

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52 performs true 4-terminal measurements of the sample impedance. The voltage measurement is performed with a multiplier circuit, in much the same way a lock in amplifier measures voltage. There are two reference signals of the same amplitude, one in phase with the drive signal, and one out of phase by 2 . The analyzer uses these to determine the in phase and out of phase amplitudes of the sample voltage at the drive frequency. Dividing these amplitudes by the current yields the resistance (in phase) and reactance (out of phase), which are the real and imaginary parts of the impedance, respectively. One can easily state these in terms of the magnitude and phase of the impedance, as was shown in chapter 3. 4.3.3 Capacitance Bridge We used two capacitance bridges in this work. Both function by the same general principles, which we present in this subsection. The first bridge used is the General Radio model 1615-A. This unit contains only the bridge circuitry and is operated in conjunction with a PAR 124A lock-in. The lock-in serves as the frequency generator, and null detector. The second bridge used in this work is the AH 2700A from Andeen-Hagerling. This unit is fully self-contained; it includes the bridge circuitry, frequency synthesizer, and null detector. Moreover, the balancing procedure is fully automatic. Use of the AH 2700A is much more convenient than the GR 1615A, which must be balanced by hand.

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53 Figure 4-8: Capacitance bridge circuit 22 A diagram of the general capacitance bridge circuitry is given in figure 4-8. A pure sine wave with precise amplitude and frequency is synthesized in the generator. This signal is sent to the ratio transformer, the center tap of which is grounded. Taps 1 and 2 are fully adjustable, and determine the voltages applied across the standard (leg 3) and unknown (leg 4) capacitors, respectively. The bridge is balanced when the voltage across the detector is precisely zero (both in phase and out of phase). For zero voltage to exist across the detector, the voltage drop across the standard (leg 3) must be identical to the voltage between tap 1 and ground, and, similarly, the voltage across the unknown (leg 4) must be exactly equal to the voltage between ground and tap 2. This statement is equivalent to the following equations: 001102002221()()11()()1xxxxxiCRVtIZItRCRiCRVtIZItRCR (4.4)

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54 In the above equation, V 1 and V 2 are the voltages between tap 1 and ground, and between ground and tap 2, respectively, I is the current through the standard and the unknown, Z 1 and Z 2 are the impedances of the standard and unknown loads, respectively, and is the driving frequency. Requiring the current to be the same through both legs (current can not enter the detector) yields the following equation: 102011()()xxVtiCVtiCRR . (4.5) We know V 1 and V 2 in terms of the generator voltage (V 0 ) and the ratio of the number of turns in the primary winding (N) to the number of turns in each secondary winding (N 1 and N 2 ) 110220()cos()()cos()NVtVtNNVtVtN (4.6) It is trivial to show that a measurement of zero voltage across the detector corresponds to 201102xxNRRNNCCN (4.7) Thus the unknown resistance and capacitance are determined in this way. A capacitance bridge provides a much more precise measure of the capacitance of an unknown load than an impedance analyzer, or similar lock-in technique. Bridge circuits, in general, are exceedingly sensitive since they detect signals that are very close to zero. It is much easier to measure a 1 nV deviation from zero voltage than it is to measure a 1 nV deviation from 10 V.

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55 The previous analysis assumes a three-terminal lead configuration, as shown in figure 4-9. This diagram represents the unknown impedance from figure 4-8. The unknown is completely shielded by a conducting guard (terminal G), which is connected to the ground of the circuit (the center transformer tap, as indicated in figure 4-8). There are two additional capacitances to consider: C HG (the capacitance between the H and G) and C LG (the capacitance between the L and G). Clearly C HG is across the transformer windings (with applied voltage V 2 ) and in parallel with the unknown, therefore the current it draws does not affect the voltage across the unknown (also V 2 ). Further, C LG shunts the detector, but since terminal L is maintained at ground during balance conditions, there is no voltage across C LG , and hence no current drawn. Thus the capacitances C HG and C LG affect neither the voltage across the unknown, nor the balance condition. CRHLG Figure 4-9: Schematic of three terminal lead configuration for capacitance measurements

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56 4.3.4 QD-6000 Physical Property Measurement System The majority of measurements performed in this work occur in the QD-6000 cryostat from Quantum Design. The Physical Property Measurement System (PPMS) consists of a liquid nitrogen jacketed liquid helium dewar, 7 tesla superconducting magnet, evacuated sample probe, electronic controller, mechanical pump, and computer. A schematic of the sample probe is given in figure 4-10. Temperature control is accomplished via a cooling annulus around the sample space, two heaters, and three thermometers. A flow control valve between the cooling annulus and the mechanical pump determines the rate at which gas is drawn through the annulus. An impedance tube is used to draw in liquid He from the dewar belly, and thus supplies the cooling annulus with He. The PPMS is capable of temperatures ranging continuously from 350 K down to 1.8 K. Temperatures below 4.2 K (the boiling point of He at atmospheric pressure) are achieved by filling the cooling annulus with liquid He, and then drawing a vacuum over this region, accomplishing evaporative cooling. The superconducting magnet surrounding the sample space is capable of producing magnetic fields ranging continuously from to +7 tesla and has a .01% uniformity over a 5.5 cm region, which contains the sample. Samples reside on the surface of a puck during measurement. Electrical connections are made between the puck and the sample while the puck is outside the sample space. Upon insertion of the puck into the PPMS, pins in the cryostat mate to receptacles in the puck. This establishes an electrical link between the PPMS and the sample. The sample space is evacuated once the puck is locked into place. The PPMS controller controls all of the functions of the sample probe, from powering the heaters and magnet, to reading the thermometers and helium level. The controller is in

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57 constant communication with a computer via IEEE-488 general purpose interface bus (GPIB), utilizing Quantum Design software, or LabVIEW. Figure 4-10: Schematic of PPMS sample probe 23 4.4 Computer Interfacing and Data Analysis Most measurements in this work are automated. We use LabVIEW, from National Instruments, to communicate with the instruments used to make our measurements. LabVIEW is a high level graphical programming language capable of communication with a wide variety of laboratory instruments by a number of methods. We use the IEEE-488 GPIB protocol, as it is extremely user friendly. Each instrument has a programmable address. Identifying each instrument by its address, a computer is used as the controller in charge of the bus, delivering commands and receiving data from

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58 each instrument in parallel (on the same bus). Most instruments with a GPIB card allow the user to remotely complete the majority of operations accessible from the front panel. For example, we can actively control the temperature and magnetic field of the PPMS while simultaneously measuring and recording the capacitance of an MIM structure with the AH-2700A capacitance bridge. In this way, large datasets are produced with little or no supervision necessary. In fact, computer control allows us to perform our most sensitive measurements inside an electrically screened room without having to be present. This is advantageous, as our presence would contribute electrical noise to the apparatus. Most measurements described in this work occur inside an electrically screened room, and communication to the instruments is accomplished via fiber-optic GPIB extender cables. Once a dataset is created, it is analyzed in an analysis package called Origin, from Microcal. Among its many positive functions, Origin allows the user to perform calculations on an original dataset, produce plots, fit the data to user-specified fitting functions, and manipulate multiple data sets in an efficient way. Origin even contains a script language that we use to fully automate our data analysis. Multiple datasets can be loaded into memory (even from other computers), combined, processed, fit to arbitrary functions, and plotted in a multitude of ways automatically by executing an appropriate script. This is especially convenient for performing extensive analysis on large datasets. An operation that would take an hour to do manually can be accomplished in seconds with an Origin script. All graphs appearing in the next chapter have been produced via data analysis using Microcal Origin.

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CHAPTER 5 EXPERIMENTAL RESULTS AND DISCUSSION This chapter serves as a detailed description of all experimental data collected in this work, as well as an interpretation of the same. All of the theoretical and experimental techniques presented in the preceding chapters are applied in our actual experimental procedures and analyses, and in an effort to avoid redundancy, the reader is frequently referred back to these chapters. This chapter is broken up into four sections, each of which describes a separate aspect of the main project. The sections are presented in the order the experiments were performed. In the first section, we present the frequency-dependent interface capacitance of Al-AlO x -Al tunnel junctions, stressing the relevance of the contribution of interface states to the measured capacitance. Next, we state our results concerning the screening contribution to the capacitance of Si-SiO x -M (M=metal) for various metals, and present comparative screening length information for Fe, Ni, and Co. We then give the details of our first attempt to observe a ferromagnetic transition via capacitance measurements. Our model system is Al-AlO x -Gd thin-film structures, and we discuss the peculiar magnetocapacitive response observed in this interesting system. Finally, we present our recent findings concerning the magnetic field dependent screening response of Pd-AlOx-Al thin-film structures. This last section is the culmination of our experimental efforts and we will present possible applications of these results in the chapter to follow. 59

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60 5.1 Frequency-Dependent Interface Capacitance of Al-AlO x -Al Tunnel Junctions We have measured the ac impedance of Al-AlO x -Al tunnel junction capacitors over a wide range of frequencies (1 mHz to 100 kHz). 24 The insulating barrier is thin enough both to facilitate tunneling, and to ensure that the majority of the potential drop occurs across the Al-AlO x interfaces. The capacitance is modeled as a frequency independent resistor (tunneling) in parallel with a lossy capacitor. We observe no loss peaks down to frequencies as low as 1 mHz and ascribe the frequency-dependence to localized states at the interfaces (interface traps). When a single junction is annealed to different tunnel junction resistance, the complex impedance data collapse onto a single universal scaling function. As shown in section 3.3, the capacitance of thin MIM structures deviates from its geometrical value because of interface processes that give rise to additional voltage drops at each metal-insulator interface. 1, 4, 25 To account for this fact, we model our capacitor structure as two capacitors in series (cf. equation (3.13)). We can then write the measured inverse areal capacitance () as 1mC 001111mgiddCCC (5.1) This idea is confirmed by a linear dependence of on electrode separation (d) with a non-zero intercept (). Previous measurements on Al-AlO 1mC 1iC x -Al capacitor structures have verified this linear dependence, and have found C i = 1.62 F/cm 2 and d 0 = 50. 4 Throughout this section, the geometrical capacitance is larger than the interface capacitance (d ~ 20 , therefore d < d 0 ), thus our analysis is predicated on the assumption

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61 that our structures are in a regime in which the impedance is dominated by the interface capacitance and the tunneling resistance. As presented in section 3.3, the screening contribution to the interface capacitance can be summed up in the parameter d 0 , given by (cf. equation 3.14) , (5.2) 02d where is the dielectric constant of AlO x (1), and is the screening length in Al (1). Krupski 0 26 gives a more sophisticated model of screening, which also includes the rearrangement of charge at the surface of the dielectric. When applied to Al-AlO x -Al capacitor structures, d 0 is calculated to be 19 , a value more than a factor of 2 less than the experimentally determined value of 50 . 4 This discrepancy is most likely due to additional diffuse scattering associated with surface roughness and the presence of electron traps at the interfaces. It is the frequency dependence of these processes that comprise the core of this section. 5.1.1 Sample Fabrication Tunnel junctions are grown on glass substrates, which are cut and cleaned according to subsection 4.1.1. A schematic of the cross stripe tunnel junction geometry is given in figure 5.1. First, a shadow mask is employed to thermally evaporate a 500 thick, 1mm wide base stripe of Al, which is oriented parallel to the long side of the coupon (1” x .3”) centered with respect to the short side. During growth, the pressure in the diffusion pumped vacuum chamber is typically 5e-7 Torr. Immediately following their growth and without breaking vacuum, base electrodes are oxidized by the plasma oxidation technique at an oxygen pressure of 50 mTorr, a voltage of 500 V, and a current of 5 mA. Oxidation times vary from 10 s to 3 min so that a variety of tunnel-junction

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62 samples with resistance values ranging from 100 to 100 M can be obtained. This procedure produces a nominal AlO x thickness of ~20 . A mask with five equally spaced 1 mm wide counterelectrode stripes is used for counterelectrode deposition. Junction areas are almost identical (1 mm 2 ) and there is little variation of resistance or capacitance for each of the five junctions fabricated in a given run. When exposed to laboratory air, Al-AlO x -Al tunnel junctions age, giving rise to an increased tunnel junction resistance (R 0 ) and a reduced capacitance. This aging effect is rather convenient, as we are able to compare the electrical response in the same structure with continuously varying tunnel barrier parameters. Pressedindium .003” gold wireI+ I-V+VGlass substrate Al-AlOx Al Figure 5.1: Cross stripe geometry for tunnel junctions

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63 5.1.2 Impedance Measurements and Analysis Using the Solartron model 1260A impedance analyzer (subsection 4.3.2), four-terminal ac impedance measurements are performed on each of the five junctions on each sample over the frequency range 10 Hz to 100 kHz. Samples with very high dc tunneling resistance (>100 M) are examined down to frequencies as low as 1 mHz. Contact is made to the electrodes with clean, freshly cleaved indium (In) metal, which is pressed into Ohmic contact with the Al electrodes, as shown in figure 5-1. Thin (3 mil) gold wires attached to the indium dots serve as electrical links between the sample and the center pins of BNC (coaxial) bulkhead connectors that are mounted to an aluminum box in which each sample resides during measurement. The box shields the sample from any external electric fields, which could give rise to spurious effects such as electrical noise. The four-terminal measurement configuration, which is shown in figure 5-1, is as follows: The output and input of the impedance analyzer are attached to the I + and I terminals, respectively, while the differential voltage inputs are attached to V + and V . In other words, an ac current is sent from I + to I while the ac voltage is measured across V + and V . The quotient of the voltage and current yields the complex impedance of the tunnel junction. An independent measurement of R 0 is made using a voltage source and a current amplifier, thus providing the additional information necessary for the calculation of the complex capacitance. This procedure is described in section 3.4.

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64 10-21001021041061.01.52.02.53.0 C1 (F/cm2)Frequency (Hz) Figure 5.2: Real part of capacitance vs. frequency for Al-AlOx-Al tunnel junction Figure 5.2 shows the real part of the areal capacitance plotted versus frequency for a sample that is almost purely capacitive down to 1mHz (R 0 > 100 M). There is no sign of a loss peak as the capacitance versus frequency exhibits positive curvature down to the lowest frequency. The pronounced frequency-dependence, which does not exist in AlO x dielectrics, is attributed to interface traps, which give rise to dissipation and capacitance changes. 27 A wide range of charging energies, or equivalently, trap depths, must exist to account for the absence of a loss peak.

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65 Figure 5-3: Areal admittance versus frequency for aged Al-AlO x -Al tunnel junction. The inset shows the scaling collapse of these same data using normalized arbitrary units and R 0 as a scaling parameter. Figure 5-3 shows the frequency dependence of the magnitude of the areal admittance ( ()Y 1 / ()Z ) for the same junction aged to six successively higher tunnel-junction resistances. These data were taken over the course of ~2 weeks, and the resistances span the range R 0 = 1360 (top curve) to R 0 = 2.35 M (bottom curve). At sufficiently low frequency, the admittance is frequency independent (resistive regime), purely real (), and given by Y = 1/AR 01 0 . Above a corner frequency, given by for each curve, the electrical response is primarily capacitive ( 01/cRC 2 ), in which case 2 2 12()()()YCC (cf. equation (3.21)). It is tempting to

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66 characterize this electrical response as that of a simple RC circuit with frequency independent capacitance, which would yield an admittance that is linearly dependent on . However, closer inspection of these data and data taken on other junctions reveals that the slope is neither unity nor constant. The resistance of a tunnel junction is exponentially sensitive to the barrier thickness (d), while the capacitance of the same is only linearly dependent on d. For this reason, further oxidation during annealing (thereby increasing d) would affect R 0 much more than it would affect 21CCC 22 . This is in fact the case, as the low frequency admittance (Y) is modified much more than the high frequency admittance ( 10R YC ). In actuality, the situation is complicated by the fact that the Al-AlO x interfaces are rough, and while the capacitance is governed by the average electrode separation, tunneling conductance is determined mostly by the thinnest portions of the barrier, since tunneling is most probable in these locations. In spite of these complications, there is a surprising simplification when the data are re-plotted as shown in the inset of figure 5-3. In this plot using normalized logarithmic axes, each of the data sets has been scaled to the topmost curve (R 0 = 1360 ) by multiplying both the abscissa and the ordinate by the same constant, i.e., the R 0 for that curve normalized to 1360 . Minor adjustments (<5 %) to the values of R 0 for each curve have been made. This scaling collapse onto a single curve implies the functional form 0()FRY 0R , where is a scaling function with the shape shown in the inset of figure 5-3. The phase angle () is found to scale in a similar 0FR

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67 manner. This scaling behavior points to an unexpected (and incompletely understood) simplification in categorizing the frequency response of MIM tunnel junctions. Figure 5-4: Complex capacitance plot for aged Al-AlO x -Al tunnel junction. The inset schematically illustrates the response of a leaky capacitor (vertical dashed line) and a “universal” constant phase angle lossy capacitor (dashed line inclined at the angle with respect to the C 1 axis). An additional understanding of the physical processes occurring during tunnel-junction aging can be gained by presenting the complex capacitance data on a Cole-Cole plot in which C is plotted against . This dependence is shown in figure 5-4 for a subset of three junctions in which and C have been calculated from equations (3.23) and (3.24) using the indicated tunnel-junction resistances. The arrow indicates the direction of increasing frequency. We note that all of the curves have 2() 1()C1(C ) 2()

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68 positive curvature and there is no indication of a loss peak over the measured frequency range. Since C represents the frequency-dependent loss, at sufficiently low frequency, it must roll over to zero after first reaching a peak (i.e. ). Experimentally, this low frequency region is difficult to characterize because of the long measurement times required and the sensitivity of the calculation of to the small differences between 2() 0(0)ZR2()C ()cos()Z and R 0 (cf. equation (3.24)). 1() 5.1.3 Interpretation and Discussion The high-frequency limits of two common complex capacitive responses are shown in the inset of figure 5-4. The first of these, the vertical dashed line, represents an elementary leaky capacitor, which is modeled by a parallel combination of a frequency-independent capacitor and dc resistor. The similarity in the behavior of this elementary RC model to the tunnel-junction data occurs only at low frequency where the dependence of on C becomes increasingly steep. The second response, shown as the dashed line inclined at the angle with respect to the axis, represents the high frequency response of a lossy capacitor, which, in contrast to a leaky capacitor, does not pass a dc current. This constant phase angle (CPA) response has been seen in literally hundreds of materials and, since the work of Jonscher, 2()C 1()C1()C 28 has been united under the common name of “universal dielectric response.” The point of this discussion is that the power law dependence on frequency of the “universal” capacitance, usually attributed to glass like behavior, is not observed. With increasing , C 2 does not extrapolate with a linear dependence to zero at a readily identified point on the C 1 axis. Rather, C 2 approaches zero asymptotically with positive curvature and constantly diminishing phase

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69 angle. We refer to this rather unusual behavior as an asymptotic phase angle (APA) response and are not aware of its existence in other dielectric systems. We cannot, however, exclude the possibility of CPA behavior at frequencies higher than 100 kHz. It is reasonable to expect that the physical processes giving rise to our observed low-frequency behavior are associated with electronic traps at the tunnel-junction interfaces. The interfaces are not uniform and contain defects, such as incompletely oxidized aluminum, or impurities, which give rise to localized states with a distribution of trapping energies. The localized states hybridize with conduction electrons to form interface states, which affect the current-voltage characteristics, generate low-frequency noise, and change the capacitance. 27 The change in capacitance is proportional to the length of time a tunneling electron spends trapped at a defect site. Clearly, the presence of such states will introduce diffuse scattering and will change the details of the potential versus position discussed in chapter 3. If we assume that the aging or annealing process described above removes a subset of these traps, then many of the trends seen in our data can be readily explained. The removal certainly causes an increase in R 0 , since for each trap removed, a parallel process for elastic tunneling via a trap has been eliminated. Our observation that the dominant effect of annealing is on C 2 rather than C 1 confirms this interpretation and leads us to conclude that a removal of traps rather than a thickening of the barrier is the primary consequence of aging. Interesting questions remain. For example, our results are, strictly speaking, independent of junction area but might be expected to be substantially different if the area is small enough to include only a few defect sites. Indeed, experiments on small-area Al-AlO x -Al tunnel junctions, 29, 30 which exhibit Coulomb effects and have lateral dimensions

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70 in the range 80-150 nm, have interface capacitance in the range 3-6, substantially larger than the 1.6 of larger-area (4 e-4 cm 2F/cm 2F/cm2F/cm 2 ) junctions. 4 The presumed absence of interface traps in these small junctions and the corresponding smaller drop in voltage across the interface results in a smaller d 0 and a larger C i . An even larger interface capacitance of ~35 has been reported for alkanethiol self-assembled monolayers used as a dielectric spacing between liquid-mercury electrodes. 31 Since mercury would be expected to have a surface that is smooth, compliant and free of defects, this result leads us to suspect that roughness may play a critical role in determining the ac response of MIM tunnel junctions. 5.2 Capacitive Response of Si-SiO x -Metal Structures Motivated by Zhang’s theoretical predictions 9 concerning the spin-dependent screening lengths in ferromagnetic Fe, Ni and Co, we have performed capacitance measurements on Si-SiO x -M (M = Fe, Ni and Co) structures of varying insulator thickness to obtain comparative screening length information. Plots of C -1 vs d reveal the relevant screening length information via the negative of the x – intercept (d 0 ), as before. Base electrodes in this section are composed of n-type Si (phosphorous doped), and the thermally grown oxide of Si provides a smooth (~5 rms roughness) substrate onto which the ferromagnetic counterelectrode is sputtered. Our results are not in agreement with Zhang’s predictions, 9 as the order of increasing (measured) d 0 is: Co, Ni, Fe, while the theoretically predicted increasing order is Ni, Fe, Co. We cannot rule out the possibility of interfacial states, which differ from one counterelectrode to another, comprising the root of this discrepancy.

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71 In the model of capacitance, which includes screening effects (but not roughness, interface traps, defects, etc.), presented in chapter 3, we calculate the inverse areal capacitance in terms of the dielectric thickness and the screening lengths in the electrodes, and the result is repeated in equation (5.1). The same set of arguments holds in the present geometry (Si-SiO x -M), i.e. there is a series contribution to the capacitance due to electric field penetration into the metallic and semiconducting electrodes. For the semiconducting electrode, a different model of screening should be employed if the carrier concentration is very low, but this will only modify the effective length over which the electric field penetrates. In the present case, we will assume the Si-SiO x interfaces are of identical quality independent of the counterelectrode material, thus any observed differences in d 0 are due solely to the SiO x -M interfaces (i.e. the screening lengths in the ferromagnetic metals). 5.2.1 Sample Fabrication Fabrication begins with seven n-Si wafers (~1e17 phosphorous dopants/cm 3 , .06-.14 cm), each having a different thickness of thermally grown SiO x ranging from 34 to 391 . Wafers are cut into square (1 cm 2 ) substrates and cleaned according to the procedures detailed in chapter 4. Electrical contact is then made to the backside of each substrate in the following way. One substrate of each oxide thickness is loaded into a 9-substrate puck with the rough (back) side facing outward. To avoid scratching the surface of the SiO x , the smooth side of the substrates (on which the counterelectrode will be grown) is suspended above the puck by a shoulder that runs around the perimeter of the substrate. The puck is then loaded into a diffusion pumped vacuum system and all 7 substrates are ion-milled to remove the SiO x from the backside surface (the front side is not exposed to the ion beam, and is therefore unaffected by this procedure). Figure 5-5

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72 shows a diagram of the geometry during ion-milling. An ion gun similar to the one used in RIBS (subsection 4.1.3) accomplishes milling. Without breaking vacuum, a 500 layer of Al is thermally evaporated onto the freshly milled surface, and a 200 layer of Au is grown on top of the Al. Al provides Ohmic contact to the Si (no Schottky barrier) and the Au layer prevents any oxidation of the contact. SubstratePuck Ion millBackside Figure 5-5: Diagram showing geometry during ion-milling procedure Once electrodes are grown on the backsides, each substrate is flipped over in the puck, thereby exposing the front sides. A shadow mask with .1” diameter circular holes is attached to the puck on top of the substrates. The puck is then loaded into a cryopumped vacuum chamber, which is evacuated to a base pressure of ~3e-9 Torr. Deposition of the metal counterelectrodes (Fe, Ni or Co) through the shadow mask is

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73 accomplished via rf-magnetron sputtering. All 7 counterelectrode depositions occur simultaneously so that consistent film quality is maintained. A schematic of the cross section of a completed sample is given in figure 5-6. n-Si Fe, Ni or Co SiOx Al Au Figure 5-6: Cross section of Si-SiOx-M capacitor structure Completed samples are then attached to glass coupons with electrically conducting silver (Ag) paint. A small drop of paint is placed in the center of a coupon and a sample (backside down) is set on top of the drop. The sample is then pressed lightly with tweezers so that a small amount of Ag paint is forced out from between the sample and the glass on both sides of the sample. After the paint is allowed to dry, freshly cleaved indium (In) metal is pressed into contact with the glass on each side of the sample, and gently rolled toward the silver paint until electrical contact is made. In this way, the backside of each sample is contacted electrically. The top electrode is electrically contacted in the following way. Thin (.001” diameter) gold wire is cut into 1” lengths. With tweezers, one end of each wire is rolled into a tiny loop (~.01” diameter), dipped into wet Ag paint, forming a small drop of paint

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74 on the looped end of the wire, and set on top of the circular ferromagnetic electrode on top of the sample. Two electrical leads are attached to each counterelectrode in this way. An In anchor is pressed into contact with the glass on each side of the sample. After the Ag paint has dried, the non-looped ends of the gold wires are tinned with fresh In using a soldering iron and pressed into electrical contact with the In anchors. The anchors serve as bulkhead connections to the measurement apparatus and greatly reduce the strain of each electrical connection to the counterelectrode. A cross section of an electrically contacted sample is given in figure 5.7. Glass couponGold wire (.001”)Ag paint In I+I-V-V+ Figure 5-7: Diagram of electrical connections for Si-SiO x -M capacitor structure 5.2.2 Measurements and Analysis Electrical impedance measurements (four-terminal) are performed on each sample with the Solartron model 1260A, and the real part of the capacitance is calculated as before. The electrical lead configuration is shown in figure 5-7: the current enters the sample at the ferromagnetic electrode and is removed at the electrical connection to the

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75 backside while voltage is measured differentially at the same locations with separate leads. Samples are fully enclosed in an electrically shielded box and connections are made to the box using BNC coaxial cables, as before. All ac measurements in this section are performed at voltage amplitude 50 mV. 050100150200250300350400024681012 d0=12.4 4.4 =4.16 0.07Ci=2.97 1.1 F/cm2A/C1 (cm2/F)d () Figure 5-8: Inverse capacitance versus dielectric thickness for Si-SiO x -Ni Shown in figure 5-8 is a plot of (the real part of) the inverse areal capacitance versus dielectric thickness for 7 different samples of Si-SiO x (d)-Ni measured at 10 Hz. This data represents one Ni deposition, as all counterelectrodes of the 7 different samples were grown in the same run. The linear dependence and non-zero intercept substantiate our claim that this system can be modeled as the series sum of two capacitors (cf. equation (5.1)). Performing a linear regression on this data, using equation (5.1), yields the dielectric constant of SiO x (= 4.16), the interface capacitance (C i = 2.97), 2F/cm

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76 and the effective additional dielectric thickness (d 0 = 12.4 ). The data presented in this figure are typical and we suppress some 30 datasets that are virtually indistinguishable from figure 5-8, displaying only the results from the linear regressions performed on each in the paragraphs to follow. In doped semiconductors, a moderate electric field can deplete all of the charge from the conduction band at the surface of the semiconductor. In this case, the electric field falls off linearly in what is referred to as the depletion region (region of constant induced charge density). Sufficiently far inside the semiconductor, where the electric field has been screened for the main part, there exists enough mobile charge for exponential electric field decay. The application of a dc voltage bias across a semiconductor-insulator-metal structure effectively broadens and narrows this depletion layer, depending on the polarity of the bias. For electron-doped material (n-type), a positive bias on the metallic side induces additional (negatively charged) carriers onto the semiconductor, thereby making the depletion region thinner. Conversely, a negative bias on the metallic side has the opposite effect, depleting charge and broadening the depletion region. The capacitance is sensitive to the thickness of the depletion region as the further the electric field penetrates, the larger the potential drop across the semiconducting electrode, and hence the smaller the capacitance of the structure. In an effort to vary the depletion region thickness, we have measured the capacitance of our Si-SiO x -M structures at 10 Hz with an applied dc bias voltage spanning .5 V to +0.5 V for M = Fe, Ni and Co. The results of these measurements are summarized in figure 5-9.

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77 -0.6-0.4-0.20.00.20.40.6051015202530 Fe Ni Cod0 ()Vbias (V) Figure 5-9: Effective additional dielectric thickness (d 0 ) for Si-SiO x -M structures The above plot is a summary of a large amount of experimental data. Each data point represents the results of a linear regression of a plot similar to figure 5-8 at the applied bias and of the counterelectrode material indicated in the figure. The additional effective thickness d 0 can be separated into the sum of two terms: one associated with electric field penetration into the metal, and one associated with electric field penetration into the semiconductor. The term for the metal can be written as (5.3) 0metalmetald and the semiconducting term should be independent of the composition of the counterelectrode. Therefore, the d 0 obtained for each metal at a particular value of dc

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78 bias can be compared with the same quantity for the other metals, and in this way, comparative screening length information is acquired. 5.2.3 Results and Discussion As can be readily seen from figure 5-9, we observe d 0 for Co counterelectrodes to be the smallest of the three ferromagnetic metals at almost every value of bias. Similarly, the d 0 associated with Fe is the longest of the three with Ni in the middle. This is in contrast to the predictions of Zhang. 9 He calculates the screening length for Fe, Ni and Co using a Thomas-Fermi model similar to the one presented in section 2.6, and using band parameters from the literature 32, 33 determines that Ni should have the shortest screening length, followed by Fe, and Co should have the longest. We are still unsure as to the exact origin of this discrepancy, but perhaps a closer inspection of figure 5-9 will reveal some pertinent details. We would expect d to be independent of dc bias, as this represents the distance over which the electric field penetrates the surface of the metal multiplied by the dielectric constant of the insulator (cf. equation (5.3)). If this is the only parameter that changes when the counterelectrode is varied, the shapes of the three curves in figure 5-9 should be the same. The curves should be offset from one another in the y-direction only. We see that this is not quite the case. The curves for Ni and Co are qualitatively similar, in that they are roughly monotonically decreasing functions of bias, as expected. However, the difference in the two curves is not constant. The Fe curve even has qualitatively different behavior, as it is peaked near zero bias. These considerations lead us to believe that there are actual differences in the quality of the SiO 0metal x -M interfaces giving rise to dispersion and changed capacitance. These spurious effects obscure the

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79 determination of the physics of screening in these systems. To accurately probe the spin-dependence of the screening response of ferromagnetic metals, we need a knob that only perturbs the system a small amount in a clearly defined way, unlike the knob that varies counterelectrode material. The appropriate knob in this situation is magnetic field. 5.3 Magnetocapacitance of Al-AlO x -Gd Capacitor Structures We have measured the magnetic field dependence of the capacitance (magnetocapacitance) of Al-AlO x -Gd thin-film structures at temperatures spanning the range 10 K to 300 K. Capacitance changes as large as 3 % have been observed in applied magnetic fields of 7 T for structures with AlO x thickness of 50 . No changes in the capacitive response of these structures occur at the Curie temperature of the Gd films, which has been measured by SQUID magnetometry to be T C ~ 220 K. The observed magnetocapacitance is negative above a crossover temperature (T x ) of approximately 60 K, but changes sign and becomes positive below T x . This sign change is quite unexpected as there are no other observable features (in magnetization, resistance, etc.) at T x . Though a portion of the magnetocapacitance is ascribed to the sensitivity of the screening length in Gd to magnetic fields, we are unsure as to the origin of the sign change. We believe there is either a structural rearrangement of the surface (surface transition) at T x , or a sharp, magnetic field dependent loss mechanism, which, at T x , is resonant with the driving frequency (1 kHz). With these observations, we demonstrate the sensitivity of magnetocapacitance measurements to the interfacial (surface) properties of MIM structures.

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80 5.3.1 Sample Fabrication Si squares (1 cm 2 ) are employed as substrates onto which Al-AlO x -Gd capacitor structures are grown. Substrates are first cut and cleaned, exactly as before (see chapter 4). Then, in a diffusion pumped vacuum system (base pressure of 3 e-7 Torr), 1000 of Al is thermally evaporated, uniformly coating an entire substrate. The coated sample is then loaded into a cryopumped vacuum system (base pressure of 1 e-6 Torr) and a uniform, 50 layer of AlO x is grown on the surface of the freshly evaporated Al. Reactive ion beam sputtering (RIBS) accomplishes the AlO x growth with an oxygen partial pressure of 6 e-5 Torr and a total pressure (Ar gas comprises the balance) of 1 e-4 Torr during sputtering. We find that for our 3 cm ion gun, a beam current of 20 mA maintained at 500 V produces AlO x films with maximal breakdown strength. Under these deposition conditions, AlO x is grown at a rate of approximately 1 /min. The corners of each sample are masked during the AlO x deposition step so that Ohmic contact to the Al layer can be made after the counterelectrode is grown. Immediately following the AlO x growth, the sample is loaded into another cryopumped vacuum chamber (base pressure of 3 e-9 Torr) in which Gd (99.9% purity) is rf-magnetron sputtered through a shadow mask (with .1” diameter circular holes) onto the AlO x layer. Ultra-pure (99.999%) Ar is used as the sputtering gas in this step, and the pressure in the chamber is maintained at 1 e-4 Torr during the deposition. This final step completes the MIM structure, and a diagram of an Al-AlO x -Gd thin-film structure is shown in figure 5-10.

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81 Si Gd AlOx Al Figure 5-10: Diagram of Al-AlO x -Gd capacitor structure Electrical connections are made to the Al-AlO x -Gd structures in much the same way as in the Si-SiO x -M work, except it is not necessary to contact the backside of the substrates. A sample is attached to a glass coupon with rubber cement, and freshly cleaved In is pressed into Ohmic contact with a corner (which is not covered with AlOx) of the substrate. Another piece of In is pressed into contact with the glass, and serves as the bulkhead connector to the counterelectrode. One end of a thin (.001” diameter) gold wire is attached to the Gd counterelectrode with Ag paint, as in section 5.2, and the other end is tinned with In, and pressed into Ohmic contact with the In bulkhead. A diagram of a completed, electrically contacted Al-AlO x -Gd capacitor structure is shown in figure 5-11.

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82 Glass couponPressed indium Gold wire+_ Figure 5-11: Diagram of electrically contacted Al-AlOx-Gd capacitor structure 5.3.2 Magnetocapacitance Measurements A General Radio model 1615-A capacitance bridge is employed to measure the capacitance of the Al-AlO x -Gd structures. A PAR 124A lock-in amplifier serves two purposes. It generates the ac signal (1 kHz), which drives both the capacitance bridge circuitry and the unknown (Al-AlO x -Gd) capacitor, and it detects the off-balance voltage, or serves as null detector. The theory behind the operation of a capacitance bridge is presented in section 4.3. The terminal marked + (figure 5-11) is connected to the high side of the bridge circuitry (cf. figure 4-8, unknown impedance connections) and the terminal marked – is connected to the low side. In this way (it is our convention), an ac current flows from the Gd counterelectrode to the Al base electrode, which is maintained very close to ground.

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83 The sample is placed in a special capacitance probe, which is inserted into the PPMS cryostat during the capacitance measurements. The capacitance probe consists of a hollow, stainless steel tube, which houses coaxial electrical leads, an electrically isolated can, which fully encloses the sample, and isolated ground BNC bulkhead connectors (outside the cryostat, top of probe), which are attached to the capacitance bridge with BNC cables. In this way, true 3-terminal measurements (see figure 4-9) are made of the capacitance of Al-AlO x -Gd structures in the PPMS cryostat, as the BNC bulkhead outer shields serve as the only electrical connections to the isolated can, and these are connected directly to the capacitance bridge. Acquiring a single dataset involves a magnetic field sweep from 0 to 7 T and back to 0 at fixed temperature (T) while simultaneously measuring capacitance. The procedure is as follows. First, the temperature of the cryostat is set to the desired value. It is necessary to then wait 15 minutes for temperature stabilization as the temperature of the sample lags in time behind that of the cryostat. This is especially important for magnetocapacitance measurements, as the capacitance of our structures is exceedingly sensitive to temperature (cf. figure 5-13 below). Also, since the sample is electrically isolated from the cryostat, it is necessarily somewhat thermally isolated, as well. This is because the majority of heat is removed from and added to the sample via a direct thermal link (as opposed to radiation or exchange gas). After waiting for temperature stability, the capacitance bridge is balanced, and the capacitance and loss (at H = 0 T) are recorded by hand. Balancing involves the minimization of both the in-phase and out of phase components of the detector signal by adjusting the variable capacitor and variable resistor, the parallel sum of which comprise the standard (cf. figure 4-8). The analog

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84 output of the lock-in is connected to a voltmeter, which is read by the computer via the GPIB. The computer is also used to control the PPMS, and in this way temperature and magnetic field are swept at the touch of a button. LabVIEW ties it all together into a user-friendly interface. A magnetic field sweep is then initiated, and the output of the voltmeter is recorded as a function of magnetic field. All measurements are taken inside an electrically isolated and screened room, and communication between the computer, which is outside the screened room, and the instruments occurs via fiber-optic cables. Once the magnetic field reaches 7 T, the bridge is rebalanced, and the new values of capacitance and loss are recorded. We assume that the off-balance signal of the lock-in (read by the voltmeter) is linear in the change in capacitance. If we define the voltage of the lock-in at 7 T as V 7T , we can calculate the capacitance at any magnetic field as 0707()HHTTVCCCCV , (5.4) where C 0 and C 7T are the capacitances at H = 0 T and H = 7 T, respectively, and V H is the voltage at the specified magnetic field. The magnetic field is then swept back to zero while recording the output of the voltmeter, and the bridge is rebalanced and capacitance and loss are again recorded. The capacitance and loss before and after the sweep are found to be identical to within 1 part in 10 5 in the samples used in this work. For the downward magnetic field sweep, the capacitance can be calculated in a similar fashion as above, yielding 7070()HHTTVCCCCV , (5.5)

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85 where V 0 is the measured voltage when H reaches zero. In the unlikely event that the upward and downward sweeping magnetocapacitance curves do not overlap, the two are averaged. 02468-3.0-2.0-1.00.01.02.0 10 K30 K50 K70 K90 K150 K300 K C1/C1 (%)Magnetic Field H (T) Figure 5-12: Change in capacitance versus magnetic field for Al-AlO x (50 )-Gd Shown in figure 5-12 is the normalized change in capacitance 00HCCCCC versus magnetic field (magnetocapacitance) for an Al-AlOx(50 )-Gd structure at the temperatures indicated. There is pronounced magnetic field dependence even at room temperature (300 K). The magnetocapacitance is negative above a crossover temperature (T x ~ 60K), and positive below T x . Far from T x on both sides of the crossover, the magnetocapacitance is roughly quadratic. In the language of screening, positive

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86 (negative) magnetocapacitance corresponds to a decreasing (increasing) screening length with applied magnetic field. The effect is quite large, especially in the crossover regime, where it is maximal (~3%) at 70 K. The capacitance bridge used in this measurement is sensitive to approximately 1 part in 10 5 , therefore the magnetocapacitance in these structures is extremely easy to detect. 050100150200250300-3-2-1012 C1/C1 (%)Temperature (K)0501001502002503001.221.241.261.281.301.321.341.361.381.401.42 H = 0 T H = 7 TC1 (F/cm2)Temperature (K) Figure 5-13: Capacitance versus temperature at H = 0 T and H = 7 T for Al-AlO x (50 )-Gd. The inset shows the normalized change in capacitance (at H = 7 T) versus temperature for the same sample. Another way to visualize the magnetocapacitance of these structures is to plot the capacitance versus temperature at H = 0 T (open circles) and H = 7 T (solid squares). This plot is shown in figure 5-13 with the normalized change in capacitance

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87 700TCCCCC versus temperature in the inset. We observe that the sign change in the magnetocapacitance at T x is extremely sharp. The four data points in the center of the crossover region (open circles in the main plot, solid squares in the inset, ~60 K) span only 2 degrees. It is clear from the absolute scale of the capacitance in the main plot that this sample is in the interface regime, since the capacitance is very near the interface value for Al-AlO x -Al structures, for which C i = 1.62 . The interface capacitance for Al-AlO 2/Fcm x -Gd structures is expected to be similar to this value, as Gd is metallic and is expected to have a screening length similar to that of Al. 1502002503000.000.050.10 TC MH = 100 OeMagnetization (B / ion)Temperature (K)-2.0-1.5-1.0-0.50.0 dM/dT (10-6B/ ion / K) dM/dT Figure 5-14: Magnetization and dM/dT versus temperature for 1000 Gd on Si

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88 The sign change in the magnetocapacitance at T x is quite unexpected. To better understand its origin, we have measured the magnetization versus temperature in a SQUID magnetometer cryostat (Magnetic Property Measurement System, or MPMS) from Quantum Design. There are no detectable features at T x , but we do find a significantly reduced value of the Curie temperature for our Gd films. Shown in figure 5-14 are plots of both the magnetization (M) and the temperature derivative of magnetization (dM/dT) versus temperature for 1000 of Gd on a Si substrate. The applied field is H = 100 Oe, and the field is aligned with the plane of the Gd film. The inflection point in M versus T (extremum in dM/dT versus T) identifies the Curie temperature as T. The bulk Curie temperature for Gd is significantly higher (), and we attribute the difference to the granular, disordered nature of our films, which reduces T 220KC 293KCT C . 5.3.3 Interpretation and Discussion We have thus demonstrated the sensitivity of magnetocapacitance measurements in the interface regime (d ~ 50 ) to the magnetic properties of the interfaces of MIM structures. We attribute all of the magnetocapacitive effects to processes occurring at the AlO x -Gd interface. Justification for this position rests in the fact that we observe no detectable (down to 1 part in 10 5 ) magnetocapacitive effects for symmetric (Al-AlO x -Al) structures using the same measurement technique. We observe no changes in the capacitive response of our Al-AlO x -Gd structures as the temperature is swept through the measured Curie temperature of Gd (T). We originally chose Gd as our model counterelectrode material because of the proximity of its T 220KC C to room temperature. Spurred by Zhang’s predictions concerning the spin

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89 dependence of the screening response of ferromagnets, 9 we expected to see measurable capacitance changes as we swept the temperature of our structures through T C . As exchange interactions become important, and the screening length is enhanced or reduced, the voltage drop into the Gd electrode should be modified. We believe there are a number of reasons we do not observe this effect. Firstly, since Gd is a local moment system, Zhang’s calculations do not readily apply. He calculates the modification of the Thomas-Fermi screening length due to exchange interactions between carriers in itinerant ferromagnets. Since the carriers in Gd are not responsible for the ferromagnetism directly, the band structure may be only mildly affected by the presence of ferromagnetism. 34 Since capacitance is related via screening to band structure (cf. chapters 2 and 3), it may not be sensitive to magnetic phase transitions in local-moment ferromagnets, like Gd. Another possible explanation for our lack of sensitivity to the magnetic phase transition in this system is that the temperature-dependence of the capacitance is strong, as shown in figure 5-13. Therefore, unless the transition is exceedingly sharp, the temperature-dependent background would wash out any capacitance change. We do expect our transition to be rather broad as our films are disordered and have varying grain sizes, as evidenced by the reduced Curie temperature. 35 There is likely a distribution of position-dependent Curie temperatures 36 in our films due to finite size effects and disorder. Though we are insensitive to the bulk ferromagnetic transition in Gd, we are extremely sensitive to magnetic fields and surface effects, as indicated by the strong magnetocapacitance and sharp temperature-dependence of the same. Though we are unsure of the origin of the crossover from positive to negative magnetocapacitance with

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90 increasing temperature at T x , we are confident that it is related to the interface between Gd and AlO x . The sensitivity of capacitance to magnetic fields in this system persists beyond the bulk Curie temperature of Gd, which suggests that this technique could be used to measure the spin-dependence of the screening response of paramagnets. 5.4 Magnetic Field Dependent Screening in Pd-AlO x -Al Structures The magnetic field dependence of the capacitance of Pd-AlOx-Al thin-film structures has been measured. The observed quadratic dependence of capacitance on magnetic field is consistent with the theoretical model presented in section 2.3, which includes the effect of a spin-dependent electrochemical potential on electron screening in the paramagnetic Pd. This spin-dependent electrochemical potential is related to the Zeeman splitting of the narrow d-bands in Pd. The quantitative details depend on the electronic band structure at the surface of Pd. Motivated by Zhang’s theoretical work 9 involving electron screening in ferromagnets, we have explored the magnetic field dependence of the screening length of paramagnetic Pd experimentally. Electron screening in ferromagnets depends on both coulomb and exchange interactions. This fact is represented theoretically by a spin-dependent potential decaying exponentially into the surface of a ferromagnet in the presence of an applied electric field. The spin-dependence originates from the exchange splitting of spin-up and spin-down bands. In this section, we present the magnetic field dependence of the length () over which an applied electric field penetrates the surface of a paramagnet where the spin splitting is not built in, but rather arises from an external magnetic field. By measuring the capacitance while continuously varying the magnetic field, we have measured the spin-dependence of the screening potential in Pd. We wish

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91 to point out that ours is a static probe of magnetic field-induced spin-dependent potentials involving a voltage and no current. This is in contrast to previous work 37 involving current-driven spin-accumulation. When a voltage is applied between the electrodes of a thin metal-insulator-metal (MIM) capacitor structure, a significant portion of the potential drop occurs across the metal-insulator interfaces 3 (cf. figure 5-15, inset), as indicated in chapter 3. The applied voltage (V), the dielectric constant (), the dielectric thickness (d), and the screening length () determine the magnitude of the voltage absorbed by each electrode. The measured capacitance of a thin MIM structure is indicative of bulk dielectric as well as interfacial properties 24, 26 including . A magnetic field dependent manifests itself as a magnetic field dependent capacitance. We have chosen Pd as our model system because of its large Pauli paramagnetic susceptibility and have measured the magnetic field dependent capacitance of Pd-AlO x -Al thin film structures. We have determined that the screening length of Pd increases quadratically with applied magnetic field, consistent with equation (2.30). 5.4.1 Sample Fabrication The geometry of our Pd-AlO x -Al structures is identical to the geometry of our Al-AlO x -Gd structures from the previous section (cf. figure 5-10), except Pd comprises the base electrode while Gd comprises the counterelectrode. Our structures are grown and characterized under carefully controlled conditions. The first deposition step involves the dc-magnetron sputtering of 1000 of Pd onto the entire surface of a square silicon substrate (1 cm 2 ). A calibrated thickness of AlO x is then grown upon the entire Pd surface via reactive ion beam sputtering (RIBS) of Al in an oxygen ambient at a carefully controlled pressure, as before. This technique has been shown 4 to produce dense, high

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92 quality, amorphous AlO x . The final deposition step utilizes a shadow mask with 0.1” diameter circular holes placed in close proximity to the sample through which Al is thermally grown. Electrical connections are made as in the previous section, using Ag paint, 0.001” diameter gold wires, and pressed indium contacts. 5.4.2 Magnetocapacitance Measurements and Analyses Each sample is inserted into a Quantum Design QD6000 cryostat in a custom sample probe with coaxial electrical leads attached to the sample. As mentioned in the previous section, the bottom of the sample probe consists of an electrically isolated and enclosed conducting shield that houses the sample. Three terminal capacitance measurements (see figure 4-9) are made using an AH-2700 capacitance bridge, which is self-contained (does not require the use of a separate lock-in amplifier), and GPIB addressable. All measurements are fully automated, and performed in an electrically screened room. Capacitance measurements have been performed at 1kHz at temperatures and magnetic fields ranging from 300K to 10K and -7T to 7T respectively.

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93 d Vd0/2-50050100150200250300350012345 d0 A/C (cm2/F)d () Figure 5-15: Inverse capacitance versus dielectric thickness for Pd-AlO x -Al. The inset is a schematic illustration of electrostatic potential versus position for a thin MIM capacitor structure (cf. section 3.3). Shown in Fig. 5-15 is a plot of the inverse areal capacitance versus dielectric thickness at 10K for four Pd-AlO x -Al structures with dielectric thickness ranging from 50 to 300. The linear relationship and nonzero intercept imply that the geometrical capacitance (C g ) is in series with a thickness independent interface capacitance (C i ) determined largely by the screening lengths in the two electrodes. It should be noted that other contributions 24 to C i , such as interface states and surface roughness, do exist. C i corresponds experimentally to the reciprocal of the y intercept (open circle) and d 0 is the inferred thickness of a capacitor with a capacitance of C i when assuming a geometrical parallel plate model. As d approaches 0 (and C g diverges) the measured capacitance (C m )

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94 approaches C i . Our simple model for the capacitance of our structures is shown schematically in the inset of Fig. 1 where the electrostatic potential, which decays exponentially into each electrode, is plotted versus position. For such a structure, C m is given by 12(00mig00dAAAdwith dCCC ) (5.6) The area is given by A, and are the screening lengths in the metallic electrodes, and is the permittivity of free space. This model accurately accounts for our observed thickness dependence and verifies our observation that capacitance measurements are sensitive to the screening lengths in the electrodes for thin capacitors (d ~ d 1 2 0 0 ). 050100150200250-1.5-1.4-1.3 Slope Temperature (K)01020304050-0.20-0.15-0.10-0.050.00 Pd AlOx(75) Al 250 K 100 K 25 KC/C (%)H2 (T2) Figure 5-16: Magnetocapacitance of Pd-AlOx-Al structure at temperatures indicated in the legend. The inset shows the slopes of these curves as a function of temperature.

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95 We observe that the capacitance of our structures decreases quadratically with magnetic field (indicating a quadratic increase in ) as shown in figure 5-16. In this plot, the normalized change in capacitance versus H 2 is linear with a negative slope. The weak temperature dependence of the slope is shown in the inset. Strain effects can be ignored since the linear magnetostriction in Pd films is zero 14 to within one part in 10 6 . In observing negative magnetocapacitance, we are explicitly measuring the H dependence of the screening length of Pd since is the only H dependent quantity. The H dependence comes from the spin splitting of the conduction band of Pd with H. We apply the model of magnetic field dependent electron screening derived in chapter 2, and accounting for exchange interactions via the Stoner enhancement factor (D), we find that the screening length is modified from its Thomas-Fermi value as 21222111BTFDH , (5.7) where we have recalled the following definitions from chapter 2: 2()()()()fffN"N'NN f , (5.8) and 2201()fTFeN . (5.9) The capacitance of a structure containing one electrode with a magnetic field dependent screening length as given by equation (5.7) (to quadratic order in H) is 20()(0)(0)(0)4TFBCHCCDHCA , (5.10)

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96 where we have used the results of chapter 3 concerning the screening contribution to capacitance for MIM structures, in conjunction with equation (5.7). Consolidating all of the H dependence into the Pd electrode is justified by our observation that magnetocapacitive effects in Al-AlOx-Al structures are at least an order of magnitude smaller than the same in Pd-AlOx-Al structures. Using the inferred of Pd (~2.5) from figure 5-15 and the slope of the CC vs H 2 curve, we estimate to range from -100 to -1000 eV -2 (sample dependent). Andersen 12 performs a bulk calculation of for Pd using a rigid band approximation. He reports a value of 12 eV -2 , but it should be noted that the screening length of a metal should depend on its surface band structure, which may differ substantially from the bulk band structure. The chemical potential () in Pd lies so close to an inflection point in the density of states versus energy 12 that any perturbation resulting in a small change in can affect the magnitude and sign of . We believe the spin dependent electrochemical potential in the Pd electrode near the Pd-AlO x interface is greater than the same quantity in bulk Pd. This assumption accounts for the observation that < 0 as determined by magnetocapacitance measurements. Increasing is equivalent to doping the Pd with additional d-electrons (e.g. alloying with Ag) in which case is predicted 12 to be negative. The sign change in arises from a competition between the first and second derivatives of the state densities at the Fermi level as indicated in the definition of . We have observed positive magnetocapacitance in Pd 1-x Fe x alloys and are currently exploring this intriguing result.

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97 050100150200 C(T)/C(10K)T (K) 300 200 100 0501001502002503000.450.460.470.480.49 Pd-AlOx(100)-Al Capacitance (F/cm2)Temperature (K) Figure 5-17: Capacitance versus temperature for Pd-AlO x -Al. The inset shows the capacitance normalized to 10 K for structures with dielectric thicknesses indicated in the inset legend. The capacitance of our structures is temperature dependent, and decreases linearly (at high temperatures) with decreasing temperature, as shown in figure 5-17. The inset shows a normalized version of capacitance versus temperature for three AlOx thicknesses and indicates a trend toward stronger temperature dependence for thicker oxides. The first correction to the Thomas-Fermi screening length due to temperature is quadratic (cf. equation (2.36)); therefore the operative mechanism behind the temperature dependence is not electronic in nature except, perhaps, at the lowest temperatures. We attribute the temperature dependence in the linear regime to a varying dielectric constant, which accounts for our observation of stronger temperature dependence for thicker oxides: as

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98 the oxide thickness is increased, the capacitance is dominated by bulk dielectric properties. Other effects may contribute, such as the freezing out of electron traps at the interfaces and reduced dispersion as the temperature is lowered. The magnetocapacitance is becoming larger in magnitude as the capacitance decreases (figure 5-16 inset, y-axis contains only negative values). This is curious as the magnetocapacitance should scale with the H = 0 capacitance (5.10). Though we do not fully understand this dependence, it may have a similar origin as that of the pronounced temperature dependence of the magnetic susceptibility, 18 which exhibits a maximum at ~80K and depends on the same density of states factor,, as indicated in equation (2.46). We observe a similar maximum in the slope of the CC vs H 2 curve (figure 5-16 inset). 5.4.3 Conclusions In conclusion, we have measured the magnetic field dependence of the screening length of paramagnetic Pd via magnetocapacitance. We have proposed a model that captures the essence of the relevant physics of this effect. We have also shown that magnetocapacitance measurements reveal surface band structure, which is distinct from bulk band structure. Since magnetocapacitance is sensitive to spin-dependent electrochemical potentials, it may be a technique capable of measuring non-equilibrium spin polarization in spin-injection devices. Novel, low carrier density materials, e.g. dilute magnetic semiconductors, may show similar magnetocapacitive effects larger in magnitude due to longer screening lengths.

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CHAPTER 6 SUMMARY AND FUTURE DIRECTIONS Capacitance measurements have been applied to a variety of systems under a variety of conditions, and many conclusions have been drawn. Though this chapter marks the end of this dissertation, the collective body of data and analyses contained herein represent the beginning of a rich field of experimental condensed matter physics. After a summary of the important results and implications of this project is given, we present logical applications for some of the techniques that we have explored, and in this way provide a proposal of the future directions for this work. 6.1 Summary In summary, we have characterized the electrical properties of metal-insulator interfaces using capacitance and magnetocapacitance techniques. Specifically, we have performed detailed investigations on four distinct systems, namely Al-AlO x (~20 )-Al tunnel junctions, n-Si-SiO x (d)-F (F = Fe, Ni and Co, d spans 34 to 391 ), Al-AlO x (~50 )-Gd, and Pd-AlO x (d)-Al (d spans 50 to 300 ). The frequency-dependent impedance of Al-AlO x (~20 )-Al tunnel junctions, in a regime where the impedance is dominated by interface capacitance and tunneling resistance, reveals pronounced dispersion in these structures. 24 We attribute the enhanced frequency dependence to interface traps, which are distributed over a wide range of trapping energies. Extremely deep trapping states are observed as no loss peaks are present down to a frequency of 1 mHz. A surprising scaling relationship has been 99

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100 observed when a single junction is aged to successively higher tunneling resistance, in that the impedance versus frequency data, when properly scaled by the dc resistance, collapse onto a single universal scaling function. We have also gathered comparative screening length information for Fe, Ni and Co by measuring and plotting the inverse capacitance versus dielectric thickness (d) for n-Si-SiO x (d)-F structures. A linear relationship with non-zero intercept is observed, and the negative of the x-intercept (d 0 ) reveals the relevant screening information. We have experimentally determined that Co has the smallest effective additional dielectric thickness (d 0 ), followed by Ni, and Fe has the largest. Our model suggests that the screening lengths in these ferromagnetic materials should fall in the same order. This result is not in agreement with the theoretical prediction of Zhang. 9 Magnetocapacitance measurements have been performed on Al-AlO x (50 )-Gd structures to determine the effect of a ferromagnetic transition on screening in a metal. Though we observe no (exchange-induced) capacitance changes as the temperature is swept through the experimentally determined Curie temperature (T C 220 K), we do measure a surprisingly large (maximum of 3% at 70 K) magnetocapacitance in these structures, even well above T C . Perhaps more surprisingly, we find that the magnetocapacitance changes sign sharply (within 2 degrees Kelvin) at a crossover temperature, T x 60 K. Thus we have demonstrated the sensitivity of magnetocapacitance measurements to spin-dependent phenomena. Finally, we have used the magnetocapacitance technique to measure the spin-dependent screening response of Pd, which is an itinerant (Pauli) paramagnet with a large (Stoner enhanced) paramagnetic susceptibility. We observe that the capacitance of Pd

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101 AlO x -Al structures decreases quadratically with magnetic field. This observation is consistent with our model of screening, which takes into account the Zeeman splitting of the carriers in Pd with magnetic field. We have thus shown the sensitivity of magnetocapacitance measurements to surface band structure and spin polarization, in contrast to most other techniques (resistivity, susceptibility, heat capacity, etc.), which are sensitive to bulk band structure and bulk density of states. We have demonstrated that the measured capacitance of MIM structures reveals spin-polarization information via the screening lengths of the electrodes. Depending on the electronic band structure of the electrodes, the screening length can become longer or shorter when a net spin-polarization is induced. Since magnetocapacitance is sensitive to spin-dependent electrochemical potentials, we propose that it is also a technique capable of measuring non-equilibrium spin polarization in spin-injection devices, as well. Novel, low carrier density materials, e.g. dilute magnetic semiconductors, may show similar magnetocapacitive effects larger in magnitude due to a longer screening length. 6.2 Proposed Future Directions Since capacitance measurements are sensitive to spin-polarization, the magnetocapacitance technique can be applied in a variety of ways. For example, magnetocapacitance measurements can be used to explore the effects of spin on the screening response of a semiconductor. Once these effects are characterized, one can compare the capacitive response of a metal-insulator-semiconductor structure in the presence of a magnetic field with the response of the same structure in which a spin-polarized current, injected from a ferromagnet, is present in the semiconductor. Spin-injection efficiency can be measured in this way and understanding can be gained of the

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102 properties of ferromagnet-semiconductor interfaces that make efficient spin-injection elusive. Another proposed use of this technique is the measurement of the spin diffusion length of metals and semiconductors. This measurement will involve closely spaced contacts defined by e-beam lithography. Spin-diffusion length information is necessary for materials used in spin-injection devices, as the length over which spin information is lost sets an upper limit on the injector-detector separation distance. Since the screening length in a metal is dependent on the band structure of the metal, capacitance measurements can also be used to detect band structure changes in itinerant ferromagnets near the Curie temperature. This information is useful from a fundamental physics standpoint as it provides a new tool for the characterization of the complicated critical behavior of itinerant ferromagnets that is independent from the standard techniques, such as magnetization, resistance and specific heat. The primary aim in these proposed studies will be the application of magnetocapacitance measurements to novel spin-electronic systems to elucidate the details of spin-transport. Electrical spin-injection from ferromagnets into paramagnetic metals has been demonstrated at low temperatures 38 and at room temperature. 39 Similarly, spin-injection into semiconductors has been accomplished via optical injection using circularly polarized light, 40 and electrical injection from a magnetic semiconductor. 41 In the metals work, a ferromagnetic analyzer detects the spin-polarization in a non-local geometry to reduce the effects of anisotropic magnetoresistance and Hall effects. In the semiconducting cases, spin-polarization is determined by the polarization of the emitted electroluminescence after recombination. In both cases, a surprisingly long spin diffusion length is observed. Some workers are skeptical of the earlier spin-polarization

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103 detection data due to spurious effects while the work with semiconductors requires a sophisticated apparatus. We propose a new method for the detection of non-equilibrium spins in metals and semiconductors: magnetocapacitance measurements performed on these systems are insensitive to magnetoresistive and Hall effects and require little more than a current source and a capacitance bridge. FerromagneticinjectorTest material Aluminumanalyzers AlOx I+IFigure 6-1: Geometry for spin-diffusion length measurement The experimental procedures in this work will involve both the growth and characterization of magnetic heterostructures. We first propose to experimentally determine the spin-diffusion length in thin films of various metals (Cu, Au, Pd, Al, etc.) using the magnetocapacitance technique. To accomplish this goal, we will grow similar structures to those found in the literature, 38, 39 consisting of a narrow thin film wire of the

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104 material under study, and a ferromagnetic injector (e. g. permalloy) crossing the wire perpendicularly and maintaining ohmic contact. A schematic of this geometry is given in figure 6-1. Instead of a ferromagnetic analyzer, we will utilize a capacitor structure placed in close proximity to the injector with the wire itself as one electrode. The other electrode will consist of a crossed Al stripe separated from the wire by a thin (~50 ) layer of AlO x . The capacitor will be placed on the opposite side of the injector as the return current path (indicated by arrows in the figure) so that no (charge) current is passing through the wire at the position of the analyzer. As a spin-polarized current is injected into the wire while the capacitance of the analyzer is simultaneously measured, the capacitance reveals the spin-polarization in the wire since the capacitance varies quadratically with the spin-polarization (as indicated in the previous section). We must perform an independent measurement of the capacitance versus magnetic field for the structure to obtain a quantitative comparison between the capacitance changes induced by injected spins and by magnetic field. Using the spin-susceptibility of the material under study, we can give quantitative values of the spin-polarization of the wire at the point defined by the position of the analyzer. Multiple analyzers can be grown in close proximity at varying distances from the injector, as shown in figure 6-1, and these can be used to map out the distribution of non-equilibrium spins in the wire. The length over which spin information is lost (spin-diffusion length) can, in this way, be measured. This same technique can be applied to semiconductors with a ferromagnetic (metallic or semiconducting) injector, normal (metallic or semiconducting) drain, and a capacitive contact placed in close proximity to the injector opposite the current path. Spin-injection into a semiconductor is rather formidable, but not prohibitively so with the

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105 advent of dilute magnetic semiconductors as injectors. 41 Preliminary work must be done to characterize the magnetocapacitive response of semiconductors (GaAs based) in general. Metal-oxide-semiconductor capacitor structures must be grown and capacitance versus magnetic field measurements performed to determine the hitherto unmeasured spin-dependent screening response of semiconductors. This information will be obtained experimentally in much the same way as the spin-dependent screening response of paramagnetic metals, as described in the previous section. We expect a much longer screening length in semiconductors due to their low carrier concentration and perhaps a larger magnetic field dependence for the same reason. Once the spin-dependent screening response of semiconductors is known, we can proceed in a straightforward way paralleling the proposed metals work. Challenges in this work include the growing of a robust oxide compatible with GaAs and the efficient injection of spins into semiconductors. Since spin-diffusion lengths much longer than the same quantity in metals are reported 41 to exist in GaAs, lithographic patterning will take place on longer length scales and will be easier to perform. Magnetocapacitance will also be used as a fundamental tool to probe the band structure of ferromagnetic metals and semiconductors near the Curie temperature (T C ). As indicated in the previous section, the screening length is spin-dependent in ferromagnets (and in paramagnets in the presence of an applied field) and magnetocapacitance measurements performed as a continuous function of temperature (encompassing both sides of the transition) reveal the evolution of the electronic band structure as the sample undergoes a magnetic phase transition. Though the ferromagnetic transition in metals is fairly well understood, the same cannot be said for dilute magnetic

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106 semiconductors. These experiments will give valuable insight into the mechanism behind ferromagnetism in semiconductors.

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LIST OF REFERENCES 1 C. A. Mead, Physical Review Letters 6, 545 (1961). 2 H. Y. Ku and F. G. Ullman, Journal of Applied Physics 35, 265 (1964). 3 J. G. Simmons, Applied Physics Letters 6, 54 (1965). 4 A. F. Hebard, S. A. Ajuria, and R. H. Eick, Applied Physics Letters 51, 1349 (1987). 5 J. G. Simmons, Brittish Journal of Applied Physics 18, 269 (1967). 6 K. H. Gundlach, Physics Letters 24A, 731 (1967). 7 P. R. Hammar, B. R. Bennett, M. J. Yang, et al., Physical Review Letters 83, 203 (1999). 8 D. L. Smith and R. N. Silver, Physical Review B (Condensed Matter and Materials Physics) 64, 045323/1 (2001). 9 S. Zhang, Physical Review Letters 83, 640 (1999). 10 J. Ben Youssef, K. Bouziane, O. Koshkina, et al., Journal of Magnetism and Magnetic Materials 165, 288 (1997). 11 D. New, N. K. Lee, H. S. Tan, et al., Physical Review Letters 48, 1208 (1982). 12 O. K. Andersen, Physical Review B (Solid State) 2, 883 (1970). 13 G. N. Sapir, A. Levy, and J. C. Walker, Journal of Applied Physics 55, 2362 (1984). 14 J. E. Schmidt and L. Berger, Journal of Applied Physics 55, 1073 (1984). 15 J. E. van Dam and O. K. Andersen, Solid State Communications 14, 645 (1974). 16 M. T. Beal-Monod and J. M. Lawrence, Physical Review B (Condensed Matter) 21, 5400 (1980). 107

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108 17 N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976). 18 S. Misawa, Physical Review Letters 26, 1632 (1971). 19 L. I. Maissel and R. Glang, Handbook of Thin Film Technology (McGraw-Hill, Inc., 1970). 20 K. R. Williams and R. S. Muller, Journal of Microelectromechanical Systems 5, 256 (1996). 21 Manual (AJA International, North Scituate, MA, 1998). 22 Manual (Andeen-Hagerling, Inc., Cleveland, OH, 2001). 23 Manual (Quantum Design, San Diego, CA, 1996). 24 K. T. McCarthy, S. B. Arnason, and A. F. Hebard, Applied Physics Letters 74, 302 (1999). 25 S. Zafar, R. E. Jones, P. Chu, et al., Applied Physics Letters 72, 2820 (1998). 26 J. Krupski, Physica Status Solidi B 157, 199 (1990). 27 J. Halbritter, Journal of Applied Physics 58, 1320 (1985). 28 A. K. Jonscher, Nature 267, 673 (1977). 29 R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov, et al., Science 280, 1238 (1998). 30 P. Joyez, D. Esteve, and M. H. Devoret, Physical Review Letters 80, 1956 (1998). 31 M. A. Rampi, O. J. A. Schueller, and G. M. Whitesides, Applied Physics Letters 72, 1781 (1998). 32 D. A. Papaconstantopaulos, Handbook of Band Structures (Plenum Press, New York, 1986). 33 J. A. Hertz and K. Aoi, Physical Review B (Solid State) 8, 3252 (1973). 34 R. Ahuja, S. Auluck, B. Johansson, et al., Physical Review B (Condensed Matter) 50, 5147 (1994). 35 O. Nakamura, K. Baba, H. Ishii, et al., Journal of Applied Physics 64, 3614 (1988).

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109 36 M. Farle, K. Baberschke, U. Stetter, et al., Physical Review B (Condensed Matter) 47, 11571 (1993). 37 M. Johnson, Physical Review Letters 70, 2142 (1993). 38 M. Johnson and R. H. Silsbee, Physical Review Letters 55, 1790 (1985). 39 F. J. Jedema, A. T. Filip, and B. J. van Wees, Nature 410, 345 (2001). 40 I. Malajovich, J. M. Kikkawa, and D. D. Awschalom, Physical Review Letters 84, 1015 (2000). 41 Y. Ohno, D. K. Young, B. Beschoten, et al., Nature 402, 790 (1999).

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BIOGRAPHICAL SKETCH Kevin McCarthy was born on Mother’s Day, May 12, 1974, in Columbia, MO. Shortly thereafter, his family moved to the northeast, where he vividly remembers learning to ride his older brother’s bicycle on the hills of his Connecticut neighborhood. In the fall of 1979, the McCarthy family moved to Lutz, Florida. As the town of Lutz grew, so did the McCarthy family, and by 1983, Kevin had three siblings: an older brother and younger brother and sister. Kevin was an exceedingly curious child, and at age 9 asked his father to explain to him how an engine worked. Though his friends did not fully appreciate his newfound comprehension, he was immediately hooked on understanding. At age 11, after saving $200 from performing odd jobs for neighbors, Kevin purchased his first motorcycle. Machines were always fascinating to him, and by age 16, he was a fully accomplished mechanic. He worked through high school as a busboy to feed his expensive habit of modifying large, inefficient cars in an effort to attain the worst possible gas mileage (with the added benefit of increased performance). In the fall of 1992, Kevin began his undergraduate study in physics at the University of Florida (UF), where he quickly established a reputation as the student least afraid to ask a question or five. He spent the summers of 1995 and 1996 working as an undergraduate researcher at Los Alamos National Laboratory, and in 1996 began working for Professor Arthur Hebard at UF. Recognizing a kindred spirit in Dr. Hebard, who is also motivated by genuine curiosity and the joy of discovery, Kevin decided to stay at UF and pursue graduate studies under Dr. Hebard’s guidance. Kevin met his wonderful wife, Jen, 110

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111 shortly after becoming a graduate student, thereby substantiating his claim that staying was a good idea. This dissertation represents the culmination of his research efforts over the past five years.