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Bartosz Liedke, Ion Beam Processing of Surfaces and Interfaces

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Bartosz Liedke, Ion Beam Processing of Surfaces and Interfaces Ion beam processing of surfaces and interfaces – Modeling and atomistic simulations – DISSERTATION zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) vorgelegt der Fakult¨at Mathematik und Naturwissenschaften der Technischen Universit¨at Dresden von Bartosz Liedke geboren am 31. Juli 1982 in Bia lystok, Poland Eingereicht am 24.03.2011 Gutachter: 1. Prof. Dr. W. M¨oller, Helmholtz-Zentrum Dresden-Rossendorf 2. Prof. Dr. E. Chason, Brown University iii Abstract Self-organization of regular surface pattern under ion beam erosion was described in de- tail by Navez in 1962. Several years later in 1986 Bradley and Harper (BH) published the first self-consistent theory on this phenomenon based on the competition of surface rough- ening described by Sigmund’s sputter theory and surface smoothing by Mullins-Herring diffusion. Many papers that followed BH theory introduced other processes responsible for the surface patterning e.g. viscous flow, redeposition, phase separation, preferential sputtering, etc. The present understanding is still not sufficient to specify the dominant driving forces responsible for self-organization. 3D atomistic simulations can improve the understanding by reproducing the pattern formation with the detailed microscopic description of the driving forces. 2D simulations published so far can contribute to this understanding only partially. A novel program package for 3D atomistic simulations called trider (TRansport of Ions in matter with DEfect Relaxation), which unifies full collision cascade simulation with atomistic relaxation processes, has been developed. The collision cascades are provided by simulations based on the Binary Collision Approximation, and the relaxation processes are simulated with the 3D lattice kinetic Monte-Carlo method. This allows, without any phenomenological model, a full 3D atomistic description on experimental spatiotemporal scales. Recently discussed new mechanisms of surface patterning like ballistic mass drift or the dependence of the local morphology on sputtering yield are inherently included in our atomistic approach. The atomistic 3D simulations do not depend so much on experimental assumptions like reported 2D simulations or continuum theories. The 3D computer experiments can even be considered as ’cleanest’ possible experiments for checking continuum theories. This work aims mainly at the methodology of a novel atomistic approach, showing that: (i) In general, sputtering is not the dominant driving force responsible for the ripple formation. Processes like bulk and surface defect kinetics dominate the surface morphol- ogy evolution. Only at grazing incidence the sputtering has been found to be a direct cause of the ripple formation. Bradley and Harper theory fails in explaining the ripple dynamics because it is based on the second-order-effect ‘sputtering’. However, taking into account the new mechanisms, a ‘Bradley-Harper equation’ with redefined param- eters can be derived, which describes pattern formation satisfactorily. (ii) Kinetics of (bulk) defects has been revealed as the dominating driving force of pattern formation. Constantly created defects within the collision cascade, are responsible for local surface topography fluctuation and cause surface mass currents. The mass currents smooth the surface at normal and close to normal ion incidence angles, while ripples appear first at θ 40◦. ≥The evolution of bimetallic interfaces under ion irradiation is another application of trider described in this thesis. The collisional mixing is in competition with diffusion and phase separation. The irradiation with He+ ions is studied for two extreme cases of bimetals: (i) Irradiation of interfaces formed by immiscible elements, here Al and Pb. Ballistic interface mixing is accompanied by phase separation. Al and Pb nanoclusters show a self-ordering (banding) parallel to the interface. (ii) Irradiation of interfaces by intermetallics forming species, here Pt and Co. Well-ordered layers of phases of intermetallics appear in the sequence Pt/Pt3Co/PtCo/PtCo3/Co. The trider program package has been proven to be an appropriate technique providing a complete picture of mixing mechanisms. v Contents Abstract v Abbreviations ix 1. Introduction 1 1.1. Self-organization .............................. 1 1.2. History of self-organization of surface pattern under ionirradiation . 3 1.3. Aimandstructureofthiswork . 5 2. Simulating ion-solid interactions 7 2.1. Fundamentals of ion-solid interactions. ........ 9 2.1.1. Interatomicpotentials . 9 2.1.2. Crosssections............................. 10 Nuclearstopping ........................... 12 Electronicstopping . 13 2.1.3. Theoryofsputtering . 14 2.1.4. Ion-beammixing ........................... 17 2.2. BinaryCollisionApproximation . ... 20 2.2.1. TRIM ................................. 21 2.2.2. TRIDYN ............................... 24 2.2.3. TheoreticallimitsofBCA . 25 2.3. KineticMonte-Carlo . 27 2.3.1. Latticegases ............................. 28 2.3.2. KMCtimestep,ionfluxandionfluence . 30 2.3.3. Binaryalloys ............................. 31 2.3.4. Atom coordinates as binary arrays using bit coding technique . 32 2.4. TheinterfacebetweenBCAandKMC . 33 2.4.1. MajormodificationsinTRIM/TRIDYN . 35 2.4.2. Defectprocessing .. .. .. .. .. .. ... .. .. .. .. .. .. 37 2.4.3. Recombination ............................ 39 2.4.4. Dataflow ............................... 41 2.4.5. Demonstration of the simulation procedure . ..... 42 2.4.6. CPUtimes............................... 43 3. Ion-induced surface processes 45 3.1. DefectevolutioninSi. 49 3.1.1. Simulationparameters . 49 3.1.2. Results................................. 49 3.2. Craterformationbysingleionincidence . ...... 51 3.2.1. Simulationofsingleionincidence . ... 53 3.2.2. Fittingfunctionforcraterformation . .... 57 3.3. Rippleevolution................................ 61 3.3.1. Constantfluxpercoordinateunit . 62 Surfacemorphology. 62 Spatialevolutionofsurfaces . 65 3.3.2. Simulationwithraytracingofions . .. 70 Surfacemorphology. 70 vii Contents Withorwithoutsputtering . 72 Spatialevolution ........................... 74 3.4. Surfacemasscurrents. 77 3.4.1. Gibbs-Thomsonrelation . 79 3.4.2. Mullins-Herringdiffusionofsurface . ... 80 3.4.3. Surface mass currents under irradiation and diffusion ....... 83 4. Interface mixing of bilayer interfaces 87 4.1. Many-body interatomic potential for energies of CellularAutomata . 88 4.2. Gaugingsimulationparameters . ... 90 4.3. Simulationresults. 93 4.3.1. Al/Pbbimetalmixing . 93 4.3.2. Pt/Cobimetalmixing . 96 4.4. ComparisonofTRIDERwithTRIDYN. 98 4.5. Conclusions .................................. 101 5. Summary 103 A. Nuclear stopping in Al/Pb bimetal 107 List of Figures 111 List of Tables 115 Bibliography 117 Acknowledgments 131 Curriculum Vitae 133 List of publications 135 viii Abbreviations The list of acronyms presented below contains expressions frequently used within this work that are also common in scientific and technological literature. bca Binary Collision Approximation bcc body-centered cubic BH BradleyandHarper CA CellularAutomata CM centerofmass dft density functional theory DoG differenceofGaussians dpa displacementperatom EW EdwardsandWilkinson fcc face-centered cubic FPs Frenkelpairs IBS ionbeamsputtering kmc kinetic Monte-Carlo KPZ Kardar-Parisi-Zhang Kr-C krypton-carbon KS Kuramoto-Sivashinsky mc Monte-Carlo MCs Monte-Carlosteps md molecular dynamics MH MullinsandHearing NN nearestneighbor SOS solid-on-solid RGL RosatoGuillopeLegrand sc simple cubic srim the stopping and range of ions in matter trider transport of ions in matter with defect relaxation tridyn trim.sp dynamical trim transport of ions in matter trim.sp trim sputtering ZBL Ziegler-Biersack-Littmark ix In all science, error precedes the truth, and it is better it should go first than last. Hugh Walpole (1884 - 1941) 1 Introduction 1.1 Self-organization Self-organization is a process driving a system towards coherent structures by the system itself. Two types of self-organization mechanisms can classify systems from the thermo- dynamic point of view: (i) in closed systems, which evolve towards thermodynamic equilibrium, self-organization may reduce the entropy of sub-systems, however the en- tropy of the closed system as a whole will always rise; (ii) in open systems, which evolve towards a steady-state, high-quality energy of low entropy enters the system con- tinuously delivered by an external source. If self-organization occurs during this process, the entropy of the open system will be lowered due to entropy export. Therefore, the low-quality energy that abandons the system will have higher entropy. SELF ORGANIZATION (i) far-from equilibrium (ii) driven systems systems closed system open system (far-from equilibrium) (non-equilibrium) entropy export from sub-systems (entropy export) high-quality E low-quality E self-organized sub- systems (relaxation) entropy of total entropy the open system increases decreases reaction pathway towards systemmay evolve to equilibrium state a self-ordered via self-ordered states steady state Figure 1.1.: Two types of self-organization. In solid state physics self-organization can be found for mechanisms like phase tran- sition, crystallization, percolation of random media, surface and interface energy min- imization, epitaxial growth, etc. The first type (i) applies to all these mechanisms, 1 CHAPTER 1. INTRODUCTION where self-organization occurs as an intermediate state providing an efficient way to reduce the free energy
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