X) and Computer Simulation of Synthesis of Nanostructures
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FORSCHUNGSZENTRUM ROSSENDORF ml WISSENSCHAFTLICH-TECHNISCHEBERICHTE FZR-277 November 1999 DEOOGE882 RECEW?X) MN30ZO08 AAatthias Strobe/ C)STI Modeling and Computer Simulation of Ion Beam Synthesis of Nanostructures Dissertation -- *DE013741591* R: KS DEO13741591 ______.___–..—-–’––-–—- DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. FORSCHUNGSZENTRUM ROSSENDORF Institut fur Ionenstrahlphysik und Materialforschung I Modeling and Computer Simulation of Ion Beam Synthesis of Nanostructures von der Fakultat Mathematik und Naturwissenschaften der Technischen Universitat Dresden genehmigte Dissertation zur Erlangung des akademischen Grades Doctor Rerum Naturalism (Dr. rer. nat.) vorgelegt von Dipl.-Phys. MATTHIAS STROBEL geboren am 22. Februar 1969 in Wurzburg IE2R Tag der Einreichung: 30. Juni 1999 Tag der Verteidigung: 13. Oktober 1999 Vorsitzender der Prufungskommision: PROF. DR. GERHARD S OFF Gutachter: PROF. DR. WOLFHARD M.OLLER Technische Universitit Dresden PROF. HARRY BERNAS, PHD CNRS–CSNSM Orsay, Frankreich PROF. DR. SIGISMUND KOBE Technische Universitat Dresden Physic ist wahrlich das eigentliche Studium des Menschen Georg Christoph Lichtenberg (Deutscher Physiker und PhiIosoph, 1742- 1799) Contents Abbreviations ix 1 Introduction 1 2 Ion beam synthesis of nanostructures 7 2.110n implantation methods.. ...9 2.2 Principles of ion-solid interaction . 9 2.3 Formation of second-phase precipitates . 12 2.3.1 Impurity-substrate phase diagram . 12 2.3.2 Homogeneous nucleation. ..13 2.3.3 Nucleation in ion beam synthesis . - . 17 2.4 Growth, coarsening, and coalescence of nanoclusters . - 20 2.5 Modeling and simulation approaches . - . 23 2.5.1 Atomic description . .~~ 2.5.2 Mesoscopic and continuum descriptions . - . 28 3 Kinetic 3D lattice Monte-Carlo method 31 3.1 Basic description . ...31 3.2 Energetic and jump probabilities . - . 34 3.3 Intrinsic properties of the model... 35 3.4 Analysis ofsimulation data. ...38 3.5 Gauging of simulation parameters . - - . - . 39 3.5.1 Length scale . 40 3.5.2 Diffusion coefficient, time scale, and ion flux . 40 3.5.3 Nearest-neighbor bond strength, volubility, capillary length, and surface tension . ...42 3.6 A simple approach to collisional mixing . - - . 49 3.7 Simulation of ion implantation and annealing . 50 3.8 -Applicability of the K3DLMC method and discussion . 51 4 General description of Ostwald ripening 55 4.1 Characterization of Ostwald ripening and recent developments . 55 4.2 Fundamentals of the model . ...58 v vi CO~NTENTS 4.2.1 Evolution of a single nanocluster . 58 4.2.2 Evolution of an ensemble of nanoclusters . 59 4.3 Local mean-field approach to Ostwald ripening . 62 4.4 Numerical implementation. ...64 4.5 Simulation of diffusion and reaction controlled Ostwald ripening . 67 5 Nanocluster evolution during ion implantation 73 5.1 Nanocluster formation at constant implantation conditions . 73 5.2 Nanocluster formation at varying implantation conditions . 79 5.3 On the influence of collisional mixing . 82 5.3.1 Collisional mixing of a single nanocluster . 83 5.3.2 Nucleation, growth, and Ostwald ripening in the presence of colli- sional mixing . ...94 6 Combination of K3DLMC and reaction-diffusion equation methods 101 6.1 K3DLMC and reaction-diffusion equation simulations of homogeneous Ost- wald ripening . 101 6.1.1 K3DLMC simulations of homogeneous Ostwald ripening . 102 6.1.2 Comparison of K3DLlMC and reaction-diffusion equation simulations of Ostwald ripening . ...107 6.2 Late stage evolution of as-implanted samples . 111 6.3 Focused ion beam synthesis of nanocluster arrays . 115 7 Applications of the K3DLMC method in ion beam synthesis 119 7.1 Impurity redistribution in a reactive ambient . 119 7.1.1 Experimental observations . 120 7.1.2 Modeling of redistribution of implanted Ge in the presence of an oxidizing atmosphere . ...123 7.2 Ion beam synthesis of compound nanoclusters . 126 7.2.1 K3DLMC model for two types of interacting impurity atoms . 126 7.2.2 On core/shell nanocluster formation by sequential ion implantation 128 7.2.3 Shifted-profile compound nanocluster synthesis . 132 8 Summary and outlook 139 A Bit encoding of Monte-Carlo lattice 145 B Derivation of nanocluster source strengths 149 B.1 General formulation . 149 B.2 Monopole approximation . 152 B.3 Source strengths in monopole approximation . 154 List of Figures 155 CONTENTS vii List of Tables 159 Bibliography 161 Danksagung / Acknowledgements 179 Erklarung 181 Thesen / Major statements of the work 183 ... VIH CONTENTS Abbreviations An author of a (scientific) publication faces the conflict of using acronyms versus writing technical or often repeated expressions always in full length. Some claim that acronyms facilitate reading while others complain about the problem memorizing them. By carefully balancing the convenience of using abbreviations versus the readability of this thesis, I finally decided to introduce the following ones which are partly standard in the physical literature: BC boundary condition BCA binary collision approximation bcc body-centered cubic CA cellular automaton CBII conventional beamline ion implantation CM collisional mixing CPU central processor unit dpa displacements per atom fcc face-centered cubic FIB focused ion beam GT GIBBS-THOMSON IA impurity atom IBS ion beam synthesis K3DLiMc kinetic three-dimensional lattice Monte-Carlo KIM kinetic Is~~G model lhs left hand side LSW LIFSHITZ-SLYOZOV-WAGNER MC Monte-Carlo MCS Monte-Carlo step MD Molecular Dynamics NC! nanocluster OR OSTWALD ripening PRD particle radius distribution RBS RUTHERFORD backscattering RDE reaction-diffusion equation rhs right hand side ix x CONTENTS Sc simple-cubic SRIM Stopping ancl Range of Ions in Matter TEM transmission electron microscopy TRIM TRansport of Ions in Matter VG VOORHEES-GLICKSMAN XTEM cross-section TEi’v1 Chapter 1 Introduction Ever since the invention of particle accelerators energetic ions have been used to explore the physical laws of ion-solid interactions [1). Besides these fundamental studies the potential of ions to modify selectively the properties of substrates has been recognized and thus found a wide area of technological applications. In modern microelectronics, for instance, current integrated circuit fabrication is based on the precise control of doping of Si wafers by implantation [2]. A further example is the hardening of steels with energetic nitrogen ions, which proceeds via the formation of nitrides close to the surface [3]. Depending mostly on the implanted fluence FO, ion beam modification of materials can be roughly grouped into three major ranges: ● For fluences -FO~ 1014cm-z the implanted ions are assumed to remain isolated within the substrate. Implanted into crystals these impurities may reside on regular lattice sites and thus change the electrical properties of the host material (doping range); ● For fluences in the range 1015 cm ‘2 ~ 1’.<1016 cm–2, in the course of implantation the deposited impurities start to exceed the volubility threshold. This causes the formation of isolated domains of a new phase [in general called nanoclusters (FJCS), precipitates, quantum dots, or, if in a crystalline state, nanocrystals], which besides the mechanical may also change the optical properties of the substrate; ● For fluences F. > 1017 cm-2 the second phase domains start to coalesce, which might result in the formation of a continuous buried layer of a new composition in a predefine depth of the substrate. Ion beam synthesis (IBS) of nanostructures refers to items two and three of the above listing and consists usually of two independent steps. First, the implantation of a certain fluence F. is performed in a rather well defined parameter range, i.e. ion energy E, ion flux j, and substrate temperature ~~P. Very often this step is followed by a thermal heat treatment because (i) radiation damage is annealed out and (ii) the thermally activated redistribution of the impurities can be tailored to a large extent. As evidenced by a vast literature, a huge variety of different NC/substrate systems has been achieved by IBS. For instance, the formation of AU [4, 5], Ag [6], Cu [7] or 1 2 CILAPTER 1. INTRODUC7 Ni [8] precipitates in silica glasses or other insulators has been reported (for a revi( metallic NC formation by IBS see, e.g. MAZZOLDI et al. [9]). The synthesis of elem semiconducting hTCs in neutral (chemically inert) matrices has been observed [10], as as compound nanocrystal formation in single-type implantations due to chemical reac between impurity and substrate atoms, e.g. silicide formation for metal implantation ir [II]. Additionally, in a neutral matrix compound NCS could be detected by co- or seque implantation of various atom types, e.g. II-VI, III-V or IV-IV semiconductor N-CS in [12], AlzOS [13] or Si [14] as well as metallic compound NCS in SiOa [15]. Further exan and applications of ion beams in materials science can be found in Proceedings of ar or biannual conferences in ion beam physics (for recent examples, see Refs. [16, 17]). This work concentrates on the synthesis of NCS by ion implantation, because a p~ cclntrol of the formation of these essentially zero-dimensional structures helps to use unique physical properties in technological applications. Consisting of approximate: to 105 single atoms, the properties of N(Js are governed by a combination of effects k] from atomic and solid state physics. Hence, for their description well established con fr,~m