www.pdfgrip.com www.pdfgrip.com Roman Leitsmann, Philipp Plänitz, and Michael Schreiber In-vitro Materials Design www.pdfgrip.com Related Titles Frenking, G., Shaik, S (eds.) Schmitz, G.J., Prahl, U (eds.) The Chemical Bond Volume Set Integrative Computational Materials Engineering 2014 Concepts and Applications of a Modular Simulation Platform ISBN: 978-3-527-33318-9; also available in electronic formats 2012 Reiher, M., Wolf, A Relativistic Quantum Chemistry The Fundamental Theory of Molecular Science Second edition 2014 ISBN: 978-3-527-33415-5; also available in electronic formats Vaz Junior, M., de Souza Neto, E.A., Munoz-Rojas, P.A (eds.) 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Chemnitz Germany Cover picture courtesy of Sang-Woo Kim, Ph.D., Professor School of Advanced Materials Science & Engineering SKKU Advanced Institute of Nanotechnology (SAINT) Sungkyunkwan University (SKKU) Cheoncheon 300 Suwon 440-746 South Korea All books published by Wiley-VCH are carefully produced Nevertheless, authors, editors, and publisher not warrant the information contained in these books, including this book, to be free of errors Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at © 2015 Wiley-VCH Verlag GmbH & Co KGaA, Boschstr 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages) No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers Registered names, trademarks, etc used in this book, even when not specifically marked as such, are not to be considered unprotected by law Print ISBN: 978-3-527-33423-0 ePDF ISBN: 978-3-527-66738-3 ePub ISBN: 978-3-527-66737-6 Mobi ISBN: 978-3-527-66736-9 oBook ISBN: 978-3-527-66735-2 Cover Design Schulz Grafik-Design, Fgưnheim, Germany Typesetting Laserwords Private Limited, Chennai, India Printing and Binding Markono Print Media Pte Ltd, Singapore Printed on acid-free paper www.pdfgrip.com V Contents Preface IX Part I Basic Physical and Mathematical Principles Introduction Newtonian Mechanics and Thermodynamics 2.1 2.2 2.3 2.4 Equation of Motion Energy Conservation Many Body Systems 10 Thermodynamics 11 Operators and Fourier Transformations 3.1 3.2 3.3 Complex Numbers 17 Operators 18 Fourier Transformation 20 4.1 4.2 4.3 Quantum Mechanical Concepts 25 Heuristic Derivation 25 Stationary Schrödinger Equation 27 Expectation Value and Uncertainty Principle Chemical Properties and Quantum Theory 5.1 5.2 Atomic Model 33 Molecular Orbital Theory 39 Crystal Symmetry and Bravais Lattice 47 6.1 6.2 6.3 6.4 Symmetry in Nature 47 Symmetry in Molecules 47 Symmetry in Crystals 49 Bloch Theorem and Band Structure 53 17 33 28 www.pdfgrip.com VI Contents 57 Part II Computational Methods Introduction 59 Classical Simulation Methods 8.1 8.2 8.3 65 Molecular Mechanics 65 Simple Force-Field Approach 68 Reactive Force-Field Approach 71 9.5.1 9.5.2 9.5.3 9.6 9.6.1 9.6.2 9.6.3 9.6.4 9.7 9.7.1 9.7.2 9.7.3 9.7.4 9.7.5 9.7.5.1 9.7.5.2 9.7.5.3 77 Born–Oppenheimer Approximation and Pseudopotentials 77 Hartree–Fock Method 80 Density Functional Theory 83 Meaning of the Single-Electron Energies within DFT and HF 85 Approximations for the Exchange–Correlation Functional EXC 88 Local Density Approximation 88 Generalized Gradient Approximation 89 Hybrid Functionals 90 Wave Function Representations 91 Real-Space Representation 91 Plane Wave Representation 92 Local Basis Sets 93 Combined Basis Sets 95 Concepts Beyond HF and DFT 96 Quasiparticle Shift and the GW Approximation 97 Scissors Shift 99 Excitonic Effects 100 TDDFT 100 Post-Hartree–Fock Methods 101 Configuration Interaction (CI) 102 Coupled Cluster (CC) 102 Møller–Plesset Perturbation Theory (MPn) 103 10 Multiscale Approaches 9.1 9.2 9.3 9.4 9.5 Quantum Mechanical Simulation Methods 10.1 10.2 105 Coarse-Grained Approaches 105 QM/MM Approaches 108 11 Chemical Reactions 11.1 11.2 111 Transition State Theory 111 Nudged Elastic Band Method 114 www.pdfgrip.com Contents Part III Industrial Applications 117 12 Introduction 13 Microelectronic CMOS Technology 13.1 13.2 13.2.1 13.2.2 13.2.3 13.2.4 13.2.5 13.2.6 13.3 13.3.1 13.3.2 13.3.3 13.3.4 13.4 13.4.1 13.4.2 13.4.3 13.4.4 14 14.1 14.2 14.2.1 14.2.2 14.2.3 14.2.4 14.2.5 14.2.6 14.3 14.3.1 14.3.2 14.3.3 14.3.4 14.3.5 119 121 Introduction 121 Work Function Tunability in High-k Gate Stacks 127 Concrete Problem and Goal 127 Simulation Approach 129 Modeling of the Bulk Materials 129 Construction of the HKMG Stack Model 132 Calculation of the Band Alignment 136 Simulation Results and Practical Impact 138 Influence of Defect States in High-k Gate Stacks 141 Concrete Problem and Goal 141 Simulation Approach and Model System 144 Calculation of the Charge Transition Level 145 Simulation Results and Practical Impact 146 Ultra-Low-k Materials in the Back-End-of-Line 149 Concrete Problem and Goal 149 Simulation Approach 151 The Silylation Process: Preliminary Considerations 153 Simulation Results and Practical Impact 155 159 Introduction 159 GaN Crystal Growth 163 Concrete Problem and Goal 163 Simulation Approach 165 ReaxFF Parameter Training Scheme 166 Set of Training Structures: ab initio Modeling 168 Model System for the Growth Simulations 170 Results and Practical Impact 172 Intercalation of Ions into Cathode Materials 174 Concrete Problem and Goal 174 Simulation Approach 176 Calculation of the Cell Voltage 178 Obtained Structural Properties of Lix V2 O5 178 Results for the Cell Voltage 181 Modeling of Chemical Processes 15 Properties of Nanostructured Materials 15.1 15.2 Introduction 183 Embedded PbTe Quantum Dots 187 183 VII www.pdfgrip.com VIII Contents 15.2.1 15.2.2 15.2.3 15.2.4 15.2.5 15.2.6 15.3 15.3.1 15.3.2 15.3.3 15.3.4 15.3.5 15.3.6 Concrete Problem and Goal 187 Simulation Approach 188 Equilibrium Crystal Shape and Wulff Construction 190 Modeling of the Embedded PbTe Quantum Dots 191 Obtained Structural Properties 194 Internal Electric Fields and the Quantum Confined Stark Effect 195 Nanomagnetism 199 Concrete Problem and Goal 199 Construction of the Silicon Quantum Dots 200 Ab initio Simulation 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momentum 34 antiferromagnetic (AFM) coupling 208 atomic model 33 atomistic simulation techniques 162 azimuthal quantum number 34 b back-end-of-line (BEoL) 121 band alignment 135 – gate stack design 127, 128 – Si layers 132 – TiN layers 132 – SiO2 layers 134 – HfO2 layers 136 band bending 69 band structure 53, 54, 56 BFGS 66 biological processes 159, 160 Bloch theorem 53, 54, 56 bond breakage 73 bond-order 72 bonding angles 69 Born–Oppenheimer approximation 77–79 bra-ket notation 22, 27 Brillouin zone sampling 144, 152 Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm 66 Buckingham potential 71 c canonical ensemble 16 Cartesian coordinates catalysis 159 cathode materials 175 cell voltage 178, 181, 182 charge transition level 145, 146 chemical processes 159 chemical properties 33 chemical reactions 14 chemical synthesis 160 classical FF approach 68 classical simulation methods 65 coarse-grained approaches 105–107 cobalt-vanadium oxide 176 combustions 162 complementary metal-oxide semiconductor (CMOS) technology 121 complementary operators 31 complex numbers 17, 18 configuration interaction (CI) 102 conjugate gradient methods 66 conservative force core dislocations 172 corrosion 161 coating 163 Coulomb potential 33, 70, 74 coupled cluster (CC) 102, 103 cut-off energy 74 d deep defect states (DDS) 141 density function 28 density functional theory (DFT) 83–85 DFT see density functional theory (DFT) DFT-LDA approach 189 direct-tunneling (DT) current 126 dissociation energy 73 e eigenfunction 19, 26 eigenvalue 19, 26, 35 electrolysis 161 In-vitro Materials Design: Modern Atomistic Simulation Methods for Engineers, First Edition Roman Leitsmann, Philipp Plänitz, and Michael Schreiber © 2015 Wiley-VCH Verlag GmbH & Co KGaA Published 2015 by Wiley-VCH Verlag GmbH & Co KGaA www.pdfgrip.com 222 Index electrostatic interactions 70 endotherm 14 energy conservation 7, enthalpy 13, 15 entropy 12, 14 equation of motion 5, 6, 65 – many body systems 10, 11 equilibrium crystal shape (ECS) 190, 191 Euler’s formula 18 exchange–correlation energy 88–91 excitonic effects 100 exotherm 14 expectation value 28, 30 external forces 10 extreme ultraviolet (EUV) lithography 185 f Fermi energy 146, 148 ferromagnetic (FM) coupling 208 FF potentials 67, 72 force-field (FF) approach 65 – bond contributions 69 – electrostatic interaction 70 – Lennard-Jones (LJ) potential 71 – nonbonded interactions 69, 70 formation energy of defects 146 Fourier transformations 17, 20, 22, 31 free energy 14 friction energy 8, front-end-of-line (FEoL) 121 g gallium nitride (GaN) 163 GaN crystal growth 163 GaN crystallization process 171 Gibbs energies 14, 182 Gibbs fundamental equation 13 growth simulations 170, 172 GW approximation 97–99 h Hamilton function, Hamiltonian 11, 26, 27, 33 Hartree–Fock (HF) method 80–83 Hellmann–Feynman forces 178, 203 Hermitian operators 20 hexamethyldisilazane (HMDS) 150 HF method see Hartree–Fock (HF) method high-k metal gate (HKMG) stack 127 Hund’s rules 39 hybride vapor phase epitaxy (HVPE) 164 hydrogen atom 33 hydrogen-bridge bonds 69, 74 hyperfine structure 38 i imaginary unit 17 integrated circuits 121 intercalation 162 intermolecular forces 70 internal energy 12 internal forces 10 isothermal-isobaric ensemble 16 k kinetic energy 33 k-space 22, 27 l Lamb shift 38 Laplace operator 21 leapfrog algorithm 66 Legendre transformation 13 Lennard-Jones (LJ) potential 71 Lix V2 O5 , structural properties 178, 180 light-emitting diodes (LEDs) 198 linear operator 19 lithium (Li) ion battery systems 175 low- or ultra-low k (ULK) dielectric constant materials 127 m magnetic properties 206, 208, 209 magnetic quantum number 34 many body interactions 69 many body systems material deposition 162 matter waves 25 measurable quantities 28 metal-gate stack 123 metal-oxide semiconductor field-effect transistors (MOSFETs) 121 microcanonical ensemble 16 microelectronic CMOS technology 121 – fabrication steps, FEoL and BEoL 122 – high-k gate stacks 127 MM simulation 67 Møller–Plesset perturbation theory (MPn) 103 molecular mechanics 65 molecular orbital theory 39–43, 45, 46 Moore’s law 125 Morse potential 69, 74 Monte Carlo methods 113 n Nabla operator 21 nanomagnetism 199 www.pdfgrip.com Index nanostructured materials – description 183–185, 187 – embedded PbTe quantum dots 187 NEB see nudged elastic band method Newton’s equations of motion 65 Newtonian mechanics – thermodynamics see thermodynamics nonbonded interactions 69 nudged elastic band method 113–115 numerical integration 65 o operators 18 orbital functions 36 p p-type and n-type MOSFETs 121 Pauli exclusion principle 38, 39, 70 Pauli repulsion 71 PbTe/CdTe system 188, 190 periodic functions 21, 22 phase transition 162 post-HF methods 101 potential energy landscape 8, 66 pressure 12 principal quantum number 34 probability density 29 probability distribution 32 projector augmented wave (PAW) 190 pseudopotentials 77, 79 q QM/MM approaches 108, 109 quantum confined Stark effect 195–198 quantum confinement effect 197 quantum dots (QDs) 185 quantum mechanics (QM) 25 – advantages and drawbacks of HF and DFT 96 – atomic model 33–35, 37–39 – Born–Oppenheimer approximation 77–79 – chemical properties and quantum theory 33 – DFT method 83–85 – expectation value and uncertainty principle 28–31 – heuristic derivation 25, 26 quantum numbers 34 quantum-confined Stark effect (QCSE) 197 quasiparticle shift 97–99 r reactive force-field (FF) approach 72 – chemical bonding characteristics 71 – ReaxFF method 72 – training schemes 75 – van-der-Waals interaction potential 74 real space function 21, 23 real space representation 21, 27 ReaxFF method 72, 76 ReaxFF parameter training scheme 166, 168 reference potential method 136 rumpling effect 194 s Schrödinger equation 26, 27 scissors shift 99, 100 shallow defect states (SDS) 141 short channel effect (SCE) 125 silicon carbide (SiC) 164 silicon quantum dots 200, 201, 203 silylation process 153–155 simple FF-potentials 69 spherical coordinates 33 spin quantum number 38 spin-paired electrons 39 spin–orbit interaction 38 stationary Schrödinger equation 27, 28 stationary state 27 statistical mechanics 16 steepest descent algorithm 66 Stockmayer potential 71 stress-induced leakage current (SILC) 126 stretching 69, 73 supercell method 132, 133 supercell or slab method 132 symmetry and Bravais lattice 47 – Bloch theorem and band structure 53, 54, 56 – crystals 49–51, 53 – molecules 47–49 t TDDFT 100, 101 – wave function see wave function thermodynamics 11 – canonical ensemble 16 – energy and entropy changes 15 – first law 12, 14 – Gibbs energy 14 – internal energy 13 – isothermal-isobaric ensemble 16 – microcanonical ensemble 16 – potential 13 223 www.pdfgrip.com 224 Index thermodynamics (contd.) – second law 12 time-dependent DFT (TDDFT) 100, 101 torsions 69, 74 total energy 25 training scheme 75 training structures 168, 170 trajectory transition state theory (TST) – reaction rate constant 112 – Gibbs (free) energy 113 – transition energy 112 trap-assisted tunneling (TAT) 126, 143 TST see transition state theory (TST) u uncertainty principle 28, 30 v van-der-Waals interactions 70, 71, 73, 177 vanadium 177 vanadium oxide 176 vectors and scalar product 22 Verlet algorithm 66 Vienna ab initio simulation package (VASP) 189 w wave function 18, 25 – plane wave representation 92–96 – real-space grid 91, 92 Wigner-Seitz cells 49, 51 work function 127 Wulff construction 190, 191 www.pdfgrip.com WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA ... certain threedimensional coordinate system For simplicity, we use in this book a simple Cartesian coordinate system In- vitro Materials Design: Modern Atomistic Simulation Methods for Engineers, ... mathematical concepts can skip this part and look up certain points later if necessary In- vitro Materials Design: Modern Atomistic Simulation Methods for Engineers, First Edition Roman Leitsmann, Philipp... calculation rules to obtain the quantities E and