The Handbook of Nanotechnology. Nanometer Structures: Theory, Modeling, and Simulation (SPIE Press Book)

Preface v
Akhlesh Lakhtakia, Pennsylvania State University, USA

Foreword vii
Brian J. Thompson, University of Rochester, USA

Chapter 1 - Editorial
Akhlesh Lakhtakia, Pennsylvania State University, USA

1.1 Introduction

1.2 Coverage

1.3 Concluding remark

Chapter 2 - Sculptured Thin Films
Akhlesh Lakhtakia and Russell Messier, Pennsylvania State University, USA

2.1. Introduction 6

2.2. Genesis 7

2.2.1. Columnar thin films 7

2.2.2. Primitive STFs with nematic morphology 9

2.2.3. Chiral sculptured thin films 9

2.2.4. Sculptured thin films 10

2.3. Electromagnetic fundamentals 11

2.3.1. Linear constitutive relations 11

2.3.2. From the nanostructure to the continuum 13

2.3.3. Electromagnetic wave propagation 16

2.3.4. Reflection and transmission 17

2.4. Dielectric STFs 21

2.4.1. Relative permittivity dyadics 22

2.4.2. Local homogenization 23

2.4.3. Wave propagation 24

2.5. Applications 26

2.5.1. Optical filters 26

2.5.2. Optical fluid sensors 29

2.5.3. Chiral PBG materials 29

2.5.4. Displays 30

2.5.5. Optical interconnects 30

2.5.6. Optical pulse shapers 30

2.5.7. Biochips 30

2.5.8. Other applications 31

2.6. Directions for future research 32

References 33

List of Symbols 41

Chapter 3 - Photonic Bandgap Structures
Joseph W. Haus, The University of Dayton, USA

3.1. Introduction 46

3.2. One-dimensional structures 47

3.2.1. Finite periodic structures: arbitrary angles of incidence 47

3.2.2. Brief summary of infinite periodic structures 51

3.2.3. Finite periodic structures: perpendicular incidence 55

3.2.4. Slowly varying envelope techniques 61

3.2.5. Nonlinear optics in 1D PBGs 62

3.3. Higher dimensions 63

3.3.1. Vector wave equations 64

3.3.2. Two dimensions 65

3.3.3. Dielectric fluctuations 68

3.3.4. Band structure 69

3.3.5. Band eigenfunction symmetry and uncoupled modes 71

3.3.6. Three dimensions 73

3.4. Summary 88

3.5. Appendix A 89

3.6. Appendix B 95

References 98

List of symbols 105

Chapter 4 - Quantum Dots: Phenomenology, Photonic and Electronic Properties, Modeling and Technology
Fredrik Boxberg and Jukka Tulkki, Helsinki University of Technology, Finland

4.1. Introduction 109

4.1.1. What are they? 109

4.1.2. History 111

4.2. Fabrication 112

4.2.1. Nanocrystals 112

4.2.2. Lithographically defined quantum dots 114

4.2.3. Field-effect quantum dots 116

4.2.4. Self-assembled quantum dots 116

4.3. QD spectroscopy 118

4.3.1. Microphotoluminescence 118

4.3.2. Scanning near-field optical spectroscopy 120

4.4. Physics of quantum dots 121

4.4.1. Quantum dot eigenstates 122

4.4.2. Electromagnetic fields 123

4.4.3. Photonic properties 125

4.4.4. Carrier transport 127

4.4.5. Carrier dynamics 129

4.4.6. Dephasing 129

4.5. Modeling of atomic and electronic structure 130

4.5.1. Atomic structure calculations 131

4.5.2. Quantum confinement 132

4.6. QD technology and perspectives 133

4.6.1. Vertical-cavity surface-emitting QD laser 134

4.6.2. Biological labels 134

4.6.3. Electron pump 135

4.6.4. Applications you should be aware of 136

References 137

List of symbols

Chapter 5 - Nanoelectromagnetics of Low-Dimensional Structures
Sergey A. Maksimenko and Gregory Ya. Slepyan, Belarus State University, Belarus

5.1. Introduction 146

5.2. Electron transport in carbon nanotubes 148

5.2.1. Dispersion properties of p-electrons 148

5.2.2. Bloch equation for p-electrons 151

5.3. Linear electrodynamics of carbon nanotubes 153

5.3.1. Dynamic conductivity 153

5.3.2. Effective boundary conditions 156

5.3.3. Surface electromagnetic waves 157

5.3.4. Edge effects 159

5.4. Nonlinear processes in carbon nanotubes 162

5.4.1. Current density spectrum in an isolated CN 163

5.4.2. Negative differential conductivity in an isolated CN 167

5.5. Quantum electrodynamics of carbon nanotubes 170

5.5.1. Maxwell equations for electromagnetic field operators 170

5.5.2. Spontaneous decay of an excited atom in a CN 172

5.6. Semiconductor quantum dot in a classical electromagnetic field 177

5.6.1. Model Hamiltonian 178

5.6.2. Equations of motion 182

5.6.3. QD polarization 183

5.7. Interaction of QD with quantum light 184

5.7.1. Model Hamiltonian 184

5.7.2. Equations of motion 186

5.7.3. Interaction with single-photon states 187

5.7.4. Scattering of electromagnetic Fock qubits 189

5.7.5. Observability of depolarization 192

5.8. Concluding remarks 194

Acknowledgments 194

References 194

List of symbols 203

Chapter 6 - Atomistic Simulation Methods
Pierre A. Deymier, Vivek Kapila and Krishna Muralidharan, University of Arizona, USA

6.1. Introduction 208

6.2. Determininistic atomistic computer simulation methodologies 210

6.2.1. Microcanonical molecular dynamics 210

6.2.2. Canonical ensemble molecular dynamics 211

6.2.3. Other ensembles 215

6.2.4. Interatomic potentials 216

6.2.5. Thermostating a buckyball: an illustrative example 217

6.3. Stochastic atomistic computer simulation methodologies 221

6.3.1. Canonical Monte Carlo 221

6.3.2. Grand canonical Monte Carlo 223

6.3.3. Lattice Monte Carlo 225

6.3.4. Self-assembly of surfactants 226

6.3.5. Kinetic Monte Carlo 230

6.3.6. Application of kinetic MC to self-assembly of protein subcellular nanostructures 230

6.4. Multiscale simulation schemes 233

6.4.1. Coupling of MD and MC simulations 234

6.4.2. Coupling of an atomistic system with a continuum 239

6.5. Concluding remarks 243

References 244

List of symbols 252

Chapter 7 - Nanomechanics
Vijay B. Shenoy, Indian Institute of Science, India

7.1. Overview 256

7.1.1. Introduction 256

7.1.2. Aim and scope 256

7.1.3. Notation 261

7.2. Continuum concepts 261

7.2.1. Forces, equilibrium, and stress tensor 262

7.2.2. Kinematics: deformation and strain tensor 265

7.2.3. Principle of virtual work 268

7.2.4. Constitutive relations 269

7.2.5. Boundary value problems and finite element method 270

7.3. Atomistic models 274

7.3.1. Total energy description 274

7.3.2. Atomistic simulation methods 287

7.4. Mixed models for nanomechanics 295

7.4.1. The quasicontinuum method 295

7.4.2. Augmented continuum theories 302

7.5. Concluding remarks 311

Acknowledgments 311

References 311

List of symbols 316

Chapter 8 - Nanoscale Fluid Mechanics
P. Koumoutsakos, U. Zimmerli, T. Werder, and J. H. Walther, Swiss Federal Institute of Technology, Switzerland

8.1. Introduction 320

8.2. Computational nanoscale fluid mechanics 322

8.2.1. Quantum mechanical calculations 323

8.2.2. Ab initio calculations 324

8.2.3. Atomistic computations 327

8.2.4. Multiscaling: linking macroscopic to atomistic scales 334

8.3. Experiments in nanoscale fluid mechanics 339

8.3.1. Diagnostic techniques for the nanoscale 339

8.3.2. Atomic force microscopy for fluids at the nanoscale 344

8.4. Fluid-solid interfaces at the nanoscale 347

8.4.1. Hydrophobicity and wetting 347

8.4.2. Slip flow boundary conditions 350

8.5. Fluids in confined geometries 355

8.5.1. Flow motion in nanoscale channels 355

8.5.2. Phase transitions of water in confined geometries 360

8.6. Nanofluidic devices 362

8.6.1. Solubilization 363

8.6.2. Nanofluids 363

8.6.3. CNT as sensors and AFM tips 364

8.6.4. Carbon nanotubes as storage devices?adsorption 366

8.6.5. Nanofluidics for microscale technologies 367

8.7. Outlook?go with the flow 371

Acknowledgments 371

References 372

List of Symbols 392

Chapter 9 - Introduction to Quantum Information Theory
Mary Beth Ruskai, Tufts University, USA

9.1. Overview 397

9.1.1. Introduction 397

9.1.2. Encoding information 397

9.1.3. Effective parallelism 398

9.1.4. Choosing a basis 400

9.1.5. Perspective 403

9.2. Basic quantum principles 405

9.2.1. Isolated systems 405

9.2.2. Quantum measurement 406

9.2.3. Mixed states 407

9.2.4. Open systems 409

9.2.5. Notation and Pauli matrices 412

9.2.6. No-cloning principle 413

9.3. Entanglement 414

9.3.1. Bell states and correlations 414

9.3.2. An experiment 415

9.3.3. Bell inequalities and locality 416

9.3.4. An important identity 417

9.3.5. More on entanglement 418

9.4. Quantum computation algorithms 420

9.4.1. The Deutsch?Jozsa problem 420

9.4.2. Grover?s algorithm 422

9.4.3. Period finding via the QFT 425

9.4.4. Implementing the quantum Fourier transform 429

9.5. Other types of quantum information processing 430

9.5.1. Quantum key distribution 430

9.5.2. Quantum cryptography 432

9.5.3. Dense coding 433

9.5.4. Quantum teleportation 434

9.5.5. Quantum communication 435

9.6. Dealing with noise 436

9.6.1. Accessible information 436

9.6.2. Channel capacity 439

9.6.3. Quantum error correction 441

9.6.4. Fault-tolerant computation 444

9.6.5. DFS encoding 445

9.7. Conclusion 446

9.7.1. Remarks 446

9.7.2. Recommendations for further reading 447

Appendix 9.A. Dirac notation 449

Appendix 9.B. Trace and partial trace 450

Appendix 9.C. Singular value and Schmidt decompositions 451

Appendix 9.D. A more complete description 453

9.D.1. Continuous variables 453

9.D.2. The hidden spatial wave function 453

9.D.3. The Pauli principle 454

Acknowledgment 454

References 455

Preface

The Handbook of Nanotechnology series is intended to provide a reference to researchers in nanotechnology, offering readers a combination of tutorial material and review of the state of the art. This volume focuses on modeling and simulation at the nanoscale. Being sponsored by both SPIE, the International Society for Optical Engineering, and the American Society of Mechanical Engineering, its coverage is confined to optical and mechanical topics.

The eight substantive chapters of this volume--entitled Nanometer Structures: Theory, Modeling, and Simulation--cover nanostructured thin films, photonic band-gap structures, quantum dots, carbon nanotubes, atomistic techniques, nanomechanics, nanofluidics, and quantum information processing. Modeling and simulation research on these topics has acquired a sufficient degree of maturity as to merit inclusion. While the intent is to serve as a reference source for expert researchers, there is sufficient content for novice researchers as well. The level of presentation in each chapter assumes a fundamental background at the level of an engineering or science graduate.

I am appreciative of both SPIE and ASME for undertaking this project at a pivotal point in the evolution of nanotechnology, just when actual devices and applications seem poised to spring forth. My employer, Pennsylvania State University, kindly provided me a sabbatical leave-of-absence during the Spring 2003 semester, when the major part of my editorial duties were performed.

All contributing authors cooperated graciously during the various phases of the production of this volume and its contents, and they deserve the applause of all colleagues for putting their normal research and teaching activities aside while writing their chapters for the common good. Tim Lamkins of SPIE Press coordinated the production of this volume promptly and efficiently. I consider myself specially privileged to have worked with all of these fine people.

University Park, PA
Akhlesh Lakhtakia
January 2004