Quantum Mechanics for Nanostructures

by Vladimir V. Mitin, Dmitry I. Sementsov, Nizami Z. Vagidov

Overview

The properties of new nanoscale materials, their fabrication and applications, as well as the operational principles of nanodevices and systems, are solely determined by quantum-mechanical laws and principles. This textbook introduces engineers to quantum mechanics and the world of nanostructures, enabling them to apply the theories to numerous nanostructure problems. The textbook covers the fundamentals of quantum mechanics, including uncertainty relations, the Schrödinger equation, perturbation theory, and tunneling. These are then applied to a quantum dot, the smallest artificial atom, and compared to hydrogen, the smallest atom in nature. Nanoscale objects with higher dimensionality, such as quantum wires and quantum wells, are introduced, as well as nanoscale materials and nanodevices. Numerous examples throughout the text help students to understand the material.

Product Details

ISBN-13:	9780521763660
Publisher:	Cambridge University Press
Publication date:	05/20/2010
Pages:	448
Product dimensions:	7.40(w) x 9.70(h) x 1.00(d)

About the Author

Vladimir V. Mitin is SUNY Distinguished Professor at the Department of Electrical Engineering and Adjunct Professor of Physics at the University at Buffalo, The State University of New York. He is the author of eight textbooks and monographs and more than 490 professional publications and presentations.

Dmitry I. Sementsov is Professor of Physics at Ulyanovsk State University, Russia. He is the author of more than 420 papers in peer-reviewed journals.

Nizami Z. Vagidov is Research Assistant Professor of Electrical Engineering at the University at Buffalo, The State University of New York. He is the author of about 90 professional publications in the fields of solid-state electronics, nanoelectronics, and nanotechnology.

Table of Contents

Preface ix

List of notation xiii

1 The nanoworld and quantum physics 1

1.1 A review of milestones in nanoscience and nanotechnology 1

1.2 Nanostructures and quantum physics 4

1.3 Layered nanostructures and superlattices 8

1.4 Nanoparticles and nanoclusters 10

1.5 Carbon-based nanomaterials 14

2 Wave-particle duality and its manifestation in radiation and particle behavior 19

2.1 Blackbody radiation and photon gas 19

2.2 The quantum character of the interaction of radiation with matter 31

2.3 Wave properties of particles 39

2.4 The uncertainty relations 47

2.5 The world of the nanoscale and the wavefunction 52

2.6 The Schrödinger equation 56

2.7 Summary 63

2.8 Problems 63

3 Layered nanostructures as the simplest systems to study electron behavior in a one-dimensional potential 65

3.1 The motion of a free electron in vacuum 66

3.2 An electron in a potential well with infinite barriers 69

3.3 An electron in a potential well with finite barriers 75

3.4 Propagation of an electron above the potential well 84

3.5 Tunneling: propagation of an electron in the region of a potential barrier 89

3.6 Summary 101

3.7 Problems 101

4 Additional examples of quantized motion 105

4.1 An electron in a rectangular potential well (quantum box) 105

4.2 An electron in a spherically-symmetric potential well 109

4.3 Quantum harmonic oscillators 115

4.4 Phonons 126

4.5 Summary 133

4.6 Problems 134

5 Approximate methods of finding quantum states 136

5.1 Stationary perturbation theory for a system with non-degenerate states 136

5.2 Stationary perturbation theory for a system with degenerate states 141

5.3 Non-stationary perturbation theory 142

5.4 The quasiclassical approximation 148

5.5 Summary 151

5.6 Problems 152

6 Quantum states in atoms and molecules 155

6.1 The hydrogen atom 155

6.2 The emission spectrum of the hydrogen atom 166

6.3 The spin of an electron 169

6.4 Many-electron atoms 173

6.5 The wavefunction of a system of identical particles 181

6.6 The hydrogen molecule 184

6.7 Summary 190

6.8 Problems 191

7 Quantization in nanostructures 193

7.1 The number and density of quantum states 193

7.2 Dimensional quantization and low-dimensional structures 199

7.3 Quantum states of an electron in low-dimensional structures 204

7.4 The number of states and density of states for nanostructures 210

7.5 Double-quantum-dot structures (artificial molecules) 218

7.6 An electron in a periodic one-dimensional potential 229

7.7 A one-dimensional superlattice of quantum dots 241

7.8 A three-dimensional superlattice of quantum dots 250

7.9 Summary 254

7.10 Problems 255

8 Nanostructures and their applications 258

8.1 Methods of fabrication of nanostructures 258

8.2 Tools for characterization with nanoscale resolution 269

8.3 Selected examples of nanodevices and systems 282

Appendix A Classical dynamics of particles and waves 310

A.l Classical dynamics of particles 311

A.2 Oscillatory motion of a particle 321

A.3 Summary 334

A.4 Problems 335

Appendix B Electromagnetic fields and waves 338

B.l Equations of an electromagnetic field 338

B.2 Electromagnetic waves 345

B.3 Reflection of a plane wave from the interface between two media 353

B.4 Light and its wave properties 362

B.5 Summary 374

B.6 Problems 375

Appendix C Crystals as atomic lattices 378

C.l Crystalline structures 379

C.2 The nature of attraction and repulsion forces 385

C.3 Degenerate electron gas 392

C.4 Waves in a crystalline lattice and normal coordinates 396

C.5 The energy spectrum of an electron in a crystal 400

C.6 Electrons in semiconductors 411

C.7 Summary 420

C.8 Problems 421

Appendix D Tables of units 423

Index 427