Introduction to Nanomaterials and Devices E-Book

Omar Manasreh

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 650

Veröffentlichungsjahr: 2011

Beschreibung

An invaluable introduction to nanomaterials and their applications Offering the unique approach of applying traditional physics concepts to explain new phenomena, Introduction to Nanomaterials and Devices provides readers with a solid foundation on the subject of quantum mechanics and introduces the basic concepts of nanomaterials and the devices fabricated from them. Discussion begins with the basis for understanding the basic properties of semiconductors and gradually evolves to cover quantum structures--including single, multiple, and quantum wells--and the properties of nanomaterial systems, such as quantum wires and dots. Written by a renowned specialist in the field, this book features: * An introduction to the growth of bulk semiconductors, semiconductor thin films, and semiconductor nanomaterials * Information on the application of quantum mechanics to nanomaterial structures and quantum transport * Extensive coverage of Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein stastistics * An in-depth look at optical, electrical, and transport properties * Coverage of electronic devices and optoelectronic devices * Calculations of the energy levels in periodic potentials, quantum wells, and quantum dots Introduction to Nanomaterials and Devices provides essential groundwork for understanding the behavior and growth of nanomaterials and is a valuable resource for students and practitioners in a field full of possibilities for innovation and invention.

Leseprobe

Table of Contents

Title Page

Copyright

Dedication Page

Preface

Fundamental Constants

Chapter 1: Growth of Bulk, Thin Films, and Nanomaterials

1.1 Introduction

1.2 Growth of Bulk Semiconductors

1.3 Growth of Semiconductor Thin Films

1.4 Fabrication and Growth of Semiconductor Nanomaterials

1.5 Colloidal Growth of Nanocrystals

Bibliography

Chapter 2: Application of Quantum Mechanics to Nanomaterial Structures

2.1 Introduction

2.2 The de Broglie Relation

2.3 Wave Functions and Schrödinger Equation

2.4 Dirac Notation

2.5 Variational Method

2.6 Stationary States of a Particle in a Potential Step

2.7 Potential Barrier with a Finite Height

2.8 Potential Well with an Infinite Depth

2.9 Finite Depth Potential Well

2.10 Unbound Motion of a Particle (E > V0) in a Potential Well With a Finite Depth

2.11 Triangular Potential Well

2.12 Delta Function Potentials

2.13 Transmission in Finite Double Barrier Potential Wells

2.14 Envelope Function Approximation

2.15 Periodic Potential

2.16 Effective Mass

Bibliography

Chapter 3: Density of States in Semiconductor Materials

3.1 Introduction

3.2 Distribution Functions

3.3 Maxwell–Boltzmann Statistic

3.4 Fermi–Dirac Statistics

3.5 Bose–Einstein Statistics

3.6 Density of States

3.7 Density of States of Quantum Wells, Wires, and Dots

3.8 Density of States of Other Systems

Bibliography

Chapter 4: Optical Properties

4.1 Fundamentals

4.2 Lorentz and Drude Models

4.3 The Optical Absorption Coefficient of the Interband Transition in Direct Band Gap Semiconductors

4.4 The Optical Absorption Coefficient of the Interband Transition in Indirect Band Gap Semiconductors

4.5 The Optical Absorption Coefficient of the Interband Transition in Quantum Wells

4.6 The Optical Absorption Coefficient of the Interband Transition in Type II Superlattices

4.7 The Optical Absorption Coefficient of the Intersubband Transition in Multiple Quantum Wells

4.8 The Optical Absorption Coefficient of the Intersubband Transition in GaN/AlGaN Multiple Quantum Wells

4.9 Electronic Transitions in Multiple Quantum Dots

4.10 Selection Rules

4.11 Excitons

4.12 Cyclotron Resonance

4.13 Photoluminescence

4.14 Basic Concepts of Photoconductivity

Bibliography

Chapter 5: Electrical and Transport Properties

5.1 Introduction

5.2 The Hall Effect

5.3 Quantum Hall and Shubnikov- Haas Effects

5.4 Charge Carrier Transport in Bulk Semiconductors

5.5 Boltzmann Transport Equation

5.6 Derivation of Transport Coefficients Using the Boltzmann Transport Equation

5.7 Scattering Mechanisms in Bulk Semiconductors

5.8 Scattering in a Two-Dimensional Electron Gas

5.9 Coherence and Mesoscopic Systems

Bibliography

Chapter 6: Electronic Devices

6.1 Introduction

6.2 Schottky Diode

6.3 Metal–Semiconductor Field-Effect Transistors (MESFETs)

6.4 Junction Field-Effect Transistor (JFET)

6.5 Heterojunction Field-Effect Transistors (HFETs)

6.6 GaN/AlGaN Heterojunction Field-Effect Transistors (HFETs)

6.7 Heterojunction Bipolar Transistors (HBTs)

6.8 Tunneling Electron Transistors

6.9 The – Junction Tunneling Diode

6.10 Resonant Tunneling Diodes

6.11 Coulomb Blockade

6.12 Single-Electron Transistor

Bibliography

Chapter 7: Optoelectronic Devices

7.1 Introduction

7.2 Infrared Quantum Detectors

7.3 Light-Emitting Diodes

7.4 Semiconductor Lasers

Bibliography

Appendix A: Derivation of Heisenberg Uncertainty Principle

Appendix B: Perturbation

Bibliography

Appendix C: Angular Momentum

Appendix D: Wentzel-Kramers-Brillouin (WKB) Approximation

Bibliography

Appendix E: Parabolic Potential Well

Bibliography

Appendix F: Transmission Coefficient in Superlattices

Appendix G: Lattice Vibrations and Phonons

Appendix H: Tunneling Through Potential Barriers

Bibliography

Index

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Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Manasreh, Mahmoud Omar.

Introduction to nanomaterials and devices / Omar Manasreh. –1st ed.

p. cm.

Includes bibliographical references.

ISBN 978-0-470-92707-6 (hardback)

1. Nanostructured materials. 2. Optoelectronic devices. 3. Semiconductor nanocrystals.

4. Quantum electronics. I. Title.

[DNLM: 1. Anti-Bacterial Agents. 2. Drug Resistance, Microbial. QV 350] RM267.S55513 2011

TA418.9.N35M37 2012

620.1'15–dc23

2011022713

To my wife Taeko who focuses me on the essentials

Preface

Investigating materials and devices at the nanoscale level has become the topic of discussion in our daily life even at the dinner table. The behavior of nanoscale materials is close, to atomic behavior rather than that of bulk materials. This leads to vivid properties and well-defined concepts, even though the description of these properties can be understood in terms of quantum mechanics, which provides only a fuzzy picture. The growth of nanomaterials, such as quantum dots (also known as atomic designers), has the tendency to be viewed as an art rather than science. These nanostructures have changed our view of Nature. The invention of the transmission electron microscope, scanning electron microscope, and atomic force microscope provided a method for us to observe materials down to the atomic scale, and yet these microscopes are based on quantum mechanics concepts.

To understand quantum wells, wires, and dots, it is imperative to possess a basic knowledge of quantum mechanics and how one can apply the Schrödinger equation to calculate the quantized electronic energy levels in such a tiny structure. This requirement is due to the fact that classical mechanics is limited in providing an explanation to almost all the properties of the nanomaterials. Quantum mechanics, however, can provide an insight and reasonable predictions of phenomena observed in case of semiconductor nanomaterials. This book is by no means a complete or ideal textbook, but it is one step in a changing field full of limitless possibilities of innovations and inventions.

This book is designed to cover topics on the subject of nanomaterials growth, electrical and optical properties of nanomaterials, and devices based on these nanomaterials. It is designed to provide an introduction to nanomaterials and devices to graduate students in electrical engineering, materials engineering, and applied physics. Advanced undergraduate students as well as researchers in the field of semiconductor heterojunctions and nanostructures may benefit from it. I imagine that graduate students, who use this textbook in their studies, will continue to use it as a reference book after their graduation.

The basic properties of bulk and nanomaterial systems are discussed in order to point out the advantages of nanomaterials. This book is structured such that the discussion starts with bulk crystalline materials, which is the basis for understanding the basic properties of semiconductor. The discussion then evolves to cover quantum structures, such as single and multiple quantum wells. Then, attempts are made to discuss and explain the properties of nanomaterial systems, such as quantum wires and dots. However, since the field is still in its infancy, there are too many unknowns and many of the properties of the nanomaterial systems are yet to be understood or have even reached their full potential. Thus, the discussion regarding quantum wires and dots is limited to the more mature properties of these quantum structures.

Topics covered include an introduction to growth issues, quantum mechanics, quantization of electronic energy levels in periodic potentials, tunneling, distribution functions and density of states, optical and electronic properties, and devices. The chapters are devoted to the growth of bulk materials and nanomaterials; the introduction of quantum mechanics; calculations of the energy levels in periodic potentials, quantum wells, and quantum dots; derivation of the density of states in bulk materials, quantum wells, wires, quantum dots, and the density of states under the influence of electric or magnetic fields; optical properties; electrical and transport properties; electronic devices based on heterojunctions and nanostructures such as ohmic and Schottky contacts, diodes, resonant tunneling diodes, MODFETs, HFETs, Coulomb blockade, and single-electron transistors (known as SETs); and optoelectronic devices such as light-emitting diodes, photodetectors based on quantum wells and quantum dots, edge-emitting lasers, VCSELs, quantum cascade lasers, and laser diodes based on quantum dots. End of chapter problems, appendices, tables, and references are included.

Students registering for courses based on this textbook are required to have a basic knowledge of semiconductor materials and devices. Although knowledge in quantum mechanics is not required, it is, however, recommended that the students take undergraduate physics courses, such as university physics and/or modern physics. Chapter 1 of this book covers the growth of various material systems ranging from bulk materials to nanorods. Chapter 2 covers the basic formalism of quantum mechanics needed for a student in electrical engineering to grasp the basic idea of how to calculate the energy levels in a simple quantum well. To understand and appreciate the beauty of quantum transport in quantum structures, the readers must have some knowledge of the classical-type transport. This leads us to focus on both quantum transport, such as tunneling and coherent transport in mesoscopic systems, and classical transport, such as Boltzmann transport equation formalisms. Density of states and distribution functions are discussed in Chapter 3. Chapter 4 focuses on the optical properties, while Chapter 5 is directed toward understanding the electrical properties. In Chapter 6, we discuss several electronic devices, and optoelectronic devices are introduced in Chapter 7.

When an electronic or optoelectronic device is under the influence of an applied electric field and/or photonic excitation, the device is no longer at equilibrium, and its transport properties become more complicated. The limits of various transport regimes, which are classified according to the electron phase coherent length and compared to the de Broglie wavelength, are discussed in Chapter 5. Various scattering mechanisms, which dominate the classical regime, are also discussed. When a nanomaterial possesses a capacitance on the order of atto Farad, a new transport phenomenon occurs, which is known as Coulomb blockade. This phenomenon, in conjunction with the quantum tunneling effect, forms the basis for single-electron transistors. Discussion regarding this new class of devices is presented in Chapter 6. While these devices have the potential to revolutionize the current technology, it should be pointed out that current technology is still based on carrier-injected and CMOS devices, in which transport is dominated by carrier scattering rather than by ballistic or coherent transports.

In addition to electronic devices, a new generation of optoelectronic devices is under intense research. Recently, we heard of topics such as long-wavelength infrared detectors based on intersubband transitions, edge-emitting quantum well laser diode, vertical cavity surface-emitting lasers, and quantum cascade lasers. All these devices are discussed in Chapte 7.

Excitons play a major role in optoelectronic and photonic devices. Theoretically, the exciton binding energy in a quantum well is larger than that of excitons in the constituent bulk materials by a factor of four as discussed in Chapter 4. Furthermore, it is predicted that the exciton binding energies are even higher in quantum wires and dots. This can be translated to very fast optoelectronic devices that can operate at room temperature. We have presented a detailed discussion and derivation of the exciton binding energies in direct band gap bulk semiconductors, quantum wells, and quantum dots.

Omar Manasreh

University of Arkansas

Spring, 2011

Chapter 1

Growth of Bulk, Thin Films, and Nanomaterials

1.1 Introduction

The evolution of the growth of the high quality semiconductor materials from bulk to nanomaterials enables researchers to fabricate devices with a continued enhancement of the properties and performance. In this chapter, the discussion is directed toward the growth of semiconductor single crystals by using various techniques ranging from bulk crystal growth to the epitaxial growth of quantum dots and core/shell nanocrystals. Bulk crystal growth techniques include liquid-encapsulated Czochralski (LEC), horizontal Bridgman (HB), liquid-encapsulated Kyropoulos (LEK), and vertical gradient freezing (VGF) methods. There are many improved methods available for the growth of bulk semiconductor crystals. For example, magnetic LEC, direct synthesis-LEC, pressure-controlled LEC, and thermal baffle LEC methods are all variations of the original LEC technique, but with improved growth conditions. Other bulk growth techniques include dynamic gradient freezing, horizontal gradient freezing, magnetic LEK, and vertical Bridgman methods. The widely used epitaxial growth techniques are the molecular beam epitaxy (MBE), metal–organic chemical vapor deposition (MOCVD) techniques, and liquid-phase epitaxy (LPE). The word epitaxy is a Greek origin composed of two parts, epi (placed or resting on) and taxis (arrangement). Thus, epitaxy refers to the formation of single-crystal nanomaterials on top of a substrate. The techniques used to grow bulk materials are usually equilibrium growth techniques, while the epitaxial growth techniques, used for the production of nanomaterials, are considered nonequilibrium techniques.

The growth techniques of bulk semiconductor crystals are designed to produce large-volume crystals under equilibrium conditions with almost no flexibility in the production of alloy composition. These techniques, however, lack the ability to produce heterojunctions, ternary or quaternary semiconductor compounds needed for advanced semiconductor devices. Silicon single-crystal boules as large as 12 in. (∼300 mm) in diameters and over a meter in length are currently produced by LEC technique. GaAs single-crystal boule diameter is usually smaller than that of Si boules. Epitaxial growth is performed on submillimeter thick substrates cut from these bulk boules.

The process of preparing the boules into wafers that are used as substrates for epitaxial growth is called the wafering process. This process includes slicing, lapping, polishing, and cleaning. Since most wafers are used as substrates for epitaxial growth, the wafering process technology and the bulk crystal growth are very important for successful epitaxial growth. For example, the surface orientation accuracy, which is determined during the slicing process, affects the morphology of the epitaxial layer surface. Wafer flatness is another important parameter for high quality epitaxial growth. Single- or double-sided polished wafer flatness is defined by specific parameters, such as total thickness variation, total indicator reading, or focal plane deviation. These parameters are needed for precise photolithography. The surface roughness is also important aspect of the wafering process, since surface roughness in a subnanometer scale is required for many epitaxially grown nanomaterials.

Epitaxial growth, such as MBE and MOCVD growth, requires ready-to-use wafers. For example, thermal oxidation and/or ultraviolet/ozone oxidation processes have been effective in producing thin oxide layers, which protect the wafer surface. These oxide layers can be removed by heating prior to epitaxial growth. Packaging the wafers in nitrogen gas is an effective method against residual oxidation of polished surfaces during storage.

Crystallographic orientation of the wafers is very important for the MBE and MOCVD growth methods. The orientation is determined by Miller indices. These indices are defined as the smallest possible integers with the same rations as the inverse of the intersection of a plane with a set of axes defined by the unit vectors of the crystal. An illustration of this concept is shown in Fig. 1.1 for a cubic crystal where a plane is intersecting x-, y-, and z-axes at a distance 2a, 3a, and 4a, respectively, where a is the interatomic distance. To obtain the miller indices, one may follow the following steps: identify the intersections of the plane with the axes (in the case of Fig. 1.1, these intersections are 2, 3, and 4); take the inverse of these intercepts, which results in 1/2, 1/3, and 1/4; find the smallest multiplier factor of the denominators, which 12; and multiply the factor the inverse of the intercepts to give 6, 4, and 3. These last numbers are called miller indices, and they are usually written in the following format (643) to indicate the crystallographic orientation of the wafers. If the intercept is negative, then the negative sign “−” is usually place on the top of the index. A group of Miller indices, such as (100), (010), (001), , and , is given the following notation {100}. For hexagonal crystal structure, the Miller indices are (a1a2a3c).

Figure 1.1 A plane intersecting the x-, y-, and z-axes at 2a, 3a, and 4a, respectively, to determine the Miller indices. The interatomic distance is designated as “a.”

Most of the semiconductor materials are produced by artificial methods. Semiconductor binary, ternary, quaternary alloys (Fig. 1.2), heterojunctions, and other quantum structures such as superlattices and quantum dots are currently grown by two main epitaxial growth techniques, namely MBE and MOCVD. These growth techniques enable the synthesis of high quality single-crystal nanomaterials deposited layer by layer on suitable substrates.

Figure 1.2 The band gap as a function of the lattice constant plotted for several binary semiconductors. Silicon and Germanium are also shown. The solid lines represent the ternary compounds.