Nanotechnology: A Crash Course (SPIE Tutorial Texts Vol. TT86)

Tutorial Texts Series • Optical Design of Microscopes, George H. Seward, Vol. TT88 • Analysis and Evaluation of Sampled Imaging Systems, Richard H. Vollmerhausen, Donald A. Reago, Jr., Ronald G. Driggers, Vol. TT87 • Nanotechnology: A Crash Course, Raúl J. Martín-Palma, Akhlesh Lakhtakia, Vol. TT86 • Direct-Detection LADAR Systems, Richard D. Richmond, Stephen C. Cain, Vol. TT85 • Optical Design: Applying the Fundamentals, Max J. Riedl, Vol. TT84 • Infrared Optics and Zoom Lenses, Second Edition, Allen Mann, Vol. TT83 • Optical Engineering Fundamentals, Second Edition, Bruce H. Walker, Vol. TT82 • Fundamentals of Polarimetric Remote Sensing, John Schott, Vol. TT81 • The Design of Plastic Optical Systems, Michael P. Schaub, Vol. TT80 • Radiation Thermometry: Fundamentals and Applications in the Petrochemical Industry, Peter Saunders, Vol. TT78 • Matrix Methods for Optical Layout, Gerhard Kloos, Vol. TT77 • Fundamentals of Infrared Detector Materials, Michael A. Kinch, Vol. TT76 • Practical Applications of Infrared Thermal Sensing and Imaging Equipment, Third Edition, Herbert Kaplan, Vol. TT75 • Bioluminescence for Food and Environmental Microbiological Safety, Lubov Y. Brovko, Vol. TT74 • Introduction to Image Stabilization, Scott W. Teare, Sergio R. Restaino, Vol. TT73 • Logic-based Nonlinear Image Processing, Stephen Marshall, Vol. TT72 • The Physics and Engineering of Solid State Lasers, Yehoshua Kalisky, Vol. TT71 • Thermal Infrared Characterization of Ground Targets and Backgrounds, Second Edition, Pieter A. Jacobs, Vol. TT70 • Introduction to Confocal Fluorescence Microscopy, Michiel Müller, Vol. TT69 • Artificial Neural Networks: An Introduction, Kevin L. Priddy and Paul E. Keller, Vol. TT68 • Basics of Code Division Multiple Access (CDMA), Raghuveer Rao and Sohail Dianat, Vol. TT67 • Optical Imaging in Projection Microlithography, Alfred Kwok-Kit Wong, Vol. TT66 • Metrics for High-Quality Specular Surfaces, Lionel R. Baker, Vol. TT65 • Field Mathematics for Electromagnetics, Photonics, and Materials Science, Bernard Maxum, Vol. TT64 • High-Fidelity Medical Imaging Displays, Aldo Badano, Michael J. Flynn, and Jerzy Kanicki, Vol. TT63 • Diffractive Optics–Design, Fabrication, and Test, Donald C. O’Shea, Thomas J. Suleski, Alan D. Kathman, and Dennis W. Prather, Vol. TT62 • Fourier-Transform Spectroscopy Instrumentation Engineering, Vidi Saptari, Vol. TT61 • The Power- and Energy-Handling Capability of Optical Materials, Components, and Systems, Roger M. Wood, Vol. TT60 • Hands-on Morphological Image Processing, Edward R. Dougherty, Roberto A. Lotufo, Vol. TT59 • Integrated Optomechanical Analysis, Keith B. Doyle, Victor L. Genberg, Gregory J. Michels, Vol. TT58 • Thin-Film Design: Modulated Thickness and Other Stopband Design Methods, Bruce Perilloux, Vol. TT57 • Optische Grundlagen für Infrarotsysteme, Max J. Riedl, Vol. TT56 • An Engineering Introduction to Biotechnology, J. Patrick Fitch, Vol. TT55 • Image Performance in CRT Displays, Kenneth Compton, Vol. TT54 • Introduction to Laser Diode-Pumped Solid State Lasers, Richard Scheps, Vol. TT53 • Modulation Transfer Function in Optical and Electro-Optical Systems, Glenn D. Boreman, Vol. TT52 • Uncooled Thermal Imaging Arrays, Systems, and Applications, Paul W. Kruse, Vol. TT51 • Fundamentals of Antennas, Christos G. Christodoulou and Parveen Wahid, Vol. TT50 • Basics of Spectroscopy, David W. Ball, Vol. TT49 • Optical Design Fundamentals for Infrared Systems, Second Edition, Max J. Riedl, Vol. TT48 • Resolution Enhancement Techniques in Optical Lithography, Alfred Kwok-Kit Wong, Vol. TT47 • Copper Interconnect Technology, Christoph Steinbrüchel and Barry L. Chin, Vol. TT46 • Optical Design for Visual Systems, Bruce H. Walker, Vol. TT45

Tutorial Texts in Optical Engineering Volume TT86

Bellingham, Washington USA

Library of Congress Cataloging-in-Publication Data

Martín-Palma, Raúl J. Nanotechnology : a crash course / Raúl J. Martín-Palma and Akhlesh Lakhtakia. p. cm. – (Tutorial texts in optical engineering ; v. TT 86) Includes bibliographical references and index. ISBN 978-0-8194-8075-0 1. Nanotechnology. I. Lakhtakia, A. (Akhlesh), 1957- II. Title. T174.7.M358 2010 620 0.5–dc22 2010009455

Published by SPIE P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1 360.676.3290 Fax: +1 360.647.1445 Email: [email protected] Web: http://spie.org

c 2010 Society of Photo-Optical Instrumentation Engineers Copyright All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher. The content of this book reflects the work and thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. Printed in the United States of America.

D EDICATION To such wonderful megawords in the English language as antidisestablishmentarianism honorificabilitudinitatibus nanobioinfocognotechnology pneumonoultramicroscopicsilicovolcanoconiosis and supercalifragilisticexpialidocious

Introduction to the Series Since its inception in 1989, the Tutorial Texts (TT) series has grown to more than 85 titles covering many diverse fields of science and engineering. The initial idea for the series was to make material presented in SPIE short courses available to those who could not attend and to provide a reference text for those who could. Thus, many of the texts in this series are generated by augmenting course notes with descriptive text that further illuminates the subject. In this way, the TT becomes an excellent stand-alone reference that finds a much wider audience than only short course attendees. Tutorial Texts have grown in popularity and in the scope of material covered since 1989. They no longer necessarily stem from short courses; rather, they are often generated independently by experts in the field. They are popular because they provide a ready reference to those wishing to learn about emerging technologies or the latest information within their field. The topics within the series have grown from the initial areas of geometrical optics, optical detectors, and image processing to include the emerging fields of nanotechnology, biomedical optics, fiber optics, and laser technologies. Authors contributing to the TT series are instructed to provide introductory material so that those new to the field may use the book as a starting point to get a basic grasp of the material. It is hoped that some readers may develop sufficient interest to take a short course by the author or pursue further research in more advanced books to delve deeper into the subject. The books in this series are distinguished from other technical monographs and textbooks in the way in which the material is presented. In keeping with the tutorial nature of the series, there is an emphasis on the use of graphical and illustrative material to better elucidate basic and advanced concepts. There is also heavy use of tabular reference data and numerous examples to further explain the concepts presented. The publishing time for the books is kept to a minimum so that the books will be as timely and up-to-date as possible. Furthermore, these introductory books are competitively priced compared to more traditional books on the same subject. When a proposal for a text is received, each proposal is evaluated to determine the relevance of the proposed topic. This initial reviewing process has been very helpful to authors in identifying, early in the writing process, the need for additional material or other changes in approach that would serve to strengthen the text. Once a manuscript is completed, it is peer reviewed to ensure that chapters communicate accurately the essential ingredients of the science and technologies under discussion. It is my goal to maintain the style and quality of books in the series and to further expand the topic areas to include new emerging fields as they become of interest to our reading audience. James A. Harrington Rutgers University

Contents To the Reader ................................................................................................... xiii Acknowledgments ........................................................................................... xv Nomenclature ................................................................................................... xvii Chapter 1

Introduction ....................................................................................

1.1 Definitions .......................................................................................................... 1.2 What Is Nanotechnology, and What Should We Expect from It?.... 1.3 Nanotechnology and Society........................................................................ References ..................................................................................................................... Bibliography ................................................................................................................. Chapter 2

1 2 6 8 9

Low-Dimensional Structures.......................................................... 11

2.1 Brief Survey of Quantum Mechanics ........................................................ 2.2 Two-Dimensional Structures: Quantum Wells ....................................... 2.3 One-Dimensional Structures: Quantum Wires and Nanowires ........ 2.4 Zero-Dimensional Structures: Quantum Dots and Nanodots ............ 2.5 Chapter Summary ............................................................................................ References ..................................................................................................................... Bibliography ................................................................................................................. Chapter 3

1

12 14 20 25 28 29 29

Properties of Nanostructures......................................................... 31

3.1 Band Diagrams.................................................................................................. 3.2 Electrical-Transport Properties .................................................................... 3.3 Thermal-Transport Properties ...................................................................... 3.4 Magnetic Properties......................................................................................... 3.5 Optical Properties............................................................................................. 3.6 Mechanical Properties .................................................................................... 3.7 Chapter Summary ............................................................................................ References ..................................................................................................................... Bibliography ................................................................................................................. ix

32 33 38 39 42 47 49 50 51

x

Contents

Chapter 4

Nanofabrication .............................................................................. 53

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

53 57 58 59 60 63 63

Physical Vapor Deposition ............................................................................ Chemical Vapor Deposition .......................................................................... Atomic Layer Deposition .............................................................................. Molecular Beam Epitaxy ............................................................................... Nanolithography ............................................................................................... Nano-imprint Lithography ............................................................................ Scanning Probe Lithography ........................................................................ Focused Ion-Beam Technique, Proton-Beam Writing, and Ion-Beam Sculpting ......................................................................................... 4.9 Self-Assembly, Self-Organization, and Self-Assembled Monolayers ......................................................................................................... 4.10 Langmuir–Blodgett Method ......................................................................... 4.11 Layer-by-Layer Assembly ............................................................................ 4.12 Other Techniques.............................................................................................. References ..................................................................................................................... Bibliography .................................................................................................................

Chapter 5

6.1

6.2

6.3 6.4 6.5 6.6 6.7 6.8

67 68 70 72 73 74

Characterization of Nanostructures and Nanomaterials ............... 77

5.1 Electron Microscopy ....................................................................................... 5.2 Other Electron-Based Techniques .............................................................. 5.3 Spectroscopic Techniques ............................................................................. 5.4 Scanning Probe Microscopy ......................................................................... 5.5 Magnetic Resonance Techniques ................................................................ 5.6 Ion-Based Techniques (RBS, PIXE, ERDA, SIMS, NRA) ............... 5.7 Other Techniques.............................................................................................. References ..................................................................................................................... Bibliography ................................................................................................................. Chapter 6

65

77 81 81 85 86 87 90 92 93

Nanomaterials and Applications .................................................... 95

Carbon Nanostructures ................................................................................... 6.1.1 Spherical fullerenes ............................................................................ 6.1.2 Carbon nanotubes ............................................................................... 6.1.3 Other carbonic nanomaterials ......................................................... Porous Nanomaterials ..................................................................................... 6.2.1 Porous silicon ....................................................................................... 6.2.2 Other porous nanomaterials ............................................................ Sculptured Thin Films .................................................................................... Aerogels, etc. ..................................................................................................... Semiconductor Quantum Dots..................................................................... Langmuir–Blodgett Films ............................................................................. Nanowires, Nanorods, and Nanopillars .................................................... Polymer Nanocomposites ..............................................................................

95 95 97 100 101 101 104 105 108 112 115 117 122

Contents

xi

References ..................................................................................................................... 125 Bibliography ................................................................................................................. 126 Chapter 7

Future Prospects ............................................................................ 129

7.1 Avenues of Promise ......................................................................................... 7.2 The Evolution of Nanotechnology ............................................................. 7.3 Balancing of Risk ............................................................................................. References ..................................................................................................................... Bibliography .................................................................................................................

129 130 132 133 133

Index ................................................................................................................... 135

To the Reader Suppose that you recently graduated with a B.S. degree in science or engineering and will commence your first professional employment tomorrow. Earlier this afternoon, your manager called to ask if you know something about nanotechnology, so that tomorrow you can begin developing an internal proposal for your division. But either your college did not offer a course on nanotechnology or you decided not to take one. You need a crash course in nanotechnology, just to get you off the ground. Suppose that you are a doctoral student in a department whose candidacy examination requires you to write a 5–10-page research proposal on an emerging topic assigned by the faculty committee. Suppose that your assigned topic intersects with nanotechnology, but all that you know about nanotechnology came from a couple of hour-long graduate seminars that you attended the previous semester. You need a crash course in nanotechnology, not only to write an impressive introduction but also to acquaint yourself with terminology to conduct efficient searches on Google Scholar, Web of Science, Scopus, etc. Suppose that you are a post-doctoral researcher at either an academic or an industrial research institution. Your supervisor has asked you to advise a shining undergraduate student for a summer project in nanotechnology, although the focus of your own research is elsewhere. You need a crash course in nanotechnology, to start the student off in a promising direction. Suppose that you are a new assistant professor. Your departmental head advises that your research proposal to a government program to assist new faculty members in beginning research programs lacks that “wow” factor that would virtually guarantee success. “Put in a nano angle,” you are told. You need a crash course in nanotechnology, to clothe your proposal in the glory of “nano.” Suppose that you are a middle-aged professor undergoing a midlife crisis. Instead of changing your family or lifestyle, you may choose to change your research focus to an emerging research area. You need a crash course in nanotechnology, to assess your current resources and future needs. With your particular need in mind, we persuaded SPIE Press to publish our short and readable introduction to nanotechnology. While Nanotechnology: A Crash Course is unlikely to convert you overnight into a nanostar, it would meet your immediate need and very likely help you steer your professional life in a new direction. xiii

xiv

To the Reader

Suppose that you simply have some time on your hands and wish to enrich your mind. But your financial health does not permit you to travel to a remote part of our planet or to buy an audio or video course on an ancient civilization. You, too, may like to read Nanotechnology: A Crash Course. Borrow it from a public library, buy yourself a hard copy, or purchase it as an eBook from the SPIE Digital Library. Raúl J. Martín-Palma Madrid, Spain Akhlesh Lakhtakia University Park, PA, USA

Acknowledgments Nanotechnology encompasses so many traditional disciplines that numerous mentors, colleagues, and students are indirectly responsible for our selection and treatment of topics in Nanotechnology: A Crash Course. To all of these ladies and gentlemen: Thank you. We were successful in persuading a few technoscientists to read early versions of this book and provide us feedback. The first two among them are Russell Messier (The Pennsylvania State University), whose knowledge and understanding of thin-film morphology is legendary, and Carlo Pantano (The Pennsylvania State University), who has his finger on the pulse of materials research. Next come Fei Wang (Micron Technologies, Inc.) and Ginés Lifante (Universidad Autónoma de Madrid), both of whom have surveyed nanotechnology for various projects. Finally, we thank Muhammad Faryad (The Pennsylvania State University) for providing us the perspective of a graduate student. Unhappy readers are requested to lob rotten eggs and tomatoes at us, but not at these fine gentlemen whose only fault is that they allowed us to befriend them. Two reviewers, both unknown to us, kindly went through a draft. We were able to incorporate most of their invaluable suggestions, but noted the remainder for another book that we may write—not for another 10 years, however. We thank Leah Budin for redrawing several figures for this book. At SPIE Press, Tim Lamkins encouraged us to write this book, Beth Kelley assisted in obtaining the permissions for reprinted figures, and Dara Burrows shepherded its publication, including going through the manuscript with a fine-tooth comb. We acknowledge our debt of gratitude to all three of them.

xv

Nomenclature A acc An ~a1 , ~a2 B0 (Bx , By , Bz ) c C ~c d e E EF Eg EM En Eex Eexc (Enx , Eny , Enz ) (E x , Ey , Ez ) G g0 G0 h ~ H(~r, t) i I I k ~k kB KHP kx

cross-sectional area of a conducting strip carbon–carbon bond length for graphene coefficients of expansion basis vectors of graphene lattice magnitude of applied magnetic field Cartesian components of the magnetic field speed of light in vacuum capacitance chiral (or wrapping) vector of a carbon nanotube average grain diameter charge of an electron (= 1.602 × 10−19 C) energy Fermi energy level energy across a bandgap energy levels eigenenergy binding energy of an exciton exciting electric field eigenenergies of quantum wells, wires, and dots Cartesian components of the electric field electrical conductance thermal conductance quantum conductance quantum Planck constant (= 6.626 × 10−34 J s) reduced Planck constant (= h/2π) Hamiltonian √ (−1) electric current (Chapter 3) nuclear spin (Chapter 5) wave number wave vector Boltzmann constant constant in Hall–Petch relation particle momentum along the x axis xvii

xviii

l (L x , Ly , Lz ) m m∗ m0 n N Nc (n, m) (n x , ny , nz ) P RK R0 Rmn ~r = (x, y, z) t T U V w Z α γ γ0 ε0 λ λDB λe λF µB ρs ρ xx ρ xy σ σ xy σ0 σy τ ψ (ψnx , ψny , ψnz ) ω ωp ωlspr

Nomenclature

length of a conducting strip dimensions of a reduced-dimensionality structure along the x, y, and z axes mass effective mass rest mass of an electron (= 9.109 × 10−31 kg) quantum number number of electrons number of channels available for transport dual index to specify the structure of a carbon nanotube shell principal quantum numbers polarization von Klitzing constant (= 25812.8 Ω) resistance quantum cross-sectional radius of a carbon nanotube position vector time temperature single-electron charging energy potential width of a conducting strip acoustic impedance fine structure constant gyromagnetic ratio carbon–carbon interaction energy permittivity of vacuum (= 8.854 × 10−12 F m−1 ) free-space wavelength de Broglie wavelength mean free path of electron Fermi wavelength Bohr magneton surface charge density longitudinal resistivity Hall resistivity electric conductivity Hall conductivity frictional stress yield strength relaxation time wavefunction eigenfunctions in quantum wells, wires, and dots angular frequency plasma frequency local-surface-plasmon-resonance frequency

Chapter 1

Introduction Materials consisting of nanostructures or possessing morphology at the nanoscale are commonly found in nature. The reader’s body contains nanomaterials such as proteins and DNA. Nanomaterials are also found in smoke from fires, in volcanic ash, in sea spray, and so on. Nanoparticles have been used for a couple of millenniums to add color to glass and ceramics. Nanoparticles have also been traditionally used for catalysis and, for about a century, nanoscale thin films have been fabricated for optical devices. What is new during the past two or three decades is an explosive increase in our ability to fabricate nanostructures and nanosystems with a great degree of control and using a diversity of techniques, accompanied by a similar enhancement in our ability to characterize structures and systems at the nanoscale. In fact, only recently, many of the systems proposed in the early 20th century have been fabricated thanks to the advent of such precise techniques as molecular beam epitaxy and scanning tunneling microscopy.

1.1 Definitions The term nanotechnology has been traced to 1974, when Norio Taniguchi,1 a professor of the Tokyo Science University outlined his vision of atom-by-atom or molecule-by-molecule manipulation of matter for the semiconductor industry. That vision was substantially realized during the next four decades, as the crucial gate oxide layers in metal-oxide-semiconductor (MOS) devices—the workhorses of integrated electronics—shrank to 2 nm in thickness. Subsequent technical improvements have allowed the realization of nanoscale structures in two and three dimensions. In a decadal survey of physics published in 1999 by the U.S. National Research Council,2 a dominant theme that emerged was nanosciences and nanotechnologies. The nanoscale is two-faced like the Roman god Janus of doorways: matter at the nanoscale exhibits continuum characteristics, but molecules and their clusters of small size can still display their individuality. For that reason, the U.S. federal government began to promote research on material morphologies and architectures with at least one dimension smaller than 100 nm. Indeed, according to the U.S. National Nanotechnology Initiative,3 1

2

Chapter 1

“Nanotechnology is the understanding and control of matter at dimensions between approximately 1 and 100 nanometers, where unique phenomena enable novel applications. Encompassing nanoscale science, engineering, and technology, nanotechnology involves imaging, measuring, modeling, and manipulating matter at this length scale.” The U.S. Patents and Trademarks Office declared in 20064 that nanotechnology is “related to research and technology development at the atomic, molecular or macromolecular levels, in the length of scale of approximately 1- to 100-nm range in at least one dimension” and in 20075 defined the term nanostructure “to mean an atomic, molecular, or macromolecular structure that: (a) [h]as at least one physical dimension of approximately 1–100 nanometers; and (b) [p]ossesses a special property, provides a special function, or produces a special effect that is uniquely attributable to the structure’s nanoscale physical size.” Other definitions have also been floated. Both the Royal Society and the Royal Academy of Engineering of the United Kingdom prefer the nanoscale lengths to lie between 0.2 and 100 nm.6 After reviewing these and other definitions, Charles Tahan7 of Cambridge University proposed the following definition: “Nanotechnology, at present, is nanoparticles and nanomaterials that contain nanoparticles. Nanoparticles are defined as objects or devices with at least two dimensions in the nanoscale regime (typically under 10 nm) that exhibit new properties, physical, chemical, or biological, or change the properties of a bulk material, due to their size. Nanotechnology of the future will include atom-by-atom or molecule-by-molecule built active devices.”

1.2 What Is Nanotechnology, and What Should We Expect from It? Take an inch-long piece of thread and chop it into 25 pieces, and then chop one of those pieces into a million smaller pieces. Those itty-bitty pieces are about one nanometer long. Figure 1.1 contains examples to contextualize the typical sizes of nanoscale objects. Ultrathin sheets and coatings have one nanoscale dimension, nanowires and nanotubes have two such dimensions, whereas all three dimensions of nanoparticles are at the nanoscale. Nanoscience and nanotechnology, collectively called nanotechnology, are emerging disciplines that have attracted enormous research interest for just about two decades. Nanotechnology is not a single process; neither does it involve a specific type of material. Instead, the term covers all aspects of the production of materials, devices, and systems by manipulating matter at the nanoscale.

Introduction

3

Figure 1.1 A comparative perspective of microscale and nanoscale objects (from U.S. Department of Energy http://www.nano.gov/html/facts/nanoscale.html).

Nanotechnology is widely considered to be the latest key technology, able to change our lives in many ways, and all the more so as it is becoming increasingly linked with advances in biotechnology, information technology, and cognition science. Some of the extremely pleasant prospects of the symbiosis of these four areas are new medical treatments, both preventive and curative; monitoring systems for buildings, dams, ships, aircraft, and other structures vulnerable to natural calamities and terrorist acts; and energy-efficient production systems that produce very little waste. Compared to biotechnology and information science, nanotechnology is still in its infancy, thus requiring much more fundamental research efforts. However, many products either enabled or improved by nanotechnology have been on the market for a few years, as noted by the Meridien Institute8 as early as in 2005; see Table 1.1. A vision of products expected to emerge and become commercially significant in the near future is depicted in Fig. 1.2. Yet the relatively small number of applications that have made it through to industrial uses represents “evolutionary rather than revolutionary advances,” according to a 2004 panel report from the Royal Society of London and the Royal Academy of Engineering6 —an assessment that is still correct.

4

Chapter 1

Table 1.1 Existing and near-term applications of nanotechnology across 12 different sectors. [Reprinted with permission from Ref. 8.] Automotive Industry

Chemical Industry

Construction

Cosmetics

Lightweight construction Painting Catalysts Tires (fillers) Sensors Coatings for windshields and auto bodies

Fillers for paints Composite materials Impregnation of papers Adhesives Magnetic fluids

Materials Insulation Flame retardants Surface coatings for wood, floors, stone, tiles, roofing, etc. Mortar

Sunscreens Lipsticks Skin creams Toothpaste

Electronics

Energy

Engineering

Food and Drinks

Displays Data memory Laser diodes Fiber optics Optical switches Filters Conductive, antistatic coatings

Fuel cells Solar cells Batteries Capacitors

Protective coatings for tools and machines Lubricant-free bearings

Packaging Sensors for storage life Additives Clarifiers (for juices)

Household

Medicine

Sports/Outdoors

Textiles

Ceramic coatings for irons Odor removers Cleaners for glass, ceramics, metals, etc.

Drug delivery systems Contrast media Rapid testing systems Prostheses and implants Antimicrobial agents In-body diagnostic systems

Ski wax Tennis rackets, golf clubs Tennis balls Antifouling coatings for boats Antifogging coatings for glasses/goggles

Surface coatings Smart textiles

Indeed, nanotechnology is currently classified into three types. The industrial use of nanoparticles in automobile paints and cosmetics exemplifies incremental nanotechnology. Reduction in size of particles and other objects has been occurring relentlessly for several decades, justifying the adjective “incremental.” Nanoscale sensors exploiting the fluorescent properties of nanoparticles called quantum dots (which are 2 to 10 nm in diameter; see Section 6.5) and the electrical properties of carbon nanotubes (which are 1 to 100 nm in diameter; see Section 6.1) represent evolutionary nanotechnology; however, development of these sensors is still in the embryonic stage. Radical nanotechnology—exemplified by procreating nanorobots, which are the staple of science-fiction thrillers—is nowhere on the technological horizon. Nanotechnology is often classified as either top-down or bottom-up, based on the specific technique used for fabricating nanostructures (Chapter 4). Top-down nanotechnology is based on reducing the size of structures, generally by the use of physical techniques (lithography, for instance). Bottom-up nanotechnology employs techniques that use atomic or molecular precursors to build up nanostructures. Chemical techniques such as self-assembly are commonly used in bottom-up nanotechnologies. Hybridization of top-down and bottom-up techniques is often resorted to.

Introduction

5

Figure 1.2 Applications and products of nanotechnology expected to emerge and become commercially feasible in the near future (from U.S. Department of Energy http://www.nano.gov/html/res/200711NanotechnologyBigThingsfromaTinyWorld.html).

Material properties at the nanoscale differ from those in bulk because quantumsized effects come into play, and because of extremely large surface areas per unit volume at the nanoscale. At the same scale, matter does not simply comprise isolated atoms and/or molecules. Material properties in bulk as well as at the molecular level are understood very well, unlike nanoscale properties— as the nanoscale is the doorway between the bulk and the molecular states. Great expectations exist that the exploitation of nanoscale properties and effects would transform current practices in integrated electronics, optoelectronics, and

6

Chapter 1

medicine. But the translation from the laboratory to mass manufacturing is fraught with significant challenges, and reliable manipulation of matter at the nanoscale in a desirable manner remains very difficult to implement economically.

1.3 Nanotechnology and Society Although nanotechnology is a thriving area of research with governments and industries investing heavily, the contours of our nanotechnological future are not clear. With control of investment comes political power. The reality of political power and its exercise in the choices being made for society and their consequences lies at the heart of the various discourses taking place in the industrialized world. Fault lines exist between utopian and dystopian discourses, undoubtedly because there are many conflicting conceptions among nanoscientists, business leaders, journalists, and social-humanistic researchers. Various sections of society have formed disparate discoursing groups. In 2007 an interdisciplinary team mapped out the following nine main discoursing groups: • Nanotechnologists almost always tend to glorify nanotechnology and exploit its cachet. Whereas most industrial applications of nanotechnology are currently incremental and therefore inevitable, industrial applications of evolutionary nanotechnologies such as quantum dots and carbon nanotubes have yet to become economical despite widespread hope. Hype abounds, at least because of emphasis on publishing upbeat results, whereas negative issues are considered unnecessary distractions. • There is a generally enthusiastic business climate, with predictions that within a decade nanotechnology products will be worth more than a trillion dollars in the U.S. alone and will drive a host of commercial applications that will revolutionize our way of life in unimaginable ways. Figure 1.3 presents some forecasts that, although significantly different from each other, have in common that they predict a substantial increase of the market for nanotechnological products with a take-off sometime in the early 2010s. The leaders of major corporations as well as venture capitalists, wanting to cash in on the projected benefits, are focused on the products

Figure 1.3 Forecasts for the nanotechnology market in billions of U.S. dollars, with data from a diversity of sources. [Reprinted with permission from Hullmann.9 ]

Introduction

7

of incremental nanotechnologies for quick profits. There are conflicting desires to protect the unquestioned authority of scientific progress and to defend the basic profit-oriented instincts of business. • Official or quasi-official bodies in the industrialized and developed countries now generate a significant amount of literature which is either prescriptive for further research and development or regulatory. This interest is generated by the widely perceived huge economic potential of nanotechnology as well as by new challenges for safety and regulation that will require societal debate. Nanotechnology research and development is heavily supported by government agencies and, while there is some movement towards standardization and safety, possible impacts on the environment, energy generation and consumption, water purification and desalination, agricultural yields, space exploration, national security, and the free-market economy are also being discussed more recently. An adequate assessment of societal impacts, however, may be possible only after several decades, because there are bound to be unintended consequences of nanotechnology. • Researchers in the social sciences and humanities tend to focus on the social, economic, political, legal, religious, philosophical, and ethical implications of nanotechnology, but are just beginning to coalesce into functioning research communities. Only a skeletal legal scholarship addresses the implications of nanotechnology. Serious attention by political scientists to nanotechnology as a policy problem is very recent, the most developed sub-literature being that which focuses on the political implications of nanotechnology for military security. The most developed area in the social sciences is that of scientometrics, a significant literature existing on growth and trends, interdisciplinarity, patterns of research collaboration, and patents relating to nanotechnology. • Ethical, legal, and social aspects are complemented by research on environmental, health, and safety aspects of nanotechnology, in order to decrease uncertainty about potential risks and benefits on the basis of scientific knowledge. One example is research on the toxicity of nanomaterials and manufactured nanoparticles. Although several institutions have published reports discussing the potential environmental and health risks associated with the manufacture, use, distribution, and disposal of nanomaterials, the current and widely accepted view is that there are still numerous unanswered questions. In any case, little data exists on the health hazards of nanotechnology. • Political activists, particularly those with an environmental worldview, tend to view nanotechnology with varying degrees of apprehension. Action groups, think tanks, social movements, and churches are becoming involved in evaluating the implications of nanotechnology for the environment, health, human rights, and global justice. Although many technoscientists dismiss activists as Cassandras, there is now a grudging recognition of safety issues raised by these activists. Recognizing the unpredictable consequences of nanotechnology, some activists have called for the application of the precautionary principle as a way of managing this technology of the infinitesimal.

8

Chapter 1

• Fiction writers have put forth imaginative scenarios, both utopian and dystopian. Whereas utopian scenarios are commonly captured in science-fiction novels, the dystopic underside of nanotechnology is illustrated very well both in novels such as Michael Crichton’s Prey and Neal Stephenson’s Diamond Age, and in films such as Gattaca (1997) and The Manchurian Candidate (2004). The futures of nanotechnology imagined by technoscientists often appear to be coterminous with science fiction, which suggests that scenario planning may become indispensable for regulatory agencies as well as for business groups. • Professional science journalists and popular science writers attempt to negotiate the fault line between utopian and dystopian scenarios. While some writers seek to glorify the world that they see nanotechnology creating, others call for a cut in public funding for nanotechnology until the significant social, legal, and ethical ramifications of work in the field have been clearly identified. A few have argued for turning the clock back because they believe that no good will come by tinkering with the fundamental mechanisms of nature. • The general public has yet to significantly grapple with or discuss nanotechnology in any depth. But awareness is slowly growing, partly in response to various governmental and nongovernmental initiatives. Although the initial reaction of the U.S. public to nanotechnology has been generally positive, there is nascent awareness of potential risks. The misgivings, if any, are directed at business leaders rather than at technoscientists. There are many layers of power in the discourses of nanotechnology. Challenging the power imbalances implicit and explicit in society will require both formal and informal education of technoscientists, politicians, economists, lawyers, social scientists, school teachers, and indeed every citizen. Ignorance about the various facets and implications of progress in nanotechnology being widespread, a program of general education and information in today’s industrial societies is necessary.

References 1. N. Taniguchi, “On the basic concept of ‘nano-technology’,” Proc. Intl. Conf. Prod. Eng. Tokyo Part II, Japan Society of Precision Engineering (1974). 2. U.S. National Research Council, Condensed-Matter and Materials Physics: Basic Research for Tomorrow’s Technology, National Academy Press, Washington, DC (1999). 3. U.S. National Nanotechnology Initiative, http://www.nano.gov/. 4. http://www.uspto.gov/web/patents/biochempharm/crossref.htm. 5. http://www.uspto.gov/go/classification/uspc977/defs977.htm. 6. Royal Society and Royal Academy of Engineering, Nanoscience and Nanotechnologies: Opportunities and Uncertainties, RS Policy document 20/04, RAEng Policy document R2.19, London, United Kingdom (2004). 7. C. Tahan, “Identifying nanotechnology in society,” Adv. Computers 71, 251–271 (2007) [doi:10.1016/S0065-2458(06)71005-1].

Introduction

9

8. Meridien Institute, Nanotechnology and the Poor: Opportunities and Risks (2005) http://www.merid.org. 9. A. Hullmann, The Economic Development of Nanotechnology—An Indicators Based Analysis, European Commission, Brussels, Belgium (2006) ftp://ftp. cordis.europa.eu/pub/nanotechnology/docs/nanoarticle_hullmann_nov2006. pdf.

Bibliography Aguar, P. and J. J. Murcia-Nicolás, EU Nanotechnology R&D in the Field of Health and Environmental Impact of Nanoparticles, European Commission, Brussels, Belgium (2008) ftp://ftp.cordis.europa.eu/pub/nanotechnology/docs/ final-version.pdf. Farber, D. and A. Lakhtakia, “Scenario planning and nanotechnological futures,” Eur. J. Phys. 30, S3–S15 (2009) [doi:10.1088/0143-0807/30/4/S02]. Hullmann, A., European Activities in the Field of Ethical, Legal and Social Aspects (ELSA) and Governance of Nanotechnology, European Commission, Brussels, Belgium (2008) ftp://ftp.cordis.europa.eu/pub/nanotechnology/docs/ elsa_governance_nano.pdf. Khushf, G., “The ethics of NBIC convergence,” J. Med. Philos. 32, 185–196 (2007) [doi:10.1080/03605310701396950]. Lakhtakia, A., “Whither nanotechnology?” Economic Perspectives 10(4), 27–28 (October 2005). Lakhtakia, A., “Priming pre-university education for nanotechnology,” Curr. Sci. 90, 37–40 (2006). Mnyusiwalla, A., A. S. Daar, and P. A. Singer, “‘Mind the gap’: science and ethics in nanotechnology,” Nanotechnology 14, R9–R13 (2003) [doi:10.1088/09574484/14/3/201]. Munshi, D., P. Kurian, R. V. Bartlett, and A. Lakhtakia, “A map of the nanoworld: Sizing up the science, politics, and business of the infinitesimal,” Futures 39, 432–452 (2007) [doi:10.1016/j.futures. 2006.08.003]. Patra, D., H. Ejnavarzala, and P. K. Basu, “Nanoscience and nanotechnology: ethical, legal, social and environmental issues,” Curr. Sci. 96, 651–657 (2009). Wiek, A., L. Gasser, and M. Siegrist, “Systemic scenarios of nanotechnology: Sustainable governance of emerging technologies,” Futures 41, 284–300 (2009) [doi:10.1016/j.futures.2008.11.016].

Chapter 2

Low-Dimensional Structures When one or more of the dimensions of a solid are reduced sufficiently, its physicochemical characteristics notably depart from those of the bulk solid. With reduction in size, novel electrical, mechanical, chemical, magnetic, and optical properties can be introduced. The resulting structure is then called a low-dimensional structure (or system). The confinement of particles, usually electrons or holes, to a lowdimensional structure leads to a dramatic change in their behavior and to the manifestation of size effects that usually fall into the category of quantum-size effects. Low-dimensional structures show new properties in a way that is different from simply the miniaturization of a particular device. Although the minimum size needed to obtain new properties will vary with many material-dependent factors, the value usually falls in the range of a few nanometers. For this reason, lowdimensional structures are popularly called nanostructures. Thus, nanostructures have at least one dimension in the range of a few nanometers and exhibit new physico-chemical properties not shown by the corresponding large-scale structures of the same composition (Chapter 3). Nanostructures constitute a bridge between molecules and bulk materials. Suitable control of the properties and responses of nanostructures can lead to new devices and technologies. Accordingly, nanoscience and nanotechnology primarily deal with the synthesis, characterization, exploration, and exploitation of nanostructured materials. Table 2.1 lists common nanostructures and their typical dimensions. In Chapter 6, materials used to fabricate these nanostructures as well as relevant phenomena are presented. Low-dimensional structures are usually classified according to the number of reduced dimensions they have. More precisely, the dimensionality refers to the number of degrees of freedom in the particle momentum. Accordingly, depending on the dimensionality, the following classification is made: • Three-dimensional (3D) structure or bulk structure: No quantization of the particle motion occurs, i.e., the particle is free. • Two-dimensional (2D) structure or quantum well: Quantization of the particle motion occurs in one direction, while the particle is free to move in the other two directions. • One-dimensional (1D) structure or quantum wire: Quantization occurs in two directions, leading to free movement along only one direction. 11

12

Chapter 2

Table 2.1

Nanostructures and their typical nanoscale dimensions.

Nanostructures

Typical nanoscale dimension

Thin films and quantum wells (two-dimensional structures) Quantum wires, nanowires, nanorods and nanopillars (one-dimensional structures) Nanotubes Quantum dots, nanodots (zero-dimensional structures) Porous nanomaterials, aerogels Sculptured thin films

1–1000 nm (thickness) 1–100 nm (radius) 1–100 nm (radius) 1–10 nm (radius) 1–50 nm (particle size, pore size) 10–500 nm

• Zero-dimensional (0D) structure or quantum dot (sometimes called “quantum box”): Quantization occurs in all three directions. Tradition has determined that reduced-dimensionality structures are labeled by the remaining degrees of freedom in the particle motion, rather than by the number of directions with confinement. In this chapter, the basic properties of low-dimensional structures are described. As this book is an introductory tutorial rather than a textbook, concepts are not presented in depth; instead, the objective of this chapter is to introduce the tools required to qualitatively describe and understand the characteristic behavior of lowdimensional structures, thus allowing analysis of devices based on nanostructures. For an in-depth and rigorous discussion of specific low-dimensional structures, the reader is encouraged to refer to specific textbooks and review articles, some of which are referenced at the end of this chapter. The main concepts that the reader is expected to grasp from this chapter are summarized in Section 2.5. The reader may either read the entire chapter or skip directly to the summary.

2.1 Brief Survey of Quantum Mechanics As a spatial dimension approaches the atomic scale, a transition occurs from the classical laws to the quantum-mechanical laws of physics. Phenomena that occur on the atomic or subatomic scale cannot be explained outside the framework of quantum-mechanical laws. For example, the existence and properties of atoms, the chemical bond, and the motion of an electron in a crystal cannot be understood in terms of classical laws. Moreover, many phenomena exhibited on a macroscopic scale reveal underlying quantum phenomena. It is in this reductionist sense that quantum mechanics is proclaimed as the basis of our present understanding of all natural phenomena studied and exploited in chemistry, biology, physics, materials science, engineering, etc. Physical behavior at the nanoscale is accurately predicted by quantum mechanics, as represented by the Schrödinger equation, which therefore provides a quantitative understanding of the properties of low-dimensional structures. In quantum mechanics, the trajectory of a moving particle loses its meaning when the distance over which potential energy varies is on the order of the de Broglie

Low-Dimensional Structures

13

wavelength: 2π~ λDB = √ , 2mE

(2.1)

where ~ is the reduced Planck constant, m is the mass of the particle, and E is its energy. In other words, a basic characteristic of all matter at the nanoscale is the manifestation of the wave–particle duality—a fundamental quantum-mechanical principle that states that all matter (electrons, nuclei, photons, etc.) behaves as both waves and particles. This hypothesis was put forth by de Broglie in 1923. The quantum effects of confinement become significant when at least one of the dimensions of a structure is comparable in length to the de Broglie wavelength. At room temperature, λDB (GaAs) = 339.48 nm, and λDB (Al) = 5.74 nm. The notable difference of λDB for metals and semiconductors dictates the different properties of metallic and semiconducting nanostructures of the same dimensions. If at least one dimension of a solid is comparable to the de Broglie wavelength of the particle, a quantum-mechanical treatment of particle motion becomes necessary. In the Schrödinger description of quantum mechanics, an elementary particle—e.g., an electron, a hole (which is a virtual particle created by the absence of an electron from an energy band), and a photon—or even a physical system such as an atom is described by a wavefunction ψ(~r, t), which depends on the variables describing the degrees of freedom of the particle (or system). The square of the wavefunction is interpreted as the probability of finding a particle at spatial location ~r = (x, y, z) and time t. Thus, while the state of motion of a particle in classical mechanics is specified by the particle’s position and velocity, the state of motion in quantum mechanics is specified by the particle’s wavefunction. The wavefunction contains all of the information that may be obtained about a physical entity and is sufficient to describe a particle or system of particles. In other words, if the wavefunction of, for example, an ensemble of electrons in a device, is known, it is possible in principle—though limited by computational abilities—to calculate all of the macroscopic parameters that define the electronic performance of that device. The wavefunction of an uncharged particle with no spin satisfies the Schrödinger equation (published in 1926): ! ∂ψ(~r, t) ~2 2 − ∇ + V(~r, t) ψ(~r, t) = i~ , 2m ∂t

(2.2)

√ where ∇2 ≡ ∂ 2 /∂ x2 + ∂ 2 /∂y2 + ∂ 2 /∂z2 is the Laplacian operator, i = −1, and V(~r, t) is the spatiotemporally varying potential influencing the particle’s motion. The particle’s mass m in Eq. (2.2) has to be carefully handled. For a particle (electron or hole) in a solid, this mass is its effective mass m∗ , which is usually less than the mass of an isolated electron.

14

Chapter 2

In Eq. (2.2), the action of the Hamiltonian operator H(~r, t) ≡ − ~2 /2m∇2 +V(~r, t) on the wavefunction yields the total energy of the particle. The first part of H(~r, t)ψ(~r, t) is the kinetic energy, and the second part is the potential energy. For many real systems, the potential does not depend on time, i.e., V(~r, t) = V(~r ). Then, the dependences on time and spatial coordinates of ψ(~r, t) are separated as h i ψ(~r, t) = Re e−iEt/~ ψ(~r ) ,

(2.3)

where ψ(~r ) is a complex-valued function of space only, and E is the energy of the system. Using this representation of the wavefunction in the Schrödinger equation (2.2), the time-harmonic Schrödinger equation ! ~2 2 − ∇ + V(~r ) ψ(~r ) = Eψ(~r ) 2m

(2.4)

is obtained. Equation (2.4) is analogous in wave mechanics to Hamilton’s formulation of classical mechanics for time-independent potentials, i.e., conservative systems. Analytical solutions of the time-harmonic Schrödinger equation can be obtained for a variety of relatively simple conditions. These solutions provide an insight into the nature of quantum phenomena and sometimes provide a reasonable approximation of the behavior of more complex systems—e.g., in statistical mechanics, molecular vibrations are often approximated as harmonic oscillators. Several of the more common analytical solutions are for a free (isolated) particle: a particle in a box, a finite potential well, 1D lattice, ring, or spherically symmetric potential; the hydrogen atom or hydrogen-like atom; the quantum harmonic oscillator; the linear rigid rotor; and the symmetric top.∗ For many systems, however, there is no analytic solution to the Schrödinger equation, and the use of approximate solutions becomes necessary. Some commonly used numerical techniques are: perturbation theory, density functional theory, variational methods (such as the popular Hartree–Fock method which is the basis of many post-Hartree–Fock methods), quantum Monte Carlo methods, the Wentzel–Kramers–Brillouin (WKB) approximation, and the discrete deltapotential method. The interested reader is encouraged to consult specialized books on these methods. In the next three sections, 2D, 1D, and 0D structures are discussed. Solutions of the time-harmonic Schrödinger equation are given in terms of eigenfunctions and eigenenergies that define the physical behavior of a structure.

2.2 Two-Dimensional Structures: Quantum Wells In a 2D structure, particles are confined to a thin sheet of thickness Lz along the z axis by infinite potential barriers that create a quantum well, as illustrated ∗

Most of these problems are treated in depth by Cohen-Tannoudji et al.1 and Griffiths.2

Low-Dimensional Structures

15

in Fig. 2.1(a). A particle cannot escape from the quantum well 0 ≤ z ≤ Lz and loses no energy on colliding with its walls z = 0 and z = Lz . In real systems, this confinement is due to electrostatic potentials (generated by external electrodes, doping, strain, impurities, etc.), the presence of interfaces between different materials (e.g., in core-shell nanocrystals), the presence of surfaces (e.g., semiconductor nanocrystals), or a combination of these agents. Motion of the particle in the other two directions (i.e., in the xy plane) inside the quantum well is free. It is generally accepted that quantum confinement of electrons by the potential wells of nanometer-sized structures provides one of the most powerful and versatile means to control the electrical, optical, magnetic, and thermoelectric properties of solid state functional materials, as discussed in Chapter 3. A 1D potential profile for electrons can be physically implemented by using two heterojunctions. Figure 2.1(b) shows the most comprehensively studied quantum well structure to

Figure 2.1 (a) Two-dimensional structure represented by infinite potential barriers that create a quantum well. (b) A GaAs quantum well inserted between two Alu Ga1−u As barrier layers.

16

Chapter 2

date. It consists of a layer of GaAs inserted between two Alu Ga1−u As (0 ≤ u ≤ 1) barrier layers. The layer of GaAs is a quantum well because the barrier layers are made of a material with a larger bandgap than GaAs; the energy difference between the valence band and conduction band in a semiconductor is called the bandgap. By adjusting the aluminum content of the barrier layers and the thickness of the GaAs layer at the time of growth, quantum wells with electronic properties tailored to the user’s specifications can be created. This practice is referred to as quantum engineering. The infinitely deep 1D potential well is the simplest confinement potential to treat in quantum mechanics. In classical mechanics, the solution to the problem is trivial, since the particle will move in a straight line and always at the same speed until it reflects from a wall at an equal but opposite angle. However, in order to find the quantum-mechanical solution, many fundamental concepts need to be introduced. After restricting analysis to an infinitely deep 1D potential well aligned along the z axis [Fig. 2.1(a)] of the form ( V(z) =

0, 0 < z < Lz ∞, z ≤ 0 or z ≥ Lz ,

(2.5)

the time-harmonic Schrödinger equation can be written as −

~2 d 2 ψ(z) + V(z)ψ(z) = Eψ(z). 2m dz2

(2.6)

Outside the chosen potential well, the potential is infinite; hence, the only possible solution is ψ(z) = 0, z ≤ 0 or z ≥ Lz , which in turn implies that all values of the energy E are allowed. Within the infinitely deep potential well, the Schrödinger equation simplifies to −

~2 d2 ψ(z) = Eψ(z), 2m dz2

0 < z < Lz .

(2.7)

Note that ψ(z) must be continuous inside the well and must be zero on both walls. Furthermore, since the particle must exist somewhere on the z axis, and because 2 ψ (z) is the probability of finding the particle at a particular value of z, it follows 2 R∞ that −∞ ψ (z) dz = 1. With these stipulations, the solutions of Eq. (2.7) are infinite in number. These solutions, called eigenfunctions, may be written as s ψnz (z) =

! 2 nz πz sin , Lz Lz

0 < z < Lz , nz = 1, 2, 3, . . . .

(2.8)

The index nz = 0 is ruled out since ψ(z) = 0 then for all z ∈ (−∞, ∞), corresponding to the case where there is no particle in the infinitely deep potential well. Negative values of nz are also neglected, since they merely change the sign of the sine

Low-Dimensional Structures

17

function in Eq. (2.8). The complete solution of Eq. (2.8) is a superposition of all eigenfunctions and is given by the sum ψ(z) =

∞ X

An ψnz (z),

0 < z < Lz ,

(2.9)

nz =1

where An are the coefficients of expansion indicating the relative importance of the eigenfunctions in the solution. Determination of the coefficient values of expansion lies outside the scope of this book.† An eigenfunction–eigenenergy pair constitutes a quantum state. Figure 2.2 shows the first four quantum states of an electron in a 100-Å thick infinitely deep potential well of Si. The effective mass of an electron in Si is m∗ = 0.98m0 , m0 being the rest mass of an isolated electron. The eigenenergy associated with the nz -th eigenfunction is given by E nz =

~2 nz π 2m Lz

!2 ,

nz = 1, 2, 3, . . . ,

(2.10)

and nz is called the principal quantum number. Although the quantum states were determined for a Si structure, the discussion can be extended to the same structure made of any other material, such as GaAs, since eigenfunctions will show a qualitatively similar behavior. Each eigenfunction describes 2 a state of electron confinement. Figure 2.2 shows that the probability ψnz (z) of an electron in the nz -th quantum state being found at a specific value of z in the infinitely deep potential well is not uniform. There are certain locations (antinodes) in the potential well where the electron might be most easily found, but there are also locations (nodes) where the probability of finding the electron is zero. This result contrasts sharply with the predictions of classical mechanics wherein the probability of finding an electron is the same for all z inside the infinitely deep potential well. Quantum size effects are apparent for reduced size. Thus, a particle confined to an infinitely deep potential well has only specific (discrete) energy levels, and the zero-energy level is not one of them. The lowest possible energy level of the particle is usually called the zero-point energy or confinement energy, which can be understood in terms of the Heisenberg uncertainty principle as follows: Because the particle is constrained within a finite region, the variability in its position has an upper bound. As the variability in the particle’s momentum cannot then be zero due to the uncertainty principle, the particle must contain some energy that increases as the width Lz of the infinitely deep potential well decreases. Figure 2.2 also shows the first four energy levels (eigenenergies) of an electron confined to a 100-Å thick infinitely deep potential well of Si. Figure 2.3 shows the first four energy levels of electrons confined to an infinitely deep potential well of different thickness. The potential well is made of either †

Cohen-Tannoudji et al.1 and Griffiths2 are recommended for detailed treatments.

18

Chapter 2

Figure 2.2 First four eigenfunctions and eigenenergies (E1 to E4 ) of an electron confined to a 100-Å-thick infinitely deep potential well of Si. An eigenfunction–eigenenergy pair constitutes a quantum state. [Computer codes from Harrison3 were used for the calculations.]

Si or GaAs. All energy levels show qualitatively the same behavior, i.e., higher value for reduced thickness. In the limit case of infinite thickness (Lz → ∞, bulk limit), the confinement energy (lowest energy level) is zero. In addition, lower particle effective mass (m∗GaAs = 0.067m0 versus m∗Si = 0.98m0 ) results in higher confinement energy for a given thickness. The infinitely deep potential well is of great interest since it describes qualitatively the behavior of real systems and serves as a platform for developing the physics of two-dimensional structures. In the more realistic case of a potential well of finite depth, wherein a particle is confined to a well with finite-potential walls, the results are comparable to those of infinitely deep potentials. However, unlike the infinite-potential well, there is a probability associated with the particle being found outside the finite-potential well. The quantum-mechanical interpretation is unlike the classical interpretation, where, if the total energy of the particle is less than the barrier energy of the walls, the particle cannot be found outside the well. In the quantum interpretation, there is a probability of the particle being outside the well even when the energy of the particle is less than the barrier energy of the walls. The first four quantum states of an electron confined to a 100-Å thick Si well of 200-meV potential barrier are shown in Fig. 2.4. The spatial variations of the

Low-Dimensional Structures

19

Figure 2.3 First four energy levels (eigenenergies) versus well width for electrons confined to an infinitely deep potential well of (a) Si (m∗Si = 0.98m0 ) and (b) GaAs (m∗GaAs = 0.067m0 ). [Computer codes from Harrison3 were used for the calculations.]

wavefunctions are similar to those for an infinitely deep potential well, i.e., a sinusoidal variation of increasing frequency, but with some penetration across the walls as well. Moreover, the differences in energy levels are somewhat smaller than for the infinitely deep well. Electrons with energy greater than 200 meV are not confined by the potential barrier and behave as free particles.

20

Chapter 2

Figure 2.4 First four quantum states for an electron confined to a 100-Å-thick Si (m∗Si = 0.98m0 ) well of finite depth (barrier energy = 200 meV). [Computer codes from Harrison3 were used for the calculations.]

Finally, Fig. 2.5 shows the first four energy levels of finite potential wells (Si and GaAs) with different barrier energies. The lower effective mass of an electron in GaAs results in a higher confinement energy for a given potential barrier. When the barrier energy is small, just a few energy levels are possible, with higher energy levels exceeding the barrier energy. For GaAs quantum wells, this effect is observed for barrier energies lower than 1000 meV; for Si quantum wells, the effect is found for barrier energies below 50 meV, owing to the larger effective mass of an electron in Si.

2.3 One-Dimensional Structures: Quantum Wires and Nanowires For 1D structures—usually called quantum wires (see Section 6.7), although other systems such as rods, belts, and tubes also fall within this category—it is possible to decouple the motion along the length of the wire, which is taken to be along the x axis, as shown in Fig. 2.6. Thus, the potential V(~r) is written as the sum of a 2D confinement potential (yz plane) plus a potential along the wire (x axis) as
V ~r = V (1) (x) + V (2,3) (y, z) .

(2.11)

Low-Dimensional Structures

21

Figure 2.5 Energy levels of an electron confined to a 100-Å-thick well of finite depth (a) Si (m∗Si = 0.98m0 ) and (b) GaAs (m∗GaAs = 0.067m0 ). Values of the barrier energy vary between 10 and 5000 meV. [Computer codes from Harrison3 were used for the calculations.]

22

Chapter 2

Figure 2.6 Schematic of an infinitely deep rectangular potential well. The potential is zero within the potential well, which is bounded by infinite-potential walls.

Accordingly, the wavefunction is written as the following product of two components:
ψ ~r = ψ(1) (x) ψ(2,3) (y, z) .

(2.12)

Substitution of Eqs. (2.11) and (2.12) into the time-harmonic Schrödinger equation (2.4) yields (

! ) ∂2 ∂2 ~2 ∂ 2 (1) (2,3) + + − + V (x) + V (y, z) ψ(1) (x) ψ(2,3) (y, z) 2m ∂ x2 ∂y2 ∂z2 = Eψ(1) (x) ψ(2,3) (y, z) . (2.13)

From this equation it is possible to obtain the following two autonomous equations of motion: −

~2 d2 (1) ψ (x) = E (1) ψ(1) (x) , 2m dx2

(2.14)

∂2 ~2 ∂ 2 + ψ(2,3) (y, z) + V (2,3) (y, z) ψ(2,3) (y, z) = E (2,3) ψ(2,3) (y, z) . (2.15) 2m ∂y2 ∂z2 !

−

Equation (2.14) is satisfied by a plane wave of the form ψ(1) (x) ∼ exp(ik x x), k x being the particle’s momentum along the x axis, thus leading to the dispersion relationship E (1) =

~2 k2x . 2m

(2.16)

Low-Dimensional Structures

23

This equation gives the energy level along the x axis, in which direction the particle is free to move, and resembles that of a 3D structure (wherein confinement is not possible). Equation (2.15) is the Schrödinger equation for a 2D confinement potential that characterizes a quantum wire. The general solution of this equation, normally requiring numerical methods of solution, falls beyond the scope of this book‡ . Only the special case of an infinitely deep rectangular potential well (Fig. 2.6) n o (2,3) (y, z) is 0 inside the rectangle 0 < y < Ly ∩ is considered here. The potential V {0 < z < Lz } but infinite for all other (y, z); i.e., ( 0, {0 < y < Ly } ∩ {0 < z < Lz } (2,3) V (y, z) = (2.17) ∞, otherwise Outside the rectangular region, the wavefunction ψ(2,3) (y, z) is identically zero. Therefore, Eq. (2.15) needs to be solved only inside the rectangular region; accordingly, ! ∂2 ~2 ∂ 2 + ψ(2,3) (y, z) = E (2,3) ψ(2,3) (y, z) , − 2m ∂y2 ∂z2 n o 0 < y < Ly ∩ {0 < z < Lz } .

(2.18)

The form of the potential in this equation allows the wavefunction dependencies on y and z to be decoupled, i.e., ψ(2,3) (y, z) = ψ(2) (y) ψ(3) (z). The method of separation of variables can then be used. This method allows the energy superposition E (2,3) = E (2) + E (3) and leads to the following two decoupled equations: −

~2 d2 (2) ψ (y) = E (2) ψ(2) (y) , 2m dy2

(2.19)

~2 d2 (3) ψ (z) = E (3) ψ(3) (z) . 2m dz2

(2.20)

−

Both of these equations are identical to Eq. (2.7) and are subject to similar boundary conditions. Basically, since the potential energy outside the wire is infinite, the standard boundary condition of continuity of the wavefunction at the walls implies that the product of ψ(2) (y) and ψ(3) (z) must be zero on the walls. Hence, the eigensolutions are s

! ny πy 2 sin , Ly Ly s ! 2 nz πz (3) ψnz (z) = sin , Lz Lz

ψn(2)y (y)

‡

=

ny = 1, 2, 3, . . . ,

(2.21)

nz = 1, 2, 3, . . . ;

(2.22)

Detailed treatments are available in the books of Cohen-Tannoudji et al.1 and Griffiths.2

24

Chapter 2

thus, s ψn(2,3) (y, z) y ,nz

=

! ! ny πy 4 nz πz sin sin , Ly Lz Ly Lz

ny = 1, 2, 3, . . . , nz = 1, 2, 3, . . . .

(2.23)

Figure 2.7 shows the eigenfunction of an electron in a rectangular Si quantum wire of dimensions Ly = 10 nm and Lz = 5 nm for ny = 4 and nz = 3. As for quantum wells, there are certain locations where the probability of finding the electron is zero, and other locations where the probability is maximum. The corresponding energy levels are ~2 ny π Eny = 2m Ly

!2

~2 nz π Enz = 2m Lz

!2

,

ny = 1, 2, 3, . . . ,

(2.24)

,

nz = 1, 2, 3, . . . .

(2.25)

Thus, the eigenenergy due to 2D confinement in an infinitely deep rectangular potential well is given by

Figure 2.7 Wavefunction for ny = 4 and nz = 3 of an electron confined to an infinitely deep rectangular potential well of Si. The dimensions are Ly = 10 nm and Lz = 5 nm.

Low-Dimensional Structures

Eny ,nz

~2 π2 = 2m

25

 2   ny n2z   2 + 2  , Ly Lz

ny = 1, 2, 3, . . . , nz = 1, 2, 3, . . .

(2.26)

The quantum states in a quantum wire are described by two principal quantum numbers (ny and nz ), while only one principal quantum number is needed for a quantum well. Similarly to that for a quantum well, the eigenenergy in a quantum wire increases for decreasing size. Also, a lower effective mass results in a larger eigenenergy for a given size. Figure 2.8 shows the first four eigenenergies Eny ,nz in infinitely deep quantum wires of Si and GaAs with Lz = 100 Å and increasing width (Ly ) along the y axis from 10 to 5000 Å. In some cases degeneracy is observed, since different combinations of ny , nz , Ly , and Lz lead to the same energy values. In particular, degeneracy is clearly observed for Ly = Lz = 100 Å with {ny = 1, nz = 2} and {ny = 2, nz = 1}. This figure clearly shows that eigenenergies increase for decreasing size, and a lower effective mass (m∗GaAs < m∗Si ) results in higher eigenenergies for a given size. More realistically, a quantum wire has a finitely deep well. Then the potential V (2,3) (y, z) cannot be written as a sum of two independent potentials V (2) (y) and V (3) (z). Therefore, decoupling along the y and the z axes is not possible, and Eq. (2.15) must be solved by numerical methods.

2.4 Zero-Dimensional Structures: Quantum Dots and Nanodots As in Section 2.3, a special 0D structure is now considered: the cuboid quantum dot, more often designated as the quantum box shown in Fig. 2.9. This special case can be used for a qualitative description of the response of quantum dots (Section 6.5) of many shapes. Zero-dimensional structures of other shapes, such as spherical quantum dots, require numerical solution of the Schrödinger equation. The quantum box is a generalization of a quantum wire of rectangular crosssection, in that there is additional confinement along the x axis to 0 < x < L x . This additional confinement removes the only degree of freedom remaining in the particle’s momentum, thus localizing it in all three directions. According to the Heisenberg uncertainty principle, increased spatial confinement will result in increased energy of the confined states. For simplicity, let the potential be zero inside the quantum box but infinite everywhere else; i.e., ( V(x, y, z) =

0, {0 < x < L x } ∩ {0 < y < Ly } ∩ {0 < z < Lz } ∞, otherwise.

(2.27)

The 3D time-harmonic Schrödinger equation within the quantum box becomes −

! ∂2 ∂2 ~2 ∂ 2 + + ψ (x, y, z) = Eψ (x, y, z) . 2m ∂ x2 ∂y2 ∂z2

(2.28)

26

Chapter 2

Figure 2.8 Energy levels for (a) Si and (b) GaAs quantum wires with Lz = 100 Å and Ly varying between 10 and 5000 Å. Note that for Ly = Lz = 100 Å, degeneracy is observed. [Computer codes from Harrison3 were used for the calculations.]

Low-Dimensional Structures

27

Figure 2.9 Schematic of a quantum box with sides L x , Ly , and Lz . For a simplified analysis, the potential is assumed to be zero within the quantum box and infinite outside it.

The method of separation of variables applies, leading to eigenfunctions described by three principal quantum numbers (n x , ny , nz ) as follows: s ψnx ,ny ,nz (x, y, z) =

! ! ! ny πy 8 n x πx nz πz sin sin sin , L x Ly Lz Lx Ly Lz

n x = 1, 2, 3, . . . , ny = 1, 2, 3, . . . , nz = 1, 2, 3, . . . .

(2.29)

The eigenenergy for a specific eigenfunction is given by   2 2 ~2 π2  n2x ny nz  + , Enx ,ny ,nz =  + 2m  L2x Ly2 Lz2  n x = 1, 2, 3, . . . , ny = 1, 2, 3, . . . , nz = 1, 2, 3, . . . .

(2.30)

Of fundamental importance is the fact that Enx ,ny ,nz is the total particle energy because of 3D confinement, in contrast with the previous two cases in which the solutions for the confined states in a quantum well and a quantum wire gave us only the eigenenergies associated with transverse confinement. The discrete energy spectrum in a quantum box and the lack of free propagation are the main features distinguishing quantum boxes from quantum wells and quantum wires. As these features are typical for atoms, quantum dots and quantum boxes are often called artificial atoms. A remarkable feature of a quantum box is that when two or more of the dimensions are the same (e.g., L x = Ly ), more than one wavefunction corresponds to the same total energy; for example, the wavefunction with n x = 2 and ny = 1 has the same energy as the wavefunction with n x = 1 and ny = 2 if L x = Ly . This

28

Chapter 2

situation is called degeneracy. When exactly two wavefunctions have the same energy, that energy level is said to be doubly degenerate. Degeneracy results from the symmetry of the structure. Figure 2.10 shows the first energy level (n x , ny , nz = 1) for a 0D structure of dimensions L x , Ly , and Lz , with Ly = Lz . As with the 2D and 1D structures, smaller dimensions result in increased eigenenergies, which is a manifestation of the Heisenberg uncertainty principle.

Figure 2.10 and Lz .

First energy level (n x = ny = nz = 1) of a quantum box as a function of L x , Ly ,

2.5 Chapter Summary The reduction of spatial dimensions to nanoscale values leads to a transition from classical physics to quantum mechanics. In the latter framework, the properties of systems of particles are described in terms of wavefunctions of single particles. Essentially, the wavefunction is a measure of the probability of finding a particle at a specific spatial location and time. Confinement of particles at the nanoscale in one, two, or three dimensions results in quantization of energy. In other words, the energy levels are not continuous as they are for macroscopic systems. Moreover, the energies of particles in low-dimensional systems are higher than those of particles in bulk systems. The higher the degree of spatial confinement (smaller particles), the larger is the separation between energy levels, and the higher are the energy values.

Low-Dimensional Structures

29

References 1. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics, Wiley, New York (1977). 2. D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ (2004). 3. P. Harrison, Quantum Wells, Wires and Dots. Theoretical and Computational Physics, Wiley, Chichester, UK (2000) [doi:10.1002/0470010827.ch13].

Bibliography Corcoran, E. and G. Zorpette, “Diminishing dimensions,” in The Solid-State Century, Sci. Am., 23–33 (1997) [Special Issue]. Gersten, J. I. and F. W. Smith, The Physics and Chemistry of Materials, Wiley, New York (2001). Harrison, W. A., Applied Quantum Mechanics, World Scientific, Singapore (2000). Hook, J. R. and H. E. Hall, Solid State Physics, 2nd ed., Wiley, Chichester, UK (1991). Kittel, C., Introduction to Solid State Physics, 8th ed., Wiley, New York (2005). Kohn, W., “An essay on condensed matter physics in the twentieth century,” Rev. Mod. Phys. 71, S59–S77 (1999) [doi:10.1103/RevModPhys.71.S59]. Lakhtakia, A., Ed., Handbook of Nanotechnology. Nanometer Structures: Theory, Modeling, and Simulation. SPIE Press, Bellingham, WA (2004). Martínez-Duart, J. M., R. J. Martín-Palma, and F. Agulló-Rueda, Nanotechnology for Microelectronics and Optoelectronics, Elsevier, Amsterdam (2006). Mitin, V. V., V. A. Kochelap, and M. A. Stroscio, Quantum Heterostructures. Microelectronics and Optoelectronics, Cambridge University Press, Cambridge (1999). Moriarty, P., “Nanostructured materials,” Rep. Prog. Phys. 64, 297–381 (2001) [doi:10.1088/0034-4885/64/3/201]. Patterson, J. D. and B. C. Bailey, Solid-State Physics. Introduction to the Theory, Springer, Berlin, Germany (2007). Rao, C. N. R. and A. K. Cheetham, “Materials science at the nanoscale,” in Nanomaterials Handbook, Y. Gogotsi, Ed., CRC Press, Boca Raton, FL (2006). Wolf, E. L., Nanophysics and Nanotechnology: An Introduction to Modern Concepts in Nanoscience, Wiley-VCH, Weinheim (2004) [doi:10.1002/9783527618972]. Wang, F. and A. Lakhtakia, Eds., Selected Papers on Nanotechnology—Theory and Modeling. SPIE Press, Bellingham, WA (2006). Yu, P. Y. and M. Cardona, Fundamentals of Semiconductor Physics and Materials Properties, 3rd ed., Springer, Berlin (2001).

Chapter 3

Properties of Nanostructures In Chapter 2, the reduction of the extent of a solid in one or more dimensions was shown to lead to a dramatic alteration of the overall behavior of the solids. Generally, the physical properties of any given material can be characterized by some critical length, e.g., thermal diffusion length and attenuation distance. What makes nanoparticles very interesting and endows them with their remarkable properties is that their dimensions are smaller than a relevant critical length. Accordingly, the electron states of nanostructures are quantized, leading to new and usually striking electrical, thermal, magnetic, optical, and mechanical properties at the nanoscale. Accordingly, nanostructures are of both basic and practical interest since their physico-chemical properties can be tailored by controlling their size and shape at the nanoscale, leading to improved and/or novel applications. The energy spectrum (i.e., the ensemble of discrete eigenenergies) of a quantum well, quantum wire, or quantum dot can be engineered by controlling (i) the size and shape of the confinement region and (ii) the strength of the confinement potential. The resulting control over the physico-chemical properties of the nanostructures is limited only by the accuracy of the experimental techniques used for the fabrication of the low-dimensional structures (Chapter 4). The situation is not unlike that of quantum phenomena, many of which were described at the beginning of the 20th century but could not be demonstrated until the 1960s to 1970s when appropriate nanofabrication techniques were developed. Not only is fabrication at the nanoscale limited by the available techniques, but other practically unavoidable factors such as imperfections—known to influence the properties of any material—may have very significant impacts on the properties of nanomaterials. As such, size dispersion, shape dispersion, defects, residual stresses, impurities, etc., are of great importance for devices of reduced dimensionality. These factors may, in many instances, create a gap between expectation and realization. As in Chapter 2, the reader who is not interested in the details on how the electrical, thermal, magnetic, optical, and mechanical properties change at the nanoscale may prefer to skip to Section 3.7, wherein the most significant properties are summarized. 31

32

Chapter 3

3.1 Band Diagrams In order to understand many of the properties of nanostructured materials, a basic knowledge of band diagrams is required, along with knowledge of such concepts as bandgap energy, direct/indirect bandgaps, holes, and excitons. A band diagram depicts the energy of an allowed state of a charge-carrying particle in a particular material as a function of its momentum or, equivalently because of wave–particle duality, as a function of the wave vector ~k. The magnitude of the wave vector is the wave number denoted by k. In a band diagram, the allowed energy states are grouped into bands, the valence band and the conduction band being the most important bands for the description of the properties of many materials. As the wave vector is a 3D quantity, band diagrams should be 4D plots. However, very often only 2D and 3D plots for specific ranges of the wave vector direction are drawn; furthermore, symmetries often allow 3D plots to be developed as 2D plots. Figure 3.1 presents typical 1D band diagrams for direct- and indirect-bandgap semiconductors, the direction of the wave vector being fixed, but not its magnitude. The two basic features that play an important role in the behavior of any material can be gleaned from a band diagram: (i) the bandgap energy Eg and (ii) whether the bandgap is direct or indirect. The bandgap is an energy range wherein no states are allowed for charge carriers to occupy. As the bandgap energy is defined as the difference in energy between the lowest point of the conduction band and the highest point of the valence band, Eg is the vertical distance between these two bands in the band diagram. Typical values of the bandgap energy at room temperature are: Eg (Si) = 1.11 eV, Eg (Ge) = 0.66 eV, Eg (GaAs) = 1.43 eV, Eg (CdS) = 2.42 eV, and Eg (InP) = 1.27 eV. The traversal of bandgaps by charge carriers involves the net exchange of energy between the charge carriers on the one hand and photons and/or phonons on the other. Photons of energy ~ω are quanta of light. Phonons of energy ~ω are also

Figure 3.1 One-dimensional band diagrams containing (a) direct and (b) indirect bandgaps. These 2D plots are called 1D band diagrams because the direction of the wave vector (or momentum) has been fixed, but its magnitude is allowed to vary.

Properties of Nanostructures

33

quantum particles, being defined as quanta of excitation of the crystalline-lattice vibration modes of angular frequency ω. The concept of a phonon arises from a quantum-mechanical treatment of lattice vibrations in a solid, after assuming that a lattice-vibration mode is analogous to a simple harmonic oscillation. Phonons play an important role in the behavior of solids by affecting their optical, electrical, and thermal properties through interactions with photons, electrons, neutrons, etc. A bandgap can be either direct or indirect. In a direct-bandgap material the maximum energy of the valence band and the minimum of the conduction band occur at the same value of the momentum, as depicted in Fig. 3.1(a). Either photons supply the necessary energy for a particle to climb to the conduction band from the valence band, or photons are emitted during the transition of the particle from the conduction band to the valence band. No phonons participate in the transitions from the conduction/valence band to the valence/conduction band. Most III–V compound semiconductors, such as GaAs, are direct-bandgap semiconductors and are widely used for optoelectronic applications. An indirect-bandgap semiconductor is one in which the maximum energy of the valence band and the lowest energy of the conduction band occur at different values of the momentum, as shown in Fig. 3.1(b). Since momentum (in addition to energy) must be conserved in any interband transition, phonons need to participate in these transitions, making these transitions less likely (or less efficient) in indirectbandgap semiconductors. Silicon and germanium are examples of indirect-gap semiconductors, with limited practical use in optoelectronics. Energy bands are populated by charge carriers, i.e., electrons and holes. Holes are virtual entities that can be thought of as electron vacancies. The charge of a hole is opposite in sign but equal in magnitude to that of an electron. The effective mass of a hole is somewhat different from that of an electron, their respective effective masses being dependent on the curvatures of the valence and conduction bands. An exciton is a quasi-particle comprising an electron and a hole bound to each other. As an exciton’s energy is slightly below the bandgap energy, transitions of slightly lower energy than Eg become possible. Excitons can move through a material and transport energy, although they do not transport charge as they are electrically neutral. Typical binding energies of excitons are Eex (Si) = 14.7 meV, Eex (Ge) = 4.15 meV, Eex (GaAs) = 4.2 meV, Eex (CdS) = 29.0 meV, and Eex (InP) = 4.0 meV.

3.2 Electrical-Transport Properties The changes that occur in the electronic properties as the length scale is reduced are mainly related to the increasing influence of the wavelike properties of the electrons and the scarcity of scattering centers. As one or more dimensions become comparable with the de Broglie wavelengths of electrons (see Section 2.1), the discrete nature of the energy states becomes apparent, although a fully discrete energy spectrum is observed only in systems that are confined in all three dimensions. The finite spacing of energy states as a result of quantum-mechanical

34

Chapter 3

confinement engenders fundamental and technologically important phenomena, which are being explored for electronic nanodevices. Although electrical transport occurs through the motion of both electrons and holes, the remainder of this section is focused on electrons but can be adapted to holes. The confinement of charge carriers in two or fewer dimensions results in quantized energy levels, as discussed in Chapter 2. The confinement of electrons to a 2D structure consisting of a conducting strip of width w and length l amounts to the creation of a 2D electron gas (2DEG). Its conductance is given by w G=σ , l

(3.1)

and its conductivity by σ=

ρ s e2 τ , m∗

(3.2)

where e is the charge of an electron, ρ s is the surface charge density, and τ is a relaxation time that takes into account the delay due to the collisions of electrons with the structure. The physical definition of G is the ratio of the total current to the voltage drop across a sample of length l in the direction of current flow. For a 3D electron gas (3DEG), this relationship can be used when replacing w by the cross-sectional area A orthogonal to the current flow. Similar expressions are also valid for the thermal transport of energy, as discussed in Section 3.3. Novel size-dependent effects emerge as the dimensions w (or A) and l are reduced toward atomic dimensions in the nanometer range. The relationship expressed by Eq. (3.1) holds in the diffusive-transport regime where both w and l are greater than the mean free path λe of the electrons. As the width of the strip decreases, quantum-mechanical effects begin to emerge. The quantum-mechanical confinement of an electron in a strip of width w leads to the discretization of energy levels given by En = ~2 /2m∗ (nπ/w)2 , (n = 1, 2, 3, . . . .), per Eq. (2.10), where m∗ is the effective mass of the electron and ~ is the reduced Planck constant. The conductance is determined by the number of these w-dependent transverse confined states that are occupied. Thus, rather than a simple linear dependence of G on w, quantum mechanics forces a particular dependence of G on w. As w is altered, the energy spectrum changes, as does the number of occupied states below the Fermi energy level E F , which is the highest energy level occupied by electrons (or, more precisely, fermions) at T = 0 K; hence, the conductance changes as well. Thus, the quantum-mechanical effect of reducing the dimension w is the change of conductance in discrete steps, much like a staircase. Quantization of conductance can be observed even at room temperature in some special cases, but in general this effect is exhibited at very low temperatures. In a short quasi-1D channel formed between two regions of a 2DEG in an AlGaAs/GaAs heterostructure by the action of metallic gate electrodes deposited on top of the layered structure, as shown in Fig. 3.2(a), the conductance increases

Properties of Nanostructures

35

Figure 3.2 (a) Schematic representation of a quantum point contact, defined in a highmobility 2D electron gas at the interface of a GaAs/AlGaAs heterojunction. The point contact is formed when a negative voltage is applied to the gate electrodes on top of the AlGaAs layer. Transport measurements are made by employing contacts to the 2D electron gas at either side of the constriction. (b) Conductance quantization of a quantum point contact in units of 2e2 /h. As the gate voltage defining the constriction is made less negative, the width of the point contact increases continuously, but the number of propagating modes at the Fermi level increases stepwise. The resulting conductance steps are smeared out when the thermal energy becomes comparable to the energy separation of the modes. [Reprinted c 2005, American Institute of Physics.] with permission from van Houten and Beenakker.1

in discrete steps as the electron density in the channel is increased. Figure 3.2(b) shows a sequence of steps in the conductance of a constriction in a 2DEG, as the width w is varied by the application of a voltage across the gate. The effect on the conductance G of reducing the length l is a particularly interesting phenomenon. If the ohmic regime were to hold in Eq. (3.1), the reduction of l toward zero would make G increase without limit, and the resistance would decrease to zero. However, there is always a finite residual resistance. In the ballistic transport regime l < λe , electrons can propagate without losing their initial momentum since scattering events can be neglected. The expression for ballistic conductance including two-spin orientation (spin degeneracy) in the ideal case becomes G=

2e2 . h

This relationship is usually called the Landauer formula.

(3.3)

36

Chapter 3

Accordingly, the ballistic conductance of a 1D channel is quantized in units of the conductance quantum G0 = 2e2 /h = 7.748 × 10−5 Ω−1 , which is twice the reciprocal of the resistance quantum R0 = h/e2 = 2.581 × 104 Ω. The Landauer formula for quantum transport can be generalized to a network in which several wires connect a barrier with reservoirs, leading to an expression that sums over the contribution of each channel. Then, with Nc being the number of channels available for transport (i.e., the number of transverse modes with energies below the Fermi energy of the electrodes or electron reservoirs), we have G = Nc

2e2 . h

(3.4)

This leads to quantized conductance and well-defined steps in the measured resistance as either the Fermi energy or the effective width of the wire is changed. Thus, while the classical conductance depends linearly on the width (G ∝ w), the quantum-mechanical conductance increases in discrete steps of 2e2 /h as w increases enough to permit one more transverse-quantization state to be occupied and hence available for conduction. Quantization is very important for quantum wires of small cross-sectional dimensions and depends on how conduction electrons interact with the atoms of a material. In practice, semiconductor wires unambiguously show conductance quantization for large cross-sectional dimensions (∼100 nm) because the electronic states due to confinement are spatially extended. As a result, their Fermi wavelengths λF = hc/E F are large, which means that adjacent energy states are not widely separated since E F is inversely proportional to λF . Hence, the energy state of an electron can be resolved only at a cryogenic temperature (few Kelvin) where the thermal excitation energy is lower than the interstate energy gaps. For metals, quantization corresponding to the lowest energy state is only observed for atomic wires. Its wavelength being thus extremely small, a metallic atomic wire has widely separated energy states, which allows resistance quantization to be easily observed at room temperature. Conduction in highly confined 0D structures, such as quantum dots, is very sensitive to the presence of other charge carriers and, hence, the charge state of the dot. Transport through quantum dots shows striking effects due to the electron’s wave nature and its finite charge. If a particular quantum dot is fully decoupled from its environment, it confines a well-defined number N of electrons. For weak coupling, deviations due to tunneling through the barriers are small, leading to discrete values of the total electrostatic energy of the quantum dot. This energy can be estimated as N(N − 1)e2 /2C, where C is the capacitance of the quantum dot. Thus, Ne2 /C is the amount of energy required to increase the number of confined electrons by one. This additional energy is discretely spaced in units of e2 /C. If this charging energy exceeds the thermal energy kB T , where kB is the Boltzmann constant and T is the temperature, the electrons cannot tunnel on and off the quantum dot by thermal excitations alone, and transport can be blocked, which is referred to as a Coulomb blockade.

Properties of Nanostructures

37

Electron transport through a quantum dot is studied by connecting the quantum dot to surrounding reservoirs, as illustrated in Fig. 3.3. The fact that the charge on an electron island formed by electrons confined to the quantum dot is quantized in units of e regulates transport through the quantum dot in the Coulomb-blockade regime. Electron transfer between the reservoirs and the quantum dot occurs via tunneling through potential barriers, which are thick enough that the transfer is dominated by resonances due to quantum confinement in the quantum dot. The Coulomb blockade results in conduction processes involving single electrons; as a result, only a small amount of energy is required to operate a switch, transistor, or memory element.

Figure 3.3 Schematic energy-level diagrams within the Coulomb-blockade model∗ (a) at a Coulomb peak, where linear-response (V = 0) transport is possible; (b) between peaks, where linear-response transport is blockaded; (c) and (d) at two different applied voltages (VC and VD ), where transport occurs through the first and second occupied states, respectively. [From Bockrath et al.2 Reprinted with permission from AAAS.]

The energy-level diagrams in Fig. 3.3 show N electrons confined to a quantum dot, followed by a gap of value U + ∆E for adding the (N + 1)-th electron. Above this, additional levels separated by an energy gap ∆E are shown, which correspond to adding the (N + 1)-th electron to one of the excited single-particle states of the dot. At a voltage V corresponding to a Coulomb-blockade peak, the energy of the lowest empty state aligns with the electrochemical potential in the leads, ∗ An applet demonstrating the Coulomb blockade effect on a metal quantum dot can be found at http://www.eng.buffalo.edu/ Courses/ee240/applets/coulombblockade/coulombblockade.html.

38

Chapter 3

and single electrons can tunnel on and off the dot at V = 0 [Fig. 3.3(a)]. At gate voltages between peaks [Fig. 3.3(b)], tunneling is suppressed because of the singleelectron charging energy U. However, if V is increased so that the electrochemical potential of the right lead is pulled below the energy of the highest filled state, an electron can tunnel off the dot [Fig. 3.3(c)]. Further increasing V allows tunneling out of additional states [Fig. 3.3(d)]. Similar processes occur for negative bias, corresponding to tunneling through unoccupied states above the Coulomb gap. Quantum-dot technology is one of the most promising candidates for use in solid state quantum computation, i.e., where quantum properties are used to perform numerical operations. By applying a small voltage, one can control the flow of electrons through the quantum dot and thereby make precise measurements of the spin and other quantum properties.

3.3 Thermal-Transport Properties Thermal transport at the nanoscale differs from that at the macroscale for several basic reasons. In bulk materials, internal scattering dominates the thermal-transport processes. As the size shrinks, the frequency of collisions between phonons and boundaries increases, as does the ratio of surface/interface to the volume. The interface scattering of phonons and the associated thermal boundary resistance can dominate thermal conduction in nanostructures. The size effects, however, are not limited to the thermal processes inside nanostructures. In the vicinity of small devices, phonons become rarefied when their mean free path is comparable or larger than the device size, which effectively increases the thermal resistance for removing thermal energy from the devices. Understanding these thermal processes is not only important for the prediction of the temperature rise in a microelectronic device and its reliability, but also can enable new technologies such as lowdimensional thermoelectric materials. Depending on the size of the nanostructure, thermal conductance may exhibit quantum features. Owing to the finite spacing of vibrational frequencies, the transfer of phononic energy through an electrically nonconducting nanoparticle (i.e., a molecule, atomic chain, or a single atom) between two reservoirs exhibits characteristics similar to those of ballistic transport of electrons discussed in Section 3.2. However, thermal energy can be transferred by both phonons and electrons, which obey different statistics. Thermal energy is transported only by phonons in dielectric wires, whereas in metallic wires the thermal energy transported by electrons dominates that transported by phonons. As the size of a nanostructure becomes comparable or smaller than the mean free path of phonons, phonons collide with the boundary more often than in bulk materials. An increase in the frequency of collisions enhances the resistance to thermal transport and thus reduces the effective thermal conductivity of thin films and wires. Similar but stronger size effects occur inside 1D (quantum wires, Section 6.7) and 0D (quantum dots, Section 6.5) structures. Figure 3.4 compares the estimated thermal conductivity of thin films and wires of silicon, together with some experimental data reported on the thermal conductivity of single-crystal thin

Properties of Nanostructures

39

Figure 3.4 Estimated thermal conductivity of silicon films/wires as a function of thickness/diameter. Experimental points are for thin films of silicon. [Reprinted from Chen3 with permission from Elsevier.]

films of silicon. The thermal conductivity of wires drops faster with thickness as a result of increased phonon scattering in the direction perpendicular to the wire axis. The expression for the universal quantum of 1D thermal conductance in the ballistic transport mode is given by g0 =

π2 k2B T = 9.456 × 10−13 T WK−2 . 3h

(3.5)

The quantum of thermal conductance is determined only by fundamental constants and the absolute temperature. This magnitude is universal, independent of the characteristics of the material. This result is analogous to Eq. (3.2) for the electrical quantized conductance, which is independent of the electron velocity in a 1D channel. The quantum of thermal conductance represents the maximum possible value of energy transported per phonon mode.

3.4 Magnetic Properties Nanostructured materials have remarkable magnetic properties, which have found several practical applications. In fact, ferromagnetism—a cooperative state of matter in which a huge number of magnetic moments are all locked parallel that leads to macroscopic magnetization—can be considered a nanoscale phenomenon. In a ferromagnet, each atom has an electronic magnetic moment, these moments all being aligned in the same direction. Among the several phenomena that low-dimensional structures display under the influence of magnetic fields, giant magnetoresistance (GMR) and

40

Chapter 3

colossal magnetoresistance (CMR) must be highlighted. Magnetoresistance is a phenomenon in which the application of a dc magnetic field changes the electrical resistance of a material, and is due to the conduction electrons being forced to move in helical trajectories about an applied magnetic field. The resistance of a material is the result of the scattering of electrons out of the direction of current flow by collisions. Since magnetoresistance generally occurs at very large magnetic fields and low temperatures, only limited applications have been found. Magnetoresistance occurs in pure copper at 4 K under an applied magnetic field of 10 T [10 kG = 1 T (tesla)], resulting in a tenfold increase in resistance. In 1988 huge magnetoresistance was measured in artificial materials consisting of alternating nanometer-thin films of ferromagnetic materials (Fe, Co, etc.) and weaker magnetic or nonferromagnetic metals (Cr, Cu, etc.), as shown in Fig. 3.5. This effect was termed giant magnetoresistence (GMR). GMR has sparked the fast development of spintronics (sometimes called spin electronics or even magneto-electronics), i.e., the use of the spin of electrons in information circuits. Figure 3.6 shows the electrical resistance as a function of the applied magnetic field, whereby we can infer that resistance decreases during the magnetization process and becomes practically constant when the magnetization is saturated. GMR is obtained in antiferromagnetically coupled Fe/Cr multilayer systems by aligning the magnetization of adjacent Fe layers with the applied magnetic field. GMR occurs because of the dependence of electron scattering on the orientation of the electron spin with respect to the direction of magnetization. Electrons whose spins are not aligned along the direction of magnetization are scattered more strongly than those with their spins aligned with magnetization. The application of the magnetic field parallel to the layers forces the magnetization in all magnetic layers to be in the same direction. This causes the magnetizations that are

Figure 3.5 Magnetic multilayers consisting of nanometer-thick layers of ferromagnetic materials (Fe, Co, etc.) separated by nanometer-thick spacer layers of weaker magnetic or nonferromagnetic metals (Cr, Cu, etc.).

Properties of Nanostructures

41

Figure 3.6 Magnetoresistance measurements at 4.2 K of three Fe/Cr multilayer systems (Fe/Cr)n . The current and the applied magnetic field are along the same axis in the plane of the layers. To the far right as well as to the far left (H > H s and H < H s , H s being the saturation magnetic field), the magnetization in all iron layers is parallel to the external magnetic field. In the low-field regime, every second iron layer is magnetized antiparallel to the external magnetic field (10 kG = 1 T). [Reprinted with permission from Baibich et al.4 c 1988 by the American Physical Society.]

pointing opposite to the direction of the applied magnetic field to flip. The conduction electrons with spins aligned opposite to the magnetization are more strongly scattered at the metal–ferromagnet interface, and those aligned along the field direction are less strongly scattered. Because the two spin channels are in parallel, the lower-resistance channel determines the resistance of the material. The magnetoresistance effect in these multilayered materials is a sensitive detector of dc magnetic fields and has enabled the development of very sensitive reading heads for magnetic disks. Other material systems have been discovered to have even larger magnetoresistance than multilayered materials, so this phenomenon is called colossal magnetoresistance (CMR). Materials made of single-domain ferromagnetic nanoparticles with randomly oriented magnetizations embedded in a nonmagnetic matrix also display GMR. The magnetoresistance in these materials, unlike the multilayered materials, is isotropic. The application of a dc magnetic field rotates the magnetization vector of the ferromagnetic nanoparticles parallel to the direction of the field, which reduces the resistance. The magnitude of the effect of the applied magnetic field on the resistance increases with the magnitude of the magnetic field and as the size of the magnetic nanoparticles decreases.

42

Chapter 3

Perhaps the most remarkable property of low-dimensional systems under the influence of magnetic fields is the quantum Hall effect. This effect is observed when a large magnetic field is applied perpendicular to a 2DEG at a low temperature. On applying a magnetic field Bz in the direction perpendicular to a nanometer-thick film, as shown in Fig. 3.7, the transverse resistivity ρ xy increases in steps at high values of the applied magnetic field. At the j-th step, ρ xy = −

25812.807 h =− Ω, 2 j je

j = 1, 2, 3, . . . .

(3.6)

In the regimes where ρ xy is constant, the longitudinal resistivity ρ xx is vanishingly small. The unusual behavior of the 2DEG exhibited in Fig. 3.7 is known as the quantum Hall effect. The quantization of the Hall conductivity σ xy = 1/ρ xy has the important property of being incredibly precise. Actual measurements of the Hall conductivity have been found to be either integral or fractional multiples of 1/R0 to nearly one part in a billion. This phenomenon, referred to as exact quantization, has allowed for the definition of a new practical standard for electrical resistance: the resistance quantum R0 , sometimes referred to as the resistance unit, roughly equals 25812.8 Ω. This magnitude is referred to as the von Klitzing constant RK (after von Klitzing, the discoverer of exact quantization); since 1990, a fixed conventional value RK−90 has been used worldwide to calibrate resistors. The quantum Hall effect also provides an extremely precise independent determination of the fine structure constant α = e2 /2hcε0 , a quantity of fundamental importance in quantum electrodynamics, ε0 being the permittivity of vacuum or free space.

3.5 Optical Properties Quantum confinement in low-dimensional semiconductors splits the bulk conduction and valence bands into a series of discrete energy levels, as discussed in Chapter 2. The degeneracy and separation levels depend on the dimensionality and shape of the confinement regime. In quantum wells (Section 2.2), quantum wires (Section 2.3), and quantum dots (Section 2.4), confinement effects lead to blueshifts (i.e., shifts to shorter wavelengths and thus higher energies) of the electron and hole states. The optical transitions, which are affected by the nature of the excitons—the electron–hole-pair states introduced in Section 3.1—also become discrete. The blueshifts of electron and hole states and the discrete exciton states make the optical properties of low-dimensional structures very different from those of the bulk material; this is especially true in the case of quantum dots because of confinement in all three dimensions. In semiconductor nanocrystals (0D structures), both the electron states in the conduction band and the hole states in the valence band become quantized as a result of quantum confinement, as shown in Section 2.4. As the size reduces, the bandgap grows and can be chosen over a wide range of energies by appropriately selecting the average diameter of the nanocrystals. As a consequence, quantum

Properties of Nanostructures

43

Figure 3.7 Experimental curves for the Hall resistivity (ρ xy ) and the longitudinal resistivity (ρ xx ) of a heterostructure as a function of the applied magnetic field at a fixed carrier density, recorded at 8 mK. (Inset) Schematic for Hall-effect measurements, where I is the electric current parallel to an applied electric field E x . The transverse movements of electrons and holes due to the application of the magnetic field Bz creates a transverse current density, thereby engendering an electric field Ey . [Reprinted with permission from von Klitzing.5 c 1986 by the American Physical Society.]

44

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dots of the same material, but with different sizes, can emit light of different wavelengths (and thus colors), which is one of the optical features of quantum dots immediately noticeable to the unaided eye. In fact, while the material that makes up a quantum dot defines its intrinsic energy signature, more significant in terms of coloration is the size. Recent studies suggest that the shape of the quantum dot may also be a factor in the coloration. The absorption edge—i.e., the lowest-energy absorption state—is shifted to higher energy with respect to that of the bulk semiconductor as the size decreases. Furthermore, above the absorption edge, (i) the spectrum is stepped rather than smooth, the steps corresponding to allowed transitions between valence states and conduction states and (ii) at each step, sharp peaks appear, corresponding to confined-exciton states. The absorption intensity in nanocrystals becomes concentrated at the specific frequencies corresponding to the transitions between discrete states. Additionally, large absorption coefficients are observed. Size reduction results in a blueshift of the characteristic transition energies compared to the bulk semiconductor material. A smaller size results in an upshift of the threshold for absorption from the corresponding bulk value; in addition, a similar shift is found in the emission spectrum. Accordingly, the optical spectra of several semiconductor nanocrystals can be selected from a continuous palette across the visible spectrum simply by choosing the appropriate size. This fact makes semiconductor nanocrystals useful in applications ranging from fluorescent labels to light-emitting diodes. In particular, the larger the dot, the redder is the fluorescence; the smaller the dot, the bluer is the fluorescence. Quantitatively speaking, the bandgap energy that determines the energy (and hence color) of the fluorescence is inversely proportional to the square of the size of the quantum dot. Larger quantum dots have more energy levels that are more closely spaced. This allows the quantum dot to absorb photons containing less energy, i.e., those closer to the red end of the spectrum. Just as in atoms, the energy levels of small quantum dots can be probed by optical spectroscopic techniques. Figure 3.8 shows room-temperature optical absorption measurements for PbSe nanocrystals ranging in size from 3 to 9 nm, from which quantum-sized effects can be deduced. Since the absorption edge is given by the bandgap, the bandgap increases as the nanocrystal size decreases. Also, the intensity of the absorption increases as the size is reduced. The higherenergy peaks are associated with excitons and shift to higher energies with decreasing size. These effects are a result of the confinement of excitons. According to the Kramers–Kronig relations to which every linear causal system must adhere, a bulk semiconductor and a nanocrystal have the same overall absorption per unit volume when integrated over all frequencies, although the absorption spectra are very different.† The absorption spectrum of a typical bulk semiconductor is continuous, whereas that of a nanocrystal consists of a series of discrete transitions with very high magnitudes at the transition frequencies. These †

See Ref. 6 for details.

Properties of Nanostructures

45

Figure 3.8 Room-temperature optical absorption spectra for a series of PbSe nanocrystals measuring (a) 3.0 nm, (b) 3.5 nm, (c) 4.5 nm, (d) 5 nm, (e) 5.5 nm, (f) 7 nm, (g) 8 nm, and (h) 9 nm in diameter. [Reprinted with permission from Murray et al.7 ]

46

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strong transitions at particular frequencies have motivated the fabrication of lasers that are based on the quantized electronic transitions in quantum dots. Quantum dots are valued for displays because they emit light in very specific Gaussian distributions. Quantum-dot displays can very accurately reflect the colors that the human eye can perceive. Quantum dots also require very little power since their outputs need not be filtered for color purity. In contrast, a display made of liquid crystal devices (LCDs) is powered by a single fluorescent lamp that is color filtered to produce red, green, and blue pixels. Thus, when an LCD display shows a fully white screen, two-thirds of the light is absorbed by the filters. Displays that intrinsically produce monochromatic light can for this simple reason be more efficient. Let us think of a quantum dot as a sufficiently small metal sphere, wherein the electrons in the conduction band fill up the quantized energy levels. These quantized levels affect the optical—and the electrical—properties and can even influence the stability of the metal sphere. The optical properties of small metal spheres typically exhibit a local surface plasmon resonance (LSPR) as follows: In the presence of an external electric field, the centers of positive and negative charges in any atom in the metal sphere do not coincide. Each atom acts as an electric dipole. The metal sphere is said to be polarized. With the twin assumptions (i) that the atoms respond instantaneously to the external electric field Eexc (i.e., that the retardation effects can be ignored) and (ii) that a free-electron cloud is created inside the electrically small metal sphere, the induced polarization can be written as P=

ε0 1−

ω2p 3ω2

Eexc ,

(3.7)

where ω p is the plasma frequency of the bulk metal and ω is the √ angular frequency. The polarization thus diverges at a frequency of ωlspr = ω p / 3, called the LSPR frequency. The most striking effect is that ωlspr shifts the bulk plasma resonance of metals such as gold and silver from the ultraviolet regime into the visible regime. This result is independent of the radius of the metal sphere. In reality, however, the optical properties do depend somewhat on size due to retardation effects at larger radii, and due to losses and intraband transitions at smaller radii. Liquids or glasses containing metallic nanoparticles are often brilliantly colored due to absorption indicative of LSPR. As shown in Fig. 3.9, the LSPR bands for nanoparticles of silver and gold usually fall within the visible range. Furthermore, the LSPR bandwidth and the peak maximum strongly depend on the size and shape of the nanoparticle. As with quantum dots, size confinement also plays an important role in determining the energy levels in 1D systems such as nanowires, once the crosssectional diameter has been reduced below a critical value [such as the de Broglie wavelength (Section 2.1)] that depends on the particular nanostructure. This effect has been experimentally observed with nanowires made of different materials. For example, the absorption threshold of silicon nanowires is significantly blueshifted

Properties of Nanostructures

47

Figure 3.9 Selection of the LSPR wavelength of Au and Ag nanoparticles by choosing appropriate size, shape, and composition. [Reprinted from Kalele et al.8 ]

as compared with that of bulk silicon. Moreover, sharp, discrete features in the absorption spectra are observed along with relatively strong photoluminescence with emission energy close to the absorption edge. These features most likely originate from size-confinement effects, although surface states (energy states present at the surface of solids) might make additional contributions because of the large surface-to-volume ratio in low-dimensional structures. Furthermore, a variation in the growth direction for a nanowire usually leads to different optical signatures. For example, Si nanowires oriented along the h100i crystalline direction exhibit significantly higher transition energies across the bandgap associated with excitons when compared with the nanowires oriented along the h110i direction. Light emitted from a nanowire is highly polarized along its longitudinal axis. Hence, a striking difference exists in the photoluminescence intensities recorded in the directions parallel and perpendicular to the axis of an isolated nanowire. In some cases, this anisotropy can be quantitatively explained in terms of the large dielectric contrast between the nanowire and the surrounding environment. The polarization response has been exploited to fabricate polarization-sensitive nanoscale photodetectors for integrated photonic circuits, optical switches and interconnects, near-field imaging, and high-resolution detection systems. Additionally, nanowires with flat ends can be useful as optical resonance cavities to generate coherent light on the nanoscale. Coherent nonlinear optical phenomena such as second- and third-harmonic generation have been observed in nanowires.

3.6 Mechanical Properties The mechanical properties of a material depend fundamentally on the nature of bonding among its constituents, and on its microstructure on several length scales. Most nanograined materials, typically characterized by an average grain size that is less than several tens of nanometers, have grain-size-dependent mechanical properties that are significantly different from those of their coarse-

48

Chapter 3

grained counterparts. Two of the most widely reported differences are the departure from the Hall–Petch relation of the yield stress and the increased ductility (superplasticity). In particular, ultrapure metals are much stronger and apparently less ductile than metals with impurities. Intermetallics, i.e., compounds of two or more metals resulting in a material with different properties from the constituent metals, are also stronger, but tend to be more ductile when the grain size is small. Although these property changes are thought to be primarily controlled by grain size, they are also affected by the large percentage of atoms in grain boundaries, as well as other microstructural features. Strengthening appears to result from a limitation of the activity of dislocations, which are defects within the crystal structure of a solid, while increased ductility probably relates to the relative sliding between adjacent grains. A quantity commonly used to mechanically characterize materials is their yield strength σy , defined as the stress at which the material begins to deform plastically, resulting in permanent deformation. The yield strength of a material is related to the grain size by the empirical Hall–Petch relation: σy = σ0 + KHP · d−1/2 ,

(3.8)

where σ0 is the frictional stress opposing dislocation movement, KHP is a materialdependent constant, and d is the average grain diameter. The hardness of a material can be also described by a similar equation. Both yield strength and hardness are higher for reduced grain size. The reason for this behavior is that materials having smaller grains have more grain boundaries, thereby blocking dislocation movement. However, significant departures from the Hall–Petch behavior have been reported for materials made of grains typically less than 20–50 nm in size, depending on the particular material. The departure from the linear behavior varies from no dependence on the grain size (zero slope) to decreases in yield strength with grain size (negative slope), as shown in Fig. 3.10. These markedly different characteristics are primarily caused by the increased role played by the grain boundaries in a nanograined material. For the traditional coarsegrained materials, the grain boundary can generally be regarded as a region of almost zero thickness whose deformation contributes little to the overall plastic strain; however, when the grain size reduces to the nanometer scale, a significant population of atoms exists at the grain boundaries whose deformation can have a dominant effect on the overall plastic strain of the material, thereby resulting in permanent deformation. Additionally, tension-compression asymmetry (usually termed strength-differential effect) has also been reported for nanograined materials (see Fig. 3.10), but is absent for coarse-grained materials. Many nanostructured metals and ceramics are observed to be superplastic, in that they are able to undergo extensive deformation without forming necks or actually fracturing. Superplasticity is presumed to arise from diffusion and sliding of grain boundaries, which become increasingly significant in a finer-grained material. Overall, these effects extend the current yield strength and ductility limits

Properties of Nanostructures

49

Figure 3.10 Departure of the yield strength from the Hall–Petch plot for decreasing grain size of copper. The bottom four experimental data points were taken under tension, and the top curve was calculated under compression. There is a significant strength-differential effect between tension and compression in the nanometer range. [Adapted from Jiang and Weng9 with kind permission of Springer Science and Business Media.]

of conventional materials for which usually a gain in yield strength is offset by a corresponding loss in ductility. The increased ductility has been observed in both metals and ceramics. In this regard, nanocrystalline copper with purity better than 99.993 atomic percent and an average grain size of 28 nm has been shown to deform up to 5100% at room temperature; some composite ceramics can deform up to 1050% at 1650 ◦ C without failure.

3.7 Chapter Summary Size reduction at the nanoscale results in quantization of electrical conductance which, in some cases, is observable even at room temperature. The discovery of this quantization led to the introduction of a new fundamental constant, namely the conductance quantum. Likewise, thermal conductance becomes quantized for low-dimensional structures, and a quantum of thermal conductance, independent of the characteristics of the material, has been defined. Under the influence of magnetic fields, low-dimensional structures show giant magnetoresistance and colossal magnetoresistance, i.e., the electrical resistance is greatly increased by the application of external magnetic fields. Another

50

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remarkable property is the quantum Hall effect, in which the transverse resistivity of a 2D electron gas increases in steps at high magnitudes of the applied magnetic field, resulting in quantized Hall conductivity. The discovery of this property has led to the definition of the resistance quantum, referred to as the von Klitzing constant. From an optical point of view, quantum confinement results in shifts to shorter wavelengths (higher energies) of the absorption edge and the emission wavelength. Additionally, the typical spectra of nanostructures are stepped rather than smooth, as is generally the case for bulk materials. This opens the possibility of tuning the emission and absorption of light with size. Finally, notable departures from the linear behavior of the yield strength and hardness with grain size have been observed at the nanoscale. However, the particular behavior is very much dependent on the nanomaterial.

References 1. H. van Houten and C. W. J. Beenakker, “Quantum point contacts,” arXiv.org (2005) [arXiv:cond-mat/0512609v1]. 2. M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, “Single-electron transport in ropes of carbon nanotubes,” Science 275, 1922–1925 (1997) [doi:10.1126/science.275.5308.1922]. 3. G. Chen, “Phonon heat conduction in nanostructures,” Int. J. Therm. Sci. 39, 471–480 (2000) [doi:10.1016/S1290-0729(00)00202-7]. 4. M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, “Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices,” Phys. Rev. Lett. 61, 2472–2475 (1988) [doi:10.1103/PhysRevLett.61.2472]. 5. K. von Klitzing, “The quantized Hall effect,” Rev. Mod. Phys. 58, 519–531 (1986) [doi:10.1103/RevModPhys.58.519]. 6. C. Klingshirn, Semiconductor Optics, 2nd ed., Springer, Berlin, Germany (2005). 7. C. B. Murray, S. Sun, W. Gaschler, H. Doyle, T. A. Betley, and C. R. Kagan, “Colloidal synthesis of nanocrystals and nanocrystal superlattices,” IBM J. Res. Dev. 45, 47–56 (2001). 8. S. A. Kalele, N. R. Tiwari, S. W. Gosavi, and S. K. Kulkarni, “Plasmonassisted photonics at the nanoscale,” J. Nanophoton. 1, 012501 (2007) [doi:10.1117/1.2748429]. 9. B. Jiang and G. J. Weng, “A composite model for the grain-size dependence of yield stress of nanograined materials,” Metall. Mater. Trans. 34, 765–772 (2003) [doi:10.1007/s11661-003-1004-1].

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Bibliography Basu, P. K., Theory of Optical Processes in Semiconductors. Bulk and Microstructures, Oxford University Press, Oxford, UK (1997). Boxberg, F. and J. Tulkki, “Quantum dots: Phenomenology, photonic and electronic properties, modeling and technology,” in Handbook of Nanotechnology. Nanometer Structures: Theory, Modeling, and Simulation, A. Lakhtakia, Ed., SPIE Press, Bellingham, WA (2004). Brydson, R. M. and C. Hammond, “Generic methodologies for nanotechnology: classification and fabrication,” in Nanoscale Science and Technology, R. Kelsall, I. Hamley, and M. Geoghegan, Eds., Wiley, Chichester, UK (2005). Ciraci, S., A. Buldum, and I. P. Batra, “Quantum effects in electrical and thermal transport through nanowires,” J. Phys.: Condens. Matter 13, R537–R568 (2001) [doi:10.1088/0953-8984/13/29/201]. D’Andrea, A., R. del Sole, and K. Cho, “Exciton quantization in CdTe thin films,” Europhys. Lett. 11, 169–174 (1990) [doi:10.1209/0295-5075/11/2/013]. Dingle, R., W. Wiegmann, and C. H. Henry, “Quantum states of confined carriers in very thin Alx Ga1−x As−GaAs−Alx Ga1−x As heterostructures,” Phys. Rev. Lett. 33, 827–830 (1974) [doi:10.1103/PhysRevLett.33.827]. Hernando, A., “Magnetism in nanocrystals,” Europhys. News 34, 232–234 (2003) [doi:10.1051/epn:2003610]. Hook, J. R. and H. E. Hall, Solid State Physics, 2nd ed., Wiley, Chichester, UK (1991). Imry, Y., Introduction to Mesoscopic Physics, 2nd ed., Oxford University Press, New York (2002). Kittel, C., Introduction to Solid State Physics, 8th ed., Wiley, New York (2005). Landauer, R., “Conductance determined by transmission: probes and quantised constriction resistance,” J. Phys.: Condens. Matter 1, 8099–8110 (1989) [doi:10.1088/0953-8984/1/43/011]. Landauer, R., “Spatial variation of currents and fields due to localized scatterers in metallic conduction,” IBM J. Res. Dev. 1, 223–231 (1957). Laughlin, R. B., “Excitons in the fractional quantum Hall effect,” Physica B+C 126, 254–259 (1984) [doi:10.1016/0378-4363(84)90172-4]. Lüth, H., “Electronic properties and quantum effects,” in Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices, R. Waser, Ed., Wiley-VCH, Weinheim, Germany (2005). Meir, Y., N. S. Wingreen, and P. A. Lee, “Transport through a strongly interacting electron system: Theory of periodic conductance oscillations,” Phys. Rev. Lett. 66, 3048–3051 (1991) [doi:10.1103/PhysRevLett.66.3048].

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Ozpineci, A. and S. Ciraci, “Quantum effects of thermal conductance through atomic chains,” Phys. Rev. B 63, 125415 (2001) [doi:10.1103/PhysRevB.63.125415]. Poole, C. P., Jr. and F. J. Owens, Introduction to Nanotechnology, Wiley, Hoboken, NJ (2003). Reimann, S. M. and M. Manninen, “Electronic structure of quantum dots,” Rev. Mod. Phys. 74, 1283–1342 (2002) [doi:10.1103/RevModPhys.74.1283]. Royal Swedish Academy of Sciences, The Discovery of Giant Magnetoresistance, Stockholm, Sweden (2007). Schmitt-Rink, S., D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987) [doi:10.1103/PhysRevB.35.8113]. Siegel, R. W. and G. E. Fougere, “Mechanical properties of nanophase metals,” Nanostr. Mat. 6, 205–216 (1995) [doi:10.1016/0965-9773(95)00044-5]. Störmer, H. L., “The fractional quantum Hall effect (experiment),” Physica B+C 126, 250–253 (1984) [doi:10.1016/0378-4363(84)90171-2]. van Wees, B. J., H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60, 848–850 (1988) [doi:10.1103/PhysRevLett.60.848]. von Klitzing, K., “The quantized Hall effect,” Physica B+C 126, 242–249 (1984) [doi:10.1016/0378-4363(84)90170-0]. Weisbuch, C. and B. Vinter, Quantum Semiconductor Structures: Fundamentals and Application, Academic Press, San Diego (1991). Wolf, E. L., Nanophysics and Nanotechnology: An Introduction to Modern Concepts in Nanoscience, Wiley-VCH, Weinheim, Germany (2004) [doi:10.1002/9783527618972]. Xia, Y., P. Yang, Y. Sun, Y. Wu, B. Mayers, B. Gates, Y. Yin, F. Kim, and H. Yan, “One-dimensional nanostructures: Synthesis, characterization and applications,” Adv. Mater. 15, 353–389 (2003) [doi:10.1002/adma.200390087]. Yoffe, A. D., “Low-dimensional systems: quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems,” Adv. Phys. 51, 799–890 (2002) [doi:10.1080/00018730110117451]. Žuti´c, I., J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys. 76, 323–410 (2004) [doi:10.1103/RevModPhys.76.323].

Chapter 4

Nanofabrication The availability of new and improved methods for fabricating nanomaterials as well as the availability of new and improved tools for characterization and manipulation of nanomaterials (Chapter 5) have engendered an explosive growth of nanoscience and nanotechnology during the last decade. The fabrication of nanomaterials of tailored properties involves the control of size, shape, structure, composition, and purity of their constituents. Fabrication techniques for nanostructures can be broadly divided into two categories. Topdown approaches consist of the miniaturization or size reduction (by, e.g., etching or milling) of larger structures. Often, lithographic patterning to structure bulk materials at the nanoscale is involved. Bottom-up approaches are based on growth and self-assembly to build up nanostructures from atomic or molecular precursors. A major challenge is to create hybrid approaches and develop strategies to reliably fabricate complex material systems spanning all length scales from the molecular to the macroscopic. In fact, when developing a technique for fabricating nanostructures, the most important issue is the simultaneous control over dimensions, morphology, composition, and uniformity. Nanomaterials fabricated by different routes may have different internal structures that would affect their properties. The most common, as well as the most promising, techniques used for the fabrication of nanostructures at present are summarized in Table 4.1 and are succinctly described in the following sections.

4.1 Physical Vapor Deposition Physical vapor deposition (PVD) is a versatile method for preparing thin-film materials with structural control at the atomic or nanometer scale by carefully monitoring the processing parameters. PVD involves the generation of vapor phase species via evaporation, sputtering, or laser ablation. In thermal evaporation, atoms or clusters of atoms are removed from a crucible containing some bulk or powder material by heating the crucible either by passing a current through it or by directing a beam of electrons onto the bulk material in the crucible. The evaporation process takes place in an evacuated chamber. The vapor phase emanating from the source material condenses on a substrate, as shown in Fig. 4.1. In sputtering, atoms are ejected from the surface of the bulk material by 53

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Table 4.1 The most common and most promising techniques for nanofabrication. Fabrication technique

Principle of operation or description

Remarks

Physical vapor deposition (PVD): – Evaporation (thermal or e-beam) – Sputtering – Laser ablation

Vapor phase species—generated from a solid sample via either evaporation, sputtering, or laser ablation in high vacuum—is collected on a substrate to form a nanomaterial.

Oblique-angle deposition (OAD): Highly collimated vapor enables the fabrication of thin films with engineered nanoscale morphology. Ion-beam-assisted deposition (IBAD): Combination of ion implantation with a PVD technique

Chemical vapor deposition (CVD)

Substrate exposed to one or more volatile precursor materials, which react and/or decompose on its surface under thermal, laser, or plasma excitation

Variants: APCVD, LPCVD, UHVCVD, MPCVD, PECVD, RPECVD, AACVD, DLICVD, MOCVD, RTCVD, Cat-CVD, HWCVD, and HFCVD

Atomic layer deposition (ALD)

Alternate pulsing of the precursor gases and vapors onto the surface of a substrate and subsequent chemisorption or surface reaction of the precursors

Surface-controlled self-limiting method for depositing thin films from gaseous precursors that allows the growth of conformal thin films with precisely controlled thickness on large areas

Molecular beam epitaxy (MBE)

Molecular beams of constituent materials directed onto a heated crystalline substrate to form thin epitaxial layers

Produces ultrathin films as high-quality epitaxial layers with very sharp interfaces and good control of thickness, doping, and composition

Nanolithography: – Photolithography – X-ray lithography – Extreme ultraviolet lithography

Selective removal of parts of a thin film or substrate by using light to transfer a geometric pattern from a photomask to a layer of a photoresist on the substrate

Related techniques: Scattering with angular limitation in projection electron-beam lithography (SCALPEL), projection reduction exposure with variable-axis immersion lenses (PREVAIL), and digital lithography

– Electron-beam lithography – Ion-beam lithography Nano-imprint lithography (NIL)

Electron beam writes patterns on a surface A focused beam of ions writes patterns on a surface Patterns created by mechanical deformation of an imprinted photoresist

Variants: Step-and-flash imprint lithography, lithographically induced self-assembly (LISA), laser-assisted direct imprint (LADI), and laser-assisted nano-imprint lithography (LAN) (continued on next page)

Nanofabrication

55

Table 4.1 (continued) Fabrication technique

Principle of operation or description

Remarks

Scanning probe lithography (SPL)

Scanning tip used as mechanical, electric, and/or thermal source to induce a physico-chemical process in order to modify, deposit, remove, and manipulate materials at the nanoscale

Related technique: Dip-pen nanolithography (DPN)

Focused ion-beam (FIB)

Focused beam of slow heavy ions creates patterns at the nanoscale by modification, deposition, or sputtering. Focused beam of fast protons directly writes patterns on a photoresist.

Related technique: Ion-beam sculpting to make nanopores in a two-step process

Delicate control of surface properties for new growth to spontaneously form structures with the desired shape and size

Bottom-up techniques that generally rely on the self-assembling nature of organic molecules, including complex species such as DNA

Proton-beam (p-beam) writing

Self-assembly and self-organization

Self-assembled monolayers (SAMs) comprise organic molecules whose functionality can be modified by chemical treatment or radiation so that the subsequent layers can be selectively attached and used to direct oriented crystal growth. Langmuir–Blodgett (LB) method

Deposition from solution of monomolecular organic films on different substrates

Layer-by-layer (LbL) assembly

Alternating adsorption of positively and negatively charged species from aqueous solutions

Other techniques: – Spray conversion processing

Conformal coating of substrates of complex shapes

Atomization of chemical precursors into aerosol droplets that are dispersed throughout a gaseous medium

– Thermal spraying

Molten droplets of coating material projected at high speed onto a surface

– Sol-gel processing

Generation of a colloidal suspension (sol) which is subsequently converted to a viscous gel and then to a solid material (continued on next page)

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Table 4.1 (continued) Fabrication technique

Principle of operation or description

– Pyrolysis

Chemical decomposition of organic materials by heating in the absence of oxygen or any other reagents

– Electrochemical processes

Reactions at solid–liquid interfaces controlled by an externally applied voltage

Remarks

Figure 4.1 Schematic of a typical setup for evaporation. The source material is heated by an electrical filament in thermal evaporation, or by an electron beam in electron-beam evaporation.

the impact of energetic ions created in a plasma environment (Fig. 4.2). In laser ablation or pulsed laser deposition, an intense pulsed laser beam irradiates the bulk material, thereby releasing a vapor of atoms and clusters of atoms. As both thermal evaporation and laser ablation occur at low pressure, atoms in the vapor travel more or less rectilinearly, i.e., with minimal scattering. However, some scattering does occur during sputtering and generally yields denser films. Thermal evaporation is not very suitable for making multicomponent thin films, since some bulk materials evaporate before others due to differences in vapor pressure of the evaporating species. Sputtering is capable of depositing highmelting-point materials such as refractory metals and ceramics. This is because the vapor is created by transfer of momentum from ions to atoms, rather than

Nanofabrication

57

Figure 4.2 Typical sputtering system.

by direct heating of atoms. As the sputtered atoms carry more energy than the thermally evaporated atoms, the sputter-grown films usually have higher mass density. However, the typical deposition rate of sputtering is significantly lower than that of thermal evaporation. Laser ablation usually provides better control through simultaneous evaporation of multicomponent materials in a very short time period. Oblique angle deposition (OAD) is a PVD method that enables the fabrication of nano-engineered thin films. The vapor created is largely collimated so that the thin films grown have a columnar morphology. Developments in OAD technology during the last three decades have produced columnar nanostructures of various shapes (including vertical, tilted, helical, and chevronic) and graded-porosity thin films for use in applications ranging from sensors and actuators to optical filters, microfluidics, and catalysis. Ion-beam-assisted deposition (IBAD) is a technique that combines ion implantation with another PVD technique. IBAD is particularly effective in improving adhesion and morphology control and has the advantage of having more independent processing parameters than other PVD methods. For example, the energy and flux of bombarding ions can be exploited to modify the size and crystallographic orientation of grains.

4.2 Chemical Vapor Deposition Chemical vapor deposition (CVD) is a technique in which the substrate is exposed to one or more volatile precursor materials that react and/or decompose on the substrate surface to produce the desired deposit. This technique is used to produce high-purity, high-performance solid materials. Thermal, laser, or plasma energies are used for the decomposition of gaseous reactants. Figure 4.3 represents a

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Figure 4.3 Plasma-assisted chemical vapor deposition system.

plasma-assisted CVD system. CVD has been a well-established technique for thinfilm deposition for many years because it offers the advantages of a relatively simple apparatus, excellent uniformity, high density, high deposition rate, and amenability to large-scale production. Many forms of CVD are in wide use and are frequently referenced in the literature. These processes differ in the means by which chemical reactions are initiated (e.g., activation process) and process conditions. As such, atmosphericpressure CVD (APCVD), low-pressure CVD (LPCVD), and ultrahigh-vacuum CVD (UHVCVD) are named after the typical chamber pressure at which the reaction takes place. Depending on the characteristics of the plasma, the following forms can be found: microwave plasma-assisted CVD (MPCVD), plasmaenhanced CVD (PECVD), magneto-microwave plasma CVD, and remote plasmaenhanced CVD (RPECVD). If the characteristics of the vapor used are considered, the following two forms are commonly found: aerosol-assisted CVD (AACVD) and direct liquid-injection CVD (DLICVD). Metal-organic CVD (MOCVD) uses metal-organic precursors, while in rapid thermal CVD (RTCVD) the substrate is heated. Catalytic CVD (Cat-CVD) is based on the catalytic decomposition of precursors using a resistively heated filament. This technique is also known as hotwire CVD (HWCVD) or hot-filament CVD (HFCVD).

4.3 Atomic Layer Deposition Atomic layer deposition (ALD) is a surface-controlled self-limiting method for depositing thin films from gaseous precursors. Although ALD can be considered a modification of CVD, the distinctive feature of ALD is the self-limiting growth mechanism that affords this method several attractive properties: accurate and simple control of film thickness, production of sharp interfaces, uniformity over large areas, excellent conformality with the substrate, good reproducibility, multilayer processing capability, and desirable film qualities at relatively low temperatures. From a nanotechnological angle, the most important benefits of ALD are excellent conformality and the possibility of subnanometer control of film thickness.

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ALD relies on alternate pulsing of the precursor gases and vapors onto the substrate surface and subsequent chemisorption or surface reaction of the precursors. The reactor is purged with an inert gas between the precursor pulses. This process is schematically depicted in Fig. 4.4. With a proper adjustment of the experimental conditions, the process proceeds via saturative steps; i.e., the precursors exposed on the surface chemisorb on it (or react with the surface groups), saturatively forming a tightly bound monolayer on the surface. The subsequent purging step removes all of the excess molecules from the reactor chamber. When the next precursor is dosed in, it encounters only the surface monolayer with which it reacts, thereby producing the desired solid product and gaseous by-products. Under such conditions, the film growth is self-limiting, since the amount of solid deposited during one cycle is dictated by the amount of precursor molecules present in the saturatively formed surface monolayer. Therefore, the growth is stable, and the thickness increase is constant in each deposition cycle. The self-limiting growth mechanism facilitates the growth of conformal thin films with accurately controlled thickness on large areas. This technique also allows the growth of multilayer structures. However, a major limitation of ALD is its typically slow growth rate.

4.4 Molecular Beam Epitaxy Molecular beam epitaxy (MBE) is a technique to produce ultrathin films as highquality epitaxial layers with very sharp interfaces and good control of thickness,

Figure 4.4 Schematic representation of the typical ALD technique. In order to grow a thin film, the following four steps need to be repeated: (1) exposure to the first precursor, (2) purge of the deposition chamber to remove precursors in excess and by-products, (3) exposure to a second precursor, and (4) purge of the deposition chamber. (From http://wwwrpl.stanford.edu/user/files/www/ald1.gif.)

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doping, and composition. Deposition takes place in very high vacuum. Because of the high degree of control possible with MBE and the possibility of growing compound semiconductors, it is a valuable tool in the development of sophisticated electronic and optoelectronic devices. In MBE, the constituent materials in the form of molecular beams are deposited on a heated crystalline substrate to form a thin epitaxial layer, as depicted schematically in Fig. 4.5. Each layer has a definite crystallographic relationship with the substrate. The molecular beams are typically obtained from thermally evaporated elemental sources, but other sources include metal-organic group-III precursors (MOMBE), gaseous group-V hydride or organic precursors (gas-source MBE), or some combination [chemical beam epitaxy (CBE)]. To obtain epitaxial layers of high purity, it is critical that the source materials be extremely pure and that the entire process be carried out in an ultrahigh-vacuum environment. Growth rates are typically on the order of a few Å/s, and the molecular beams can be shuttered in a fraction of a second, allowing for almost atomically abrupt transitions from one material species to another. Given the ultrahigh-vacuum environment of the system, analytical techniques such as reflection high-energyelectron diffraction (RHEED) and mass spectrometry are often used for in situ monitoring of the growing thin film.

4.5 Nanolithography Nanolithography, or lithography at the nanoscale, refers to the fabrication of patterns with at least one lateral dimension between the size of an individual atom and approximately 100 nm. This technique comprises several lithographic techniques, including photolithography, x-ray lithography, electron-

Figure 4.5 Typical system for molecular beam epitaxy (MBE). Solid source materials are placed in effusion cells and heated to be used as molecular flux sources. The substrate is heated to the necessary temperature and, when needed, continuously rotated to improve the growth homogeneity.

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beam lithography, and ion-beam lithography, depending on the radiation employed, as explained in the following paragraphs. Photolithography (also called optical lithography), which has been the predominant patterning technique since the dawn of the age of semiconductors, is capable of producing sub-100-nm patterns with the use of very short-wavelength light (currently 193 nm). This microfabrication process is used to selectively remove parts of a thin film (or the bulk of a substrate) by first using light to transfer a geometric pattern from a photomask to a layer of a light-sensitive chemical (photoresist, or simply resist) on the substrate. A series of chemical treatments then engraves the exposure pattern into the material underneath the photoresist. In a complex integrated circuit (for example, a modern CMOS), a wafer will go through up to 50 photolithographic cycles. Photolithography resembles conventional lithography used to print on paper. It delivers exact control over the shape and size of the pattern it creates and can create patterns over a large surface (∼30-cm diameter) in one round of photolithographic cycles. The main disadvantages of photolithography are that it requires a flat substrate to start with, is not very effective at creating nonplanar shapes, and requires extremely clean operating conditions. Figure 4.6 shows a general sequence of steps for a typical photolithography process. Resolutionenhancement techniques for photolithography continue to be developed, leading to a reduction of the minimum feature size. X-ray lithography can be extended to a resolution of 15 nm by using the ultrashort wavelength of 1 nm for the illumination. Extreme ultraviolet lithography (EUV) uses the same principles as conventional optical lithography, although the exposure wavelength is typically in the range of 11–13.5 nm. Electron-beam lithography uses a beam of electrons to generate patterns on a surface. The primary advantage of this technique is that it overcomes the diffraction limit of light. With today’s electron optics, the diameters of electron beams can routinely go down to a few nanometers, limited mainly by aberrations and space charge. However, pattern generation, which is a serial process, is very slow when compared with a parallel technique such as photolithography (the current standard), in which an entire surface is patterned all at once. Therefore, electronbeam lithography has limited application in industry. A projection optical system that is geometrically equivalent to that used in optical lithography will improve throughput. In this regard, the most notable attempts to use mask projection are scattering angular-limited projection electronbeam lithography (SCALPEL), developed at Bell Laboratories and projection reduction exposure with variable-axis immersion lenses (PREVAIL), developed by IBM. A related technique is ion-projection lithography (IPL), in which the electron beam is replaced by an ion beam. In IPL, generally medium-energy (50 to 150 keV) ions (e.g., protons, H+ , He+ , Ar+ , etc.) are used, although heavy ions have also been used. IPL combines the mass-fabrication advantage of masked lithography with the remarkable properties of ions.

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Figure 4.6 Representation of the general sequence of steps for a typical photolithography process: substrate preparation, photoresist spin coat, prebake, exposure, postexposure bake, development, and postbake. Stripping the resist is the final operation in the lithographic process, taking place after the resist pattern has been transferred into the underlying layer via etching or ion implantation. This sequence is generally performed on several tools linked together into a contiguous unit called a lithographic cluster. [Reprinted from Mack.1 ]

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The recently developed digital lithography can be succinctly described as the process of jet-printing an etch mask. A thin film is first grown by any deposition technique. Then, the mask pattern is jet printed directly onto the substrate. The film is subsequently etched to reproduce the pattern, and, finally, the etch mask is removed. Among other characteristics, this technique simplifies the conventional photolithography process by reducing the number of steps. Additionally, it can be used to pattern a number of materials.

4.6 Nano-imprint Lithography Nano-imprint lithography (NIL) is a rapidly emerging method of fabricating nanoscale patterns, depicted schematically in Fig. 4.7. It is a simple and inexpensive method with high throughput and high resolution. Patterns are created by mechanical deformation of an imprint resist. The imprint resist is typically a monomer or polymer that is cured by heat or ultraviolet light during the imprinting process. Unlike conventional lithography techniques, nano-imprint lithography’s resolution is not limited by the effects of wave diffraction, scattering and interference in a resist, and backscattering from a substrate. Nano-imprint lithography is used to fabricate devices for electrical, optical, photonic, and biological applications. The hallmark of nano-imprint lithography is its ability to pattern 3D structures. Nano-imprint lithography and its variants— such as step-and-flash imprint lithography, which uses transparent templates and UV-curable materials to allow pattern replication at room temperature and low pressure; lithographically induced self-assembly (LISA), which takes advantage of the self-assembly phenomenon observed in polymer thin films; laser-assisted direct imprint (LADI), in which a single excimer laser pulse melts a thin surface layer of silicon, and a mould is embossed into the resulting liquid layer; and laser-assisted nano-imprint lithography (LAN), which combines the advantages of NIL and laserassisted direct imprint—are promising nanopattern replication technologies. Nanoimprint lithography can be combined with contact printing.

4.7 Scanning Probe Lithography Techniques grouped together as scanning probe microscopy (SPM) include scanning tunneling microscopy (STM) and atomic force microscopy (AFM). SPM is generally used to determine the topography of samples at the nanoscale (Chapter 5). Taking advantage of the sharpness of the probe tips, as well as of strong and localized tip–surface interactions, SPM has also been used to manipulate atoms on metal surfaces and to fabricate nanopatterns of metal and semiconductor surfaces. These successful examples exemplify the growing field of scanning probe lithography (SPL). Scanning probe microscopy—more specifically, STM and AFM—is increasingly used to modify, deposit, remove, and manipulate materials at the nanoscale, thus making it a powerful tool in the fabrication of nanomaterials. Some researchers date the emergence of nanotechnology to 1981, when the scanning tunneling microscope was invented. The scanning tips are used as mechanical, electric,

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Figure 4.7 Schematic of the nano-imprint technique. [Reprinted from Nie and Kumacheva2 c 2008.] with permission from Macmillan Publishers Ltd.

and/or thermal sources to induce different physico-chemical processes. SPM has the additional advantages of requiring relatively inexpensive apparatus, involving relatively easy operation, and providing the possibility for parallel operation, thus enormously increasing its throughput. Three main categories can be distinguished regarding the use of SPM in the field of nanofabrication: material modification, including resist exposure and oxidation; material addition, mainly consisting of induced deposition; and material removal, including scratching and etching. Figure 4.8 shows two examples of AFM-tip-induced oxidation on silicon substrates.

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Figure 4.8 AFM images of AFM-tip-induced oxidation lines on n-type-silicon substrates with (a) ∼90-nm linewidth and (b) ∼23-nm linewidth. [Reprinted with permission from Tseng c 2005, American Vacuum Society.] et al.3

SPM is capable of manipulating single atoms on a given surface, even on nonplanar surfaces. This fabrication technique is called atom manipulation or nanoassembly. To exemplify the products of this technique, Fig. 4.9 shows a 3D STM image of a quantum corral during construction and after completion. The quantum corral nanostructure is composed of silver atoms grown onto a silver substrate. Dip-pen nanolithography (DPN) uses an AFM tip coated with a thin film of ink molecules that react with the substrate surface to write nanoscale patterns for lithography applications. The first experiments were carried out on gold surfaces with alkanethiols as inks.

4.8 Focused Ion-Beam Technique, Proton-Beam Writing, and Ion-Beam Sculpting Focused ion-beam (FIB) and proton-beam (p-beam) writing are maskless techniques capable of fabricating sub-100-nm features. The ability of these techniques to fabricate 3D structures of flexible geometry enables rapid prototyping of micro- and nanosystems. Furthermore, these two ion techniques, together with IPL (Section 4.5), have complementary areas of application. The FIB technique uses a focused beam of slow heavy ions (with energies typically around 30 keV) to create patterns at the nanoscale by modification, deposition, or sputtering. The FIB technique is remarkable in that patterns can be produced in virtually any material, although the process is relatively slow. Protonbeam writing uses a focused beam of fast [million electron volt (MeV)] protons for directly writing patterns on several types of photoresists. Their high energy allows the incident protons to penetrate deep into the photoresist. Ion-beam sculpting is a term used to describe a two-step process to make nanopores. The first step is to make either a hole all the way through a solid or a blind hole (i.e., a hole that does not break through on the backside), most commonly using a focused ion-beam (FIB) machine. The holes are commonly ∼100 nm in diameter, although they can be made much smaller. This first step

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Figure 4.9 STM images of a quantum corral grown onto silver (a) during construction and (b) after completion of the corral, in which 36 silver atoms are used. These are observed as c 2003 white protrusions of diameter 31.2 nm. [Reprinted with permission from Hla et al.4 by the American Physical Society.]

may or may not be done at room temperature. For the second step, there are three common techniques to sculpt the hole: broad-area ion exposure, transmission electron microscopy (TEM) exposure, and FIB exposure. Holes can be closed completely, or they can be left open at a lower limit of 1–10 nm in diameter. Figure 4.10 shows an ion-beam sculpting apparatus that incorporates feedback into the fabrication process to gain dimensional control over the hole diameter at the single-nanometer length scale. In this instrument, a free-standing membrane surface containing an initial ∼100-nm hole or bowl-shaped cavity is exposed to a normal beam of low-energy ions. Since an argon-ion beam is used to create the nanopores, the rate of argon transmission through the hole provides a direct measure of its size. This rate is monitored to provide the feedback signal necessary to trigger the extinction of the ion beam when the desired hole diameter is obtained.

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Figure 4.10 Schematic of a feedback-controlled ion-beam sculpting tool. [Reprinted with c 2004, American Institute of Physics.] permission from Stein et al.5

By controlling such experimental parameters as sample material, temperature, ion flux, and time of exposure to the ion beam, the length of the hole can be made either smaller than or equal to the thickness of the solid. Hence, the process is referred to as ion beam sculpting rather than etching or sputtering.

4.9 Self-Assembly, Self-Organization, and Self-Assembled Monolayers Self-assembly and self-organization of nanoparticles involves a delicate control of surface properties so that new growth spontaneously forms structures with the desired geometry. Self-assembly includes bulk reactive methods such as the chemical formation of colloidal semiconductors. The technique has been extensively explored as a bottom-up approach for generating complex nanostructures on various length scales. Many self-assembly processes rely on the self-assembling nature of organic molecules, including complex species such as DNA. These methods are termed chemical or molecular self-assembly. Generally, molecular self-assembly is defined as the spontaneous organization of relatively rigid molecules into structurally well-defined aggregates via weak reversible interactions such as hydrogen, ionic, and van der Waals bonds. The aggregated

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structure represents a minimum-energy structure or equilibrium phase. Selfassembly is also found to occur in biological systems and in micelles and liquid crystals, and is being increasingly used in synthetic supramolecular chemistry. Other simpler methods rely on geometric self-organization, in which hard spheres or hard rods will arrange themselves into 2D and 3D structures based on packing considerations. As an example, solutions of colloidal metal particles can spontaneously order themselves into 2D hexagonally close-packed sheets on given substrates. Molecular systems such as rod-like and disc-like liquid crystals also exhibit geometric self-organization properties. A variation on geometric self-organization is templated self-organization in which an ordered nanostructure is formed by deposition of a material around a previously self-organized template. This approach can be used to produce metallic or semiconductor structures via different deposition techniques on geometrically self-organized polystyrene or silica spheres of submicron dimensions. The spheres are subsequently dissolved to leave a highly porous structure. More complex self-assembly processes involve the use of self-assembled monolayers (SAMs). SAMs comprise organic molecules whose functionality can be modified by chemical treatment or radiation (e.g., lithography) so that the subsequent layers can be selectively attached and used to direct oriented crystal growth. The ends of the molecules are usually terminated with a thiol group to provide good adhesion to a gold substrate. The molecules will order on the substrate under given conditions of concentration, pH, and temperature. Another important type of self-assembly process is the self-assembled growth of semiconductor quantum dots.

4.10 Langmuir–Blodgett Method The Langmuir–Blodgett (LB) method is a classical method used in chemistry for the deposition of molecular monolayers and multilayers. Making use of the hydrophilic/hydrophobic orientation of molecules, this method and its variants allow the deposition from solution of monomolecular organic films on different substrates. A Langmuir monolayer is generally prepared by placing a given number density of amphiphilic molecules on the surface of an aqueous solution. One end of an amphiphilic molecule is hydrophilic, while the other end is hydrophobic. The monolayer spreads spontaneously onto the surface and any volatile organic solvents, e.g., chloroform, methanol, or benzene, evaporate in a short period of time. Generally, the solution is held in a Teflon container, known as a trough, in order to control the temperature and the fraction of the water surface accessible to the monolayer as well as to measure surface tension (or surface pressure). One or more movable (typically, motorized) Teflon barriers placed across the trough serve to vary the area of the monolayer. The process of building an LB multilayer consists of periodically dipping a substrate into the solution. A layer is deposited during each dip. However, the molecules deposited during the removal step (generally termed upstroke) have their

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heads oriented toward the substrate while the molecules deposited in the immersion step (downstroke) are oriented with their tails facing the substrate. The result is that the heads in the current layer adhere to the heads in the previously deposited layer during the upstroke, and the tails of the current layer stick to the tails in the previously deposited layer during the downstroke. There are many modes for the deposition of LB films. The most common deposition mode, called the Y mode, is illustrated in Fig. 4.11. In this mode, if the substrate is initially hydrophilic, the molecules are shown to stack in a headto-head and tail-to-tail configuration. An almost perfect film can be assembled like this, monolayer by monolayer. Although the Langmuir–Blodgett method has obvious attractions, a major shortcoming until recently has been the restricted range of materials for which it can be used. Various organic materials have been deposited using this method, although the best results have been obtained with either fatty acids or their

Figure 4.11 Langmuir–Blodgett film deposition in the common mode called the Y mode. With a hydrophilic substrate, no film deposition occurs during the first immersion. The first monolayer is deposited during the first upstroke. Thereafter, the deposition of one monolayer is obtained on each immersion/emersion step (downstroke/upstroke). (a) The layer on the surface of the water, (b) the first layer grown during the upstroke, (c) the second layer formed after the downstroke (second immersion), and (d) the substrate with three layers (after second upstroke). [Reprinted from Roberts et al.6 with permission from IOP.]

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salts, since these substances possess molecules with the required hydrophilic and hydrophobic ends.

4.11 Layer-by-Layer Assembly Layer-by-layer (LbL) assembly is a versatile and quite inexpensive method to fabricate ultrathin films with nanometer-level control over their composition and structure, and thus over their specific properties. This technique is based on the alternating adsorption of positively and negatively charged species from aqueous solutions, and can be used to create highly tuned, functional thin films. LbL multilayer films have received considerable attention in both fundamental studies and applied research. A typical LbL assembly takes place as follows: A substrate is first immersed in a solution of a negatively charged polyelectrolyte, e.g., poly(styrene sulfonate) (PSS), poly(vinyl sulfate), and poly(acrylic acid) (PAA). The polyanionic species causes the surface of the coated substrate to have a negative charge. The coated substrate is then rinsed in a washing solution (generally pure water) to remove any loosely adsorbed polyelectrolyte from the substrate and dried under a nitrogen/air flow. Subsequent execution of an analogous procedure with a positively charged polyelectrolyte solution leads to the reversal of net charge on the surface, making the surface of the doubly coated substrate positively charged. Typical positively charged polyelectrolytes include poly(diallyldimethylammonium chloride) (PDDA), poly(allylamine hydrochloride) (PAH), and polyethyleneimine (PEI). After these two steps, a polyanion/polycation bilayer is fabricated on the substrate. The process is schematically depicted in Fig. 4.12. Since the surfaces of many types of substrates (including metals, silicones, and glasses) have net negative charges in solution as a consequence of surface oxidation and hydrolysis, it is possible to reverse the order of polyelectrolytes and fabricate a polycation/polyanion bilayer instead. Subsequent repetitions of the bilayer-deposition cycle result in the growth of multilayer films with the desired morphology and thickness. The roughness, thickness, and porosity of a multilayer film can be controlled at the molecular level by adjusting experimental parameters such as pH, ionic strength, and polyelectrolyte concentration. Since the thickness of a single polycation/polyanion bilayer is typically below 1 nm, nanometer-scale control is achieved. Compared to the Langmuir–Blodgett method (Section 4.10), LbL assembly is generally much simpler and faster, and usually results in more stable films. Also, the multilayer structure of LbL-deposited thin films allows much higher loadings of biologically interesting species compared to self-assembled monolayers (Section 4.9). Although the LbL technique was first applied to assemble layers of oppositely charged polymers, it has been extended to other materials. Almost any type of charged species—including inorganic molecular clusters, metal, semiconductor and polymer nanoparticles, nanotubes, nanowires, organic dyes, dendrimers,

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Figure 4.12 (a) Schematic of the film deposition process, representing the adsorption of a polycation and a polyanion, and the washing steps in deionized water. The four steps represent the basic sequence for the fabrication of the simplest thin film structure: (A/B)n . (b) Simplified molecular picture of the first two adsorption steps, depicting film deposition starting with a negatively charged substrate. Counterions are omitted for clarity. [Reprinted from Kumar and Kumar.7 ]

porphyrins, biological polysaccharides, polypeptides, nucleic acids and DNA, proteins, and viruses—can be used to fabricate multilayer films by LbL assembly. Furthermore, the formation forces of LbL films are not limited to only electrostatic interactions as in the first experiments. Assemblies relying on hydrogen bonding, charge transfer, covalent bonding, biological recognition, and hydrophobic interactions have also been investigated. This versatility translates into films of an exceptionally wide variety of functional properties. LbL assembly is additionally versatile with regard to the types of substrates, including hydrophilic and hydrophobic glasses, mica, silicon, metals, quartz, and polymers. Moreover, the substrates can be of practically any shape, including 1D tubes or 3D colloids. Furthermore, freely suspended flexible LbL structures with different shapes, compositions, and properties can be fabricated by using sacrificial substrates (planar, spherical, and cylindrical). Freestanding LbL microand nanocapsules, membranes, encapsulated nanoparticle arrays, sealed-cavity arrays, microtubules, microcubes, microcantilevers, and planar films have been made. Overall, the availability of a wide variety of component materials and substrates, and the versatility of LbL assembly result in a large variety of applications of LbL films. Potential applications of LbL films have been proposed in such areas as surface coatings, optics and optoelectronics, drug delivery, electrochemistry, fuel cells, chemical sensors, nanomechanical sensors, and nanoscale chemical reactors. Also, LbL assembly has attracted extensive attention for biomedical applications, given the possibility of heavily loading LbL films with different types of biomolecules, as well as the stability of LbL films exposed to harsh and physiological conditions. Accordingly, applications of LbL assembly in the fields

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of biomimetics, biosensors, drug delivery, protein and cell adhesion, mediation of cellular functions, and implantable materials have been proposed.

4.12 Other Techniques A rich palette of chemical techniques has been developed for fabricating lowdimensional structures with well-controlled dimensions and from a broad range of materials. Methods based on chemical synthesis usually provide attractive strategies in terms of material diversity, cost, throughput, and the potential for high-volume production. Although some of these techniques were developed many years ago, researchers are using them to find new applications for the development of nanostructured coatings. Some of the most common techniques are as follows. Spray conversion processing involves the atomization of chemical precursors into aerosol droplets that are dispersed throughout a gaseous medium. The aerosols are then transported into a heated reactor where the solution is either evaporated or combusted to form ultrafine particles or thin films. This is a versatile and inexpensive technique because of the availability of various inexpensive chemical solutions. Various aerosol generators—including pressure, electrostatic, and ultrasonic atomizers—have been used for atomization. Thermal spraying is a well-established method for forming hard coatings on selected component substrates. The coating material is heated in a gaseous medium, and molten droplets of it are projected at high speed onto a surface. Upon impact, the droplets flatten, transfer the thermal energy to the cold substrate, and solidify rapidly as splats. Sol-gel processing involves the generation of a colloidal suspension called sol, which is subsequently converted to a viscous gel and then to a solid material. In the category of wet chemical synthesis, solution-based processing routes used for the synthesis of nanoparticles include precipitation of solids from a supersaturated solution, homogeneous liquid-phase chemical reduction, and ultrasonic decomposition of chemical precursors. These processes are attractive due to their simplicity, versatility, and availability of inexpensive precursor materials. Pyrolysis, a special case of thermolysis (i.e., dissociation of particles by heat), is the chemical decomposition of organic materials by heating in the absence of oxygen or any other reagents, except possibly steam. Extreme pyrolysis, which leaves only carbon as the residue, is called carbonization. Electrochemical processes, which involve reactions at solid–liquid interfaces controlled by an externally applied voltage, are being increasingly used as quite inexpensive, easy to handle, versatile, and reliable tools for nanofabrication. In particular, electrodeposition is used for forming dense nanocrystalline materials. Its advantages include low cost and industrial applicability, as it involves little modification of existing electroplating technologies. It is simple to implement, as the electrodeposition parameters can be easily tailored to meet the required grain size, microstructure, and chemistry of products. Electrodeposition is also

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versatile, as it can produce a wide variety of pore-free materials and coatings at high production rates. Figure 4.13 shows a typical setup for electrodeposition.

Figure 4.13

Typical experimental setup for electrodeposition.

References 1. C. A. Mack, Field Guide to Optical Lithography, SPIE Press, Bellingham, WA (2006). 2. Z. Nie and E. Kumacheva, “Patterning surfaces with functional polymers,” Nat. Mater. 7, 277–290 (2008) [doi:10.1038/nmat2109]. 3. A. A. Tseng, A. Notargiacomo, and T. P. Chen, “Nanofabrication by scanning probe microscope lithography: A review,” J. Vac. Sci. Technol. B 23, 877–894 (2005) [doi:10.1116/1.1926293]. 4. S.-W. Hla, K.-F. Braun, and K.-H. Rieder, “Single-atom manipulation mechanisms during a quantum corral construction,” Phys. Rev. B 67, 201402 (2003) [doi:10.1103/PhysRevB.67.201402]. 5. D. M. Stein, C. J. McMullan, J. Li, and J. A. Golovchenko, “Feedbackcontrolled ion beam sculpting apparatus,” Rev. Sci. Instr. 75, 900–905 (2004) [doi:10.1063/1.1666986]. 6. G. G. Roberts, P. S. Vincett, and W. A. Barlow, “Technological applications of Langmuir–Blodgett films,” Phys. Technol. 12, 69–87 (1981) [doi:10.1088/03054624/12/2/I02].

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7. A. Kumar and J. Kumar, “Layer-by-layer deposition of nanoscale structures,” J. Nanophoton. 3, 030306 (2009) [doi:10.1117/1.3241043].

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M. Leskelä and M. Ritala, “Atomic layer epitaxy—a valuable tool for nanotechnology?” Nanotechnology 10, 19–24 (1999) [doi:10.1088/0957-4484/ 10/1/005]. Liu, G. Y., S. Xu, and Y. Qian, “Nanofabrication of self-assembled monolayers using scanning probe lithography,” Acc. Chem. Res. 33, 457–466 (2000) [doi:10.1021/ar980081s]. Lüth, H., “Electronic properties and quantum effects,” in Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices, R. Waser, Ed., Wiley-VCH, Weinheim, Germany (2005). Okazaki, S. and J. Moers, “Lithography,” in Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices, R. Waser, Ed., Wiley-VCH, Weinheim, Germany (2005). Poole, C. P., Jr. and F. J. Owens, Introduction to Nanotechnology, Wiley, Hoboken, NJ (2003). Salaita, K., Y. Wang, and C. A. Mirkin, “Applications of dip-pen nanolithography,” Nat. Nanotechnol. 2, 145–155 (2007) [doi:10.1038/nnano.2007.39]. Schwartz, D. K., “Langmuir–Blodgett film structure,” Surf. Sci. Rep. 27, 245–334 (1997) [doi:10.1016/S0167-5729(97)00003-4]. Street, R. A., W. S. Wong, S. E. Ready, M. L. Chabinyc, A. C. Arias, S. Limb, A. Salleo, and R. Lujan, “Jet printing flexible displays,” Mater. Today 9 (4), 32–37 (2006) [doi:10.1016/S1369-7021(06)71445-6]. Tang, Z., Y. Wang, P. Podsiadlo, and N. A. Kotov, “Biomedical applications of layer-by-layer assembly: From biomimetics to tissue engineering,” Adv. Mater. 18, 3203–3224 (2006) [doi:10.1002/adma.200600113]. Tjong, S. C. and H. Chan, “Nanocrystalline materials and coatings,” Mater. Sci. Engg. R 45, 1–88 (2004) [doi:10.1016/j.mser.2004.07.001]. Watt, F., A. A. Bettiol, J. A. Van Kan, E. J. Teo, and M. B. H. Breese, “Ion beam lithography and nanofabrication: A review,” Int. J. Nanosci. 4, 269–286 (2005) [doi:10.1142/S0219581X05003139]. Wolf, E. L., Nanophysics and Nanotechnology: An Introduction to Modern Concepts in Nanoscience, Wiley-VCH, Weinheim, Germany (2004) [doi:10.1002/9783527618972]. Xia, Q., C. Keimel, H. Ge, Z. Yu, W. Wu, and S. Y. Chou, “Ultrafast patterning of nanostructures in polymers using laser assisted nano-imprint lithography,” Appl. Phys. Lett. 83, 4417–4419 (2003) [doi:10.1063/1.1630162].

Chapter 5

Characterization of Nanostructures and Nanomaterials The characterization of nanostructures is a key issue for controlling techniques to fabricate them as well for surmising and determining new applications of nanomaterials. As such, the development of analytical techniques has been essential to the evolution of nanotechnology. Despite the increasingly large number of available analytical techniques, few can be considered to be in widespread use today. Over ten possible primary agents—including electrons, atoms, ions, light (visible, ultraviolet, infrared), x rays, neutrons, and sound—can be harnessed to excite secondary effects—involving electrons, ions, light, neutrons, x rays, sound, etc.—from the region of interest in a sample. The chosen secondary effects can be monitored as functions of one or more of at least seven variables, including energy, intensity, time, angle, phase, mass, and temperature. This leads to a theoretical number of over 700 single-signal characterization techniques, although some permutations of primary agents and secondary effects are physically impractical. Then, of course, there are multiple-signal techniques, wherein two or more secondary effects are simultaneously exploited. To date, more than 100 different techniques have been developed, most of which use photons, electrons, or ions as the primary agents. Table 5.1 summarizes the most widely used characterization techniques for nanostructures and nanomaterials, as discussed in the following sections.

5.1 Electron Microscopy Electron microscopy is an extremely important technique for the analysis of characteristic spatial features of nanostructures, since it provides direct images from which morphological details can be extracted. Electron microscopy includes transmission electron microscopy (TEM) and scanning electron microscopy (SEM), as well as their high-resolution (HR) versions: HRTEM and HRSEM. Electron microscopy uses a collimated beam of electrons that is accelerated by high voltages and focused through a series of electrostatic or magnetic lenses. In TEM/HRTEM, the electron beam travels through the sample and is 77

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Table 5.1 Summary of the characterization techniques most commonly used for the analysis of nanostructures and nanomaterials. Characterization technique

Primary agent

Secondary effect excited or signal detected

Typical applications

Electron microscopies: – TEM, HRTEM, STEM

Electrons

Transmitted electrons, x rays

– SEM, HRSEM

Electrons

– LEEM

Electrons

Backscattered and secondary electrons, x rays Scattered electrons

Imaging, elemental composition (in combination with EDS/EDX), study of crystal structure Imaging, elemental composition (in combination with EDS/EDX) Determination of crystal structure

Other electron techniques: – RHEED – LEED – EELS, LEELS

Spectroscopic techniques: – Raman spectroscopy, SERS – XPS/ESCA (UPS)

– AES

Scanning probe microscopies: – NSOM – STM – AFM Magnetic resonance techniques: – NMR

High-energy electrons Low-energy electrons Electrons

Scattered electrons

Photons Low-energy x rays (ultraviolet photons) Electrons

Scattered photons Photoelectrons

Photons

Photons

A conducting tip scans the surface A tip scans the surface

Tunneling current

Transmitted electrons

Auger electrons

Atomic forces

Magnetic fields

Spins of atomic nuclei Electron spins

High-energy ions

Backscattered ions

– PIXE (PIGE)

Ions

– ERDA

Ions

X rays (gamma rays) Recoiled atoms

– EPR (ESR) Ion-based techniques: – RBS

Magnetic fields

Scattered electrons

Determination of crystal structure Determination of crystal structure Elemental mapping (generally in combination with TEM, HRTEM or STEM) Chemical composition Elemental identification and quantification, depth profiling Elemental identification and quantification, depth profiling Topography, optical properties Topography (conducting materials) Topography

Chemical analysis Chemical analysis Elemental composition, depth profiling Elemental composition, mapping (microPIXE) Elemental composition, depth profiling (light elements) (continued on next page)

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Table 5.1 (continued) Characterization technique

Primary agent

Secondary effect excited or signal detected

Typical applications

– SIMS

Ions

Secondary ions

– NRA

Ions

Reaction products

Elemental and isotopic composition, depth profiling Elemental composition, depth profiling

X rays

Diffracted x rays

– Infrared spectroscopy (IR, FTIR) – Optical spectrometry

IR Photons

IR Photons

Photons

– Ellipsometry – Luminescence, fluorescence

Photons Photons

Reflected and transmitted photons Reflected photons Emitted photons

Other techniques: – XRD

Crystal structure, nanocrystal size, orientation distribution Composition Optical properties

Optical properties Composition

focused on a detector plate. Images are formed because different atoms interact with and absorb electrons to a different extent. Since electrons interact much more strongly with matter than do x rays or neutrons with comparable energies or wavelengths, the best results are obtained for sample thicknesses that are comparable to the mean free path of the electrons (the average distance traveled by the electrons between scattering events). The recommended thickness varies from a few dozen nanometers for samples containing light elements to tens or hundreds of nanometers for samples made of heavy elements. The theoretical resolving power of TEM is theoretically subatomic, although resolutions around 0.1 nm have been achieved in practice. Additionally, TEM allows researchers to generate diffraction patterns for determining the crystallographic structures of samples. Figure 5.1 shows an HRTEM image of a porous silicon–silicon interface. Image processing can be used to increase the information obtained from TEM/HRTEM, thus enhancing some features close to the noise level. By the use of a highly efficient technique such as fast Fourier transform, information similar to that contained in diffraction patterns can be obtained. In an SEM/HRSEM, the electron beam is rastered over the sample in a manner similar to that used in old-fashioned television sets with cathode-ray tubes. The number of backscattered electrons and/or the secondary electrons generated by the beam that emerge from the sample depends on the local composition and topography of the sample. These electrons are collected by an electron detector, and an image is formed by plotting the detector signal as a function of the beam location. This technique has lower resolution than TEM, typically over 1 nm. Figure 5.2 shows a cross-sectional HRSEM image of a chalcogenide multilayer structure grown onto a Si substrate. Features in the nanometer range are resolved.

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Figure 5.1 HRTEM image of a porous silicon–silicon interface. [Reprinted with permission c 2004, American Institute of Physics.] from Martín-Palma et al.1

Figure 5.2 Cross-sectional HRSEM image of a multilayer structure showing alternate GeSbSe layers grown at different angles by the oblique-angle-deposition technique. [Reprinted from Martín-Palma et al.2 with permission from IOP.]

Scanning transmission electron microscopy (STEM) combines features of both SEM and TEM by providing high-resolution imaging of the inner microstructure and the surface of a thin sample or a small particle. Energy dispersive x-ray spectroscopy (EDS or EDX) is a chemical microanalysis technique used in conjunction with either TEM/HRTEM or SEM/HRSEM. The EDS technique detects x rays emitted from the sample during bombardment by an electron beam to characterize the elemental composition of the analyzed volume. Features or phases as small as 1 µm or less can be analyzed. Low-energy electron microscopy (LEEM) involves forming a diffraction pattern using elastically scattered electrons from a crystalline surface. Usually, one diffracted beam is extracted and imaged on a screen using conventional electronmicroscope lenses. Typical energies used are in the 100–3000-eV range. The resolution is as fine as 2 nm. LEEM is useful for determining the crystal structure

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on the nanometer scale. Features such as surface steps, dislocations, imperfections, islands of adsorbates, superlattice structure, grains, and surface inhomogeneity can be analyzed with LEEM.

5.2 Other Electron-Based Techniques Electrons furnish a very important probe of surface structures as, in general, the surface-specific signal can be extremely weak relative to the bulk. In this regard, two techniques for the structural analysis of surfaces at the nanoscale using electrons are reflection high-energy electron diffraction (RHEED) and low-energy electron diffraction (LEED). These two techniques are usually employed for the determination of the periodic 2D arrangements of atoms at surfaces. Since electrons are scattered much more strongly by matter than either x rays or neutrons, they penetrate less deeply. In RHEED, a beam of high-energy electrons (typically ∼10–100 keV) is directed at grazing angles of incidence (usually between 0.1 and 5 deg) onto the surface of the sample, thus minimizing penetration. This experimental arrangement results in a series of diffraction peaks that are used to determine the crystallographic structure of the surface. The scattering mechanism is Coulombic, with dominant scattering in the near-forward direction, and with particular sensitivity to the surface structure of the sample. In LEED, a beam of low-energy electrons (typically ∼10–1000 eV) hits the sample surface normally, resulting in a diffraction pattern. The elastically backscattered electrons are accelerated toward a fluorescent screen or camera, while the inelastically scattered electrons are rejected by grids held at a slightly positive potential. Given that the energy of the electrons is low, the penetration depth is usually low. Accordingly, LEED is a tool that provides information about the surface and the first few atomic layers of the material under study. Both RHEED and LEED intensities can be recorded and modeled aiming to obtain information on where atoms of different types are located on or near the surface. Electron energy loss spectroscopy (EELS) in TEM, HRTEM or STEM involves analysis of the inelastic scattering suffered by the electron beam via measurement of the energy distribution of the transmitted electrons. The technique allows highresolution elemental mapping of the measurement of local electronic structures for the determination of the local chemical bonding, such as that present at an interface or defect. Figure 5.3 shows an energy-loss spectrum of two silicon thin films. As in LEED, the technique of low-energy electron loss spectroscopy (LEELS) involves directing a beam of electrons at a surface. In LEELS, however, it is the energy loss of the electrons that is studied, rather than their elastic scattering.

5.3 Spectroscopic Techniques Basically, all spectroscopic techniques (optical, UV, IR, x-ray, electron, etc.) are based on spectral measurements of the following quantities: transmission, absorption, reflection, and emission. Thereby, these techniques probe the energy differences between electronic, vibrational, and sometimes, rotational quantum

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Figure 5.3 Energy-loss spectrum of a thin region (dashed line) and a thick region (solid line) of silicon, with their zero-loss peaks matched in height. [Reprinted from Egerton3 with permission from IOP.]

energy states of atoms, as well as the lifetimes of excited states and their energy relaxation channels. Another experimental variable is the polarization state of the incident, reflected, transmitted, or emitted radiation. Raman spectroscopy is based on the Raman effect (also known as Raman scattering), which is the inelastic scattering of photons after their interaction with vibrating molecules of a given material. During this interaction, photons either transfer energy to (Stokes) or receive energy from (anti-Stokes) molecular vibrations, i.e., phonons. Thus, the energy change of the scattered photons corresponds to the vibrational-energy levels of the molecules in the sample. Since the vibrational-energy spectrum depends on the chemical composition of the sample (type of atoms, bond strength, bond angles, crystallographic symmetry, etc.), a Raman spectrum is chemically very specific and provides an excellent chemical fingerprint of the sample. The typical apparatus used in Raman spectroscopy consists of a laser that provides the optical signal used to produce the Raman effect, a fiber that collects optical signals exiting the sample, and a spectrograph connected to a data processing unit. As the scattered light consists of radiation of the same frequency as the laser frequency (Rayleigh scattering) as well as sidebands at lower (Stokes-shifted) and higher (anti-Stokes-shifted) frequencies, Raman signals usually require powerful lasers and sensitive detectors. Surface-enhanced Raman spectroscopy (SERS) is a variation of Raman spectroscopy that provides a greatly enhanced Raman signal from Raman-active analyte molecules that have been adsorbed onto certain specially prepared metal surfaces. Increases in the intensity of Raman signal have been regularly observed on the order of 104 to 106 , and can be as high as 108 and even 1014 for some specific systems. A measured SERS spectrum of benzenethiol adsorbed on arrays of Ag nanoparticles is shown in Fig. 5.4.

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Figure 5.4 Representative SERS spectrum of benzenethiol adsorbed on Ag nanoparticle arrays. [Reproduced from Dieringer et al.4 by permission of the Royal Society of Chemistry.]

Raman spectroscopy involves the determination of energy level transitions associated with phonons. However, phonons are categorized as either optical or acoustic. Acoustic phonons can have frequencies of vibration (or energies) that are about one-thousand-fold higher than those of optical phonons. The typical values for acoustic phonons are ∼1.5×1010 Hz (0.5 cm−1 ). Raman scattering from acoustic phonons is referred to as Brillouin scattering. X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) have been applied to what is most likely the widest range of material surfaces. Both XPS and AES are dependent on the analysis of low-energy electrons emitted from surfaces, typically in the 10–3000-eV range. As a result, the two techniques can use the same electron-spectroscopy instrumentation, although they generally use different excitation sources. In XPS, the sample is irradiated by a beam of usually monochromatic lowenergy x rays. Photoelectron emission results from the atoms on the sample’s surface. The kinetic energy distribution of the ejected photoelectrons is directly measured using an electron spectrometer. Each surface atom possesses core-level electrons that are not directly involved with chemical bonding, but are influenced slightly by the chemical environment of the atom. The binding energy of each core-level electron (approximately its ionization energy) is characteristic of the atom and the specific orbital to which it belongs. Since the energy of the incident x rays is known, the measured kinetic energy of a core-level photoelectron peak can be related directly to its characteristic binding energy. The binding energies of the various photoelectron peaks (i.e., 1s, 2s, 2p, etc.) have been tabulated; therefore, XPS provides a means of elemental identification that can also be quantified via measurement of integrated photoelectron peak intensities and the use of a standard

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set of sensitivity factors to give a surface atomic composition. In Fig. 5.5, a highsensitivity XPS survey scan of a polycrystalline iron surface is presented. The low-binding-energy region of the XPS spectrum is usually excited with an ultraviolet photon source, leading to a technique called ultraviolet photoelectron spectroscopy (UPS), which provides data on the valence-band electronic structure of the surface. In UPS, electrons are promoted from occupied states below the Fermi level to states above the vacuum level. The vacuum level is defined as the energy of an electron at rest far from the influence of the potential of the solid. The photon’s energy must exceed the work function of the material being studied. After the photoemission of a core electron, the ion is left in an excited state and must decay to the ground state. Energy is released when an electron drops back into the core hole and can escape as an x-ray photon (leading to x-ray fluorescence); alternatively, the ion can eject a third weakly bounded outer-shell core electron named the Auger electron. The characteristic kinetic energy of the Auger electron is dependent only on the binding energies of the core levels within the target atom. Accordingly, Auger electron spectroscopy (AES) makes use of Auger electrons to determine the elemental composition of a sample surface. The sole requirement for the ejection of an Auger electron is the formation of an initial core-electron-level hole that can be generated by an electron beam, x rays, ions, or even thermal energy. However, AES has traditionally been implemented by excitation with primary low-energy electron sources of a few keV. Auger-electron bands are designated using classical x-ray notation (K, L, M) referring to the electron energy levels involved in the relaxation process. Auger peaks may be identified and quantified to give surface composition, similar to XPS. Figure 5.6 shows an in-depth AES profile of the different elements that are present in a silver-based multilayer lowemissivity coating with layer thickness in the nanometer range. As the surface is

Figure 5.5 High-sensitivity XPS survey scan of the surface of polycrystalline iron, taken at pass energy of 30 eV with a step size of 1.0 eV. [Reprinted from Bhargava et al.5 with permission from Elsevier.]

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Figure 5.6 In-depth AES profile of the different elements present in a silver-based multilayer low-emissivity coating, with the structure SnO2 (38 nm)/Ni-Cr(1 nm)/Ag(9 nm)/NiCr(3 nm)/SnO2 (38 nm) grown onto a Si substrate. The five layers that compose the multilayer structure can be clearly identified. [Reprinted from Martín-Palma et al.6 with permission from IOP.]

being sputtered away with time, the AES depth profile is determined from the external surface to the substrate. Interatomic distances in a crystal may be accurately determined by a careful analysis of the x-ray absorption spectrum. This possibility has given rise to a method called extended x-ray absorption fine-structure (EXAFS) spectroscopy. AES has been combined with SEM to devise a technique known as scanning Auger microscopy (SAM). Related techniques, such as photoelectron spectroscopy and Bremsstrahlung isochromat spectroscopy (BIS), also provide similar information.

5.4 Scanning Probe Microscopy In scanning probe microscopy, an extremely sharp tip scans the surface of a sample. The resolution is determined by the effective range of the interaction between the probe and the sample, rather than by the wavelength of the probe particle as in optical microscopy. Scanning and optical probes can be adapted in order to expand the imaging function to include providing information about the electrical, vibrational, optical, and magnetic properties of nanostructures. Scanning microscopy can provide information on the topography and defect structure over distances close to the atomic scale. Near-field scanning optical microscopy (NSOM) is a surface analysis technique that provides resolution beyond the diffraction limit. NSOM uses an optical fiber,

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one end of which tapers to a tip of cross-sectional diameter typically between 20 and 500 nm. When light is fed at the other end of the fiber, an evanescent field is created in and around the tip, since the tip diameter is smaller than the wavelength of the light. The spatial resolution is excellent because the evanescent field excites only a very small region of the sample, the intensity falling off exponentially from the tip. In scanning tunneling microscopy (STM), a sharp metal tip, preferably one with a single atom protruding at the end, is brought to within a nanometer of the conducting sample to be examined. The position of the tip is controlled with picometer precision using piezoelectric materials that expand or contract in response to electrical signals from a control system. A bias voltage is applied to the sample, and a tunneling current flowing between the tip and the sample is measured. The current is proportional to the tunneling probability across the gap between the tip and the sample. This tunneling current, which varies exponentially with the probe-surface atom separation, depends on the nature of the probe tip and the composition of the sample surface. STM thus tracks the surface topography, and very small changes in the height of the surface (1 µm), chemical composition, and single-crystalline morphology. VLS processes are based on the dissolution of gaseous reactants into nanodroplets of a liquefied metal, followed by nucleation and growth of single-crystalline nanorods and, subsequently, nanowires. Nanowires, nanorods, and nanopillars of many different materials have thus been grown, among which Si, InP, GaN, In2 O3 , ZnO, Au, Ag, CdSe, and InAs can be highlighted. The most intuitive opportunities for applying 1D nanostructures are in the field of electronics, where smaller dimensions have historically allowed the production of denser and faster circuits, and where the ability to produce nanostructures may lead to new types of devices operating on quantum-mechanical principles. In particular, nanowires should play an important role as both interconnects and active components in fabricating nanoscale electronic devices. Prototype

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Figure 6.18 SEM images of a ZnO nanopillar array arranged hexagonally on a substrate: (a) low-magnification top view of the nanopillar array, (b) enlarged top view of a part of the array, and (c) corresponding perspective view. The inset shows the distributional statistics of c 2006, Wiley-VCH the nanopillar diameters. [Reproduced with permission from Fan et al.14 Verlag GmbH & Co. KGaA.]

devices incorporating nanowires that have been demonstrated include field-effect transistors (FETs) with nanowires as both the conducting channel and the gate electrode, p–n junctions, bipolar junction transistors, complementary inverters, resonant tunneling diodes, light-emitting diodes (LEDs), various logic gates (OR, AND, and NOR), and memory elements. A range of nonelectronics applications of 1D nanostructures also exists. Light absorption and emission in nanowires is highly dependent on the polarization state of the exciting electromagnetic field—in consequence of the intrinsic shapes

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of nanowires. The magnitude of polarization anisotropy can be explained in terms of the dielectric contrast between the nanowire, nanorod, or nanopillar and its surrounding environment. The high dependence on the polarization state can be exploited to fabricate polarization-sensitive nanoscale photodetectors for use in integrated photonic circuits, optical switches and interconnects, near-field imaging systems, and high-resolution detectors. Since coherent nonlinear optical phenomena such as second- and third-harmonic generation depend explicitly on the crystallographic structure of a medium as well as on the polarization state, semiconductor nanowires might also be used as frequency converters or logic/routing elements in nanoscale optoelectronic circuitry. Nanowires with flat facets at their ends can be exploited as optical resonance cavities to generate coherent light on the nanoscale. In this respect, roomtemperature UV lasing by several nanowire systems has been demonstrated. The lasing thresholds vary across several orders of magnitude as a consequence of the dimensions of the nanowires, the quality of the particular nanowire cavities, and the coupling to a substrate. The most useful applications for nanowire lasers require that they be integrated in circuits and activated by an electron-injection process rather than by optical pumping. More robust assembly methods appropriate to a larger variety of materials will enable the use of injection nanowire lasers for optical sensing, optical communications, and probe microscopy. Additionally, nanorods with sharp tips are promising candidates for applications related to field emission of electrons from cold cathodes. These nanorods might be useful as active components in field-emission display devices. Electronic conductivity in semiconductor nanowires is notably enhanced by exposing these structures to photons of energy above their bandgaps. Highly sensitive photoconducting nanowires could serve as very sensitive light detectors in many applications such as microanalysis, and as fast-switching devices for nanoscale optoelectronics applications where ON and OFF states can be addressed optically. One quite promising application of 1D nanostructures is in nanowire photovoltaics. Nanowires and nanopillars have been proposed for the development of photovoltaic devices, with these structures in solar cells being used as light absorbers, charge-separation interfaces, and electron-transporting elements. The use of nanopillar arrays can improve charge collection and raise power-conversion efficiencies. Theoretical predictions indicate that solar cells containing nanopillar arrays with the appropriate cross-sectional diameter and lattice spacing should outperform traditional solar cells. Figure 6.19 shows a representation of a dyesensitized solar cell containing a dense assembly of nanowires. The dense array of nanowires provides both high surface area and direct connectivity to the electrode over distances up to the lengths of the nanowires. A close-packed array of nanowires 40 nm in diameter and 10 µm long would give a surface area about 103 times that of a flat film. Nanowire fabrication techniques can yield single-crystalline structures with a much lower density of line defects than is typically found in bulk materials. As a result, these 1D nanostructures often feature mechanical strength, stiffness, and

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Figure 6.19 Schematic representation of a nanowire-based dye-sensitized solar cell. The nanowires form a disordered network. [Reprinted with permission from Baxter and Aydil.15 c 2005, American Institute of Physics.]

toughness approaching the theoretical limits of perfect crystals, thereby becoming attractive for use in composites and as actuators in NEMSs. In particular, the large Young’s modulus associated with SiC nanorods implies that these materials are promising candidates as reinforcing elements in strong composites with a ceramic, metal, or polymer serving as the matrix material. Another major application of nanowires, nanorods, and nanopillars is related to the sensing of molecules for medical, environmental, and security purposes. The extremely high surface-to-volume ratios associated with these nanostructures endow them with inherently high sensitivity to species adsorbed on their surfaces and short response time. In this regard, Fig. 6.20 exemplifies the detection of single viruses using Si nanowires. Binding a virus particle to the antibody receptor on a nanowire device results in a change of the conductance from the baseline value. When the virus unbinds, the conductance returns to the baseline value. This effect can be used for sensing viruses. Size reduction in 1D magnetic nanostructures may alter their magnetic behavior, an effect with relevance in data storage and sensing. Magnetic nanorods and nanowires, in addition to exhibiting large anisotropy, can act as their own interconnects, making them attractive for use in sensing and as active elements in spintronic devices. Ferroelectric BaTiO3 nanowires have been demonstrated to store high-density information by polarizing the domains with a scanning-probemicroscope (SPM) tip.

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Figure 6.20 Detection of single viruses with nanowires. Nanowires 1 and 2 are modified with different antibody receptors (left, top), and conductance is recorded. Specific binding of a single virus to the receptors on nanowire 2 (middle, left) yields a conductance change only in nanowire 2 (middle, right). When the virus unbinds from the surface (bottom, left), the conductance returns to the baseline value (bottom, right). [Reprinted from Patolsky et al.16 ]

6.8 Polymer Nanocomposites Since the late 1980s, polymer nanocomposites (PNCs) have attracted a great deal of academic and industrial attention. These materials can be described as composite materials comprising nanoparticles (such as spheres, rods, and plates) dispersed in a polymer host material. The nanoparticles are often called inclusions, and the host material a matrix. In contrast to conventional composite materials where the size of the inclusions is on the order of micrometers, the inclusions in a PNC possess at least one dimension on the order of a few nanometers. PNCs are expected to not only expand the overall performance of traditional inclusion-loaded polymers, but to introduce novel properties, thus improving traditional applications and/or enabling new ones. The vast number of the types of nanoparticles, polymeric resins, and specific applications suggests that the scope of PNCs is immense. To name a few, nanometric inclusions include carbonic particles (e.g., single-walled

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carbon nanotubes, multiwalled carbon nanotubes, carbon black, nanographite, nanodiamond), oxides (clay, ziroconium phosphate, halloysite, silica, titania, BaTiO3 , Fe2 O3 , etc.), metals (gold, silver, platinum, palladium, etc.), and intermetallic materials (such as CoPt). Figure 6.21 presents a hierarchy of nanoparticles based on increasing functionality and, thus, the potential to enhance the functionality of the composite material relative to that of the polymer matrix. Many techniques for fabricating PNCs have been developed. In fact, creating a single universal technique for the fabrication of PNCs is nearly impossible, given the physical and chemical differences between different inclusion–matrix material pairs and the diversity of equipment available. Each inclusion–matrix material pair requires a special set of fabrication parameters to be determined, based on the processing efficiency and the desired final properties. Moreover, different fabrication techniques for the same inclusion–matrix material pair, in general, do not yield equivalent results. Traditionally, inclusions such as minerals, ceramics, and metals have been dispersed in polymers. PNCs extend the function and utility of the host polymers

Figure 6.21 Categorization of nanoparticles based on increasing functionality and, thus, potential to enhance the functionality of the PNC relative to that of the polymer matrix. Nanometric particles and clusters are polydisperse in size (σ size ) and composition (σcomp ). One-dimensional elements are compositionally uniform, with narrow size dispersion in one dimension (δ1D ), but polydisperse in the other two (δ2D ). Three-dimensional elements exhibit narrow size dispersion in all dimensions (δ3D ). [Reprinted from Vaia and Wagner17 with permission from Elsevier.]

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without requiring significant capital investment beyond that for traditional composite materials. Generally, PNCs containing between 1 and 5% v/v of nanoparticles display enhanced properties comparable to traditional composite materials containing between 15 and 50% v/v of microscale inclusions. Inclusion size may drop by three orders of magnitude, thereby greatly enhancing by six orders of magnitude the interfacial surface area between the two constituent materials, which leads to property enhancement. The importance of inclusion–matrix interactions is amplified in PNCs such that the interface and the interaction between nanoparticles dominate the macroscopic properties of the matrix. For example, weak forces between particles, such as the van der Waals force, are more pronounced for nanoparticles, due to the lower surface roughness and the smaller average interparticle separations. The greater the number density of inclusions, the more likely it is that they will form a continuous network. As the inclusion size decreases, the aspect ratio of many types of inclusions can approach 100:1 or more. These high-aspectratio nanoscale inclusions can form a continuous network even when the total volumetric fraction of the inclusion material in the composite material is very small. For instance, the inclusion volume fraction typically has to be around 25% for the metallic particles dispersed in a composite material to form a network that can conduct electricity. With nanoscale inclusions, that threshold (called the percolation threshold) drops to a value of less than 5%. Rather than simply replacing existing materials and traditional filled polymers, novel applications of PNCs are being actively explored. These applications include using PNCs as shape-memory materials for morphing aircraft fuselages, as self-passivating films for satellites, and as piezoresistive materials for MEMSbased sensors. Furthermore, major sums of revenue are forecasted from large commercial opportunities—such as automobile parts, coatings, flame retardants, and packaging—where lower-cost but higher-performance materials would improve durability and design flexibility while lowering unit price and life-cycle cost. More advanced composites, namely adaptive composites, are expected to mimic biological responsive functionality while operating in extreme environments. By drawing inspiration from biology and engineered fiber-reinforced composites, PNCs with spatially controlled morphology are beginning to provide viable options to critical components of active devices, such as fuel-cell membranes, batteries, photovoltaics, sensors, and actuators. The dispersal of more than one type of nanoparticles in a polymer matrix can engender multiple functionalities, some significantly enhanced but others totally new. The enhanced as well as the new functionalities should be enabled by careful selection of materials as well as careful selection of the shapes and sizes of the nanoparticles. In time, PNCs will exemplify nanoengineered metamaterials, i.e., materials with morphology engineered at the nanoscale that enable them to exhibit a host of significant functionalities that do not occur together or do not even occur singly.

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Chapter 7

Future Prospects Nanotechnology today is probably like Mozart when he was five years old: bursting with promise, with the best yet to come after a few years of nurturance. All indicators predict that nanotechnology will continue to grow in the coming years. The annual production of scientific papers, the number of patents awarded annually, and the global investment in nanotechnology research and development are exponentially increasing. In the short term, i.e., over the next 5–10 years, nanotechnoscientists will move in new directions and face new challenges as they begin a transition from investigating single phenomena and devising canonical nanoscale devices to studying complex and active nanostructures and even molecular nanosystems. Moreover, a remarkable convergence of nanotechnology, biotechnology, information technology, and cognitive science, although still embryonic, will lead to complex and innovative hybrid technologies. As these developments unfold, nanotechnology will continue its proliferation from academic and industrial laboratories to the marketplace, impacting the production and dissemination of energy and food and the delivery of healthcare, and relieving bottlenecks in transportation and communications.

7.1 Avenues of Promise Although any specific technology can develop in completely unanticipated directions, nanotechnology is commonly expected to offer breakthrough applications in the following fields: Nanomagnetism. Very fast nanotransistors consuming very low energy will enable new data storage technologies with gigantic capacities. These nanotransistors will be based on 0D and 1D magnetic nanostructures Nanoelectronics and quantum electronics. Both the capacity and the speed of data manipulation in computers will continue to grow as rapidly as they did during the last 40 years, fueled by the emergence of transistors made of carbon nanotubes, semiconductor quantum dots, and nanowires Displays. Quantum dots and nanowires are expected to be used for ultrathin and flexible visual displays that, coupled with remote servers for cloud computing, will enable the delivery of textual and graphic information on expandable credit-cardsized devices. Will printed books and newspapers vanish in the near future? Nanomaterials and nanocomposites. Nanomaterials with novel properties and multifunctional capabilities will greatly influence the design, manufacture, and 129

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deployment of all sorts of devices. Many a nanomaterial will actually be a nanocomposite whose constituent materials will be mixed on the nanoscale. The constituent materials will differ both in molecular composition and characteristic dimensions on the nanoscale. Singly and jointly, the constituent materials will impart many different functionalities to the nanocomposite. These characteristics would justify calling this nanocomposite a nanoengineered metamaterial. Engineered biomimicry. The nanotechnological techniques discussed in Chapter 4 for fabricating nanostructures will be pressed into the service of biomimesis: the emulation of natural devices and mechanisms. Nanophotonics. Nanophotonic components will increase the speed and lower the cost of data transmission between electronic chips as well as inside hybrid optoelectronic chips. Increased application of nanophotonics for sensing and identification of biochemical materials as well as for monitoring the health of structures and systems (including humans) will occur. Molecular electronics. Currently, a very basic field of active research is to make a single molecule function as a transistor. The fruition of single-electron transistors would be the ultimate accomplishment in high-density electronics. Nanomechanical tools (nanotools). Nanotweezers, molecular-scale balances, nanosieves and nanofluid management systems, and ultraprecision machinery will also play important roles in the production of nanoelectronic and nanophotonic devices and systems, besides being useful as nanoprostheses. Nanosensors and nano-actuators. Smaller, more sensitive, and more selective sensors and actuators will accommodate voice, vision, and tactile senses and stimulation, as well as offer new applications for biometrics and environmental monitoring. Nanobiotechnology. The convergence of nanotechnology and biotechnology will produce new ways of delivering precise quantities of chemicals—from pesticides to lubricants—to specific locations in structures and systems, thereby revolutionizing agriculture, food processing, and countless industrial processes. Nanomedicine. Applications of nanobiotechnology for in vivo imaging of specific tissue and for targeted delivery of drugs promise to revolutionize medicine, once the possibly enhanced toxicity of nanomaterials has been offset.

7.2 The Evolution of Nanotechnology The U.S. National Nanotechnology Initiative envisages the systematic control and manufacture at the nanoscale to evolve during the first few decades of the 21st century in four overlapping generations of new nanotechnology products. Shown in Fig. 7.1, these four generations are as follows: Passive nanostructures (2000–). First-generation nanotech products are designed to take advantage of the passive properties of nanomaterials. Once incorporated in a product, the nanomaterial itself remains unchanged. Nanostructured coatings and nanocomposites used in bulk exemplify the prevalence of incremental nanotechnology.

Future Prospects

Figure 7.1

131

Timelines for four generations of nanotech products. [Reprinted from Roco.1 ]

Active nanostructures (2005–). An active nanostructure changes its state during use, responding in predicable ways to stimulating factors in its environment. The design of second-generation nanotech products—such as post-CMOS nanoelectronic components, targeted drugs and chemicals, and artificial “muscles”—requires a greater understanding of how the structure of a nanomaterial determines its properties. The fabrication and deployment of these nanotech products raise new challenges, stimulating evolutionary nanotechnology. Systems of nanosystems (2010–). Evolutionary nanotechnology flowers as significant advancements in robotics, biotechnology, and information technology are translated into third-generation nanotech products. These are assemblies of nano-objects and nanotools that operate synchronously and sequentially and perform reliably at the press of a button. A key challenge is the rapid exchange of information between the main component nanosystems of thirdgeneration products. Research focus shifts toward heterogeneous nanostructures and supramolecular-system engineering. The spotlight shines on directed multiscale self-assembly methods, artificial tissues and sensorial systems, quantum interactions within nanoscale systems, processing of information using photons or electron spin, assemblies of nanoscale electromechanical systems (NEMSs), and converging technology (nano-bio-info-cogno) platfoms integrated from the nanoscale. Heterogeneous molecular nanosystems (2015–). Radical nanotechnology begins to emerge, as matter for fourth-generation nanotech products is crafted at the molecular and even atomic level to take advantage of the specific nanoscale properties of different elements. Each molecule in a nanosystem has a specific set

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of roles. A single nanotech product integrates a wide variety of capacities including independent power generation, information processing and communication, and mechanical operation. Nanodevices roam inside a living body, fixing the DNA of damaged cells, monitoring vital conditions, and displaying data in a readable form on skin cells in a form similar to a tattoo. Computers operate by reading the brain waves of their operators. The Joint Economic Committee of the U.S. Congress forecasted the following fifth generation of nanotech products. The Singularity (2020–). Sustained demands for multifunctional materials and competitive pressures continue to drive technology forward. Computers with artificially intelligent processors enhance and accelerate the pace of technoscientific discovery; i.e., intelligent machines start to produce discoveries that are too complex for humans to contemplate. An implicit assumption is that solutions to most of today’s problems, including material scarcity, human health, and environmental degradation, can be solved by technology—if not by us, then by the computers we eventually develop.

7.3 Balancing of Risk A mood of extreme optimism pervades the previous sections. The techno-utopian hype rarely fails to elicit bemused smiles from many contemporary commentators and students of human societies, who regard such predictions as naïve at best and socially irresponsible at worst. Far from alleviating human misery, they think that excessive reliance on technology simply engenders new ways to inflict misery on diverse segments of human societies. Their concerns must not be dismissed as the evocations of neo-Luddites. The potential of quantum dots for medical applications provides an excellent illustration of the risks and benefits of nanotechnology. Controlled injection of water-dispersable quantum dots would assist in imaging of cancerous and otherwise diseased tissue. However, quantum dots must also be biocompatible; i.e., their toxicity must be offset by surface functionalization with biofriendly materials. Furthermore, inadvertent intake of quantum dots, perhaps at sites in or near quantum-dot factories could seriously imperil the health of an unwary population. Given the rapid pace of technology research and development, technoscientists must actively embrace the management of the associated risks for societies. Although economic, political, and legal decisions are generally made by non-technoscientists, these people need to be guided by technoscientists. Nanotechnoscientists must consider the societal implications of their research and development activities while conducting those activities, guide their own research and development activities thereby, and advise economic, political, and legal decision makers. Technology is Janusian: it benefits as well as harms. Technoscientists must face up to ethical issues wrought by their activities. Just as Principle 16 of the Rio Declaration on Environment and Development declares “that the polluter should,

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in principle, bear the cost of pollution, with due regard to the public interest and without distorting international trade and investment,” technoscientists may, in future, be held liable by societies suffering distress caused by even unintended by-products of technoscientific products and services. In order to do so, the education of nanotechnoscientists must evolve to meaningfully include societal implications. Scenario planning may assist them. This is a way to describe the present state of the world and develop several hypotheses about the future of the world, thereby enabling discussions about how the world ought to be. Scenario planning thus is not only a tool for learning and foresight, but also for leadership. Informed decision making by experts and political leaders becomes possible, while simultaneously allaying public perception of the risks of new and emerging technologies. However, placing the onus solely on nanotechnoscientists is unfair, because the products of their labors are enjoyed by all societal segments in one way or another. Formal education on socially transformative technologies must be imparted to all students at pre-university and university levels, irrespective of areas of specialization. Informal education too must be conducted at several levels: multidisciplinary teams from universities, industry, and governments should conduct seminars for industry leaders, government officials, and legislators; town councils must fund series of public lectures and panel discussions; and schools, public libraries, and community groups should be provided financial support by government agencies and private foundations. Focused education of all segments of society will greatly facilitate serious and necessary engagement with the issues and concerns engendered by nanotechnology.

References 1. M. C. Roco, “National nanotechnology initiative—past, present, future,” in Handbook of Nanoscience, Engineering, and Technology, W. A. Goddard III, D. W. Brenner, S. E. Lyshevski, and G. J. Iafrate, Eds., 2nd ed., CRC Press, Boca Raton, FL (2007).

Bibliography Cavin, R. K., V. V. Zhirnov, G. I. Bourianoff, J. A. Hutchby, D. J. C. Herr, H. H. Hosack, W. H. Joyner, and T. A. Wooldridge, “A long-term view of research targets in nanoelectronics,” J. Nanopart. Res. 7, 573–586 (2005) [doi:10.1007/s11051-005-7528-0]. Davies, J. C., Oversight of Next Generation Nanotechnology, Woodrow Wilson International Center for Scholars, Washington, DC (2009). Drexler, K. E., “Toward integrated nanosystems: Fundamental issues in design and modeling,” J. Comput. Theor. Nanosci. 3, 1–10 (2006) [doi:10.1166/jctn.2006.001].

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European Commission, Vision 2020—Nanoelectronics at the Centre of Change. European Commission, Brussels, Belgium. http://www.eniac.eu/web/SRA/ e-vision-2020.pdf, 2004. Farber, D. and A. Lakhtakia, “Scenario planning and nanotechnological futures,” Eur. J. Phys. 30, S3–S15 (2009) [doi:10.1088/0143-0807/30/4/S02]. Goddard III, W. A., D. W. Brenner, E. W. Lyshevski, and G. J. Iafrate, Eds., Handbook of Nanoscience, Engineering, and Technology, 2nd ed., CRC Press, Boca Raton, FL (2007). Hullmann, A., The Economic Development of Nanotechnology—An Indicators Based Analysis. European Commission, Brussels, Belgium. ftp://ftp.cordis. europa.eu/pub/nanotechnology/docs/nanoarticle_hullmann_nov2006.pdf, 2006. Kostoff, R. N., R. G. Koytcheff, and C. G. Y. Lou, “Global nanotechnology research literature overview,” Curr. Sci. 92, 1492–1498 (2007). Marks, R., D. Cullen, I. Karube, C. R. Lowe, and H. H. Weetall, Eds., Handbook of Biosensors and Biochips. Wiley, Chichester, UK (2007). McKibben, B., Enough: Staying Human in an Engineered Age, Henry Holt, New York (2003). Montague, P., “Welcome to NanoWorld: nanotechnology and the precautionary principle imperative,” Multinational Monitor 25 (9), 16–19 (2004). Saxton, J. and U.S. Congress Joint Economic Committee, Nanotechnology: The Future is Coming Sooner Than You Think. U.S. Congress, Washington, DC. http: //www.house.gov/jec/publications/110/nanotechnology_03-22-07.pdf, 2007. United Nations Environment Program, GEO-2000 Economic Instruments, http:// www.unep.org/Geo2000/english/0138htm, 2000.

Index A absorption edge, 44 acoustic impedance, 111 aerogels, 108, 110 artificial atoms, 27 atomic force microscopy (AFM), 63, 65, 86–87 atomic layer deposition (ALD), 58–59 Auger electron spectroscopy (AES), 83–85

colossal magnetoresistance (CMR), 41 columnar thin films (CTFs), 105–106 conductance, 34 conductance quantization, 35 conductance quantum, 36 conductivity, 34 confinement energy, 17 conformal-evaporated-film-byrotation (CEFR) technique, 107 Coulomb blockade, 36, 112 Coulomb-blockade model, 37 Coulomb-blockade regime, 37 cryogel, 110

B ballistic transport, 35 band diagram, 32 bandgap, 113 bandgap energy, 32 biomimetics, 130 bottom-up approaches, 53 bottom-up nanotechnology, 4 Buckminsterfullerene, 95–96 bulk structure, 11

D de Broglie wavelength, 12 degeneracy, 25, 28 diamond nanocrystallites, 100 digital lithography, 63 dip-pen nanolithography (DPN), 65 direct bandgap, 32–33 displays, 129

C C60 , 95, 96 carbon aerogels, 111 carbon megatubes, 100 carbon nano-onions, 100 carbon nanobuds, 100 carbon nanotube (CNT), 97, 100 carbonization, 72 charge carriers, 33 chemical vapor deposition (CVD), 57–58 circular Bragg phenomenon, 107

E eigenenergy, 17, 24–25, 27 eigenfunctions, 16, 24, 27 elastic recoil detection analysis (ERDA), 89–90 electrical transport, 34 electrochemical processes, 72 electrodeposition, 72–73 electron-beam lithography, 61 135

136

electron energy loss spectroscopy (EELS), 81 electron microscopy, 77 electron paramagnetic resonance (EPR), 86–88 electron spin resonance (ESR), 86 ellipsometry, 91 energy dispersive x-ray spectroscopy (EDS or EDX), 80 energy levels, 24, 28 evaporation, 53, 56 exact quantization, 42 exciton, 33 extended x-ray absorption fine-structure (EXAFS), 85 extreme ultraviolet lithography (EUV), 61 F ferromagnetism, 39 fine structure constant, 42 fluorophores, 115 focused ion-beam (FIB) writing, 65 friction force microscope, 86 G geometric self-organization, 68 giant magnetoresistence (GMR), 40 graphene, 95, 98 H Hall conductivity, 42 Hall–Petch, 49 Hall–Petch relation, 48 Hall resistivity, 43 Heisenberg uncertainty principle, 28, 102 high-resolution scanning electron microscopy (HRSEM), 80 high-resolution transmission electron microscopy (HRTEM), 77 holes, 33 I indirect bandgap, 32–33

Index

infrared (IR) spectroscopy, 91 injection lasers, 113 ion-beam analysis, 87 ion-beam-assisted deposition (IBAD), 57 ion-beam sculpting, 65, 67 ion-projection lithography (IPL), 61 L Landauer formula, 35 Langmuir–Blodgett (LB) film, 115 Langmuir–Blodgett (LB) film deposition, 69 Langmuir–Blodgett (LB) method, 68, 70 Langmuir–Blodgett patterning, 117 Langmuir monolayer, 116 laser ablation, 56 laser-assisted direct imprint (LADI), 63 laser-assisted nano-imprint lithography (LAN), 63 lateral-force microscope (LFM), 86 layer-by-layer (LbL) assembly, 70 lithographically induced self-assembly (LISA), 63 local surface plasmon resonance (LSPR), 46 local surface plasmon resonance frequency, 46 low-dimensional structures, 11 low-energy electron diffraction (LEED), 81 low-energy electron loss spectroscopy (LEELS), 81 low-energy electron microscopy (LEEM), 80 luminescence, 91 M magnetoresistance, 40–41 metamaterials, 124, 130 molecular beam epitaxy (MBE), 59, 60, 114 molecular electronics, 130

Index

multiwalled carbon nanotube (MWCNT), 97 N nano-actuators, 130 nano-imprint lithography (NIL), 63 nano-imprint technique, 64 nanobiotechnology, 130 nanocolumns, 105 nanocomposite, 112, 129 nanocrystals, 101 nanodots, 112 nanoelectronics, 129 nanolithography, 60 nanomagnetism, 129 nanomaterials, 129 nanomechanical tools (nanotools), 130 nanomedicine, 130 nanoparticles, 2 nanophotonics, 130 nanopillar, 117, 119 nanorods, 117 nanoscience, 11 nanosensors, 130 nanostructure, 2, 11 nanotechnology, 2, 11 nanotools, 130 nanowires, 118, 122, 129 near-field scanning optical microscopy (NSOM), 85 nuclear magnetic resonance (NMR), 86 nuclear reaction analysis (NRA), 90 O oblique angle deposition (OAD), 57, 105, 106 one-dimensional (1D) structure, 11 optical absorption, 44–45 optical lithography, 61 optical spectrometry, 91 P particle-induced x-ray emission (PIXE), 89

137

photolithography, 61–62 photoluminescence (PL), 91, 101, 103, 115 photons, 32 polymer nanocomposite (PNC), 122, 123 porous silicon (PS), 101–102 principal quantum number, 17 proton-beam (p-beam) writing, 65 proton-induced x-ray emission, 89 pulsed laser deposition, 56 pyrolysis, 72 Q quantum confinement effects, 101 quantum dots (QDs), 12, 46, 112–114, 129, 132 quantum electronics, 129 quantum engineering, 16 quantum Hall effect, 42 quantum mechanics, 12 quantum-mechanical conductance, 36 quantum numbers, 25 quantum of 1D thermal conductance, 39 quantum point contact, 35 quantum state, 17 quantum well, 11 quantum wire, 11 R Raman spectroscopy, 82 reflection high-energy electron diffraction (RHEED), 81 resistance quantum, 36, 42 Rutherford backscattering spectrometry (RBS), 88–89 S scanning Auger microscopy (SAM), 85 scanning electron microscopy (SEM), 77 scanning probe lithography (SPL), 63 scanning probe microscopy (SPM), 63, 85

138

scanning transmission electron microscopy (STEM), 80 scanning tunneling microscopy (STM), 63, 66, 86 Schrödinger equation, 13, 23 sculptured thin films (STFs), 105–106 secondary-ion mass spectrometry (SIMS), 89 self-assembled monolayers, 68 self-assembly, 67 self-organization, 67 SEM/HRSEM, 79 single-walled carbon nanotubes (SWCNT), 97, 99 sol gel, 109 sol-gel processing, 72 solar cells, 114–115, 120–121 spectroscopic techniques, 81 spintronics, 40 spray conversion processing, 72 sputtering, 53, 57, 89 step-and-flash imprint lithography, 63 superplasticity, 48 surface-enhanced Raman spectroscopy (SERS), 82–83 T templated self-organization, 68 thermal conductivity, 38, 112 thermal spraying, 72 thermolysis, 72 three-dimensional (3D) structure, 11 time-harmonic Schrödinger equation, 14, 25

Index

top-down approaches, 53 top-down nanotechnology, 4 transmission electron microscopy (TEM), 77 2D electron gas, 34–35 two-dimensional (2D) structure, 11 U ultraviolet photoelectron spectroscopy (UPS), 84 V VLS processes, 118 von Klitzing constant, 42 W wave number, 32 wave vector, 32 wavefunction, 13 wave–particle duality, 13 X x-ray diffraction (XRD), 90 x-ray lithography, 61 x-ray photoelectron spectroscopy (XPS), 83–84 xerogel, 110–111 Y yield strength, 48–49 Z zero-dimensional (0D) structure, 12 zero-point energy, 17

Raúl J. Martín-Palma (b. Madrid, Spain, 1972) is a professor of physics at the Universidad Autónoma de Madrid (Spain). He received his M.S. degree in applied physics in 1995 and his Ph.D. in physics in 2000, both from the Universidad Autónoma de Madrid. He has been a post-doctoral Fellow at the New Jersey Institute of Technology (Newark, NJ, USA) and a visiting professor at The Pennsylvania State University (USA). He has received young scientists’ awards from the European Materials Research Society and Materials Research Society (USA) for his research on nanostructured materials. Akhlesh Lakhtakia (b. Lucknow, India, 1957) is the Charles Godfrey Binder Professor of Engineering Science and Mechanics at The Pennsylvania State University and is Editor-in-Chief of SPIE’s Journal of Nanophotonics. He obtained B.Tech. (1979) and D.Sc. (2006) degrees in electronics engineering from the Banaras Hindu University, and M.S. (1981) and Ph.D. (1983) degrees in electrical engineering from the University of Utah. He is a Fellow of SPIE, the Optical Society of America, the Institute of Physics (UK), and the American Association for the Advancement of Science.