We begin this chapter with a brief review of electromagnetic radiation and its interactions with materials and interfaces. We consider nonlinear optical effects, and give an overview of lasers. After a quick review of photonics technology in the context of telecommunications, we consider nanophotonics – optical phenomena involving nanostructured materials. This includes dielectric mirrors and their three-dimensional generalization, photonic band gap structures, as well as plasmonic nanostructures. Research in plasmonics has become extremely fast-paced lately, in part because of the availability of new experimental and computational tools, and in part because of the promise of surface enhanced spectroscopies and more exotic effects such as “perfect” lenses and invisibility cloaks.

As always, entire books have been written on the various components of nanophotonics. Here we will look specifically at the “nano” aspects of these electromagnetic phenomena, with an emphasis on the underlying physics, the synergy between electromagnetic meta materials and electronic structure of materials, and how those ideas lead to rich, fascinating, and useful phenomenology.

Electromagnetic radiation in a nutshell

In the many-photon limit, photonics is better known as the manipulation of classical electromagnetic radiation. All of the interesting effects in nanophotonics originate from underlying equations that govern the interactions of EM radiation and matter, and the electromagnetic response functions of the matter itself. In full generality this can be incredibly messy. Boundary conditions for the E and B fields must be satisfied at all times everywhere, including interfaces between materials that can have very different intrinsic properties. The materials themselves can have electromagnetic response functions (e.g., the dielectric function and the magnetic permeability) that can be tensorial, nonlinear, and strongly dependent on frequency.

Maxwell and waves

Let's start with Maxwell's equations:

∇ · D = ρ, (8.1)

∇ · B = 0, (8.2)

Equation (8.1), with D ≡ ∈E ≡ κ∈0E, and ρ as the volume charge density source term, is nothing more than Gauss' Law.

Biology has clear, direct relevance to nanoscale science and technology. The organelles within our cells are exquisite nanoscale machines, with the capability to fabricate complex structures with molecular precision in a fluctuating electrolytic environment. Individual protein molecules can function as motors and pumps, transducing chemical energy into useful mechanical or electrochemical work. Biological systems can build complex structures from the nano to the macro scale incorporating inorganic as well as organic constituents. Moreover, there is a tremendous societal drive toward greater understanding of this biological apparatus, motivated by the quest for basic knowledge, the desire to leverage biological mechanisms to accomplish useful tasks, and the obvious ramifications for clinical treatment of disease.

Because of the vast diversity of biological systems, this chapter does not remotely attempt to survey all of bionanotechnology. Rather, I will emphasize a handful of key concepts relevant to molecular and cell biology and highlight major research directions. View this as a very simple primer more than as a textbook-depth explication. For a book-length discussion of many of these topics, I recommend D. S. Goodsell's Bionanotechnology: Lessons from Nature (Wiley-Liss, 2004) as a good place to start.

Basic elements and tools of bionano

Intermolecular interactions relevant to bionano

Biological activity has evolved to take place in a complex, fluctuating chemical environment near room temperature (though extremophile bacteria push the limits of this generalization). So that biological systems can respond to their environments, metabolize nutrients, and generally carry on the business of living, they support many mechanical and chemical processes that operate on energy scales comparable to kBT. As a result, while covalent interactions at the eV energy scale remain very important, many interesting biological materials and processes depend on noncovalent interactions closer to the thermal energy available from the surroundings.

Figure 11.1 schematically highlights four relevant noncovalent interactions.

This chapter gives a necessarily brief overview of the techniques employed to create structures at the nanometer scale, and the tools used to examine matter down to that level. Entire books have been written about many of these topics. Here the emphasis will be broad exposure, and where possible explanations of the strengths and limitations of the various approaches.

Characterization

Characterizing materials at the nanoscale can be very challenging. It's easy to say what we want, as practitioners in this field. When presented with a sample or nanoscale structure, it would be wonderful if there were some tool or set of tools that could tell us, nondestructively, the position and composition of every atom in the sample, with atomic resolution. Unfortunately, this remains a fantasy. Over the years, however, a wide variety of experimental techniques have been brought to bear on the problem of materials characterization, applying different physical principles to acquire information about various aspects of the systems of interest. Some of these same techniques have been adapted or spun off into related approaches to nanoscale patterning and fabrication.

One can broadly divide the characterization techniques into two categories, bulk or global, and local. Bulk methods generally interrogate a volume or area of sample that is often much larger than the nanoscale, but nonetheless can reveal incredibly precise nanoscale information. Diffraction is the classic example. Local methods, in contrast, directly interrogate a nanoscale volume of sample, and somehow transduce those local interactions into macro scale signals.

X-ray techniques

Since their discovery in the late nineteenth century, x-rays have been incredibly useful for looking at the structure of materials. X-rays are electromagnetic radiation with photon energies in the keV to tens of keV range, and corresponding wavelengths down to subatomic scales. X-rays interact primarily with the inner electrons of atoms, and therefore their scattering is relatively greater for elements of higher atomic number.

From the earliest discussions of nanotechnology, there has been an interest in the development of mechanical devices with moving parts on the nanoscale. Biological systems demonstrate that this is possible, as cells routinely employ molecular machines with mechanical motions and degrees of freedom. Here we give an overview of the principles of the mechanics of solids, also known as continuum mechanics, with its concepts of stress, strain, and elastic moduli. As its name implies, continuum mechanics is based on the assumption of matter being continuous, rather than made up of discrete atomic units. In analogy with our previous treatment of electronic structure, it is interesting to explore the limits of this approach, which clearly must fail in the limit that chemistry becomes a more appropriate formalism. We also consider the origins of irreversibility in mechanical systems, including plastic deformation and friction, and see that nanoscale tools have been invaluable in increasing our understanding. After surveying Micro- and nanoelectromechanical systems (MEMS and NEMS) as they are employed in current technologies, we will conclude with a discussion of the frontiers of nanomechanics.

Basics of solid continuum mechanics

We need to define some basic terms so that we can discuss the elastic properties of solids, the relationship between the deformation of a piece of material and the forces acting on that object. Consider a block of material at rest being acted upon by several forces that sum vectorially to zero, so that the block is not accelerating. Now imagine dividing the block into two pieces. Clearly the sum of forces acting on each piece must equal zero, since neither piece is accelerating, as before. That implies that one piece of the material is exerting forces on the other piece, and vice versa. In this example, the material deforms due to the actions of the external forces, developing the necessary internal forces to maintain static equilibrium as a result of that deformation.

We have examined the mechanical response of solids as they approach the nanoscale, paying particular attention to the adequacy of the continuum approach to elasticity and the origins of friction and dissipation, as macro scale motions excite microscopic degrees of freedom. We now turn to fluids with similar goals in mind. After a brief overview of some concepts of fluid mechanics and a discussion of dimensional analysis, we discuss fluid flows of particular interest in the Micro- and nanoscale. Microfluidic applications are discussed in brief, and the chapter concludes with a look at nanofluidic frontiers.

Basic fluid mechanics

Fluids are materials that are unable to resist shear and take on the shapes of their containers. In the case of a gas, the typical separation between constituent particles is considerably larger than the size of a particle; in contrast, in a liquid the molecular constituents are essentially “cheek by jowl”. One additional length scale is the characteristic size of a fluid container, which we will call L. Another is the mean free path, ℓ, for collisions between the fluid molecules. We can define a dimensionless quantity called the Knudsen number, Kn ≡ ℓ/L. When Kn ≪ 1, the statistical description of the fluid as an effective continuum is valid. For liquids, this implies that we should not run into problems with the continuum description until the liquid is confined on a scale comparable to molecular dimensions.

While it deforms continuously under shear, a fluid does exert shear stresses on an adjacent solid (or fluid) interface.

Solid state physics, or condensed matter as it is now more commonly known, is the underpinning of the vast majority of modern technology. This (long) chapter will examine key elements of the solid state physics of bulk systems. Understanding the origins of the properties of macro scale materials leads to insights about why nanoscale materials are different. This is not intended to be a complete treatment of modern solid state physics – that would take hundreds of pages alone! At the end of the chapter I list a few of the many excellent books on this vast subject for those interested in learning more.

As shall become clear, the quantum mechanical character of electrons is essential to understanding matter in the solid state, even though the more exotic quantum effects evade everyday experience. However, describing realistic solids is, in principle, incredibly complicated. Restricting the discussion to relatively low energy scales, in a cubic centimeter of copper are ∼ 1023 nuclei, surrounded by ∼ 1024 electrons. Exactly solving the detailed quantum many-body problem for this system is clearly a practical impossibility. This makes the case for the other key component of approaches to understanding the solid state: statistical physics. Solving classical equations of motion for every gas molecule in your room is just as impractical as the solid state problem. Fortunately, statistical mechanics has been developed, allowing us to consider distributions of particle velocities. Similar approaches are routinely applied in the solid state, along with related concepts like a density of states.

Note that all of the electrons and nuclei are electrically charged and therefore interact with one another. These interactions are not necessarily weak! Strongly interacting many-body problems are exceedingly hard to solve, but the observation that atoms remain a useful way of thinking about solid materials hints at a way out of this dilemma.

As previous chapters have shown, new technologies now exist to manipulate matter down to the atomic scale. Material properties at these scales differ from those of bulk systems as different physical processes become relevant. Nanotechnology is based on engineering these new properties into useful devices. These capabilities are already having a significant technological impact on many disciplines, from consumer electronics and information technology to optical communications to biology.

Where is this all going? Is reality going to live up to the early hype surrounding nanotechnology? Will nanoscale engineering lead to a new industrial revolution, enabling solutions to many of the major problems facing humanity? Alternatively, will practitioners of this new science and engineering meta discipline bring forth “a nightmarish, dystopic future too small to see” (The Onion [942])? In this chapter we look briefly at two particular areas: nanotechnology's potential impact on humanity's energy crisis, and the potential dangers of these new capabilities. Disclaimer: more so than the rest of this book, this chapter is a bit of an opinion piece, and should be viewed as such.

Nanotechnology and energy

Humanity faces, in very real terms, an energy crisis, though there are political disagreements on the extent of the problem. The per capita demand for energy, both for transportation and electricity, of the “first world” nations is vast and growing. Moreover, as economic development spreads over the planet, increasing portions of the global populace are experiencing higher standards of living (generally agreed to be a good thing), and a corresponding increase in energy demands. There are very serious questions about the sustainability of this trajectory, in terms of economic and environmental impact. There are also certainly negative consequences for the species if we are unable to continue raising the global standard of living.

This chapter continues our overview of bulk materials, and introduces the major materials systems relevant for the remainder of the book.

One sensible way to classify materials is by the arrangement of their constituent atoms – their structure. Macroscopic materials consisting of large numbers of atoms are readily grouped into two categories: ordered and disordered. More precisely, one can examine the density–density correlation function,

S(r) ≡ 〈ρ(r0)ρ(r0 + r)〉.

The intensity of elastic diffraction at some wave vector transfer q from a bulk material is proportional to the Fourier transform of S(r).

In a completely disordered system, the position of one atom is uncorrelated with the position of any of the other atoms. Thus S(r) ∝ δ(r). This is the case for a dilute, classical gas. For a liquid or supercritical fluid, particles are squeezed together closely enough that the finite size of the constituent atoms becomes relevant. In that case there is some typical nearest-neighbor distance, though there is no long range pattern to the arrangement of atoms. Mathematically S(r) has a broad peak where |r| equals the nearest neighbor separation as well as at r = 0, but little other structure. An essentially identical pattern results for a completely amorphous solid such as a glass. With increasing positional order, additional peaks develop in S(r). The limit of this would be a perfect single crystal, in which S(r) would have delta function peaks at each lattice vector, r = R.

An alternative classification scheme can be built around a material's response to mechanical stresses. Fluids are defined by their inability to support shear stresses. That is, for a given patch of area at the boundary of a fluid, if a force is applied in the plane of that surface, the fluid will begin to deform, and will continue to deform at some rate as long as the shearing force is applied. In contrast, solids are said to resist shear.

Now that we have discussed the physics of infinite, perfectly ordered, bulk materials with essentially non-interacting electrons, it is time to consider what happens in systems that are less “ideal”.

Defects

No real material is ever perfect. The basic argument for the existence of some nonzero density of defects is an entropic one, and makes perfect sense from the perspective of free energy. Even if there is a moderate energetic cost for the creation of a defect, if there are a very large number of possible configurations for the defect (e.g., sites where the defect can reside), the system's total free energy can be lowered through defect formation. Common defects can be zero-dimensional (point defects), one-dimensional (line defects), or two-dimensional (grain boundaries or interfaces).

What are the effects of these defects, particularly on the electronic properties of the materials? The Bloch condition and our picture of Bloch waves as single-particle eigenstates of the lattice are predicated on the assumption of the perfect, infinite spatial periodicity of the lattice. That is, the single-particle Hamiltonian in crystalline solids is assumed to be invariant under discrete translational symmetry. Strictly speaking, once that symmetry is broken by defects, the Bloch states are no longer exact solutions to the single-particle problem.

If the defect density is low, then we generally don't care. It's hard to imagine that a handful of defects in a crystal could have a large impact on the electronic structure of a crystal containing 1022 atoms (though see Exercises). The vast majority of single-particle states in the crystal are still approximated very well as Bloch waves in this case. However, the defects do alter the spectrum of allowed states, and these changes can be significant if the number of atoms near defects becomes a substantial fraction of the total number of atoms. We discuss this further below.

This book is intended to provide a physical foundation for students interested in nanoscale science and technology. Developed while teaching a two-course graduate sequence on the topic, this book is my attempt to lay out the physical underpinnings of this incredibly broad topic while striking a balance between depth and approachability.

When I set out to develop and teach these courses, I found that most books on this subject were very specialized (for example, dealing only with nanoscale electronics), more focused on research rather then pedagogy (collections of review articles rather than an actual textbook), or not sufficiently technical (more like a series of Scientific American articles rather than a quantitative approach). I have tried to get to the physical basis of nanoscale science, the origins of the fascinating properties of materials at previously inaccessible size scales. A common thread through much of the material is the breakdown of the simplifying approximations that we have made in developing our physical models of macroscopic systems. I've also tried to indicate the underlying connections between some superficially disparate topics (e.g., band theory, coupled mechanical oscillators, and plasmons). Hopefully this approach allows students to develop an intuition for, and the ability to reason critically about, the nanoscale world. By focusing on the fundamentals rather than the latest research results (though those are mentioned when appropriate), I also hope that this text will stand the test of time, rather than appearing dated as soon as it is published. Of course, during the writing of this book, a number of other texts more or less in a similar or complementary spirit have appeared. These include Introduction to Nanoscale Science and Technology, edited by M. Di Ventra, S. Evoy, and J. R. Heflin, Jr. (Springer, 2004); and Introduction to Nanoscience by S. Lindsay (Oxford, 2009).

When teaching this material as a course or course sequence, I recommend supplementing the exercises with short-answer questions based on readings from the current literature.

Nanotechnology has seized both the public and scientific communities' imaginations, and it's not hard to see why. From K. Eric Drexler's and Ray Kurzweil's visions of self-reproducing engineered nanomachines building macroscale structures out of single crystal diamond and swimming through our capillaries repairing damaged cells, to talk of building an elevator directly to geosynchronous orbit, the promise of nanoscale science and engineering has been described to an enthusiastic public. Billions of dollars of research funding have been directed into this area, and further billions of dollars are already being spent on commercial products that are self-described as examples of nanotechnology. Estimates of the global economic impact of nanotechnology in the next ten years exceed $1 trillion, and are rising.

How seriously should we take these exciting visions? Is nanotechnology a “disruptive technology”, a distinct advance that will reshape the world? What are the real potential impacts of the ability to engineer the structure and composition of materials on the nanometer scale? What are the limitations imposed by Nature (that is, physics and chemistry) on what is possible? What physical principles become relevant at small scales that on the one hand set limitations, but on the other provide new opportunities? What scientific questions remain to be answered at the nanometer scale, and why? How can people manipulate and characterize materials on these scales?

Hopefully this book will help you answer these questions, or at least give you a good idea of what to consider when trying. Even though the nanometer scale is very different from our everyday experience, it is possible to develop an intuition about how matter will behave at that extremely small level.

What is nanotechnology?

Nanotechnology is an extraordinarily broad term. According to the US government, nanotechnology is “Research and technology development at the atomic, molecular or macromolecular levels, in the length scale of approximately 1 – 100 nanometer range, to provide a fundamental understanding of phenomena and materials at the nanoscale and to create and use structures, devices and systems that have novel properties and functions because of their small and/or intermediate size.”