Invitation to a Contemporary Physics (2004)

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array architecture may be constructed with magnetic tunnel junctions. But, in this case, as the sense current has to flow perpendicular to the layers and so can proceed through many elements and not just the one at the intersection, a diode is placed at every intersection so that the current is forced through the desired path and only in one direction.

While the development of MRAM chips is racing ahead, spurred on by a huge global market, there have been several other directions of research in materials and spin transport that suggest possible applications. The search for useful materials exhibiting enhanced polarization continues apace, and the range of materials studied has significantly increased, including novel ferromagnetic semiconductors, hightemperature superconductors, and carbon nanotubes. It was found that a family of perovskite materials (Chapter 3) exhibit very large magnetoresistance, up to 100 000%, but at very high magnetic fields (6 T), an e ect termed ‘colossal’ (CMR). Even more interesting is the extraordinary magnetoresistance (EMR) exhibited by non-magnetic narrow-gap semiconductors with an embedded non-magnetic metallic inhomogeneity. Room temperature EMR in excess of 100% at 0.05 T and 3 million percent at 5 T has been obtained. Researchers have already demonstrated that mesoscopic read-heads made of nonmagnetic silicon-doped indium antimonide, operating on the EMR principle, were sensitive enough to read data at 116 Gbits per square inch, auguring well for the future of terabit-per-square-inch recording media.

Several schemes for spin transistors, in which the flow of spin-aligned electrons is controlled by a magnetic field, have been proposed. The general intent is to search for ways to construct smaller, more rugged multifunctional devices, that not only could function as switches or valves and amplify signals, but would also possess intrinsic memory, and could be seamlessly integrated with traditional electronic technology.

Beyond perfecting existing technology, there is an even more ambitious vision for spintronics of fully exploiting the quantum nature of spin. Central to this picture is the tantalizing possibility of building spin-based quantum computers. The basic idea of quantum computing (to be explained in more detail in Chapter 6) is to exploit the laws of quantum mechanics to process information. Whereas the basic unit of information in a conventional computer is a binary digit, either a ‘0’ or a ‘1’, a quantum computer processes information by quantum bits, or qubits, which are representations of arbitrary linear combinations of both values, thus vastly expanding the power of computing. To be useful as carriers of information, the states of many qubits, which represent pieces of data, must be controlled precisely and must remain coherent, or undisturbed by interactions with their environment, for a long time. This makes electron spin an ideal candidate for the qubits. O hand, spins should have long coherence times because they are una ected by the long-range electrostatic interactions between charges, which are the most pervasive kind of force in solid-state surroundings. Experiments have verified that it is indeed the case. David Awschalom and co-workers have demonstrated that electron spins

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could survive in a coherent state for more than 100 nanoseconds, su cient for the standard operations on a memory chip, and coherently precessing electronic spins could travel without a substantial increase in decoherence (losing information) over distances exceeding 100 µm, comparable to the size of a typical electronic device.

5.6.5Summary

Traditional electronics is based on the flow of the electron charge. A new field, called spintronics, intends to use both the flow of charge and the flow of the electron spin to develop new materials and devices that can perform more than is possible with today’s products. In particular, two magnetic-layered structures — spin valves and magnetic tunnel junctions — exhibit a large magnetoresistive e ect, which has been exploited to make sensors, recording heads and memory cells.

5.7Nanos at Large

In our discussion, we have focused on only three classes of nanostructures, at the exclusion of many other cases of equally great interest. Even in the optoelectronics field, which we have considered in some detail, we left out the important invention of the photonic band-gap crystals. These structures are based on periodic variations of the dielectric constant, and can produce many of the same phenomena for photons as an ordinary crystal does for electrons. This is a good example of how scientists can exercise control over the optical properties of materials and, in so doing, engineer materials that reflect light of any polarization incident at any angle, or allow its propagation only in certain directions at certain frequencies, or localize light in specified areas.

Structural materials too can be improved by a control over their make-up at the nanometric level. Where conventionally produced materials tend to be gross and irregular in structure and composition, nanostructured materials can be created in regular and flawless shapes, or with high strength and low weight, or with a controlled brittle behavior. These materials, being more finely grained, have a greater surface-to-volume ratio than conventional materials and, therefore, find many applications in paint and coatings, and in catalysis. They can even be designed so that they contain pores that admit particles of a particular size, thus opening the way to ‘smart’ membranes that can selectively block out certain molecules.

Polymers are long-chain molecules in which a molecular unit repeats itself along the length of the chain. We are in daily contact with them in the form of adhesives, plastics and fibers (e.g., nylon and rayon). Silk, wool, and the molecule of deoxyribonucleic acid (DNA) are examples of naturally occurring polymers. The interest of the physicist in these materials is aroused particularly by the discovery that polyacetylene could be made conductive by suitable doping, thus opening the possibility of controlling conductivity in materials normally regarded as good insulators (they

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are then called conjugated polymers). Block copolymers result from two reactant oligomer species that form polymeric chains having segments (or blocks) that are attracted to one another. They can give rise to nanoscale phases (which may, for example, be present as spheres, rods or sheets) and provide the framework for manufacturing a wealth of materials — including catalysts, ceramics and insulators — with unique properties. Proteins are an example of block copolymers with two phases, in the form of helical coils and sheets. Polymers have also been used in medical applications, say, to produce artificial skin, dental fillings, and high-density polyethylene for knee prostheses.

These polymers are examples of materials belonging to an interesting and vast class called biomolecular materials, or biomaterials. Biological molecules, that nature has been perfecting for millions or even billions of years, have important lessons to teach and inspire us, especially for applications to nanotechnology. Biological sources have presented us with proof that proteins fold into precisely defined three-dimensional shapes, and nucleic acids assemble according to well-understood rules; and that antibodies are extremely specific in recognizing and binding their ligands, and molecular motors can perform specialized tasks in the cell.

A key feature of biomaterials is their ability to undergo self-assembly, a process in which aggregates of molecules and components arrange themselves into ordered, functioning entities without external intervention. It is inextricably linked to the idea of molecular recognition, according to which subunits, entrusted by nature with sets of instructions, recognize each other and bind to each other, selectively. From this observation, the chemist has constructed a model of biomembrane, a ectionately called SAM for self-assembled monolayer (Fig. 5.17). It is a oneto two-nanometer thick film of organic molecules that form a two-dimensional crystal

Figure 5.17: Schematic illustration of the molecular structure of a self-assembled monolayer on a surface substrate.

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on an adsorbing, typically metallic, surface. The molecules in a SAM are longer than they are wide, and have an atom or atomic grouping at one end that ‘sticks’ spontaneously (by chemical a nity) to the substrate. When attached, they protrude from the substrate, like a vast forest of identical trees planted in a perfect array. At the other end, scientists can attach selected molecular fragments to give the SAM a well-defined chemical surface property. For example, the molecular layer can be made to attract or repel water, which in turn can a ect its adhesion, corrosion and lubrication. SAMs find applications in biological sciences, for example, in the study of interactions of cells with surfaces, neural synaptic integration in planar neural arrays. A long-term goal of research in organic thin films is to find ways of making electronic devices in which the components are individual molecules that self-assemble on substrates from solution or by deposition from interfaces.

Biosensors, devices that couple a biological or biologically-derived sensing element with a physico-chemical transducer, have been known for many decades (for example, in applications to analytical problems in health care, environmental monitoring, defense and security). They are all based on the observation that biological species (from dogs and snakes to enzymes and microbes) may sense the presence of certain molecular species with extreme sensitivity and selectivity. When miniaturized to nanoscale size, they could be implanted in the patient’s body, and regulate a controlled release of drugs in phase with the body’s changing demands. Recent advances in nanotechnology are broadening their already considerable range of utility. For example, nanotubes filled with enzymes or coated with DNA could be used as electrodes for biosensors. They are so small that an array of them containing di erent enzymes could be integrated with a single microelectrode enabling many simultaneous analyses.

In the development of sensors and, more generally, in bioelectronics and other biologically related fields, the biomimetic approach plays an increasingly important role. It involves directly mimicking biological systems or processes to produce improved materials, or applying techniques observed in nature in a di erent context or using di erent materials. For instance, neural networks have arisen from attempts to reproduce the architecture of the human brain, but are implemented using standard electronic and optoelectronic components. Bioengineers, following this path, have succeeded in synthesizing new chain molecules, which then may self-assemble into desirable structures with new or improved properties. They have obtained in this way a variety of designer polymers, such as natural proteins (like silk or collagen) and their modified forms, and synthetic proteins that have no close natural analogues.

As we all know, Nature is not only a genius in physics and chemistry, but also a superb engineer: witness the many sophisticated molecular motors she has built. It has been known for some time that much of the molecular transport in biological systems proceeds not by di usion but by transport. These biomotors are proteins that use the energy of ATP (adenosine triphosphate) hydrolysis to shuttle along individual fibers: myosin, responsible for muscle contraction, moves on an actin

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filament; and kinesin, responsible for cellular transport, moves on a microtubule. Recent single-molecule experiments have shown that motor proteins like these act in a discrete, stepwise fashion with very high e ciency, much like a thermal ratchet. A number of researchers have proposed schemes by which such molecular motors could be harnessed to deliver molecules, one at a time, and assemble nanoscale devices in a sort of Lilliputian assembly-line factory. In fact, some micro-organisms have already been employed in making semiconducting quantum dots: when introduced to a potentially lethal concentration of cadmium, the organisms respond by synthesizing crystalline spheres of cadmium sulphide coated with a peptide molecule.

A final but not least important example of the marriage of electronics and molecular biology centers on the ‘molecule of life’ itself. During the last half-century, researchers have concentrated in studying its biological properties. But many of the same methods they have painstakingly developed — to identify and extract fragments of DNA, to recombine them with other sections to create a new genetic material, to modify the molecule’s ends for anchorage to appropriate surfaces — can be applied, together with the tools of nanotechnology, to investigate its remarkable physical properties as well. They have studied, for instance, its electrical conductivity (‘Is it a conductor or an insulator?’) and the mechanisms of electron transfer within the molecule (‘Is it a single-step tunneling process or a multi-step hopping?’).

As is generally known, the DNA carries with it an incredibly complex quatranary code. But can it compute? In a pioneering experiment, Leonard Adleman and colleagues showed that a computer constructed of specially encoded strands of DNA could solve a very di cult computational problem (of the ‘traveling salesman’ type) with 20 variables and find the only correct answer from over a million possible solutions. This is a very exciting result, which could turn out to be a watershed in DNA computation. The DNA, with its unique assembly and recognition properties together with its exceptional stability and adaptability, is bound to become one of the key components in the future molecular electronics.

This chapter is just a snapshot of a young field in vigorous growth. Most of the results discussed in these pages are less than a decade old; yet, at the pace advances are being made, some results will rapidly date, but many will last, with enduring value. The next few decades will see explosive waves of scientific and technological development that will transform our lives to a far greater extent than we have seen in the past, especially in the areas where nanoscience overlaps information science and molecular biology, the two other most promising major areas of scientific activities of our times.

5.7.1Summary

We have discussed in detail three specific areas in nanoscience: optoelectronics, carbon fullerenes and nanotubes, and spintronics. But there are other areas just as active, such as structural and biological materials, bioelectronics and molecular electronics, from which we expect important developments near term.

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5.8 Further Reading

Nanoscience and Nanotechnology

•G. Binning and H. Rohrer, In Touch with Atoms, Rev. Mod. Phys. 71 S324–320 (1999).

•R. Service, Atom-scale Research Gets Real, Science 290 1523–1531 (2000).

•M. Rourkes, Plenty of Room Indeed, Scientific American, September, 2001, pp. 48–57.

•http://www.research.ibm.com/nanoscience/ (IBM nanoscience site).

Quantum Devices

•J. Faist et al., Quantum Cascade Laser, Science 264 553–556 (1994).

•F. Capasso et al., Quantum Cascade Lasers, Physics Today, May, 2002, pp. 34–40.

•Marc Kastner, Artificial Atoms, Physics Today, January, 1993, pp. 24–31.

• Mark Reed, Quantum Dots, Scientific American, January, 1993,

pp.118–123.

•R.C. Ashoori, Electrons in Artificial Atoms, Nature, 1 February, 1996,

pp.413–419.

Fullerenes and Nanotubes

•Robert Curl, Dawn of Fullerenes, Rev. Mod. Phys. 69 691–701 (1997); Harold Kroto, Symmetry, Space, Stars and C60, ibid. 703–722; Richard Smalley, Discovering Fullerenes, ibid. 723–730.

•C. Dekker, Carbon Nanotubes as Molecular Quantum Wires, Physics Today, May, 1999, pp. 22–28.

•R. Saito, G. Dresselhaus and M.S. Dresselhaus, Physical Properties of Nanotubes (Imperial College Press, London, 1998).

•P. Harris, Carbon Nanotubes and Related Structures (Cambridge U. Press, Cambridge, 1999).

•http://buckminster.physics.sunysb.edu/ (SUNY Stony Brook site).

Spintronics

• G.A. Prinz, Spin-polarized Transport, Physics Today, April, 1995,

pp. 58–63; Magnetoelectronics, Science 282 1660–1663 (1998).

•D. Awschalom, M. Flatte and N. Samarth, Spintronics, Scientific American, June, 2002, pp. 67–73.

•http://www.almaden.ibm.com/st/projects/magneto (IBM magnetoelectronics site).

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Biomolecules

•G.M. Whitesides, Self-Assembling Materials, Scientific American, September, 1995, pp. 146–149.

•D. Goodsell, Biomolecules and Nanotechnology, American Scientist, May, 2000.

•M. Reed and J. Tour, Computing with Molecules, Scientific American, June, 2000, pp. 86–93.

5.9Problems

5.1Using the position–momentum uncertainty relation (Appendix B), explain why it is not possible to have confinement in a thin film of vanishingly small thickness.

5.2Consider an electron trapped in an infinitely deep square potential of width

d, for which the energy spectrum is given by En = (nh)2/(8m d2), as stated in the text. We assume m is 7% of the electron mass (given by me = 0.5 × 106 eV/c2, where c is the speed of light). Calculate the excitation energies ∆E21 = E2 − E1 and ∆E32 = E3 − E2 for d = 10 nm. If these are converted into photons, what are their wavelengths? Repeat the calculations

for d = 5 nm; which region of the light spectrum are we in?

5.3The alloy cadmium–selenium can be fabricated as powder of crystallites, each a few nm across. It is observed that the powder with the larger-sized grains appears red, whereas it appears yellow with the smaller-sized grains. Explain why it is so.

5.4In the model of confinement in one dimension by an infinite potential of width d, the excitation to the first excited state requires the energy ∆E21, as defined in Prob. 5.2. In order to eliminate this dimension from the particle dynamics,

we must require ∆E21 > kT . Find the corresponding condition on d, and calculate its limiting values for m = me and m = 0.07me, where me is the mass of the electron. Assume kT = 0.026 eV.

5.5Consider electrons flowing through a 1D channel to which we have applied a small voltage V . Using the uncertainty relation ∆E∆t h and the Pauli principle, derive an expression for the conductance quantum G0.

5.6The Coulomb energy for a single electron in a sphere of radius R in a surround-

ing medium with dielectric constant ε is given by Ec = e2/εR (cgs units). Using the data e = 4.8 × 10−10 esu, 1 eV = 1.6 × 10−12 erg and ε = 12 (for silicon), find the limiting value of R from the condition Ec > kT for room temperature.

5.7Why is the electron–electron interaction relatively more important in artificial atoms than in natural atoms?

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5.8The charging energy of a quantum dot of capacitance C holding charge Q is given by E(Q, VG) = QVG + Q2/2C, where VG is the voltage responsible for the charging. We assume that VG = (N + δ)/C, where N is an integer and −0.5 ≤ δ ≤ 0.5, and take e = 1 to simplify.

(a) Calculate for given δ (hence VG) the charging energy E(N, δ) for a quantum dot with charge Q = −N, and the energies it would cost us to add or remove one electron, defined by ∆+(N, δ) = E(N + 1) − E(N), and ∆−(N, δ) = E(N − 1) − E(N). Calculate ∆+ + ∆−. Remark on how these quantities depend on N, VG and C.

(b) Show that when VG takes the values 1/2C, 3/2C, (2N + 1)/2C, it costs absolutely no energy to add an electron to a dot containing 0, 1, N electrons, or to remove an electron from a dot holding 1, 2, N + 1 electrons.

5.9How many kinds of vertices and how many of each kind are there in C60? How many hexagons are there? Given that the average edge is 0.142 nm long (which is the carbon–carbon bond length), calculate the diameter of C60.

5.10The C70 molecule may be considered a rugbyball-shaped cavity, constructed by inserting a ring of ten atoms between the split halves of a C60 structure. How many pentagonal and hexagonal faces are there in C70? Given that the average edge is approximately 0.142 nm long, estimate the width and length (from end to end) of the cavity.

5.11For a polyhedron containing only pentagonal and hexagonal faces, the number of pentagons is given by p = 12. How is this relation modified when the structure includes, in addition, heptagons and octagons?

5.12On a hexagon, one may always define two vectors, called a1 and a2, separated by an angle of 60◦, starting from the same vertex and going to the opposite vertices. Given a the edge length, what is the lengths of a1 and a2? On a hexagonal lattice, let a vector be given by C = na1 + ma2. Show that the

length of C and the angle between C and a1 are given by

√

|C| = 3a(n2 + nm + m2)1/2

and

√

θ = arctan[ 3m/(2n + m)] .

The winding angle defined in the text is given by φ = 30◦ − θ.

5.13Assuming the C60 radius is 0.34 nm, identify the indices of the nanotubes that can be capped by the split halves of that molecule. Which of them are metallic?

5.14Explain why in copper (and other nonmagnetic metals), the up and down spin bands line up at the same energy level, and so there is no population imbalance.

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5.15Consider the problem of storing data on a magnetic medium. If it is given that the data-storage density is x Gbits per square inch, what is the area (in square nanometers) occupied by a bit? Assuming that a bit contains N grains, each a square of size L, what is the storage density x? For a density of 1 Gbit/in2 and L = 15 nm, how many grains are required to store one bit? Recall that 1 inch equals 2.54 cm.

5.16A standard compact disk has 12.8 square inch of usable surface. As in the previous exercise, each bit contains N square grains of sides L. Assuming that L = 10 nm, how much data can a CD store if N = 3000, and if N = 1? Let us now assume, following the late Richard Feynman, that all the books ever published amount to 1 Pbit = 1015 bits, how many CDs do we need to store all that, in either case?

A grain of size L = 10 nm contains about 1500 atoms. This is the limit in today’s technology, below which the magnetic noise makes signals unreadable. Suppose however that somehow this limit can be lowered to, say, L = 3.5 nm. How many CDs do we need to store 1 Pbit, assuming N = 1?

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