IMM Report Number 3

New Components

New material and components extend the range of nanometer scale systems that we can build. Of particular value are stiff components, which can limit the effects of thermal vibration on positional errors.

Functionalized nanotubes as AFM tips

In the first paper summarized in this section S.S. Wong et al., writing in [Nature 394:52-55 2Jul98] describe using functionalized nanotubes as AFM tips.

Nanotubes are essentially cylinders of graphite. When nanotubes are subjected to aggressive oxidizers, they shorten. When nanotubes have been shortened by oxidation, their ends have been found to be covered with carboxyl, -COOH, groups. Carboxyl groups have a rich and well understood chemistry. The authors exploited this chemistry to covalently bond several types of end groups to nanotubes, which they then used as AFM tips to probe surfaces.

The authors prepared their nanotubes by oxidation in air at 700°C, burning off all but 2% of the original material. They treated these tubes in four ways, yielding tips with a variety of chemical properties:

1. retaining the original carboxyl groups produced by the oxidation. These tips are acidic.

2. forming an amide bond to benzylamine
   (C₆H₅CH₂NH₂), terminating the tip with a hydrocarbon. These tips are hydrophobic.

3. forming an amide bond to one of the amine groups in ethylenediamine, (H₂NCH₂CH₂NH₂), thus terminating the tip with an amine. These tips are basic.

4. forming an amide bond to a biotin derivative, thus terminating the tip with biotin. These tips show a specific binding to streptavidin.

The authors demonstrated that the contact forces between their tips and selected substrates were sensitive to pH and to the chemical details of the substrate in ways consistent with the tips’ intended chemistry. They demonstrated that the carboxyl-terminated tips behaved like carboxylic acids, adhering to hydroxyl-terminated substrates with a force that dropped when the pH was raised past 4.5 and the tip ionized. They demonstrated that the amine-terminated tips behaved like weak bases, adhering to hydroxyl-terminated substrates at high pH and not adhering at low pH (where the amines are in an ionized, protonated form). They demonstrated hydrophobic bonding of their hydrocarbon-terminated tips to a hydrocarbon-terminated substrate. They demonstrated selective binding of their biotin-bound tips to a streptavidin coated substrate.

These tips have three closely related advantages over previous techniques.

1. Unlike tips built with bulk techniques, the ends of these tips are very different from their sides. If one puts a functional group on the apex of an Si₃N₄ tip or an SiO₂ tip, it is very difficult to avoid getting the groups on the sides of the tip as well. If one then wants to use the tip as a tool, there is a constant hazard that contact with the sides of the tip will alter the workpiece in unwanted places. These nanotube tips don’t have this problem. The carboxyl groups are on the ends of the tube, not on the sides.

2. These tips have lateral dimensions set by the nanoscale dimensions of nanotubes, not by top-down fabrication techniques. The authors write: "…the small effective radius of nanotube tips significantly improves resolution beyond what can be achieved using commercial silicon tips." and "The multi-walled nanotubes used here can have diameters of 15-50 nm, but we have recently demonstrated that lateral resolution of <3nm can be achieved by using COOH-terminated single-walled nanotubes tips" (This has been submitted to J. Am. Chem. Soc.)

3. The tips based on single-walled nanotubes are much closer to yielding
   truly single atom tips with controlled chemistry than any alternative that
   I am aware of. A (10,10) nanotube has a diameter of 1.4 nm, and has just 20
   atoms at an open end. Even if there is a statistical distribution of tubes
   with varying numbers of carboxyl groups attached to their ends, one should
   be able to build a ligand which covers the whole end of the tube.
   This would yield a method for ensuring that just one molecule, of known
   structure and orientation, was present at the end of the probe.

The authors are optimistic about using these tips for atomically precise
sensing and fabrication, writing:

"In particular, recent studies in which we have extended the covalent modification procedures to single-walled nanotubes suggest the possibility of mapping functional groups with true molecular resolution. Among intriguing future applications is the use of the highly selective and robust chemistry described here to link catalysts, such as transition-metal complexes, to nanotube ends to create tools that could modify or create structures at the molecular scale."

For more information, see

http://www.foresight.org/hotnews/archive.html#FunctNTAFM
.

Stable 3-stranded beta sheet structure

In the second paper summarized in this section T. Kortemme, M. Ramirez-Alvarado, and L. Serrano, writing in [Science 281:253-256 10Jul98], describe the design, synthesis, and characterization of a 20 residue peptide which forms a stable 3-stranded beta sheet structure in solution.

The design process for this peptide went through several phases. They extended an 8 residue two-strand peptide from a previous design in several steps. They used "statistical analysis of the protein structure database and favorable van der Waals contacts, using rotamer modeling" to pick the residues used to extend the beta sheet to a third strand. This design was further refined by introducing an aromatic residue into the new strand (while making corresponding changes to the middle strand) to increase the amount of buried hydrophobic surface in the folded structure.

The resulting structure, named "Betanova" by the authors "was soluble in water and monomeric up to a concentration of 2.6 mM." The monomeric behavior is important because "a major obstacle to the study of beta-sheet structures is the tendency of isolated beta-sheet secondary elements to aggregate."

The authors demonstrated that their peptide formed a beta sheet in solution by measuring NMR spectra. NMR spectra are sensitive to interatomic distances, and they found that their peptide had indeed folded as designed, placing residues on opposite sides of the fold (but distant in the linear sequence) close together. One odd feature of the structure is that, "although there is a hydrophobic cluster on one face of the beta sheet, most of the residues involved in the packing also have polar groups."

Despite the difficulty of designing beta folds, Betanova is even shorter than the shortest stably folding alpha-helical peptide that I am aware of, a 23 residue peptide reported in [Science 271:342-345 19Jan96]. Short peptides with stable secondary structures are valuable because they lower the bound on how many of the residues in a protein must be devoted to maintaining the stability of its shape. Betanova improves this lower bound without unnatural amino acids or disulfide bridges. It marks a significant improvement in the control of protein folding. This enhances the prospects for using proteins as components with precisely controlled 3D structures in nanotechnology.

Soluble fullerenes

In the third paper summarized in this section M.D. Diener and J.M. Alford, writing in [Nature 393:668-671 18Jun98] describe the solubilization of C₇₄ and C₈₀.

C₇₄ is known to be present in fullerene soots because it is regularly observed "by mass spectrometry, but it is not soluble." Like the better known fullerenes, C₇₄ "possesses only one isolated pentagon [low strain] structure." The problem with C₇₄ is that it has two electrons in two closely spaced orbitals, so it can act like a diradical and form insoluble, polymerized solids.

The authors were able to solubilize C₇₄ by electrolytic reduction in benzonitrile with (n-Bu)₄N⁺ as a counterion. Presumably it was reduced to C₇₄^2-. They could plate it out again by reoxidation on a platinum electrode. Similar behavior is seen with C₈₀.

These new fullerenes are stiff polycyclic structures. Adding them to the set of availible building blocks adds to our options for creating nanometer scale structures able to function in the presence of thermal vibrations.

Incorporating metals into DNA

In the fourth paper summarized in this section D.J. Hurley and Y. Tor, writing in [J. Am. Chem. Soc. 120:2194-2195 11Mar98], describe "a general methodology for the incorporation of polypyridine metal complexes into oligonucleotides using automated DNA synthesizers."

The authors synthesized derivatives of thymine where the methyl group of the base is replaced by a covalent link to a metal complex. The covalent link was an ethnyl (-CC-) group. The complexes used were of osmium and ruthenium, both complexed with two bipyridine ligands and with one 1,10 phenanthroline ligand. The substituted thymine was sufficiently similar to the normal base that

• A (phosphoramidite) coupling chemistry normally used to link DNA nucleotides
  into oligonucleotides incorporated the modified nucleotides with better
  than 90% yield.

• 20-mer oligonucleotides containing the modified bases could be synthesized.

• The modified nucleotides could be incorporated in any position in the oligonucleotide. Previous methods could only place metal-containing nucleotides at the terminii of oligonucleotides.

• Oigonucleotides containing the modified bases "form stable DNA duplexes." These DNA duplexes have nearly the same thermal stability as ones formed from unmodified DNA.

Much work has been done building structures from DNA, notably N. Seeman’s polyhedral structures. The current authors’ work helps add functional groups to these structures. The authors demonstrated fluorescence of the ruthenium complex and quenching of that fluorescence by energy transfer to an osmium complex in a nearby position in a complementary DNA strand. Other functional uses for metal complexes in DNA structures may include enabling redox reactions and catalytic functions. Structurally, they could also serve as binding sites for groups that can coordinate with the metals.

Water cluster at room temperature

In the fifth paper summarized in this section L.J. Barbour, G.W. Orr & J.L. Atwood, writing in [Nature 393:671-673 18Jun98] describe finding water in a crystal structure in a surprisingly large ordered cluster: a decamer.

The authors synthesized a dinuclear copper complex with the pair of copper atoms bridged by four copies of a somewhat complex bidentate ligand. On determining the crystal structure of the complex, they found that water was present between the complexes in a rather unusual form. The water formed decamers, bound to copper ions at two of the waters, and with a structure close to that present in ice I_c.

The presence of such a large water cluster with an ice structure at room temperature may have favorable implications for the design of stiff structures from biopolymers which contain hydrophilic groups. It shows that even a rather large water-filled volume in a structure may be sufficiently stabilized by its environment to permit the water’s hydrogen bonds to form a well-defined, atomically precise network. This may also permit higher stiffnesses in such structures than disordered water molecules would permit.

Supramolecular systems

While covalent systems can be very stiff and precise, sufficiently large systems will always need interfaces between parts which are not bound together covalently. The papers in this section include advances in the control of systems including non-covalent interfaces on a nanometer scale.

Molecular rotor

In the first paper summarized in this section J.K. Gimzewski et al., writing in [Science 281:531-533 24Jul98] describe the observation of a molecular rotor operating within a void in a 2-D lattice.

The authors evaporated a propeller-shaped molecule, hexa-tert-butyl decacyclene (HB-DC) on a clean Cu(100) surface. HB-DC contains a core of ten fused aromatic rings, centered on a single benzene ring, with 3-fold rotational symmetry. HB-DC’s core is lifted off the copper surface by six bulky saturated hydrocarbon tert-butyl, (CH₃)₃C- legs. HB-DC molecules have a diameter of roughly 1.5 nm.

When much less than a single layer of HB-DC covers the copper surface, the molecules diffuse so rapidly that they cannot be seen in STM images. While rotational symmetry of HB-DC is 3-fold, the perimeter of the molecule is close to hexagonal. When a full monolayer is deposited on a copper surface, the molecules form a hexagonal lattice. Under these conditions the legs of the molecules can be seen in an STM image as distinct dots. The molecule as a whole is seen as "six lobes arranged in a hexagonal lattice [sic] with alternating distances of 0.6 and 0.8 nm between the lobes."

The authors observed that at just less than a monolayer’s coverage, "there is a random array of nanoscopic voids in the [HB-DC] layer… In these voids – and only there – we observed images of certain individual molecules with the expected overall dimensions of the six-lobed species but displaying internal contrast in the form of a torus." They go on to explain that molecules which are in contact with four of their neighbors and aligned with their normal lattice position are locked into position, while slipping the molecule 0.26 nm away from its neighbors lets it rotate, much like a poorly gripped hex nut can slip in a crescent wrench.

The authors did a molecular mechanics simulation of the rotational barriers
seen by a HB-DC when aligned with 4 neighbors, and when slipped out 0.26 nm.
They calculated that the aligned molecule saw a barrier of 117 kJ/mol, which
is sufficient to lock it in place, but the displaced one saw a barrier of
only 29 kJ/mol, which is low enough to permit rotation. Note that even the
lower barrier is still >kT. The barrier is low enough to permit rotation
which is much faster than STM imaging (in fact, faster than is visible in
tunneling current frequency spectra up to 30 kHz), but this is not yet quite
so finely tuned as to bring barriers below kT.

While the observed rotation is driven by thermal noise, the authors suggest that added non-thermal noise, such as temperature differences produced by tunnel current heating of the rotor, could be rectified by asymmetries in the rotor/neighbor potential energy curve, and could turn the rotor unidirectionally.

These experiments demonstrate that Van der Waals bearings can indeed operate in
molecular systems, that we are not limited to sigma bond bearings but can
build multiatomic bearing surfaces with higher load capacities, that these
bearings can run with no lubricants, and that they have sufficiently low
barriers that thermal vibrations can turn them.

For more information, see

http://www.foresight.org/hotnews/archive.html#MolRotorSTM
.

Workpiece holders for C₆₀ molecules

In the second paper summarized in this section V.V. Kolesov, V.I. Panov, and E.A. Fedorov, writing in [J. Commun. Technol. Electron. (Russia) 42:818-821 Jul97], describe a technique for placing individual fullerene molecules in perforated Langmuir-Blodgett films.

The authors prepared their perforated films by depositing a film of a two component mixture on a graphite substrate, polymerizing one component with UV, then washing out the other component with hexane. The component which was polymerized had a long hydrocarbon tail containing a double bond. The second component (which was present as 8% of the molecules in the film) was tetra-tert-butyl-porphyrazine. The porphyrazine derivative can form a film by itself, but it is roughly pancake shaped, and it lies flat on the water surface, occupying roughly 150 Ų. This is close to the size of a C₆₀, so the removal of the porphyrazine leaves the right sized hole for the C₆₀.

After preparing their perforated films, the authors found holes which "were almost cylindrical in shape, about 15 Å in diameter, and of different depth (30 and 10 Å). The perforations differed in depth probably because the solvent treatment had left some of the porphyrazine molecules in the monolayer matrix."

The authors deposited a solution of C₆₀ on their perforated film. They were able to manipulate C₆₀ molecules into the perforation with an STM tip. They found that the film with C₆₀ molecules in it was durable enough that they could still be detected even after several months of storage.

This paper shows that a receptor for C₆₀ could be built using a molecule of similar shape as a template rather than C₆₀ itself. It puts C₆₀ in a stable holder. The authors used this to obtain I(V) spectra without pushing the molecule away from the tip. Perhaps similar receptors could also be used to selectively attach groups to one side of a workpiece by physically blocking access to other sites.

Nanostructured silica/organic composite

In the third paper summarized in this section A. Sellinger et al., writing in [Nature 394:256-260 16Jul98] demonstrated formation of a nanostructured silica/organic composite which mimics the layered structure of nacre.

The authors’ system goes through several states in the course of forming their nanostructures. It starts as a uniform liquid, forms micelles as it partially evaporates, self-assembles into parallel layers roughly 3 nm thick, then is polymerized into a robust composite.

This system has quite a few components. The "precursor solutions were prepared by addition of cationic surfactant, organic monomer, crosslinker, initiator, and unsaturated alkyltrialkoxysilane (used in our study as a coupling agent) to an acidic silica sol." The silica sol contained roughly 70% ethanol, which initially dissolved the organic components of the mixture. Preferential evaporation of the ethanol made the monomer (dodecylmethacrylate) drop out of solution as micelles, along with the organic tails of the coupling agent, and surrounded by a surfactant layer. Further evaporation forms parallel layers of monomer and silica layer, linked by the condensation of the alkyltrialkoxysilane with the silica. Formation of the final structure is completed when "organic polymerization (induced by light or heat), combined with continued inorganic polymerization, lock-in the nanocomposite architecture and covalently bond the organic-inorganic interface."

This system is stronger than its organic polymer component. The authors performed nano-indentation measurements and found hardnesses of 0.8 – 1.0 GPa, almost equal to the 1 GPa measured for pure silica films.

As it stands, this is not an atomically precise system. It does, however, display structuring of a stiff inorganic material by bonding with a more compliant organic polymer, which might be amenable to more precise control. The dimensions of the films are small enough that they could be spanned by proteins with controlled 3D structures, which might, in turn, allow precise control of stiff materials such as the silica in this system.

Diagnostics

Not all attempts to fabricate nanoscale systems will succeed. Not all correctly constructed nanoscale systems will prove to have the properties anticipated. It is therefore important to have techniques for probing nanoscale systems, both geometrically and functionally. It is particularly useful for such techniques to be sensitive to individual molecules, since, in some cases, only a handful may have been constructed. The papers described in this section advance these techniques.

Measuring vibrations of single molecules

In the first paper summarized in this section B.C. Stipe, M.A.Rezaei, and W. Ho, writing in [Science 280:1732-1735 12Jun98] describe observation of vibrational spectra of single molecules via STM measurements at 8K.

Vibrational spectra tell us a great deal about molecules. Organic chemists use them routinely as a tool to help determine the structures of unknown compounds. There has been interest in using scanning tunneling microscopes (STMs) to detect vibrational spectra since shortly after STMs were invented. Some preliminary results date back to 1987, but were plagued by the effects of diffusion of the adsorbed molecules.

A vibrational mode of an adsorbed molecule affects tunneling current by providing another “channel” by which tunneling can occur. In this channel, the tunneling electron is inelastically scattered, making the molecule vibrate at its characteristic frequency. The electron therefore loses energy to the molecule as it tunnels from the scanning tip through the molecule to the substrate. This process can only occur when the electron’s energy is greater than the energy of a quantum of the vibrational mode. The process is visible in the STM’s current as an increase in the conductance of the tip/molecule/substrate structure as the threshold energy is passed. The authors saw conductivity increases of 12% when probing C-H bonds with particularly sharp STM tips.

The authors of this paper have been able to combine a number of techniques to
successfully acquire vibrational spectra from STM measurements.

• They operated at 8K.

• They have built an STM which is extremely stable mechanically. Since tunneling current changes about an order of magnitude per angstrom, the mechanical noise must be less than 0.05 Å in order to see these effects at all.

• They picked a system, acetylene adsorbed on Cu(100), with strong chemisorption.
  This minimizes the adsorbate diffusion problems.

• They positioned their tip over the center of the acetylene "with lateral and vertical resolution of better than 0.1 Å and 0.01 Å, respectively."

• They modulated the voltage of STM tip sinusoidally while using lock-in
  detection to isolate the second harmonic of the voltage modulation, a signal
  proportional to d²I/dV².

• They averaged their signals across many scans, in one case using 10 hours of
  scanning over one molecule.

• They measured reference spectra on nearby clean Cu(100) surfaces and subtracted
  them from the spectra of the adsorbed acetylene.

Using these techniques, the authors were able to observe a C-H stretch peak in acetylene adsorbed on Cu(100). They were able to observe the corresponding C-D peak in deuterated acetylene with the expected frequency shift due to the greater mass of the deuterium atoms. They were able to image the current due to just the vibrational channel, and presented striking pictures showing just the C₂H₂ or just the C₂D₂, depending on which vibrational energy they selected.

This technique is superior to the Raman technique reported in S. Nie and S.R. Emory [Science 275:1102-1106 21Feb97] because this technique can be used on any molecule that can be located on a flat substrate, not just molecules that are bound to unpredictable "hot spots" on Ag nanoparticles. The authors of the current article write that "It may soon be possible to use single-molecule vibrational spectroscopy and microscopy to determine the identity and arrangement of functional groups within a single molecule and to study its chemical transformations." Vibrational spectroscopy also provides direct information on the stiffness of molecular structures, useful feedback for mechanical design on a nanometer scale.

Nanotube conductance

In the second paper summarized in this section S. Frank, P. Poncharal, Z.L. Wang, & W.A. de Heer, writing in [Science 280:1744-1746 12Jun98] describe experiments measuring the conductance of MWNTs with liquid metal contacts.

Unlike the earlier work of Collins, Bando & Zettl, where nanotubes were slowly withdrawn from a nanotube "felt", this technique allowed the authors to repeatedly lower the nanotube into the metal and raise it out. The contact was sufficiently good that the authors "did not adjust for a ‘series contact resistor’ as is often done for metal nanowires to align the conductance plateaus with conductance quanta."

The authors used three different liquid metals for contact: mercury, gallium, and a lead-bismuth alloy called Cerrolow-117. Essentially the same results were found with all three metals. The dipping frequency was 0.1 – 10 Hz, with a peak-to-peak amplitude of 0.1 – 7 microns. "Typically 200 to 1000 dipping cycles with 50,000 measured points per cycle were recorded."

This work shows experimentally that contact resistance to nanotubes can be
small, so the theoretically achievable conductance can truly be realized
in two terminal resistors, not just as differential measurements in systems
with large contact resistances.

The authors mostly saw conductance steps of size G₀ = 2e²/h, indicating the complete opening of a new quantum channel. They interpret these steps as contact with additional tubes in a bundle of tubes. They also saw some short conductance plateaus at 1/2 G₀. These plateaus are “up to twice as long as the diameter of the corresponding tube”, typically ~40 nm long. The authors interpret these short plateaus to be due to elastic scattering at a tapered tip. They see this effect in roughly 30% of their tips. I hope that they try their technique on oxidatively shortened nanotubes. Perhaps they can see if oxidation really does cut the tubes cleanly, eliminating uncontrolled tapering at the tip.

This new technique should also permit much better characterization of electronic devices (such as diodes) which are present in nanotubes. For example, initial dips of a nanotube could locate the position of a diode, then later dips could measure its response to perturbation such as light or charged particles.

In addition to their dipping measurement, the authors examined nanotube conduction at high power dissipation. They applied 6 volts across a nanotube, dissipating 3 mW. They calculate: "If we assume that this power is dissipated uniformly along the length of the nanotube and assume a bulk thermal conductivity of 10 W cm^-1 K^-1, then the middle of a nanotube 1 µm long and 20 nm in diameter would attain a temperature T_max = 20,000 K". This would burn the nanotube, so they conclude that the dissipation must happen in the leads, as expected for a quantum wire. This should permit much higher power control densities in quantum wire devices than one would extrapolate from macroscopic devices.

Electronic Properties

Both today’s nanoscale sensing by tunneling microscopy and a number of proposed applications of nanotechnology rely on electronic properties of nanostructures. The papers in this section advance our understanding of these effects.

Electrically charging gold nanoparticles

In the first paper summarized in this section S. Chen et al., writing in [Science 280:2098-2101 26Jun98] describe experiments that probed the transition from molecule-like charging to metal-sphere-like charging of gold nanoparticles as their size was changed.

The experiments covered core diameters ranging from 1.1 to 1.9 nm, corresponding to particle masses from 8 to 38 kilodaltons (kD) or roughly Au₃₈ to Au₂₀₀. The nanoparticles were covered with a dielectric monolayer of alkanethiolate, hexanethiolate C₆H₁₃SH in some experiments and butanethiolate C₄H₉SH in others.

The authors examined the energies required to add or remove electrons from these clusters in two different ways. They performed electrochemical experiments (differential pulse voltammograms) on solutions of the particles, finding current peaks at voltages that added electrons to the particles. They also examined optical absorbtion spectra of the particles.

For particles with masses of 28 kD or more, they found nearly regularly spaced energies for adding electrons, just as one would expect for a classical metal sphere. This regime is dominated by the change in the sphere’s voltage as it is charged, one electron at a time. For particles with masses of 8 kD, however, the spacing between the two voltages around zero is 1.2 volts, considerably larger than the spacing to the next voltage peaks which are roughly 0.3 volts above and below this pair of peaks. This spacing difference shows that the quantum structure of the energy levels in 8 kD particles is contributing roughly 0.9 volts to the voltage spread. This is confirmed by the optical measurements, which show a 0.9 eV gap for 8 kD particles, a 0.6 eV gap for 14 kD particles, and a gap of <0.4 eV for 28 kD particles.

This experiment helps establish the limits of treating nanometer gold particles as classical conductors. If the quantum structure of the particles interferes with conduction, it may also set a minimum useful size for gold conductors, suggesting that a diameter of 5 atoms may be needed to obtain non-quantum behavior.

Single atom electrical contacts

In the second paper summarized in this section E. Scheer et al., writing in [Nature 394:154-157 9Jul98], investigated single atom electrical contacts of Pb, Al, Nb, and Au, finding that the number of conduction channels through the contacts can be predicted from the valence orbitals of the atoms. Very roughly speaking, they found that the number of quantum channels is bounded by the number of valence orbitals in the contact atom. The conductance, however, is also limited by the transmission probability of each of the channels.

The authors measured conductance as a function of distance in each type of contact. Measuring the conductance gives the sum of the conductances of the quantum channels. The authors also measured current as a function of voltage at a number of distances for each type of contact. This additional information let them extract the individual transmission probabilities (T_n) of each of the channels.

They placed the single atom contacts between superconductors. In this geometry, single electrons can only tunnel if the voltage difference is large enough to break up a pair of superconducting electrons on both sides of the contact, so this only happens for V>2 delta/e. At lower voltages "multiple Andreev reflections are possible, involving the transfer of m electrons while two quasiparticles [unpaired electrons] are created [in the superconducting electrodes]. These processes, which have a probability proportional to (T_n)^m for small T_n, generate current steps at voltages V=2 delta/me within the gap [for the single electron process]." Since the authors knew this I(V) structure for channels of transmission probability T_n, they could fit the observed I(V) structure for the contact to a sum of these functions. Thus they could determine how many channels were present and what their T_ns were.

For each metal the authors found plateaus of conductance as they stretched their junctions. In the last plateau before the conductance started to drop exponentially (indicating tunneling across a gap), they typically saw one channel for gold, three for lead and aluminum, and five for niobium. Some of these channels had fairly small transmission probabilities. For instance, one of their lead contacts had "T₁ = 0.955, T₂ = 0.355, T₃ = 0.085, T₄ = 0.005" T₄ is below the 1% cutoff that the authors set for their channel count.

The authors did detailed theoretical predictions of the T_n for their contacts. They modelled two pyramids of close-packed metal atoms sharing a tip atom quantum mechanically. The detailed models "are in good agreement with our experimental observations", matching the number of observed channels and observed total conductance. For example "[experimentally] Pb contacts just before breaking most frequently have a G [conductance] between 1 G₀ and 3 G₀" (G₀ = 2 e²/h = (12.9 kohm)^-1) while their theoretical prediction is roughly 2.5 G₀.

This work improves our understanding of single atom electrical contacts, "the simplest imaginable circuit." The simple relationship found between the number of quantum channels and the number of valence orbitals is the sort of insight which is useful in design work. For instance, this suggests that devices might be built which make use of simultaneous transmission through two quantum channels through a single atom, perhaps for interferometric measurements.

Applications

Nanotechnology is, after all, intended to be a technology, producing useful devices and systems. The papers described in this section look towards the application of nanotechnology to computing.

Defect-tolerant computer design

In the first paper summarized in this section J.R. Heath, P.J. Kuekes, G.S. Snider, and R.S. Williams, writing in [Science 280:1716-1721 12Jun98] describe the contruction of a computer with a highly defect-tolerant design. This design is specifically intended to be well suited for eventual implementation with nanotechnology. This machine "has been successfully configured into a number of parallel architectures and used for extremely demanding computations."

The authors designed their machine to tolerate defects which result today from inexpensive production processes, but which they anticipate would mimic the effects of chemical synthesis of nanocomputers with less than perfect yield. They write: "Although Teramac was constructed with conventional silicon integrated-circuit technology, many of the problems associated with the machine are similar to the challenges that are faced by scientists exploring nanoscale paradigms for electronic computation."

There are three main strategies used in Teramac.

1. A single chip type (a custom field programmable gate array) was used throughout the machine. It was used for both logic and communications. It was cheaper to ignore the unused logic elements on the chips which were used purely for communications than to pay the design costs for two separate types of chips.

2. Massively redundant communications links were incorporated in Teramac. At each layer in the hierarchy a "fat tree" connected multiple nodes at the higher level with all of the nodes at the lower level.

3. Defects were circumvented by a static compilation step. Teramac was tested, creating a database of defects throughout the machine. A compiler then exploited this database to map the target architecture into Teramac, avoiding the now known defects.

One discovery from this experiment was that both the time required to find the defects in the machine and the time required to route around them scaled up only linearly with the machine size. The authors didn’t attempt to find an optimal mapping, but found that the redundant communications links in Teramac made finding a sufficiently good choice surprisingly fast.

Teramac does not attempt to be fault tolerant. It relies on the stability of the defects found during testing. The authors emphasize the increasing cost of attempting to make large, perfect processors, and suggest that "another model is to fabricate cheap processors by the techniques of chemical assembly, and then train the devices up to the desired level of proficiency with computor tutors that find the defects and record their locations in databases."

Single electron transistor memory cell

In the second paper summarized in this section N.J. Stone and H. Ahmed, writing in [Microelectronic Engineering 41/42:511-514 Mar98] describe a memory cell built out of single electron transistors (SETs).

The memory cell has two active SETs and a storage capacitance. One of the SETs allows charge to flow into and out of the cell’s capacitance when its Coulomb blockade voltage is reached. The other SET acts as an electrometer, nondestructively reading the charge on the storage node. The current between the electrometer SET’s source and drain terminals depends on how many electrons are on the storage capacitance. There is a third SET in the circuit which is used to help characterize the charge gating SET but which is deactivated when the circuit is used as a memory.

The SETs in this circuit are not themselves atomically precise devices. They are "nominally 1 µm long by 70 nm wide and 40 nm in height." They contain a series of islands connected by tunnel barriers. The electrostatic repulsion of electrons on the SET’s islands is what makes the device sensitive to single electrons.

Electrically, the charge gating SET acts somewhat like a zener diode with scaled down voltages. When the voltage across its source and drain terminals is high enough, the energy gain for an electron to tunnel on to an island is high enough to offset the repulsion between it and the electrons already on the island, so current can flow through the island. When the voltage is too low, no current can flow. As a result, the cell capacitance can store a voltage from roughly -V_c/2 (where V_c is the blockade voltage) to roughly +V_c/2. This is the basic memory mechanism of the cell. SETs’ conduction also depends on the voltage on a gate electrode capacitively coupled to the conductive island(s) in the SETs’ source-drain channel. The electrometer SET uses this effect to detect the voltage on the storage node.

Present day SETs are cryogenic devices, because thermal noise must be less than the electrostatic energy required to add an electron to their islands. This circuit "can operate at a maximum temperature of around 10K."

Improvement in fabrication, driving island size down towards molecular scales, will increase the electrostatic energy of electrons confined to smaller islands, pushing the temperature of operation up to room temperature. This paper demonstrates a circuit configuration that can then be used as an information storage application of nanotechnology.

Jeffrey Soreff is an IMM research associate.