From Wise Nano

Contents 1 Basic Theory and Observations 1.1 Scaling laws 1.2 Atomic granularity 1.3 Information delivery rate 1.4 Error sources 1.5 Error handling 1.6 Scaling up production: exponential manufacturing 1.7 Mechanosynthesis

Basic Theory and Observations

This section explores several topics that will be applicable to a broad range of nanosystems, including nanoscale manufacturing systems. Scaling laws indicate that nanosystems will have extremely high performance. The granularity of atoms presents an opportunity for manufacturing systems that create products with no loss of dimensional precision. Nanoscale manufacturing systems will need a high data input rate in order to create highly functional products—so high that the data will need to be processed at the nanoscale. Sources of error are discussed, along with ways of dealing with error. Two approaches to scaling up production are contrasted. Mechanosynthesis, the use of mechanical systems to do controlled molecular synthesis reactions, is too large a topic to discuss in any detail, but the range of available options is briefly surveyed. Design rules and observations relating to efficient motion at the nanoscale are presented, including a comparison of efficient design in soft vs. stiff machines. Finally, the per-atom energy budget of a kilogram-scale nanofactory is discussed.

Scaling laws

Several important measures of performance improve as machines shrink.1 Machines can be characterized by simple measures and ratios; for example, a manufacturing system can handle its own mass of materials in a certain number of seconds, and a motor will handle a certain amount of power per unit volume. Broadly speaking, these numbers vary in predictable ways according to the size of the system. These relationships are called “scaling laws.”

The speed of linear motion stays roughly constant regardless of scale; this means that as a machine shrinks, its frequency of operation will increase proportionally. Motions cross less distance, taking less time. This in turn implies that the relative throughput of a manufacturing system—the fraction of its own mass that it can process per second—will also increase proportionally to the decrease in size, assuming the components it handles scale along with the machine. Each motion transfers a part proportional to the size of the device, but at a higher frequency.

Mass decreases as the cube of the size. This means that, while the relative throughput of a machine shrunk by a factor of 10 will increase by a factor of 10, its absolute throughput will decrease by a factor of 100. To maintain throughput as machines are shrunk to the nanoscale, vast numbers will need to be operated in parallel. If the machines are arranged in a sheet one layer thick, then the area of the sheet will not change as the machines shrink; the number of machines will increase by the square of the shrinkage; the mass of the sheet will shrink in proportion with its thickness; and the throughput will remain unchanged. Thus, due to the higher relative throughput, the total mass of nanoscale machines can be orders of magnitude less for the same absolute throughput. The rapid decrease in mass with size also means that gravity will usually be unnoticeable in nanoscale machinery, momentum and inertia will be extremely small, and acceleration will be correspondingly high.

The linear relationship between size and relative throughput assumes that the machine handles components scaled to the size of the machine. If the component size is held invariant (e.g. small molecules) as the machine scales, then the dependence of relative throughput on machine size is far stronger. A 10-cm machine such as a scanning probe microscope would take on the rough order of 10¹⁸ years to manipulate its own mass of individual molecules. But the cube scaling of mass, combined with the linear scaling of operation frequency, implies that a 100-nm machine could manipulate its own mass of molecules in 30 seconds.

Power density varies inversely with machine size. This is because forces are proportional to area and decrease as the square of the size, while volume is proportional to the cube of the size. Speed is constant; power is force times speed; power density is power divided by volume. This implies that nanoscale motors could have power densities on the order of terawatts per cubic meter. (Obviously, it would be difficult to cool large aggregates of such motors.)

In systems that are subject to wear, the lifetime decreases proportionally with the size. This has been a serious problem for MEMS. However, due to atomic granularity and the properties of certain interfaces, atomically precise molecular manufacturing systems need not be subject to incremental wear. Just as replacing an analog system with a digital one replaces analog noise with digital error probabilities, incremental wear is replaced by speed-dependent damage probabilities which typically drop off exponentially with stress on a part.

For a given material, stiffness decreases in proportion to size. This will pose some interesting design challenges for mechanical systems, but the use of stiff covalent solids will help. (Diamond has a Young’s modulus of about 1000 GPa.)

Atomic granularity

At the energy levels at which nanoscale machinery operates, atoms are indivisible, and all atoms of an isotope are identical (different isotopes of the same element are identical for most purposes; advanced nanosystems will be able to sort isotopes by mass as required). Two components built of atoms covalently bonded in the same arrangement will have identical shapes. (The shapes will be transiently distorted by thermal motion, but the average shapes will be identical.) Construction operations that are sufficiently precise to cause atoms or molecules to attach in predictable configurations can make perfectly precise products.

The inherent precision of covalent products indicates that manufacturing operations need not involve post-processing steps (analogous perhaps to polishing or lapping) to improve precision. This is equally true regardless of whether the precision in the manufacturing system is achieved by open-loop or closed-loop control. Machines of adequate reliability and repeatability will be able to make perfect products without any observation or feedback. Of course, any system will have a non-zero error rate, but the error will be a random failure, not be the result of imprecision or accumulation of wear. A molecular manufacturing system might make several products with perfect precision, and then a product that is broken due to incorrect molecular structure; it will not make products that accumulate imprecision incrementally. If the products include manufacturing systems, then multiple generations can be made with no loss of precision.

Products built near atomic scale will not be subject to wear in the ordinary sense, because it is impossible to remove a fraction of an atom, and removing an entire atom would constitute breakage, not wear. The forces exerted by nanoscale machinery will typically be too small and distributed to break inter-atomic bonds. Although the granularity of atoms makes perfectly smooth surfaces impossible, smoothly moving bearings can still be implemented; see “Bearings” in the "High Performance Nano and Micro Systems" section.

One problematic consequence of atomic granularity is that machines cannot be designed with the dimensional precision common in macro-scale machining, where a centimeter-scale feature may have a tolerance of a few microns. A nanometer-scale feature in a regular molecular lattice can only have its size specified within a few tenths of a nanometer, though carefully designed modifications of the molecular structure can improve this. The fact that atoms are soft and have smooth interactions reduces the impact of this limitation; what would cause lockup or chatter in a metal machine will simply be a more or less tight fit in an atomic-scale interface.

Information delivery rate

In order to build intricate, precise, heterogeneous nanostructures with individually specified features, enormous amounts of information must be delivered from the computer, through whatever tools are used, to the nanoscale. Existing technologies and proposed nanomanufacturing technologies cannot accomplish this. The few technologies that have a high data rate are not atomically precise because they use beams that cannot be focused tightly enough.

A limitation of self-assembly is that the information must be embodied in the component molecules. For example, DNA structures have been built that contain thousands of bases, but the synthesis process requires many thousands of seconds, corresponding to an information delivery rate of at most a few bytes per second. The manufacture of large unique molecules is expensive, even when stepwise polymerization techniques are used. Mixing multiple prefabricated molecules might help with these problems, but would increase the error rate and the time required for diffusion.

Scanning probe microscopes can be atomically precise, but because their actuation systems are large, they move relatively slowly. Semiconductor lithography masks require a long time to manufacture, so although they can deliver information quickly once they are created, the overall data transfer rate from computer to nanoscale is low, and the products are not precise. Electron and ion beams may perform operations corresponding to kilobytes or even megabytes per second of information, but they are not atomically precise tools.

The scaling of operation speed indicates that to embody information in the manufactured product via rapid physical manipulation, it will be necessary to use small actuators. Inkjet printers represent a step in this direction; their print head actuators are a few microns in size, and they can deliver megabytes per second. Furthermore, an inkjet printer can print its weight in ink in about a day. IBM's Millipede, a MEMS-based highly parallel scanning probe microscope array, can modify a substrate rapidly enough to be a serious candidate for computer data storage. Both of these technologies produce only two-dimensional “product,” but inkjet technology has been adapted to form three-dimensional products, and scanning probe arrays have been used for dip-pen nanolithography (DPN). Nanoscale actuators, being smaller, will be able to operate faster and handle higher data rates.

To route a high-rate information stream to multiple actuators, to efficiently handle errors locally, and to interpret efficient data formats, not only actuators but digital logic must be shrunk to the nanoscale. Researchers are working on molecular electronics that can perform digital logic from a wide variety of approaches, including carbon buckytube transistors at IBM2, single atom cobalt-based transistors at Cornell3, HP's recently announced "crossbar,"4 and the rotaxane switches at UCLA5; this work indicates that transistors can be built from individual molecules and that logic circuits can be built from supramolecular structures.

Error sources

A non-zero error rate is inevitable, but the rate can be quite low in well-characterized systems. Wear and manufacturing slop will not be sources of dimensional variation in covalent components. The major source of dimensional variation will be thermal motion, which is ubiquitous and significant in nanoscale systems. (Quantum and Heisenberg uncertainty are typically much smaller effects.) Thermal motion will cause positional variance. For most nanoscale machine components, the effect of thermal motion on position can be estimated from the stiffness of the component. Thermal motion is random, but high energy motions are rare; in general, thermal motion will not provide enough energy to break a single bond, and a single bond provides sufficient stiffness to limit motion to a fraction of a nanometer. This implies that even very small interlocked machine parts, on the scale of a single nanometer, can be designed not to slip past each other due to thermal perturbation.

To resist thermal motion driving a system from a set state to an undesired state, an energy barrier is required. Depending on several factors, a suitable barrier will typically be in the range of 30 to 80 times k_BT (120 to 320 zJ6 at room temperature). This does not mean that systems must spend 120 zJ for each state change; see the section on “Energy requirements.” Note that a particular state will always encompass a range of positions; some designs may tolerate quite large positional variance, as long as the system is not allowed to slip into a state that is functionally different. Energy will be required to “compress” a system into a tightly constrained configuration, but this energy may be recovered if and when the system is allowed to relax (this is equally true for mechanical and entropic springs).

Due to adverse scaling of stiffness with size, operations that require fractional-nanometer precision require careful design to provide adequate stiffness and alignment. Design and analysis indicate that 100-nm-scale machines built of stiff covalent solids will be stiff enough to maintain the position of an articulated component within a fraction of an atomic diameter.

Ionizing radiation is an inescapable source of damage. An ionizing event can disrupt the structure of a molecular machine. A cubic micron volume will have on the order of several percent probability of damage per year unless large amounts of shielding are used. Non-ionizing photons may excite bonds and cause damage, but can be excluded by a fraction of a micron of metal shielding.

Error handling

In a kilogram of nanomachines, no matter how well designed, there will inevitably be a large number (though small percentage) of broken machines. The appropriate method of error handling will be determined by the architecture of the system. This section will consider error handling in several kinds of manufacturing systems; some of these methods will also be useful for various kinds of products.

One approach to scaling up production involves many small independent fabricators, each capable of producing more fabricators or small products. If each fabricator is independent of the others (for example, free-floating and driven by broadcast signals7), then failure of a fabricator can be ignored, since it will only result in the system producing marginally fewer nanoscale products than requested. (This assumes that failed fabricators will not be able to create generations of flawed-but-functioning fabricators, but this is probably a safe assumption given the digital nature of errors.) As long as the error rate of a fabricator is lower than the number of operations required to build another fabricator or product, it will produce a useful percentage of good product even if no error checking at all is implemented during manufacturing. Of course, a percentage of products will also be non-functional, which may require post-manufacture error detection depending on the application.

The other approach to increasing production uses large integrated manufacturing systems. In such a system, failures must be detected. If each machine is responsible for producing its own fraction of a large product, then the product will have a component failure rate at least as high as the percentage of undetected errors in the system that made it. In multi-generational manufacturing, this would not be sustainable. Even if the resulting manufacturing system could function with large parts of itself non-functional or missing, failure to detect and compensate for the errors would result in accumulation of errors from generation to generation. However, this does not require every operation to be checked for error; all that is necessary is that a broken subsystem not be tasked with producing its full share of the product, and that no critical part of the product be omitted.

Any large nanomachine-based product, including integrated manufacturing systems, must expect and cope with a non-zero component failure rate. In a system that is structured hierarchically, this can be accomplished by modest degrees of redundancy on multiple levels. In a system organized this way, errors need not be reported outside the node where they are detected. If a sub-node fails, the node reassigns tasks to its remaining working nodes. If too many sub-nodes fail, the node signals failure to its super-node. If the failure rate of sub-nodes is small, then the chance of multiple sub-nodes failing and causing the failure of a node will be quite a lot smaller; a system with multiple levels of redundancy can have rapidly decreasing probability of system failure even as the size of the system increases.

For example, suppose that product operation depends on 2⁵⁷ (~1.4x10¹⁷) components, and the components are arranged in a hierarchical 8-way tree 19 levels deep with no functional sharing between substages or components (they all need to work). Adding one additional redundant component at the lowest stage, and one additional substage at each of the next three stages (9-for-8 redundancy at each of the four lowest levels), will increase the overall mass by 60%. But if component failure rate is 0.0024 (approximately a ten-year radiation dose for a 200-micron cube), this level of redundancy will ensure that the chance of even a single one of the 2⁴⁵ non-redundant fifth-level substages becoming unavailable is 0.00001.8 Additional design effort will greatly reduce the mass penalty of redundancy, but simple redundancy at multiple levels is a useful starting point.

Space or high-altitude applications face an additional complication. Cosmic rays not only increase the dose of radiation, they also create a different pattern of damage. A cosmic ray is a very heavy charged particle—the nucleus of an atom—moving at very high speed. It does not create randomly spaced points of damage; instead it creates a dense track. Where cosmic rays are present, error handling designs must cope with multiple simultaneous failures in adjacent machinery; this means that any critical functionality must be distributed at several separate points.

Scaling up production: exponential manufacturing

No matter how rapidly a single nanoscale manufacturing system operates, it will not be able to make a gram of product. In order to produce useful quantities of product, vast numbers of machines must be run in parallel. There are several different ways to do this, but all methods involve manufacturing systems that build other manufacturing systems. When the available machinery can double in constant time, throughput increases quite rapidly; only about 60 doublings are required for one 100-nm machine to produce a kilogram of machines.

One approach is for small machines to produce many small products. In this way, the mass of machines increases, but the machine and product size remain at the nanoscale. Large numbers of nanoscale products can be useful as networked computers, as pharmaceuticals, or as components in larger products. Modular robotics may be used to make large products from aggregates of nanoscale robots; proposed architectures include J. Hall's “Utility Fog,”9 T. Toth-Fejel's "Kinematic Cellular Automata Self-Replicating System,"10 and NASA's “Autonomous NanoTechnology Swarm” (ANTS)11. Toth-Fejel's paper "Legos to the Stars" summarizes earlier work.12

Another approach is to build integrated systems containing numerous manufacturing subsystems attached to a framework. This would allow nanoscale building blocks to be joined together, forming a large integrated product. An attractive architecture for a large, advanced, integrated factory is a planar arrangement that produces blocks of approximately micron size from each subsystem, attaching them to a growing product. Scaling analysis indicates that block deposition rate (mass per second, or thickness per second) does not depend on the size of the blocks, since the smaller volume of smaller blocks is compensated by the greater number of producers that can be packed into a plane and the increased operating frequency of each device. A planar architecture is also good for primitive manufacturing systems, since it allows each subsystem to deposit its portion of the product on adjacent sites of a nearby planar substrate; this provides the proper form for a planar manufacturing system to build a duplicate manufacturing system. As more advanced versions of the system are developed, the planar organization can be retained.

Small manufacturing systems require less internal architecture than integrated systems, but may be difficult to interface with external controllers. It would be difficult to supply high-bandwidth information and power efficiently to free-floating machines. Also, although small products can be useful, large integrated products have a much broader range of applications.

Mechanosynthesis

Mechanosynthesis is the use of mechanical systems to control individual molecular reactions with atomic precision in order to build precise structures. The definition covers several different kinds of fabrication operations and types of control. Mechanosynthesis can be performed either in solution with only some of the molecules controlled, or with all potentially reactive molecules controlled (“machine phase” or “vacuum phase” chemistry). Mechanosynthesis can add small molecular fragments to selected positions on a large molecule, add selected monomers to the end of a polymer, or add large molecular building blocks to a larger structure. It can also be used to pull molecules apart or transfer atoms between molecules.

In order to make a reaction happen, reactants must be brought together in the right position and orientation. In some cases an energy barrier must be overcome to make the reaction happen. If the barrier is within a certain range, then thermal motion can supply the energy, and the mechanical system can accelerate the reaction simply by holding the reactants near each other, increasing the effective concentration by several orders of magnitude. If the barrier is too high for simple positioning to work, it can often be lowered by pushing the molecules together. (The conventional form of this, applying hydrostatic pressure to affect reaction rates, is called piezochemistry.) Light can also supply energy to activate molecules and overcome barriers. Light cannot be focused with nanometer precision, and even with near-field techniques some photons will be created which may be absorbed by distant molecules. (Plasmons might be useful to deliver optical energies more precisely.) However, if the mechanosynthesis technique can guarantee that only the target molecules are in a position in which photochemical excitation will cause bonding, then even diffuse light can be used to activate bonding in only the desired locations.

Mechanosynthesis can reduce the rate of unwanted side reactions by preventing the reactants from contacting each other in ways that would allow those reactions to happen. This allows a particular deposition site to be selected from among many chemically similar sites. Engineered heterogeneous products can be built by mechanosynthesis that would be nearly impossible to build by self-assembly or common solution chemistry.

In machine-phase chemistry, the lack of chemically active solvent simplifies computational chemistry simulations. However, it does not necessarily limit the richness of available synthetic reactions. Water, a very complex medium, was thought by some to be necessary for complex chemistry; however, practical experience shows that natural enzymes and antibodies can work as well, if not better, without water—sometimes, without any solvent at all.13 A diverse set of machine-phase reactions has been accomplished using scanning probe microscopes.

Lack of solvent allows higher-energy molecules to be used—for example, radicals that would not be stable in solution. The ability to create radicals in one process and then bring them together in a chosen orientation in a second, separate process should open new territories of chemistry. In particular, it seems well suited to the creation of highly crosslinked materials, such as covalent solids, since the surface can be locally depassivated in preparation for a precise deposition reaction. The use of higher-energy (extremely reactive) molecules can increase reliability of both the actual reaction and simulations of it, because the energy difference between desired and undesired outcomes can be much larger than is common in solution chemistry.

Several kinds of reaction are available. One is the formation of standard covalent bonds. This can be triggered by light, by electric fields or currents, by mechanical pressure14, or simply by holding reactive molecules near each other until thermal energy overcomes the reaction barrier. Weaker bonds, including hydrogen bonds and sulfur bonds, can link molecules large enough to include several bond sites. In solvent, free-floating ions can play a part in the bonding; for example, zinc coordinates tetrahedrally with cysteine and/or histidine amino acids, forming a fairly strong bond; see Fig. 1. In vacuum or moderate-pressure gas, surface forces (also called dispersion forces and van der Waals forces) can hold things together quite tightly—up to 5% of the strength of diamond. Binding by surface forces is not actually a chemical reaction, but surface forces form the weak end of a continuum, and the molecular manufacturing design approach described here can apply to systems based on non-chemical fastening—as long as the parts being fastened are atomically precise, and precisely placed.

Fig. 1. Zinc binding and photochemical binding are proposed for use in primitive molecular manufacturing systems.

For several reasons, simulations of mechanosynthetic reactions may have more predictive value than simulations of ordinary solvated reactions. Mechanosynthetic processes can physically constrain molecules in a way that avoids many unwanted reactions entirely. Applying modest pressure to reactants can significantly alter the energetics of the reaction and thus shift reaction rates and equilibria in desired directions. These advantages hold for both solvated and machine-phase mechanosynthesis. The ability to use extremely reactive species in machine-phase mechanosynthesis allows reactions in which the change in energy is far larger than in solution-phase chemistry. If the difference in energy between desired and undesired states is far greater than the inaccuracy of the program, then computational chemistry tools that must be used with caution for unconstrained solution chemistry may be used with more confidence to evaluate mechanosynthetic reactions.

Energy requirements

The large number of operations necessary to build large objects by manipulation of individual molecules is grounds for concern about the energy budget of such operations. An early target is 100 kWh/kg, which would cost about $10/kg at today's energy rates. More advanced nanofactories that implemented recovery of mechanosynthetic reaction energy might achieve 10 kWh/kg, suitable for a desktop device. This corresponds to about 720 zJ (7.2x10^-17 J) per atom. (Some products, such as nano-structured computer chips, would be worth many millions of dollars per kilogram in today's market. However, the corresponding power densities would make small kilogram-per-hour nanofactories impossible to cool.)

Digital computation can use a lot of energy. An early design for a 32-bit 1 GHz CPU was calculated to use 74,000 zJ per clock cycle. This design was mechanical, but reasonably efficient; it used reversible logic, and split its energy between overcoming friction and erasing bits. (For thermodynamic reasons, clearing a byte of information dissipates about 23 zJ at room temperature: ln(2)k_BT per bit.) This indicates that custom circuits (or even mechanically fixed trajectories) rather than general-purpose computation should be used for low-level control of machines handling small numbers of atoms per operation.

A covalent reaction may dissipate around 500 zJ, although this energy can be recovered if the reactants are held by mechanisms in a sufficiently stiff manner to avoid “snapping” from one position to another.

It is often useful for a subsystem to maintain a certain state until pushed to the next state by another subsystem. This is useful for at least two reasons: it simplifies the control architecture, and it saves the energy that would be required to “compress” a system from an unknown state into a known state. In a macro-scale system, keeping a component in a definite state might be accomplished with a detent or ratchet that imposes an energy barrier to movement. However, the size of the barrier does not scale to the nanoscale; no matter how small the machine, the barrier must be at least 120 zJ to resist thermal motion (at room temperature). Simply pushing past the barrier, without a mechanism to recover the 120 zJ as the system snaps into the new position, would be quite wasteful. An efficient design will attach to a system in a known state, remove the barrier, move the system to the new state, replace the barrier with the system now on the other side, and then release the attachment. The only losses in such a mechanism will be frictional. In Fig. 2, the function of the barrier is fulfilled by the latching pin; the external latch is engaged by the driving pin; the bar actuator moves the bar to the new state after the latching pin is withdrawn; and then the driving pin is removed after the latching pin is re-engaged. No energy is wasted in abrupt “downhill” transitions.

Fig. 2. A schematic of a thermodynamically efficient repositioning system.