Nanocell Logic Gates for Molecular Computing

Nanotecnologie 1 Saverio Minutoli and Paolo Spiga

Nanocell Logic Gates for Molecular Computing

J. M. Tour, W. L. Van Zandt,

C. P. Husband, S. M. Husband, L. S. Wilson,

P. D. Franzon and D. P. NackashiIEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 1, NO. 2, pp. 100-109, JUNE 2002


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Molecular electronics

Molecular electronics seeks to build electrical devices to implement computation using individual or small collections of molecules that are approximately one million times smaller in area than their present solid state counterparts.


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•Goals: reducing device size and fabrication costs

•Requirements: molecular switches and scaled interconnections

•Challenges: placement and interconnection (bottom-up vs. top-down approach)


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Potential advantages of molecular electronic systems could be:

• reducing the complexity and cost of current integrated circuit fabrication technologies;

• reducing heat generation by using only a few electrons per bit of information;

• providing a route to meet the ever-continuing demand for miniaturization.


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A scaled interconnect technology is necessary for:

• building logic blocks and discrete device components, analogously to VLSI architectures;

• selective connection to mesoscopically defined input-output.


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Molecular electronics: NANOCELL

The nanocell approach described here, differently from other solutions, is not dependent on placing molecules in precise orientations or locations, but it needs a programming activity in the postfabrication to achieve the desired design.


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A nanocell is a two-dimensional (2-D) network of self-assembled metallic particles connected by molecules that show reprogrammable (can be turned ON or OFF) negative differential resistance (NDR).


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Unlike typical chip fabrication but similar in some respects to an FPGA, the nanocell is not constructed as a specific logic gate and the internal topology is, for the most part, disordered. Logic is created in the nanocell by training its postfabrication.


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Even if this approach is only a few percent efficient in the use of the nanocell, very high logic densities will be possible. Moreover, the nanocell has the potential to be reprogrammed throughout a computational process via changes in the ON and OFF states of the molecules (molecular switches), thereby creating a real-time dynamic reconfigurable hard-wired logic.


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Molecular electronics:from NANOCELL to computer

The central processing unit of the computer would be comprised of arrays of nanocells wherein each nanocell would have the functionality of many transistors working in concert.


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Pure hierarchical structure in a regular array of nanocells or underlying CMOS programming?

• a few nanocells, once programmed, should be capable of programming their neighboring nanocells;

or• arrays could be programmed one nanocell at a time

via an underlying CMOS platform.


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Objects:

• search of a nanocell programming algorithm to create functionality from disorder

• defect, fault-tolerance and performance analysis by SPICE simulations


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NANOCELL

Example of aself-assembled nanocell

with I/O leads

(gray cell area 1m²)


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NANOCELL

This cell has been obtained depositing a 2-D array of metal nanoparticles on an oxide surface; a molecular self-assembled monolayer coating each nanoparticle would control the spacing between nanoparticles.


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NANOCELL:

molecular switches

Molecular switches are added to create barriers around each nanoparticle into the inert monolayer and to inter-link in a controllable way adjacent nanoparticles.


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NANOCELL:molecular switches

• There could be multiple switches between pairs of nanoparticles.

• Each molecular switch could be set into an ON state or an OFF state.


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NANOCELL: nanoparticles

• Nanoparticle diameter 60 nm

• Nanoparticle spacing 3 nm• Regular grid placement• 200 - 250 nanoparticles in a

single nanocell


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NANOCELL:nanoparticles and molecular switches

• Nanoparticle placement according to a regular grid is not necessary, but it lets us to:

determine the possible connections within the nanocell;

estimate the number of switches with the proper orientation between adjacent nanoparticles.


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NANOCELL

Once the physical topology of the self-assembly is formed in the nanocell, it remains static; the only changeable behavior is in the molecular switch states.


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NANOCELL

I/O leads are interchangeable: only in the programming phase designer reveals their own identity, relatively to the requested function for the nanocell.


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NANOCELL

Enormous space savings could be attained since a nanocell could possess the functionality of numerous transistors working in concert to produce a specified logic function


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NANOCELL

We can accept the use of a CMOS gain transistor at the output of a nanocell, without wasting the area reduction compared to a CMOS realization. We can suppose to build internal gain elements based upon nanoparticles and molecular switches.


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MOLECULAR SWITCH

A molecular switch is a molecule terminated on both its end with molecular alligator clips, such as thiols, and inserted between adjacent nanoparticles via self-assembly with molecule-metal chemical bonding to establish electrical contacts.


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MOLECULAR SWITCH

Each molecular switch can be reversibly turned ON or OFF in the postfabrication, using voltage pulses at nearby lithographically defined contact pads in the periphery of the cell.


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MOLECULAR SWITCH

The functionality of the entire nanocell depends largely on the I(V) characteristics of molecular switches; in particular it is interesting the use of a molecular switch with a Negative Differential Resistance in order to build logic devices that exhibit negating functionality such as nand or xor.


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MOLECULAR SWITCH

Examples of I(V) responses with NDR


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MOLECULAR SWITCH

A number of devices with the previous I(V) response have been tested for over one year with no signs of degradation over nearly 109 switching events.


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NANOCELL programming

The object in programming or training a nanocell is to take a random nanocell with a fixed topology and turn its switches ON and OFF until it functions as a target logic device.


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NANOCELL programming:

OMNISCIENCE

Location and state of each switch and connections within the nanocell are known.


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OMNIPOTENCE

The search algorithm knows the location of each molecular switch and has precise and selective access to reversibly set its ON or OFF state (omnipotence implies omniscience).


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MORTAL SWITCHING

The algorithm does not know the connections within the nanocell or locations of the switches and switching is limited to voltage pulses applied to the I/O pins.


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NANOCELL programming:MORTAL SWITCHING

Nanocell is considered as a black box.

Programming has to find:• switch states such that the given nanocell functions

as the target logic device;• a series of voltage pulses (applied to the I/O pins)

that give rise to these desired switch states.


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NANOCELL programming:MORTAL SWITCHING

• Given a certain density of nanoparticles and molecular switches, can any random nanocell be trained as some target logic device?

• Which are the switch states where a nanocells works as a target logic device?

• How have we got to build the training for a nanocell using voltage pulses at the I/O pins?


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NANOCELL programming:nanocell modeling

• A nanocell is generated as a hexagonal grid of metallic particles with distributed molecular switch.

• To train the nanocell, we have to evaluate the output current resulting from the voltage traces applied to input.

• In the following simulations individual molecules have been modeled as nonlinear resistors.


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NANOCELL programming:nanocell search space

• Programming a nanocell, we have to solve a combinatorial optimization problem whose search space is the set of all possible switch states in the cell; in particular we have to find the minimization of a function evaluating nanocell behaviour.

• Here a Genetic Algorithm is used to search the solution space for a given nanocell.


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NANOCELL programming:nanocell search space

For an actual nanocell of 1m² with 250-1000 nanoparticles and 750-10000 molecular switches, the search space is minimally 2750 (the number of elemental particles in the universe is estimated at 2300).


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Genetic algorithms

Genetic algorithms work by taking a population of individuals, represented as strings of “1s” and “0s” (chromosomes) quantifying their fitness, then recombining them to generate a new population of children.


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Genetic algorithms

Usually the first generation is randomly created and then three operators are used to produce each subsequent generation:

•selection•crossover•mutation


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Genetic algorithms

•Among the individuals of each generation the two most fit are chosen to reproduce the next.

•Crossover and mutation of bits representing the chromosome preserve the main feature of good individuals without leaving unexplored far regions in the solution space.


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Training nanocells with a genetic algorithm

•In order to find configurations that perform the desired logic function, some pins of the nanocell are set to input or output.

•The nanocell is treated as a voltage-in current-out device, so VIH, VIL, IOH and IOL have to be defined.


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•Using VIH, VIL, IOH and IOL values we can build a function f evaluating the fitness of the nanocell.

• In the following simulations the condition f=0 assures that nanocell works properly to achieve the desired logic function.


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•It is quite important to choose a good function evaluating the performance of the nanocell.

•Fitness expression f is not independent of the desired function for the nanocell; every contribution to f must be weighed to assure convergence for solutions.


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GA training results : inverter

Example of nanocell performing INVERTER


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GA training results: inverter

• Twelve nanocells were randomly generated and all were successfully trained as inverters.

• It took an average of four generation to train each inverter (with 25 individuals for each generation).

• Final result: pin A is set to input and pin 1 is set to output.


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GA training results: nand gate

Example of nanocell performing NAND gate


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GA training results: nand gate

• Twelve nanocells were randomly generated and all were successfully trained and tested as robust nands.

• On average it took about nine generations for each nand to converge.

• A configuration with adjacent I/O pins was hunted.

• Final result: pins A and B are set to input and pin 1 is set to output.


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GA training results: full-adder

Example of nanocell performing 1-bit adder


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GA training results: full-adder

• Full-adder has been trained on a nanocell with 70 nanoparticles and 1000 molecular switches.

• Final results:pins A, B and C are set to input and

pins 1 and 2 are set to output;a nanocell can be trained as a complex

logic device with multiple outputs.


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GA training results

• The simulation time depends primarily on the number of molecular switches in the nanocell.

• Because of the vast solution space, in lucky events we can find functioning devices in the initial random population.

• A test of robustness is opportune to value nanocell properties and performance.


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Adjunctive GA training results for nands

• Nands are particularly attractive since they constitute a functionally complete logic set: any logic function could be created from nand sets.

• Simulation has been run to exhaustively evaluate every possible combination of switch states for 50 small nanocells (516 switches 25216 switch state combinations.


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• In particular the score of every possible set of switch states for a cell with 14 molecular switches has been evaluated, using a Gray-code approach:

in the 50 test nanocells, 3%–19% of the switch states functioned as nand.


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These results indicate that a nanocell, here trained as a nand, is defect tolerant because the performance of the logic gate does not depend on a single set of switch states.

Fault tolerance is guaranteed by the presence of multiple switches between each pair of nanoparticles (every switch oriented in one direction will switch state simultaneously.)


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Results for a nanocell trained as nand gate; 13%

of the possible switch states functioned as a

nand.


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GA training results

There are two important problems to solve about the possible success of nanocells for molecular computing:

ON to OFF ratio; threshold definition (VIH, VIL, IOH and IOL values).


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GA training results

ON to OFF ratio depends on length of molecular connections.

Threshold values change from a nanocell to another.It is necessary to find values that allow multiple

internal interconnections to build complex logic device and it would be a success to be able to control them (for outward interface CMOS transistors can be used).


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GA training results:

independent logics on the same nanocell

Example of nanocell containing 4 nand gates


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multiple independent nands

• This device has been trained on a nanocell with 900 nanoparticles and 9000 molecular switches, with multiple switches between adjacent nanoparticles.

• Final result: pins A and B, C and D, E and F, G and H are set to input and pins 1, 2, 3, 4 are the respective output.


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multiple independent logics

GA trials and exhaustive tests indicates that to train a nanocell it is simply necessary to have enough molecular switches in the ON state near the input and output pins (switches in the internal area are in the OFF state to isolate distinct devices).


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multiple independent logics

• A single nanocell could be trained as several independent gates.

• Inside a single device the number of ON molecules between each input and the relative outputs should be approximately the same.


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Summarizing …

The use of nanocells to build logic devices allows enormous saving of occupied area and power consumption and dissipation; at the same time it enables power voltage lowering.

Each nanocell could be reconfigured “on-the-fly”. Compile time (inexpensive) is preferred to

manifacturing precision.


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Summarizing …

This technology allows reduced fabrication costs for a relatively-simple fabrication process with high defect tolerance; device interfacing could be problematic.

It is impossible to re-use the results of other previous training process because of the intrinsically random (without strict topological constraints) fabrication of nanocells.


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Summarizing …

Different threshold values for distinct developed devices make interconnection among nanocells critical.

Interconnection difficulties suggest that complex logical function should be entirely realized by training a single nanocell and preparing at the most an output gain conventional stage; however an increase in the complexity of the sought logic function involves a rise in the time of convergence to solution.


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Expectations

• In the near future CMOS technology could not support the fast trend of Moore’s Law.

• The rapid convergence to solutions on small nanocells leave researchers encouraged with regard to achieve even better results.


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CHALLENGES

• The same nanocell could be used both for memory and logic as required.

• Different Spice model and various types of molecular switches could be employed.

• Other interesting search, optimization and classification algorithms are theoretically available for training nanocell as a black box.

Nanocell Logic Gates for Molecular Computing

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