Reducing variation in randomized nanoscale circuit connections

A method and apparatus of reducing variations in nanoscale circuit connections. One exemplary embodiment includes: placing a first connector between a first addressing wire and a first nanowire in a partial circuit; and applying bias to the partial circuit so that a second connector is placed between a second addressing wire and a second nanowire. This method of bias connections is repeated for each wire in the full circuit. Thus, bias is used to influence the positioning of connectors on additional wires (if any) in the full circuit.

TECHNICAL FIELD

Embodiments of the present invention relate generally to the field of circuits. More particularly, embodiments of the present invention permit reducing variation in randomized nanoscale circuit connections.

BACKGROUND

Nanoscale electronic circuits offer the possibility of high density, high speed, and low cost, compared to current devices. However, a major difficulty in nanoscale circuits is in establishing communication circuitry for input and output. Using multiplexers and demultiplexers as the interfacial circuits can address this problem. For example,FIG. 1shows a basic multiplexer circuit100, in which eight nanowires (marked as1-8) can be addressed by three addressing wires (marked as A, B, and C). The dot at each cross point is a molecule switch such as a two-way AND element, which can be a resistor, diode, or a transistor. With the multiplexer100shown inFIG. 1, only one of the nanowires will be addressed by each combination of signals on A, B, and C (e.g., 1, 1, 0 for A, B, C, respectively, will address the nanowire7). In general, such multiplexer/demultiplexer circuits allow n wires to address 2nnanowires, which can establish efficient interfacial circuitry for nanoscale circuits.

Forming multiplexers/demultiplexers (or other circuits) requires the ability to selectively connect or disconnect nanowires and addressing wires at each cross point. Unfortunately, fabricating this precise pattern of logic elements at the intersections is very difficult at the nanometer scale.

One approach combines lithographic patterning for the more significant bits of the addresses with random connections for the less significant bits, as disclosed in commonly-assigned U.S. Pat. No. 6,256,767, by Kuekes et al., issued Jul. 3, 2001, entitled “DEMULTIPLEXER FOR A MOLECULAR WIRE CROSSBAR NETWORK (MWCN DEMUX)”. U.S. Pat. No. 6,256,767 is fully incorporated herein by reference. InFIG. 1, addressing wire A specifies the most significant bit of the address and wire C specifies the least significant. As shown inFIG. 1, the more significant bits of the address involve large groups of adjacent nanowires with the same connections.

When sufficiently large, the groups can be created by patterns specified by conventional techniques such as photolithography. The less significant bits, on the other hand, require precise connections alternating on a fine scale, beyond current capabilities to precisely fabricate. The previous proposals address this problem by replacing precise connections with methods that make connections randomly, i.e., without precise control of their locations. This randomness precludes creating multiplexer circuits with the precise desired pattern of connections (e.g., as shown in FIG.1). Nevertheless, the previous proposals show that adding a certain number of extra addressing wires ensures a high probability of unique addresses for the nanowires. In other words, the added redundancies may provide a high probability of correct functionality for the circuit. While these extra wires enable constructing a reliable interface circuit, they also disadvantageously increase the overall size of the circuit.

Therefore, current technologies are limited in their capabilities and suffer from at least the above constraints.

SUMMARY OF EMBODIMENTS OF THE INVENTION

In one embodiment of the invention, a method of reducing variations in nanoscale circuit connections, includes: placing a first connector between a first addressing wire and a first nanowire in a partial circuit; and applying bias to the partial circuit so that a second connector is placed between a second addressing wire and a second nanowire. This method of reducing variation by use of bias is repeated for each wire in the full circuit. Thus, bias is used to influence the positioning of connectors on additional wires (if any) in the full circuit.

In another embodiment, a nanoscale circuit, includes: a first addressing wire; a first nanowire; a first connector placed between the first addressing wire and a first nanowire in a partial circuit in a random manner; a second addressing wire; a second nanowire; and a second connector placed between the second addressing wire and a second nanowire by application of bias to the partial circuit.

In yet another embodiment, an apparatus for reducing variations in nanoscale circuit connections, includes: means for placing a first connector between a first addressing wire and a first nanowire in a partial circuit; and means for applying bias to the partial circuit so that a second connector is placed between a second addressing wire and a second nanowire.

In yet another embodiment, a method of reducing variations in nanoscale circuit connections, includes:placing a first connector between a first addressing wire and a first nanowire in a partial circuit; andapplying bias to the partial circuit to influence a positioning of a second connector on a second nanowire, the application of bias permitting a reduction in variance the number of connectors in each nanowire.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Embodiments of the invention advantageously reduce the number of additional addressing wires required to ensure reliable circuits from random connections. Arranging for some correlation among the random connections reduces the variation in the number of connections on different nanowires. This allows reliable addressing with fewer additional addressing wires, thereby reducing overall circuit size. In particular, if the connections are made randomly but in such a way so as to ensure the same number of connections to each nanowire, the number of additional addressing wires is reduced by about a factor of 2.5 (as discussed below).

Referring now toFIG. 2, there is shown a block diagram of a method of creating random connections with correlated placement, in accordance with an embodiment of the invention. Assume that there are two nanowires210and215and two addressing wires220and225. At this point, assume that a random connection have been made for the addressing wire (A)220, giving the single connection (“molecule”)205between the addressing wire220and the nanowire210. The molecule205is commonly known as a switch molecule and is sandwiched at the intersection or junction of the two wires210and220. Note that various examples of devices may be used as a molecule205. Actual circuits may turn out to use somewhat different devices. As an example and as described in the above referenced U.S. Pat. No. 6,256,767 by Kuekes et al., when an appropriate voltage is applied across the wires, the switch molecules are either oxidized or reduced. When a molecule is oxidized (reduced), then a second species is reduced (oxidized) so that charge is balanced. These two species are then called a redox pair. One example of this device would be for one molecule to be reduced, and then a second molecule (the other half of the redox pair) is oxidized. In another example, a molecule is reduced, and one of the wires is oxidized. In a third example, a molecule is oxidized, and one of the wires is reduced. In a fourth example, one wire is oxidized, and an oxide associated with the other wire is reduced. In all cases, oxidation or reduction will affect the tunneling distance or the tunneling barrier height between the two wires, thus exponentially altering the rate of charge transport across the wire junction and serving as the basis for a switch.

The above molecules permit electronic devices to be formed with a size on the order of tens of nanometers to a few nanometers by simply making contact between two wires. By choosing the molecules which form a doping layer on the wires (modulation doping), it is possible to build devices with a wide variety of specifically desired electrical properties. The possibility of reversibly or even irreversibly changing the properties of the device via an electrochemical reaction with a large hysteresis loop in its I-V characteristic enables devices to be altered after they are built and may provide new and useful functions.

If completely random connections are made to the addressing wire (B)225, forming each connection with the probability ½, the possible resulting connections are shown as possibilities (configurations) I to IV inFIG. 3. Aconfiguration may be part of a full circuit, or in some cases, may be the full circuit itself. Each of these possibilities inFIG. 3has probability ¼. However, only configuration III has an equal number of connections (i.e., one) for both nanowires210and215. In particular, a molecule305has been formed as connection between wires215and225in configuration III. If the addressing wires220and225were the only two addressing wires in a full circuit, then configuration III would also be the only configuration giving unique addresses for both wires.

In contrast, configurations I, II, and IV do not have an equal number of connections for both nanowires210and215. For example, in configuration I, the molecule210is formed as a connection for nanowire205, while no molecule is formed as a connection for nanowire215. In configuration II, the molecules205and305are formed as connections for nanowire210, while no molecule is formed as a connection for nanowire215. In configuration IV, molecules205and305are formed as connections for nanowire210, while only one molecule (molecule310) is formed as a connection for nanowire215.

To improve the situation where an equal number of connections are highly likely achieved for each nanowire, an embodiment of the invention provides a method of using an interaction among the partially connected wires and new connections to preferentially place new connections on nanowires with relatively few connections (or no connections) from previously connected addressing wires. For instance, after completing the connections (e.g.,205) to wire (A)220, as shown inFIG. 4, introducing a voltage “V” on wire (A)220would produce a current410in nanowire210(because nanowire210is connected to wire220), but would not produce a current in nanowire215(because nanowire215is not connected to wire220). The function above is valid, provided that the ends of the nanowires210and215are grounded. It is also understood that the direction of current410depends on the potential of voltage V.

Alternatively, an embodiment of the invention provides a method where the existing connections (e.g.,205) could be used to place charge on the nanowires210and215. Conversely, if an end of the addressing wire (A)220is grounded and voltage applied to all the nanowires (such as nanowires210and215), a current415would flow in those wires connected to wire (A)220, while those wires (e.g., nanowire215) not connected to wire (A)220would be charged.

Thus, with suitable chemical properties of the molecule205, the particular bias in the wires will cause a high probability that a second molecule305will be placed as a connection between wire (B)225and nanowire215. The wires will be biased based upon the current flowing through or charges on (or lack of current or charges) particular ones of nanowires210and215and/or wires220and225. A second molecule305will be attracted to (or repelled by) a wire with current flow or with charge, depending on the pre-selected chemical properties of the particular molecule305.

In previous approaches, connections were made by adding enough material to make approximately half of the possible connections, but with no control over which particular connections are made. In contrast, an embodiment of the invention provides a method that achieves the following result. If new potential connectors (e.g., molecule305) for wire (B)225are repelled by these currents or charges on connected wires (such nanowire210and wire220in the example ofFIG. 4) and/or attracted to those currents (or lack of current) of unconnected wires (such as nanowire215and wire225in the example of FIG.4), then the new potential connectors will preferentially connect to the wire with fewer connections (i.e., nanowire215in the example of FIG.4). This result will raise the probability of obtaining the desirable configuration III as shown in FIG.3. The new potential connectors will be attracted to, for example, wires with no currents or charges because the connectors themselves may be selected to have an opposite charge or are polarizable.

More generally, an embodiment of the invention provides a method that affects some property of the nanowires (e.g., nanowires210and215) based on how many connections they already have from the random connections placed on previous addressing wires. If this property, in turn, makes new connections for subsequent addressing wires more likely to occur on nanowires with few connections, the resulting pattern of connections will be more uniform than if all connections are made independently at random. Ideally, the method would make it possible for each nanowire to receive the same number of connections (molecules). More realistically, in practice the method can be expected to substantially reduce, but not eliminate, the variation in number of connections (molecules) between nanowires, and this substantial reduction in variation advantageously reduces the number of additional addressing wires for a circuit, as discussed below.

The nanowires with especially few connections or many connections cause the most difficulty for forming unique addresses. As an extreme example, if any wire has no connections at all, then the wire is not addressable no matter what connections are made for other wires. Conversely, if a wire is connected to all the addressing wires, then addressing the wire will also address all other wires with one or more connections. Thus it is particularly useful to reduce the likelihood of these extreme cases or events. Even a relatively small bias in attracting new connections to wires with few existing connections, or repelling the new connections from wires with especially many existing connections, will be particularly helpful in avoiding the above-mentioned extreme cases.

The steps described in embodiments of the above methods may be performed by use of circuit fabrication equipment, along with testing equipment.

Reduction in Variation Reduces Number of Additional Required Addressing Wires

This section describes the benefit from reducing the above-mentioned variation, namely reducing the number of additional addressing wires to ensure unique addresses with high probability. In particular, if the connections are made randomly but in such a way so as to ensure the same number of connections to each nanowire, the number of additional addressing wires is reduced by about a factor of 2.5.

Reference is made to the graph inFIG. 5to illustrate the requirements for forming unique addresses with random connections (molecules) by evaluating randomly generated samples. Specifically, to evaluate the ability to fully address N data wires (i.e., nanowires in this context) with M addressing wires, we generate a connectivity matrix in which each element is independently selected to be 1 with a specified probability p. We then compare the addresses of each pair of data wires (i.e., columns in the connectivity matrix) to see whether using one of the addresses would select both wires. If so, the address is not unique. Performing this check on each pair determines the number of uniquely addressable data wires for a particular connectivity matrix.

With a large number of data wires, the probability for unique addresses exhibits a sharp threshold with relatively few addressing wires. To see this, for p=0.5,FIG. 5shows the probability for all data lines to have unique addresses as a function of M/log2(N), for N=16, 32 and 64. In case the circuit has more wires than the numbers used in this illustration, these correspond to using random connections for the least significant 4, 5 or 6 bits of the addresses, respectively.

With this scaling, the thresholds overlap near 5, as shown by point505. Thus the threshold occurs for M≈5log2N.

When connections are completely random, the combinatorial expression for the probability for unique addresses is complicated. Nevertheless, we can estimate the location of the threshold by assuming each pair of wires can be considered independently. Consider the connections on two data wires, i and j. For each of these data wires to be separately addressable, there must be at least one addressing wire connecting to wire i but not wire j, and at least one other addressing wire with the opposite connections. The probability that an addressing wire connects to wire i but not j is α=p(1−p), and similarly for connecting to j but not i. Since the connections for each wire are made independently, for M addressing wires, the probability none connects to i but not j is (1−α)M. Similarly, for having none connecting to j but not i, the same expression (1−α)M. Finally, the probability for neither type of connection is (1−2α)M. Thus the probability this pair, at least, is correctly connected is Ppair=1−2(1−α)M+(1−2α)M.

For all wires to be uniquely addressable, every pair must be correctly connected. Under the approximation in which each pair's correctness is assumed to be independent of the others, the overall probability for unique addresses for all data wires is Punique=(Ppair)(N2). For 0<p<1, 0<α≦¼ with the maximum at p=½. To identify the threshold under this approximation, we consider the behavior when M and N are large. In this case,Punique≈exp(-(N2)⁢2⁢(1-α)M).
The threshold Punique=e−1then corresponds to N2(1−α)M≈1 orM≈-2⁢⁢ln⁡(2)ln⁡(1-α)⁢log2⁡(N).
The coefficient is smallest when p=½, in which case it becomesM≈-2⁢⁢ln⁡(2)ln⁡(3/4)⁢log2⁡(N)≈4.8⁢⁢log2⁡(N).
This expression is quite close to the observed threshold based on random samples, so the independence assumption is in fact fairly accurate.

To illustrate the benefit of reducing the variation in number of connections on the nanowires, consider the situation in which each data wire is connected to exactly h of the M addressing wires, but the choice of these connections is random. In this case, there areT=(Mh)
ways to pick the connections for a wire, each of which is equally likely. With N data wires, the addresses can be selected in TNways, but they are all unique in only T(T−1) . . . (T−N+1) ways. Thus the probability the addresses are unique is the ratio of these quantities:Punique=(1-1T)⁢⁢⋯⁢⁢(1-N-1T).
For a given number of wires N, the larger the number of choices T, the higher the probability all the addresses are unique. Since the binomial coefficients are largest in the middle of their range, T is maximum when h=M/2, i.e., when half the connections are made. When the number of possible addresses is much larger than the number of data wires (T>>N), Punique≈e−N2/(2T). Defining the threshold location as Punique≈e−1then corresponds toT=12⁢N2.
Stirling's approximation for the binomial coefficient gives T growing as T≈eM H(h/M)where H(x)=−x1n(x)−(1−x)1n(1−x) is the entropy function. Thus the threshold condition becomesM≈2H⁡(h/M)⁢ln⁡(N).
The smallest threshold, corresponding to the largest value of the entropy, is when h=M/2, givingM≈2ln⁡(2)⁢ln⁡(N)=2⁢⁢log2⁢N.
In other words, when the number of connectors on each data wire is uniform, then the threshold is at approximately 2, as shown inFIG. 5, and this indicates that fewer addressing wires are required to give a high probability for correct addressing for the full circuit.

This discussion not only shows why the number of addressing wires required to reach the threshold grows only logarithmically, but also indicates the difference between two methods of producing random connections: 1) random connections constrained to have exactly the same number of connections per data wire, and 2) random connections made completely independently, i.e., with no constraint. Specifically, the thresholds for these cases is at 2 log2(N) and about 5 log2(N), respectively, as shown in FIG.5. Thus, even though both methods give the same number of connections on average, the variation in the number of connections in the second case increases the likelihood of duplicate addresses. This difference shows the potential for reducing the number of addressing wires by reducing the variation in number of connections made to each wire.

FIG. 6is a method600of reducing variation in randomized nanoscale circuit connections, in accordance with an embodiment of the invention. A connector (molecule) is placed (605) between a first nanowire and a first addressing wire in a partial circuit. A bias is then provided (610) in the partial circuit so that a second connector (molecule) is placed between a second nanowire and a second addressing wire, so that each nanowire in the partial circuit has an equal number of connectors or the number of connectors in each nanowire is reduced in variance. Various methods of providing the bias in the partial circuit have been previously described above. The action (605) and action (610) above may be repeated (615) for other partial circuits (if any) that will form the full circuit, so that the number of connectors in each nanowire in the full circuit is reduced in variance.

When a first connector is placed in another partial circuit that will form the full circuit (i.e., the connectors have already been placed in the first partial circuit that will form the full circuit), the first connector will also be influenced by the bias in the first part of the circuit. Thus, only the very first connector in the full circuit is placed randomly.

For purposes of describing an embodiment of the invention, action (610) inFIG. 6illustrates the ideal case where the bias may permit each nanowire to have an equal number of connectors (as discussed above). However, in practice, typically the bias may only reduce the variation in the number of connectors for each nanowire.

Application to Other Circuits

Sharp statistical thresholds give reliability from random connections. The precise location of the thresholds, and hence the extra components required to achieve reliability, depends on the breadth of the distribution in individual circuit composition. Reducing variance can thus reduce circuit size. On the other hand, introducing correlations may make the fabrication process for the individual components more complicated than using uniform random choices.

It is further noted that the above-mentioned methods for reducing variance, in order to reduce the number of wires, may apply to other types of circuits besides multiplexers and demultiplexers.

Reference throughout this specification to “one embodiment”, “an embodiment”, or “a specific embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrases “in one embodiment”, “in an embodiment”, or “in a specific embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

Other variations and modifications of the above-described embodiments and methods are possible in light of the foregoing teaching. Further, at least some of the components of an embodiment of the invention may be implemented by using a programmed general purpose digital computer, by using application specific integrated circuits, programmable logic devices, or field programmable gate arrays, or by using a network of interconnected components and circuits. Connections may be wired, wireless, by modem, and the like.

It is also within the scope of the present invention to implement a program or code that can be stored in a machine-readable medium to permit a computer to perform any of the methods described above.

Additionally, the signal arrows in the drawings/Figures are considered as exemplary and are not limiting, unless otherwise specifically noted. Furthermore, the term “or” as used in this disclosure is generally intended to mean “and/or” unless otherwise indicated. Combinations of components or steps will also be considered as being noted, where terminology is foreseen as rendering the ability to separate or combine is unclear.