## Quantum Dot Based Neuromorphic Architectures

In 1995, Roychowdhury and coworkers proposed a revolutionary new idea for utilizing quantum dots for signal processing and computation.[17,18] Their scheme was not based on logic circuits, so that they did not need the properties necessary to build logic circuits. Instead, they proposed to build a neural network architecture. They also realized that making connections to quantum dots will be a nearly insurmountable challenge because quantum dots are so small that aligning multiple (or for that matter any) contact to them is very difficult. They overcame this problem by proposing a locally interconnected architecture, where every device is connected only to its nearest neighbors. Thus, in a rectangular lattice structure, every device will be connected to at most four nearest neighbors. The connections did not have to be metallic lines (wires) either. They could simply be the resistive and capacitive couplings between neighboring quantum dots that exist whenever the dots are embedded in a semiinsulating medium. For certain applications, the exact values of the resistances and capacitances of these couplings also did not matter so much as long as they were relatively uniform. Therefore, this architecture did not present much of a fabrication challenge at all to self-assembly (in fact, it was partly inspired by advances in self-assembly). We now describe this architecture.

Consider the system shown in Fig. 8. It consists of a two-dimensional periodic array of nanometer-sized metallic islands (or clusters), with nearest neighbor electrical interconnections, self-assembled (and self-aligned) on mesas whose current-voltage characteristics (for vertical transport) have a non-monotonic non-linearity.

aThere are five basic requirements for a logic device. They are listed in the textbook: David A. Hodges and Horace G. Jackson, Analysis and Design of Digital Integrated Circuits, 2nd edition, McGraw-Hill, New York, 1988, Chapter 1, p. 2.

The above system displays a fundamental kind of computational effect based on non-linear cooperative charge interactions between the dots and the underlying non-ohmic substrate. A number of publications'17-201 have shown that this system realizes the content addressable models of associative memory, can exhibit image-processing capability, and can solve combinatorial optimization problems. It is a neuromorphic network inspired by the simple realization that, in any large-scale system, comprising tens of billions of nanoscale devices, there will be inherent randomness. It is easier to exploit that in realizing computational activity through collective computational models, than to strive against it to realize logic. Moreover, this network is massively parallel and fault-tolerant. Even a 100% variation in the size of an individual device is quite tolerable. The relative insensitivity to size variation stems from the fact that the size determines the capacitance of an individual device. A 100% variation in the size of an individual device will result in a similar variation in the capacitance and this does not affect the performance of the circuit very much as a whole because of the "collective'' nature of the computation. Here the collective activities of all devices acting cooperatively matter, rather than the characteristic of a single device. Similar ideas were later proposed by Wu, Shibata, and Amemiya.[21]

We will not discuss the detailed theory of this architecture because that has already been described in Refs.[17-20]. Instead, we will focus on the realization of this system based on our technique of electrochemical self-assembly.

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