## The Concept of Superdot for Image Processing Applications

The pitch of the 2-D quantum dot array (dot diameter plus interdot separation) in oxalic acid anodized templates is about 70-80 nm. Considering that the edge of a pixel in an image should be perhaps 10 times the wavelength of light (we will assume light of wavelength 550 nm which is in the middle of the visible range), therefore the edge of a pixel is 5500/70 = 80 times larger than the pitch of the quantum dot array. Therefore, approximately 80 x 80 = 6400 dots will represent a pixel. Thus, we will assume that a dot cluster of about 6400 dots can be approximated as an equivalent "superdot,'' which will act as a single node interacting with the light wave in image-processing applications. Hence, its dynamical behavior can be modeled by treating it as a single dot if the circuit parameter values are modified accordingly. This means that the superdot-to-substrate capacitance is 6400 times the single dot capacitance, i.e., 6400 x 0.5 = 3.2 fF, the intersuper-dot resistance is 80 times smaller than the interdot resistance (because the edge of the superdot contains 80 single dots), i.e., 640/80 = 8MO, and the peak current for a superdot is 6400 x 15 pA = 0.1 mA. The peak-to-valley ratio can be improved by annealing the structures at some optimum temperature to promote uniform grain growth. This requires a systematic study, which is reserved for future work. It stands to reason that the peak to valley ratio can be improved to at least 10:1. One parameter that we have not been able to measure is the interdot capacitance. Therefore, we will estimate it assuming a parallel-plate geometry for simplicity. The relative dielectric constant of alumina is roughly 4; therefore, the interdot capacitance is 5 aF if the anodization is carried out in oxalic acid. Here we have assumed that the quantum dot is 50 nm wide for oxalic acid anodization and 50 nm thick (to electrodeposit 50 nm of metals within the pores takes only a few seconds of electrodeposition). Based on this, the inter-superdot capacitance is 4fF for oxalic acid anodization. The circuit parameters for the super-dot are given in Table 1.

Circuit theorists have simulated the system architecture described here for image-processing applications using the circuit parameter values of Table 1.[25] They found that the simple self-assembled architecture, in its most primitive form, can perform image-processing tasks. The natural dynamics of the system result in a response similar to edge detection. A preprocessing of input images may be necessary to handle more specific tasks. The response time of the circuits is few tens of nanoseconds. Together with the immense processing density, this makes the quantum dot array a fast and high-resolution image processor candidate for several applications.

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