Description of works performed in 2017 on the project of the RSF 16-19-00135

In the course of research during 2017 we have studied theoretically and experimentally new synchronization effects of oscillators including memristors and specific features of electrical switching for planar and sandwich switches at scaling. We have proposed a type of thermal coupling that is alternative to electrical coupling and is promising for 3D oscillator networks integration and all-to-all coupling. We have performed research of synchronization effect on subharmonics to increase classification capacity of an oscillator system and pattern recognition as well as long-distance synchronization. 
The described findings are mostly of a universal character and may be used in other switching structures including the ones based on semiconducting components that are mass produced. 
1. We fabricated planar switching structures with interelectrode spacing a from 500 to 3000 nm using electron and laser lithography with magnetron sputtering. We found out experimentally that threshold currents and voltages, time of switch-on and off, and threshold  power decreased with the decrease  of a value. Generalized dependences of threshold characteristics on switching area scale and film features were revealed using numerical modeling. 
Evaluation of maximal oscillation frequencies seems to be the most interesting thing so we simulated the operation of a switch included into the oscillator scheme. Evaluation of oscillator self-frequency F0 at specific capacity (C=10 nF) shows that F0 falls insignificantly when the dimensions of a switching structure decrease despite the reduction of switching time characteristics. Moreover, with the decrease of а it is possible to decrease minimal capacity at which oscillations still exist. Thus, when a~100 nm, maximum oscillation frequency may reach F0~20 MHz and F0~300 MHz in some cases. 
We have shown that sandwich structures are easy to use when studying the physics of single nanostructures switching, for instance, the structures based on amorphous anode film VO2 are good model objects. Therefore we have developed a stand including an atomic-force microscope SMM-2000 to obtain topographical maps and capacity distribution map for the studied surface before and after electrical formation (in situ). 
We used the stand to study the process of electrical formation in a vanadium oxide film ~50 nm thick. We showed that after electrical formation a modified area with increased conductivity was formed; this area corresponded to the formed channel of ~500 nm in diameter that in its turn consisted of nanochannels of 10-100 nm in diameter. 
To conclude, it is preferable to use planar structures at this stage because sandwich technology lacks channel electrical formation. Nevertheless, amorphous VO2 sandwich structures are promising in developing 3D technology of elements integration and miniaturization. 
2. It is shown that there are some possibilities to use memristors of both types in oscillation circuits; however, transition between states for an unipolar resistive memory requires more complex schemes that include a current controlled stopper. For a bipolar memory the transition scheme is much simpler as it is possible to create alternative impulses of positive and negative polarity on certain branches of an oscillation circuit. 
It is shown that bipolar memory displays a multistability character when low resistance state may vary in a wide range. It is appropriate to speak about a quasi-stable state because cell resistance depends not only on the value of applied voltage but on the time as well. Such behavior stems from field control of oxygen vacancies concentration in the interelectrode space. At positive polarity their concentration increases; when this happens back diffusion is observed eventually resulting in recovery of resistance equilibrium values. 
Two-electrode Ti, Ta, Nb, V oxide-based MOS (MOM) sandwich structures were formed using reactive magnetron sputtering and anodic oxidation. A bipolar memory was obtained without preliminary formation in most cases which is a definite advantage because formation leads to the increase of switch-on current and multistability suppression. . 
Niobium and vanadium anodic amorphous films seem to be good candidates to perform the role of a multistable bipolar memory but for one disadvantage – liquid electrolyte usage. Therefore it must be concluded that a multistable bipolar memory on the basis of the mentioned oxides may become the element for modeling a synaptic plasticity of a neural network. 
3.  We have developed a schematic model of a bipolar memory that resembled quasi-stable behavior of real cells in its I-V characteristics dynamics. Here we used an analogy of vacancies concentration to the capacitor voltage that depended not only on the input voltage amplitude but on the time as well because of resistive charging and discharging. 
A model cell (memristor) was used in schemes of single and double coupled circuits. In the first scheme we observed a very interesting mode when the pattern of the voltage oscillogram on the memristors reminds a burst neural activity and is caused by sequential change of a single oscillator operation mode. 
The scheme of coupled oscillators with a memory cell was created to simulate the education process. A memristor is often used in simulating organism’s neural systems as an element that allows for simulation of a synaptic plasticity effect expressed in the increase of synaptic coupling force when postsynaptic receptors are activated. To simulate the effect of synaptic plasticity we used two neurons-oscillators linked by a memristor and sequential capacity. The capacity was necessary to realize unipolar voltage impulses in a memory cell during oscillations. The first oscillator operating at a normal mode excited the second oscillator in a subthreshold mode when the value of supply current was not enough to cause oscillations. Memristor’s resistance started to decrease under the influence of voltage impulses, i.e. the electric coupling between circuits became stronger. When memristor’s resistance fell down to some threshold level the second oscillator switched on. 
Thus, we have shown the dynamics of a single and two coupled oscillators with a memristor included into the scheme that simulates the effects of neurons’ train activity and synaptic plasticity and associated educational process.
4. We have developed a scheme of two thermally coupled oscillators with load resistances (Rx, Ry) represented as 3×3 matrix of photoconductive converters. Two galvanically isolated photoconductors in one field of the matrix are illuminated simultaneously and the matrix itself is a sensor of illuminated images (figures). A specific pattern of light and dark fields and certain values of Rx and Ry and therefore its own SHR (if the static parameters of the scheme are adequate) correspond to each figure. Thus this system consisting of two oscillators is able to classify and recognize patterns with regard to figure symmetry. 
5. We have performed experimental research and numerical modeling of a switching channel dynamics in planar vanadium dioxide-based structures and have established some regularities of behavior for transition time from high to low impedance states and back depending on the impulse amplitude and duration and the value of base voltage. The obtained data together with the calculated ones and the results of temperature measurements in the switching channel indicate that in vanadium dioxide “metal-semiconductor” phase transition induced by Joule heating plays an essential role. 
We have proposed a type of thermal coupling that is alternative to electrical coupling and is promising for 3D oscillator networks integration, all-to-all coupling and the effect of subharmonic synchronization. 
Thermal coupling between oscillators is realized because of heat transfer through the substrate where the oscillator elements are located. To do this circuit elements should act as heat sources of variable power during oscillations generation (it could be any resistive element suitable for current flow including a switching element itself) and the parameter of the surrounding oscillators should be highly dependent on temperature (for instance, threshold voltage of a switch depends heavily on temperature). 
We have obtained the calculated dependences of thermal coupling radii RTC corresponding ΔT ~ 0.2 K on the capacity value and limit resistor. This proves that the force and radius of coupling could be controlled not only by the static values such as the space between the structures and substrate heat constants, but also by the dynamic values through varying the scheme parameters. 
Experimental and numerical studies of oscillations of two thermally coupled oscillators led us to the phenomenon of subharmonic synchronization (partial synchronization). This phenomenon indicates that synchronization may occur on nonbasic (divisible) harmonics of an oscillation spectrum. 
We have developed a rather simple but effective algorithm based on phase transition that determines the presence of synchronization effect, synchronization effectiveness µ and SHR value (ratio of harmonic order at synchronization frequency). 
A map of the form of Arnold’s tongue was calculated for synchronous states in the area of power currents. Twelve various states were obtained for the cases of strong coupling that corresponded to experimental parameters and noise level. For other system parameters with lower noise level the number of possible states could increase significantly and could reach 200 allowing for 20 first harmonics. 
Thus, the subharminic synchronization effect possesses a large potential for classification and may be used for pattern recognition problems. 
6.  It has been shown that the synchronization effect at long distances may be observed in the chain of thermally coupled oscillators when the synchronization parameter (SHR) between the outermost chain elements is expressed by product of neighboring oscillators. Therefore the sunharmonics synchronization effect enables us to realize synchronization at larger distances through pairwise interaction of oscillators comprising the coupling chain. It has been shown that when power current for two first oscillators (I1, I2) in the chain of N=100 oscillators is varied then the distribution SHR1,100  in the area of controlling current has the gradient only along I1 axes in contrast to two-oscillators scheme. At the same time the symmetry of synchronous states remains diagonal thus highlighting the role of mutual current ratio of neighboring oscillators for the physics of synchronism spreading along the chain. However, the synchronization areas are distributed unevenly and do not form a striking system of Arnold’s tongues. 
When power currents of central oscillators (I51, I52) are varied we obtain the distribution of only one single state SHR1,100=1/1, this seems to be caused by unchanged frequencies of outermost oscillators. Thus, the ratio I51 и I52 performs the role of a trigger that switches on and off the synchronization process of the outermost oscillators. 
7.  We consider that the phenomenon of subharmonic synchronization should be used as the main method of pattern recognition that increases the classification capacity of an oscillator system. We have studied thermal coupling in the course of our work, however, analogous effects of partial synchronization may be obtained for other coupling types (R- and C-type), because the physical mechanism of subharmonic synchronization is universal.

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