Description of works performed in 2016 on the project of the RSF 16-19-00135

1) A technology has been developed for the fabrication of planar switching elements based on VO2 films with the metal–insulator phase transition (MIPT). Thin (~ 200 nm) vanadium dioxide films are obtained by DC magnetron sputtering followed by annealing in an oxygen atmosphere (10 mTorr, 480°C, t = 40 min.). The best for the electrical switching are the non-stoichiometric VO2 films with the resistivity jump at MIPT of up to two orders of magnitude, the phase transition temperature of ~ 60°C (as compared with Tt ≈ 70°C in stoichiometric VO2) and with an increased conductivity. By optical lithography and lift-off process, planar switching structures are formed with two electrodes (50-nm thick V-Au bilayer metallic contacts) and an interelectrode gap of about 2.5 microns; the electrode width is ~ 10 microns. The I-V characteristics of the switch are S-shaped with a threshold voltage of 1 to 15 Volts; a current jump at the switching threshold voltage Vth is about 10, and at the switching-off voltage Vh it is ~5; the dynamic resistances in the ON and OFF states are Ron ~ 40 Ohm and Roff  ~ 1.1 kOhm. Static resistance in the ON state is nonlinear and varies from 40 to 200 Ohms in the voltage range from Vh to Vth.
This technology has allowed us to obtain two-electrode structures, with the stable switching effect, that can withstand more than 10E8 switching cycles, as well as to install the switches onto breadboards for further study in vacuum.

2) To observe the auto-oscillation, a circuit has been assembled on the basis of a single VO2 switch. The series resistance Rs and the power supply voltage Vdd (in the range of 20 to 100 V) are chosen so that the load line passes across the negative differential resistance (NDR) region, which is a condition for the oscillation to occur. By variation of the conditions and regimes of film preparation (in particular, the annealing time t), the optimum parameters are selected for which the minimum value of Vth and the maximum ratio of the holding current to the threshold current Ih/Ith are reached. This provides the maximum slope of the NDR region and hence a better stability of the resulting oscillations.
Using the LTSpice software, the model of a VO2-switch is built, which describes the switching structure behavior. Experimental waveforms of oscillation of the voltage drop across the switch, as well as and the oscillation spectrum, coincide, with a high degree of accuracy, with the corresponding theoretical curves obtained within this model. A broadening of spectral peaks associated with the presence of noise in the subthreshold region is found, which leads to a weak frequency modulation of auto-oscillations by a chaotic signal; also, the stochastic resonance effects are observed.
When studying a single circuit, the phenomenon of bistability is observed, which consists in a controlled oscillation switching “ON” and “OFF” by an external pulse. This effect is caused by the total structure heating due to the fact that, during one oscillation period, the switching channel does not have time to cool down to the equilibrium temperature. To terminate the auto-oscillations, a pulse of reverse polarity is applied with an amplitude sufficient to switch-off the structure and duration equal to the time of the channel cooling to the equilibrium temperature. One can utilize this effect to create oscillatory memory cells, as well as in order to implement and a pulse communication mode in artificial neural networks.

3) It is shown that electron-beam modification (EBM) substantially changes the MIPT parameters, lowers the transition temperature Tt and results in a general decrease in resistance both in metallic and in semiconducting phase. This decrease in the Roff and Tt values, in turn, causes a reduction of Vth.  
A quantum-chemical calculation of the energies of formation of oxygen vacancies and oxygen migration in the monoclinic and tetragonal phases of vanadium dioxide has been performed. It is shown that diffusion in both phases of vanadium dioxide has a preferential direction of migration of oxygen along the crystallographic axis a in the monoclinic phase (T < Tt), while it does preferentially along the axis c in the tetragonal rutile phase (T > Tt). The difference in the rate of generation of oxygen vacancies under electron-beam exposure above and below the MIPT temperature is due to a jump (by a factor of ~1.5) of the oxygen diffusion activation energy at the structural phase transition, which changes the mobility of oxygen (oxygen vacancies) by more than an order of magnitude. Calculations of the electronic structure of the crystal have been carried out using the Quantum Espresso software package.
Next we have studied the EBM of the I-V curve threshold parameters of a VO2-switch and oscillation frequency in a circuit based on it. It is shown that EBM conducted in vacuum possesses a reversible nature, and the parameters can be recovered in air at a pressure of 150 Pa. At EBM with a dose of 3 C/cm2, the voltages Vth and Vh, as well as the OFF state resistance Roff  decrease down to 50% of the initial values. The oscillation frequency increases by 30% at an EBM dose of 0.7 C/cm2. The physical mechanism of the observed processes is associated with redox reactions and formation of oxygen vacancies as a result of EBM, taking into account the above-described differences in contributions of metallic and semiconducting phases of the switching channel.
Controllable EBM allows fulfillment of electron-beam forming of switches with preset parameters, and EBM can be used in artificial neural networks for pattern recognition based on frequency shift keying.

4) Numerical simulation of the dynamics of oscillations, taking into account the switch parameters change at EBM, as well as calculation of the temporal characteristics and temperature distribution in the channel switch, have been carried out. For this, the two approaches are utilized: 1) the use of standard mathematical complexes that can predict the operation of a circuit (LTSpice package) and to simulate physical processes in microstructures (COMSOL Multiphysics package); 2) the creation of the own software systems using ab initio methods and analytical evaluation of the parameters of simplest oscillation circuits.
It is shown that the theoretical (obtained by numerical simulation) curves accurately fit the experimental data, in particular, such as the dependence of the oscillator frequency on the EBM radiation dose, temporary characteristics of recovery after EBM in the metal and semiconductor phases, as well as the stationary current-voltage curves and temperature distribution in a planar switch.

5) The switching dynamics of two coupled VO2-based oscillators with resistive and capacitive coupling has been studied, and the capability of their application in oscillatory neural networks has been explored. An adequate SPICE model to describe the modes of operation of coupled oscillator circuits is proposed. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified.
For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. At the minimum coupling strength value, is neither frequency nor phase synchronization of oscillator circuits is observed. When resistive coupling lies in the range 3 kOhm < Rcoup < 10 kOhm, there is a gradual irregular distortion of the voltage oscillation waveforms. This change is due to a bypass of one switch by another at their mutual switching into a high-conductivity phase. In this range of the resistive coupling, spectra distortion is observe accompanied by the appearance of new harmonics at mutual modulation, and oscillations in general have a quasi-periodic character.
For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations, and the evolution to chaos occurs via the period doubling. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. Thus, oscillators coupled via capacitance shows a greater variety of operation modes as compared to the resistive coupling. At the capacitive coupling, oscillations are observed in the entire range of the Ccoup values. In the weak-coupling mode, with an increase in the coupling capacity, the oscillators’ frequencies tend to converge, and beyond the threshold Ccoup ~ 2.5 nF, the oscillators are synchronized. Unlike the resistive coupling, the phase difference after synchronization can be controllably varied over a wide range (from 30º to 170º), so the use of this type of coupling is more preferable in the pattern recognition systems using phase shift based detection schemes (phase shift keying).
As an application of the considered systems of coupled oscillators, a joint operation of R- and C-couplings in the ensemble of four oscillator, to simulate the central pattern generator (CPG), is demonstrated.

6) The effect of electron irradiation on the synchronization of coupled oscillators has been studied. Initial frequencies of oscillators are 850 Hz and 770 Hz, which do not provide synchronization at the capacitive coupling of Ccoup = 10 nF. To get synchronization, the frequency of one of the oscillators has been changed using EBM. It is shown that synchronization is established at a radiation dose of ~1 C/cm2, and upon further irradiation, desynchronization occurs.
The response of the oscillatory system to the electron beam exposure is thus demonstrated, and an important aspect here is the direction of the frequency change under EBM. Also, we note the fact that even in the presence of a noisiness of the oscillation frequency parameters, one can fairly accurately predict the occurrence of synchronization, basing upon the behavior of the phase difference. Therefore, the method of phase detection of synchronization may be a key method for the analysis of oscillatory neural networks.

7) A photoresistor connected in series has been added to the auto-oscillation circuit. It is shown that the illumination of this photoresistor affects the oscillation frequency. The illumination values (1.25 - 4.1 lux, for the photoresistor type LDR GL5516), at which stable oscillations commence, are found. When the illumination is I < 1.25 lux, the switch is in a steady off state, and when I > 4.1 lux, it is in a steady on state. This method of controlling the parameters of oscillation in circuits based on VO2-switch is similar to the above-described method with EBM. However, the need of e-beam modification of the switch may not always be appropriate because of the complexity of the electron exposure system and because of the vacuum conditions requirement.

8) The simulation of the recognition of a vector image function, using the method of the oscillation phase synchronization, has been carried out. The recognition technique when using such a system consists in the establishment of an initial (input) phase difference Δφt (input phase vector) and identification, after some time Δts, a finite phase difference Δφij, which is one of the stored eigenvector images. In the model experiment, we have used three single oscillator circuit based on VO2-switches connected, via coupling capacities, in the “asterisk” topology. For modeling, the NGSpice medium, equipped with a software for the model experiment automation (written in C++) for calculations in conditions of variation of the circuit parameter values, is used. The simulation results have shown that, the smaller the difference between the input and eigen phase vectors, the smaller is phase stabilization time, and the act of recognition consists in the identification of the "winner" (the least time criterion) from the set of input vectors.

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