Horizontal Capacitor Research Articles

Nonlinear regimes of electric convection of poorly conducting fluids in weightlessness at low frequencies of an electric field

Electrothermal convection in a poorly conducting fluid in an alternating electric field of a horizontal capacitor is studied. The nonlinear regimes of electric convection in weightlessness are studies at low frequencies of the electric field on the basis of the pentamodal model within the framework of the electroconductive charge formation mechanism. Hysteresis transitions between two different synchronous and subharmonic regimes are found to exist. Transitions to chaos occur by means of either interemittance or a subharmonic cascade.

Electro-Thermo-Convection of a Dielectric Liquid in the External DC and AC Electric Fields

The electro-thermo-convection of a dielectric liquid in a horizontal capacitor is investigated under the autonomous charge injection from the cathode and heating from above. In the case of a DC electric field, the linear stability analysis is carried out, and the thresholds of monotonic and oscillatory instability are determined. The finite difference method is used for the numerical simulation of the nonlinear behavior of electro-thermo-convective patterns: stationary convection and traveling waves. In the case of AC, electric field transient and permanent oscillations are analyzed. Two types of stable solutions are found. The modulated traveling waves are characterized by the quasiperiodic oscillations of convective characteristics. Another solution is modulated electroconvection (MEC). The patterns of MEC oscillate around some average flow synchronously with the external AC field and do not move laterally. The average intensity of convective mixing in modulated traveling waves is several times less than in modulated electroconvection. The spatiotemporal evolution of the stream function, temperature, and charge distributions for different types of transient and permanent solutions are analyzed.

Математическое моделирование нелинейной электроконвекции идеального жидкого диэлектрика в переменном электрическом поле

Mathematical modeling of nonlinear electroconvective regimes of an ideal liquid dielectric in an alternating electric field of a horizontal capacitor is carried out. The study was carried out using a low-mode electroconvection model for the case of weightlessness. As a result of the analysis of the obtained time dependences, their Fourier-spectra, calculations of the heat flow and the higher Lyapunov exponents, a map of nonlinear electroconvective regimes is constructed. The boundaries of the periodicity windows in the chaos region are determined. In the windows of periodicity, chaos occurs according to the Feigenbaum scenario.

Electroconvection of a weakly conducting liquid subjected to unipolar injection and heated from above

The problem of a weakly conducting viscous incompressible liquid placed in an infinite horizontal capacitor is solved numerically by the two-field method using finite difference schemes. It is assumed that a free charge arises in the liquid (heated from above) due to a homogeneous unipolar autonomous injection from the cathode. In mechanical equilibrium, the Coulomb force acting on the charge injected from the cathode and the buoyancy force are oppositely directed, and the oscillatory instability and wave supercritical modes of convection occur. The problem is investigated in full statement, i.e., the electric field redistribution created by the charge redistribution is taken into account. Periodic boundary conditions are used on the lateral boundaries of the studied area, which makes it possible to detect and analyze not only the mode of stationary electroconvection, but also the solutions in the form of traveling waves. A mixed convection regime that arises as a result of a direct Hopf bifurcation from the state of mechanical equilibrium was found and investigated. In this regime, the phases of standing and traveling waves happen one after another. Traveling waves, modulated traveling waves and stationary convection successively replace each other with an increase in the control parameter (the electric Rayleigh number) proportional to the voltage on the capacitor plates. A bifurcation diagram that characterizes the intensity and phase velocity of supercritical fluid flow modes is plotted. The intensity of the stationary electroconvective flow is an order of magnitude higher than the intensity of the flow in the traveling wave mode. The influence of the grid scale on the observed regimes is studied.

Устойчивость слабопроводящей жидкости в электрическом поле при униполярной автономной инжекции заряда

We study a model of autonomous unipolar charge injection from the cathode in a poorly conductive liquid in a steady electric field of a flat horizontal capacitor. According to this model, the charge density injected into the liquid has a constant term and a term directly proportional to the electric field strength in the capacitor. An electrohydrodynamic approximation is used. The case of weightlessness in an isothermal liquid is considered. The equilibrium distributions of the electric potential and charge density in the limiting case were found in analytical and numerical form. The linear stability of the poorly conductive liquid was studied. The boundary value problem was solved numerically by the targeting method using the Runge–Kutta–Fehlberg integration procedure. Neutral curves were obtained. Critical parameters were determined. The dependences of the convection thresholds on two injection parameters were found. With an increase in the modulus of either of the two injection parameters, the threshold for the occurrence of electroconvection decreases, it occurs with a smaller electric field.

An Optimum Structure of Scalable Capacitors in 3D Crosspoint Memory Technology

Memory chips need large capacitors in their periphery to drive boosted word-lines and bit-lines for read and write operations. In a previous work, scalable capacitors were proposed for 3D crosspoint memory to keep the area for the capacitors constant over technology generations. This paper proposes the capacitance models of three types of wiring capacitors: (1) vertical capacitor, (2) vertical and horizontal capacitor with next-neighbor wires connected with the other terminal, and (3) vertical and horizontal capacitor with next-neighbor pairs connected with the other terminal. These models are based on Wong’s crossover capacitor model to determine the capacitor structure with the highest capacitance density in 3D crosspoint memory technology. One can determine the best structure through optimizing the process parameters such as the height H of the insulation material between the metal wires and the thickness T of the metal wires and the design rules such as the width W and space S of metal wires. The model accuracy was in good agreement with the measurement of twelve types of capacitor structures fabricated in a 180 nm 6 metal standard CMOS process with the maximum error of 20%. Contour plots of the capacitance density across H vs. S where it is assumed that W = T = S are shown. As a result, the boundary condition regarding H and S is determined per 3D crosspoint memory technology with three, four, or five levels of wires.

Electrical Properties of Horizontal Array Capacitor Using Composite Organic Dielectric Layer of Impregnated Glass-Fiber Epoxy

We introduce a horizontal array capacitor with nine capacitances in a single body using an organic dielectric layer impregnated with glass fiber as a prepreg sheet. An organic solid horizontal array capacitor with a dielectric of prepreg materials of the epoxy type can implement the nine capacitances in a single body via a unique simple lamination and cutting process. We then investigate the basic electrical properties of a horizontal array capacitor. The organic solid array capacitors with five electrodes and four dielectrics are Cu/PPG layer/Cu/PPG layer/Cu/PPG layer/Cu/PPG layer/Cu with a horizontal array structure. The size of a completed array capacitor is 2.85 × 2.85 mm. The height of the fabricated array capacitor in the vertical direction is 0.5 mm, with nine capacitances possessing a series-type structure. The average capacitance value of C1, C2, C3, and C4 is 1.98 nF, and each tolerance has a value within 1% based on the average value. The temperature change rate in the capacitance maintains a nearly linear characteristic, but the rate of change tends to increase finely from 120°C or more. The capacitance values of C5, C6, and C7 with the parallel circuit were measured according to the voltage. Impedance and ESR (equivalent series resistor) of C1 were measured according to frequency and temperature.

Wave Regimes of Electroconvection of a Low Conducting Liquid under Unipolar Injection of a Charge in a Steady Electric Field

We have analyzed nonlinear regimes for a nonuniformly heated low conducting liquid in a horizontal capacitor in the gravity field and in a steady electric field under unipolar injection of a charge from the cathode and heating from above. We have considered a model in which the density of charges injected from the cathode is proportional to the electric field strength in the capacitor. For thermal Rayleigh number Ra = –1000, we have constructed the bifurcation diagram of regimes. We have analyzed various electroconvection regimes (stationary regime as well as the regime of standing and traveling waves). Analyzing the effect of increasing heating from above, we have detected transitions between the regimes: the traveling wave regime changes to the standing wave regime, which is transformed into the regime of a modulated standing wave.

Periodic and Chaotic Oscillations in a Low Conducting Liquid in an Alternating Electric Field

We study the oscillatory and chaotic evolution of electroconvective flows of a nonisothermal low conducting liquid in the AC electric field of a horizontal capacitor. An analysis is carried out of liquids in which the temperature dependence of the electrical conductivity generates the volume charge. The periodic and chaotic regimes of liquid flow are investigated in the case of a finite relaxation time. It is found that all periodic oscillatory electroconvective regimes are synchronous with the external electric field, and can be divided into three classes with different time shift properties. Bifurcation maps and diagrams of electroconvective regimes are obtained, and the hysteretic transitions between oscillatory electroconvective regimes with different periodicity are studied. We also analyse the scenarios of transition to chaotic oscillations. Depending on the external field frequency, the transition from periodic to chaotic oscillations can occur via quasiperiodicity, a subharmonic cascade, or intermittence.

Model of Electrothermal Convection of a Poorly Conducting Liquid in a Horizontal Capacitor

A five-mode model is used to analyze the electroconvection of a weakly conducting liquid in an alternating electric field of a horizontal capacitor with hard boundaries in the case of instantaneous charge relaxation. The nonlinear regimes of electroconvection are investigated. A pattern diagram is constructed. The quasi-periodic and synchronous oscillation regimes of convection are revealed. It is discovered that, depending on the external field frequency, the transition to chaos occurs either by quasi-periodicity or alternation.

Electric convection of low-conductivity liquid in a horizontal capacitor in the presence of unipolar charge injection

Electric convection of low-conductivity liquid in a horizontal plane capacitor is analyzed with allowance for unipolar charge injection. Dynamics of charge transfer through stationary isothermal liquid in the presence of modulated electric field is studied. Effect of modulation amplitude and frequency on the spatiotemporal distribution of charge density and electric potential is considered. Nonlinear electric convection of nonisothermal low-conductivity liquid is studied in the presence of static electric field in a 2D system. Hysteresis transitions between two different (with respect to intensity) regimes of electric convection are analyzed.

Переходы между электроконвективными режимами слабопроводящей жидкости при инжекции заряда в горизонтальном конденсаторе

Nonlinear regimes of electroconvection in a horizontal capacitor of the nonisotermal poorly conductive liquid in a steady electric field have been studied. Electroconvection is given rise by unipolar injection of charge from a cathode. Different heatings from below are considered. Hysteresis transitions between two regimes of electroconvection are investigated

Model of electrothermal convection of an ideal dielectric in a horizontal capacitor

The behavior of a nonuniformly heated dielectric in a variable electric field of a horizontal capacitor is studied. The action of the dielectrophoretic mechanism of instability associated with the temperature dependence of the dielectric permeability is considered. The model of electroconvection of the ideal dielectric is obtained for the boundary conditions corresponding to the no-flow condition on the rigid surface. Nonlinear flow regimes are investigated in the case of microgravity. A map of the regimes is constructed.

Simulations of oscillatory electroconvection in a horizontal capacitor with a large aspect ratio

Simulations of oscillatory electroconvection in a horizontal capacitor with a large aspect ratio

Simulations of oscillatory electroconvection in a horizontal capacitor with a large aspect ratio

Simulations of oscillatory electroconvection in a horizontal capacitor with a large aspect ratio

Stationary solutions of the equations for nonisothermal electroconvection of a weakly conducting incompressible polymeric liquid

Some mathematical model is formulated and its stationary solutions are obtained which describe the flows of a weakly conducting polymeric liquid in a horizontal capacitor (a channel).

Electroconvection of a poorly conducting fluid under unipolar charge injection in a steady electric field

We study the stability of equilibrium and nonlinear regimes of a nonuniformly heated poorly conducting fluid in a horizontal capacitor in the gravity field and in a dc electric field under a unipolar charge injection. A model in which the density of charges injected from the cathode is proportional to the electric field strength in the capacitor is considered. The dependences of critical parameters on the degree of heating and charge injection are determined. The effect of the Prandtl number on the equilibrium instability boundary and on the frequency of neutral vibrations is analyzed. Nonlinear regimes of electroconvection are studied for heating from below.

Numerical simulation of electroconvection of a poorly conducting fluid in an alternating electric field

Electroconvection of a poorly conducting fluid in an alternating electric field of a horizontal capacitor is studied. Electroconductive charge formation mechanism which is associated with the temperature dependence of electrical conductivity is considered The simulation is carried out, taking into account a finite charge relaxation time, for a set of problem parameters corresponding to real fluids used in electrical engineering, e.g. capacitor or transformer oils. A system of eight nonlinear differential equations is obtained using the Galerkin method. The system is solved by the Runge-Kutta-Merson fourth-order method. The mechanical-equilibrium stability boundary of the fluid in the capacitor is constructed on the parameter plane “modulation amplitude -external field period”. The evolution of arising flows in the supercritical area is analyzed, and the relationship between the intensity of convective flows and the dimensionless electric parameter is obtained at several frequencies. The spectral composition of the dynamic system response is determined using the fast Fourier transform. Different types of electroconvection oscillatory regimes are detected. It is shown that the solutions belong to the synchronous response at all frequencies of the external field, but they can be divided into two groups, which differ by the value of a heat flow through the capacitor. The areas of coexistence of regimes with different heat flow values are found. A transition from periodic to chaotic oscillations is investigated. It has been found that the transition to chaos is realized through a period-doubling cascade.

Dynamics of electroconvective wave flows in a modulated electric field

Wave regimes of finite-amplitude electroconvection in a poorly conducting fluid heated from above in a modulated field of a horizontal capacitor are analyzed. Low conductivity of the fluid is ensured by the charges injected from the anode and intrinsic (dissociated) ions. A bifurcation diagram of solutions is constructed. Apart from the regimes of modulated standing and traveling waves, stable waves changing their direction of motion are detected, as well as waves with a chaotically varying phase velocity.

Electroconvection of a poorly conducting fluid in a steady electric field

The emergence of electroconvection and nonlinear flows of a nonisothermal poorly conducting fluid in a steady electric field of a horizontal capacitor is investigated. The main mechanism of charge formation in the fluids under investigation is electric conduction due to the temperature dependence of the charge mobility. The Galerkin method is used for obtaining a system of nonlinear differential equations for the amplitudes of spatial modes; on the basis of this system, steady-state, periodic, and random nonlinear regimes of the fluid flow are investigated. The scenarios of transition to chaotic flows (via intermittence and a subharmonic cascade) are discovered. The interrelation between the electroconductive and thermogravitational mechanisms of convection is analyzed, and hysteretic transitions between monotonic and oscillatory regimes are studied. Qualitative comparison with the experiment is carried out.