Plate Capacitor Research Articles

The System’s Point of View Applied to Dielectrophoresis in Plate Capacitor and Pointed-versus-Pointed Electrode Chambers

The DEP force is usually calculated from the object's point of view using the interaction of the object's induced dipole moment with the inducing field. Recently, we described the DEP behavior of high- and low-conductive 200-µm 2D spheres in a square 1 × 1-mm chamber with a plane-versus-pointed electrode configuration from the system's point of view. Here we extend our previous considerations to the plane-versus-plane and pointed-versus-pointed electrode configurations. The trajectories of the sphere center and the corresponding DEP forces were calculated from the gradient of the system's overall energy dissipation for given starting points. The dissipation's dependence on the sphere's position in the chamber is described by the numerical "conductance field", which is the DC equivalent of the capacitive charge-work field. While the plane-versus-plane electrode configuration is field-gradient free without an object, the presence of the highly or low-conductive spheres generates structures in the conductance fields, which result in very similar DEP trajectories. For both electrode configurations, the model describes trajectories with multiple endpoints, watersheds, and saddle points, very high attractive and repulsive forces in front of pointed electrodes, and the effect of mirror charges. Because the model accounts for inhomogeneous objectpolarization by inhomogeneous external fields, the approach allows the modeling of the complicated interplay of attractive and repulsive forces near electrode surfaces and chamber edges. Non-reversible DEP forces or asymmetric magnitudes for the highly and low-conductive spheres in large areas of the chamber indicate the presence of higher-order moments, mirror charges, etc.

Multifunctional soft stretchable strain sensor for complementary optical and electrical sensing of fatigue cracks

Fatigue-induced cracking in steel components and other brittle materials of civil structures is one of the primary mechanisms of degrading structural integrity and can lead to sudden failures. However, these cracks are often difficult to detect during visual inspections, and off-the-shelf sensing technologies can generally only be used to monitor already identified cracks because of their spatial localization. A solution is to leverage advances in large area electronics to cover large surfaces with skin-type sensors. Here, the authors propose an elastic and stretchable multifunctional skin sensor that combines optical and capacitive sensing properties. The multifunctional sensor consists of a soft stretchable structural color film sandwiched between transparent carbon nanotube electrodes to form a parallel plate capacitor. The resulting device exhibits a reversible and repeatable structural color change from light blue to deep blue with an angle-independent property, as well as a measurable change in capacitance, under external mechanical strain. The optical function is passive and engineered to visually assist in localizing fatigue cracks, and the electrical function is added to send timely warnings to infrastructure operators. The performance of the device is characterized in a free-standing configuration and further extended to a fatigue crack monitoring application. A correlation coefficient-based image processing method is developed to quantify the strain measured by the optical color response. Results show that the sensor performs well in detecting and quantifying fatigue cracks using both the color and capacitive signals. In particular, the color signal can be measured with inexpensive cameras, and the electrical signal yields good linearity, resolution, and accuracy. Tests conducted on two steel specimens demonstrate a minimum detectable crack length of 0.84 mm.

Study and simulation of MEMS electrostatic actuators

The desire for cutting-edge technologies is at an all-time high as the world becomes more digital. To suit the unique requirements, numerous systems and their associated devices are on the market. One such developing technology for producing devices is Micro Electro Mechanical System (MEMS). The simplest description of MEMS technology is the combination of tiny mechanical and electromechanical components on a single chip using micromanufacturing techniques. Its benefits include low cost, lightweight, accurate measurement in small places, and low power usage. The main objective of this proposed work is to design, analyze and compare various electrostatic actuators. Analyses of the device's electrostatic actuation, capacitive sensing, displacement, Eigen frequency, resonant frequency, time domain response of parallel plate actuation electrodes with variable gap actuator, differential capacitive sensing, parallel plate capacitance, and balanced actuation are all done in-depth.

Low-temperature processing of screen-printed piezoelectric KNbO3 with integration onto biodegradable paper substrates

The development of fully solution-processed, biodegradable piezoelectrics is a critical step in the development of green electronics towards the worldwide reduction of harmful electronic waste. However, recent printing processes for piezoelectrics are hindered by the high sintering temperatures required for conventional perovskite fabrication techniques. Thus, a process was developed to manufacture lead-free printed piezoelectric devices at low temperatures to enable integration with eco-friendly substrates and electrodes. A printable ink was developed for screen printing potassium niobate (KNbO3) piezoelectric layers in microns of thickness at a maximum processing temperature of 120 °C with high reproducibility. Characteristic parallel plate capacitor and cantilever devices were designed and manufactured to assess the quality of this ink and evaluate its physical, dielectric, and piezoelectric characteristics; including a comparison of behaviour between conventional silicon and biodegradable paper substrates. The printed layers were 10.7–11.2 μm thick, with acceptable surface roughness values in the range of 0.4–1.1 μm. The relative permittivity of the piezoelectric layer was 29.3. The poling parameters were optimised for the piezoelectric response, with an average longitudinal piezoelectric coefficient for samples printed on paper substrates measured as d33, eff, paper = 13.57 ± 2.84 pC/N; the largest measured value was 18.37 pC/N on paper substrates. This approach to printable biodegradable piezoelectrics opens the way forward for fully solution-processed green piezoelectric devices.

Fatigue behaviour of piezoelectric ceramic stack under large cyclic dynamic loading

The fatigue behaviour of a piezoelectric ceramic stack co-fired at low temperatures under the influence of a large cyclic dynamic load was studied. The piezoelectric ceramic stack is equivalent to a parallel plate capacitor with a charge source in parallel. The equations for the total current, output current and capacitor charging current of an equivalent device for an applied load were derived using Kirchhoff’s theoretical formula. A new type of fatigue test equipment was developed for continuous long-term M-shaped wave output. The piezoelectric ceramic stack is positioned between two concrete slabs, forming a pavement-subgrade piezoelectric structure. The fatigue behaviour of the piezoelectric ceramic stack was observed for 800,000 cycles of dynamic load. The results show that the dynamic load studied produced fatigue damage in the piezoelectric ceramic stack. As the number of dynamic loads increased, the electric output capacity of the piezoelectric ceramic stack decreased. Evident stage divisions were observed in the fatigue behaviour of the piezoelectric ceramic stack under cyclic dynamic loading. The electric output capacity of the stack decreased as the number of dynamic loads increased in the early and late stages, whereas it exhibited negligible change during the stable period.

Calculations of vacuum mean values of spinor field current and energy–momentum tensor in a constant electric background

In the framework of strong-field QED with x-steps, we study vacuum mean values of the current density and energy–momentum tensor of the quantized spinor field placed in the so-called L-constant electric background. The latter background can be, for example, understood as the electric field confined between capacitor plates, which are separated by a sufficiently large distance L. First, we reveal peculiarities of nonperturbative calculating of mean values in strong-field QED with x-steps in general and, in the L-constant electric field, in particular. We propose a new renormalization and volume regularization procedures that are adequate for these calculations. We find necessary representations for singular spinor functions in the background under consideration. With their help, we calculate the above mentioned vacuum means. In the obtained expressions, we show how to separate global contributions due to the particle creation and local ones due to the vacuum polarization. We demonstrate how these contributions can be related to the renormalized effective Heisenberg–Euler Lagrangian.

Design of a Hybrid Frequency Selective Rasorber With Wideband Reflection Suppression

A hybrid frequency selective rasorber is presented in this letter based on hybrid lossy layers. The hybrid lossy layers is composed of an absorption-transmission (A-T) layer and a transmission-absorption (T-A) layer, which are responsible for the absorption performance in the low and high frequency respectively. The A-T layer is composed of a lumped-resistors loaded cross-frame structure (CFS), which connects four parallel inductor and capacitor resonators. The T-A layer is constructed by a parallel plate capacitor loaded square loop resonator connecting four lumped-resistor loaded T-shaped metal branches. The frequency selective surface layer is composed of metal square slot. The hybrid frequency selective rasorber provides a transmission window around 10 GHz and two-sided absorption bands in 3.19—9 GHz and 11.85–21.18 GHz, meanwhile the wideband reflection suppression (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> <−10 dB) is achieved from 3.2 to 21.18 GHz (147%). An assembled prototype is measured to verify the simulated results.

Modular Electromagnetic Transducer for Optimized Energy Transfer via Electric and/or Magnetic Fields.

In this paper, a modular electromagnetic transducer that achieves the optimal transfer of energy from the electric and/or magnetic fields is proposed. Both the magnetic field resonance coupling and the influence of the electric field near the copper transducers of the printed circuit board and inside the FR4-type epoxy material are considered. In our printed arrays of flat transducers, we consider face-to-face capacitances for the study of resonance coupling. Because the space between coil turns is almost double the plate thickness, the coplanar capacitance can be ignored for frequencies under 2 MHz. A radio frequency (RF) transmitter and transducer were built to demonstrate the increased energy transfer efficiency when using both electric and magnetic fields in the near-field region. The transversal leakage flux coupling of a long RF coil was more efficient than a simple axial magnetic field coupling when using pancake transceiver coils. The optimal configuration having one long coil at the base and two or more flat coils as capacitor plates near coil ends generated the highest tandem of magnetic and electrical fields. A power regression tool was used to convert and simplify the transducer current and voltage variation with distance. In this regard, the current change corresponded to magnetic field variation and the voltage change to the electric field variation. New formulas for estimating the near-field region and the self-capacitance of the RF transformer coil are proposed; the optimal function in the frequency domain for a given transducer distance was defined by simulation.

Demonstration experiment for the initial stage of introducing the displacement current concept

A simple demonstration installation is proposed, containing a plate air-dielectric capacitor, an alternating voltage generator, and three identical neon lamps. Two lamps are inserted in the breaks of the wires connecting the capacitor to the generator. The third lamp is located between the capacitor plates. The gas in all three lamps glows, when the AC voltage is applied to the capacitor. This shows that in the experiment, there is a normal conduction current through the lamps. Around this electric current, as it is well known to students, there is a magnetic field. When removing the neon lamp from the capacitor, they observe that the glow of the lamps in the wires does not change. This means that a small neon lamp practically does not affect the field in the capacitor. Therefore, it is natural to think that the time-varying electric field in the capacitor produces a vortex magnetic field, as well as the conduction current flowing through the lamp. So a time-varying electric field can be considered an electric current. Maxwell called it the displacement current to distinguish it from the real conduction current. The displacement current closes an electrical circuit that is broken by a capacitor for direct current. It is advisable to use the demonstration described in the article when introducing the concept of displacement current in the Bachelor’s general physics course.

Self-powered piezoelectric NaNbO3 induced band position rearrangement and electrocatalysis in MoS2/NaNbO3 heterojunction for generation of reactive oxygen species for organic pollutant removal

Piezocatalytic heterojunction was synthesized using sodium niobate (NaNbO3, NBO) and molybdenum disulfide sheets (MoS2, MS), and characterized via SEM, XRD, XPS, UPS, EPR, PFM, and EIS. Metronidazole (MET) removal using MS(x)/NBO heterojunction was tested via batch experiments in an ultrasonicator (40 kHz and 150 W) for 160 min. MET removal obtained under optimized MS(30)/NBO (30 wt% of MS) was 82.8%, and the removal mechanism was governed by .OH formed due to reduction of H2O2, electrocatalytic oxidation at MS anode, and oxidation by holes in depletion region at MS-water and MS-NBO interface. Scavenging and quantification studies confirmed the formation of H2O2 (∼27 µM) due to piezoelectric effect induced electrocatalysis. In the absence of piezoelectric effect, MET removal and .OH formation were insignificant. Moreover, COMSOL simulation revealed the role of orthorhombic NBO as parallel plate capacitor in the heterojunction that created electrocatalysis and formation of depletion and accumulation regions at MS-NBO and MS-water interface. Finally, effects of pH (2–12), competitive anions (Cl−, NO3–, SO42−, CO32–, and PO43−) and working temperature (28–63 ℃) on piezocatalytic MET removal were investigated through experiments and theoretical understanding. The increase in temperature due to ultrasonication improved efficiency of MET removal due to improvement in interfacial charge transfer, and increase in thermodynamic feasibility of .OH generation. Overall, MS(30)/NBO activity could be attributed to generation of charge carriers due to mechanical excitation and formation of piezoelectric effect due to cavitation under ultrasonic waves.

Mechanism of blistering of deformed coil coated sheets in marine climate

The tendency to blistering of coil coated steel sheets after deformation was investigated in both accelerated tests and marine climate. Corrosion processes played a crucial role in the blistering mechanism in deformed areas and blistering increased with induced strain. The inferior performance in deformed areas was associated mainly with higher permeability of organic coatings due to formation of additional defects. Localized water uptake measurements by the parallel plate capacitor technique were successfully applied to quantify the total damage to protective coatings induced by deformation. A link was found between blistering behaviour and the relative increase in water uptake.

Using parallel plates capacitor as a volumetric flow rate sensor and direction detection for microfluidic/nanofluidic and extra smaller applications

This paper shows how a single parallel plate capacitor can be used to sense volumetric flow rate in micro/nano and smaller scale fluidic conduits and how a double parallel plate capacitor can be used to sense both volumetric flow rate and direction of flow. The concept was developed based on the principles of conservation of energy with some fundamentals of electricity and electromagnetics. Furthermore, the concept was validated experimentally to be accurate. Upon validation the measurement of the sensor was found to be in good agreement with experimental measurement with more accuracy obtained as the supplied voltage for the sensor is increased. Also, the accuracy of the developed concept increases as the characteristic length of the conduit decreases which makes the developed concept even more suitable for smaller scales applications. The concept consumes extremely low power and can be used directly without calibration provided that accurate value for magnetic permittivity of fluid is available. Moreover, the concept can be used for any type of fluid of any conduit shape with easy incorporation onto lab-on-a-chip or MEMS technology. The sensitivity of the sensor is approximately 0.03 A/(m3/s) which is good compared to other sensors.

Modelling, Fabrication and Testing of RF Micro-Electro-Mechanical-Systems Switch

This paper presents an approach to evaluate capacitance developed by perforated membrane of RF MEMS switch with high accuracy. An analytical model is developed for both upstate and downstate of switch by including parasitic and fringing field capacitance in parallel plate capacitance model. The proposed analytical model includes the ligament efficiency term directly in the formula which reduce the efforts to calculate it individually for various perforation sizes. The capacitance analysis has been carried out by varying the physical parameters to optimize the switch dimensions and these analytical results are compared with the simulation results carried out by 3D FEM tool COMSOL multiphysics for validation. The proposed analytical model results are then compared with benchmark models to understand the efficiency of proposed model in estimating the up and downstate capacitances. The proposed analytical model proved to be good with less error percentage of 2.13% at upstate and 2.59% at downstate whereas the other benchmark models gives greater than 5% error. The switch is then fabricated using 4-mask surface micromachining process and experimental evaluation of capacitance at both upstate and downstate is carried out by DC probe station. Experimentally, the upstate capacitance is obtained as 37.4 fF and downstate as 2.43 pF and the analytical models exhibited low error percentage of 3.95% at upstate and 2.05% at downstate condition for μ=0.5.

Increased fatigue resistance in transparent lead zirconate titanate thin films with interdigitated electrodes

This work compares the fatigue behavior of fully transparent lead zirconate titanate films with a composition at the morphotropic phase boundary on fused silica glass or sapphire, respectively, fitted with coplanar interdigitated top electrodes and no bottom electrodes to that of the same systems in a traditional metal–insulator–metal parallel plate capacitor geometry. While the polarization hysteresis in the latter geometry decreases rapidly during bipolar electrical cycling, systems with coplanar electrodes show no notable fatigue up to 107 cycles. The difference is explained based on the columnar microstructure of the films: for coplanar electrode geometries, the grain boundaries of the columnar structure act as trapping sites for oxygen vacancies, preventing the build-up of agglomerates that cause fatigue by domain wall pinning.

Plate capacitor problem as a benchmark case for verifying the finite element implementation

In this work, parallel plate capacitors are numerically simulated by solving weak forms within the framework of the finite element method. Two different domains are studied. We study the infinite parallel plate capacitor problem and verify the implementation by deriving analytical solutions with a single layer and multiple layers between two plates. Furthermore, we study the finite parallel plate capacitor problem and verify it by Love’s potential equation and Xiang’s capacitance equation. Moreover, the fringing effect is considered and extended to problems with multiple dielectric layers, such a solution is not possible by means of the existing analytical solutions. Besides, we realize the possibility of choosing different boundary conditions (electric potential boundary conditions and charge density boundary conditions) by changing the weak form. Finally, a transient solution that includes dielectric loss and calculates the quality factor of a capacitor is presented, which may be used in capacitor design. Convergence and consistency of results are demonstrated by comparing the results between analytical and numerical solutions and also the results from different boundary conditions.

Electric Field and Strain Tuning of 2D Semiconductor van der Waals Heterostructures for Tunnel Field-Effect Transistors.

Heterostacks consisting of low-dimensional materials are attractive candidates for future electronic nanodevices in the post-silicon era. In this paper, using first-principles calculations based on density functional theory (DFT), we explore the structural and electronic properties of MoTe2/ZrS2 heterostructures with various stacking patterns and thicknesses. Our simulations show that the valence band (VB) edge of MoTe2 is almost aligned with the conduction band (CB) edge of ZrS2, and (MoTe2)m/(ZrS2)m (m = 1, 2) heterostructures exhibit the long-sought broken gap band alignment, which is pivotal for realizing tunneling transistors. Electrons are found to spontaneously flow from MoTe2 to ZrS2, and the system resembles an ultrascaled parallel plate capacitor with an intrinsic electric field pointed from MoTe2 to ZrS2. The effects of strain and external electric fields on the electronic properties are also investigated. For vertical compressive strains, the charge transfer increases due to the decreased coupling between the layers, whereas tensile strains lead to the opposite behavior. For negative electric fields a transition from the type-III to the type-II band alignment is induced. In contrast, by increasing the positive electric fields, a larger overlap between the valence and conduction bands is observed, leading to a larger band-to-band tunneling (BTBT) current. Low-strained heterostructures with various rotation angles between the constituent layers are also considered. We find only small variations in the energies of the VB and CB edges with respect to the Fermi level, for different rotation angles up to 30°. Overall, our simulations offer insights into the fundamental properties of low-dimensional heterostructures and pave the way for their future application in energy-efficient electronic nanodevices.

On Effects of Shear Deformation on the Static Pull-in Instability Behaviour of Narrow Rectangular Timoshenko Microbeams

MEMS devices utilize electrostatics as preferred actuation method. The accurate determination of pull-in instability parameters (i.e., pull-in voltage and pull-in displacement) of such devices is critical for their correct design. It should be noted that similar to parallel plate capacitors, the electrostatic force between the surface of the deformable microbeam and stationary ground is non-linear in nature. Hence the analysis associated with MEMS devices is always inherently non-linear. In the literature, these devices have been majorly analyzed as Bernoulli-Euler microbeams with cantilever or clamped-clamped beam end conditions. However, Dileesh et al. (doi: 10.1115/ESDA2012-82536) have studied the static and dynamic pull-in instability behavior of slender cantilever microbeams by developing a six-nodded spectral finite element based on the Timoshenko beam theory (TBT-SFE). They have demonstrated the accuracy of the TBT-SFE by comparing their results with corresponding results of COMSOL-based three-dimensional finite element simulations. In addition, effects of shear deformation also start to play significant role as the beam thickness-to-length ratio increases. In this paper, authors have developed the TBT-SFE based on the work by Dileesh et al. for the case of statics. However, unlike Dileesh et al. where they have developed a six-nodded TBT-SFE, authors have investigated the best combination of number of nodes per element and total number of elements to carry out the study. For this purpose, authors have first calculated results of the maximum beam transverse displacement, for a shear deformable propped-cantilever microbeam under the action of uniformly distributed transverse load, obtained by utilizing the developed TBT-SFE with different combinations of number of nodes per element and total number of elements. These results are then compared with corresponding analytical results available in the literature to arrive at the best combination of number of nodes per element and total number of elements for the electrostatic-elastic analysis. In the second step, the finalized TBT-SFE is utilized to determine static pull-in instability parameters of narrow microbeams with various fixity conditions and beam thickness-to-length ratios. This study highlights the importance of transverse shear effects on pull-in instability parameters of Timoshenko microbeams.

Granular aluminium nanojunction fluxonium qubit.

Mesoscopic Josephson junctions, consisting of overlapping superconducting electrodes separated by a nanometre-thin oxide layer, provide a precious source of nonlinearity for superconducting quantum circuits. Here we show that in a fluxonium qubit, the role of the Josephson junction can also be played by a lithographically defined, self-structured granular aluminium nanojunction: a superconductor-insulator-superconductor Josephson junction obtained in a single-layer, zero-angle evaporation. The measured spectrum of the resulting qubit, which we nickname gralmonium, is indistinguishable from that of a standard fluxonium. Remarkably, the lack of a mesoscopic parallel plate capacitor gives rise to an intrinsically large granular aluminium nanojunction charging energy in the range of tens of gigahertz, comparable to its Josephson energy. We measure coherence times in the microsecond range and we observe spontaneous jumps of the value of the Josephson energy on timescales from milliseconds to days, which offers a powerful diagnostics tool for microscopic defects in superconducting materials.

Enlightening Visualization of Charge on Capacitors and Capacitor Circuits

The ideal parallel plate capacitor in general physics textbooks lacks electrostatic perspectives regarding how conducting surfaces are charged. The current textbooks somewhat neglect close connections between capacitors and electrostatics, leaving students in limbo when analyzing charge distribution on capacitors in circuits. This paper will suggest a new generalized model of the ideal capacitor and offer learners, mainly from the electrostatic perspective, a better train of thought in analyzing how charges are distributed on various surfaces in capacitor circuits. This paper offers a relatively complete review and framework of the ideal capacitor and can serve as supplementary reading material for general physics learners and instructors for in-depth explanations of fundamental topics unavailable in the current textbooks.

Magnetic energy in quasistatic systems

Magnetic energy is often presented solely as an energy stored by an inductor or in a magnetic field, in contrast to electrostatic energy which is introduced through the concepts of electric interaction between point-charges. Quasistatics, with its many applications in everyday life and important pedagogical appeal, has many similarities to statics and can allow a discussion of magnetic energy in terms which reinforces the parallel between magnetostatics and electrostatics. With this goal in mind, we consider two simple examples in textbooks involving a parallel plate capacitor and a flattened solenoid, to discuss the interplay between the work of external forces, the work of the electric interaction forces between the charges and currents and the electric and magnetic energies stored in these devices.