Capacitor Research Articles

Compact Superconducting Microwave Resonators Based on Al-AlOx -Al Capacitors

We address the scaling-up problem for superconducting quantum circuits by using lumped-element resonators based on an alternative fabrication method of aluminum-aluminum oxide-aluminum (Al-${\mathrm{AlO}}_{x}$-Al) parallel-plate capacitors. The size of the resonators is only $0.04\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{2}$, which is more than one order smaller than the typical size of coplanar resonators ($1\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{2}$). The fabrication method we develop easily fits into the standard superconducting qubit fabrication process. We obtain capacitance per area $14\phantom{\rule{0.2em}{0ex}}\mathrm{fF}/\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ and the internal quality factor $1\ifmmode\times\else\texttimes\fi{}{10}^{3}$--$8\ifmmode\times\else\texttimes\fi{}{10}^{3}$ at the single-photon level. Our results show that such devices based on Al-${\mathrm{AlO}}_{x}$-Al capacitors could be further applied to the qubit readout scheme, including resonators, filters, amplifiers, as well as microwave metamaterials and innovative types of qubits, such as $0\ensuremath{-}\ensuremath{\pi}$ qubit.

Solid–liquid interface disjoining pressure of frozen clay and its effect on water transport

To account for the influence mechanism of solid–liquid interface disjoining pressure on water migration during clay freezing, this study first provides a theoretical calculation model of solid–liquid interface disjoining pressure by combining the thermodynamic equilibrium relation of solid–liquid interface with the parallel plate capacitor model. This is done at the molecular level. An implicit equation for calculating the film thickness d of unfrozen water is also given and the accuracy of the model verified. Secondly, considering that unfrozen water film is anisotropic, the concept of tensor is introduced to show the distribution characteristics and functions of solid–liquid interface disjoining pressure in unfrozen water film. Finally, the effects of solution concentration and undercooling degree on film thickness d of unfrozen water are discussed. The results show that solid–liquid interface disjoining pressure can be expressed by the excess free energy on the surface of charged media, and it is a single-valued function of unfrozen water film thickness. Solid–liquid interface disjoining pressure not only provides an effective driving force for water migration, but also provides growth space for ice lenses; the thickness of unfrozen water film d is negatively correlated with solution concentration and undercooling degree. The research results can provide a theoretical reference for the study of frost heave mechanism in clay soils.

A Calculation Method for the Optimal Initial Polar Distance of Capacitive Force Sensors

For capacitive sensors, the initial polar distance of capacitors has a vital influence on the performances of capacitive sensors; however, there are few current studies on the method of calculating the initial polar distance of capacitors, leading to a lack of corresponding theoretical basis for the design of capacitive sensors. In this article, a calculation method for the optimal initial polar distance based on minimum error is proposed. The total error expression is derived from error analysis, which clarifies the complex relationship between the total error and the initial polar distance, and the optimal initial polar distance is solved by Newton’s method. A capacitive torque sensor is used in the experiment to verify the calculation method for the optimal initial polar distance, the theoretical error and experimental error of the sensor are compared, and the results show that the experimental error is consistent with the theoretical error curve. The optimal initial polar distance obtained by the calculation method is 0.8479 mm, which is within the range of 0.8–0.9 mm determined by the experiment. The theoretical minimum total error is 0.211% and the experimental minimum total error is 0.208%. The total error expression proposed in this article is accurate, and the calculation method of the initial polar distance is effective. In addition, theoretical analysis reveals that the differential parallel plate capacitor has the characteristic that any small deformation of the moving plate can be equivalent to a translation whose magnitude is the mean value of the deformation.

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.

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.

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.

In-Operando Optical Spectroscopy of Field-Effect-Gated Al-Doped ZnO

Transparent conductive oxides (TCO) have the unique characteristics of combining optical transparency with high electrical conductivity; such a property makes them uniquely alluring for applications in visible and infrared photonics. One of their most interesting features is the large sensitivity of their optical response to the doping level. We performed the active electrical manipulation of the dielectric properties of aluminum-doped ZnO (AZO), a TCO-based on Earth-abundant elements. We actively tuned the optical and electric performances of AZO films by means of an applied voltage in a parallel-plate capacitor configuration, with SrTiO3 as the dielectric, and monitored the effect of charge injection/depletion by means of in-operando spectroscopic ellipsometry. Calculations of the optical response of the gated system allowed us to extract the spatially resolved variations in the dielectric function of the TCO and infer the injected/depleted charge profile at the interface.

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.

Deformation of substrate by epitaxial piezoelectric film and implications for interferometry

Advanced micro- and nano-electro-mechanical systems benefit from single-crystal-type epitaxial piezoelectric films, whose high crystal quality ensures excellent performance. Strong mechanical coupling in such films to non-piezoelectric substrates defines a difference in their operation with respect to purely piezoelectric counterparts. This is often described by a limiting case of a thick non-deformable substrate, whereas the film has out-of-plane deformations only. Here we consider a general practically relevant case, when converse piezoelectric effect in the film causes bending of the substrate. We provide a thermodynamic description and deliver analytical expressions for curvature, stress release, and thickness changes in a stack of the parallel-plate thin-film capacitor coherent to the substrate. It is shown that substrate deformations cannot be neglected and the d33 piezoelectric modulus receives comparable contributions from the film and the substrate. Implications for the interferometric measurement of the converse piezoelectric response are discussed.