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Showing papers on "Capacitance published in 1991"


Journal ArticleDOI
TL;DR: The transition between battery and supercapacitor behavior arising from a range of degrees of oxidation/reduction that arise over an appreciable range of potentials is discussed in this article.
Abstract: The storage of electrochemical energy in battery, "supercapacitor," and double‐layer capacitor devices is considered. A comparison of the mechanisms and performance of such systems enables their essential features to be recognized and distinguished, and the conditions for transition between supercapacitor and "battery" behavior to be characterized. Supercapacitor systems based on two‐dimensional underpotential deposition reactions are highly reversible and their behavior arises from the pseudocapacitance associated with potential‐dependence of two‐dimensional coverage of electroactive adatoms on an electrode substrate surface. Such capacitance can be 10–100 times the double‐layer capacitance of the same electrode area. An essential fundamental difference from battery behavior arises because, in such systems, the chemical and associated electrode potentials are a continuous function of degree of charge, unlike the thermodynamic behavior of single‐phase battery reactants. Quasi‐two‐dimensional systems, such as hyperextended hydrous , also exhibit large pseudocapacitance which, in this case, is associated with a sequence of redox processes that are highly reversible. Such oxide redox systems give rise to the best supercapacitor behavior and capacitances of farads per gram can be achieved. Other examples are the conducting polymer electrodes and Li intercalate systems. These systems provide examples of the transition between battery and supercapacitor behavior arising from a range of degrees of oxidation/ reduction that arise over an appreciable range of potentials. The impedance behavior of an supercapacitor is illustrated but is far from that expected for an electrostatic capacitor.

2,000 citations


Journal ArticleDOI
TL;DR: In this article, a new analytical potential fluctuations model for the interpretation of current/voltage and capacitance/voltages measurements on spatially inhomogeneous Schottky contacts is presented.
Abstract: We present a new analytical potential fluctuations model for the interpretation of current/voltage and capacitance/voltage measurements on spatially inhomogeneous Schottky contacts. A new evaluation schema of current and capacitance barriers permits a quantitative analysis of spatially distributed Schottky barriers. In addition, our analysis shows also that the ideality coefficient n of abrupt Schottky contacts reflects the deformation of the barrier distribution under applied bias; a general temperature dependence for the ideality n is predicted. Our model offers a solution for the so‐called T0 problem. Not only our own measurements on PtSi/Si diodes, but also previously published ideality data for Schottky diodes on Si, GaAs, and InP agree with our theory.

1,439 citations


Journal ArticleDOI
TL;DR: Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times slower than the iterative method alone, depending on required accuracy.
Abstract: A fast algorithm for computing the capacitance of a complicated three-dimensional geometry of ideal conductors in a uniform dielectric is described and its performance in the capacitance extractor FastCap is examined. The algorithm is an acceleration of the boundary-element technique for solving the integral equation associated with the multiconductor capacitance extraction problem. The authors present a generalized conjugate residual iterative algorithm with a multipole approximation to compute the iterates. This combination reduces the complexity so that accurate multiconductor capacitance calculations grow nearly as nm, where m is the number of conductors. Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times faster than the iterative method alone, depending on required accuracy. >

859 citations


Journal ArticleDOI
TL;DR: It is interesting to note that the nonlinear capacitance will dynamically influence the time constant of the OHC during acoustically evoked receptor potential generation.
Abstract: Outer hair cells (OHC) from the organ of Corti are capable of fast voltage-induced length changes (Santos-Sacchi and Dilger, 1988), suggesting that an associated voltage sensor should reside in the OHC plasma membrane. Voltage-dependent mechanical responses and nonlinear charge movement of isolated OHCs from the guinea pig were analyzed using the whole-cell voltage-clamp technique. Ionic currents in the cells were blocked. Nonlinear voltage-dependent charge movement or, correspondingly, voltage-dependent capacitance was measured with step or AC analysis. OHC movements were measured either from video or using a differential photodiode technique. Maximum charge movements up to 2.5 pC were measured in OHCs from the low-frequency region of the cochlea. Both AC and step analyses indicated a peak nonlinear capacitance of 16- 17 pF. The voltage dependence was fit to a Boltzmann relation with the step analysis indicating a maximum nonlinear capacitance at -23 mV step potential from a holding potential of about -120 mV, and AC analysis indicating a maximum at a holding potential near -40 mV. AC analysis probably provides a more accurate evaluation of voltage dependence. Measures of OHC motility magnitude versus voltage follow the nonlinear capacitance-voltage function obtained from AC measures. Treatment of the cells with gadolinium ions (0.5-1 mM) blocked OHC motility. This treatment also produced a shift of the nonlinear capacitance function along the voltage axis in the depolarizing direction, which can be explained by membrane surface charge screening. However, maximum capacitance was reduced as well and may correspond to the reduction or abolition of OHC motility in response to gadolinium treatment. Gadolinium effects were reversible. Nonlinear capacitance is not a function of membrane deformation due to length changes, since removal of OHC cytosol via the patch pipette abolished longitudinal movement but did not reduce nonlinear charge movement. It is interesting to note that the nonlinear capacitance will dynamically influence the time constant of the OHC during acoustically evoked receptor potential generation.

380 citations


Journal ArticleDOI
TL;DR: In this paper, a variant of the scanning capacitance microscope (SCaM) is described, which is based on the atomic force microscope and involves a cantilever beam that is used to press a conducting tip against a conducting substrate coated with a dielectric film.
Abstract: In this paper we describe a variant of the scanning capacitance microscope (SCaM) which is based on the atomic force microscope. Our SCaM involves a cantilever beam that is used to press a conducting tip against a conducting substrate coated with a dielectric film. A capacitance sensor is then used to measure the tip‐sample capacitance as a function of lateral position. The deflection of the cantilever can also be used to measure independently the surface topography. This microscope can be used to measure electrical properties of dielectric films and their underlying substrates. We have applied this microscope to the study of the nitride‐oxide‐silicon (NOS) system. This system has been studied extensively because of its ability to store information by trapping charge in the silicon nitride. Commercial semiconductor nonvolatile memories have been designed using this NOS technology. We have used the SCaM tip to apply a localized bias to the NOS sample, causing charge to tunnel through the oxide layer and to...

235 citations


Journal ArticleDOI
TL;DR: In this paper, the capacitance of coplanar lines is measured with two new techniques, one utilizing the resistance of the line and the other that of a resistor embedded in the line.
Abstract: The capacitance of coplanar lines is measured with two new techniques, one utilizing the resistance of the line and the other that of a resistor embedded in the line. The results of both measurements agree closely with calculations. A technique for directly comparing the capacitances of two similar transmission lines is also demonstrated. The relevance of these measurements to the determination of characteristic impedance is discussed. >

206 citations


Journal ArticleDOI
TL;DR: In this paper, the basic diode charge control model used in SPICE is extended to include reverse recovery, and the model is derived from the semiconductor charge transport equations using the lumped charged concept of Linvill, and demonstrated on the Saber simulator for simple inductive and resistive load circuits.
Abstract: The basic diode charge-control model used in SPICE is extended to include reverse recovery. The model is derived from the semiconductor charge transport equations. The diode charge transport equations are simplified using the lumped charged concept of Linvill, and the model is demonstrated on the Saber simulator for simple inductive and resistive load circuits. The two model parameters, diode lifetime and diffusion transit time, can easily be determined from a switching waveform. >

204 citations



Journal ArticleDOI
TL;DR: In this article, the authors measured the charge on the junction capacitance, which is directly related to the average value of n, as a function of the bias voltage using a Fulton-Dolan electrometer.
Abstract: The circuit formed by a nanoscale tunnel junction in series with a capacitance and a voltage source is the building block of most multi-junction circuits of single electronics. The state of this “single electron box” is entirely determined by the numbern of extra electrons on the intermediate “island” electrode between the junction and the capacitance. We have fabricated such a system and measured the charge on the junction capacitance, which is directly related to the average value ofn, as a function of the bias voltage using a Fulton-Dolan electrometer. At low temperature, the junction charge followed thee-periodic sawtooth function expected from the theory of macroscopic charge quantization. Strikingly,e-periodic variations were also observed when the box was superconducting. The thermal rounding of the sawtooth function is well explained by a simple model, except at the lowest temperatures.

194 citations


Patent
27 Sep 1991
TL;DR: In this article, an apparatus for detecting a surgical implement in human or animal tissue comprises a battery powered marker, which is secured to the surgical implement and positioned within a surgical wound.
Abstract: An apparatus for detecting a surgical implement in human or animal tissue comprises a battery powered marker. The marker (20) is secured to the surgical implement (16) and positioned within a surgical wound (12). A detection means (30) has an antenna (32) disposed in close proximity of the tissue (2). Means are provided for capacitance coupling of both the marker and the antenna to the tissue. A signal generating means (22) generates a signal having a predetermined frequency band ranging from about 10MHz to 1GHz. The signal generated by the signal generating means causes a field generating means (27) to generate an electromagnetic field providing the marker with signal identity.

172 citations


Journal Article
TL;DR: In this article, the authors measured the charge on the junction capacitance, which is directly related to the average value of n, as a function of the bias voltage using a Fulton-Dolan electrometer.
Abstract: The circuit formed by a nanoscale tunnel junction in series with a capacitance and a voltage source is the building block of most multi-junction circuits of single electronics. The state of this “single electron box” is entirely determined by the numbern of extra electrons on the intermediate “island” electrode between the junction and the capacitance. We have fabricated such a system and measured the charge on the junction capacitance, which is directly related to the average value ofn, as a function of the bias voltage using a Fulton-Dolan electrometer. At low temperature, the junction charge followed thee-periodic sawtooth function expected from the theory of macroscopic charge quantization. Strikingly,e-periodic variations were also observed when the box was superconducting. The thermal rounding of the sawtooth function is well explained by a simple model, except at the lowest temperatures.

Journal ArticleDOI
TL;DR: In this article, the performance of mixed oxide capacitors was investigated for detection at the concentration range of hundreds of ppm, and at a percentage level, respectively, and the results showed that the capacitance change of on exposure to was small, it was greatly enhanced by the combination with.
Abstract: Oxide capacitors consisting of and an oxide are studied as a sensor for detection. Although the capacitance change of on exposure to was small, it was greatly enhanced by the combination with . Sensitivity to and optimum operating temperature were strongly dependent on the oxide combined with . The element which contains basic oxides such as and , is highly sensitive to , but the operating temperature exceeded 1073 K. Among the elements investigated in this study, exhibited the highest sensitivity to . selectively responded to , and this element could distinguish the concentrations up to 6%. On the other hand, the capacitance of decreased linearly with increasing concentration up to 20%. Mixed oxide capacitors of and , therefore, are suitable for sensing at the concentration range of hundreds of ppm, and at a percentage level, respectively.

Proceedings ArticleDOI
14 May 1991
TL;DR: A switched-capacitor interface of a capacitive pressure sensor is developed which provides linear digital outputs and is best suited for a smart silicon capacitivepressure sensor.
Abstract: A switched-capacitor interface for a capacitive pressure sensor is developed which provides a linear digital output. It consists basically of a sample/hold circuit followed by a charge-balancing analog-to-digital converter. The sensor capacitance changes hyperbolically with an applied pressure. To convert the nonlinear capacitance change into the linear digital output, two linearization methods are investigated. In either method, a linear digital output with an accuracy higher than 8-b is obtained. Because of its high-accuracy capability and compatible fabrication process, the interface described is best suited for a smart silicon capacitive pressure sensor. >

Patent
10 May 1991
TL;DR: In this article, a light blocking layer, the storage capacitance electrodes and the storage lines are formed of the same material and at the same time, in an active matrix structure for liquid crystal display elements which includes pixel electrodes arranged in a matrix form on a glass base plate.
Abstract: In an active matrix structure for liquid crystal display elements which includes pixel electrodes arranged in a matrix form on a glass base plate, thin film transistors having their drains connected to the pixel electrodes, respectively, data lines each connected to sources of the thin film transistors of one column and gate lines connected to gates of the thin film transistors of one row, there are provided in the same plane a light blocking layer disposed opposite each of the thin film transistors across an insulating layer, a storage capacitance electrode disposed partly opposite each of the pixel electrodes across the insulating layer and storage capacitance lines for interconnecting the capacitance electrodes. The light blocking layers, the storage capacitance electrodes and the storage capacitance lines are formed of the same material and at the same time.


Patent
27 Aug 1991
TL;DR: In this article, a printed circuit board is disclosed which includes a high capacitance power distribution core, the manufacture of which is compatible with standard printed circuit boards assembly technology, and the resulting capacitance is typically sufficient to totally eliminate the need for decoupling capacitors on a typical printed circuit.
Abstract: A printed circuit board is disclosed which includes a high capacitance power distribution core, the manufacture of which is compatible with standard printed circuit board assembly technology. The high capacitance core consists of a ground plane and a power plane separated by a planar element having a high dielectric constant. The high dielectric constant material is typically glass fiber impregnated with a bonding material, such as epoxy resin loaded with a ferro-electric ceramic substance having a high dielectric constant. The ferro-electric ceramic substance is typically a nanopowder combined with an epoxy bonding material. The resulting capacitance of the power distribution core is typically sufficient to totally eliminate the need for decoupling capacitors on a typical printed circuit board.

Journal ArticleDOI
TL;DR: In this paper, the dependence of the geometrical properties of the interdigital capacitors and the sensitivity of SO2 sensors has been investigated, and it has been shown that the sensitivity can be improved by alterations in their geometry.
Abstract: Dielectric gas sensors for SO2 (ranges 1–200 vpm and 10–6000 vpm) with low cross-sensitivity to other gases and humidity have been developed. The sensors consist of planar interdigital capacitors (IDCs) with a heteropolysiloxane (HPS) coating containing tertiary amino groups as a sensitive layer. For the first time, the dependence of the geometrical properties of the interdigital capacitors and the sensitivity have been investigated. The sensitivity of the gas sensors can be improved by alterations in their geometrical properties. In the electrical adsorption saturation of SO2, depending on the sensitive film, a capacitance change of up to 40% can be obtained at a frequency of 10 kHz with an electrode distance of 26 μm.

Journal ArticleDOI
TL;DR: In this paper, a power supply specifically designed for capacitor-charging applications that uses a series-resonant circuit topology, a constant on-time/variable frequency control scheme, and zero-current switching techniques has been developed.
Abstract: A power supply specifically designed for capacitor-charging applications that uses a series-resonant circuit topology, a constant on-time/variable frequency control scheme, and zero-current switching techniques has been developed The performance of this capacitor-charging power supply (CCPS) has been evaluated in the laboratory by charging several values of load capacitance at various repetition rates The CCPS has charged a 1 mu F capacitor from 0 to 1500 V DC in 750 mu s, exhibiting a charging power of 1500 J/s This operation has been repeated at a rate of 800 charges per second, which corresponds to an average power output of 900 W A 10 mu F capacitor has been charged from 0-1500 V DC in 8 ms These results indicate that this design is feasible for use in capacitor-charging applications >

Journal ArticleDOI
TL;DR: In this paper, the sampling error resulting from input-dependent charge injection of the sampling switch is attenuated by sampling the input voltage onto a capacitance that is small during the sample mode but is, in effect, increased during the transition to the hold mode through the action of Miller feedback.
Abstract: A circuit technique is introduced for increasing the precision of an open-loop sample-and-hold circuit without significantly reducing the sampling speed. With this technique, the sampling error resulting from input-dependent charge injection of the sampling switch is significantly attenuated by sampling the input voltage onto a capacitance that is small during the sample mode but is, in effect, increased during the transition to the hold mode through the action of Miller feedback. The technique thus allows for a high sampling speed without the precision penalty traditionally associated with open-loop sample-and-hold circuits. A sample-and-hold circuit based on the proposed approach has been designed and fabricated in a 1- mu m CMOS technology, and an order-of-magnitude of reduction in the input-dependent charge injection has been demonstrated experimentally. This prototype circuit is capable of sampling an input to a precision of 8 b with an acquisition time of 5 ns. The experimental sample-and-hold circuit operates from a single 5-V supply and dissipates 26.5 mW. >

Journal ArticleDOI
TL;DR: In this paper, a self-aligned stacked-capacitor cell called the CROWN cell was developed for experimental 64-Mb-DRAMs operated at 1.5 V.
Abstract: A self-aligned stacked-capacitor cell called the CROWN cell (a crown-shaped stacked-capacitor cell), used for experimental 64-Mb-DRAMs operated at 1.5 V, has been developed using 0.3- mu m electron-beam lithography. This memory cell has an area of 1.28 mu m/sup 2/. The word-line pitch and sense-amplifier pitch of this cell are 0.8 and 1.6 mu m, respectively. In spite of this small cell area, the CROWN cell has a large capacitor surface area of 3.7 mu m/sup 2/ because (1) it has a crown-shaped capacitor electrode, (2) its capacitor is on the data line, and (3) it has a self-aligned memory cell fabrication process and structure. The large capacitor area and a Ta/sub 2/O/sub 5/ film equivalent to a 2.8-nm SiO/sub 2/ film ensure a large storage charge of 33 fC (storage capacitance equals 44 fF) for 1.5-V operation. A small CROWN cell array and a memory test circuit were successfully used to achieve a basic DRAM cell operation. >

Patent
02 Oct 1991
TL;DR: In this article, a capacitance sensing probe is described for measuring features on a workpiece surface, with two electrodes (E 1, E 2 ) spaced apart in the direction of movement of the probe with the electrodes being disposed in an attitude normal to the surface.
Abstract: A capacitance sensing probe is disclosed for taking measurements of features on a workpiece surface. The probe has two electrodes (E 1 , E 2 ) spaced apart in the direction of movement of the probe with the electrodes being disposed in an attitude normal to the surface. Only the edge of the electrodes are exposed to the surface and an electric circuit (EC) is provided for determining the effect of the surface on the fringe field capacitance between the electrodes. Guard electrodes are used to reduce the stray capacitance being measured. Various embodiments are shown with different numbers and arrangements of electrodes.

Journal ArticleDOI
TL;DR: In this article, an experimental technique and associated analysis for the measurement of the dielectric constants of liquids at microwave frequencies using an open-ended coax probe is described, including radiative corrections to the probe-liquid interface impedance.
Abstract: An experimental technique and associated analysis are described for the measurement of the dielectric constants of liquids at microwave frequencies using an open-ended coax probe. The analysis includes radiative corrections to the probe-liquid interface impedance. The technique is applicable to liquid and liquid-like (e.g., biological) samples, having dielectric constants comparable to water, at frequencies up to 20 GHz and possibly as high as 40 GHz. >

Patent
15 May 1991
TL;DR: In this article, a circuit and method for reducing switching losses in a full bridge, resonant transition, switching power converter is presented, which includes a bridge switching circuit having an FET switch in each leg of the bridge, each FET has a parasitic drain-to-source capacitance.
Abstract: The present invention is a circuit and method for reducing switching losses in a full bridge, resonant transition, switching power converter. The converter circuit includes a bridge switching circuit having an FET switch in each leg of the bridge. Each FET has a parasitic drain-to-source capacitance. The primary of a power transformer is connected across the bridge. Two secondary windings of the transformer are connected in a center-tapped configuration. A saturable reactor and a rectifier is connected in series with each secondary winding. A control means controls the conduction interval of the FET switches to produce a first and a second half-cycle of converter operation, each half-cycle including an on-time and a free-wheeling interval. The saturable reactors force unequal current distribution in the secondary windings during the free-wheeling intervals such that a primary current is caused to flow. This primary current is used to charge the parasitic capacitances of the FET switches such that each FET is switched ON only when its drain-to-source voltage is near zero.

Journal ArticleDOI
TL;DR: In this article, a new analysis of the differential capacitance of an ideally polarized electrode without specific ionic adsorption was proposed, which was obtained by separating from the experimental inner-layer capacitance C i a contribution C m obtained via a theoretical calculation and which represents the effect of the metal and its coupling with the solvent.

Patent
12 Mar 1991
TL;DR: In this paper, the capacitance and leakage current characteristics of solid electrolytic capacitors are improved by using a dielectric film and a conductive polymer layer in a resin casing as not directly contacting the element with the resin casing.
Abstract: Solid electrolytic capacitors comprise a capacitor element having a valve metal substrate, a dielectric film formed thereon, and a conductive polymer layer formed on the dielectric film. The capacitor element is encased in a resin casing as not directly contacting the element with the resin casing. The capacitance and leakage current characteristics are improved. Alternatively, a capacitor element includes a valve metal substrate, a dielectric film, an inorganic conductive layer and a conductive polymer layer formed on the substrate in this order, wherein the conductive polymer layer is formed after anodization of the inorganic conductive layer bearing substrate. The life of the resulting capacitor is significantly prolonged. This capacitor element may be encased in a resin casing in a manner as set forth above. Methods for manufacturing the solid electrolytic capacitor are also provided.

Journal ArticleDOI
TL;DR: An analytic charge sheet capacitance model for short-channel MOSFETs is derived and implemented in SPICE based on a surface potential formulation which computes the approximate surface potential without iterations.
Abstract: An analytic charge sheet capacitance model for short-channel MOSFETs is derived and implemented in SPICE. It is based on a surface potential formulation which computes the approximate surface potential without iterations. The DC current, charges, and their first and second derivatives are continuous under all operating regions. Equations for node charges are derived to guarantee charge conservation. Short-channel effects such as velocity saturation, channel-length modulation, and channel-side-fringing-field capacitances are included in the model equations. The model shows good agreement with the measured gate capacitance for long- and short-channel MOSFETs. The SPICE simulation of a ring oscillator using this model shows the significant variation of circuit performance due to the short-channel effects on capacitances. >

Journal ArticleDOI
TL;DR: In this paper, a theoretical analysis of the Kelvin probe circuit taking into account both the parallel capacity induced by the connecting cables and fringing fields is presented, which is primarily intended for UHV applications where shielding problems, due either to connecting cables within the system or nonideal system configurations, are nontrivial.
Abstract: We present a theoretical analysis of the Kelvin probe circuit taking into account both the parallel capacity induced by the connecting cables and fringing fields. We demonstrate a simple explicit solution for low modulation index e and suggest an optimized detection method for e close to unity. We extend the analysis to include stray capacitance terms for both the static‐ and vibrating‐plate earthed (spe, vpe) configurations and examine the variation in apparent contact potential difference Vapp as a function of the Kelvin probe mean spacing. This analysis is primarily intended for UHV applications where shielding problems, due either to connecting cables within the system or nonideal system configurations, e.g., imposed by sample mounting constraints, are nontrivial. Using a specially developed computer‐steered Kelvin probe and shield potential Vs coupled to a data acquisition system (DAS) we have tested the above model. We find Vapp to be linear with Vs and varies quadratically with mean spacing in both...

Proceedings ArticleDOI
24 Jun 1991
TL;DR: In this paper, the static and dynamic characteristics of a zero-voltage-switched half-bridge converter are analyzed quantitatively and the effects of circuit parameters, such as the input capacitance, and the transformer leakage inductance are discussed through the comparison of analytical and experimental results.
Abstract: The static and dynamic characteristics of a zero-voltage-switched half-bridge converter are analyzed quantitatively. This converter is controlled by pulse width modulation (PWM) with the asymmetrical drive of a pair of semiconductor switches and the zero-voltage switching is maintained by the partial resonance during the off interval of both switches. The effects of circuit parameters, such as the input capacitance, and the transformer leakage inductance are discussed through the comparison of analytical and experimental results. >

Journal ArticleDOI
TL;DR: In this paper, the small-amplitude periodic optical transmittance response of redox polymer films is derived and related to the corresponding electrical behaviour. But the authors do not discuss the relationship between the modulated transmittances and the film capacitance.
Abstract: The small-amplitude periodic optical transmittance response of redox polymer films is derived and related to the corresponding electrical behaviour. The combination of optical and electrical measurements allows Faradaic and non-Faradaic charging processes to be distinguished. The analysis of the modulated transmission data obtained for polyaniline films on indium-doped tin oxide coated transparent electrodes in 1.0 mol dm–3 H2SO4 indicates that the capacitance measured in a.c. experiments is associated with redox transformations in the PANI film. The a.c. capacitance was found to be lower than the pseudo-capacitance derived from cyclic voltammograms and possible reasons for this discrepancy are discussed. The absorption coefficient of the polaron has been derived from the relationship between the modulated transmittance and the film capacitance which also shows that bipolaron states are formed at potentials more positive than 0.15 V vs. SCE.

Journal ArticleDOI
P.A. Kok1, D. De Zutter1
TL;DR: In this article, the capacitance of a simplified model of a via hole is calculated based on an integral equation approach for the surface charge density, and it is found that the via capacitance is proportional to the square root of its height, at least for the range of realistic geometrical data considered.
Abstract: The capacitance of a simplified model of a via hole is calculated based on an integral equation approach for the surface charge density. The formulation of the problem is based on an integral equation for the surface charges combined with an analytical solution at the ground plane opening. The finite ground plane thickness is explicitly taken into account. Numerical data are obtained for a large range of realistic geometrical data. The relative importance of the contribution to the total capacitance coming from the ground plane opening is explicitly evaluated. It is found that the via capacitance is proportional to the square root of its height, at least for the range of geometrical data considered. >