Leaky Dielectrics Research Articles

Two‐phase electro‐hydrodynamic flow modeling by a conservative level set model

The principles of electro-hydrodynamic (EHD) flow have been known for more than a century and have been adopted for various industrial applications, for example, fluid mixing and demixing. Analytical solutions of such EHD flow only exist in a limited number of scenarios, for example, predicting a small deformation of a single droplet in a uniform electric field. Numerical modeling of such phenomena can provide significant insights about EHDs multiphase flows. During the last decade, many numerical results have been reported to provide novel and useful tools of studying the multiphase EHD flow. Based on a conservative level set method, the proposed model is able to simulate large deformations of a droplet by a steady electric field, which is beyond the region of theoretic prediction. The model is validated for both leaky dielectrics and perfect dielectrics, and is found to be in excellent agreement with existing analytical solutions and numerical studies in the literature. Furthermore, simulations of the deformation of a water droplet in decyl alcohol in a steady electric field match better with published experimental data than the theoretical prediction for large deformations. Therefore the proposed model can serve as a practical and accurate tool for simulating two-phase EHD flow.

A Liquid Spheroidal Drop in a Viscous Incompressible Fluid under a Steady Electric Field

An analytical approach to the problem of a liquid spheroidal drop in a viscous incompressible fluid under a steady electric field is presented. It is assumed that the drop and ambient fluid are slightly conducting (leaky dielectrics) with no net charge. The velocity field inside and outside the drop is governed by the Stokes equations and is represented in terms of four generalized analytic functions which are found from the velocity and stress boundary conditions. For the case of equal viscosities, the velocity field admits an integral-form solution, whereas for an arbitrary viscosity ratio $\lambda$, it is given by a series of spheroidal harmonics in the prolate spheroidal coordinates. Both solution forms hold for prolate and oblate spheroids. The axes ratio of a spheroid closest to a steady shape (or “steady” spheroid) is a minimizer of the kinematic condition error. However, the entire dependence of the “steady” spheroid's axes ratio on an electric capillary number ${\rm Ca}_E$ can be estimated analytically with the inverse problem: for each spheroid's axes ratio, find ${\rm Ca}_E$ that minimizes the kinematic condition error. The inverse problem, being quadratic with respect to $1/{\rm Ca}_E$, has a simple analytical solution, which identifies critical ${\rm Ca}_E$ for spheroidal drops and includes an “unstable” solution. Remarkably, as functions of ${\rm Ca}_E$, the deformation parameters $D$ for the “steady” spheroids and for “true” steady shapes (obtained based on boundary-integral equations) have the same qualitative behavior for various viscosity, conductivity, and permittivity ratios ($\lambda$, $R$, and $Q$, respectively), and are virtually identical within the range $-0.4\le D\le0.4$ for all investigated $\lambda$, $R$, and $Q$. This shows that the presented analytical approach for spheroidal drops is by far superior to Taylor's small-perturbation theory and Ajayi's second-order correction ($O({\rm Ca}_E)$ and $O({\rm Ca}_E^2)$ theories, respectively) and can replace numerical solutions from boundary-integral equations up to large deformations.

Vesicle electrohydrodynamics

A small amplitude perturbation analysis is developed to describe the effect of a uniform electric field on the dynamics of a lipid bilayer vesicle in a simple shear flow. All media are treated as leaky dielectrics and fluid motion is described by the Stokes equations. The instantaneous vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. We find that in the absence of ambient shear flow, it is possible that an applied stepwise uniform dc electric field could cause the vesicle shape to evolve from oblate to prolate over time if the encapsulated fluid is less conducting than the suspending fluid. For a vesicle in ambient shear flow, the electric field damps the tumbling motion, leading to a stable tank-treading state.

Extrinsic origins of the apparent relaxorlike behavior in CaCu3Ti4O12 ceramics at high temperatures: A cautionary tale

Although the origins of the high effective permittivity observed in CaCu3Ti4O12 (CCTO) ceramics and single crystals at ∼100–400 K have been resolved, the relaxorlike temperature- and frequency-dependence of permittivity obtained from fixed frequency capacitance measurements at higher temperatures reported in the literature remains unexplained, especially as CCTO adopts a centrosymmetric cubic crystal structure in the range of ∼35–1273 K. Impedance spectroscopy studies reveal that this type of relaxorlike behavior is an artifact induced mainly by a nonohmic sample-electrode contact impedance. In addition, an instrument-related parasitic series inductance and resistance effect modifies the measured capacitance values as the sample resistance decreases with increasing temperature. This can lead to an underestimation of the sample capacitance and, in extreme cases, to so-called ‘negative capacitance.’ Such a relaxorlike artifact and negative capacitance behavior are not unique to CCTO and may be expected in other leaky dielectrics whose resistance is low.

On the rheology of a dilute emulsion in a uniform electric field

A small-deformation perturbation analysis is developed to describe the effect of a uniform electric field on drop deformation and orientation in linear flows and emulsion shear rheology. All media are treated as leaky dielectrics, and fluid motion is described by the Stokes equations. The one-particle contribution to the effective stress of a dilute emulsion is obtained from the drop stresslet. Analytical solutions are derived as regular perturbations in the limits of small capillary number and large viscosity ratio. The results show that both shape distortion and charge convection modify emulsion rheology. Drop deformation due to application of an electric field in a direction perpendicular to the shear flow gives rise to normal stresses and may lead to shear thickening or shear thinning, depending on the electric properties of the fluids. Charge convection due to the imposed shear affects both the shear viscosity and normal stresses.

Interfacial instability in electrified plane Couette flow

The dynamics of a plane interface separating two sheared, density and viscosity matched fluids in the vertical gap between parallel plate electrodes are studied computationally. A Couette profile is imposed onto the fluids by moving the rigid plates at equal speeds in opposite directions. In addition, a vertical electric field is applied to the shear flow by impressing a constant voltage difference on the electrodes. The stability of the initially flat interface is a very subtle balance between surface tension, inertia, viscosity and electric field effects. Under unstable conditions, the potential difference in the fluid results in an electrostatic pressure that amplifies disturbance waves on the two-fluid interface at characteristic wave lengths. Various mechanisms determining the growth rate of the most unstable mode are addressed in a systematic parameter study. The applied methodology involves a combination of numerical simulation and analytical work. Linear stability theory is employed to identify unstable parametric conditions of the perturbed Couette flow. Particular attention is given to the effect of the applied electric field on the instability of the perturbed two-fluid interface. The normal mode analyses are followed up by numerical simulations. The applied method relies on solving the governing equations for the fluid mechanics and the electrostatics in a one-fluid approximation by using a finite-volume technique combined with explicit tracking of the evolving interface. The numerical results confirm those of linear theory and, furthermore, reveal a rich array of dynamical behaviour. The elementary fluid instabilities are finger-like structures of interpenetrating fluids. For weakly unstable situations a single fingering instability emerges on the interface. Increasing the growth rates causes the finger to form a drop-like tip region connected by a long thinning fluids neck. Even more striking fluid motion occurs at higher values of the electric field parameter for which multiple fluid branches develop on the interface. For a pair of perfect dielectrics the vertical electric field was found to enhance interfacial motion irrespective of the permittivity ratio, while in leaky dielectrics the electric field can either stabilize or destabilize the interface, depending on the conductivity and permittivity ratio between the fluids.

Electrohydrodynamic instabilities at interfaces subjected to alternating electric field

Instabilities at the interface of two immiscible fluids, either perfect or leaky dielectrics, subjected to alternating electric fields, is studied using a linear stability analysis in the limit of the electrode spacing being large compared to the wavelength of the perturbation. The Floquet analysis of the stability of this system indicates a significant effect of the frequency on the value of smax, the growth rate of the fastest growing instabilities and ETaylor, the minimum field required to excite an instability. It is seen that alternating fields act to damp the system instabilities compared to the direct current (dc) case. Moreover, the growth rate of the instabilities can be tuned from that of leaky dielectric fluids subjected to dc fields, in the low frequency limit, to that of perfect dielectrics in the high frequency limit. It is also observed that for a leaky dielectric-leaky dielectric interface, the alternating current (ac) fields can induce instabilities in a system which is stable at zero frequency, by increasing the frequency of the applied voltage.

Frequency-dependent electrodeformation of giant phospholipid vesicles in AC electric field.

A model of vesicle electrodeformation is described which obtains a parametrized vesicle shape by minimizing the sum of the membrane bending energy and the energy due to the electric field. Both the vesicle membrane and the aqueous media inside and outside the vesicle are treated as leaky dielectrics, and the vesicle itself is modeled as a nearly spherical shape enclosed within a thin membrane. It is demonstrated (a) that the model achieves a good quantitative agreement with the experimentally determined prolate-to-oblate transition frequencies in the kilohertz range and (b) that the model can explain a phase diagram of shapes of giant phospholipid vesicles with respect to two parameters: the frequency of the applied alternating current electric field and the ratio of the electrical conductivities of the aqueous media inside and outside the vesicle, explored in a recent paper (S. Aranda etal., Biophys J 95:L19-L21, 2008). A possible use of the frequency-dependent shape transitions of phospholipid vesicles in conductometry of microliter samples is discussed.

Investigation of Anomalous Inversion C–V Characteristics for Long-Channel MOSFETs With Leaky Dielectrics: Mechanisms and Reconstruction

This paper investigates anomalous inversion capacitance-voltage (C-V) attenuation for MOSFETs with leaky dielectrics. We propose to reconstruct the inversion C-V characteristic based on long-channel MOSFETs using the concept of intrinsic input resistance (Rii). The concept of Rii has been validated by segmented BSIM4/SPICE simulation. Our reconstructed C-V characteristics show poly-depletion effects, which are not visible in the two-frequency three-element method and agree well with the North Carolina State University-CVC simulation results. The intrinsic input resistance dominates the overall gate-current-induced debiasing effect (~95% for L = 20 mum) and can be extracted directly from the I-V characteristics. Due to its simplicity, our proposed Rii approach may provide an option for regular process monitoring purposes.

Axisymmetric deformation and stability of a viscous drop in a steady electric field

We consider a neutrally buoyant and initially uncharged drop in a second liquid subjected to a uniform electric field. Both liquids are taken to be leaky dielectrics. The jump in electrical properties creates an electric stress balanced by hydrodynamic and capillary stresses. Assuming creeping flow conditions and axisymmetry of the problem, the electric and flow fields are solved numerically withboundary integral techniques. The system is characterized by the physical property ratios R (resistivities), Q (permitivities) and λ (dynamic viscosities). Depending on these parameters, the drop deforms into a prolate or an oblate spheroid. The relative importance of the electric stress and of the drop/medium interfacial tension is measured by the dimensionless electric capillary number, Cae. For λ = 1, we present a survey of the various behaviours obtained for a wide range of R and Q. We delineate regions in the (R,Q)-plane in which the drop either attains a steady shape under any field strength or reaches a fold-point instability past a critical Cae. We identify the latter with linear instability of the steady shape to axisymmetric disturbances. Various break-up modes are identified, as well as more complex behaviours such as bifurcations and transition from unstable to stable solution branches. We also show how the viscosity contrast can stabilize the drop or advance break-up in the different situations encountered for λ = 1.

Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel

We study the electrohydrodynamic stability of the interface between two superposed viscous fluids in a channel subjected to a normal electric field. The two fluids can have different densities, viscosities, permittivities and conductivities. The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids. The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky dielectrics. In the framework of the long-wave linear stability analysis, the wave speed is expressed in terms of the ratio of viscosities, densities, permittivities and conductivities of the two fluids. For perfect dielectrics, the electric field always has a destabilizing effect, whereas for leaky dielectrics, the electric field can have either a destabilizing or a stabilizing effect depending on the ratios of permittivities and conductivities of the two fluids. In addition, the linear stability analysis for all wavenumbers is carried out numerically using the Chebyshev spectral method, and the various types of neutral stability curves (NSC) obtained are discussed.

Self-propagation of an electrode in leaky dielectrics and its possible relation to bacterial flagellar motors

In this letter, the origin of a force resulting in steady-state propagation of a spherical electrode in a leaky dielectric is explained and the force is calculated. The phenomenon of self-propagation begins from a perturbation in any direction resulting in the electrode motion in that direction. After that, the process sustains itself and a macroscopic electrode moves in the direction of the initial perturbation with a constant velocity U proportional to the potential difference ΔV applied to the system. Microscopic electrodes and bacterial flagellar motors should move with a velocity U∼(ΔV)2. The predicted velocities agree fairly well with the experimental data.

Evolution of a compound droplet attached to a core-shell nozzle under the action of a strong electric field

The shape evolution of small compound droplets at the exit of a core-shell system in the presence of a sufficiently strong electric field is studied both experimentally and theoretically. It is shown that the jetting effect at the tip of the shell nozzle does not necessarily cause entrainment of the core fluid, in which case the co-electrospinning process fails to produce core-shell nanofibers. The remedy lies in extending the core nozzle outside its shell counterpart by about half the radius of the latter. The results also show that the free charges migrate very rapidly from both fluids and their interface to the free surface of the shell. This reflects the fact that most of the prejetting evolution of the droplet can be effectively described in terms of the perfect conductor model, even though the fluids can be characterized as leaky dielectrics. The stress level at the core-shell interface is of the order of 5×103g∕(cms2), the relevant value in assessing the viability of viruses, bacteria, DNA molecules, drugs, enzymes, chromophores, and proteins to be encapsulated in nanofibers via co-electrospinning.

Electrohydrodynamic linear stability of two immiscible fluids in channel flow

The electrohydrodynamic instability of the interface between two viscous fluids with different electrical properties in plane Poiseuille flow has recently found applications in mixing and droplet formation in microfluidic devices. In this paper, we perform the stability analysis in the case where the fluids are assumed to be leaky dielectrics. The two-layer system is subjected to an electric field normal to the interface between the two fluids. We make no assumption on the magnitude of the ratio of fluid to electric time scales, and thus solve the full conservation equation for the interfacial charge. The electric field is found to be either stabilizing or destabilizing, and the influence of the various parameters of the problem on the interface stability is thoroughly analyzed.

Electrohydrodynamic instability of the interface between two fluids confined in a channel

The stability of the interface between two dielectric fluids confined between parallel plates subjected to a normal electric field in the zero Reynolds number limit is studied analytically using linear and weakly nonlinear analyses, and numerically using a thin-layer approximation for long waves and the boundary element technique for waves with wavelength comparable to the fluid thickness. Both the perfect dielectric and leaky dielectric models are studied. The perfect dielectric model is applicable for nonconducting fluids, whereas the leaky dielectric fluid model is applicable to fluids where the time scale for charge relaxation, (ϵϵ0∕σ), is small compared to the fluid time scale (μR∕Γ), where ϵ0 is the dielectric permittivity of the free space, ϵ and σ are the dielectric constant and the conductivity of the fluid, μ and Γ are the fluid viscosity and surface tension, and R is the characteristic length scale. The linear stability analysis shows that the interface becomes unstable when the applied potential exceeds a critical value, and the critical potential depends on the ratio of dielectric constants, electrical conductivities, thicknesses of the two fluids, and surface tension. The critical potential is found to be lower for leaky dielectrics than for perfect dielectrics. The weakly nonlinear analysis shows that the bifurcation is supercritical in a small range of ratio of dielectric constants when the wavelength is comparable to the film thickness, and subcritical for all other values of dielectric constant ratio in the long-wave limit. The thin-film and boundary integral calculations are in agreement with the weakly nonlinear analysis, and the boundary integral calculation indicates the presence of a secondary subcritical bifurcation at a potential slightly larger than the critical potential when the instability is supercritical. When a mean shear flow is applied to the fluids, the critical potential for the instability increases, and the flow tends to alter the nature of the bifurcation from subcritical to supercritical.

Instability of the interface between thin fluid films subjected to electric fields

The effect of an externally applied electric field on the stability of the interface between two thin leaky dielectric fluid films of thickness ratio β and viscosity ratio μ r is analyzed using a linear stability analysis in the long-wave limit. A systematic asymptotic expansion is employed in this limit to derive the coupled nonlinear differential equations describing the evolution of the position of the interface between the fluids and the interfacial free charge distribution. The linearized stability of these equations is determined and the effect of the ratio of the conductivities, dielectric constants, thicknesses, and viscosities on the wavenumber of the fastest growing mode, k max, and the growth rate of the most unstable mode, s max, is examined in detail. Specific configurations considered in previous studies, such as a perfect dielectric–air interface, leaky dielectric–air interface, etc., emerge as limiting cases from the general formulation developed in this paper. Our results show that the viscosity ratio, μ r , does not have any significant effect on k max for the interface between perfect and leaky dielectric fluids. In marked contrast, however, μ r is shown to have a significant effect on the interface between two leaky dielectrics. Increasing μ r from 0.1 to 10 could decrease k max up to a factor of 5. In general, our results show that the presence of nonzero conductivity in either one or both of the fluids has a profound influence on the length-scale characteristic of the linear instability: a reduction even by a factor of 1/50 in the length scale can be effected when compared to the interface between two perfect dielectrics. These predictions could have important implications in pattern formation applications in thin fluid films that employ electric fields. The variation of k max and s max on the thickness ratio, β, indicates in general that k max∝ β − α , and s max∝ β − θ , where the exponents α and θ (both >0) are found to depend only on the ratio of conductivities, and are largely independent of other system parameters.

The RF-CV method for characterization of leaky gate dielectrics

This paper presents a new method, developed for the capacitance–voltage ( C– V) characterization of leaky dielectrics. The method comprises measurements in the gigahertz range on specially designed RF test structures. The method is verified against high-frequency C– V measurements on NMOS and PMOS structures. It yields reliable results even when the gate leakage is in excess of 100 A/cm 2.

Linear oscillations and stability of a liquid bridge in an axial electric field

Small amplitude oscillations of viscous, capillary bridges are studied in the presence of an electric dc field. The electric field is proposed as a means to maintain bridges longer than their perimeter and of uniform cylindrical shape. This is desired in the fabrication of semiconductor crystals. The material of the bridge and the surrounding medium is modeled either as a perfect or as a leaky dielectric. The frequency and the damping rate of the oscillations are calculated numerically by solving a generalized eigenvalue problem. It is shown that they depend on the ratios of the dielectric constants, ε=εin/εout, and conductivities, S=σin/σout, of the two materials, the aspect ratio of the bridge, Λ=πR̃/L̃, the ratio of viscous to the capillary force, Oh=Re−1, which can also be viewed as the inverse Reynolds number of the flow, and, finally, the electrical Bond number, Cel, which is the ratio of the electric stresses to the capillary force. The stability limit of an initially cylindrical bridge is determined with respect to varicose disturbances. In agreement with previous studies it is shown that, if both materials are perfect dielectrics, application of an electric field has a stabilizing effect on the bridge, in the sense that the minimum value, Λmin, of the aspect ratio for the bridge to remain stable drops below 0.5, irrespective of the specific value of the ratio ε. If both materials are leaky dielectrics, bridge stability is determined by the sign of (S−ε) and (S−1)(ε−1), with the positive sign indicating bridge stabilization. The factor (S−ε) arises due to the appearance of a tangential electric stress in the perturbed state for leaky dielectrics. For both cases of leaky and perfect dielectrics, the most unstable mode is the one leading to amphora shaped bridges. It was also found that, when application of an electric field stabilizes the bridge, leaky dielectrics require a lower field than perfect dielectrics and that a large enough field tends to stabilize the bridge for almost the entire range of values of the aspect ratio Λ. These findings concur with earlier analytical results for the stability of jets in longitudinal electric fields and, in conjunction with certain experimental observations, point to the usefulness of the leaky dielectric model pertaining to the stability of bridges.

Measuring Interface State Distributions in Ultra-Thin Mos Capacitors with Direct Tunnel Current Leakage

ABSTRACTUsing a leakage-compensated charge (LCCV) technique to obtain static capacitance-voltage (C-V) curves, we extend the standard high-low C-V method for determining the interface state level density, Dit as a function of energy in the silicon band gap to metal-oxide-silicon capacitors in the direct tunneling regime (oxide thickness ∼<3.5 nm). The LCCV technique yields true static C-V curves for oxides at least as thin as 2.8 nm, where the tunnel leakage current is so high that the usual quasistatic C-V measurement is not possible. As applications of this method, Dit is compared for fresh oxides of different tunnel thickness, and Dit is measured before and after constant voltage stress of a 3.5-nm oxide. The stress results indicate, as in other work on thicker oxides, that interface traps are created during the stress, with peak densities both below and above midgap. This approach is expected to be useful for evaluating both ultra-thin oxides and leaky alternate gate dielectrics.

Double integration of current transients in response to an abrupt change of applied bias: Application to dielectrics

The depolarization current transients are processed in two consecutive steps: initially the feedback capacitor of a charge-to-voltage converter (QVC) is charged by the transient current, which is followed by integrating the output of the QVC via a gated integrator operated in the mode of exponential averaging. Unlike charge transient spectroscopy [QTS; J. W. Farmer, C. D. Lamp, and J. M. Meese, Appl. Phys. Lett. 41, 1063 (1982)], intended originally for high-resistivity semiconductors, the gate aperture duration is set to intervals comparable to the rate window. Since a single channel of our advanced system represents an unrestored time-domain filter, output signals of the three gated integrators are properly combined in an analog mixer, to get a second-order filter [Crowell and Alipanahi, Solid-State Electron. 24, 25 (1980)]. Apart from the selectivity improvement, our multichannel scheme eliminates parasitic charges due to leaky dielectrics. The formalism of the evaluation of kinetic parameters of dipoles is applied to experimentally observed relaxation peaks from Gd-doped CaF2 crystals.