Dielectric Breakdown Model Research Articles

Modelling-Augmented Failure Diagnostics in Planar SiC MOS Devices Using TDDB Measurements

In this study we analyzed the physical mechanisms governing time-dependent dielectric breakdown (TDDB) and we used TDDB physical model of dielectric breakdown, implemented in the defect-centric Ginestra® modeling platform, to deconvolute the intrinsic material properties effects and geometry feature impact on the gate oxide (GOx) and SiC-device breakdown.

Quantitative modeling of oxide growth in plasma electrolytic oxidation of titanium

Plasma electrolytic oxidation (PEO) has been extensively applied in the past to improve tribological properties of titanium and its alloys allowing their widespread use in industrial applications. However, the complete PEO mechanism of action remains unclear. While there are several mathematical models providing useful insights into the PEO process, they do not fully incorporate the effect of applied potential on the outcomes of PEO. In this work, we develop an experimentally informed computational model by expanding on the dielectric breakdown model. We incorporate experimental data to extract key parameters, exploring the iterative dependency of the oxide thickness and ionic current density to predict the oxide growth at various applied external voltages. The model reproduces the PEO process at different potentiostatic conditions and the simulation results for the oxide coating thickness over time is in good agreement with the experimental data, validating the application of Faraday's law and Pyun and Hong's model in describing the coating growth kinetics for the PEO process (Dehnavi et al., 2014/07/25/ 2014; Arrabal et al., 2009/05/30/ 2009; Rakoch et al., 2006/03/01 2006; Ma et al., 2017/10/10/ 2017; Pyun and Hong, 1992/02/01/ 1992; Caire et al., 2007/02/07 2007) [1-6].

Modeling of Charge-to-Breakdown with an Electron Trapping Model for Analysis of Thermal Gate Oxide Failure Mechanism in SiC Power MOSFETs.

The failure mechanism of thermal gate oxide in silicon carbide (SiC) power metal oxide semiconductor field effect transistors (MOSFETs), whether it is field-driven breakdown or charge-driven breakdown, has always been a controversial topic. Previous studies have demonstrated that the failure time of thermally grown silicon dioxide (SiO2) on SiC stressed with a constant voltage is indicated as charge driven rather than field driven through the observation of Weibull Slope β. Considering the importance of the accurate failure mechanism for the thermal gate oxide lifetime prediction model of time-dependent dielectric breakdown (TDDB), charge-driven breakdown needs to be further fundamentally justified. In this work, the charge-to-breakdown (QBD) of the thermal gate oxide in a type of commercial planar SiC power MOSFETs, under the constant current stress (CCS), constant voltage stress (CVS), and pulsed voltage stress (PVS) are extracted, respectively. A mathematical electron trapping model in thermal SiO2 grown on single crystal silicon (Si) under CCS, which was proposed by M. Liang et al., is proven to work equally well with thermal SiO2 grown on SiC and used to deduce the QBD model of the device under test (DUT). Compared with the QBD obtained under the three stress conditions, the charge-driven breakdown mechanism is validated in the thermal gate oxide of SiC power MOSFETs.

SPICE simulation of the time-dependent clustering model for dielectric breakdown

In this letter, a method for dealing with the time-dependent dielectric breakdown (TDDB) of oxide layers in MOS and MIM structures in the framework of SPICE simulations is reported. In particular, we focus the attention on the clustering model (Burr’s XII distribution) for dielectric breakdown which can be considered an extension of the well known Weibull model. The oxide time-to-breakdown for both models is calculated using the inversion method for the cumulative distribution function. For the sake of completeness, the proposed approach includes uncorrelated variability both in the initial and final resistance states. For illustrative purposes, it is also shown how voltage acceleration, progressive breakdown or any other correlation factor can be introduced in the simulation parameters. As an application example, the proposed method is used to simulate the simplest case of a gate-to-drain dielectric breakdown of a NMOS-based inverter circuit.

Stability of Regularized Hastings–Levitov Aggregation in the Subcritical Regime

We prove bulk scaling limits and fluctuation scaling limits for a two-parameter class ALE(α,η)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha },\\eta )$$\\end{document} of continuum planar aggregation models. The class includes regularized versions of the Hastings–Levitov family HL(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha })$$\\end{document} and continuum versions of the family of dielectric-breakdown models, where the local attachment intensity for new particles is specified as a negative power -η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\eta $$\\end{document} of the density of arc length with respect to harmonic measure. The limit dynamics follow solutions of a certain Loewner–Kufarev equation, where the driving measure is made to depend on the solution and on the parameter ζ=α+η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\zeta }={\\alpha }+\\eta $$\\end{document}. Our results are subject to a subcriticality condition ζ⩽1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\zeta }\\leqslant 1$$\\end{document}: this includes HL(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha })$$\\end{document} for α⩽1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\alpha }\\leqslant 1$$\\end{document} and also the case α=2,η=-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\alpha }=2,\\eta =-1$$\\end{document} corresponding to a continuum Eden model. Hastings and Levitov predicted a change in behaviour for HL(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha })$$\\end{document} at α=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\alpha }=1$$\\end{document}, consistent with our results. In the regularized regime considered, the fluctuations around the scaling limit are shown to be Gaussian, with independent Ornstein–Uhlenbeck processes driving each Fourier mode, which are seen to be stable if and only if ζ⩽1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\zeta }\\leqslant 1$$\\end{document}.

Modeling and simulation of successive breakdown events in thin gate dielectrics using standard reliability growth models

The application of constant electrical stress to a metal–insulator-semiconductor (MOS) or metal–insulator-metal (MIM) structure can generate multiple breakdown events in the dielectric film. Very often, these events are detected as small jumps in the current–time characteristic of the device under test and can be treated from the stochastic viewpoint as a counting process. In this letter, a wide variety of standard reliability growth models for this process are assessed in order to determine which option provides the best simulation results compatible with the experimental observations. For the generation of the breakdown event arrivals, two alternative stochastic methods for the power-law Poisson process are investigated: first, the inversion algorithm for the cumulative distribution function and second, an on-the-fly method based on the so-called rejection algorithm. Though both methods are equivalent, the first one is more appropriate for data analysis using spreadsheet calculations while the second one is highly suitable for circuit simulation environments like LTSpice. The connection of the selected nonhomogeneous Poisson process with the Weibull model for dielectric breakdown is also discussed.

In-situ observation and evaluation of silver precipitation behavior in borosilicate glass

Applying voltage to alkali-containing glass, doped with silver ions by the solid-state ion-exchange method, yields silver precipitates inside the glass. We attempted in-situ observation of the precipitation phenomena to elucidate the silver precipitation mechanisms, where the direction of the voltage application was rotated 90 deg. to increase the precipitation area compared to that of our previous method. The results show that the shape of the precipitate changed from clumpy to dendritic as the applied voltage increased. The shape of the precipitate, predicted by the dielectric breakdown model, implied that the higher the precipitation probability (i.e., the higher the frequency of a silver ion to encounter with the precipitate), the more branches the precipitate formed. In addition, the un-doped, silver-doped, and silver-precipitated areas inside the glass were modeled as electrical resistances to predict the growth behavior of the precipitated areas.

Energy storage optimization of ferroelectric ceramics during phase-transition process of amorphous/nanocrystalline and polycrystalline by using a phase-field model for dielectric breakdown

Ferroelectric ceramics have the potential to be widely applied in the modern industry and military power systems due to their ultrafast charging/discharging speed and high energy density. Considering the structural design and electrical properties of ferroelectric capacitor, it is still a challenge to find out the optimal energy storage of ferroelectric ceramics during the phase-transition process of amorphous/nanocrystalline and polycrystalline. In this work, a finite element model suitable for the multiphase ceramic system is constructed based on the phase field breakdown theory. The nonlinear coupling relationship of multiple physical fields between multiphase ceramics was taken into account in this model. The basic structures of multiphase ceramics are generated by using the Voronoi diagram construction method. The specified structure of multiphase ceramics in the phase- transition process of amorphous/nanocrystalline and polycrystalline was further obtained through the grain boundary diffusion equation. The simulation results show that the multiphase ceramics have an optimal energy storage in the process of amorphous polycrystalline transformation, and the energy storage density reaches the maximum when the crystallinity is 13.96% and the volume fraction of grain is 2.08%. It provides a research plan and idea for revealing the correlation between microstructure and breakdown characteristics of multiphase ceramics. This simulation model realizes the nonlinear coupling of the multiphase ceramic mesoscopic structure and the phase field breakdown. It provides a reference scheme for the structural design and performance optimization of ferroelectric ceramics.

Reliability of Wide Band Gap Power Electronic Semiconductor and Packaging: A Review

Wide band gap (WBG) power electronic devices, such as silicon carbide metal–oxide–semiconductor field-effect transistors (SiC MOSFETs) and gallium–nitride high-electron-mobility transistors (GaN HEMTs) have been widely used in various fields and occupied a certain share of the market with rapid momentum, owing to their excellent electrical, mechanical, and thermal properties. The reliability of WBG power electronic devices is inseparable from the reliability of power electronic systems and is a significant concern for the industry and for academia. This review attempts to summarize the recent progress in the failure mechanisms of WBG power electronic semiconductor chips, the reliability of WBG power electronic packaging, and the reliability models for predicting the remaining life of WBG devices. Firstly, the typical structures and dominant failure mechanisms of SiC MOSFETs and GaN HEMTs are discussed. This is followed by a description of power electronic packaging failure mechanisms and available packaging materials for WBG power electronic devices. In addition, the reliability models based on physics-of-failure (including time-dependent dielectric breakdown models, stress–strain models, and thermal cycling models), and data-driven models are introduced. This review may provide useful references for the reliability research of WBG power devices.

Memristor compact model with oxygen vacancy concentrations as state variables

We present a unique compact model for oxide memristors based upon the concentration of oxygen vacancies as state variables. In this model, the increase (decrease) in oxygen vacancy concentration is similar in effect to the reduction (expansion) of the tunnel gap used as a state variable in existing compact models, providing a mechanism for the electronic current to increase (decrease) based upon the polarity of the applied voltage. Rate equations defining the dynamics of state variables are obtained from simplifications of a recent paper in which electronic processes (i.e., electron capture/emission) were combined with atomic processes (i.e., Frenkel-pair generation/recombination, diffusion) stemming from the thermochemical model of dielectric breakdown. Central to the proposed model is the effect of the electron occupancy of oxygen vacancy traps on resistive switching dynamics. The electronic current is calculated considering Ohmic, band-to-band, and bound-to-band contributions. The model includes uniform self-heating with Joule heating and conductive loss terms. The model is calibrated using experimental current–voltage characteristics for HfO2 memristors with different electrode materials. Though a general model is presented, a delta-shaped density of states profile for oxygen vacancies is found capable of accurately representing experimental data while providing a minimal description of bound-to-band transitions. The model is implemented in Verilog-A and tested using read/write operations in a 4×4 1T1R nonvolatile memory array to evaluate its ability to perform circuit simulations of practical interest. A particular benefit is that the model does not make strong assumptions regarding filament geometry of which scant experimental-evidence exists to support.

Numerical Simulation of the Lightning Leader Development and Upward Leader Initiation for Rotating Wind Turbine

Lightning accidents seriously threaten safe operation of wind turbines because the influence mechanisms of wind turbine rotation on corona and upward leader initiation are, so far, not clear. A three-dimensional stochastic evolution model of the lightning downward leader was established by combining the dielectric breakdown model and the lightning current shunt method, according to which the charge density distribution of leader branches was determined. The corona and leader initiation mechanisms of rotating wind turbine were studied based on the 3D drift and diffusion model of ion flow in the neighboring space of a rotating wind turbine. The results show that due to blade rotation, the charged particles are unevenly distributed near the blade tip and the contours are in a strip-like shape. As the rotating speed increases, the blade tip is more susceptible to initiating corona discharge. Combining the three-dimensional stochastic development model of the lightning downward leader and ion distribution model near a rotating wind turbine, the initiation direction of the upward leader was analyzed, and in 66% of cases, the initiation direction of the upward leader on the blade tip was on the back side of the blade rotation.

Influence of rate of voltage rise on positive leader inception in long-air-gap discharge

Positive leader inception under different rates of voltage rise is a key element in physical modeling of dielectric breakdown of long air gaps and evolution of natural lightning. The leader inception phase comes first in long-air-gap discharge, including first corona, primary dark period, and second corona, which is also called “leader corona,” portending leader inception. The Les Renardières Group has stated that the primary dark period is determined by the electrode curvature, based on which no leader inception model currently in use considers the influence of the rate of the applied voltage. To determine whether that assertion is true, an experimental scheme is designed so that impulse voltages can be applied with a large range of rise rates. With an increasing rate of voltage rise, the test results clearly show the following: (i) the curves relating the injected charge and inception voltage of the first corona present regular differences; (ii) the duration of the primary dark period decreases exponentially; (iii) the leader inception voltage and the difference between the leader and first-corona inception voltages present decreasing trends. These findings indicate that the formation of the dark period is related to more than just the electrode curvature, which is just one cause but may not be the essential reason for the dark period. The present findings suggest that the rate at which the applied voltage rises impacts the physical process of the streamer-to-leader transition during the dark period.

SPICE Simulation of RRAM-Based Cross-Point Arrays Using the Dynamic Memdiode Model

We thoroughly investigate the performance of the Dynamic Memdiode Model (DMM) when used for simulating the synaptic weights in large RRAM-based cross-point arrays (CPA) intended for neuromorphic computing. The DMM is in line with Prof. Chua’s memristive devices theory, in which the hysteresis phenomenon in electroformed metal-insulator-metal structures is represented by means of two coupled equations: one equation for the current-voltage characteristic of the device based on an extension of the quantum point-contact (QPC) model for dielectric breakdown and a second equation for the memory state, responsible for keeping track of the previous history of the device. By considering ex-situ training of the CPA aimed at classifying the handwritten characters of the MNIST database, we evaluate the performance of a Write-Verify iterative scheme for setting the crosspoint conductances to their target values. The total programming time, the programming error, and the inference accuracy obtained with such writing scheme are investigated in depth. The role played by parasitic components such as the line resistance as well as some CPA’s particular features like the dynamical range of the memdiodes are discussed. The interrelationship between the frequency and amplitude values of the write pulses is explored in detail. In addition, the effect of the resistance shift for the case of a CPA programmed with no errors is studied for a variety of input signals, providing a design guideline for selecting the appropriate pulse’s amplitude and frequency.

Breakdown strength and energy density enhancement in polymer-ceramic nanocomposites: Role of particle size distribution

Polymer-ceramic nanocomposites play a very promising role for energy-storage in high power electronics and advanced pulsed power systems, due to their extremely fast charge-discharge capability. The low energy density is the key factor hindering their application, for which large endeavors have been made in the modulation of the fraction, morphology, size, and dispersion of the particle fillers but small in that of the size distribution, which is critical for energy-storage performance. We first investigated the role of this based on simulated nanocomposites with controlled lognormal distributions via a generation algorithm devised in this work. Dielectric response, breakdown behavior and energy-storage performance were explored for distributions with different standard deviations (SD) and mean values (MV), which were solved with the energy equivalence basis and a phase-field dielectric breakdown model. With the decrease of SD and MV, the effective permittivity declines slightly with enhanced permittivity change, which was related with the enhanced local electric field with intensified fluctuation and should be originated from the major contribution of the polymer matrix from the local energy perspective; whereas improved nominal breakdown strength was achieved owing to the weakened local maximum electric field, which leads to distinctly increased nominal energy density despite the slight decline of the permittivity. Keeping the fillers within a narrow disperse outperforms employing super fine particles. This work demonstrates that enhancement in breakdown strength and energy density can be attained via particle size distribution modulation, paving a new way for the further improvement of the energy-storage performance of polymer-ceramic nanocomposites.

Phase field modeling of dielectric breakdown of ferroelectric polymers subjected to mechanical and electrical loadings

Ferroelectric polymers have attracted increasing attention due to their distinguished dielectric and piezoelectric properties. Dielectric breakdown is one of the main failure behaviors for ferroelectric polymers. Understanding dielectric breakdown of ferroelectric polymers under mechanical and electrical loadings is crucial to their applications in energy storage and conversion devices with high-energy-density. In the present work, a multi-field coupling phase field model is developed to investigate the dielectric breakdown of ferroelectric polymers under mechanical and electrical loadings. To describe the effect of mechanical stresses on the evolution path and critical electric field of dielectric breakdown, a strain-dependent breakdown energy is proposed in the phase field model. The phase field simulations show that a compressive stress restrains the branching of the breakdown path and increases the critical electric field of breakdown. On the contrary, a tensile stress accelerates the branching of the breakdown path and decreases the critical electric field of breakdown. The results in the present work may stimulate further experimental investigations on the effect of mechanical stresses on the dielectric breakdown of ferroelectric polymers and provide a guidance for improving the breakdown strength of ferroelectric polymers through a mechanical way.

Significantly enhanced dielectric breakdown strength of ferroelectric energy-storage ceramics via grain size uniformity control: Phase-field simulation and experimental realization

The utilization of ferroelectric ceramics in electrical energy storage has become a hot topic due to the urgent need for advanced pulsed power and high power energy storage applications. Much attention has been paid to achieving nanograined ferroelectric ceramics but little to the effect of grain size uniformity, which is critical for dielectric breakdown and reliability. We first investigated this effect via a model based on virtually constructed ceramic samples solved with the phase-field method. Ferroelectric ceramic samples with the same average grain size of typically 100 nm but different uniformity degrees by the variation of the standard deviation values of 83.7, 81.9, 80.1, and 78.7 were constructed via Voronoi tessellation based on a controlled seeding method. The effect of grain size uniformity on the dielectric breakdown was studied through a phase-field dielectric breakdown model. The results indicate that with the standard deviation decreasing, the dielectric breakdown strength is distinctly enhanced. Experimentally, BaTiO3-based ceramics with the same average grain size of 100 nm but different uniformity degrees were realized via conventional sintering and two-step sintering methods. The grain size uniformity of two-step sintered ceramics is greatly improved, which leads to the breakdown strength and discharge energy density of the two-step sintered ceramics about 50% and 100% larger than those of the conventionally sintered ones. This work demonstrates that significant enhancement in dielectric breakdown strength of ferroelectric energy-storage ceramics can be achieved via grain size uniformity control, shedding light on the meticulous design and fine tuning of the energy-storage properties of ferroelectric ceramics.

Numerical modeling and simulation of the electric breakdown of rocks immersed in water using high voltage pulses

Selective breakdown of mineralized particles by using high-voltage pulses (HVP) has been reported, yet its mechanisms are not fully understood, and the HVP setting factors affecting its efficacy in ore pre-concentration for the mining industry are not established. This study investigates the electro-dynamic mechanisms of electric breakdown by using the time-transient dielectric breakdown model and the finite-difference numerical method. Monte-Carlo method with random sampling is applied to calculate breakdown probabilities. The model and the selected parameters have been validated by the published experimental data of the electric breakdown of mineralized synthetic particles. The simulations of pulse rising time from 150 ns to 1 μs showed that the HVP breakdown threshold of rock particles gradually increased as the pulse rising time decreased. This suggests that to minimize the mis-breakdown of barren rocks in the HVP-enabled ore pre-concentration application, it is important to use a generator with a short pulse rising time. Shorter pulses also led to a higher probability of the internal breakdown of the mineralized particles. The simulations indicate that inhomogeneity of conductivity in an ore particle caused the streamers to bend toward the area of inclusion with high conductivity in a host rock matrix, which increased the probabilities of the breakdown of this mineralized particle. This phenomenon was more pronounced as conductivity rose. High-conductivity inclusions can reduce the minimum voltages required for the breakdown of the mineralized particles.

Life-time degradation of STT-MRAM by self-heating effect with TDDB model

Spin-transfer torque magnetic random access memory (STT-MRAM) is one of the most promising candidates for “universal memory” with the ultra-fast access speed, radiation resistance and theoretically unlimited endurance. However, there are many practical aspects that could degrade the life-time of STT-MRAM. In this paper, degradation on the life-time of the STT-MTJ device is observed experimentally, which is attributed to the so-called “self-heating effect” of the device. Simulation on the device is conducted on the self-heating effect to obtain the internal temperature inside the device. The self-heating effect of the STT-MTJ device is analyzed and its influence on the life-time degradation of the STT-MTJ is included in the time dependent dielectric breakdown model (TDDB, 1/E model). This inclusion should improve the accuracy of the estimation on the life-time.

Proposal of finite element analysis method for dielectric breakdown based on Maxwell’s equations

This paper proposes a new approach to the simulation of discharge phenomena in dielectric breakdown including field fluctuations based on Maxwell’s equations in the finite element framework without introducing the artificial stochastic disturbance. This method is based on the idea that field fluctuations caused by the development of electrical treeing propagates as electromagnetic wave governed by Maxwell’s equations, and triggers next dielectric breakdown in a chain reaction. The obtained model can be regarded as the equivalent circuit model in which the resistors representing local property of material are arranged. The key point of the proposed method is the ease of expressing dielectric breakdown as replacement of the arranged resistors. Dielectric breakdown expressed as the local change of conductivity leads to the inhomogeneity of the conductivity. In addition to this simplest model for dielectric breakdown, constraint on the discharge paths to the finite edges in the circuit is applied. This corresponds to the introduction of the implicit inhomogeneity. This implicit inhomogeneity plays a significant role in the process of formation of branching discharge patterns. The capability of introduction of the implicit inhomogeneity and the constraint on the possible candidates for propagation paths enable the proposed method to find out a bifurcated solution and make it easier to analyze formation of discharge patterns in dielectric breakdown. This paper explains these features of the proposed mathematical model with results of numerical simulation of several example problems.

On the rock-breaking mechanism of plasma channel drilling technology

Plasma channel drilling (PCD), which is also known as high-voltage electric pulse drilling, is a highly efficient rock-breaking drilling technology with great development potential. This paper presents a method to study the rock-breaking mechanism of PCD technology. Then based on the predecessor's foundation, the factors affecting the development of plasma channels are explored using the dielectric breakdown model (DBM). Finally, a numerical rock-breaking model considering electric-thermal-mechanical three fields is established. This paper reveals the basic rock-breaking process of PCD and how the formation pressure affects the rock-breaking process of PCD technology. The main conclusions are: the formation law of plasma channel is related to the electrode structure and the inputting electrical parameters, the electrical properties of the rock and the type of rock; the plasma channel has an internal dynamic effect on the rock breaking process, and this internal dynamic effect of the plasma channel is sharply weakened after the channel is formed; shear cracks play a lead role in PCD, and the number of shear cracks is larger than that of conventional mechanical-rotary drilling; the formation pressure has little effect on the rock failure, the total volume of the chips, and the total number of cracks in the PCD, and the rock-breaking efficiency is not limited by the drilling depth. Finally, in order to improve the rock breaking-efficiency, it is recommended that the PCD technology be used in conjunction with slim hole drilling technology or jet drilling technology.