A fractal model of dielectric breakdown and prebreakdown in solid dielectrics

Wiesmann, H. J.; Zeller, H. R.

doi:10.1063/1.337219

Cited by 290 publications

(107 citation statements)

References 4 publications

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“…It is also still not very clear how the molecular dissociation affects the electron behavior and the breakdown strength. Other models, such as the filamentary theories 10,11 for the creation of a breakdown path and the simulation models 12,13 for the shape of breakdown paths, use the breakdown strength as a parameter. They are not concerned with the physics behind the transition of the electron state in the breakdown process.…”

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confidence: 99%

Percolation model for electrical breakdown in insulating polymers

Dissado

Okamoto

2004

Applied Physics Letters

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It is suggested that an electric field above a given value eliminates the barriers to the transport of trapped charge carriers so as to produce an extended state in the form of a percolation cluster, and that the consequent current multiplication results in electrical breakdown. This model provides an estimated value of intrinsic breakdown strength close to the actual value. By considering the interactions between trap barrier potentials, the effect of electrical aging can be explained in terms of an increase in trap density. Many phenomena, such as the effect of weak points and the change of breakdown strength with the content of co-monomers or additives, can also be explained using The mechanism of intrinsic breakdown associated with the transition of electron behavior at high electrical field in insulating polymers is still not clearly understood. Their conduction band is near or above the vacuum level, a large energy gap ͑ϳ8 eV͒ exists between the valence and the conduction bands, 1 and the mean free path is less than 3 nm. 2,3These factors cause the breakdown strength calculated from the classical models for electron driven breakdown to be above 10 9 V/m, 2 much larger than experimental values of the order of 10 8 V / m. It is usually argued that this reduction is related to weak points, such as free volume, submicrovoids, and low-density regions. In the model of free-volume breakdown 4,5 it is noted that the largest empty spaces in polymers may be as large as several decades of nanometers, 5 the longest free path of electron can therefore be large enough for electrons to overcome the trap barrier or to induce impact ionization. However, this model seems only able to describe the development of degradation around the large free volume regions, it is unsatisfactory to explain the overall current multiplication in an intrinsic breakdown process. A contrary example is partial discharge in which breakdown may not occur at all even though the internal gas cavity has been discharged.In respect of electrical aging it has been suggested that the creation of low-density regions near the electrodes at high fields is a necessary step leading to breakdown. 6,7 The formation of such regions is associated with molecular dissociation due to the energy released in the trapping process of hot electrons, 2 in kinetic energy transfer during spacecharge injection and extraction processes, 8 or lattice deformation on charge trapping.9 However, these aging models do not seem suitable for instantaneous impulse breakdown when low-density regions have no time to form. It is also still not very clear how the molecular dissociation affects the electron behavior and the breakdown strength. Other models, such as the filamentary theories 10,11 for the creation of a breakdown path and the simulation models 12,13 for the shape of breakdown paths, use the breakdown strength as a parameter. They are not concerned with the physics behind the transition of the electron state in the breakdown process. This letter proposes a percolation model f...

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confidence: 99%

Percolation model for electrical breakdown in insulating polymers

Dissado

Okamoto

2004

Applied Physics Letters

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“…In all of their papers, they solve numerically the problem of the leader channel development within the framework of a Poisson three-dimensional equation with allowance for the external field and the use of a stochastic model of the dielectric breakdown, which dates back to fundamental works [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Modeling of the Intracloud Lightning Discharge Radio Emission

Иудин

Iudin

Hayakawa³

2015

Radiophys Quantum El

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This paper aims at analyzing the broadband part of electromagnetic emission from thunderclouds in a frequency range of tens of kilohertz to hundreds of megahertz. A model of the intracloud lightning discharge formation is presented. The lightning formation is described as a stochastic growth of the branching discharge channels, which is determined by the electrostatic field. The dynamics of the electric field and of the charge distribution over the lightning structure is calculated deterministically. The effect of the initial charge density in the cloud and the parameters of the conducting channels on spatio-temporal characteristics of the currents and structure of the lightning discharge is studied. The discharge radio emission is calculated by summing up the radiation fields of each channel at the observation point. The standard model for a separate discharge current is adopted, and the electromagnetic radiation in the far zone is estimated. It is found that the obtained frequency spectra exhibit a universal power-law behavior. The results of the modeling agree with known experimental data.

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“…The presence of such patterns is typical when dielectric breakdown has occured, where the direction of the growth follows the regions of highest electric field strength. 24 From the experimental data it is reasonable to assume that at an increased voltage the active area at the pore tip is increased such that a higher porosity results. Figure 19 shows the thickness of the porous sub-layers versus the transferred charge obtained from the last PECE experiment performed in the section Voltage controlled experiments (see Table IV) with adjusted time intervals.…”

Section: Discussionmentioning

confidence: 99%

Stacked Layers of Different Porosity in 4H SiC Substrates Applying a Photoelectrochemical Approach

Leitgeb

Zellner

Hufnagl

et al. 2017

J. Electrochem. Soc.

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Porous 4H-SiC layers were prepared from monocrystalline samples applying photo-electrochemical etching in hydrofluoric acid. The influence of both current and voltage controlled mode during photo-electrochemical porosification was investigated. It was found that the resulting degree of porosity, the homogeneity in porosity as well as the pore morphology mainly depend on the applied voltage, whereas the current level has an almost negligible impact on these important parameters. Based on these results, it is proposed that the formation of porous SiC during photo-electrochemical etching can be described by fractal growth. Finally the gathered knowledge allowed to detach the porous 4H-SiC layers, which comprised several sub-layers of alternating degree of porosity, from the 4H-SiC substrate. Such layers of tailored porosity are key components for several advanced device concepts such as optical filters or membranes for biological applications. A common method to prepare porous Si is electrochemical etching in HF based solutions.1 There are numerous application scenarios of porous Si, such as electrode material in super-capacitors, 2 as sacrificial layer in the production of MEMS devices 3 or as optical filters in bio-or vapor-sensors. 4,5 In the last application scenario, a stacked layer of porous silicon is electrochemically etched into a silicon wafer. The individual porous layers of the stack show alternating degrees of porosity and thus have a different index of refraction. This results in a wavelength selective reflection of optical light.6 Undoubtedly, porous Si is a well-established material for future micro-or nanomachined device architectures, but it shows a poor chemical stability when exposed to e.g. air at higher temperatures or alkaline electrolytes. 7,8 Therefore it has to be covered with a dense protective layer when operation in harsh or biological environments is targeted.9 This drawback encourages research devoted to other porous materials that can be used instead of porous Si without a surface protection. A promising candidate is porous SiC prepared from single crystalline wafers because it shows a higher chemical stability than silicon.10 In contrast to electrochemical etching of Si, photo-electrochemical etching (PECE) of SiC in HF based etching solutions is a comparably challenging task and hence, only a limited number of publications exist.11,12 Some authors report a skin layer on top of the porous structure, which exhibits only a few pores with diameters in the nm range.13,14 This skin layer is followed by a cap layer which shows an irregular porous structure. 15 This problem has been addressed recently by a combination of metal assisted photochemical etching with PECE. 16 Metal assisted photochemical etching (MAPCE) can be utilized to generate a layer in the μm range prior to PECE. The pore tips of this porous layer provide initiation sites for PECE. Thus, neither a skin nor a cap layer are observed.Furthermore some authors report about an increased porosity at the bottom of the porous laye...

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A fractal model of dielectric breakdown and prebreakdown in solid dielectrics

Cited by 290 publications

References 4 publications

Percolation model for electrical breakdown in insulating polymers

Percolation model for electrical breakdown in insulating polymers

Modeling of the Intracloud Lightning Discharge Radio Emission

Stacked Layers of Different Porosity in 4H SiC Substrates Applying a Photoelectrochemical Approach

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