Breakdown Voltage Research Articles

Electrical surface breakdown characteristics of micro- and nano-Al2O3 particle co-doped epoxy composites

Abstract Epoxy microcomposites are basic materials for gas-insulated switchgear (GIS) spacers that are subjected to huge electrical stress. Previous works have indicated that nanoparticles are beneficial to dielectric performance. However, surface electrical breakdown, a typical fault in GIS of co-doped micro- and nanoparticles in epoxy composites, is seldom studied. In this work, numerous concentrations of micro- and nano-Al2O3 are co-doped into an epoxy matrix; the surface traps, surface charging, and surface breakdown voltages (V sb) of the co-doped composites are studied, and the influence of micro- and nano-Al2O3 on the electrical surface breakdown is clarified. The results show that V sb first decreases and then increases with the microparticles, and V sb decreases from 25.34 kV to 19.52 kV. As the number of nanoparticles increases, V sb increases and then decreases when the microparticle loading is low, but decreases and then increases when the microparticle loading exceeds 40 wt%. Micro-Al2O3 particles introduce surface shallow traps into epoxy composites, while small amounts of nano-Al2O3 introduce deep traps. Two different mechanisms dominate the surface charging and V sb of epoxy micro-nanocomposites. When the surface conductivity is lower than 7 × 10−14 S, the surface charges are reduced by the suppression of electrode injection as the trap depth increases, and V sb increases. When the surface conductivity exceeds 7 × 10−14 S, the surface charge dissipation rate increases with the surface conductivity and V sb increases as the surface conductivity increases. Our work indicates that co-doped micro- and nano-particles should keep the surface conductivity away from the specic value (7 × 10−14 S) to safeguard insulation properties for GIS spacers.

Performance Recovery of p‐GaN Etch‐Induced Degradation via Atomic Layer Deposition In Situ N2 Plasma and Postanneal‐Assisted Passivation

The etching of p‐GaN requires extremely strict control over etching depth and morphology; otherwise, it will result in poor electrical characteristics. This work uses ALD(Atomic layer deposition) in situ N2 plasma and postanneal‐assisted passivation to effectively recover the electrical properties degraded by p‐GaN etching. Compared to unpassivated devices, this approach eliminates surface oxygen bonds, recovering drain current from 10 to 126 mA mm−1, reducing gate leakage by an order of magnitude, achieving an ON/OFF current ratio exceeding 108, a breakdown voltage of 930 V at 1 μA mm−1, and effectively suppressing current collapse.

Revealing two-dimensional electric field crowding effect in breakdown performance of DPPT-TT polymer-based OFETs

The diketopyrrolopyrrole-based polymer (DPPT-TT) has been employed in organic power field effect transistors due to its exceptional off-state breakdown performance. The impact of organic semiconductor layer thickness on the breakdown performance has not been explored. In this study, we investigate the impact of DPPT-TT layer thickness on the breakdown voltage (BV) by fabricating organic field effect transistors (OFETs) with various DPPT-TT layer thicknesses. Our findings reveal that the devices' BV is a strong function of DPPT-TT layer thickness, and reducing the DPPT-TT layer thickness from 68 to 15 nm results in a decrease in BV from 291 to 86 V, attributed to the two-dimensional (2D) electric field crowding effect. An analytical model utilizing the 2D Poisson equation reveals an electric field at the DPPT-TT layer's surface. Thinner DPPT-TT layer exhibits larger electric field peak, leading to premature breakdown near the drain electrode. The relationship between breakdown electric field and DPPT-TT layer thickness was established by fitting the experimental data to the model, revealing an average BV error of only 8.8%. This phenomenon is validated to be ubiquitous in polymer based OFETs via DPPT-TT-based and P3HT-based devices. According to the proposed model, this 2D electric field crowding effect can be mitigated by adjusting the dielectric layer thickness (tD) and/or the dielectric material.

Improvement of Single Event Transient Effects for a Novel AlGaN/GaN High Electron-Mobility Transistor with a P-GaN Buried Layer and a Locally Doped Barrier Layer

In this paper, a novel AlGaN/GaN HEMT structure with a P-GaN buried layer in the buffer layer and a locally doped barrier layer under the gate (PN-HEMT) is proposed to enhance its resistance to single event transient (SET) effects while also overcoming the degradation of other characteristics. The device operation mechanism and characteristics are investigated by TCAD simulation. The results show that the peak electric field and impact ionization at the gate edges are reduced in the PN-HEMT due to the introduced P-GaN buried layer in the buffer layer. This leads to a decrease in the peak drain current (Ipeak) induced by the SET effect and an improvement in the breakdown voltage (BV). Additionally, the locally doped barrier layer provides extra electrons to the channel, resulting in higher saturated drain current (ID,sat) and maximum transconductance (gmax). The Ipeak of the PN-HEMT (1.37 A/mm) is 71.8% lower than that of the conventional AlGaN/GaN HEMT (C-HEMT) (4.85 A/mm) at 0.6 pC/µm. Simultaneously, ID,sat and BV are increased by 21.2% and 63.9%, respectively. Therefore, the PN-HEMT enhances the hardened SET effect of the device without sacrificing other key characteristics of the AlGaN/GaN HEMT.

Improvement of DC Performance and RF Characteristics in GaN-Based HEMTs Using SiNx Stress-Engineering Technique

In this work, the DC performance and RF characteristics of GaN-based high-electron-mobility transistors (HEMTs) using the SiNx stress-engineered technique were systematically investigated. It was observed that a significant reduction in the peak electric field and an increase in the effective barrier thickness in the devices with compressive SiNx passivation contributed to the suppression of Fowler–Nordheim (FN) tunneling. As a result, the gate leakage decreased by more than an order of magnitude, and the breakdown voltage (BV) increased from 44 V to 84 V. Moreover, benefiting from enhanced gate control capability, the devices with compressive stress SiNx passivation showed improved peak transconductance from 315 mS/mm to 366 mS/mm, along with a higher cutoff frequency (ft) and maximum oscillation frequency (fmax) of 21.15 GHz and 35.66 GHz, respectively. Due to its enhanced frequency performance and improved pinch-off characteristics, the power performance of the devices with compressive stress SiNx passivation was markedly superior to that of the devices with stress-free SiNx passivation. These results confirm the substantial potential of the SiNx stress-engineered technique for high-frequency and high-output power applications, which are crucial for future communication systems.

Study on the electrical performance degradation mechanism of β -Ga2O3 p-n diode under heavy ion radiation

The impact of heavy ion irradiation on the β-Ga2O3 p-n diode and its physical mechanism have been studied in this Letter. After the irradiation fluence of 1 × 108 cm−2, it is observed that the electrical performance of the device is significantly degraded. The forward current density (JF) is reduced by 49.4%, the reverse current density (JR) is increased by more than two orders of magnitude, and the breakdown voltage (VBR) is decreased by 30%. Based on the results of the deep-level transient spectroscopy measurement, it is concluded that acceptor-like traps generated with an energy level of EC-0.75 eV in the β-Ga2O3 drift layer dominate the JF degradation of the device, which are most likely related to Ga vacancies. These acceptor-like traps result in the reduction of change carrier concentration, which in turn leads to a decrease in JF. In addition, according to the conductive atomic force microscope measurements and theoretical calculation, it is clearly observed that the latent tracks induced by heavy ion irradiation can act as leakage paths, leading to a significant degradation of JR and VBR.

Review on Short-Circuit Protection Methods for SiC MOSFETs

SiC MOSFETs have been a game-changer in the domain of power electronics, thanks to their exceptional electrical traits. They are endowed with a high breakdown voltage, reduced on-resistance, and superior thermal conductivity, which make them supremely suitable for high-power and resilient applications across aviation, automotive, and renewable energy sectors. Despite their intrinsic advantages, SiC MOSFETs also necessitate advanced safeguarding mechanisms to counteract the vulnerability to short-circuit conditions due to their lower short-circuit robustness. This review paper offers an in-depth analysis of the array of short-circuit protection (SCP) methods applied to SiC MOSFETs. This paper scrutinizes techniques such as desaturation detection, di/dt detection, gate charge characteristics monitoring, two-dimensional monitoring, Rogowski coil-based detection, and two-stage turn-off strategies. The paper meticulously explores the operational principles, merits, and limitations of each method, with an emphasis on their adaptability to various fault types, including hard switching faults and load-induced faults. This review acts as a thorough compendium, guiding the choice of pertinent SCP strategies, ensuring the secure and efficient functioning of SiC MOSFETs in demanding applications.

Experimental investigation of zinc ferrite/insulation oil nanofluid natural convection heat transfer, AC dielectric breakdown voltage, and thermophysical properties

Improving the thermal and dielectric properties of insulation oil (INO) with nanoadditives is an important challenge, and achieving dispersion stability in these nanofluids is quite challenging, necessitating further investigation. The main goal of this study is the synthesis and use of the hydrophobicity of zinc ferrite (ZnFe2O4) nanoparticles, which can improve both the thermal and dielectric properties of the INO. This oil is made from distillate (petroleum), including severely hydrotreated light naphthenic oil (75–85%) and severely hydrotreated light paraffinic oil (15–25%). A comprehensive investigation was carried out, involving the creation of nanofluids with ZnFe2O4 nanoparticles at various concentrations, and employing various characterization methods such as X-ray diffraction (XRD), Fourier-transform infrared (FTIR), scanning electron microscopy, energy dispersive X-ray (EDX), zeta potential analysis, and dynamic light scattering (DLS). The KD2 Pro thermal analyzer was used to investigate the thermal characteristics, including the thermal conductivity coefficient (TCC) and volumetric heat capacity (VHC). Under free convection conditions, the free convection heat transfer coefficient (FCHTC) and Nusselt numbers (Nu) were evaluated, revealing enhancements ranging from 14.15 to 11.7%. Furthermore, the most significant improvement observed in the AC Breakdown voltage (BDV) for nanofluids containing 0.1 wt% of ZnFe2O4 amounted to 17.3%. The most significant finding of this study is the improvement in the heat transfer performance, AC BDV, and stability of the nanofluids.

Operational Characteristics of AlGaN/GaN High-Electron-Mobility Transistors with Various Dielectric Passivation Structures for High-Power and High-Frequency Operations: A Simulation Study

This study investigates the operational characteristics of AlGaN/GaN high-electron-mobility transistors (HEMTs) by employing various passivation materials with different dielectric constants and passivation structures. To ensure the simulation reliability, the parameters were calibrated based on the measured data from the fabricated basic Si3N4 passivation structure of the HEMT. The Si3N4 passivation material was replaced with high-k materials, such as Al2O3 and HfO2, to improve the breakdown voltage. The Al2O3 and HfO2 passivation structures achieved breakdown voltage improvements of 6.62% and 17.45%, respectively, compared to the basic Si3N4 passivation structure. However, the increased parasitic capacitances reduced the cut-off frequency. To mitigate this reduction, the operational characteristics of hybrid and partial passivation structures were analyzed. Compared with the HfO2 passivation structure, the HfO2 partial passivation structure exhibited a 7.6% reduction in breakdown voltage but a substantial 82.76% increase in cut-off frequency. In addition, the HfO2 partial passivation structure exhibited the highest Johnson’s figure of merit. Consequently, considering the trade-off relationship between breakdown voltage and frequency characteristics, the HfO2 partial passivation structure emerged as a promising candidate for high-power and high-frequency AlGaN/GaN HEMT applications.

Ultra-Low On-Resistance W/β-Ga2O3 Junction Barrier Schottky Rectifiers

The on-resistance of Ga2O3 rectifiers with different metal anodes was measured from the forward current-voltage characteristics. The use of W anode metal produces low on-resistance of 0.34 mΩ.cm2 for W/Au/ β-Ga2O3 Schottky Barrier Diode (SBD) rectifiers and 0.22 mΩ.cm2 for heterojunction Diode (HJD) NiO/β-Ga2O3 rectifiers, overcoming the generally much larger values obtained using Ni or Pt metal. These are the lowest on-resistances reported for Ga2O3 rectifiers. The turn-on voltage was 0.22 V for SBD and 1.69 V for HJDs. By changing the anode metal, we varied the effective barrier height, which also affects reverse breakdown voltage. The switching characteristics were measured for the different device types, with reverse recovery times of 30.6 ns for SBDs and 33.0 ns for HJDs and slew rates of 2 A.μs−1 for both types of devices. Using a simple change of anode metal allows the achievement of a broad range of breakdown voltage and on-resistance, which allows for tailoring the rectifier performance depending on the application.

Lateral NiO/AlN Heterojunction Rectifiers with Breakdown Voltage >11 kV

Lateral NiO/AIN heterojunction diodes (HJDs) with breakdown voltage up to 11.6 kV and Ni/Au/AlN Schottky barrier diodes (SBDs) with VB of 8.6 kV were fabricated on layers grown on sapphire substrates by metalorganic chemical vapor phase deposition. The power figure-of-merits VB 2/RON where RON is the on-resistance were 0.31 MW·cm−2 for HJD and 0.16 MW·cm−2 for SBD. The lowest turn-on voltages were ∼2.03 and 1.91 V for HJDs and SBDs, respectively, with ON/OFF ratios up to 102. The maximum field before breakdown was 0.45 MV·cm−1 in HJDs and 0.31 MV·cm−1 in SBDs. These correspond to <3% of the critical field in AlN of ∼15 MV·cm−1. This work demonstrates there is still significant optimization to be done in the overall quality of the AlN, including purity, crystal perfection, and defect density to realize the potential of this material as an ultra-wide bandgap semiconductor for efficient multi-kV power switching applications. Our results also demonstrate the promise of NiO as a p-type conducting oxide for forming heterojunctions with AlN.

Capacitance reduction in AlGaN/GaN heterojunction diodes through thermally oxidized NiO anode

In this study, a thin barrier AlGaN/GaN heterojunction diode with a NiO anode is proposed. NiO as an anode combined with a 5 nm AlGaN barrier layer can significantly deplete two-dimensional electron gas in the anode region of the device. Combined with the etching-free technology, the damage caused by etching the AlGaN barrier layer is successfully avoided. The capacitance of the device was reduced from 28 pF mm−1 (Schottky) to 966 fF/mm (NiO) which reduced 97%. At the same time the NiO anode devices with a reverse current leakage of ~10−8 A/mm@−100V achieved a high current ON/OFF ratio of ~10-8. NiO not only reduces the capacitance and leakage of the device but also enhances its anti-collapse ability. Without using the structure of field plates, the breakdown voltage of the device was also increased compared with the Schottky diode.

Ta5+-substitution effects on crystal structure and ferroelectric property in HfO2-based films

To investigate the Ta5+-substitution effects on crystal structure and ferroelectric property in HfO2-based films, Ta x Hf1−x O2+δ films with various film thicknesses and Ta content were prepared. The ferroelectric orthorhombic phase was formed in a wide film thickness range of 20–100 nm while in a narrow composition range of x = 0.10–0.14. These thickness-insensitive and composition-sensitive characteristics of Ta5+-substituted HfO2 film are similar to Y3+ rather than Zr4+. The X-ray photoelectron spectroscopy measurement suggests that the ionic state of Ta is not reduced and Ta x Hf1−x O2+δ film has an excess oxygen state. The excess oxygen may consist of a combination of oxygen vacancies and more interstitial oxygens. These defects facilitate the formation of the ferroelectric phasebut also decrease the breakdown voltage and increase the leakage current in Ta5+-substituted HfO2 films. On the other hand, the generation of excess oxygen indicates the possibility of controlling oxygen vacancies which deteriorate fatigue and retention properties.

Impact of silicon carbide, boron nitride, and zirconium dioxide nanoparticles on ester‐based dielectric fluids

AbstractThis research study investigates the influence of various nanoparticles on the dielectric breakdown voltage, oil dissipation factor, viscosity, and thermal conductivity of nanofluids. Nanofluids were prepared using synthetic ester oil as the base fluid, and three nanoparticles, silicon carbide (SiC), boron nitride (BN), and zirconium dioxide (ZrO2), were added at different concentrations (0.125 wt%, 0.250 wt%, and 0.375 wt%), which are basically the nano‐sized powder that can be blended in the oil. The dielectric breakdown voltage testing was conducted to evaluate the electrical performance of the nanofluids. Additionally, rheological measurements were performed to study the kinematic viscosity, while thermal conductivity was determined using appropriate techniques. The enhancements in each property were evaluated and compared for the different nanoparticle concentrations and types. Previous studies focused only on the investigation of the electrical properties of nanofluids. However, in the present study, the electrical as well as thermo‐physical characterisation of nanofluids is performed and analysed as they directly affect the cooling performance of transformers. The results provide dielectric and thermo‐physical characterisation that exhibit excellent insulation and cooling functionalities and valuable insights into the potential applications of nanofluids as dielectrics in various high‐voltage electrical equipment. ZrO2 and SiC nanoparticles exhibited a reduction in the oil dissipation factor. SiC consistently improved breakdown voltage (Bdv), while ZrO2 nanoparticles showed concentration‐dependent effects, enhancing Bdv at low concentrations but degrading it at higher ones. Unexpectedly, nanoparticle dispersion and lubrication effects can lead to viscosity reductions, countering conventional expectations. Surprisingly, at the highest concentration, the thermal conductivity decreases compared to the lower nano‐concentrations in synthetic ester oil.

Effects of NiO doping and trench wall tilt on Ga2O3 PiN diodes performance

Gallium Oxide (Ga2O3) is a promising material for next-generation power semiconductors due to its wide bandgap (∼4.9 eV), high Baliga's figure of merit (FOM) (3444 W/cmK), and high breakdown field (Ec, 8 MV/cm). To achieve high blocking and low leakage current, research has been conducted on PN heterojunctions and bevel structures. In this paper, we performed simulations using Sentaurus TCAD to investigate the impact of NiO doping concentration and NiO's trench tilt angle on the electrical characteristics of NiO/Ga2O3 PiN diodes with trench NiO. As the NiO doping concentration increased, the resistance decreased from 21.5 to 7.5 mΩcm2, and we observed the expansion of depletion from NiO to the NiO/Ga2O3 interface. Furthermore, we confirmed a reduction in resistance and a change in breakdown voltage with an increase in NiO trench tilt. By understanding the optimal angle to mitigate the concentration of high electric fields in the edge region, we anticipate the fabrication of stable Ga2O3 PiN diodes.

Enhanced breakdown voltage for p-GaN gate AlGaN/GaN HEMT on AlN/Si with triple trenches: A simulation study

This study presents an analysis of an AlGaN/GaN high-electron-mobility transistor (HEMT) with a triple-trench structure (TT-HEMT) for the enhancement of breakdown voltage, which is often limited by the high electric field near the gate edge. Using COMSOL Multiphysics, simulations were run, with trenches made of gallium nitride (GaN) constructed between the GaN and aluminum nitride (AlN) nucleation layers. Each trench was positioned directly beneath the source, gate, and drain contacts. Under the metal gate, a p-type doped GaN cap is added to produce an enhancement mode device, which is more desirable in high-power applications. The results indicate that the effective dispersion of the electric field distribution enhances the breakdown voltage of the device by 70 % in comparison to a conventional HEMT. Additionally, the impact of various design parameters, such as the p-GaN doping concentration and the metal gate work function on the electrical performance, was also investigated. Overall, the proposed device structure exhibits superior electrical properties for high-power applications.

Achievement of low turn-on voltage in Ga2O3 Schottky and heterojunction hybrid rectifiers using W/Au anode contact

The use of the low work function (4.5 eV) tungsten (W) as a rectifying contact was studied to obtain low on-voltages in W/Ga2O3 Schottky rectifiers and NiO/Ga2O3 heterojunction rectifiers that were simultaneously fabricated on a single wafer. The devices were produced with varying proportions of relative areas and diameters, encompassing a spectrum from pure Schottky Barrier Diode (SBD) to pure Heterojunction Diode (HJD) configurations. The turn-on voltages with W contacts ranged from 0.22 V for pure Schottky rectifiers to 1.50 V for pure HJDs, compared to 0.66 and 1.77 V, respectively, for Ni/Au contacts. The reverse recovery times ranged from 31.2 to 33.5 ns for pure Schottky and heterojunction rectifiers. Switching energy losses for the SBD with W contacts were ∼20% of those for HJDs. The reverse breakdown voltages ranged from 600 V for SBDs to 2400 V for HJDs. These are the lowest reported turn-on voltage values for 600/1200 V-class Ga2O3 rectifiers that extend the range of applications of these devices down to the voltages of interest for electric vehicle charging applications.

The impact of LSM pretreatment on the growth behavior, electrical insulation and corrosion resistance properties of PEO coating on 6061 aluminum alloy

This work reported the influence of laser surface melting (LSM) pretreatment on the growth behavior, electrical insulation and corrosion resistance of plasma electrolytic oxidation (PEO) film on 6061 aluminum alloy. It is found that the LSM pretreatment refines the surface structure of original Al metal, generating defects that store excessive energy, thereby enhancing reaction kinetics and phase transition during the PEO process. By LSM pretreatment, uniform electrical discharge and film growth can be obtained, resulting in fewer defects and lower porosity in PEO layers. Additionally, a large amount of columnar crystals comprising of SiO2 phase are observed, which transformed from the SiO32− deposited on the surface, and the LSM pretreatment significantly improves the electrical insulation, corrosion resistance, and substrate adhesion of following PEO layer. Under the same PEO treatment duration, the breakdown voltage of coating increased by 100 V, and icorr decreased from 3.26 × 10−4 to 9.13 × 10−6 A cm−2. It is expected that the combination of LSM and PEO processes can not only enhance the surface properties of Al metal, but also expand the practical application of aluminum alloy in high-power electronic devices and related fields.

Parametric Analysis of Indium Gallium Arsenide Wafer-based Thin Body (5 nm) Double-gate MOSFETs for Hybrid RF Applications.

The electrical behavior of a high-performance Indium Gallium Arsenide (In- GaAs) wafer-based n-type Double-Gate (DG) MOSFET with a gate length (LG1= LG2) of 2 nm was analyzed. The relationship of channel length, gate length, top and bottom gate oxide layer thickness, a gate oxide material, and the rectangular wafer with upgraded structural characteristics and the parameters, such as switch current ratio (ION/IOFF) and transconductance (Gm) was analyzed for hybrid RF applications. This work was carried out at 300 K utilizing a Non-Equilibrium Green Function (NEGF) mechanism for the proposed DG MOSFET architecture with La2O3 (EOT=1 nm) as gate dielectric oxide and source-drain device length (LSD) of 45 nm. It resulted in a maximum drain current (IDmax) of 4.52 mA, where the drain-source voltage (VDS) varied between 0 V and 0.5 V at the fixed gate to source voltage (VGS) = 0.5 V. The ON current(ION), leakage current (IOFF), and (ION/IOFF) switching current ratios of 1.56 mA, 8.49Í10-6 μA, and 18.3Í107 μA were obtained when the gate to source voltage (VGS) varied between 0 and 0.5 V at fixed drain-source voltage (VDS)=0.5V. The simulated result showed the values of maximum current density (Jmax), one and twodimensional electron density (N1D and N2D), electron mobility (μn), transconductance (Gm), and Subthreshold Slope (SS) are 52.4 μA/m2, 3.6Í107 cm-1, 11.36Í1012 cm-2, 1417 cm2V-1S-1, 3140 μS/μm, and 178 mV/dec, respectively. The Fermi-Dirac statistics were employed to limit the charge distribution of holes and electrons at a semiconductor-insulator interface. The flat-band voltage (VFB) of - 0.45 V for the fixed threshold voltage greatly impacted the breakdown voltage. The results were obtained by applying carriers to the channels with the (001) axis perpendicular to the gate oxide. The sub-band energy profile and electron density were well implemented and derived using the Non-Equilibrium Green's Function (NEGF) formalism. Further, a few advantages of the proposed heterostructure-based DG MOSFET structure over the other structures were observed. This proposed patent design, with a reduction in the leakage current characteristics, is mainly suitable for advanced Silicon-based solid-state CMOS devices, Microelectronics, Nanotechnologies, and future-generation device applications.

Influence of different factors on gap breakdown process with hot electrode and high temperature gas medium in low voltage circuit breaker chamber based on particle-in-cell/Monte-Carlo collision simulation

Different factors such as gas composition inside the low voltage circuit breaker (LVCB) chamber and the residual plasma in the post-arc stage affect the breakdown process, which in turn affects the breaking capacity of LVCBs. In this paper, the effects of non-parallel electrode structure, gas temperature and pressure, electrode temperature, and gap distance on gap breakdown of hot electrode under high temperature gas conditions were studied, for which a particle-in-cell/Monte-Carlo collision simulation model has been established, which takes into account the effects of high-temperature gas components, cathode electron thermal emission, electron collision ionization and other effects, and simulation studies have been conducted. The simulation results show that the increase in gap gas temperature, the decrease in air pressure, and the increase in electrode temperature will lead to the gap breakdown more easily. With the increase in the gap length, the breakdown voltage increases, but the average electric field intensity required for breakdown decreases. In the non-parallel electrode structure, the breakdown occurs first at the position with the shortest gap distance, then the cathode sheath forms and extends along the electrode surface to other areas, and finally, the entire gap breaks down.