Breakdown Measurements Research Articles

(Invited) Beta- Gallium (Aluminum) Oxide Epitaxial Thin Films, Heterostructures and in-Situ Dielectrics for High Performance Electronics

In this talk, we will provide an overview of epitaxial growth, doping and channel engineering techniques towards β-Ga2O3 high-performance power and high frequency devices. Metal-organic vapor phase epitaxy (MOVPE) offers several advantages such as high carrier mobility, scalability, and in-situ growth of various heterostructures including Aluminum Gallium Oxide ternary alloys and Al2O3 in-situ dielectrics.Study of intentional silicon doping is undertaken to understand uniform doping, delta doping and modulation doping in β-Ga2O3 thin films and heterostructures. Low temperature epitaxy is demonstrated with sharp doping profiles and high carrier mobility, enhancing the growth window of high quality β-Ga2O3 thin films. By understanding surface riding of dopants, delta doping is achieved in MOVPE-grown β-Ga2O3 with a sharp doping profile by controlling the substrate temperature. This also enabled the first demonstration of MOVPE-grown pure 2D electron channel in β-Ga2O3 material system without any parallel conduction in the Aluminum Gallium Oxide barrier layer. The absence of parallel conduction is confirmed using low temperature hall measurements. A low-temperature undoped buffer scheme developed resulted in record high electron mobilities in uniformly Si-doped β-Ga2O3 thin films. Material quality is further evidenced by high current β-Ga2O3 fin shape transistors with power figure of merit close to 1 GW/cm2. In-situ growth of Al2O3 dielectrics on β-Ga2O3 epilayers with breakdown field strength as high as 6-10 MV/cm is achieved, showing promise towards realization of β-Ga2O3 MOSFETs with in-situ dielectrics.Vertical power devices require high purity, low-doped drift layers. To this effect, we report on the growth of both intentionally low-doped (~ 7 x 1015 cm-3 ) and unintentionally doped (UID) β-Ga2O3 homoepitaxial films (~ 2 x 1015 cm-3) using MOCVD with high room temperature mobilities and thicknesses of up to 187-190 cm2/V•s and 4.5- 6.2 μm respectively. By optimizing the VI/III ratio, 6.3 μm UID film was grown with a flat charge density profile (verified by isolated Van der Pauw Hall and vertical C-V measurements) of 2.4 x 1015 cm-3, a high Hall mobility of 190 cm2/V•s, and RMS surface roughness values of 1.3 nm. Vertical Schottky barrier diodes were formed on the 6.3 μm thick drift layer and the J-V measurements showed a high rectification ratio of >109. Finally, breakdown measurements were performed and the parallel plane field at the center of the anode was found to be 2.05 MV/cm (without any field management), which is the highest reported for any MOVPE-grown vertical diode. The mobility values in the intentional and unintentionally doped films are the highest reported at these background concentration levels and suggest very low compensation in the grown films. The growth of these high-mobility and low background concentration thick β-Ga2O3 films is a crucial step forward towards realizing thick epitaxial drift layers for efficient > 10 kV vertical power devices, which can be very attractive for grid-scale electronics.We acknowledge funding from the Coherent/II–VI Foundation Block Gift Program and Air Force Office of Scientific Research, under Award No. FA9550-21-1-0078 (Program Manager: Dr.Ali Sayir).

Hypersonic Stability and Breakdown Measurements on the AFRL/AFOSR BOLT II Flight Geometry

The Air Force Research Laboratory/Air Force Office of Scientific Research (AFRL/AFOSR) introduced the Boundary Layer Turbulence (BOLT II) flight experiment to further the understanding and modeling of a hypersonic turbulent boundary layer on a geometry that features concave surfaces with swept leading edges. In support of the flight experiment, this paper identifies and documents the transition instabilities and quantifies the breakdown to turbulence on a 25%-scale BOLT II model in hypersonic flow. Experiments were conducted in the conventional Actively Controlled Expansion wind tunnel facility and the Mach 6 Quiet Tunnel located at the Texas A&M University National Aerothermochemistry and Hypersonics Laboratory. Global surface heating was viewed using infrared thermography with on-surface measurements made using high-frequency Kulite and PCB Piezotronics surface pressure transducers. Modal growth was observed among the sensors both upstream and downstream of the model. Off-surface measurements were made in the mixed-mode region utilizing constant-temperature hot-film anemometry in the Mach 6 Quiet Tunnel. Comparisons were made to the Direct Numerical Simulation (DNS) results from the University of Minnesota. Amplified content was observed between f=53 and 75 kHz in the root-mean-square voltage fluctuations of the hot-film measurements.

Electrical breakdown mechanism and life prediction of thermal-aged epoxy/glass fibre composites

Epoxy/glass fibre composites possess excellent mechanical and electrical properties and are widely utilised in electrical and electronic power equipment. However, the composites exhibit relatively poor thermal conductivity, causing the temperature of the composites to increase during the operation of power equipment, resulting in a significant reduction in the electrical breakdown strength. Although the effects of thermal aging on polymeric materials have been widely studied, its influence on electrical strength mechanisms has not been investigated at the molecular level. In this study, epoxy/glass fibre composite specimens were subjected to accelerated thermal aging treatment for 360 h at 180 °C. Functional groups, molecular chain dynamics, and electrical breakdown are characterised using infrared spectroscopy, dielectric spectroscopy, and breakdown measurement. Subsequently, electrical breakdown mechanism and life prediction of the thermally aged composites are discussed. During thermal aging, the epoxy resin molecular chains undergo continuous oxidation and chain scission, which generate numerous polar functional groups and short chains and an increase in the free volume. This triggers an enhancement in the chain segmental dynamics, thereby significantly reducing the activation energy of the epoxy resin. After 360 h, activation energy decreased from 0.78 eV to 0.67 eV. The DC breakdown voltages of the specimens decreased from 168.28 kV/mm to 134.91 kV/mm. An insulation life prediction model for thermally aged epoxy/glass fibre composites is established based on the time-temperature equivalence theory. The prediction results indicate that the service life of the operational composites is approximately 11.2 years at 353 K, which is consistent with engineering experience.

Electrodes for High‐𝜅 Molecular Crystal Antimony Trioxide Gate Dielectrics for 2D Electronics

AbstractWafer‐scale deposition of high‐𝜅 gate dielectrics compatible with atomically thin van der Waals layered semiconductors (e.g., MoS2, WS2, WSe2) is urgently needed for practical applications of field effect transistors based on 2D materials. A study on a high‐𝜅 molecular crystal antimony trioxide (Sb2O3) gate dielectric examined the role of electrode material on dielectric degradation and breakdown. It is demonstrated that the thin films of Sb2O3 can be uniformly deposited on a wafer scale. The current–voltage (I–V) curves show tightly controlled distributions of both leakage current and breakdown voltage. Electrical measurements reveal that defects are generated gradually upon electrical stressing. The evaluation of degradation is based on charge trapping, stress‐induced leakage current, and dielectric breakdown measurements. The breakdown voltage distribution follows a tight monomodal Weibull distribution suggesting a high quality of the film. Comparing Ti and Au as gate electrodes, both the breakdown field and the tunnel current are affected by the choice of electrode material. Transmission electron microscopy reveals that the chemistry at the electrode/Sb2O3 interface plays an important role and that Ti scavenges oxygen from the Sb2O3, forming a defective oxide layer at the Ti/Sb2O3 interface. For the Au electrode, this interfacial reaction is completely absent, improving the dielectric performance.

Ferroelectric Aluminum Scandium Nitride Transistors with Intrinsic Switching Characteristics and Artificial Synaptic Functions for Neuromorphic Computing.

Aluminum Scandium Nitride (Al1-xScxN) has received attention for its exceptional ferroelectric properties, whereas the fundamental mechanism determining its dynamic response and reliability remains elusive. In this work, an unreported nucleation-based polarization switching mechanism in Al0.7Sc0.3N (AlScN) is unveiled, driven by its intrinsic ferroelectricity rooted in the ionic displacement. Fast polarization switching, characterized by a remarkably low characteristic time of 0.00183ps, is captured, and effectively simulated using a nucleation-limited switching (NLS) model, where the profound effect of defects on the nucleation and domain propagation is systematically studied. These findings are further integrated into Monte Carlo simulations to unravel the influence of the activation energy for ferroelectric switching on the distributions of switching thresholds. The long-term reliability of devices is also confirmed by time-dependent dielectric breakdown (TDDB) measurements, and the effect of thickness scaling is discussed. Ferroelectric field-effect transistors (FeFETs) are demonstrated through the integration of AlScN and 2D MoS2 channel, where biological synaptic functions can be emulated with optimized operation voltage. The artificial neural network built from AlScN-based FeFETs achieves 93.8% recognition accuracy of handwritten digits, demonstrating the potential of ferroelectric AlScN in future neuromorphic computing applications.

An analog to digital converter in a SiC CMOS technology for high-temperature applications

Integrated circuits based on wide bandgap semiconductors are considered an attractive option for meeting the demand for high-temperature electronics. Here, we report an analog-to-digital converter fabricated in a silicon carbide complementary metal–oxide–semiconductor technology now available through Europractice. The MOSFET component in this technology was measured up to 500 °C, and the key parameters, such as threshold voltage, field-effect mobility, and channel-length modulation parameters, were extracted. A 4-bit flash data converter, consisting of 266 transistors, is implemented with this technology and demonstrates correct operation up to 400 °C. Finally, the gate oxide quality is investigated by time-dependent dielectric breakdown measurements at 500 °C. A field-acceleration factor of 4.4 dec/(MV/cm) is obtained by applying the E model.

Deposition of high-quality, nanoscale SiO2 films and 3D structures

Silicon dioxide (SiO2) is ubiquitous in biomedical diagnostics and other applications as a capture medium for nucleic acids and proteins. Diagnostic devices have seen rapid miniaturisation in recent years, due to the increased demand for portable point-of-care diagnostics. However, there are increasing challenges with incorporating SiO2 nanostructures into diagnostic devices, due to the complexity of nanostructured SiO2 synthesis, often involving etching and chemical vapour deposition under high vacuum conditions.We report a novel and straightforward method for deposition of high-quality, nanoscale SiO2 films and 3D SiO2 structures using thermal decomposition of polydimethylsiloxane (PDMS), in a furnace at atmospheric pressure at 500 °C. This method allows individual nanometre controllability of conformal pinhole-free layers on a variety of materials and morphologies. The temperature ramp rate is a key factor in determining the SiO2 deposit morphology, with slower ramp rates leading to highly conformal 2D films and faster ones yielding 3D nanodentrite structures. For the 2D films, the film thickness, as determined by spectroscopic ellipsometry and confirmed by SEM data, is shown to correlate excellently with initial PDMS source material mass in the thickness range 0.8–18 nm. Fits to ellipsometry models confirm that the refractive index of the deposited film matches the expected value for SiO2, while electrical breakdown measurements confirm that the breakdown strength of the films is comparable to that of high-quality thermal oxides. Depositions on high aspect ratio ZnO nanostructures are shown to be highly conformal, leading to core-shell ZnO-SiO2 nanostructures whose shell thickness is in excellent agreement with the expected values from deposition on planar substrates. At faster ramp rates an abrupt morphological transition is seen to a deposit which displays a 3D nanodentrite morphology. The possibilities for applications of both morphologies (and core-shell combinations with other nanostructured materials) in biosensing and related areas are briefly discussed, and the DNA capture capabilities of each nanostructure are measured. The high aspect ratio nanodendrite structures allow for significant DNA capture within microfluidic devices in the presence of low DNA concentrations, with a maximum average capture efficiency of 43.4 % achieved in the presence of 10 ng/mL of DNA, which is an improvement by a factor of ∼ 3 over planar Si surfaces. Improvements by factors of >10 over planar surfaces were achieved at higher DNA concentrations of 100 and 1000 ng/mL.

A novel approach towards parametric assessment of reliability and resilience of high voltage mica‐based insulation systems by statistical analysis of experimental failure data

AbstractInsulation systems in high‐voltage electric machines play a pivotal role in the reliable operation and longevity of the equipment. Mica‐based insulation materials have proven to possess and maintain excellent dielectric properties in the long run and prevent premature insulation degradation. Numerous qualifications tests, such as voltage endurance, are outlined in IEC and IEEE standards. The authors, however, take a different parametric approach, opting for reliability assessment of insulation systems using derived three‐parameter Weibull models. Therefore, instead of simple pass–fail criteria, empirical data is employed to determine failure rate probabilities quantitatively and objectively. Experimental data, including breakdown, dissipation factor, and partial discharge measurements, are used to construct the Weibull distribution model to predict fault and failure rates and calculate hazard functions. The rigorous examinations interpreted through the analytical model help assess insulation system resilience and particularly the impact of electrical field stress and mica content. Variation of electrical stress from 66.75 to 71.20 V/mil demonstrated how the mean time to failure of the system changed from 146.4 to 85.1 at 3 Un, hence identifying opportunities for design improvement and uncovering performance boundaries. Ultimately, the developed framework enhances comprehension of insulation system failure probabilities, guiding design decisions and ensuring a secure and reliable operation of electrical machines across applications.

Dielectric breakdown behavior of ferroelectric HfO2 capacitors by constant voltage stress studied by in situ laser-based photoemission electron microscopy

In situ laser-based photoemission electron microscopy observations with time-dependent dielectric breakdown measurements of TiN/Hf0.5Zr0.5O2(HZO)/TiN ferroelectric capacitors were performed to reveal the dielectric breakdown (DB) mechanism. We succeeded in visualizing the hard DB spots through the top electrode. We found that capacitors with short- and long-lifetime distributions were broken down near and far from the edge of the capacitors, respectively. This indicates that the DB is either topography-dependent or film-quality-dependent. This work demonstrates an effective method of detecting DB in a non-destructive manner to provide an insight for achieving higher endurance HfO2-based ferroelectric capacitors.

Graphene-All-Around Cobalt Interconnect with a Back-End-of-Line Compatible Process.

The graphene-all-around (GAA) structure has been verified to grow directly at 380 °C using hot-wire chemical vapor deposition, within the thermal budget of the back end of the line (BEOL). The cobalt (Co) interconnects with the GAA structure have demonstrated a 10.8% increase in current density, a 27% reduction in resistance, and a 36 times longer electromigration lifetime. X-ray photoelectron spectroscopy and density functional theory calculations have revealed the presence of bonding between carbon and Co, which makes the Co atom more stable to resist external forces. The ability of graphene to act as a diffusion barrier in the GAA structure was confirmed through time-dependent dielectric breakdown measurement. The Co interconnect within the GAA structure exhibits enhanced electrical properties and reliability, which indicates compatibility applications as next-generation interconnect materials in CMOS BEOL.

Wide‐Bandgap Nickel Oxide with Tunable Acceptor Concentration for Multidimensional Power Devices

AbstractMultidimensional power devices can achieve performance beyond conventional limits by deploying charge‐balanced p‐n junctions. A key obstacle to developing such devices in many wide‐bandgap (WBG) and ultra‐wide bandgap (UWBG) semiconductors is the difficulty of native p‐type doping. Here the WBG nickel oxide (NiO) as an alternative p‐type material is investigated. The acceptor concentration (NA) in NiO is modulated by oxygen partial pressure during magnetron sputtering and characterized using a p‐n+ heterojunction diode fabricated on gallium oxide (Ga2O3) substrate. Capacitance and breakdown measurements reveal a tunable NA from < 1018 cm−3 to 2×1018 cm−3 with the practical breakdown field (EB) of 3.8 to 6.3 MV cm−1. This NA range allows for charge balance to n‐type region with reasonable process latitude, and EB is high enough to pair with many WBG and UWBG semiconductors. The extracted NA is then used to design a multidimensional Ga2O3 diode with NiO field‐modulation structure. The diodes fabricated with two different NA both achieve 8000 V breakdown voltage and 4.7 MV cm−1 average electric field. This field is over three times higher than the best report in prior multi‐kilovolt lateral devices. These results show the promise of p‐type NiO for pushing the performance limits of power devices.

MoS2 as an Effective Cu Diffusion Barrier with a Back-End Compatible Process.

This study demonstrates molybdenum disulfide (MoS2) as a superior candidate as a diffusion barrier and liner. This research explores a newly developed process to show how effectively MoS2 can be applied. First, a new approach is developed to prepare molybdenum disulfide (MoS2) by microwave plasma-enhanced sulfurization (MW-PES). MW-PES can rapidly and directly grow on the target substrate at low temperatures, which is compatible with the back-end-of-line (BEOL) technology. Second, the performance of MW-PES MoS2 as a diffusion barrier and liner is reported in the subsequent section. Through time-dependent dielectric breakdown (TDDB) measurements, MoS2 is shown to have a barrier property better than that of the current material, Ta, with the same thickness. According to the model fitting, the lifetime of the device is about 45.2 times the lifetime under normal operating conditions. Furthermore, MoS2 shows its superior thermal stability in maintaining the barrier properties. MoS2 is proven to be an excellent interface as a liner as it can provide sufficient adhesion and wettability to further effectively reduce the surface scattering of copper (Cu) and significantly lower the circuit resistance.

Electrical characteristics of in situ Mg-doped β-Ga2O3 current-blocking layer for vertical devices

The lack of p-type doping has impeded the development of vertical gallium oxide (Ga2O3) devices. Current blocking layers (CBLs) using implanted deep acceptors have been used to demonstrate vertical devices. This paper presents a pioneering demonstration of in situ Mg-doped β-Ga2O3 CBLs grown using metal–organic chemical vapor deposition. The Mg-doping density during growth was calibrated by quantitative secondary ion mass spectroscopy. Electrical test structures were designed with in situ Mg doped layers with various targeted Mg doping concentrations. The effectiveness of the CBL is characterized by using temperature-dependent current–voltage measurements using n-Mg-doped-n structures, providing crucial insight into the underlying mechanisms. Pulsed measurements show similar blocking characteristics as DC. To further validate the experimental results, a TCAD simulation is performed, and the electrically active effective doping is found to be dependent on the Mg-doping density, offering an alternate perspective on the optimization of CBL performance. Breakdown measurements show a peak 4 MV/cm field strength.

Size effect and electrical ageing of PDMS dielectric elastomer with competing failure modes

Large-scale dielectric elastomer generators dielectric elastomer generators (DEGs) such as those employed in wave energy converter projects require a significant volume of electrically stressed materials. Meanwhile, predictions of energy output from such systems are generally extrapolated from electrical and mechanical breakdown measurements performed on small scale samples, where the presence of small defects can be extremely small. This can lead to overly optimistic upscaled predictions for the performance and reliability of full-scale devices. In this study, multilayer DEGs were prepared to evaluate the dielectric breakdown strength of thin polydimethylsiloxane PDMS elastomer at different values of active areas. The results indicated the presence of two separate breakdown mechanisms resulting in an enhanced size effect and a reduced reliability for the larger samples. Electrical ageing tests were performed on three different sample geometries and the dielectric breakdown strength was found to be marginally affected by the time under stress. A Weibull competing failure model was applied to the distribution of experimental breakdowns and electrical reliability was accurately modeled over more than four decades of variation in the electrode area.

Synergism in SF6 mixtures with C=C−C backbone compounds

A positive synergy in the electric strength was observed in a previous study in SF6/HFO1234ze(E) mixtures which was shown to result from a strong electron energy moderation capability of HFO1234ze(E) combined with thermal electron attachment of SF6 (Egüz et al 2022 J. Phys. D: Appl. Phys. 55 315203). In the present work, the electron energy moderation properties of compounds with a similar C=C−C backbone are investigated. Swarm and breakdown measurements are performed in pure gases and in mixtures with SF6. Compounds with a trifluoromethyl group (−CF3) showed lower characteristic energy and as a consequence a positive synergism with SF6. Descriptors related to electron energy moderation are identified and computed; a clear trend is found from the analysis of descriptors related to inelastic processes which suggest(s) that vibrational excitations may be the main source of electron energy loss in the compounds showing positive synergy.

1/f noise of short-channel indium tin oxide transistors under stress

In this work, we investigate the reliability and stability of short-channel indium tin oxide (ITO) field-effect transistors through 1/f noise characterization at elevated temperature with positive bias temperature instability (PBTI). The 1/f noise behavior of a short-channel 60-nm-long channel ITO transistor can be described by the carrier number fluctuation model, suggesting that carrier trapping and de-trapping by trap states within the 5 nm thin high-κ HfLaO dielectric are the dominant mechanisms affecting 1/f noise. Small positive threshold voltage shifts of 0.042 and 0.057 V after PBTI measurements of 3000 s at 25 and 85 °C have been obtained, respectively. The higher gate leakage current at elevated temperature leads to an earlier breakdown in the time-dependent dielectric breakdown measurement. Furthermore, 1/f noise after PBTI has also been carried out at elevated temperature, and the degradations after stress can also be attributed to the stress induced traps inside the gate dielectric.

Measurements of Breakdown and Buildup of Thixotropy in Cement Pastes Containing Diatomaceous Earth

This paper proposes a comprehensive series of protocols that can make quantitative measurements on both breakdown and buildup aspects of thixotropic behaviors of cement pastes. While measuring breakdown and buildup separately, the correlations between these two aspects have also been investigated. Cement pastes with different water-to-binder ratios (w/b=0.4, 0.5 and 0.6) and different replacement levels of Diatomaceous Earth (DE) (0%, 2%, 6% and 10% by weight of cement) were studied. To simulate the real on-site conditions, parameters such as pressure and temperature were also considered during the measurement. The research found that increase in DE replacement dosage can reduce the energy required to breakdown thixotropic structure of cement pastes while no specific trend on buildup aspect was observed. Among the three used w/b ratios, the 0.5 w/b ratio has the most reduction effect in breakdown energy, where using 10% DE can lead to 65% of energy reduction in breakdown compared to the control sample. However, the measured yield stress for these specimens were very similar to each other. In addition, increase in temperature significantly increases the buildup ratio of cement pastes while increase in pressure as high as 20 MPa has a minimal impact on thixotropic properties of cement pastes.

Capacitive Extensometry for the Estimation of Meaningful Stretch-Dependent Dielectric Strength of Dielectric Elastomer

The electromechanical performance of a dielectric elastomer (DE) is greatly influenced by the dielectric strength of the elastomeric materials. The dielectric strength of an elastomer profoundly depends on the state of mechanical stretch. In this work, the stretch-dependent dielectric strength for DE is measured for all possible modes of stretches using compliant electrodes. Dielectric breakdown measurement using compliant electrodes considers voltage-induced deformation, which reflects the actual working condition energy transduction. Hence, the measured strength is for a meaningful value of a working DE. Capacitive extensometry and optical method are the two leading methods for the same. We compare the extensometry and optical methods in estimating the true value of dielectric breakdown strength of DEs at high prestretches. Furthermore, we propose a modified thickness stretch-based power law for the dielectric breakdown strength. Using the capacitive extensometry method, we verify the model on comprehensive experimental data on three types of elastomers, i.e., acrylic, silicone, and natural rubber. This work proposes a general framework for estimating the meaningful stretch-dependent dielectric strength of DEs.

MoS2 Synthesized by Atomic Layer Deposition as Cu Diffusion Barrier

AbstractMiniaturization in integrated circuits requires that the Cu diffusion barriers located in interconnects between the Cu metal line and the dielectric material should scale down. Replacing the conventional TaN with a 2D transition metal dichalcogenide barrier potentially offers the opportunity to scale to 1–2 nm thick barriers. In this article, it is demonstrated that MoS2 synthesized by atomic layer deposition (ALD) can be employed as a Cu diffusion barrier. ALD offers a controlled growth process at back‐end‐of‐line (BEOL) compatible temperatures. MoS2 films of different thicknesses (i.e., 2.2, 4.3, and 6.5 nm) are tested by time‐dependent dielectric breakdown (TDDB) measurements, demonstrating that ALD‐grown MoS2 can enhance dielectric lifetime by a factor up to 17 at an electric field of 7 MV cm−1. Extrapolation to lower E‐fields shows that the MoS2 barriers prepared by ALD have at least an order of magnitude higher median‐time‐to‐failure during device operation at 0.5 MV cm−1 compared with MoS2 barriers prepared by other methods. By scaling the thickness further down in future work, the ALD MoS2 films can be applied as ultrathin Cu diffusion barriers.

Enhancement-mode vertical (100) β-Ga2O3 FinFETs with an average breakdown strength of 2.7 MV cm−1

In this work, we report on the realization of vertical (100) β-Ga2O3 FinFET devices for the use in power electronics applications. The experiments are carried out on structures consisting of highly conducting (100) β-Ga2O3 substrates with a doping concentration N D of 3 × 1018 cm−3, and epitaxially grown layers with N D of 5 × 1016 cm−3 for the drift and channel region. The fabricated FinFET devices feature enhancement-mode properties with a threshold voltage of +4.2 V and on/off-current ratio of 105. Moreover, breakdown measurements of these devices reveal an average breakdown strength of 2.7 MV cm−1. Additional device simulation indicates the presence of electric field peaks near the gate edge outside the active device as high as 7 and 5 MV cm−1 in the Al2O3 gate oxide and β-Ga2O3 semiconductor, respectively.