Two-dimensional Electric Field Distribution Research Articles

Charge Imbalance Tolerance of 4H-SiC Superjunction Devices Featuring Breakdown Path Variation

In this letter, the impact of charge imbalance on silicon carbide (SiC) superjunction (SJ) device is studied thoroughly. The breakdown path variation under different degrees of charge imbalance is revealed for the first time by joint analysis of the SiC anisotropy of impact ionization and the charge-imbalanced SJ two-dimensional electric field distribution. Primarily due to this anisotropy, it is a significant finding that the breakdown voltage could be even higher than the balance case when either P or N pillar is slightly under-doped. Furthermore, an SJ design methodology is proposed based on figure-of-merit (FOM) sensitivity and process tolerance, which guides how to better design low-sensitivity SJ devices within a certain range of charge imbalance degree. It is indicated that the wide pillar is suggested for large process tolerance and the under-doped case is less sensitive to charge imbalance than the over-doped case. In brief, the aforementioned revelation can gain new physics-level insights into various charge-imbalanced SJ cases and the methodology can achieve not only the high FOM based on practical process capability but also the required process tolerance based on target performance.

Simulation of diamond synthesis by microwave plasma chemical vapor deposition with multiple substrates in a substrate holder

To simulate the electric field distribution in a cylindrical resonant cavity during diamond crystal growth by microwave plasma chemical vapor deposition (MPCVD), a three-dimensional (3D) model, based on the electromagnetic field part of the finite element simulation solver COMSOL Multiphysics software, was established in this study. It was found that precise fillet treatment for the edge of the sample holder in the cavity can effectively improve the distribution of the electric field in this area, which is more conducive for the epitaxial growth of diamond. Based on the actual experimental requirements, nine diamond substrates were added to the holder with a previously processed edge fillet. By comparing with the simulated situation without substrates, it was proved that the addition of substrates influences the electric field distribution nearby. Furthermore, a new groove substrate holder with rounded corners was designed. Nine substrates with specific spacing were added to the groove holder, and the 3D and two-dimensional electric field distribution in this region were obtained. The optimized substrate holder makes the substrates less exposed to strong microwave plasma, which aids in high-quality single-crystal diamond synthesis. The simulation results were further verified experimentally.

Calculation of Electric Field Distribution in the Simulating Device for Animal Experiment

A main way to investigate the biological effects of 50Hz electromagnetic field is to conduct animal experiments by using the simulating device of 50Hz electromagnetic field. In order to determine the exposure strength of experimental animals in rearing cages in simulating device more accurately, the distribution of electric field should be simulated. Based on ANSYS, a software of finite element analysis, we simulated two-dimensional (2D) electric field distribution of the proposed simulating device of high voltage 50Hz electric field for a case when there were no rearing cages, and we validated those simulation results by comparison with actual measurements. Additionally, we simulated three-dimensional (3D) electric field distribution in the rearing cages for the cases when there was one rearing cage and when there were 8 rearing cages in the simulating device respectively. The simulation results showed that distribution of 50Hz electric field in rearing cage was not uniform when there were rearing cages in the simulating device, and the maximum difference was about 9kV/m. Therefore, based on the movement tracking of animals and the distribution of 50Hz electric field in rearing cages, the cumulative exposure dose of experimental animals could be determined accurately through integral method in order to increase the accuracy of experiments.

Effect of charge coupling on breakdown voltage of high voltage trench-gate-type super barrier rectifier

With the rapidly increasing demands pertaining to high voltage applications in modern power electronic systems, power devices have become widely used in today’s power applications. As a major carrier device without unreliable metal-semiconductor Schottky contact, super barrier rectifier (SBR) has been one of promising substitutions for traditional diodes since it was first introduced, owing to its excellent performance and reliability. The main principle behind SBR approach is to create an adjustable potential barrier in the MOS channel. The height of this barrier can be easily adjusted by the doping concentration in the channel and by the oxide thickness. Trench-gate-type SBR (TSBR) with a trench gate is so designed that the junction-type field-effect transistor effect of planar gate structure enables TSBR to be eliminated to have ultralow forward voltages and a good tradeoff between the forward voltages and reverse leakage currents. However, the charge coupling effect under reverse bias, which is usually neglected and not intensively studied, plays an important role in determining the breakdown voltage of TSBR for high voltage applications (above 200 V). In this paper, the two-dimensional electric field distribution influenced by the charge coupling effect is explained and verified by the analytical model and device simulations with TCAD software Sentaurus. Adjusting the key parameters including the trench depth, oxide thickness and mesa width can improve the tradeoff between the forward voltage drops and breakdown voltages. The optimization of key parameters can provide the significant guidance for designing the device structure. Furthermore, some considerations for designing the TSBRs are discussed in this paper. In addition, a novel TSBR with the stepped oxide structure (SO-TSBR) is proposed and demonstrated. Similar to, yet different from, the stepped oxide structure for dual trench MOSFET, the stepped oxide design equipped with this new rectifier possesses the ability to enhance the forward conduction. As indicated by the simulation results, the SO-TSBR reduces the forward voltage drop by 51.49% at a forward current density of 2.5 A/cm<sup>2</sup> compared with the normal structure of TSBR, with almost the same breakdown voltage of 270 V. The optimized TSBRs and SO-TSBRs are very promising rectifiers that can be used in high power electronic systems, because their breakdown voltages are both greater than 250 V.

Interaction between spoof localized surface plasmon and terahertz vortex beam

We theoretically and experimentally investigate a method of exciting multipole plasmons, including terahertz dark spoof localized surface plasmon (Spoof-LSP) modes, by using normally incident terahertz vortex beam. The vortex beam with angular intensity profile and phase singularities, has well-defined angular momentum which can be decomposed into the polarization-state-related spin angular momentum (SAM) for characterizing the spin feature of photon, and the helical-wavefront-related orbital angular momentum (OAM) that is characterized by an integer <inline-formula><tex-math id="Z-20200915102424-1">\begin{document}$ (l) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20200695_Z-20200915102424-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20200695_Z-20200915102424-1.png"/></alternatives></inline-formula>, called the topological charge. By illuminating terahertz vortex beam on the metallic disk with periodic subwavelength grooves normally, we find that the terahertz dark multipole plasmons can be excited by the terahertz vortex beam carrying different OAM and SAM. We analyze the correspondence between the spin and orbital angular momentum of vortex beam and the excited dark multipolar plasmon modes. In the experiment, a terahertz stepped spiral phase plate (SPP) with high transmission and low dispersion based on the Tsurupica olefin polymer is developed and the stepped SPP can generate a terahertz vortex beam having a topological charge of 1. Then, we further study the excitation of dark multipolar Spoof-LSPs by utilizing the stepped SPP in combination with the near-field scanning terahertz microscopy. The collimated terahertz wave, which is radiated from a 100 fs (<i>λ</i> = 780 nm) laser pulse pumped photoconductive antenna emitter, is converted into terahertz circular polarized light (CPL) which can carry SAM by the combination of the quarter wave plate and the polarizer, and then terahertz CPL impinges on the stepped SPP, producing the terahertz vortex beam which can carry OAM. The spatial two-dimensional electric field distribution is collected in steps of 0.02 mm along the <i>x</i>-direction and <i>y</i>-direction by a commercial terahertz near-field probe which is located close (≈ 10 μm) to the one side of polyimide film by three-dimensional electric translation stage and a microscope (FORTUNE TECHPLOGY FT-FH1080). The experimental results are in good agreement with simulations. We believe that our method will open the way for detailed research on the terahertz physics, plasma and imaging fields.

A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging.

We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations.

Application of Two-Dimensional Discrete Dipole Approximation in Simulating Electric Field of a Microwave Breast Imaging System.

The two-dimensional electric field distribution of the microwave imaging system is numerically simulated for a simplified breast tumour model. The proposed two-dimensional discrete dipole approximation (DDA) has the potential to improve computational speed compared to other numerical methods while retaining comparable accuracy. We have modeled the field distributions in COMSOL Multiphysics as baseline results to benchmark the DDA simulations. We have also investigated the adequate sampling size and the effect of inclusion size and property contrast on solution accuracy. In this way, we can utilize the 2D DDA as an alternative, fast and reliable forward solver for microwave tomography. From a mathematical perspective, the derivation of the 2D DDA and its application to microwave imaging is new and not previously implemented. The simulation results and the measurements show that the 2D DDA is a well-grounded forward solver for the specified microwave breast imaging system.

Two-dimensional mapping of the electric field distribution inside vacuum microgaps observed in a scanning electron microscope

In this paper, we present an in-situ measurement method to directly observe the distribution of the local electric field between vacuum microgaps. The measurement was performed in-situ inside a high resolution scanning electron microscope (SEM), and the nature of the local electric field was characterized through secondary electron contrast images with the aid of Rutherford scattering theory. Based on the regular fringes in these contrast images, the distribution of the local electric field could be extracted from the contour lines of the fringes while the magnitude of the local electric field could be evaluated qualitatively by the gradient of the contour lines. The finite element method (FEM) simulation and the three-electrodes imaging experiment were also conducted, and the obtained two-dimensional electric field distribution agreed well with the FEM simulation, suggesting that the in-situ visualization technique could be useful for determining the local field enhancement behavior for various geometrical configurations and microscale structures. A physical mechanism for the local electric field mapping is suggested. This study demonstrates the potential of SEM imaging for obtaining information about the local electric field within microelectronic structures and devices.

Analytical model for high-voltage SOI device with composite-k dielectric buried layer

An analytical model for a novel high voltage silicon-on-insulator device with composite-k (relative permittivity) dielectric buried layer (CK SOI) is proposed. In this structure, the composite-k buried layer is composed by alternating Si3N4 and low-k (k = 2.65) dielectric in the lateral direction. Due to the composite-k buried layer, the breakdown voltage (BV) is improved both by the vertical and lateral direction. Taking the modulation effect of accumulated interface holes into account, an analytical model is developed. In the blocking state, the proposed model revealed the mechanism of hole accumulation above the Si3N4 buried layer and investigated the modulation effect of accumulated holes on the two-dimensional (2-D) potential and electric field distributions. This analytical model is verified by the simulation results. Compared with the low-k dielectric buried layer SOI (LK SOI), simulation results show that the BV for CK SOI is enhanced by 21% and the specific on-resistance is reduced by 32%, respectively.

Single-shot diagnostic for the three-dimensional field distribution of a terahertz pulse based on pulsed digital holography

In this Letter, a pulsed digital holographic approach for detecting the three-dimensional (3D) field distribution of a freely propagating single terahertz (THz) pulse based on an electro-optic (E-O) sampling technique is proposed, by which the 3D field distribution of a single THz pulse sampled at different time points can be recorded in real-time on a series of subholograms and will be finally reconstructed as a series of two-dimensional spatial electric field distributions in a time series with a time resolution of femtosecond order. Simulation is carried out to demonstrate the process of the implementation, which confirmed the feasibility of the proposal.

Particle modelling of the hybrid negative ion source

In this paper we present results of different particle-based models of expansion and extraction regions for the ITER negative ion source. Results show the important role of electron-induced processes (eV excitation and dissociation) and gas–surface and plasma–surface interactions (atom recombinative desorption and ion neutralization) for the production of negative ion precursors. The spatial distribution of neutral and ionized caesium as well as the drag due to the deuterium flow and its re-evaporation from the plasma grid is calculated. The self-consistent two-dimensional electric field distribution in the extraction region allows a better understanding of the transport of surface-produced negative ions towards the orifice. The model delivers an extraction probability of less than 25%.

Maximum Average SAR Measurement Procedure for Multi-Antenna Transmitters

This paper proposes and verifies a specific absorption rate (SAR) measurement procedure for multi-antenna transmitters that requires measurement of two-dimensional electric field distributions for the number of antennas and calculation in order to obtain the three-dimensional SAR distributions for arbitrary weighting coefficients of the antennas prior to determining the average SAR. The proposed procedure is verified based on Finite-Difference Time-Domain (FDTD) calculation and measurement using electro-optic (EO) probes. For two reference dipoles, the differences in the 10g SAR obtained based on the proposed procedure compared numerically and experimentally to that based on the original calculated three-dimensional SAR distribution are at most 4.8% and 3.6%, respectively, at 1950MHz. At 3500MHz, this difference is at most 5.2% in the numerical verification.

On the field distribution in electrorotation chambers—Influence of electrode shape

The electrorotation method can be applied to characterize the passive electric properties of individual cells or particles. For this, their frequency-dependent speed of rotation is registered microscopically. Commonly, object rotation is induced in harmonic rotating fields which are generated in four electrode chambers. The rotation speed of the objects is proportional to the square of the field strength. In this study, we calculated the two-dimensional electric field distribution in electrorotation chips using the FEMLAB finite element program (Comsol, Sweden). For reasons of symmetry, a perfectly circular field is generated at the centers of the four electrode chambers. Nevertheless, the field strength is reduced with respect to the quotient of electrode voltage and distance for any electrode shape. Distant from the center, the field polarization is elliptical with an eccentricity increasing with the distance to the center. For optimizing the electrode shape, the deviations in torques for given distances from the center have been calculated. These deviations have been compared for various electrode shapes in order to find an optimal chip design. Another criterion was a large electrode distance in the corners of the electrode arrangement in order to avoid field hot spots and to minimize dielectrophoretic particle collection.

Simulation of electromigration failure by variable resistance model

The electromigration failure in a thin metallic conductor has been simulated by the temporal resistance change. This change is related to the crack propagation on both sides of the conductor. The geometrical change affects the two-dimensional electric field distribution, which in turn influences the two-dimensional current density distribution in the conductor. The two-dimensional electric field and current density maps can be realized by solving the Laplace equation. By integrating the power density over the entire conductor, the resistance change due to the crack development can be obtained. On the other hand, the development of the crack is attributed to the accumulation of vacancies over the cross section of the conductor. We assume that the crack length is proportional to the excess vacancies over the cross section. From the one-dimensional diffusion-drift equation, we obtained the temporal growth of crack length. The temporal resistance change can thus be simulated. The effects of vacancy diffusion, and field-induced drift on the crack-growth kinetics have been demonstrated.

Effects of silicon layer properties on device reliability for 0.1-μm SOI n-MOSFET design strategies

We employ an advanced simulation method to investigate the effects of silicon layer properties on hot-electron-induced reliability for two 0.1-/spl mu/m SOI n-MOSFET design strategies. The simulation approach features a Monte Carlo device simulator in conjunction with commercially available process and device simulators. The two channel designs are: 1) a lightly-doped (10/sup 16/ cm/sup -3/) channel and 2) a heavily-doped (10/sup 18/ cm/sup -3/) channel. For each design, the silicon layer thicknesses (T/sub Si/) of 30, 60, and 90 nm are considered. The devices are biased under low-voltage conditions where the drain voltage is considerably less than the Si/SiO/sub 2/ barrier height for electron injection. A comparative analysis of the Monte Carlo simulation results shows that an increase in T/sub Si/ results in decreasing hot electron injection into the back oxide in both device designs. However, electron injection into the front oxide exhibits opposite trends of increasing injection for the heavily-doped channel design and decreasing injection for the lightly-doped channel design. These important trends are attributed to highly two-dimensional electric field and current density distributions. Simulations also show that the lightly-doped channel design is about three times more reliable for thick silicon layers. However, as the silicon layer is thinned to 30 nm, the heavily-doped channel design becomes about 10% more reliable instead.

A 2-D boundary element method approach to the simulation of DMOS transistors

A boundary element method is introduced for the calculation of two-dimensional potential and electric field distributions in high-voltage DMOS transistors. An algorithm is proposed to determine the dimensions of the depletion layers in two-dimensional geometries. Regions with different permittivities are taken into account using appropriate boundary conditions. As an application, the high-voltage behavior of the DMOS transistors is investigated, and the avalanche breakdown conditions of the transistors are determined by calculating the ionization integral. The results are compared with simulations based on finite difference methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Studies of polar current systems using the IMS Scandinavian magnetometer array

As a contribution to the International Magnetospheric Study (IMS, 1976–1979) a two-dimensional array of 42 temporary magnetometer stations was run in Scandinavia, supplementary to the permanent observatories and concentrated in the northern part of the region. This effort aimed at the time-dependent (periods above about 100 s) determination of the two-dimensional structure of substorm-related magnetic fields at the Earth's surface with highest reasonable spatial resolution (about 100 km, corresponding to the height of the ionosphere) near the footpoints of field-aligned electric currents that couple the disturbed magnetosphere to the ionosphere at auroral latitudes. It has been of particular advantage for cooperative studies that not only simultaneous data were available from all-sky cameras, riometers, balloons, rockets, and satellites, but also from the STARE radar facility yielding colocated two-dimensional ionospheric electric field distributions. In many cases it therefore was possible to infer the three-dimensional regional structure of substorm-related ionospheric current systems. The first part of this review outlines the basic relationships and methods that have been used or have been developed for such studies. The second short part presents typical equivalent current patterns observed by the magnetometer array in the course of substorms. Finally we review main results of studies that have been based on the magnetometer array observations and on additional data, omitting studies on geomagnetic pulsations. These studies contributed to a clarification of the nature of auroral electrojets including the Harang discontinuity and of ionospheric current systems related to auroral features such as the break-up at midnight, the westward traveling surge, eastward drifting omega bands, and spirals.

Two-Dimensional Kerr Electrooptic Measurement of Nonuniform Electric Fields by CT Method

It is very difficult to measure nonuniform electric field distributions in insulators. The optical measurements of the electric field were investigated in nitrobenzene using the Kerr effect. A sphere-to-sphere electrode or a sphere-to-plane electrode system was used to produce the nonuniform electric field. A rectangular test cell was made of teflon with two glass windows. A He-Ne laser was used for a light source. The intensity of the light transmitted through the cell was measured with a photodiode. The two-dimensional electric field distribution expressed in absolute value was reconstructed by the computed tomography (CT) method. The measured electric fields were compared with the theoretical one and good agreement was obtained.

High-sensitivity Kerr-effect technique for determination of 2-dimensional electric fields

On the basis of the Kerr electrooptic effect, a highly sensitive measurement method, which could be used for measuring two-dimensional electric field distributions in liquid dielectrics, is proposed. By applying a pulse voltage to an optical phase modulator, the authors changed the incident light from a linearly polarized light into two elliptically polarized components. Modulating both states of polarization of these two components as well as the DC electric field with an AC electric field, they determined the amplitudes and directions of both the AC and DC electric field intensity in liquids with small Kerr constants ( approximately 10/sup -15/ m/V/sup 2/). The proposed method is automatic and has a sensitivity approximately=100 V/cm. The two-dimensional electric field distributions in tricresyl phosphate liquid dielectric are measured with this method. >

FAMA/FAMULUS: Programs for the fast calculation of two-dimensional distributions of magnetic and electric fields

One of the most popular codes for the calculation of two-dimensional magnetic or electric field distributions is the POISSON package. To accelerate such calculations we developed a similar code which uses the multigrid method resulting in noticeable smaller computer times and some new features.