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TWO STEPS CHEMICAL-MECHANICAL POLISHING OF RIGID DISK SUBSTRATE TO GET ATOM-SCALE PLANARIZATION SURFACE 被引量:11
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作者 LEI Hong LUO Jianbin LU Xinchun 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2006年第4期496-499,共4页
In order to get atomic smooth rigid disk substrate surface, ultra-fined alumina slurry and nanometer silica slurry are prepared, and two steps chemical-mechanical polishing (CMP) of rigid disk substrate in the two s... In order to get atomic smooth rigid disk substrate surface, ultra-fined alumina slurry and nanometer silica slurry are prepared, and two steps chemical-mechanical polishing (CMP) of rigid disk substrate in the two slurries are studied. The results show that, during the first step CMP in the alumina slurry, a high material removal rate is reached, and the average roughness (Ra) and the average waviness (Wa) of the polished surfaces can be decreased from previous 1.4 nm and 1.6 nm to about 0.6 nm and 0.7 nm, respectively. By using the nanometer silica slurry and optimized polishing process parameters in the second step CMP, the Ra and the Wa of the polished surfaces can be further reduced to 0.038 nm and 0.06 am, respectively. Atom force microscopy (AFM) analysis shows that the final polished surfaces are ultra-smooth without micro-defects. 展开更多
关键词 TWo steps Chemical-mechanical polishing(CMP) Rigid disk substrateatom-scale planarization Slurry
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5-methyl-1H-benzotriazole as potential corrosion inhibitor for electrochemical-mechanical planarization of copper 被引量:1
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作者 边燕飞 翟文杰 朱宝全 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2013年第8期2431-2438,共8页
According to the electrochemical analysis, the corrosion inhibition efficiency of 5-methyl-lH-benzotriazole (m-BTA) is higher than that of benzotrizaole (BTA). The inhibition capability of the m-BTA passive film f... According to the electrochemical analysis, the corrosion inhibition efficiency of 5-methyl-lH-benzotriazole (m-BTA) is higher than that of benzotrizaole (BTA). The inhibition capability of the m-BTA passive film formed in hydroxyethylidenediphosphonic acid (HEDP) electrolyte containing both m-BTA and chloride ions is superior to that formed in m-BTA-alone electrolyte, even at a high anodic potential. The results of electrical impedance spectroscopy, nano-scratch experiments and energy dispersive analysis of X-ray (EDAX) indicate that the enhancement of m-BTA inhibition capability may be due to the increasing thickness of passive film. Furthermore, X-ray photoelectron spectrometry (XPS) analysis indicates that the increase in passive film thickness can be attributed to the incorporation of C1 into the m-BTA passive film and the formation of [Cu(I)CI(rn-BTA)], polymer film on Cu surface. Therefore, the introduction of C1- into m-BTA-containing HEDP electrolyte is effective to enhance the passivation capability of m-BTA passive film, thus extending the operating potential window. 展开更多
关键词 electrochemical-mechanical planarization 5-methyl-lH-benzotriazole corrosion inhibitor chloride ion
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Chemical Mechanical Planarization (CMP) for Microelectronic Applications 被引量:4
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作者 Li Yuzhuo 《合成化学》 CAS CSCD 2004年第z1期115-115,共1页
关键词 CMP for Microelectronic Applications Chemical Mechanical planarization
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Mechanism of amorphous Ge_2Sb_2Te_5 removal during chemical mechanical planarization in acidic H_2O_2 slurry
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作者 何敖东 宋志棠 +4 位作者 刘波 钟旻 王良咏 吕业刚 封松林 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第1期547-551,共5页
In this paper, chemical mechanical planarization (CMP) of amorphous Ge2Sb2Te5 (a-GST) in acidic H2O2 slurry is investigated. It was found that the removal rate of a-GST is strongly dependent on H2O2 concentration ... In this paper, chemical mechanical planarization (CMP) of amorphous Ge2Sb2Te5 (a-GST) in acidic H2O2 slurry is investigated. It was found that the removal rate of a-GST is strongly dependent on H2O2 concentration and gradually increases with the increase in H2O2 concentration, but the static etch rate first increases and then slowly decreases with the increase in H2O2 concentration. To understand the chemical reaction behavior of H2O2 on the a-GST surface, the potentiodynamic polarization curve, surface morphology and cross-section of a-GST immersed in acidic slurry are measured and the results reveal that a-GST exhibits a from active to passive behavior for from low to high concentration of H2O2. Finally, a possible removal mechanism of a-GST in different concentrations of H2O2 in the acidic slurry is described. 展开更多
关键词 H2O2 chemical mechanical planarization Ge2Sb2Te5
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Improvement of High Dynamic Range Capacitive Displacement Sensor by a Globalm Planarization
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作者 Daesil Kang Wonkyu Moon 《Journal of Sensor Technology》 2011年第4期99-107,共9页
This study presents an improvement of high dynamic range contact-type capacitive displacement sensor by applying planarization. The sensor is called the contact-type linear encoder-like capacitive displacement sensor ... This study presents an improvement of high dynamic range contact-type capacitive displacement sensor by applying planarization. The sensor is called the contact-type linear encoder-like capacitive displacement sensor (CLECDiS), is a nano-meter-resolution sensor with a wide dynamic range. However, height differences due to patterned electrodes may cause a variety of problems or performance degradation. In devices of two glass wafer surfaces with patterned structures assembled face-to-face and in sliding contact, the heights of the patterns crucially affect their performance and practicality, so it should be planarized for reducing the problem. A number of techniques for planarizing glass wafer surfaces with patterned chrome electrodes were evaluated and the following three were selected as adequate: lift-off, etch-back, and chemical mechanical polishing (CMP). The fabricated samples showed that CMP provided the best planarization. CMP was successfully employed to produce CLECDiS with improved signal reliability due to reduced collisions between electrodes. 展开更多
关键词 High Dynamic RANGE Capacitive DISPLACEMENT SENSOR planarization CONTACT Method
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Pseudo Jahn-Teller Effect in Puckering and Planarization of Heterocyclic Compounds
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作者 Natalia Gorinchoy 《International Journal of Organic Chemistry》 2018年第1期142-159,共18页
The goal of this brief partly review paper is to summarize the results of the works published over the last few years regarding the origin of the out-of-plane distortions (puckering) of heterocyclic compounds. In all ... The goal of this brief partly review paper is to summarize the results of the works published over the last few years regarding the origin of the out-of-plane distortions (puckering) of heterocyclic compounds. In all the papers devoted to this problem, it is shown that the instability of planar configurations of heterocyclic molecules leading to symmetry breaking and distortions is induced by the pseudo Jahn-Teller effect (PJTE). Special attention in this work is paid to the mechanism of suppression and enhancement of the PJTE distortions of heterocycles by oxidation, reduction, and chemical substitutions. It is demonstrated that oxidation of 1,4-dithiine containing compounds leads to suppression of the PJTE and to restoration of their planar nuclear configurations. An example of a dibenzo[1,2]dithiine molecule is used to demonstrate the mechanism of enhancement of the PJTE by reduction. It is shown that the reduction of the neutral C12H8S2 molecule up to the dianion (C12H8S2)2- enhances the PJTE, followed by the S-S bond cleavage and significant structural distortions of the system. The change of the PJTE by chemical substitutions, accompanied either by puckering or by planarization of heterocyclic compounds, is discussed using as examples 1,4-ditinine and its S-oxygenated derivatives. 展开更多
关键词 PSEUDO JAHN-TELLER Effect (PJTE) VIBRONIC Coupling PUCKERING and planarization in HETEROCYCLIC Systems
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Planar Hall Effect in the Charge-Density-Wave Bi_(2)Rh_(3)Se_(2)
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作者 蔡明桔 陈正 +7 位作者 杨扬 朱相德 孙浩翔 朱安康 刘学 韩玉岩 高文帅 田明亮 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第7期126-131,共6页
We systematically investigate in-plane transport properties of ternary chalcogenideBi_(2)Rh_(3)Se_(2).Upon rotating the magnetic field within the plane of the sample, one can distinctly detect the presence of both pla... We systematically investigate in-plane transport properties of ternary chalcogenideBi_(2)Rh_(3)Se_(2).Upon rotating the magnetic field within the plane of the sample, one can distinctly detect the presence of both planar Hall resistance and anisotropic longitudinal resistance, and the phenomena appeared are precisely described by the theoretical formulation of the planar Hall effect (PHE). In addition, anisotropic orbital magnetoresistance rather than topologically nontrivial chiral anomalies dominates the PHE in Bi_(2)Rh_(3)Se_(2). The finding not only provides another platform for understanding the mechanism of PHE, but could also be beneficial for future planar Hall sensors based on two-dimensional materials. 展开更多
关键词 materials planar ANISOTROPIC
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High-performance GaSb planar PN junction detector
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作者 Yuanzhi Cui Hongyue Hao +13 位作者 Shihao Zhang Shuo Wang Jing Zhang Yifan Shan Ruoyu Xie Xiaoyu Wang Chuang Wang Mengchen Liu Dongwei Jiang Yingqiang Xu Guowei Wang Donghai Wu Zhichuan Niu Derang Cao 《Journal of Semiconductors》 EI CAS CSCD 2024年第9期48-52,共5页
This paper examines GaSb short-wavelength infrared detectors employing planar PN junctions. The fabrication was based on the Zn diffusion process and the diffusion temperature was optimized. Characterization revealed ... This paper examines GaSb short-wavelength infrared detectors employing planar PN junctions. The fabrication was based on the Zn diffusion process and the diffusion temperature was optimized. Characterization revealed a 50% cut-off wavelength of 1.73 μm, a maximum detectivity of 8.73 × 10^(10) cm·Hz^(1/2)/W, and a minimum dark current density of 1.02 × 10^(-5) A/cm^(2).Additionally, a maximum quantum efficiency of 60.3% was achieved. Subsequent optimization of fabrication enabled the realization of a 320 × 256 focal plane array that exhibited satisfactory imaging results. Remarkably, the GaSb planar detectors demonstrated potential in low-cost short wavelength infrared imaging, without requiring material epitaxy or deposition. 展开更多
关键词 ANTIMONIDE short-wave infrared planar junction zinc diffusion
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Compact magneto-optical traps using planar optics
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作者 Zhi Tan Bo Lu +1 位作者 Chengyin Han Chaohong Lee 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期93-108,共16页
Magneto-optical traps (MOTs) composed of magnetic fields and light fields have been widely utilized to cool andconfine microscopic particles. Practical technology applications require miniaturized MOTs. The advancemen... Magneto-optical traps (MOTs) composed of magnetic fields and light fields have been widely utilized to cool andconfine microscopic particles. Practical technology applications require miniaturized MOTs. The advancement of planaroptics has promoted the development of compact MOTs. In this article, we review the development of compact MOTs basedon planar optics. First, we introduce the standardMOTs. We then introduce the gratingMOTs with micron structures, whichhave been used to build cold atomic clocks, cold atomic interferometers, and ultra-cold sources. Further, we introducethe integrated MOTs based on nano-scale metasurfaces. These new compact MOTs greatly reduce volume and powerconsumption, and provide new opportunities for fundamental research and practical applications. 展开更多
关键词 magneto-optical trap (MOT) planar optics grating MOT metasurface MOT
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Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide
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作者 Xin Zhao Zhong Du +2 位作者 Li-Jian Zhou Rong-Xiang Liu Xu-Hu Wang 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第11期154-160,共7页
We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on L... We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on Lax pair obtained by us,we derive the infinitely-many conservation laws.We give the bright one-,two-,and N-soliton solutions,and the first-,second-,and Nth-order breather solutions based on the N-fold DT.We conclude that the velocities of the bright solitons are influenced by the distributed gain function,g(z),and variable coefficients in equation,h1(z),p1(z),r1(z),and s1(z)via the asymptotic analysis,where z represents the propagation variable or spatial coordinate.We also graphically observe that:the velocities of the first-and second-order breathers will be affected by h1(z),p1(z),r1(z),and s1(z),and the background wave depends on g(z). 展开更多
关键词 optical fiber planar waveguide Darboux transformation bright soliton BREATHER
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Angular and planar transport properties of antiferromagnetic V_(5)S_(8)
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作者 吴晓凯 王彬 +4 位作者 吴德桐 陈博文 弭孟娟 王以林 沈冰 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第2期66-71,共6页
Systemically angular and planar transport investigations are performed in layered antiferromagnetic(AF)V_(5)S_(8).In this AF system,obvious anomalous Hall effect(AHE)is observed with a large Hall angle of 0.1 compared... Systemically angular and planar transport investigations are performed in layered antiferromagnetic(AF)V_(5)S_(8).In this AF system,obvious anomalous Hall effect(AHE)is observed with a large Hall angle of 0.1 compared to that in ferromagnetic(FM)system.It can persist to the temperatures above AF transition and exhibit strong angular field dependence.The phase diagram reveals various magnetic states by rotating the applied field.By analyzing the anisotropic transport behavior,magnon contributions are revealed and exhibit obvious angular dependence with a spin-flop vanishing line.The observed prominent planar Hall effect and anisotropic magnetoresisitivity exhibit two-fold systematical angular dependent oscillations.These behaviors are attributed to the scattering from spin–orbital coupling instead of nontrivial topological origin.Our results reveal anisotropic interactions of magnetism and electron in V5S8,suggesting potential opportunities for the AF spintronic sensor and devices. 展开更多
关键词 ANTIFERROMAGNETISM planar Hall effect magnetic and topological properties
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An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes
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作者 Xiaojuan Yang Jie Hu +1 位作者 Honglei Sun Jun Zheng 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第4期1305-1314,共10页
Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar slid... Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angleγlim.However,the assignment ofγlim is currently used generally based on an empirical criterion.This study aims to propose an approach for determining the value ofγlim in deterministic and probabilistic kinematic planar sliding analysis.A new perspective is presented to reveal thatγlim essentially influences the probability of forming a potential planar sliding block.The procedure to calculate this probability is introduced using the block theory method.It is found that the probability is correlated with the number of discontinuity sets presented in rock masses.Thus,different values ofγlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses;whereas a fixed value ofγlim is commonly assigned to different types of rock masses in traditional method.Finally,an engineering case was used to compare the proposed and traditional kinematic analysis methods.The error rates of the traditional method vary from 45%to 119%,while that of the proposed method ranges between 1%and 17%.Therefore,it is likely that the proposed method is superior to the traditional one. 展开更多
关键词 Kinematic analysis Block theory planar sliding Lateral limit angle Rock slope
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Nonlinear dynamic modeling of planar moving Timoshenko beam considering non-rigid non-elastic axial effects
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作者 M.ABBASI GAVARI M.R.HOMAEINEZHAD 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第3期479-496,共18页
Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipula... Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipulator consists of an elastic arm,a rotary motor,and a rigid carrier,and undergoes general in-plane rigid body motion along with elastic transverse deformation.To accurately model the elastic behavior,Timoshenko’s beam theory is used to describe the flexible arm,which accounts for rotary inertia and shear deformation effects.By applying Newton’s second law,the nonlinear governing equations of motion for the manipulator are derived as a coupled system of ordinary differential equations(ODEs)and partial differential equations(PDEs).Then,the assumed mode method(AMM)is used to solve this nonlinear system of governing equations with appropriate shape functions.The assumed modes can be obtained after solving the characteristic equation of a Timoshenko beam with clamped boundary conditions at one end and an attached mass/inertia at the other.In addition,the effect of the transverse vibration of the inextensible arm on its axial behavior is investigated.Despite the axial rigidity,the effect makes the rigid body dynamics invalid for the axial behavior of the arm.Finally,numerical simulations are conducted to evaluate the performance of the developed model,and the results are compared with those obtained by the finite element approach.The comparison confirms the validity of the proposed dynamic model for the system.According to the mentioned features,this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms. 展开更多
关键词 planar moving Timoshenko beam non-rigid non-elastic axial effect as-sumed mode method(AMM) nonlinear motion analysis
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On the (Δ + 2)-Total-Colorability of Planar Graphs with 7-Cycles Containing at Most Two Chords
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作者 Jian Chang Jingru Liu Fan Zhang 《Journal of Applied Mathematics and Physics》 2024年第7期2702-2710,共9页
The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove tha... The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove that TCC holds for planar graph with Δ = 6 and every 7-cycle contains at most two chords. 展开更多
关键词 planar Graph 7-Cycle 8-Totally-Colorable Maximum Degree
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HEVC帧内预测Planar和DC模式的VLSI架构设计与实现 被引量:3
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作者 周巍 黄晓东 +2 位作者 朱洪翔 郭龙 张仁鹏 《计算机工程与应用》 CSCD 北大核心 2015年第8期160-164,共5页
在研究新一代高性能视频编码标准(HEVC)帧内预测中planar和DC模式预测算法的基础上,分别设计了高效VLSI架构,通过状态机的自适应控制和模块的复用来实现速度的提高和面积的减少。针对planar模式,设计了一种基于状态机自适应控制的寄存... 在研究新一代高性能视频编码标准(HEVC)帧内预测中planar和DC模式预测算法的基础上,分别设计了高效VLSI架构,通过状态机的自适应控制和模块的复用来实现速度的提高和面积的减少。针对planar模式,设计了一种基于状态机自适应控制的寄存器累加架构;针对DC模式,设计了一种基于算法的分割处理架构。实验结果表明,所设计的架构在TSMC180 nm的工艺下最高频率为350 MHz,面积合计为68.1 kgate,能够实现对4∶2∶0格式7 680×4 320@30 f/s视频序列的实时编码,最高工作频率可以达到23.4 MHz。 展开更多
关键词 高性能视频编码标准(HEVC) 帧内预测 planar模式 DC模式 超大规模集成电路(VLSI)架构设计
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Development of the High-performance Synchronous Permanent Magnet Planar Motor and Its Key Technologies 被引量:6
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作者 寇宝泉 张鲁 +2 位作者 邢丰 李立毅 张赫 《中国电机工程学报》 EI CSCD 北大核心 2013年第9期I0011-I0011,共1页
永磁同步平面电机具有直接驱动、出力密度高、低热耗、高精度等特点,在现代精密、超精密加工装备,特别是在极紫外光刻机中具有广阔的应用前景。根据永磁阵列和线圈阵列的结构形式将永磁同步平面电机划分为组合式、半组合式、绕组层叠式... 永磁同步平面电机具有直接驱动、出力密度高、低热耗、高精度等特点,在现代精密、超精密加工装备,特别是在极紫外光刻机中具有广阔的应用前景。根据永磁阵列和线圈阵列的结构形式将永磁同步平面电机划分为组合式、半组合式、绕组层叠式和对称式永磁同步平面电机4类,并介绍了各种类型平面电机的特点,总结了永磁同步平面电机关键技术的发展现状,针对目前永磁同步平面电机存在的不足,讨论了未来永磁同步平面电机发展的趋势与方向。 展开更多
关键词 平面电机 光刻技术 永磁 同步 性能 集成电路制造 平版印刷技术 定位系统
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Static Induction Devices with Planar Type Buried Gate 被引量:1
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作者 王永顺 李思渊 胡冬青 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2004年第2期126-132,共7页
Based on the surface-gate and buried-gate structures,a novel buried-gate structure called the planar type buried-gate (PTBG) structure for static induction devices (SIDs) is proposed.An approach to realize a buried-ga... Based on the surface-gate and buried-gate structures,a novel buried-gate structure called the planar type buried-gate (PTBG) structure for static induction devices (SIDs) is proposed.An approach to realize a buried-gate type static induction transistor by conventional planar process technology is presented.Using this structure,it is successfully avoided the second epitaxy with a high degree of difficulty and the complicated mesa process in conventional buried gate.The experimental results demonstrate that this structure is desirable for application in power SIDs.Its advantages are high breakdown voltage and blocking gain. 展开更多
关键词 static induction device planar type buried gate structure blocking voltage limiting field ring
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微带Rotman透镜基于Planar EM的快速仿真 被引量:3
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作者 纪学军 《无线电工程》 2006年第6期45-47,共3页
通过合理的排列端口位置,建立了透镜的仿真模型。讨论了几种快速仿真的办法,并针对透镜的具体形式得到合理有效的仿真方法,然后对透镜的整体性能进行仿真分析,通过与实测结果的比较,证实快速仿真方法的准确性。仿真讨论不同的端口长度... 通过合理的排列端口位置,建立了透镜的仿真模型。讨论了几种快速仿真的办法,并针对透镜的具体形式得到合理有效的仿真方法,然后对透镜的整体性能进行仿真分析,通过与实测结果的比较,证实快速仿真方法的准确性。仿真讨论不同的端口长度、不同的渐变形状对透镜性能的影响,从而为透镜端口的进一步优化设计提供依据。 展开更多
关键词 ROTMAN透镜 planar EM 快速仿真 端口回波
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HEVC帧内预测Planar和DC模式算法的并行化设计 被引量:5
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作者 谢晓燕 徐卫芳 刘帆 《电视技术》 北大核心 2015年第5期4-8,60,共6页
针对HEVC帧内预测Planar和DC模式算法的特点,提出实现这两种模式的并行化方法。该方法是通过分析推导Planar和DC模式算法之间的可并行性,以西安邮电大学自主设计的一款面向图形、图像应用的阵列处理器PAAG(Polymorphic Array Architectu... 针对HEVC帧内预测Planar和DC模式算法的特点,提出实现这两种模式的并行化方法。该方法是通过分析推导Planar和DC模式算法之间的可并行性,以西安邮电大学自主设计的一款面向图形、图像应用的阵列处理器PAAG(Polymorphic Array Architecture for Graphics and Image Processing)平台为基础,采用最优的数据分配方式,合理地设计了多处理单元并行工作的算法程序。实验结果表明Planar预测模式和DC预测模式在多处理单元上的并行实现,相比于单核的串行运算速度分别提高了84%和81%,串/并行加速比分别达到6.34和5.44。该并行化算法减少了视频的编解码时间,其数据分配方案对于帧内预测算法在多核结构上的并行化研究也有一定的参考价值。 展开更多
关键词 HEVC 帧内预测 并行化 数据分配 阵列处理器
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关于Planar Ferromagnets and Antiferromagnets泛函的径向极小元的注记
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作者 齐龙兴 雷雨田 《南京师大学报(自然科学版)》 CAS CSCD 北大核心 2007年第3期15-20,共6页
就Bethuel,Brezis和Helein提出的问题讨论了Planar Ferromagnets and Antiferromagnets泛函在H={u(x)=(sinf(r)|xx|,cosf(r))∈H1(B1,S2);f(0)=0,f(1)=2π,r=|x|}中的径向极小元的一些性质,其中包括此泛函的径向极小元的零点的分布及若... 就Bethuel,Brezis和Helein提出的问题讨论了Planar Ferromagnets and Antiferromagnets泛函在H={u(x)=(sinf(r)|xx|,cosf(r))∈H1(B1,S2);f(0)=0,f(1)=2π,r=|x|}中的径向极小元的一些性质,其中包括此泛函的径向极小元的零点的分布及若干个上界估计,并给出了这一问题的肯定回答. 展开更多
关键词 planar FERROMAGNETS and Antiferromagnets泛函 径向极小元 一致估计 planar FERROMAGNETS and Antiferromagnets泛函 径向极小元 一致估计
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