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题名一维线性波动方程耦合组的精确边界同步能观性
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作者
王珂
石志娟
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机构
东华大学数学系
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出处
《数学年刊（A辑）》
CSCD
北大核心
2020年第2期139-152,共14页
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基金
国家自然科学基金(No.11601074)
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文摘
作者介绍了多种精确同步能观性,并对一维波动方程耦合组在多种边界条件下分别实现了精确边界同步能观性,分组精确边界同步能观性以及分组精确边界零能观性与同步能观性.
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关键词
精确边界同步能观性
分组精确边界同步能观性
分组精确边界零能观性与同步能观性
一维波动方程耦合组
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Keywords
Exact boundary synchronizable observability
Exact boundary synchronizable observability by groups
Exact null observability and synchronizable observability by groups
coupled system of 1-d wave equations
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分类号
O175.27
[理学—基础数学]
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题名表面等离子体无掩膜干涉光刻系统的数值分析(英文)
被引量：5
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作者
董启明
郭小伟
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机构
电子科技大学光电信息学院
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出处
《光子学报》
EI
CAS
CSCD
北大核心
2012年第5期558-564,共7页
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基金
The National Natural Science Foundation of China(No.60906052)
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文摘
表面等离子体激元具有近场增强效应,可以代替光子作为曝光源形成纳米级特征尺寸的图像.本文数值分析了棱镜辅助表面等离子体干涉系统的参量空间,并给出了计算原理和方法.结果表明,适当地选择高折射率棱镜、低银层厚度、入射波长和光刻胶折射率,可以获得高曝光度、高对比度的干涉图像.入射波长为431nm时,选择40nm厚的银层,曝光深度可达200nm,条纹周期为110nm.数值分析结果为实验的安排提供了理论支持.
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关键词
干涉光刻
表面等离子体激元
克莱舒曼结构
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Keywords
Interference lithography
Surface plasmon plortiton
Kretschmann structureCLCN: TN305.7 Document Code:A Article ID:1004-4213(2012)05-0558-70 IntroductionThere is a growing interest in exploring new nanolithography techniques with high efficiency,low cost and large-area fabrication to fabricate nanoscale devices for nanotechnology applications.Conventional photolithography has remained a useful microfabrication technology because of its ease of repetition and suitability for large-area fabrication[1].The diffraction limit,however,restricts the fabrication scale of photolithography[2].Potential solutions that have actually been pursued require increasingly shorter illumination wavelengths for replicating smaller structures.It is becoming more difficult and complicated to use the short optical wavelengths to reach the desired feature sizes.Other methods such as electron beam lithography[3],ion beam lithography[4],scanning probe lithography[5],nanoimprint lithography(NIL)[6],and evanescent near-field optical lithography(ENFOL)[7] have been developed in order to achieve nanometer-scale features.As we know,the former three techniques need scanning and accordingly are highly inefficient.In NIL,the leveling of the imprint template and the substrate during the printing process,which determines the uniformity of the imprint result,is a challenging issue of this method.ENFOL have the potential to produce subwavelength structures with high efficiency,but it encounters the fact that the evanescent field decays rapidly through the aperture,thus attenuating the transmission intensity at the exit plane and limiting the exposure distance to the scale of a few tens of nanometers from the mask.In recent years,the use of surface-plasmon polaritons(SPPs) instead of photons as an exposure source was rapidly developed to fabricate nanoscale structures.SPPs are characterized by its near field enhancement so that SPP-based lithography can greatly extend exposure depth and improve pattern contrast.Grating-assisted SPP interference,such as SPP resonant interference nanolithography[8] and SPP-assisted interference nanolithography[9],achieved a sub-100nm interference pattern.The techniques,however,are necessary to fabricate a metal grating with a very fine period and only suitable for small-area interference.To avoid the fabrication of the metal grating,a prism-based SPP maskless interference lithography was proposed in 2006,which promises good lithography performance.The approach offers potential to achieve sub-65nm and even sub-32nm feature sizes.However,the structure parameters are always not ideal in a real system.One wants to know how much influence the parameter variations have on the pattern resolution and what variations of the parameters are allowed to obtain an effective interference.Thus,it is necessary to explore the parameter spaces.1 SPP maskless interference lithography systemThe SPP maskless interference lithography system is shown in Fig.1.A p-polarized laser is divided into two beams by a grating splitter,and then goes into the prism-based multilayer system.Under a given condition,the metal film can exhibit collective electron oscillations known as SPPs which are charge density waves that are characterized by intense electromagnetic fields confined to the metallic surface.If the metal layer Fig.1 Schematic for SPP maskless interference lithography systemis sufficiently thin,plasma waves at both metal interfaces are coupled,resulting in symmetric and antisymmetric SPPs.When the thickness h of metal film,dielectric constant ε1,ε2,ε3 of medium above,inside,below the metal film are specified,the coupling equation is shown as followstanh(S2h)(ε1ε3S22+ε22S1S3)+(ε1ε2S2S3+ε2ε3S1S2)=0
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分类号
TN305.7
[电子电信—物理电子学]
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