远场超分辨率成像与亚波长聚焦的研究
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摘要
随着纳米科学和生命科学的研究不断深入,在光学显微成像、光刻、光信息存储等诸多光学应用领域,由于存在光学衍射效应,导致聚焦焦斑和远场成像出现极限分辨率问题。要想获得更高分辨率,就必须突破衍射极限,尤其是在远场实现超分辨率聚焦和成像,需要采取有效手段将更多的隐逝波分量送达远场参与聚焦或成像过程。根据表面等离子体激元(Surface Plasmon Polaritons, SPPs)独特的短波长、表面局域和近场增强特性,本文分别提出了基于亚波长金属结构的远场成像透镜模型和超聚焦透镜模型,利用特定结构对SPPs进行操控从而可以超越衍射限制,在远场实现超分辨率成像和亚波长聚焦。本文主要包括以下研究内容：
首先,针对投影光刻成像模拟系统中忽略掩模厚度、入射光的倾斜角度、偏振等因素直接用标量衍射理论进行空间像计算导致预测严重失真的问题,采用严格的矢量电磁理论,借助波导方法分析了三维掩模在离轴照明条件下的近场衍射分布,得到通用的三维掩模模型。该模型综合考虑了入射角、入射方位角、偏振角以及掩模厚度对近场分布的影响,能够反映出亚波长光刻中倾斜入射平面波对三维掩模产生的阴影效应和偏振效应。对分辨率增强技术——光学邻近效应校正(OPC)进行了验证,发现OPC技术可以有效改善掩模的近场分布,从而达到提高远场光刻分辨率的目的。此外通过数值模拟得到了最佳入射角度,与工艺经验值完全吻合。
根据金属-介质交替构成的圆柱形双曲透镜能够突破传统光学衍射限制实现超分辨率远场成像的机理,对双曲透镜结构进行了优化分析,将其应用到193纳米光刻系统中,使用铝和二氧化钛构成各向异性非常强的双曲色散媒质,更有利于远场缩小成像。通过数值分析发现,优化后的双曲透镜,结合相移掩模技术可以实现20纳米以下技术节点,这为拓展和延伸193纳米光刻机提供了新的途径和理论依据。
由于圆柱双曲透镜可以实现缩小/放大成像,但是圆弧形的内外表面不利于物的放置和像的测量；而平板超级透镜有平坦的表面却不具备缩小/放大的功能,因此综合这两种透镜模型各自的优势,设计了具有平坦物面和像面的凹形双曲透镜Concave Hyperlens模型,能够实现超分辨率的缩小/放大成像。利用传递矩阵方法TMM详细分析了光通过该多层结构透镜模型的传播行为,在共焦椭圆坐标系中引入马丢函数得到透射光场的半解析表达式。通过数值方法验证了该透镜所具有的高对比度缩小成像能力,并与多层平板透镜、平板双曲透镜进行了成像性能比较,显现出该透镜模型具有非均匀成像特性。
为了实现高效率远场超聚焦,在环形金属透镜基础上,提出了两种特定结构的金属透镜模型,一种是用介质光栅调制出射面的光场,将径向偏振照明条件下的近场焦斑搬移到远场,实现远场亚波长高效率聚焦；另一种是基于无辐射电磁波干涉,金属透镜出射面用各向异性的超材料媒质填充,可将近场汇聚的能量传递到远场从而得到亚波长焦斑。文中对第一种远场超聚焦透镜进行了详细分析,给出了结构参数的设计方法,并通过数值仿真得到优化后的结构参数及其亚波长聚焦性能。同时为了适应各种应用的需求,可以改变缝的结构参数或者增减光栅槽数进行焦距调节。
综合上述研究结果可知,本文提出的基于亚波长金属结构的远场超分辨率成像透镜和高效率亚波长聚焦透镜,可以突破衍射极限在远场实现亚波长分辨率的超聚焦和成像,这将对纳米加工技术、光刻技术、光存储、生物传感、新型光源、分析与检测技术等光学领域具有重要的理论价值和应用前景。
With the deep research on nanometer scale technology and life science, the diffraction effect that limits the resolution of focusing and imaging in far field is becoming a fetal barrier to super-resolution in the domain of optics, for example optical microscopy, microlithography, optical data storage and etc. In order to obtain a higher resolution in far field, the diffraction limit should be conquered or circumvented by means of some special methods to make evanescent components contribute to the far field focalization or imaging with super-resolution. The surface plasmon polaritons (SPPs) with particular features of such as shorter wavelength than the incident light of excitation, surface localization and near-field enhancement provide a great idea to surpass the diffraction limit and attract more and more attention in related research fields. Based on the sub-wavelength metallic structures, the lens models of far-field sub-wavelength imaging and super-focusing were proposed and the principals were studied in this dissertation. It is observed that the elaborate structures were designed to manipulate the SPPs so that the sub-diffraction-limit imaging and sub-wavelength focal spot could be formed in far-field beyond the resolution limit.
As the thickness of the mask, the oblique incident angles and polarization of the incidence wave were ignored when the scale diffraction theory was applied to calculate the aerial image in the traditional lithography simulation system, there was a great error between the prediction and the actual results transferred from mask to the wafer. The rigorous vectorial electromagnetic theory should be utilized and we exploit the waveguide method to acquire the near field distribution of the three-dimensional (3D) mask with off-axis illumination. A general 3D mask model with respect to the incident angles and the thickness of the mask is derived, which is convenient for aerial image calculation in the simulation of the sub-wavelength lithography fast and precisely. The shadow effect and the polarization effect induced by oblique illumination are illustrated by the numerical method. Furthermore, one of the resolution enhancement technologies, optical proximity effect correction (OPC), combined with the general 3D mask model are verified by related simulations. It was found that the OPC process can amend the near field distribution and enhance the final resolution of the project lithography. Also the optimal incident angles have been obtained by the numerical method, which are consistent with the actual value in practices.
Based on the principle of cylindrical hyperlens, which was made of metal-dielectric alternating multilayer and could distinguish sub-wavelength objects in the far field beyond the traditional diffraction limit, we further optimized the structure of the hyperlens for lithography working at 193nm wavelength. The materials of the metal and the dielectric were replaced by aluminum (Al) and titanic oxide (TiO2) and they exhibited strong anisotropic with hyperbolic dispersion relation, which is propitious to shrinking imaging in far-field. The simulation results show that the 20nm technology node and below can be realized by the optimized hyperlens banding together with the phase-shifting mask,. This scheme can extend the life of the expensive 193nm lithography machines and supply a new precept for nano-scale manufacture.
Although the cylindrical hyperlens is capable of magnification or demagnification, the curved inner and exterior surfaces have serious disadvantages on object location and image measurement. While the slab superlens has planar surfaces but cannot magnify or demagnify the image. Combined with the advantages of the planar Superlens and the cylindrical Hyperlens, we had put forward a Concave Hyperlens model, which provided with planar object plane and image plane for ease of usage and measurement, and is capable of shrinking or enlarging the image beyond the resolution limit. The electromagnetic propagation behavior via the multilayer of concave hyperlens has been derived rigorously with the transfer matrix method (TMM). Also the Mathieu functions have been introduced into TMM to study the field propagation in the confocal elliptical coordinate system and the semi-analysis expression for the transmitted field was deduced. The results of numerical calculation demonstrated that the concave hyperlens had demagnification imaging performance with high image contrast. Compared with multilayer planar superlens and planar hyperlens, our concave hyperlens takes on a distinctive non-uniform demagnification ratio.
In order to focus the incident light in far-field with a high efficiency, we brought forward two kinds of nano-focusing schemes based on annular metallic lens with radially polarization illumination. One scheme shifted the near-field focal spot to far field by the modulation of the surface dielectric grating upon the exit plane of the metallic lens. The other one was based on radiationless electromagnetic interference (REI), through the anisotropic metamaterials adjacent to the exit plane of the metallic lens; the evanescent waves are amplified and converged in far-field to form a sub-wavelength focal spot efficiently. Taking advantage of the full wave simulation, we studied the first scheme of far-field sub-wavelength focusing in details and the parameters of the lens structure are optimized through numerical method. The simulation results showed that the far-field sub-wavelength focusing lens has a high focusing efficiency and figures of merit. Further the method to adjust the focal length by changing the annular slits'parameters or the numbers of grooves has been discussed, which are flexible to meet the practical applications.
On all accounts, the overall results of this thesis illustrate that the proposed sub-wavelength metallic structures for far-field super-resolution imaging and the super-nanofocusing can conquer the traditional diffraction limit. The related study on super-resolution imaging and sub-wavelength super-focusing has great theoretical and practical value and is potential for nanometer manufacture technology, optical lithography, high density data storage, biology sensor, new type optical source, analysis and detecting technology and so on.
首先,针对投影光刻成像模拟系统中忽略掩模厚度、入射光的倾斜角度、偏振等因素直接用标量衍射理论进行空间像计算导致预测严重失真的问题,采用严格的矢量电磁理论,借助波导方法分析了三维掩模在离轴照明条件下的近场衍射分布,得到通用的三维掩模模型。该模型综合考虑了入射角、入射方位角、偏振角以及掩模厚度对近场分布的影响,能够反映出亚波长光刻中倾斜入射平面波对三维掩模产生的阴影效应和偏振效应。对分辨率增强技术——光学邻近效应校正(OPC)进行了验证,发现OPC技术可以有效改善掩模的近场分布,从而达到提高远场光刻分辨率的目的。此外通过数值模拟得到了最佳入射角度,与工艺经验值完全吻合。
根据金属-介质交替构成的圆柱形双曲透镜能够突破传统光学衍射限制实现超分辨率远场成像的机理,对双曲透镜结构进行了优化分析,将其应用到193纳米光刻系统中,使用铝和二氧化钛构成各向异性非常强的双曲色散媒质,更有利于远场缩小成像。通过数值分析发现,优化后的双曲透镜,结合相移掩模技术可以实现20纳米以下技术节点,这为拓展和延伸193纳米光刻机提供了新的途径和理论依据。
由于圆柱双曲透镜可以实现缩小/放大成像,但是圆弧形的内外表面不利于物的放置和像的测量；而平板超级透镜有平坦的表面却不具备缩小/放大的功能,因此综合这两种透镜模型各自的优势,设计了具有平坦物面和像面的凹形双曲透镜Concave Hyperlens模型,能够实现超分辨率的缩小/放大成像。利用传递矩阵方法TMM详细分析了光通过该多层结构透镜模型的传播行为,在共焦椭圆坐标系中引入马丢函数得到透射光场的半解析表达式。通过数值方法验证了该透镜所具有的高对比度缩小成像能力,并与多层平板透镜、平板双曲透镜进行了成像性能比较,显现出该透镜模型具有非均匀成像特性。
为了实现高效率远场超聚焦,在环形金属透镜基础上,提出了两种特定结构的金属透镜模型,一种是用介质光栅调制出射面的光场,将径向偏振照明条件下的近场焦斑搬移到远场,实现远场亚波长高效率聚焦；另一种是基于无辐射电磁波干涉,金属透镜出射面用各向异性的超材料媒质填充,可将近场汇聚的能量传递到远场从而得到亚波长焦斑。文中对第一种远场超聚焦透镜进行了详细分析,给出了结构参数的设计方法,并通过数值仿真得到优化后的结构参数及其亚波长聚焦性能。同时为了适应各种应用的需求,可以改变缝的结构参数或者增减光栅槽数进行焦距调节。
综合上述研究结果可知,本文提出的基于亚波长金属结构的远场超分辨率成像透镜和高效率亚波长聚焦透镜,可以突破衍射极限在远场实现亚波长分辨率的超聚焦和成像,这将对纳米加工技术、光刻技术、光存储、生物传感、新型光源、分析与检测技术等光学领域具有重要的理论价值和应用前景。
With the deep research on nanometer scale technology and life science, the diffraction effect that limits the resolution of focusing and imaging in far field is becoming a fetal barrier to super-resolution in the domain of optics, for example optical microscopy, microlithography, optical data storage and etc. In order to obtain a higher resolution in far field, the diffraction limit should be conquered or circumvented by means of some special methods to make evanescent components contribute to the far field focalization or imaging with super-resolution. The surface plasmon polaritons (SPPs) with particular features of such as shorter wavelength than the incident light of excitation, surface localization and near-field enhancement provide a great idea to surpass the diffraction limit and attract more and more attention in related research fields. Based on the sub-wavelength metallic structures, the lens models of far-field sub-wavelength imaging and super-focusing were proposed and the principals were studied in this dissertation. It is observed that the elaborate structures were designed to manipulate the SPPs so that the sub-diffraction-limit imaging and sub-wavelength focal spot could be formed in far-field beyond the resolution limit.
As the thickness of the mask, the oblique incident angles and polarization of the incidence wave were ignored when the scale diffraction theory was applied to calculate the aerial image in the traditional lithography simulation system, there was a great error between the prediction and the actual results transferred from mask to the wafer. The rigorous vectorial electromagnetic theory should be utilized and we exploit the waveguide method to acquire the near field distribution of the three-dimensional (3D) mask with off-axis illumination. A general 3D mask model with respect to the incident angles and the thickness of the mask is derived, which is convenient for aerial image calculation in the simulation of the sub-wavelength lithography fast and precisely. The shadow effect and the polarization effect induced by oblique illumination are illustrated by the numerical method. Furthermore, one of the resolution enhancement technologies, optical proximity effect correction (OPC), combined with the general 3D mask model are verified by related simulations. It was found that the OPC process can amend the near field distribution and enhance the final resolution of the project lithography. Also the optimal incident angles have been obtained by the numerical method, which are consistent with the actual value in practices.
Based on the principle of cylindrical hyperlens, which was made of metal-dielectric alternating multilayer and could distinguish sub-wavelength objects in the far field beyond the traditional diffraction limit, we further optimized the structure of the hyperlens for lithography working at 193nm wavelength. The materials of the metal and the dielectric were replaced by aluminum (Al) and titanic oxide (TiO2) and they exhibited strong anisotropic with hyperbolic dispersion relation, which is propitious to shrinking imaging in far-field. The simulation results show that the 20nm technology node and below can be realized by the optimized hyperlens banding together with the phase-shifting mask,. This scheme can extend the life of the expensive 193nm lithography machines and supply a new precept for nano-scale manufacture.
Although the cylindrical hyperlens is capable of magnification or demagnification, the curved inner and exterior surfaces have serious disadvantages on object location and image measurement. While the slab superlens has planar surfaces but cannot magnify or demagnify the image. Combined with the advantages of the planar Superlens and the cylindrical Hyperlens, we had put forward a Concave Hyperlens model, which provided with planar object plane and image plane for ease of usage and measurement, and is capable of shrinking or enlarging the image beyond the resolution limit. The electromagnetic propagation behavior via the multilayer of concave hyperlens has been derived rigorously with the transfer matrix method (TMM). Also the Mathieu functions have been introduced into TMM to study the field propagation in the confocal elliptical coordinate system and the semi-analysis expression for the transmitted field was deduced. The results of numerical calculation demonstrated that the concave hyperlens had demagnification imaging performance with high image contrast. Compared with multilayer planar superlens and planar hyperlens, our concave hyperlens takes on a distinctive non-uniform demagnification ratio.
In order to focus the incident light in far-field with a high efficiency, we brought forward two kinds of nano-focusing schemes based on annular metallic lens with radially polarization illumination. One scheme shifted the near-field focal spot to far field by the modulation of the surface dielectric grating upon the exit plane of the metallic lens. The other one was based on radiationless electromagnetic interference (REI), through the anisotropic metamaterials adjacent to the exit plane of the metallic lens; the evanescent waves are amplified and converged in far-field to form a sub-wavelength focal spot efficiently. Taking advantage of the full wave simulation, we studied the first scheme of far-field sub-wavelength focusing in details and the parameters of the lens structure are optimized through numerical method. The simulation results showed that the far-field sub-wavelength focusing lens has a high focusing efficiency and figures of merit. Further the method to adjust the focal length by changing the annular slits'parameters or the numbers of grooves has been discussed, which are flexible to meet the practical applications.
On all accounts, the overall results of this thesis illustrate that the proposed sub-wavelength metallic structures for far-field super-resolution imaging and the super-nanofocusing can conquer the traditional diffraction limit. The related study on super-resolution imaging and sub-wavelength super-focusing has great theoretical and practical value and is potential for nanometer manufacture technology, optical lithography, high density data storage, biology sensor, new type optical source, analysis and detecting technology and so on.
引文
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