相移点衍射干涉仪深亚纳米精度参考波前研究
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摘要
极紫外光刻(Extreme Ultraviolet Lithography, EUVL)是适应于27nm~11nm节点的数代超大规模集成电路制造的光刻工艺，它采用13.5nm的曝光波长将掩膜上的电路图形成像到晶圆上。在EUV波段，各种材料的折射率接近于1，且吸收很大，EUVL投影物镜系统必须由镀有多层膜的光学非球面组成的全反射式光学系统。投影物镜系统为了实现衍射极限的分辨率，根据Marachel判据，要求系统波像差达到1.0nm RMS。系统中非球面光学元件在全频段的误差以及多层膜的质量都将影响物镜系统的性能，对于六镜系统，要求非球面面形误差达到0.2nm RMS。
EUVL对投影物镜的高性能要求，给光学加工、检测和装调带来了前所未有的挑战。传统菲索干涉仪或泰曼-格林干涉仪由于受参考元件精度的限制，其测量精度远远无法满足EUVL的检测精度要求。点衍射干涉仪(Point DiffractionInterferometer, PDI)采用准点源衍射产生的球面波作为参考光，避免了常规干涉仪采用参考元件的做法，可以实现深亚纳米量级的检测精度。影响PDI检测精度的因素包括衍射参考球面波的质量、图像采集系统和环境因素等，其中衍射参考球面波的质量直接限定了PDI的检测精度。作为PDI最核心部件的微孔反射镜，其结构和特性决定了衍射参考球面波的质量，从而决定了PDI所能达到的测量精度。
本文针对EUVL曝光光学系统光学元件面形误差和系统波像差高精度检测问题，开展PDI衍射参考波前的理论和实验研究。主要研究内容如下：
1、采用理查德-沃尔夫矢量衍射积分公式，研究在线偏振光和圆偏振光照明条件下，PDI聚焦物镜的像差对焦面上的场强和相位分布的影响情况。聚焦物镜像差和微孔装调误差的存在，照明微孔的光波不再是平面波，在仿真计算中，将聚焦照明光场近似为理想平面波的做法是不妥的。
2、采用光波导理论，研究光纤点衍射干涉仪中单模光纤内的场分布及空间滤波作用。单模光纤只能传输LP01模，耦合入光纤前，系统元件引入的像差将得到有效地滤除。采用标量瑞利-索末菲衍射积分公式，获得了场分布按照Bessel函数分布的端面倾斜光纤远场衍射波前分布的解析表达式。分析了实验中所使用的光纤的远场衍射波前偏差，光纤端面的倾角不影响衍射波前的质量，远场衍射波前在NA0.1内将是理想球面波。
3、采用矢量瑞利-索末菲衍射积分公式分析倾斜照明情况下，零厚度、电导率无限大的导电屏上的微孔，远场衍射波前分布情况，比较线偏振光和圆偏振光照明条件下，远场衍射波前质量的差别。倾斜照明光波不影响微孔衍射波前的质量，仅使衍射波前的强度分布偏离微孔中心轴线，而不影响衍射波前偏差。采用线偏振光照明和圆偏振光照明，远场衍射波前偏差在同一个数量级，线偏振情况下，衍射波前中存在较大的像散，而圆偏振光照明时，衍射波前中主要旋转对称的像差。
4、采用矢量瑞利-索末菲衍射积分公式分析微孔圆度误差对远场衍射波前质量的影响情况。微孔边缘粗糙度对衍射波前偏差有着显著的影响，对强度分布几乎无影响。微孔椭圆度对衍射波前偏差的影响较小，对强度分布则有重要的影响。
5、对有限厚度有限电导率的微孔进行FDTD仿真分析，对影响微孔衍射波前质量的因素（包括微孔材料、厚度、直径大小、形状，聚焦物镜像差，微孔漂移、离焦和倾斜）进行了仿真分析。Cr是微孔材料的首选，Al次之。微孔的厚度不宜小于200nm。当检测NA0.3的系统时，采用直径800nm的微孔较为适宜，当检测NA0.3的元件时，采用直径500nm的微孔较为适宜。在微孔的装调过程中，微孔的离焦量需大于-175nm，漂移量应控制在125nm内。
6、采用格拉姆-施密特正交化法进行高精度矢量多项式波面拟合。该算法同样适用于环形Zernike多项式的拟合，且具有同样的精度。
7、采用杨氏双孔干涉法对光纤衍射参考波前偏差进行实验测量，并分析实验中的系统误差。两球面波点源的间距将给测量结果引入彗差，而探测器的倾斜将给测量结果引入像散。对OPD进行了高阶的二项式展开，以减小高NA情况下的近似误差。对两对光纤衍射参考波前偏差进行了测量，测得两对光纤衍射波前在NA0.1内的偏差分别为0.1416±0.0084nm RMS和0.1560±0.0211nmRMS，即实验测得光纤衍射波前的偏差约为λ/3500RMS。
总之，本文从理论和实验两方面对PDI衍射参考波前进行了理论和实验研究，获得了满足EUVL元件面形误差和系统波像差检测要求的深亚纳米精度参考波前。本文的研究工作将为EUVL系统波像差的高精度检测储备技术条件，为大NAPDI衍射参考波前偏差以及大NAPDI测量精度的评定提供方法，奠定基础。
Extreme Ultraviolet Lithography (also known as EUVL) is a lithographyprocess adapt to the mass production of ultra-large-scale integrated circuits with27nm~11nm features. The image of a desired circuit pattern is formed on asemiconductor wafer with an optical imaging system that operates at a wavelength of13.5nm. At the extreme ultraviolet wavelengths, the complex refractive index of anymedium is very close to one, and extreme ultraviolet projection lithography utilizesall-reflective multilayer-coated optics due to the strong absorption of EUV radiationby all materials. In order to achieve diffraction-limited performance, according toMarachel’s criterion, the wave front aberration of the projection objective lensshould be less than1.0nm RMS. Wave front errors of the aspheric reflective opticalelements over the entire range of spatial frequencies as well as the multilayer coatingdefects will affect the performance of the projection objective lens, the figure errorof the aspheric elements in the six-mirrors system should be less than0.2nm RMS.
The high-performance requirements of the projection lens in EUVL, poseunprecedented challenges to optical fabrication, optical testing and optical alignment.The measurement accuracy of the traditional interferometers, such as Fizeauinterferometer or a Twyman-Green interferometer, is limited by the referenceelement, far able to meet the requirements during EUVL development. A pointdiffraction interferometer (PDI) with sub-nanometer wave front-measuring accuracy can be realized by using the near-perfect spherical wave diffracted by a quasi-pointsource. The measurement accuracy of a PDI is limited by many factors, such as thequality of the diffracted reference spherical wave, the image acquisition system, themeasurement environment, and so on. The quality of the diffracted referencespherical wave, which determined by the quality of the tiny pinhole in a pinholeplate, is the most subtle one that limited the measurement accuracy of a PDI.
Due to the figure error of the optical elements and the wave front aberration ofthe imaging system in EUVL should be characterized with high accuracy, it isnecessary to study the quality of the diffracted reference wave front in a PDI both bytheoretically and experimentally. The main contents in this paper are as follows:
1Based on Richard-Wolf vector diffraction integral formula and the incidentlight is linearly polarized light or circularly polarized light, the effect of theaberrations presented in the focusing lens on the intensity and phase distribution nearthe focal plane is in depth-study this time. The wave in the focal plane is no longer aperfect plane wave due to focusing lens aberrations and the miss-alignment of thepinhole mirror, and the results will be different if use the plane wave as the incidentwave during pinhole diffraction calculation.
2The field distribution within a single-mode fiber in fiber point diffractioninterferometer is calculated base on the theory of optical waveguide. Single-modefiber can only transfer the LP01mode. The aberrations, introduced by previouselements in a system, coupled into the fiber, will be effectively filtered. The far fielddistribution of a single mode optical fiber with tilted end face is calculated analyticalby using the Scalar Rayleigh-Sommerfeld diffraction integral formula, the initialfield used in calculated is in the form of Bessel function. The deviation of the farfield diffracted by the single mode optical fiber used in this experiment is thencalculated. The fiber end face inclination does not affect the sphericity of itsdiffracted wave front.
3The distribution of the far field diffracted by a tiny pinhole on a conductivescreen with zero thickness and infinite conductivity is calculated base on vector Rayleigh-Sommerfeld integral formula in the case of oblique illumination. Thedifference of the diffracted far field for linearly polarized light and circularlypolarized light illumination is then clearly. The oblique angle of the incident wavedoes not affect the sphericity of the diffracted wave front. Only the intensitydistribution in the diffracted wave deviates from the center axis of the pinhole. Thesphericity of the diffracted wave front is almost the same for linearly polarizedillumination and circularly polarized illumination. The main aberration present inthe diffracted wave is astigmatism when the incident light is linearly polarized andthe rotationally symmetric aberration when the incident light is circularly polarized.
4The effect of the pinhole roundness on the quality of the diffracted wave frontin the far field is analyzed by using the vector Rayleigh-Sommerfeld integral. Edgeroughness of the tiny pinhole has a significant impact on the deviation of the wavefront, and has little effect on the intensity, while the ovality of the tiny pinhole has alittle impact on wave front deviations, but has an important impact on the intensitydistribution.
5The FDTD simulation is carried out to calculate the diffraction of a tinypinhole on the screen with finite conductivity and finite thickness. The factorsaffecting the quality of the diffracted wave front, including the material, thethickness, the diameter, the size and the shape of a pinhole, the aberrations present inthe focusing lens, the miss-alignment of the pinhole, and so on. The candidate forpinhole material is Cr and Al, and their thickness should not be less than200nm.When a system with NA0.3is under testing, then the pinhole with a diameter of800nm is a good choice, while for testing an element of NA0.3, the diameter of thepinhole should be about500nm. In the alignment process of the pinhole, the amountof defocus must be greater than-175nm, and the amount of shift should be no morethan125nm.
6The high precision wave front fitting is realized by using the algorithm ofGram-Schmidt. The algorithm can also be used in the annular Zernike polynomialfitting, and has the same accuracy.
7The deviation of the wave front diffracted by a single mode optical fiber ismeasured analogous to Young's two-hole experiment. The systematic errors in theexperiment are precision analyzed. The separation of the two point sources willintroduce the comatic aberration to the testing result, and the incline of the detectorduring the measurement will introduce the astigmatism to the testing result. Toreduce the approximation error in wave front with large NA, the OPD is expanded tobinomial and the high power terms are considered. The deviation of the wave frontdiffracted by each fiber is measured by experimentally. The deviation of the wavefront diffracted by two pairs of fiber are0.1416±0.0084nm RMS and0.1560±0.0211nm RMS, respectively; therefore, the measured deviation of the wave frontdiffracted by the single mode optical fiber is about λ/3500RMS.
In a word, the deep sub-nanometer accuracy diffracted reference wave front in aPDI is studied both by theoretically and experimentally in this paper, which is meetthe measuring accuracy requirement in testing the figure error of the optical elementand wave front aberration of the imaging system in EUVL. This work Reservetechnical conditions for testing EUVL projection optics with high accuracy, and laysfoundation for assessing the sphericity of the reference wave front with moredivergence angle and measurement accuracy of a PDI with large NA.
EUVL对投影物镜的高性能要求，给光学加工、检测和装调带来了前所未有的挑战。传统菲索干涉仪或泰曼-格林干涉仪由于受参考元件精度的限制，其测量精度远远无法满足EUVL的检测精度要求。点衍射干涉仪(Point DiffractionInterferometer, PDI)采用准点源衍射产生的球面波作为参考光，避免了常规干涉仪采用参考元件的做法，可以实现深亚纳米量级的检测精度。影响PDI检测精度的因素包括衍射参考球面波的质量、图像采集系统和环境因素等，其中衍射参考球面波的质量直接限定了PDI的检测精度。作为PDI最核心部件的微孔反射镜，其结构和特性决定了衍射参考球面波的质量，从而决定了PDI所能达到的测量精度。
本文针对EUVL曝光光学系统光学元件面形误差和系统波像差高精度检测问题，开展PDI衍射参考波前的理论和实验研究。主要研究内容如下：
1、采用理查德-沃尔夫矢量衍射积分公式，研究在线偏振光和圆偏振光照明条件下，PDI聚焦物镜的像差对焦面上的场强和相位分布的影响情况。聚焦物镜像差和微孔装调误差的存在，照明微孔的光波不再是平面波，在仿真计算中，将聚焦照明光场近似为理想平面波的做法是不妥的。
2、采用光波导理论，研究光纤点衍射干涉仪中单模光纤内的场分布及空间滤波作用。单模光纤只能传输LP01模，耦合入光纤前，系统元件引入的像差将得到有效地滤除。采用标量瑞利-索末菲衍射积分公式，获得了场分布按照Bessel函数分布的端面倾斜光纤远场衍射波前分布的解析表达式。分析了实验中所使用的光纤的远场衍射波前偏差，光纤端面的倾角不影响衍射波前的质量，远场衍射波前在NA0.1内将是理想球面波。
3、采用矢量瑞利-索末菲衍射积分公式分析倾斜照明情况下，零厚度、电导率无限大的导电屏上的微孔，远场衍射波前分布情况，比较线偏振光和圆偏振光照明条件下，远场衍射波前质量的差别。倾斜照明光波不影响微孔衍射波前的质量，仅使衍射波前的强度分布偏离微孔中心轴线，而不影响衍射波前偏差。采用线偏振光照明和圆偏振光照明，远场衍射波前偏差在同一个数量级，线偏振情况下，衍射波前中存在较大的像散，而圆偏振光照明时，衍射波前中主要旋转对称的像差。
4、采用矢量瑞利-索末菲衍射积分公式分析微孔圆度误差对远场衍射波前质量的影响情况。微孔边缘粗糙度对衍射波前偏差有着显著的影响，对强度分布几乎无影响。微孔椭圆度对衍射波前偏差的影响较小，对强度分布则有重要的影响。
5、对有限厚度有限电导率的微孔进行FDTD仿真分析，对影响微孔衍射波前质量的因素（包括微孔材料、厚度、直径大小、形状，聚焦物镜像差，微孔漂移、离焦和倾斜）进行了仿真分析。Cr是微孔材料的首选，Al次之。微孔的厚度不宜小于200nm。当检测NA0.3的系统时，采用直径800nm的微孔较为适宜，当检测NA0.3的元件时，采用直径500nm的微孔较为适宜。在微孔的装调过程中，微孔的离焦量需大于-175nm，漂移量应控制在125nm内。
6、采用格拉姆-施密特正交化法进行高精度矢量多项式波面拟合。该算法同样适用于环形Zernike多项式的拟合，且具有同样的精度。
7、采用杨氏双孔干涉法对光纤衍射参考波前偏差进行实验测量，并分析实验中的系统误差。两球面波点源的间距将给测量结果引入彗差，而探测器的倾斜将给测量结果引入像散。对OPD进行了高阶的二项式展开，以减小高NA情况下的近似误差。对两对光纤衍射参考波前偏差进行了测量，测得两对光纤衍射波前在NA0.1内的偏差分别为0.1416±0.0084nm RMS和0.1560±0.0211nmRMS，即实验测得光纤衍射波前的偏差约为λ/3500RMS。
总之，本文从理论和实验两方面对PDI衍射参考波前进行了理论和实验研究，获得了满足EUVL元件面形误差和系统波像差检测要求的深亚纳米精度参考波前。本文的研究工作将为EUVL系统波像差的高精度检测储备技术条件，为大NAPDI衍射参考波前偏差以及大NAPDI测量精度的评定提供方法，奠定基础。
Extreme Ultraviolet Lithography (also known as EUVL) is a lithographyprocess adapt to the mass production of ultra-large-scale integrated circuits with27nm~11nm features. The image of a desired circuit pattern is formed on asemiconductor wafer with an optical imaging system that operates at a wavelength of13.5nm. At the extreme ultraviolet wavelengths, the complex refractive index of anymedium is very close to one, and extreme ultraviolet projection lithography utilizesall-reflective multilayer-coated optics due to the strong absorption of EUV radiationby all materials. In order to achieve diffraction-limited performance, according toMarachel’s criterion, the wave front aberration of the projection objective lensshould be less than1.0nm RMS. Wave front errors of the aspheric reflective opticalelements over the entire range of spatial frequencies as well as the multilayer coatingdefects will affect the performance of the projection objective lens, the figure errorof the aspheric elements in the six-mirrors system should be less than0.2nm RMS.
The high-performance requirements of the projection lens in EUVL, poseunprecedented challenges to optical fabrication, optical testing and optical alignment.The measurement accuracy of the traditional interferometers, such as Fizeauinterferometer or a Twyman-Green interferometer, is limited by the referenceelement, far able to meet the requirements during EUVL development. A pointdiffraction interferometer (PDI) with sub-nanometer wave front-measuring accuracy can be realized by using the near-perfect spherical wave diffracted by a quasi-pointsource. The measurement accuracy of a PDI is limited by many factors, such as thequality of the diffracted reference spherical wave, the image acquisition system, themeasurement environment, and so on. The quality of the diffracted referencespherical wave, which determined by the quality of the tiny pinhole in a pinholeplate, is the most subtle one that limited the measurement accuracy of a PDI.
Due to the figure error of the optical elements and the wave front aberration ofthe imaging system in EUVL should be characterized with high accuracy, it isnecessary to study the quality of the diffracted reference wave front in a PDI both bytheoretically and experimentally. The main contents in this paper are as follows:
1Based on Richard-Wolf vector diffraction integral formula and the incidentlight is linearly polarized light or circularly polarized light, the effect of theaberrations presented in the focusing lens on the intensity and phase distribution nearthe focal plane is in depth-study this time. The wave in the focal plane is no longer aperfect plane wave due to focusing lens aberrations and the miss-alignment of thepinhole mirror, and the results will be different if use the plane wave as the incidentwave during pinhole diffraction calculation.
2The field distribution within a single-mode fiber in fiber point diffractioninterferometer is calculated base on the theory of optical waveguide. Single-modefiber can only transfer the LP01mode. The aberrations, introduced by previouselements in a system, coupled into the fiber, will be effectively filtered. The far fielddistribution of a single mode optical fiber with tilted end face is calculated analyticalby using the Scalar Rayleigh-Sommerfeld diffraction integral formula, the initialfield used in calculated is in the form of Bessel function. The deviation of the farfield diffracted by the single mode optical fiber used in this experiment is thencalculated. The fiber end face inclination does not affect the sphericity of itsdiffracted wave front.
3The distribution of the far field diffracted by a tiny pinhole on a conductivescreen with zero thickness and infinite conductivity is calculated base on vector Rayleigh-Sommerfeld integral formula in the case of oblique illumination. Thedifference of the diffracted far field for linearly polarized light and circularlypolarized light illumination is then clearly. The oblique angle of the incident wavedoes not affect the sphericity of the diffracted wave front. Only the intensitydistribution in the diffracted wave deviates from the center axis of the pinhole. Thesphericity of the diffracted wave front is almost the same for linearly polarizedillumination and circularly polarized illumination. The main aberration present inthe diffracted wave is astigmatism when the incident light is linearly polarized andthe rotationally symmetric aberration when the incident light is circularly polarized.
4The effect of the pinhole roundness on the quality of the diffracted wave frontin the far field is analyzed by using the vector Rayleigh-Sommerfeld integral. Edgeroughness of the tiny pinhole has a significant impact on the deviation of the wavefront, and has little effect on the intensity, while the ovality of the tiny pinhole has alittle impact on wave front deviations, but has an important impact on the intensitydistribution.
5The FDTD simulation is carried out to calculate the diffraction of a tinypinhole on the screen with finite conductivity and finite thickness. The factorsaffecting the quality of the diffracted wave front, including the material, thethickness, the diameter, the size and the shape of a pinhole, the aberrations present inthe focusing lens, the miss-alignment of the pinhole, and so on. The candidate forpinhole material is Cr and Al, and their thickness should not be less than200nm.When a system with NA0.3is under testing, then the pinhole with a diameter of800nm is a good choice, while for testing an element of NA0.3, the diameter of thepinhole should be about500nm. In the alignment process of the pinhole, the amountof defocus must be greater than-175nm, and the amount of shift should be no morethan125nm.
6The high precision wave front fitting is realized by using the algorithm ofGram-Schmidt. The algorithm can also be used in the annular Zernike polynomialfitting, and has the same accuracy.
7The deviation of the wave front diffracted by a single mode optical fiber ismeasured analogous to Young's two-hole experiment. The systematic errors in theexperiment are precision analyzed. The separation of the two point sources willintroduce the comatic aberration to the testing result, and the incline of the detectorduring the measurement will introduce the astigmatism to the testing result. Toreduce the approximation error in wave front with large NA, the OPD is expanded tobinomial and the high power terms are considered. The deviation of the wave frontdiffracted by each fiber is measured by experimentally. The deviation of the wavefront diffracted by two pairs of fiber are0.1416±0.0084nm RMS and0.1560±0.0211nm RMS, respectively; therefore, the measured deviation of the wave frontdiffracted by the single mode optical fiber is about λ/3500RMS.
In a word, the deep sub-nanometer accuracy diffracted reference wave front in aPDI is studied both by theoretically and experimentally in this paper, which is meetthe measuring accuracy requirement in testing the figure error of the optical elementand wave front aberration of the imaging system in EUVL. This work Reservetechnical conditions for testing EUVL projection optics with high accuracy, and laysfoundation for assessing the sphericity of the reference wave front with moredivergence angle and measurement accuracy of a PDI with large NA.
引文
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