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计量是关于测量的科学,但不同于测量,其主要任务在于实现量值单位统一、确保测量结果准确可靠。计量学的每一次发展变革都将为科技发展带来新的突破进展。1999年,国际计量局在《米制公约》中确定将稳频激光器输出的光的波长频率作为“米”的国际标准谱线,并利用该标准谱线作为计量基准,用于校准计量型纳米测量仪器,这是纳米工艺实现规范化的首要突破[18]。2018年,第26届国际计量大会上通过了国际单位制(SI)重新定义的决议,七个基本单位全部溯源于基本自然常数,为精密制造和校准产业带来了跨越式发展。在量子信息技术发展日异月新的当下,国际计量体系也逐渐向计量基准量子化和量值传递扁平化发展。计量的发展也将带动精密测量技术的不断进步,是科研革新、工业制造等领域的推进器。传统的精密测量主要使用量块、千分表等标定标准物质对样片尺寸进行测量或对仪器设备进行校准,在该计量校准溯源体系中需要将测量值与已知值的参考标准进行比较,随后溯源至SI标准或基本自然常数,因此多维误差将从多个溯源阶段参与进最终测量结果中,显著提高校准不确定度。为了降低设备误差、环境误差等因素,引入具有计量特性的标准物质对需求参数进行精密测量,能够提高测量结果的可重复性和可靠性。文中使用的自溯源型光栅由于其计量特性引入了新型计量溯源体系,能够有效缩短测量校准溯源链,将测量结果稳定溯源到基本自然常数,实现测量结果精密可靠。
自溯源铬光栅基于原子光刻技术进行制造,一维原子光刻技术可以用于制备周期自溯源于铬原子跃迁能级7S3→7P40对应波长λ的一维λ/2周期的自溯源光栅。原子光刻的基本原理是原子在驻波场中运动时与光的相互作用,其中偶极力是形成光栅的关键,当原子处于空间电场强度变化的光场中时,会受到与电场强度梯度成正比的偶极力,表示为$F = - \nabla U$,从量子角度分析并构建半经典模型[19],在激光光强较小且失谐量较大的情况下,原子跃迁到激发态的概率较小,自发辐射率较小。假设铬原子为二能级原子且在保守势场中运动,其基态原子势能可表示为:
$$ U = \frac{{\hbar {\gamma ^2}}}{{8\Delta }}\frac{I}{{{I_s}}} $$ (1) 式中:$\hbar = h/2\pi $为约化普朗克常数;$\gamma $为原子跃迁的自然线宽;$\Delta $为激光频率与原子共振频率的失谐量;I为空间变化的光场强度;Is为原子跃迁的饱和强度。通过公式(1)可知,当$\Delta > 0$时,光场强度最小处,原子势能最小,向光强最小处移动,沉积于驻波场波节处。同理,$\Delta < 0$时,原子沉积于波腹处,文中使用的是在$\Delta > 0$条件下制备的一维原子光刻铬光栅。如图1所示为光栅结构AFM扫描图像,由激光频率锁定于铬原子跃迁频率可得,制备所得光栅的周期为λ/2,即铬原子跃迁频率对应波长的一半,直接溯源于原子跃迁频率这一自然常数,其理论节距值[20]为(212.7705±0.0049) nm。实验中基于多普勒效应进行激光稳频、利用光与原子作用的自发辐射力降低原子横向速度进行激光冷却,减小原子束出射发散角,实现大面积高均一性自溯源光栅制备,光栅平均节距[21]为(212.782±0.008) nm,具有极高的准确性。
自溯源光栅由于其能够以极小的不确定度固化基本自然常数这一特性,作为纳米级长度标准物质具有独特优势,同时其天然的溯源特性也有效缩短了应用中进行测量与校准的溯源链,将测量值直接与稳定的自然常数进行对比,确保了测量校准的准确性和可靠性。此外,采用正负失谐法、偏振梯度法、多光束干涉法等可有效缩小铬光栅节距,同时原子光刻技术结合软X射线干涉光刻技术可将光栅节距缩小至53.2 nm,提升了纳米尺度下的测量校准精度。自溯源光栅作为一种精准的纳米级长度标准物质,特别是在集成电路产业工艺节点进入纳米级的当下,在纳米技术中具有重要应用价值。二维材料由于其具有高载流子迁移率的特性,在晶圆级集成电路以及电子器件制造领域有着极高的应用潜力。因此,使用自溯源光栅对二维材料的光电特性进行精密研究是一个刻不容缓的课题。
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hBN/自溯源光栅复合结构形成了对PhPs的周期性调制作用,考虑到原子光刻铬光栅的自溯源特性,使测得的PhPs近场光学图像展现出与光栅周期相符的激发增强条纹,条纹间距可溯源至铬原子跃迁频率对应波长的一半λ/2,即212.782 nm,其中光栅样品引入的测量不确定度为0.008 nm。此外,成像设备SNOM通过收集针尖和样品之间的近场相互作用散射场信号进行测量,其成像分辨率受到探针尖端曲率的限制,该实验所用SNOM分辨率为10 nm,且基于原子力显微镜(Atomic Force Microscope, AFM)搭建的SNOM无法避免扫描不同尺寸图像的过程中,电动位移台会引入的位移误差。利用AFM和SNOM对同一样品位置不同扫描范围进行了近场光学信号测量精度的对比性研究,图5(a)~(c)分别为1 µm×1 µm、5 µm×5 µm以及10 µm×10 µm不同扫描范围的AFM图像,图5(d)~(f)为对应的SNOM成像。采用图像分析软件分析干涉条纹周期以及自溯源光栅图像分析方法,对不同扫描范围的SNOM成像进行对比研究,测量结果表现出自溯源光栅对测量值精度的有效提升,见表1。
采用图像分析软件对近场显微图中干涉条纹的周期进行线性拟合,提取干涉条纹的周期数值,该图像分析软件测量精度为0.001 µm,因此使用该方法测得干涉条纹周期值保留至1 nm位数。利用该方法所得测量结果表现出,当扫描范围较小时,测量误差较大;扫描范围较大时,由于SNOM图像中有多个干涉条纹用于数据拟合,因此测量误差较小。但是,对比三种不同扫描范围,整体测量结果具有不稳定性,考虑到设备分辨率为10 nm,标准偏差值可计算为4 nm。
自溯源光栅图像分析方法通过编写图像分析程序,对干涉条纹周期与自溯源光栅进行比对测量,以光栅周期为标尺,测定干涉条纹周期,在测量过程中,设置光栅节距大小为212.78 nm,精确至0.01 nm,因此利用该方法的测量结果保留两位小数。文中1 µm×1 µm、5 µm×5 µm以及10 µm×10 µm三种扫描范围的图像中,自溯源光栅节距值始终稳定,能够在不同扫描范围下作为稳定的标尺使用,对干涉条纹周期的测量值标准偏差为0.34 nm。与图像分析软件中数据拟合的测量方法得到的标准偏差为4 nm相比,文中提出的自溯源光栅图像分析方案将测量精度提升了一个数量级,实现了亚纳米精度的测量。为进一步降低测量偏差值,一方面可采用高度较高的自溯源光栅与hBN相结合,以提供更强的耦合信号,提升计算准确率;另一方面,在二维材料制备过程中确保边缘整齐、高度均匀,以提供分布均匀的边缘激发信号。此外,自溯源光栅的引入,不仅能够测量周期尺寸,也可对探测设备的测量位置进行校准。以该研究测试设备SNOM为例,图5(f)中已测量的条纹周期为261.41 nm,与图像分析软件拟合测量值为257 nm,因此设备位移装置应校准尺寸$ \mathrm{\Delta }U $约为−0.18 nm/pt,校准不确定度与光栅不确定度相关,具有亚纳米级准确度。然而,实际测量中仍需考虑设备分辨率对测量准确度产生的影响。仍以SNOM为例,其位移台在二维XY方向精度<0.2 nm,接近校准需求,则在实际校准中,受机械结构固有精度影响仅可在极限位移精度下完成精确校准。
图 5 不同扫描范围的hBN/光栅复合结构的AFM图像及SNOM图像对比性研究。(a)~(c) 样品表面结构AFM成像(成像大小分别为1 µm×1 µm、5 µm×5 µm、10 µm×10 µm); (d)~(f) 样品近场光学成像 (成像大小分别与上图对应)
Figure 5. A comparative study of AFM and SNOM images of hBN/grating composite structures with different scanning ranges. (a)-(c) AFM imaging of the sample surface morphology (The imaging sizes are 1 µm×1 µm, 5 µm×5 µm, and 10 µm×10 µm, respectively); (d)-(f) Near-field optical imaging of the sample corresponding to the previous images (The imaging sizes are the same as mentioned above)
表 1 不同扫描范围图像干涉条纹周期测量
Table 1. Measurement of interference fringe period in images with different scanning ranges
Scanning range/µm2 Image analysis and period fitting/nm Image analysis of self-traceable grating/nm 1×1 264 261.28 5×5 254 260.35 10×10 257 261.41 S. D. 4 0.34
Research on precise measurement of phonon-polariton interference fringe period
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摘要: 二维材料由于其独特的物理化学性质,对纳米光子学及光电子学的应用与发展具有重要研究价值。特别是二维材料中声子与光子耦合激发产生的声子极化激元高度局域在纳米尺度,在片上光子学的光学操控和能量传输等前沿研究领域具有极大的应用潜力。同时,光电器件制造进入纳米节点,器件应用对材料表征精度具有纳米级的要求。然而目前对声子极化激元特性分析的关键之一在于测量其干涉条纹周期,测量结果准确性依赖于仪器设备校准。因此,为实现对声子极化激元干涉条纹的精确测量,文中提出构建铬原子自溯源型光栅与二维材料的复合结构,分析金属光栅结构周期性变化对二维材料的声子极化激元耦合增强与调制作用,以及基于该原理实现对声子极化激元干涉条纹周期的精密测量。研究实现了测量干涉条纹周期为(261.01±0.34) nm的亚纳米级高精度测量,相比具有不确定度为4 nm的传统拟合测量方式具有可溯源的计量精度,同时实现了对测量仪器的亚纳米级精密校准。自溯源光栅天然溯源至基本自然常数的特性使得测量结果具备极好的准确性和可靠性,为二维材料在微纳光子学器件领域的应用提供了保障。Abstract:
Objective Two-dimensional materials have garnered widespread attention due to their unique photoelectric properties at the nanoscale, showcasing distinctive application advantages in the fields of nano-electronic devices, optics, and energy. Notably, the phonon polaritons generated by the coupled excitation of phonons and photons in two-dimensional materials exhibit highly localized at the nanometer scale, presenting substantial application potential in cutting-edge research fields such as optical manipulation and energy transmission of on-chip photonics. Infrared imaging of the sample revealed that at the sample's edge, the mutual interference of phonon polaritons resulted in the fomation of polarization standing wave fringes parallel to the edge. The fringe period effectively reflects the coupling characteristics of phonon polaritons. Therefore, the study of modulated phonon polariton coupling primarily relies on the precise measurement of the interference fringe period. The current measurement method depends on the linear fitting calculation of image analysis software, and its accuracy is constrained by the image resolution. Additionally, the displacement errors occur in the sample loading stage of SNOM. To enhance measurement accuracy and minimize the impact of the these errors on the measured value, this paper proposes the use a self-traceable chromium grating for the precise measurement of the period of the polariton interference fringe in hBN. Methods In this paper, we present a self-traceable grating-hBN composite structure. The construction involves depositing a chromium grating on the silicon substrate using atomic lithography. The gaps between adjacent grating structures consist of air, and the two-dimensional polar material hBN is placed on the chromium grating. The dispersion of phonon polaritons generated by the recombination of hBN and different media is analyzed using Fabry-Perot quantization conditions. The study further investigates the phonon polariton coupling enhancement and modulation characteristics of two-dimensional polar materials resulting from periodic changes in metal grating structures. Scanning near-field optical microscopy (SNOM) was employed to image the phonon polaritons of the composite structure in near-field space during sample processing. Imaging of different sizes is conducted at the same point, and two methods are employed for image processing for comparison. The first method involves traditional linear fitting based on Gwyddion for calculating the interference fringe period, while the second one utilizes the use of image analysis program to perform self-traceable grating comparison measurement on the fringe period. Results and Discussions When using the traditional Gwyddion-based linear fitting for calculating the interference fringe period, the measured fringe period in the 1 µm×1 µm near-field optical imaging is 0.264 µm, in the 5 µm×5 µm image is 0.254 µm, and in the 10 µm×10 µm image is 0.257 µm. It is observed that when the size of the measurement image is small, the error offset is large. After a large-scale scanning, the measurement value tends to stabilize, yet the overall measurement result remains unstable. Considering the 10 nm resolution of SNOM, the standard deviation value is calculated as 4 nm. Simultaneously, the image analysis program is employed to perform self-traceable grating comparison measurement on the fringe period, The grating period serves as the scale for measuring the interference fringe period. The fringe periods measured in 1 µm×1 µm, 5 µm×5 µm and 10 µm×10 µm images are 261.28 nm, 260.35 nm, 261.41 nm respectively, with a standard deviation of the measured values at 0.34 nm. Compared with the standard deviation of 4 nm from the traditional measurement method, this presents an order of magnitude reduction, achieving higher precision. When the self-traceable grating is employed, it not only measure the period size, but also calibrate the measurement point of the detection equipment. Taking SNOM in this study as an example, the calibration size ΔU of the equipment displacement device is approximately −0.18 nm/pt, with uncertainty related to the grating uncertainty, achieving sub-nanometer accuracy. However, the actual measurement still needs to consider the impact of the device resolution on measurement accuracy. Conclusions By constructing a composite structure comprising a self-traceable chromium grating and a two-dimensional polar material hBN, this study leverages the periodic enhancement principle of phonon polariton intensity generated by the structural changes in the substrate grating material. Employing a scanning near-field optical microscope for imaging, the resulting composite structure exhibits coupling-enhancing fringes consistent with the self-tracing grating pitch distribution. Through image analysis and measurement, the self-traceable grating period of 212.782 nm is utilized as the scale. The interference fringe period is measured to be (261.01±0.34) nm, achieving a measurement with higher accuracy than the uncertainty of the traditional fitting method. Simultaneously, nanoscale calibration of the device can be realized based on the measurement results. In this paper, the imaging calibration of the SNOM device is determined to be −0.18 nm/pt, with uncertainty linked to the grating uncertainty. This grating metrology method offers a measurement approach with superior accuracy and reliability for precisely measuring the excitation wavelength of phonon polaritons and controlling the coupling of photon and phonon. Additionally, it provides an experimental basis for the design and regulation of two-dimensional materials applied to nanoscale devices. -
图 4 (a) 样品测试设备,BRUKER公司纳米级红外光谱仪Anasys nanoIR3-s,具有10 nm空间分辨率;(b) 样品近场光学成像,其中蓝色为hBN/自溯源光栅复合结构区域,黄色为自溯源光栅区域;(c) 样品表面结构AFM成像
Figure 4. (a) Sample testing equipment, BRUKER Company’s nanoscale infrared spectrometer Anasys nanoIR3-s, with 10 nm spatial resolution; (b) Near-field optical imaging of the sample, where the blue color represents the region of the hBN/self-traceable grating structure, and the yellow color represents the region of the self-traceable grating; (c) Atomic Force Microscopy imaging of the surface structure of the sample
图 5 不同扫描范围的hBN/光栅复合结构的AFM图像及SNOM图像对比性研究。(a)~(c) 样品表面结构AFM成像(成像大小分别为1 µm×1 µm、5 µm×5 µm、10 µm×10 µm); (d)~(f) 样品近场光学成像 (成像大小分别与上图对应)
Figure 5. A comparative study of AFM and SNOM images of hBN/grating composite structures with different scanning ranges. (a)-(c) AFM imaging of the sample surface morphology (The imaging sizes are 1 µm×1 µm, 5 µm×5 µm, and 10 µm×10 µm, respectively); (d)-(f) Near-field optical imaging of the sample corresponding to the previous images (The imaging sizes are the same as mentioned above)
表 1 不同扫描范围图像干涉条纹周期测量
Table 1. Measurement of interference fringe period in images with different scanning ranges
Scanning range/µm2 Image analysis and period fitting/nm Image analysis of self-traceable grating/nm 1×1 264 261.28 5×5 254 260.35 10×10 257 261.41 S. D. 4 0.34 -
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