Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed,and a method to eliminate this effect is proposed.Based on the simulation result of the SE measurement on a silicon sphere by ray tracking,we find that the sphere makes the parallel incident beam of the SE be divergent after reflection,and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory.By settling an aperture in front of the detector of the SE,we can almost eliminate the error.For the silicon sphere with a diameter of 94 mm used in the Avogadro project,the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method.The principle of the method and the results of the experimental verification are presented.     

基于飞秒光频梳的双频He-Ne激光器频率测量

利用光纤飞秒光频梳和外腔可调谐半导体激光器, 建立了一套双频He-Ne激光器频率测量系统. 选用铷钟作为系统的频率基准, 通过将外腔半导体激光锁定至光频梳使得其频率溯源至铷钟, 再利用外腔可调谐半导体激光与双频He-Ne激光器输出的正交偏振激光拍频, 同时测量两路正交偏振激光频率. 将可调谐半导体激光器锁定至光频梳第1894449个梳齿, 其绝对频率为473612190000.0±2.7 kHz, 相对不确定度为5.7×10^-12. 对商品双频He-Ne激光器进行频率测量实验, 双频He-Ne激光器水平方向偏振激光频率均值为473612229934 kHz, 竖直方向偏振激光频率均值为473612232111 kHz, 平均时间为1024 s的相对Allan标准差为5.2×10^-11, 频差均值为2.177 MHz, 标准偏差为2 kHz.     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.     

基于飞秒光频梳的压电陶瓷闭环位移控制系统

利用飞秒光频梳、外腔可调谐半导体激光器和法布里-珀罗干涉仪建立了一套压电陶瓷亚纳米级闭环位移控制系统. 将可调谐半导体激光器锁定至光频梳, 通过精确调谐光频梳的重复频率, 实现了半导体激光器在其工作频率范围内的精密调谐. 利用Pound-Drever-Hall锁定技术将带有压电陶瓷的法布里-珀罗腔锁定至半导体激光器, 进而通过频率发生系统控制压电陶瓷产生亚纳米级分辨率的位移. 实验研究发现锁定至光频梳后可调谐半导体激光器1 s的Allan标准偏差为1.68×10^-12, 将其在30.9496 GHz范围内进行连续闭环调谐, 可获得压电陶瓷的位移行程约为4.8 μm; 以3.75 Hz的步长扫描光频梳的重复频率, 实现了压电陶瓷的450 pm闭环位移分辨率并测定了压电陶瓷的磁滞特性曲线. 该系统不存在非线性测量误差, 且激光频率及压电陶瓷位移均溯源至铷钟频率源. 关键词： 光频梳 压电陶瓷 法布里-珀罗腔 可调谐半导体激光器     

Determination of Mean Thickness of an Oxide Layer on a Silicon Sphere by Spectroscopic Ellipsometry

One of the biggest obstacles to reduce the uncertainty of the Avogadro constant NA is such that there will be an oxide layers on the surface of a silicon sphere. The thickness of this layer is measured by a modified spectroscopic ellipsometer, which can eliminate the influence of the curved surface, and the results are calibrated by x-ray reflectivity. Fifty positions distributed nearly uniformly on the surface of the silicon sphere are measured twice. The results show that the mean thickness of the overall oxide layer is 3.75 nm with the standard uncertainty of 0.21 nm, which means that the relative uncertainty component of NA owing to this layer can be reduced to 1.2 × 10^-8.     

Uncertainty reevaluation in determining the volume of a silicon sphere by spherical harmonics in an Avogadro project

To determine the Avogadro constant with a target relative uncertainty of 2 × 10^-8, the uncertainty component of the silicon sphere's volume introduced by the spherical harmonics method, which is usually used in determining the sphere's volume, is reevaluated. By means of representing the shape of the silicon sphere by an ellipsoid with Gaussian white noise in its diameters, the uncertainty of the current mapping methods based on the spherical harmonics theory can be estimated theoretically. It is evidenced that the uncertainty component attributed to the current mapping method is underestimated. To eliminate this effect as much as possible, the number of mapping points should be increased to more than before. Moreover, a new mapping method is proposed to accomplish the equal-area mapping with large number points on the silicon sphere.     

利用光频梳提高台阶高度测量准确度的方法

提出一种利用光频梳和可调谐半导体激光器提高台阶高度测量准确度的方法. 通过将可调谐激光器锁定至光频梳,可对激光器的输出波长进行精确锁定与测量.基于可调合成波长链原理,利用锁定后的半导体激光器构建了一套台阶高度测量方案,该方案可消除合成波长误差对台阶高度测量不确定度的影响. 采用一台可调谐半导体激光器和光频梳进行了5000 s的连续锁定实验, 结果表明,锁定后的可调谐半导体激光器的频率稳定度达 1.8×10^-12.该方法的理论测量不确定度约为7.9 nm, 且测量结果可溯源至时间频率基准.