Spectroscopic ellipsometry and its applications in the study of thin film materials
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摘要: 椭圆偏振光谱测量技术通过测量线偏振光经材料表面反射后光的相对振幅与相位改变量计算得到椭偏参数，再通过椭偏参数的拟合获取样品光学性质。由于其具有非接触、高灵敏度、非破坏性等优势，广泛应用于物理、化学、材料科学和微电子等方面，是一种不可或缺的光学测量手段。本文首先简要回顾了该技术的发展历程，接着阐述了传统椭偏仪的基本原理，按照测量原理的不同可将椭偏仪分为消光式和光度式。随后，本文简单介绍了一些常用椭偏仪的基本架构、测量原理和相关应用，并比较了他们的优缺点，重点展示了复旦大学研制的双重傅立叶变换红外椭偏光谱系统。然后按照椭偏参数处理的基本步骤：测量、建模与拟合3个方面，阐述了其过程，详细剖析了参数拟合所使用的各种光学色散模型，同时通过应用实例介绍了各色散模型的应用情况。最后，对未来椭偏技术的发展方向进行了展望。Abstract: Spectroscopic ellipsometry is used to measure the relative amplitude and phase change of linearly polarized light reflected by a material surface, so as to obtain the ellipsometric parameters. The optical properties of a material can be deduced by fitting these parameters. This technique is advantageous for being non-contact, highly sensitive, non-destructive, so it is widely used in physics, chemistry, materials science and microelectronics, etc, being an indispensable optical measurement method. This article first introduces the development history of the technology, and then presents the basic principle of the traditional ellipsometer. According to different measurement principles, ellipsometers can be divided into two types:extinction and photometric. The basic structure, measurement principle and related application of these two different types of ellipsometer are briefly clarified. After comparing these various ellipsometers, their advantages and disadvantages are introduced. At this point, a double Fourier transform infrared ellipsometry system developed by Fudan University is highlighted. Then, according to the basic steps of ellipsometric parameter manipulation, a measurement, modeling and fitting process is introduced. The equations of various optical dispersion models used for parameter fitting are introduced in detail and application examples are illustrated. Finally, the future development direction of spectroscopic ellipsometry is proposed.
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图 1 1941年至今主题包含“ellipsometry”(椭偏技术)的论文发表情况统计。(a)论文发表篇数统计，(b)发表论文研究方向统计图。(数据来源：Isi Web of Science)
Figure 1. Statistical analysis of published papers with the topic of 'ellipsometry' from 1941 to the present. (a)Publication statistics of papers, (b)research direction of published papers. (Source:ISI Web of Science)
图 7 双重傅立叶变换红外椭偏光谱系统。(a)系统整体结构示意图，1.偏振器；2.分析仪；3.步进电机；4.检测臂旋转平台；5.样品旋转平台；6.样品安装板；7.固定镜；8.移动镜[49]，(b)RAP型椭偏仪原理图(其中P和A的方位角相对s轴顺时针旋转)[50]
Figure 7. Apparatus configuration of the infrared double-Fourier spectro-ellipsometer. (a)System overall structure diagram, 1.polarizer, 2.analyzer, 3.stepping motors, 4.rotating stage of detection arm, 5.rotating stage of sample, 6.sample mounting plate, 7.fixed mirrors, 8.moving mirror[49], (b)optical configuration of the RAP ellipsometric system(in which the azimuthal angles of the rotating P and A are clockwise to the s axis)[50]
图 11 椭圆偏振光谱分析Sn薄膜的光学性质。(a)65°, 70°, 75°入射时测得的Sn薄膜椭偏参数，(b)Sn薄膜的折射率n和消光系数k与波长的关系[65]
Figure 11. Optical properties of Sn thin films studied by spectroscopic ellipsometry. (a)Spectral ellipsometry parameters of Sn films measured at 65°, 70°, and 75° at room temperature, (b)refractive index n and extinction coefficient k of the Sn film vary with wavelength[65]
图 15 逐点椭偏参数反演方法分析ZrO2超薄膜。(a)ZrO2超薄膜的光学模型，(b)点对点分析中使用的简化光学模型，(c)厚度为2.72 nm的ZrO2超薄膜在入射光子能量为3~6 eV内的ε2[72]
Figure 15. Analysis results of ultrathin ZrO2 films by point-by-point method. (a)Optical model of ZrO2 samples, (b)simplified one for point-by-point analysis in this work, (c)imaginary model of dielectric constants of the effective ZrO2 film with a thickness of 2.72 nm when incident photon energy is 3~6 eV range[72]
图 16 逐点椭偏参数反演方法分析WS2超薄膜。(a)WS2超薄膜的光学模型，(b)和(c)分别是点对点拟合得到的WS2超薄膜复介电函数实部ε1和虚部ε2(入射光子能量范围为1.2~6.3 eV，S1、S2和S3分别代表溅射时间为20、50和70 s的3种样品)[73]
Figure 16. Analysis results of ultrathin WS2 films by point-by-point method. (a)Optical model of WS2 samples, (b) and (c) are real part ε1 and imaginary part ε2 for dielectric function extracted from point-by-point fitting respectively. (the photon energy range is 1.2~6.3 eV, S1, S2 and S3 are represeroted the sample for the sputtering times, 20 s, 50 s, and 70 s, respectively)[73]
图 19 GO薄膜的椭偏光谱分析。(a)Lorentz模型3个振子中心能量按退火温度线性拓展(C1(方块)，C2(圆圈)，C3(三角))；(b)λ=600 nm时不同退火温度下本征GO薄膜和束缚水的GO综合体系的光学常数曲线(本征GO薄膜的nGO(1)，kGO(3)，混合体系n(2)，k(4)，阴影部分为除去束缚水层的温度区间)[84]
Figure 19. Ellipsometric spectral analysis of GO thin films. (a)Three vibrator center energies of Lorentz model linearly expand according to annealing temperature (C1(squares), C2(circles), and C3(triangles)), (b)optical constant curve of GO synthesis system of intrinsic GO film and bound water nGO(1), kGO(3), and total n(2), k(4) vs. Tann for λ=600 nm. Dashed region denotes temperature interval where water is expelled[84]
图 23 400 ℃退火后不同厚度的TiO2超薄膜复折射率谱。(a)折射率n，(b)消光系数k。(图(a)的插图显示了峰位置与ALD循环数的关系，图(b)的插图显示了在400 ℃下退火后不同厚度的TiO2超薄膜的(αE)1/2vs.E图)[95]
Figure 23. Complex refractive index spectra for TiO2 ultrathin films with different thicknesses after annealing at 400 ℃. (a)Refractive index n spectra, (b)extinction coefficient k spectra.(The insert of (a) shows plot of peak position versus ALD cycles. The insert of (b) shows plots of (αE)1/2vs. E for TiO2 ultrathin films with different thicknesses after annealing at 400 ℃)[95]
图 36 用于分析(a)薄膜和(b)纳米结构的椭偏技术和其他表征技术“合作情况”的分布统计图(AFM：原子力显微镜；SEM：扫描电子显微镜；TEM：透射电子显微镜；XPS：X射线光电子能谱；XRD：X射线衍射光谱)[114]
Figure 36. Distribution of techniques corroborating spectroscopic ellipsometry(SE) for analysis of (a)thin films and (b)nanostructures(AFM:atomic force microscopy; SEM:scanning electron microscopy; TEM:transmission electron microscopy; XPS:X-ray photoelectron spectroscopy; XRD:X-ray diffraction)[114]
表 1 几种光度式椭偏仪优缺点总结[34]
Table 1. Advantages and disadvantages of several photometric ellipsometers[34]
椭偏仪结构 优点 缺点 RAE/RPE
(不含补偿器)①结构简单 ①Stokes的S3分量测试受限(-180°≤Δ＜0°) ②工作在消光模式 ②在Δ等于0°和180°处有较大的测量误差 RAE/RPE ①椭偏参数(ψ，Δ)在全光谱范围可测 ①相比RAE测试时间更长 ②可以测量去极化谱 ②相比RAE结构更复杂 ③全光谱范围椭偏参数测量敏感度相同 RCE ①椭偏参数(ψ，Δ)在全光谱范围可测 相比RAE结构更复杂 ②可以测量去极化谱 ③全光谱范围椭偏参数测量敏感度相同 PME ①测试快速 ①单次测量无法同时测试Stokes的S1和S2分量 ②在远红外波段可以实时测试 ②椭偏参数(ψ，Δ)在某些区域测试误差大 ③可以测量去极化谱 
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