E-mail Alert
RSS
Measurement of polarization correlation coefficients of light source and spectrometer in spectroscopic ellipsometry
-
摘要:
光谱椭偏测量技术已广泛应用于材料科学、微电子、物理化学和生物医学等领域。在光谱椭偏测量系统中，由于起偏器和检偏器存在漏光等瑕疵，光源子系统的偏振度和光谱仪子系统的偏振敏感度会影响光谱椭偏系统的测量精度。针对这一问题，本文建立了光谱椭偏测量系统的偏振相关系数的修正模型；并提出了一种同时测量光源子系统和光谱仪子系统偏振相关系数的方法。利用现有实验室内的宽带光源系统和宽带光谱仪验证了这种测量方法的可行性。
Abstract:Spectroscopic ellipsometry has been widely used in materials science, microelectronics, physical chemistry and biomedicine. In the spectroscopic ellipsometry system, the degree of polarization of the light source subsystem and the polarization sensitivity of the spectrometer subsystem will affect the measurement accuracy of the spectroscopic ellipsometry considering the leakage of polarizer and analyzer. To remove this systematic error, we included the degree of polarization of light from source and the polarization sensitivity of the spectroscopic ellipsometry in our calibration model; a method for measuring the polarization state of light source subsystem and polarization sensitivity of a spectrometer subsystem is proposed. To verify the method, we present the measurement setup and results for a commercial broadband light source and broadband spectrometer.
-
Overview: Spectroscopic ellipsometry has been widely used in materials science, microelectronics, physical chemistry and biomedicine due to the advantages of non-destructive, non-interference, fast speed and high accuracy. Many researchers have improved system models to correct the effect by artifacts of spectroscopic ellipsometry system, including those artifacts of polarizer due to its optical activity, leakage and stress birefringence, artifact of wave plate compensator, the correction to finite numerical aperture and the finite spectral bandwidth, as well as those artifacts by focusing lens due to the optical activity and stress birefringence. Additionally, we considered in this paper the influence of polarization degree of the light source and polarization sensitivity of spectrometer, and find that these artifacts need to be corrected for ultra-high accuracy measurement. Furthermore, we presented here a method to measure the polarization correlation coefficients simultaneously for light source and spectrometer. Theoretically, the polarization correlation coefficients of the light source can be measured by a spectrometer with known polarization characteristics, and the polarization correlation coefficients of the spectrometer can be measured by a light source with known polarization state. However, these measurement methods rely on additional characterized light sources and spectrometers, which can be troublesome often.
In this article, we analyzed the effect of polarization parameters of light source and spectrometer on spectroscopic ellipsometry via a correction model; and proposed a method for measuring the polarization correlation coefficients of light source subsystem and spectrometer subsystem simultaneously and mutually. This is done by adding polarizers or combination of polarizers and wave plates between light source and spectrometer subsystem. For illustration of the measurement method, we demonstrated the feasibility by measuring the polarization correlation coefficients of the light source and spectrometer in our laboratory. The measurement results show that the degree of polarization of our light source has a relatively large variation over 400 nm~800 nm range, and a sharp spike in 425 nm~460 nm is found. Since this band coincident with the combination band of a deuterium lamp and a halogen lamp, this may indicate a large polarization dependent reflectivity of the beam combiner. The polarization correlation coefficient of the spectrometer is below 0.05, which shows that the spectrometer may take polarization insensitive design to reduce the polarization dependence of reflective gratings.
-
-
图 1 光谱椭圆偏振测量系统结构原理图
Figure 1. Structural schematic diagram of spectroscopic ellipsometry measurement system
图 2 光源子系统和光谱仪子系统偏振相关系数测量装置示意图。其中P, A为偏振器，C为波片。(a) (A1，A2，P1，P2)测量装置图；(b) P3测量装置图；(c) A3测量装置图
Figure 2. Schematic diagram of polarization correlation coefficients measurement setup for light source subsystem and spectrometer subsystem, where P, A are polarizers and C is a wave plate. (a) Schematic diagram of (A1, A2, P1, P2) measurement setup; (b) Schematic diagram of P3 measurement setup; (c) Schematic diagram of A3 measurement setup
图 3 光源和光谱仪偏振相关系数测定实验装置
Figure 3. Experimental device for measuring polarization correlation coefficient of light source and spectrometer
-
[1] 周毅, 吴国松, 代伟, 等.椭偏与光度法联用精确测定吸收薄膜的光学常数与厚度[J].物理学报, 2010, 59(4): 2356–2363. http://d.old.wanfangdata.com.cn/Periodical/wlxb201004030
Zhou Y, Wu G S, Dai W, et al. Accurate determination of optical constants and thickness of absorbing thin films by a combined ellipsometry and spectrophotometry approach[J]. Acta Physica Sinica, 2010, 59(4): 2356–2363. http://d.old.wanfangdata.com.cn/Periodical/wlxb201004030
[2] 宋国志.宽光谱椭偏仪在集成电路中的研究与应用[D].成都: 电子科技大学, 2014.
Song G Z. Broadband Spectroscopy Ellipsometry and its application & research in Integrated Circuits[D]. Chengdu: University of Electronic Science and Technology of China, 2014.
[3] Chen C, An I, Collins R W. Multichannel Mueller matrix ellipsometry for simultaneous real-time measurement of bulk isotropic and surface anisotropic complex dielectric functions of semiconductors[J]. Physical Review Letters, 2003, 90(21): 217402. doi: 10.1103/PhysRevLett.90.217402
[4] Berrier A, Gompf B, Fu L W, et al. Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy[J]. Physical Review B, 2014, 89(19): 195434. doi: 10.1103/PhysRevB.89.195434
[5] Arwin H. Application of ellipsometry techniques to biological materials[J]. Thin Solid Films, 2011, 519(9): 2589–2592. doi: 10.1016/j.tsf.2010.11.082
[6] Fujiwara H. Spectroscopic Ellipsometry: Principles and Applications[M]. Hoboken: Wiley, 2007.
[7] Li S F. Jones-matrix analysis with Pauli matrices: application to ellipsometry[J]. Journal of the Optical Society of America A, 2000, 17(5): 920–926. doi: 10.1364/JOSAA.17.000920
[8] Gu H G, Liu S Y, Chen X G, et al. Calibration of misalignment errors in composite waveplates using Mueller matrix ellipsometry[J]. Applied Optics, 2015, 54(4): 684–693. doi: 10.1364/AO.54.000684
[9] Li W Q, Zhang C W, Jiang H, et al. Depolarization artifacts in dual rotating-compensator Mueller matrix ellipsometry[J]. Journal of Optics, 2016, 18(5): 055701. doi: 10.1088/2040-8978/18/5/055701
[10] Fan Z T, Tang Y Y, Wei K, et al. Calibration of focusing lens artifacts in a dual rotating-compensator Mueller matrix ellipsometer[J]. Applied Optics, 2018, 57(15): 4145–4152. doi: 10.1364/AO.57.004145
[11] 李金金, 孙晓兵, 康晴, 等.偏振光谱仪偏振探测精度分析[J].红外与激光工程, 2018, 47(1): 0123002. doi: 10.3788/IRLA201847.0123002
Li J J, Sun X B, Kang Q, et al. Polarization detection accuracy analysis of spectropolarimeter[J]. Infrared and Laser Engineering, 2018, 47(1): 0123002. doi: 10.3788/IRLA201847.0123002
[12] 王宏博, 胡秀清, 张璐, 等.光栅色散型成像光谱仪的偏振校正方法研究[J].光学学报, 2016, 36(8): 0812004. 10.3788/AOS201636.0812004
Wang H B, Hu X Q, Zhang L, et al. Polarization correction for grating dispersive imaging spectrometer[J]. Acta Optica Sinica, 2016, 36(8): 0812004. 10.3788/AOS201636.0812004
[13] Collins R W, Koh J. Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy of surfaces and films[J]. Journal of the Optical Society of America A, 1999, 16(8): 1997–2006. doi: 10.1364/JOSAA.16.001997
[14] Lee J, Koh J, Collins R W. Dual rotating-compensator multichannel ellipsometer: Instrument development for high-speed Mueller matrix spectroscopy of surfaces and thin films[J]. Review of Scientific Instruments, 2001, 72(3): 1742–1754. doi: 10.1063/1.1347969
[15] Hauge P S, Muller R H, Smith C G. Conventions and formulas for using the Mueller-Stokes calculus in ellipsometry[J]. Surface Science, 1980, 96(1–3): 81–107. doi: 10.1016/0039-6028(80)90296-4
[16] 姚本溪, 饶长辉, 顾乃庭. 1.8 m太阳望远镜偏振标定单元设计[J].光电工程, 2018, 45(11): 180058. doi: 10.12086/oee.2018.180058
Yao B X, Rao C H, Gu N T. Polarization calibration unit design of 1.8 m Chinese large solar telescope[J]. Opto-Electronic Engineering, 2018, 45(11): 180058. doi: 10.12086/oee.2018.180058
[17] 宋国志, 刘涛, 谌雅琴, 等.利用多个标准样品校准光谱椭圆偏振仪[J].光学学报, 2014, 34(3): 0312003. doi: 10.3788/AOS201434.0312003
Song G Z, Liu T, Chen Y Q, et al. Calibration of spectroscopic ellipsometer using multiple standard samples[J]. Acta Optica Sinica, 2014, 34(3): 0312003. doi: 10.3788/AOS201434.0312003
-
下载:
点击扫一扫
图(4)
计量
- 文章访问数:
- PDF下载数:
- 施引文献: 0
