FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry
Spectroscopic ellipsometry (SE) is an effective method to measure the optical constants of thin film materials which is very sensitive to the surface topography of thin films. When performing ellipsometric measurements of the optical constants of solid materials with rough surfaces, the equivalent m...
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MDPI AG
2022-08-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/9/9/621 |
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| author | Wanpei Yu Changcai Cui Huihui Li Subiao Bian Xi Chen |
| author_facet | Wanpei Yu Changcai Cui Huihui Li Subiao Bian Xi Chen |
| author_sort | Wanpei Yu |
| collection | DOAJ |
| description | Spectroscopic ellipsometry (SE) is an effective method to measure the optical constants of thin film materials which is very sensitive to the surface topography of thin films. When performing ellipsometric measurements of the optical constants of solid materials with rough surfaces, the equivalent medium approximation (EMA) model is often used to characterize the surface topography. The EMA model is determined by two parameters of equivalent thickness <i>d</i><sub>EMA</sub> and the void volume fraction <i>f</i>. In most applications, the void volume fraction parameter <i>f</i> is always set to an empirical 50% without any instructions, and then the thickness parameter <i>d</i><sub>EMA</sub> is determined by fitting. In order to improve the accuracy of the fitting results, it is necessary to validate the construction law of the EMA model in the ellipsometry analysis considering characteristic parameters of the actual surface topography. In this paper, the influence of the surface topographical parameters on EMA model is analyzed. The method of FDTD (finite difference time domain) is employed to simulate the SiO<sub>2</sub> films with different topographical parameters and EMA model are carried out on these samples. The analysis results show that the EMA model constructed with <i>d</i><sub>EMA</sub> = <i>σ</i> + 0.80 <i>h</i> (<i>σ</i>: the root mean square height, <i>h</i>: the average height) can better fit the SE parameters. The proposed method can facilitate a better understanding and utilization of the EMA model in SE application. |
| first_indexed | 2024-03-09T22:48:45Z |
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| id | doaj.art-cd16207101c749b6b47b3a51c089630e |
| institution | Directory Open Access Journal |
| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-09T22:48:45Z |
| publishDate | 2022-08-01 |
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| record_format | Article |
| series | Photonics |
| spelling | doaj.art-cd16207101c749b6b47b3a51c089630e2023-11-23T18:24:29ZengMDPI AGPhotonics2304-67322022-08-019962110.3390/photonics9090621FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic EllipsometryWanpei Yu0Changcai Cui1Huihui Li2Subiao Bian3Xi Chen4Institute of Manufacturing Engineering, Huaqiao University, Xiamen 361021, ChinaInstitute of Manufacturing Engineering, Huaqiao University, Xiamen 361021, ChinaInstitute of Manufacturing Engineering, Huaqiao University, Xiamen 361021, ChinaInstitute of Manufacturing Engineering, Huaqiao University, Xiamen 361021, ChinaInstitute of Manufacturing Engineering, Huaqiao University, Xiamen 361021, ChinaSpectroscopic ellipsometry (SE) is an effective method to measure the optical constants of thin film materials which is very sensitive to the surface topography of thin films. When performing ellipsometric measurements of the optical constants of solid materials with rough surfaces, the equivalent medium approximation (EMA) model is often used to characterize the surface topography. The EMA model is determined by two parameters of equivalent thickness <i>d</i><sub>EMA</sub> and the void volume fraction <i>f</i>. In most applications, the void volume fraction parameter <i>f</i> is always set to an empirical 50% without any instructions, and then the thickness parameter <i>d</i><sub>EMA</sub> is determined by fitting. In order to improve the accuracy of the fitting results, it is necessary to validate the construction law of the EMA model in the ellipsometry analysis considering characteristic parameters of the actual surface topography. In this paper, the influence of the surface topographical parameters on EMA model is analyzed. The method of FDTD (finite difference time domain) is employed to simulate the SiO<sub>2</sub> films with different topographical parameters and EMA model are carried out on these samples. The analysis results show that the EMA model constructed with <i>d</i><sub>EMA</sub> = <i>σ</i> + 0.80 <i>h</i> (<i>σ</i>: the root mean square height, <i>h</i>: the average height) can better fit the SE parameters. The proposed method can facilitate a better understanding and utilization of the EMA model in SE application.https://www.mdpi.com/2304-6732/9/9/621spectroscopic ellipsometry (SE)rough surfaceequivalent medium approximation (EMA)finite difference time domain (FDTD) |
| spellingShingle | Wanpei Yu Changcai Cui Huihui Li Subiao Bian Xi Chen FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry Photonics spectroscopic ellipsometry (SE) rough surface equivalent medium approximation (EMA) finite difference time domain (FDTD) |
| title | FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry |
| title_full | FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry |
| title_fullStr | FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry |
| title_full_unstemmed | FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry |
| title_short | FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry |
| title_sort | fdtd based study on equivalent medium approximation model of surface roughness for thin films characterization using spectroscopic ellipsometry |
| topic | spectroscopic ellipsometry (SE) rough surface equivalent medium approximation (EMA) finite difference time domain (FDTD) |
| url | https://www.mdpi.com/2304-6732/9/9/621 |
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