| AVS 62nd International Symposium & Exhibition | |
| Spectroscopic Ellipsometry Focus Topic | Thursday Sessions |
| Session EL+EM+EN-ThM |
| Session: | Spectroscopic Ellipsometry: Novel Applications and Theoretical Approaches |
| Presenter: | Weiqi Li, Huazhong University of Science and Technology, China |
| Authors: | W.Q. Li, Huazhong University of Science and Technology, China H. Jiang, Huazhong University of Science and Technology, China C.W. Zhang, Huazhong University of Science and Technology, China X.G. Chen, Huazhong University of Science and Technology, China S.Y. Liu, Huazhong University of Science and Technology, China |
| Correspondent: | Click to Email |
Determining curvature radius of a curved surface by use of Mueller matrix ellipsometry
Weiqi Li, Hao Jiang, Chuanwei Zhang, Xiuguo Chen, and Shiyuan Liu*
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China.
* Corresponding author: shyliu@hust.edu.cn
Ellipsometry is a powerful metrology tool for the characterization of surfaces and thin films. Generally, the basic principle of conventional ellipsometry is based on the assumption that the studied film or structure is on a planar surface [1], in another word, the conventional ellipsometry works the best for a flat surface. When the studied surface is tilted or curved, the measurement accuracy of the conventional ellipsometry will be significantly degraded, or even be incorrect. It is thus important to develop a method to deal with the cases when the surface for characterization is tilted or curved. Comparing with the conventional ellipsometry, the Mueller matrix ellipsometry (MME) can provide all 16 elements of a 4 by 4 Mueller matrix, and consequently can acquire much more useful information about the curved surface and thereby shows great potential in the curved surface metrology.
In this work, we propose an optical model that is able to process curved surface based on our in-house developed dual rotating-compensator MME [2] to characterize the surface layer of a single crystal silicon sphere crown with a radius of about 51 mm for demonstration. Focus probe accessory is used in the MME to achieve sufficient small spot on the curved surface so that the detected area on the spherical surface can be approximately regarded as a tilted one. We found that some of the measured off-diagonal Mueller matrix elements are very sensitive to the offset between the actual detected spot and the surface vertex, which is proportional to the deviation angle α of the surface normal across the surface vertex. An optical model of the spherical layer is proposed by considering the curved surface of the silicon sphere crown and the offset. With the proposed model, the deviation angle α as well as the surface layer thickness can be extracted from the measured Mueller matrix spectrum, and then the curvature radius of the sphere crown can be achieved. Experiments are performed on the silicon sphere crown show that not only the accuracy of measurement can be improved but also the curvature radius of the sphere crown is capable to be measured using the proposed optical model.
[1] R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1992).
[2] S. Y. Liu, X. G. Chen, and C. W. Zhang, Thin Solid Films 584, 176-185 (2015).