*Article* **Method for Analyzing the Measurement Error with Respect to Azimuth and Incident Angle for the Rotating Polarizer Analyzer Ellipsometer**

**Huatian Tu <sup>1</sup> , Yuxiang Zheng 1,\*, Yao Shan <sup>1</sup> , Yao Chen <sup>1</sup> , Haotian Zhang <sup>1</sup> , Rongjun Zhang <sup>1</sup> , Songyou Wang <sup>1</sup> , Jing Li <sup>1</sup> , YoungPak Lee 1,2 and Liangyao Chen 1,\***



**Citation:** Tu, H.; Zheng, Y.; Shan, Y.; Chen, Y.; Zhang, H.; Zhang, R.; Wang, S.; Li, J.; Lee, Y.; Chen, L. Method for Analyzing the Measurement Error with Respect to Azimuth and Incident Angle for the Rotating Polarizer Analyzer Ellipsometer. *Crystals* **2021**, *11*, 349. https://doi.org/10.3390/ cryst11040349

Academic Editors: Valentina Domenici and Yun-Han Lee

Received: 2 March 2021 Accepted: 25 March 2021 Published: 29 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Abstract:** We proposed a method to study the effects of azimuth and the incident angle on the accuracy and stability of rotating polarizer analyzer ellipsometer (RPAE) with bulk Au. The dielectric function was obtained at various incident angles in a range of 55◦–80◦ and analyzed with the spectrum of the principal angle. The initial orientations of rotating polarizing elements were deviated by a series of angles to act as the azimuthal errors in various modes. The spectroscopic measurements were performed in a wavelength range of 300–800 nm with an interval of 10 nm. The repeatedly-measured ellipsometric parameters and determined dielectric constants were recorded monochromatically at wavelengths of 350, 550, and 750 nm. The mean absolute relative error was employed to evaluate quantitatively the performance of instrument. Apart from the RPAE, the experimental error analysis implemented in this work is also applicable to other rotating element ellipsometers.

**Keywords:** ellipsometry; error analysis; spectroscopy; high-accuracy measurement; optical metrology; dielectric constants
