Yuan Lin, Guo Tong, Tang Dawei, Liu Haitao, Guo Xinyuan
Opt Express. 2022 Jan 3;30(1):349-363. doi: 10.1364/OE.447830.
Film is widely used in optoelectronic and semiconductor industries. The accurate measurement of the film thickness and refractive index, as well as the surface topography of the top and bottom surfaces are necessary to ensure its processing quality. Multiple measurement methods were developed; however, they are limited by the requirements of a known dispersion model and initial values of thickness and refractive index. Further, their systems are rarely compatible with surface topography measurement methods. We propose a constrained nonlinear fitting method to simultaneously measure the thickness and refractive index of film in a simple white-light spectral interferometer. The nonlinear phase extracted by the spectral phase-shifting is fitted with the theoretical nonlinear phase obtained by multiple reflection model. The constraints of nonlinear fitting are obtained by the interferometric signal of vertical scanning, reconstructed by the integration of the white-light spectral signal to avoid local minima. The proposed method does not require a priori knowledge of the dispersion model and initial values of thickness and refractive index, and its system is compatible with the vertical scanning interferometry (VSI) method to reconstruct the surface topography of the top and bottom surfaces of film. Three SiO films with different thicknesses are measured, and the results show that the measured refractive index is within the theoretical value range of wavelength bandwidth and the measured thicknesses are closely aligned with the values provided by the commercial instrument. The measurement repeatability of refractive index reaches 10. Measurements on a polymer film demonstrate that this method is feasible for measuring the film without a priori information.
薄膜广泛应用于光电和半导体行业。准确测量薄膜厚度、折射率以及薄膜上下表面的形貌对于确保其加工质量至关重要。人们开发了多种测量方法；然而，这些方法受到已知色散模型以及厚度和折射率初始值要求的限制。此外，它们的系统很少能与表面形貌测量方法兼容。我们提出一种约束非线性拟合方法，用于在简单的白光光谱干涉仪中同时测量薄膜的厚度和折射率。通过光谱相移提取的非线性相位与由多次反射模型获得的理论非线性相位进行拟合。非线性拟合的约束条件通过垂直扫描的干涉信号获得，该信号通过对白光光谱信号进行积分重建，以避免局部最小值。所提出的方法不需要色散模型的先验知识以及厚度和折射率的初始值，并且其系统与垂直扫描干涉测量法（VSI）兼容，可用于重建薄膜上下表面的形貌。对三种不同厚度的SiO薄膜进行了测量，结果表明，测得的折射率在波长带宽的理论值范围内，测得的厚度与商用仪器提供的值紧密吻合。折射率的测量重复性达到10。对聚合物薄膜的测量表明，该方法在没有先验信息的情况下测量薄膜是可行的。
