Author: Jinlong Zhu 2014-09-12
Optical scatterometry is a model-based metrology technique, which has been applied in many scopes with great success, such as the process control for back-end-of-the-line, the in-chip critical dimension (CD) and overlay metrology, and in-situ measurement of pattern reflow in nanoimprinting. In order to reconstruct the nanostructure profile, advanced mathematical methods are introduced to minimize a pre-defined objective function to quantify the difference between the measured signature and the numerical one. Currently, in optical scatterometry the objective function is commonly chosen as the least squares (LSQ) function, which implies the belief that the measurement errors in the measured signature are normally distributed with zero means. However, the statistic characteristic of the measurement errors is far more complex than the oversimplified normal distribution, since they come from the superimposed effect of different error sources such as the power fluctuation of the incident beam, the imperfect modeling, the finite numerical aperture of the scatterometer and the spectral resolution of the monochromator. These abnormal distributed measurement errors cannot be effectively dealt with by traditional mathematical methods, thus these errors will affect the profile reconstruction accuracy of nanostructure to some extend.
Recently, Prof. Shiyuan Liu’s research group in WLNO proposed a novel nanostructure profile reconstruction method based on the principle of robust statistics. Compared with the conventional LSQ-based method, the proposed robust method introduces an additional robust regression procedure at the end of each iteration of the Gauss-Newton (GN) method so as to reduce the effect of abnormal distributed errors on the iterative results. Supported by the National Instrument Development Specific Project of China, Prof. Liu’s group has developed an in-house broad-band Mueller matrix ellipsometer, and has performed a variety of numerical simulations and experiments on a one-dimensional trapezoidal etched silicon grating. Both of the simulated and experimental results have demonstrated that it is not always valid to assume that the measurement errors in optical scatterometry are normally distributed. In this case, if the objective function is set as the LSQ function, the traditional iterative methods like the GN method leads to a biased estimation of profile parameters. As a comparison, the proposed robust method has been proved to achieve more accuracy than the traditional GN method.
The work was funded by the National Natural Science Foundation of China (Grant Nos. 51475191 and 51405172), the National Instrument Development Specific Project of China Grant No. 2011YQ160002), and the Program for Changjiang Scholars and Innovative Research Team in University of China. The work was published in OSA journal of Optics Express, 22(18), 22031-22042 (2014).