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As the dimensions of integrated circuit devices continue to shrink, the effect of line edge roughness (LER) of resist patterns on the device performance is becoming a serious problem. Therefore, the desire to measure LER with more accuracy is growing. We have proposed the method for LER measurement by using the wavelet multiresolution analysis. It is still required that a wavelet filter is optimized to reveal line edges from noisy SEM signal profile to achieve more accuracy. In this paper, we try to estimate statistically a wavelet that is matched to measure LER from the scanning electron microscopy (SEM) signal profile. Here we propose a novel mathematical and statistical modeling of the SEM signal profile. The mathematical model has been deduced from a variety of SE signal shapes which have been calculated by Monte Carlo simulations. It is also necessary to consider statistical effects such as the property of the atoms within the nanostructures and the fluctuation of the exposure. We then formulate a model by considering four characteristics of critical dimension (CD) in photolithography: the exponential distribution of the image intensity around the impinging electron beam, the spatial frequency distribution of LER, phase difference between both sides of a line pattern, and shot noise in SEM images. Statistically matched wavelet is estimated from local signal profiles around true edge positions. As a result, it was seen that there was a high degree of similarity between real and model SEM images. We also compared performance in accuracy of CD measurement between the matched wavelet and the first-order derivative Gaussian wavelet, which has selected as the most suitable one for lithography metrology in previous work. CDs measured by both wavelets were almost equal since the matched wavelet has relatively small effect on noise reduction.
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