Measuring line edge roughness with pixel sizes larger than its value: a mathematical and computational approach

In this work, we present a sound mathematical result that may correct the pixelization bias in the calculation of the line edge roughness (LER) even when the pixel size of SEM images is much larger than its rms value. This result can be useful in the LER metrology of current and future lithographic patterns where the desired rms value of LER is in the deep sub-nm range and smaller than the used pixel sizes. We computationally justify the predictions of the mathematical result and then demonstrate its application in synthesized SEM images where we can separate the impact of noise and focus on the pixelization effects in LER measurements. Furthermore, this result emphasizes the power of mathematical and computational methods to enhance the metrological output of SEM images in deep nanometer scale.