Unbiased Roughness Measurements from Low Signal-to-Noise Ratio SEM Images

Background: Measuring and subtracting SEM noise from a biased measurement of roughness leads to an unbiased roughness measurement. This unbiasing procedure becomes harder as the noise in the image increases. For low image signal-to-noise ratio (below about 2), unbiased roughness measurement becomes less reliable. Aim: It is important to understand the mechanism for the sensitivity of unbiased roughness accuracy to linescan signal-to-noise ratio in order to look for ways to improve unbiased roughness measurement for very noisy images. Approach: Using a combination of mathematical analysis, simulations, and experimental data, the role of pixel size and pitch in the signal-to-noise ratio sensitivity are explored. Results: All evidence points to the correlation of edge detection noise to true edge position as the cause of the errors in unbiased roughness measurement for very noisy images. For small pitch patterns, changes in feature edge position caused by feature roughness changes the linescan slope, which changes the sensitivity of edge detection to SEM image noise. Conclusions: Smaller pixel sizes and larger feature sizes are less sensitive to the signal-to-noise ratio effects described here. For any algorithm used to measure unbiased roughness, the impact of linescan signal-tonoise must be carefully assessed.