We have investigated in a numerical study the determination of sidewall roughness (SWR) from top down scanning electron microscopy (SEM) images. In a typical metrology application, top-down SEM images are acquired in a (critical-dimension) SEM and the roughness is analyzed. However, the true size, shape and roughness characteristics of resist features are not fully investigated in the analysis of top-down SEM images. In reality, rough resist features are complex three-dimensional structures and the characterization naturally extends to the analysis of SWR.
In this study we randomly generate images of rough lines and spaces, where the lines are made of PMMA on a silicon substrate. The lines that we study have a length of 2 µm, a width of 32nm and a height of 32 nm. The SWR is modeled by using the power spectral density (PSD) function of Palasantzas, which characterizes roughness by the standard deviation σ, correlation length ξ and roughness exponent α . The actual roughness is generated by application of the method of Thorsos in two dimensions. The images are constructed by using a home-built program for simulating electron-specimen interactions. The program that we have developed is optimized for complex arbitrary geometries and large number of incident low energy primary electrons by using multi-core CPUs and GPUs. The program uses the dielectric function model for inelastic scattering events and has an implementation specifically for low energy electrons. A satisfactory comparison is made between the secondary electron yields from the home-built program and another program found in literature. In order to reduce the risk of shrinkage, we use a beam energy of 300 eV and a spot size of 3 nm. Each pixel is exposed with 20 electrons on average (≈ 276 µC/cm2), following the Poisson distribution to account for illumination shot noise. We have assumed that the detection of electrons is perfect and does not introduce additional noise.
We measure line edge roughness (LER) in simulated top-down SEM images of randomly generated rough lines by using PSD analysis. The measurements are then compared to the actual SWR that was used to generate the rough lines. We conclude that the bias in the determination of SWR is a non-linear function of the correlation length ξ3D of the actual SWR. The measured correlation length ξ 2D shows a linear trend with the correlation length ξ 3D of the SWR. From another simulation run, we conclude that the relation between measured LER in the top-down image and the standard deviation ξ 3D of the SWR is linearly biased. We see that the amount of bias relates to the correlation length ξ 3D of the SWR: The bias in the determination of SWR from top-down images increases for decreasing correlation length ξ 3D of the actual SWR. The results of this study, with respect to the metrology of rough resist features, touches upon the reliability and comparability of roughness characterization in top-down images.