The effect of sidewall roughness on line edge roughness in top-down scanning electron microscopy images

Abstract

We have investigated in a numerical study the determination of sidewall roughness (SWR) from topdown 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 32 nm 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 multicore 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/cm 2 ), 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 ξ 3D 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 σ 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.

Sensitivity of secondary electron yields and SEM images to scattering parameters in MC simulations

“…We investigate the cross-section sensitivity by using our own high-performance simulation tool [6] and discriminate between three scattering processes: quasi-elastic phonon scattering [7], elastic Mott scattering [8] and inelastic scattering using the dielectric function model [9] surprise, we observe that the influence of the (quasi-elastic) acoustic phonon scattering cross-sections in Fig. 1 is seen all the way up to the incident primary electron energy of 10 keV.…”

“…The calculation, in which the pattern is exposed to an electron beam with energy 300 eV, is essentially identical to Ref. [6], except for the fact that for each case, we have scaled the scattering cross-sections of one particular scattering process. In other words, we have obtained one SEM image corresponding to the default scattering cross-sections and three SEM images where either the phonon, elastic Mott or inelastic scattering cross-sections are multiplied by a factor of two.…”

“…Recently, we have reduced the computation time further by rewriting the GEANT4 extension from FEI company, see Ref. [1], for the purpose of SEM imaging and lithography simulations [6].…”

Understanding the influence of 3D sidewall roughness on observed line-edge roughness in scanning electron microscopy images

“…Simulation studies have also been performed. [13][14][15] These studies start with a known geometry and obtain corresponding CD-SEM images using full electron scattering simulations. These simulation studies all confirm that the measured 3σ LER can be up to a factor 2 less than the true 3σ SWR.…”

Simulation of shotnoise induced side-wall roughness in electron lithography

“…† More details on the sources for the scattering cross-sections, which are used in our Monte-Carlo electron-matter interaction simulator, can be found in Ref 9…”