Determining the validity domain of roughness measurements as a function of CD-SEM acquisition conditions

Abstract

In the effort of continuing improving patterning strategies for increasing circuit density while reducing dimensions, several challenges regarding patterning fidelity emerge. In recent years, stochastic effects had their relative importance increased, and therefore the need for closely monitoring those effects is also increasing [1]. Among other stochastic effects, within-feature roughness is significant as it can impact circuit electrical behavior, decreasing time and power performance, and even lead to failures. The workhorse method of the industry for measuring roughness is based on top-down CD-SEM (Critical Dimension Scanning Electron Microscope) image. In recent years, methods have been proposed as a way to improve and standardize the roughness measurement [2, 3]. Those methods rely on the obtention of the power spectral density (PSD) from the detected edges of the features in SEM images, in order to determine their roughness. However, one important aspect is the impact of the CD-SEM image acquisition conditions on the limitation of the observed PSD. As the acquisition parameters changes, different frequencies may be more or less observable in a SEM image, potentially leading to errors in the metrology evaluation [4]. The goal of this study is to first, present the impact of the CD-SEM image acquisition conditions in the roughness measurement, and, second, propose a method to determine the validity domain of the roughness measurements as a function of the acquisition conditions. The proposed method relies on a compact SEM image model. For each acquisition condition, the model is calibrated based on experimental SEM images, from several design samples. Using this calibrated model, synthetic SEM images are generated with a known sample, including its programmed roughness signature (input-PSD), which can be a white noise (defined by a constant PSD). The next step relies on a robust-to-noise edge detection algorithm [5], which is then used to compute the PSD by applying the method proposed in [4]. As the input-PSD is known, it is possible to compute the transfer function of the acquisition system [6], for each of the evaluated acquisition conditions. We call ‘limit-PSD’ the transfer function which may be considered as the signature of the acquisition conditions in the frequency domain. It can be seen as a low-pass filter and it defines the validity domain of the roughness measurements. For each input-PSD (simulated or experimental), if it is ‘below’ the limit-PSD (within the low-pass filter), the measurement is within the validity domain. If the resulting measurement reaches the limit-PSD, it is not possible to know if some roughness information was lost due to the acquisition conditions. Such relationship is illustrated in Figure 1, presenting one case where the input-PSD is inside the validity domain and a second case where the actual roughness is underestimated. Thanks to the produced results, the information of different acquisition conditions and detected roughness can be obtained and stored in what we call condition tables. For each acquisition condition, the limits of frequency range and roughness parameters range (ξ, H) of the measurable roughness are stored (Figure 2). These condition tables are very useful for assisting metrology specialists in choosing the most suitable acquisition conditions for the CD-SEM, if prior knowledge about the expected roughness is available, or in accounting for the validity domain of the roughness measurement. As a final step, the proposed method is applied to experimental data – an example of observed PSD over an experimental SEM image is shown in Figure 3. The experimental dataset is composed of SEM images acquired under different conditions (notably a large variation in landing energy – 300eV to 4000eV), and different sample materials (post-etch and post-litho samples). The obtained results confirmed the applicability of the proposed method in a real environment, and will be fully demonstrated in the final work.