Stress Component Decoupling Analysis Based on Large Numerical Aperture Objective Lens, an Impractical Approach

Micro Raman spectroscopy is an effective method to quantitatively analyse the internal stress of semiconductor materials and structures. However, the decoupling analysis of the stress components for {100} monocrystalline silicon (c-Si) remains difficult. In the work outlined, physical and simulation experiments were combined to study the influence of the objective lens numerical aperture (NA) on the Raman stress characterization. The physical experiments and simulation experiments show that the spectral results obtained by using lenses with different NAs can accurately obtain the principal stress sum but cannot decouple the components of the in-plane stress. Even if the spectral resolution of the simulated experiment is ideal (The random errors of the polarization directions of less than ±1° and the systematic random errors of less than ±0.02 cm^-1). The analysis based on the theoretical model demonstrates that the proportion of the principal stress sum in the Raman shift obtained in an actual experiment exceeded 98.7%, while the proportion of the principal stress difference part was almost negligible. This result made it difficult to identify the variable effects of different stress states from the experimental results. Further simulation experiments in this work verify that when the principal stress sum was identical, the differences in the Raman shifts caused by different stress states were much smaller than the resolution of the existing Raman microscope system, which was hardly possible to identify in the experimental results. It was proven that decoupling analysis of stress components using the large-NA objective lens lacked actual practicability.