X-ray mask distortion analysis using the boundary element method

Abstract

The influence of absorber and membrane stresses on x-ray mask distortions were examined both by simulation and experiments. The boundary element method was used for the numerical simulation of the distortions. Investigations were focused on the distortions appearing in the bulk-Si etching step of the subtractive x-ray mask fabrication method. Distortion measurements were performed using two types of masks in order to investigate the distortions caused by only the membrane stress and both the absorber and membrane stresses, separately. The simulated results show good agreement with the experimental results. Some guidelines to suppress the process-induced distortions were derived by the simulation. The value of the product of stress and thickness of the membrane must be restricted to within 10×104 dyn/cm in order not to deform the Si frame. Pattern position shift is almost suppressed when the membrane stress is nearly equal to the absorber stress. The membrane stress should be controlled to values slightly larger than the absorber stress. If the mask is constructed of a 1 mm thick, 3 in. diam Si frame having a 23×23 mm window region with a Ta stress of 1×108 dyn/cm2 , the SiN membrane stress should be controlled in the region of 1–4×108 dyn/cm2 . This condition limits the shift in position of patterns arranged within the window region to less than 0.03 μm (3σ).