Interference harmonics and rigorous EM spectrum analysis method for low-k1 CD Bossung tilt correction

This paper discusses the CD Bossung tilt phenomena in low-k1 lithography using interference harmonics and rigorous EM spectrum analysis. Interference harmonics analysis is introduced to explain the interaction of diffraction orders in the focal region leading to this abnormal CD behavior. This method decomposes the vector image formula into a superposition of cosine components to describe the interference of diffraction orders. The symmetry properties of components of an optical projection system were investigated to find out three potential sources for the asymmetric Bossung behavior, namely mask 3D (M3D) effect, lens aberration, and wafer reflectivity. Under good lens aberration and substrate reflectivity controls, the M3D effect accounts for most of the CD Bossung tilt. A rigorous EM mask spectral analysis was performed to reveal the impact of mask topography on the near-field intensity of mask transmission and the far-field image formation. From the analysis, the asymmetric phase distribution in the mask spectrum is the root cause for CD Bossung tilt. Using both the interference harmonics and the rigorous EM spectrum analysis, the effect of various resolution enhancement techniques (RET) to the Bossung tilt is also studied to find the best RET combination for M3D immunity. In addition, a pupil optimization algorithm based on these two analyses is proposed to generate the phase compensation map for M3D effect counteraction.