Understanding the forbidden pitch and assist feature placement

TLDR: In this article, it has been shown that the variation of the critical dimension as well as the exposure latitude of the main feature is a direct consequence of light field interference between the main features and the neighboring features.

Abstract: Optical proximity effect is a well-known phenomenon in photolithography. Such an effect results from the structural interaction between the main feature and the neighboring features. Recent observations have shown that such structural interactions not only affect the critical dimension of the main feature at the image plane, but also the exposure latitude of the main feature. In this paper, it has been shown that the variation of the critical dimension as well as the exposure latitude of the main feature is a direct consequence of light field interference between the main feature and the neighboring features. Depending on the phase of the field produced by the neighboring features, the main feature critical dimension and exposure latitude can be improved by constructive light field interference, or degraded by destructive light field interference. The phase of the field produced by the neighboring features can be shown to be in the location where the field produced by the neighboring features can be shown to be dependent on the pitch as well as the illumination angle. For a given illumination, the forbidden pitch lies in the location where the field produced by the neighboring features interferes with the field of the main feature destructively. The theoretical analysis given here offers the tool to map out the forbidden pitch locations for any feature size and illumination conditions. More importantly, it provides the theoretical ground for illumination design in order to suppress the forbidden pitch phenomenon, and for scattering bar placement to achieve optimal performance as well.