Gradient-based resolution enhancement optimization methods based on vector imaging model

Abstract

Recently, a set of gradient-based optical proximity correction (OPC) and phase shifting mask (PSM) optimization methods have been developed to solve for the inverse lithography problem under scalar imaging models, which are only accurate for numerical apertures (NA) less than approximately 0.4. However, as the lithography technology node enters the 45nm realm, immersion lithography systems with hyper-NA (NA>1) are now extensively used in the semiconductor industry. For the hyper-NA lithography systems, the vector nature of the electromagnetic field must be taken into account, leading to the vector imaging models. Thus, the OPC and PSM optimization approaches developed under the scalar imaging models are inadequate to enhance the resolution in the immersion lithography systems. This paper focuses on developing gradient-based OPC and PSM optimization algorithms under vector imaging models. The mask optimization framework is first formulated, in which the imaging process of the optical lithography system is represented by an integrative and analytic vector imaging model. The steepest descent algorithm is then used to optimize the mask iteratively. Subsequently, a generalized wavelet penalty (GWP) is proposed to improve the manufacturability of the mask, and results in smaller pattern errors and CD errors than the traditional wavelet penalty (WP). Finally, a set of algorithm acceleration techniques are exploited to speed up the proposed algorithms.