Optical proximity correction (OPC) and phase shifting mask (PSM) are the most widely used resolution enhancement
techniques (RET) in the semiconductor industry. Recently, a set of OPC and PSM optimization
algorithms have been developed to solve for the inverse lithography problem, which are only designed for the
nominal imaging parameters without giving sufficient attention to the process variations due to the aberrations,
defocus and dose variation. However, the effects of process variations existing in the practical optical lithography
systems become more pronounced as the critical dimension (CD) continuously shrinks. On the other hand, the
lithography systems with larger NA (NA>0.6) are now extensively used, rendering the scalar imaging models
inadequate to describe the vector nature of the electromagnetic field in the current optical lithography systems.
In order to tackle the above problems, this paper focuses on developing robust gradient-based OPC and PSM
optimization algorithms to the process variations under a vector imaging model. To achieve this goal, an integrative
and analytic vector imaging model is applied to formulate the optimization problem, where the effects
of process variations are explicitly incorporated in the optimization framework. The steepest descent algorithm
is used to optimize the mask iteratively. In order to improve the efficiency of the proposed algorithms, a set of
algorithm acceleration techniques (AAT) are exploited during the optimization procedure.