  Image modeling and simulation are critical to extending the limits of leading
edge lithography technologies used for IC making. Simultaneous source mask
optimization (SMO) has become an important objective in the field of
computational lithography. SMO is considered essential to extending immersion
lithography beyond the 45nm node. However, SMO is computationally extremely
challenging and time-consuming. The key challenges are due to run time vs.
accuracy tradeoffs of the imaging models used for the computational
lithography. We present a new technique to be incorporated in the SMO flow.
This new approach is based on the reduced basis method (RBM) applied to the
simulation of light transmission through the lithography masks. It provides a
rigorous approximation to the exact lithographical problem, based on fully
vectorial Maxwell's equations. Using the reduced basis method, the optimization
process is divided into an offline and an online steps. In the offline step, a
RBM model with variable geometrical parameters is built self-adaptively and
using a Finite Element (FEM) based solver. In the online step, the RBM model
can be solved very fast for arbitrary illumination and geometrical parameters,
such as dimensions of OPC features, line widths, etc. This approach
dramatically reduces computational costs of the optimization procedure while
providing accuracy superior to the approaches involving simplified mask models.
RBM furthermore provides rigorous error estimators, which assure the quality
and reliability of the reduced basis solutions. We apply the reduced basis
method to a 3D SMO example. We quantify performance, computational costs and
accuracy of our method.
