Computational Lithography

Chapter 10

Coherent Thick-Mask Optimization

In the previous chapters, a variety of OPC and PSM optimization algorithms are developed in coherent and partially coherent imaging systems. In addition, these algorithms are extended to the realm of joint optimization of source and mask. All these algorithms, however, have been developed under the thin-mask assumption, where Kirchhoff's boundary condition is directly applied to the mask topology and consequently the mask is treated as a 2D object [4, 81, 82]. As the critical dimension (CD) printed on the wafer shrinks into the subwavelength regime, the thick-mask effects become very pronounced such that these effects should be taken into account in the mask optimization. Thick-mask effects include polarization dependence due to the different boundary conditions for the electric and magnetic fields, transmission error in small openings, diffraction edge effects or electromagnetic coupling, and so on [4]. The thick-mask effects can be rigorously represented by the near-field pattern of the mask, which is different from the Kirchhoff approximation of the mask topography. Two decades ago, Wong and Neureuther discovered the of alternating PSM, and applied the finite-difference time-domain (FDTD) method to study the mask topography effects in the projection printing of PSM [89, 90]. This phenomenon was proven by experimental results later [62]. Yuan exploited the waveguide (WG) method to model the light diffraction of 2D phase-shifting masks ...