To accurately model the physical processes governing the post-exposure bake step advanced diffusion modeling is required. In addition to simple diffusion simulation with a constant diffusivity, evaporating boundary conditions and material inhomogeneities must be considered. Especially for chemically amplified resist systems such advanced models are necessary. By linking the exposure module to the AMIGOS simulator [252,253]--a flexible, analytical, object-oriented modeling environment--many new insights in the resist reactions could be gained.
Finally, the differential method could be used to rigorously simulate--in addition to the EM field calculation inside the inhomogeneous resist--two other relevant optical phenomena occurring in lithography. The first is a rigorous investigation of mask diffraction effects. This point becomes increasingly important for phase-shifting masks since the thickness of the phase-shifting elements cannot be neglected in comparison to the wavelength. For example, in sub-resolution assisted phase-shifting masks their impact on the mask operation has to be investigated. For such problems the assumptions made in Fourier optics lose their validity and rigorous methods are the only means to simulate them. The second application is the study of alignment marks. Due to the increasingly larger wafer diameters alignment is of utmost importance. A rigorous study is important not only for photolithography but also for non-optical techniques since alignment is always performed optically. From a simulation point of view the interesting quantities are now either the outgoing or reflected waves of the simulation domain (cf. Figure 6.1). The differential method could readily be applied to such problems, only the post-processing, i.e., the evaluation of the outgoing or reflected amplitudes, has to be newly developed.
As can be seen, enough problems are open for future research!