3.3.2 Feature-Size Simulation and Advanced Physical Modeling

At least, when feature sizes smaller than the wavelength should be resolved, the scalar approximation commonly used throughout large area approaches fails and the vector nature of the light has to be considered. This means that a rigorous electromagnetic simulation becomes necessary to account for the wave property of the light. Additionally, the interaction of the exposing light with the irradiated resist as well as the thermal treatment of the resist after exposure have to be modeled accurately. Without advanced resist process modeling the exact electromagnetic calculation of the light distribution does not make much sense since one is primarily interested in the final developed resist profile. The extremely high computational requirements of such sophisticated models restrict the size of the simulation domain to a small number of features. In the following some possible applications of advanced physical modeling are presented.

Rigorous electromagnetic simulation. Two important examples that require an electromagnetic treatment are a rigorous simulation of edge effects occurring in phase-shifting masks and scattering and notching from substrate topography. In conventional imaging simulation the photomask is assumed to be infinitesimally thin with ideal transmission characteristics. The emerging field is thereby approximated by a nonphysical square wave modulation. For small mask openings and large vertical steps in phase-shifting masks, a more detailed characterization becomes necessary. Actual fields have tapered on-off transitions, polarization dependent effects due to different boundary conditions for the electric and magnetic field occur as well as a lateral cross-mixing in passing through the mask. Simulation has been used to investigate the extent to which such edge effects are present [68,69]. The second point is electromagnetic light scattering at nonplanar surfaces. Substrate topography can cause a sudden linewidth change or reflective notching. This is extremely important in process technologies where features must be defined between existing topographical structures like a trench or a bird's peak of a field oxide. In such cases, the resulting light distribution cannot be adequately described by a scalar approximation as the interference between waves traveling in opposite directions depends on the orientation of their vectors components. Also here, simulation has been successfully used to investigate such phenomena since it is the only means to quantify topography effects on the light distribution because of the impossibility of direct field measurements [70,71,72,73].

Advanced resist processes modeling. The behavior of DUV resist systems under exposure radiation is extremely difficult to understand and model. For conventional DQN resists a well-established and widely accepted simulation model exists [74,75]. The physical and chemical processes occurring in contrast enhancement or antireflective layers as well as in chemically amplified or silylated resists are less understood and extremely difficult to model. Beside optical absorption and modification, the temperature sensitivity of catalytic reactions and movement of photo-generated species have to be accounted for. A simultaneous diffusion simulation with concentration dependent coefficients and rate equations becomes necessary. Adequate boundary conditions at the resist surface have to be established. Recently, a large number of resist models has been proposed in the literature [74,76,77,78,75,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]. Research on this topic is still a demanding and especially important problem as simulation can provide additional understanding of the role of bake steps and resist systems in relation to the mask illumination and exposure tool. Furthermore, a three-dimensional simulation of the development process is necessary since the etch front during dissolution does not solely penetrate vertically but also expands laterally. Especially for dense layouts and in assessing the printability of defects three-dimensional effects during development become critically important.