Analysis of a model for imaging in photolithography

AbstractThe governing equation of a model for imaging in photolithography is studied. The density p of the photoactive component of the resist, which is a function of time and position, decreases at a rate assumed proportional to the local light intensity. It satisfies a nonlinear differential equation dϱdt (t) = F(ϱ(t)), of which an evaluation of the right-hand side requires solving Maxwell's equations in a periodic 2D-configuration of dielectrics consisting of the resist and the substrate. The electric permittivity of the resist is a function of position which depends on ϱ. The Maxwell problem is studied by applying the limiting absorption principle. It is proved using the contraction mapping theorem that for every exposure time and every initial density (∗) has a unique solution which is a smooth function of time and position when all data are smooth