Rapid simulation of silylation and the role of physical mechanisms in profile shapes

A rigorous simulator which includes the highly nonlinear diffusion and stress dependent reactions present in silylation is presented and used to asses the role of the key physical parameters in the resultant profile shapes for silicon uptake. The silylation model implemented includes a) the relaxation of the polymer during silylation, b) the resultant increase in the diffusivity of the silylating agent as a function of the resist matrix expansion, as well as a c) local reaction rate retardation due to stresses associated with nonuniform resist swelling. The resulting differential equations are solved utilizing a Krylov subspace Newton convergence accelerator. A greater than one order of magnitude decrease is observed in simulation times as compared to traditional numerical techniques. Simulations of silylated profiles with various silylation uptake regimes elucidate the interplay of the physical mechanisms model in determining final silylation depth and sidewall angle.