An application of Chebyshev spectral method in modeling the diffusion of the acid during PEB process

The distribution of the acid concentration in the chemically amplified resist (CAR) plays an important role in the formation of the final resist profile. During post exposure bake (PEB) process, acid will diffuse and be neutralized in the resist to influence the acid concentration distribution and the process can be described as a reaction-diffusion system in a set of partial differential equations (PDEs). We use Chebyshev spectral method to solve those equations and it turns out to be very fast along with certain accuracy. Our simulation results indicate that Chebyshev spectral method is quite computationally efficient in dealing with PDEs during PEB process in some cases.