Molecular Scale E-Beam Resist Development Simulation for Pattern Fluctuation Analysis

To better understand nanometer scale pattern fluctuation in lithography, we present a new model for electron-beam exposed (poly)methyl-methacrylate resist development, which considers the molecular scale material structure. The polymer chains in the resist are represented as spheres with a radius proportional to the square root of the chain length. Monte Carlo electron scattering simulation in the resist gives the local absorbed energy, which in turn sets the local molecular weight distribution. The development model uses the Poisson probability for removing each surface polymer chain in a small time step. The Poisson removal rate is derived using a mass equivalence with macroscopic etch rate models. The simulations predict the macroscopic shape of patterned resisi features as well as microscopic surface roughness and nanometer scale line-edge variation. Observations with atomic force microscopy confirm the simulation results, including 10 nm edge variation and rough developed surfaces at exposures doses near the transition from low etch rate to high etch rate.