Numerical simulations of thin film thermal flow

Abstract

The thin film thermal flow process in long trenches is analyzed using a simulator which solves the equations which govern viscous, incompressible fluid flow. The total thermal baking process is divided into small time steps. At each time step, we solve the governing equations using the penalty function formulation and the Galerkin finite element method to obtain local velocity vectors. The free surface of the flowing film is updated according to these local velocity vectors. As an example application, we simulate the flow of boron and phosphorus doped silicon dioxide glass films in 2 μm high by 2 μm wide, infinitely long trenches, for which two-dimensional profile evolution is appropriate. The simulated film profiles show that the local levelling rate of a film is a sensitive function of surface curvature. The simulation program predicts that lower viscosity and thicker films have superior planarization properties compared with higher viscosity and thinner films. These trends are in agreement with empirical observations and previous modelling and simulation work on glass film planarization processes.