NUMERICAL SIMULATIONS OF THIN-FILM THERMAL FLOW

The thin film thermal flow process in long trenches is analyzed using a simulator which solves the equations which govern viscous, incompres sible fluid flow. The total thermal baking process is divided into sma ll time steps. At each time step, we solve the governing equations usi ng the penalty function formulation and the Galerkin finite element me thod to obtain local velocity vectors. The free surface of the flowing film is updated according to these local velocity vectors. As an exam ple application, we simulate the flow of baron and phosphorus doped si licon dioxide glass films in 2 mu m high by 2 mu m wide, infinitely lo ng trenches, for which two-dimensional profile evolution is appropriat e. The simulated film profiles show that the local leveling rate of a film is a sensitive function of surface curvature. The simulation prog ram predicts that lower viscosity and thicker films have superior plan arization properties compared with higher viscosity and thinner films. These trends are in agreement with empirical observations and previou s modeling and simulation work on glass film planarization processes.