3-D numerical modeling of thermal flow for insulating thin film using surface diffusion

This paper presents a three-dimensional (3-D) numerical surface diffusion model of BPSG glass flow of surface tension. The analysis region is divided into small cubic cells. Material surface is described as an equi-concentration (equi-existence rate) area which is obtained by linear interpolation between the cells. 3-D surface curvature is defined as the ratio of the increment of surface area to that of volume in a small interface area. Flux of flow is proportional to gradient of the surface curvature, and the direction is from positions of larger curvature to that of small curvature. The flow algorithm is that particles move from the mass-center of the equi-concentration area of a cell to that of the neighbor cells across the contact lines of the cell boundary and the equi-concentration area. This paper presents two 3-D simulations of flow which show that this model can be applied for not only cylindrical symmetry but also general 3-D topography. Also, the surface diffusion coefficient for the total concentration (C_imp : P₂O₅ and B₂O₃) is derived using the model by fitting 2-D simulations to the experiments at 850°C