3-D NUMERICAL MODELING OF THERMAL FLOW FOR INSULATING THIN-FILM USINGSURFACE-DIFFUSION

This paper presents a three-dimensional (3-D) numerical surface diffus ion model of BPSG glass flow of surface tension. The analysis region i s divided into small cubic cells. Material surface is described as an equi-concentration (equi-existence rate) area which is obtained by lin ear 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 s mall interface area. Flux of flow is proportional to gradient of the s urface curvature, and the direction is from positions of larger curvat ure to that of small curvature. The flow algorithm is that particles m ove from the mass-center of the equi-concentration area of a cell to t hat of the neighbor cells across the contact lines of the cell boundar y and the equi-concentration area. This paper presents two 3-D simulat ions of flow which show that this model can be applied for not only cy lindrical symmetry but also general 3-D topography. Also, the surface diffusion coefficient for the total concentration (C-imp: P2O5 and B2O 3) is derived using the model by fitting 2-D simulations to the experi ments at 850 degrees C.