Diffusion Simulation Using Boundary-fitted Coordinate Transformation

Abstract

Diffksion simulation in an arbitrarily shaped region has been performed using boundary-fitted coordinate transformation. The meshes were generated by solving the Poisson equation as proposed by Thompson[l].A novel method is proposed to formulate a diffusion equation in a complicated region like a trench structure. First, complicatedly shaped boundaries are placed inside the simulation area to reduce mesh distortion. Socendly, a new approximation concerning segregation flux is proposed. A diffusion equation with a segregation flux between complicated regions can be solved quickly and accurately using this method.The following are two examples of diffusion simulation.(1) LOCOS oxidation Figure 1 shows the contours of boron concentration after local oxidation. A boron dose of 60x was implant-a ed at 50 keV and driven in for 60 min. in wet 0, at 1OOoC. The boundary condition was placed so that the meshes were orthogonal to the boundary in the silicon region, and were approximately orthogonal to the boundary in the Si02 region. The transformed diffusion equation in the transformed space became simple, because this boundary Fig.1 contoun of boron concentration condition made the meshes nearly afta locd oxidation for 60 min. in wet oahogonal in the entire region. %at 1OOOC.(2) Trench oxidation Figure. 2 shows the contom of arsenic concentration after trench oxidation. The process steps were as follows: after silicon etching of trench shape, arsenic was driven from silicate glass with l o x l O l *~m -~ of arsenic for 60 min. at 1OOOC . After removing the arsenic silicate glass, oxidization was performed for 5 min. in wet 0, at 1°C.As shown in Fig. 2, the silicon/oxide boundary was placed inside the simulation area to reduce mesh distortion. However, a difficulty due to segregation emerged. The impurity concentration became a doublcvalued function at the interface, because of 79