Authors: K. Garikipati, V.S. Rao, M.Y. Hao, E. Ibok, I. De Wolf and R.W. Dutton
Affilation: Stanford University, United States
Pages: 180 - 183
Keywords: mathematical modelling, continuum mechanics, viscoelasticity, semiconductor processing, finite element methods
The mathematics and mechanics of the Shallow Trench Isolation process are described. The diffusion reaction problem is posed in terms of fundamental mass balance laws. Finite strain kinematics is invoked to model the large expansion of SiO2, dielectrics are modelled as viscoelastic solids and annealing-induced density relaxation of SiO2 is incorporated as a history-dependent process. A levelset framework is used to describe the moving Si/SiO2 interface. Sophisticated finite element methods are employed to solve the mathematical equations posed for each phenomenon. Mechanical properties of viscoelastic solids are extracted directly from stress-strain data, following which, parameters for the diffusion-reaction problem are obtained. Comparison with micro-Raman spectroscopy provides validation of the model.