Stresses in silicon substrates near isolation trenches

We describe a methodology for obtaining stresses near isolation trenches in silicon considering the entire trench forming process. A two-dimensional plane strain finite element stress analysis is performed for a trench with a thermal SiO2 sidewall and polysilicon ‘‘fill’’ which includes the cumulative stresses from the superposition of (i) residual stresses from the thermal oxidation step, (ii) the intrinsic stress from the polysilicon deposition, and (iii) stresses due to the coefficient of thermal expansion mismatch between SiO2 and silicon during the temperature cycles involved in the process. The thermal oxidation step is simulated using a two-dimensional nonlinear viscoelastic program novel [in Proceedings of the Second International Symposium on Process Physics and Modeling in Semiconductor Technology, edited by G. R. Srinivasan, J. D. Plummer, and S. T. Pantelides (Electrochemical Society, Pennington, NJ, 1991), p. 772], that produces the oxide shape and stress at the oxide-silicon interface which is converted into equivalent nodal forces on the finite element grid. We have also made a three-dimensional finite element analysis of the thermal mismatch stresses between a parallelopipedic oxide inclusion in silicon with anisotropic properties and have compared these results with the analytical results [J. Appl. Phys. 66, 2741 (1989); 67, 1092 (1990)] in which the oxide and silicon are assumed to have identical isotropic elastic properties.