The effect of trench corner shapes on local stress fields: athree-dimensional finite-element modeling study

Local stress fields associated with deep trench structures are modeled in three dimensions utilizing a finite-element method. A model consisting of a SiO₂-filled deep trench residing in a silicon substrate is utilized, and stress is generated by differential thermal contraction. It is shown that corner regions, especially convex, `outside' corners, dramatically enhance the elastic energy density and shear stresses locally compared to noncorner regions. The effects of the specific corner geometry on these local stress fields is then investigated and it is shown that subtle geometric changes can yield substantial decreases in the magnitude and lateral extent of the fields