Dummy-feature placement for chemical-mechanical polishing uniformity in a shallow-trench isolation process

Manufacturability of a design that is processed with shallow-trench isolation (STI) depends on the uniformity of the chemical-mechanical polishing (CMP) step in STI. The CMP step in STI is a dual-material polish for which all previous studies on dummy-feature placement for single-material polish by Kahng et al. (1999), Tian et al. (2000), and Chen et al. (2000) are not applicable. Based on recent semiphysical models of polish-pad bending by Ouma et al (1998), local polish-pad compression by Grillaert (1999) and Smith (1999), and different polish rates for materials present in a dual-material polish by Grillaert (1999) and Tugbawa et al. (1999), this paper derives a time-dependent relation between post-CMP topography and layout pattern density for CMP in STI. Using the dependencies derived, the first formulation of dummy-feature placement for CMP in STI is given as a nonlinear-programming problem. An iterative approach is proposed to solve the dummy-feature placement problem. Computational experience on four layouts from Motorola is given.