A collocation grids method for determining pad conditioning coverage and density under long time conditioning process

In the Chemical Mechanical Planarization (CMP) process for semiconductor wafer fabrication, the polishing pads need to be continuously conditioned to ensure appropriate surface characteristics, which causes wear to the pads and subsequently affects the quality of CMP. Tuning the conditioning parameters is typically determined through expensive experimental trials. An effective pad conditioning simulation platform to model the conditioning process can significantly reduce the time and cost of the process development cycle. However, to mimic the real-life pad conditioning process, the simulation needs to track hundreds or even thousands of micro-sized diamond tips to check the contact points on the pads continuously during the conditioning process that spans many hours. This makes simulating pad conditioning over the entire pad for the duration of the process very challenging. In this work, we propose a low-cost numerical approach for simulating the pad conditioning process based on a collocation grid method and parametric mapping. Important numerical aspects such as time step size characterization, jump-over ratio, simulation efficiency, and error control are systematically analysed and discussed. Several benchmark examples are performed to evaluate the effectiveness of the proposed method.