1 Optimization of Carrier Morphology in Chemical Mechanical Polishing Process

In this paper, a 2D axisymmetric quasic-static finite element model for chemical-mechanical polishing process (i.e., CMP for short) and quasi-Newton method were combined to develop a novel optimal model for the carrier surface morphology. Firstly, revolutions of the wafer and the pad were assumed to be the same and an axisymmetric uniformly distributed pressure form was given to establish a 2D axisymmetric quasic-static model for CMP. Regarding the wafer-pad interface and the wafer-film interface as contact interfaces, a 2D axisymmetric quasic-static finite element model was developed and a MARC software package was used to calculate the von Mises stress distribution of the wafer surface. Next, height of the contact interface between the carrier and the film near zone of the nonuniform von Mises stress distribution of the wafer surface was changed to be similar to square-wave series. Amplitude was considered as a design variable, and then quasi-Newton method was utilized to solve coefficients of the square-wave series under the condition of minimum nonuniformity of the wafer surface to obtain optimal square-wave morphology. Compared the simulated results under the conditions of the optimal square-wave surface and the flat surface of the carrier, it was found that nonuniformity of the wafer surface has been reduced remarkably under the optimal square-wave surface of the carrier and the improved rate reached to 89.02%