Optimization of carrier morphology in terms of Fourier sine series for chemical mechanical polishing process

To establish a 2D axisymmetric quasi–static finite element model during the chemical mechanical polishing process, revolutions of the wafer and the pad were assumed to be the same, the axisymmetric uniformly distributed pressure form was given, and both the wafer–pad interface and wafer–film interface were considered as contact boundaries. Next, the height of the contact interface between the carrier and the film near the zone of nonuniform von Mises stress distribution of the wafer surface was changed to the form of a Fourier sine series. Finally, a quadratic programming method was utilized to solve the coefficients of the Fourier sine series and then an optimal morphology in terms of Fourier sine series under the condition of minimum nonuniformity of the wafer surface was achieved. The result found that the nonuniformity was reduced remarkably and its improved rate reaches 88.45% under the optimal surface of the carrier.