A hybrid model combining simulation and optimization in chemical mechanical polishing process

Abstract

A hybrid model composing of 2D axisymmetric quasic-static finite element method, back-propagation network, and direct complex searching optimization for chemical mechanical polishing process (CMP) was established to investigate the optimal parameter sets under the minimum nonuniformity (NU) on wafer surface. During polishing, the revolutions of the wafer and the pad were assumed to be the same, the force form of carrier was axisymmetric and uniformly distributed, and the minimum potential energy principle and the Hooke's law were considered. Thus, a 2D axisymmetric quasic-static finite element model was developed in which the wafer carrier, carrier film, wafer, and pad were involved. Under the conditions that the carrier load varied from 0.03448 MPa to 0.10345 MPa, the pad's elastic modulus was from 1.1448 MPa to 3.4345 MPa, and the pad's thickness was from 0.6985 mm to 2.0955 mm, a total of 35 sets of finite element simulated results were then used as the database of the back-propagation neural network-learning model. Among them, 27 sets of data were constituted in the training data, and the other 8 sets of data were the test data. Using these datasets, the network-learning model concerning the relationship between the von Mises stress on the wafer surface and the process parameters, including the carrier load, pad's elastic modulus, and thickness of pad, could be established. Finally, direct complex searching optimization was applied to obtain the optimal parameter sets under the minimum NU on the wafer surface. The results showed that under the optimal condition of the carrier's load of 0.052 MPa, pad's elastic modulus of 3.19 MPa and pad's thickness of 0.699 mm, the minimum NU of 1.65995 could be achieved.