Analysis of the tribological mechanisms arising in the chemical mechanical polishing of copper-film wafers when using a pad with concentric grooves

An average Reynolds equation considering the effects of a pad's annular grooves and surface roughness is developed in this study to examine mixed lubrication in the chemical mechanical polishing (CMP) of a copper-film silicon wafer. This equation is obtained on the basis of the principle that the pressure gradients and volume flow rates in the direction normal to the border of a groove and a plateau as well as on two sides of the border must be equal. The continuities of volume flow rates and hydrodynamic pressure on two sides of the border as well as in the direction normal to the border of a groove and a plateau are satisfied in order to develop this Reynolds equation. The removal rate model is obtained by taking the concentration of active abrasives in the slurry and the pad grooves into account. Theoretical results are also shown in order to investigate the effects of changing the groove depth and width on the removal rate and the nonuniformity of a copper-film wafer. The application of concentric grooves in general can lower the suction pressure (negative pressure) formed between the pad and the wafer, elevate the wear rate, and reduce the nonuniformity. However, the influences of the groove depth on wear rate and nonuniformity become insignificant when the depth is excessively large. The removal rate is reduced by increasing the groove width such that it finally approaches to the result of a nongrooved pad.