Pad-wafer-slurry interface information from force data

This paper describes a model and algorithm for converting pad-wafer shear force and normal force data measured during chemical-mechanical planarization (CMP) into information about the conditions at the lubricated interface between the pad and wafer. Insight into this interface has been notably difficult due to its inaccessibility. Results indicate that force data contain detailed information about the wafer attitude relative to the pad and information about mean solid contact and fluid pressures in the interface. Fluid pressures are particularly interesting since they are difficult to detect directly but are coupled to solid contact pressures and can therefore affect uniformity. Fluid pressures can also underlie problems like wafer slippage. As part of the analysis of the model, we derive a highly accurate analytic approximation to the solution of the Reynolds equation for the mean fluid pressure in the slurry layer during CMP. Two algorithms are discussed for converting force data. The fastest is considerably faster than real-time force acquisition.