Contact Mechanics and Lubrication Hydrodynamics of Chemical Mechanical Polishing

Abstract

A preliminary model for the contact mechanics and fluid mechanics of the chemical mechanical polishing process is presented. Only the basic equations of elastic contact surface mechanics and hydrodynamic lubrication are required. Although the model is highly idealized, no ad hoc assumptions or adjustable parameters are required. Some new experimental results are presented, reinforcing the counterintuitive experimental determination of suction fluid pressure below the pad. The model correctly predicts the magnitude of the suction pressure and the effect of load, speed, and roughness. © 1999 The Electrochemical Society. All rights reserved.

Material Removal Mechanisms in Lapping and Polishing

“…Pad glazing was found to lead to hydrodynamic conditions. In further work by the same research group [57,58] a physical model was put forward to attempt to explain the sub-atmospheric pressures which had been experimentally observed. An interaction of the pad/wafer contact mechanics and the fluid hydrodynamics was identified as the cause.…”

Analysis of Feature-Scale Wear in Chemical Mechanical Polishing: Modeling and Experiments

“…Fluid mechanics: The effect of flowfield and hydrodynamic pressure of the slurry was not taken into account in this model. Past models have suggested that the slurry shear rate directly affects the wear of the wafer sample [1,26,27], while other studies have shown that the sample contact stress is affected by the slurry hydrodynamic pressure [35,36]. Neither of such assumptions are taken into account in the current model.…”

Modeling and calculation of slurry-chemistry effects on chemical–mechanical planarization with a grooved pad

“…The half-width of the wafer is taken to be a = 50 mm, the wafer back pressure p back = 20 kPa, and the relative sliding speed V = 0.43 m/s, as in the work of Shan et al [11]. Furthermore, following Tichy et al [10], the stiffness parameter for calculating the compressed groove depth is taken to be K = 2.5 MPa/mm (corresponding to a pad thickness on the order of a few millimeters). The friction coefficient between the pad and wafer (and retaining ring) surfaces is f = 0.8.…”

“…The mean slurry flowrate q , however, increases dramatically with d groove . This makes sense, because (10) indicates that the volumetric slurry flowrate q(x, t) has a cubic dependence on h(x, t) and hence is much more sensitive to the groove depth variation (which dominates the slurry-film thickness variation) than the fluid pressure is.…”

“…A number of other theoretical models exist in the literature (e.g., [10][11][12]), each considering certain aspects of the CMP process. To our knowledge, one of the simplest models that calculates the contact stress on the pad-wafer interface, which then determines the slurry-film thickness, was proposed by Shan et al [11] for CMP with a flat pad.…”