Lubrication Layer Perturbations in Chemical-Mechanical Polishing

Bhattacharya, A. and Breward, C.J.W. and Gratton, M. and Evans, J. and Nicholas, M. and Please, C. and Schwendeman, D. and Surles, M. and Witelski, T. (2005) Lubrication Layer Perturbations in Chemical-Mechanical Polishing. US Workshop on Mathematical Problems in Industry > 21st MPI [Worcester 13/6/2005 - 17/6/2005].

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Problem Statement

In chemical-mechanical polishing, a process that is used to polish and planarize wafer surfaces during integrated circuit manufacturing, a soft polymeric pad with a rough surface is used in conjunction with a liquid slurry containing very fine abrasive particles to gently remove material. Asperities, or summits, on the pad surface are on the order of tens of microns in height. Various measurements of the mean fluid thickness between the wafer and pad are in general agreement that the mean fluid thickness is also on the order of a few tens of microns. Slurry particles, by contrast, are usually a few tens to a few hundreds of nanometers in diameter. Since the pad asperities are soft, theories of elastohydrodynamic lubrication (Hamrock) suggest that a very thin lubrication layer, on the order of nanometers, forms between asperity tips and the wafer surface and that the fluid pressures in this region deform the tip shapes. This nanolubrication layer presumably interacts with the slurry particle distribution in some way. For example, very small particles should transit the layer easily; particles on the order of the layer thickness may become trapped between the pad and wafer, making them "active" in the polishing process; and particles much larger than the layer thickness may be excluded but may become trapped at the layer leading edge. Those particles that become trapped by some mechanism not only become active in the removal process, but also bear some of the load between the wafer and pad and therefore have the potential to perturb the lubrication layer thickness and shape. Currently, only relatively simple theories exist concerning the subpopulation of the particle distribution that becomes active, and there is no theory about how the solid loading or size distribution of the slurry particles might perturb the nanolubrication layer. Several goals might be identified in the study of this problem:

1. As a warmup, estimate the nanolayer thickness and shape, either numerically or analytically, for a fluid without slurry particles as a function of pad mechanical properties, fluid viscosity, sliding speed, undeformed asperity tip curvature and asperity height for a fluid without abrasive particles.

2. For a slurry with a very dilute particle loading, estimate the subpopulation that becomes active and assess, on average, the perturbation that the active particles introduce into the nanolayer shape.

3. Assuming that (1) and (2) can be done, consider asperities with a distribution of heights and tip curvatures and determine how the microscopic interactions combine to produce a macroscopic theory.

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