(186x) Continuum Modeling of Foam-Based Cleaning of Silicon Wafers in a Rotation Cell

As feature sizes in the microelectronics industry diminish, cleanliness becomes an ever more important requirement. We present a new wet-cleaning method to remove strongly adhered 90-nm, Si₃N₄ contaminant test particles from silicon wafers. The proposed cleaning solution consists of a foamed aqueous dispersion of insoluble solids with average size of 50 μm. Contaminant removal increases with solids concentration, foam quality, process time, and shear rate and can approach 100 %.

We study particle removal efficiency in a rotational cell, which is relevant for commercial application. In this cell, a particle-contaminated horizontal wafer is rotated below a fixed rectangular cleaning-fluid-supply manifold at a gap height typically 1 mm. We observe that in the case of unfoamed suspension essentially all removal happens during the first rotation, when the cleaning fluid is being delivered and dispensed over the dry wafer. When the foamed suspension is used, every rotation contributes to the contaminant particle removal. Exponential decline of surface concentration of adhered particles with time is observed in this case. The same particle removal is reached at significantly lower solids concentration as compared to the unfoamed suspension, everything else being equal. In both cases, we observe radial variation of particle removal: the particle removal decreases with distance from the wafer center leveling off at the wafer edges.

A binary-collision rate model is derived to predict particle detachment. In this model, the flux of solids along or equivalently the shear along the wafer surface plays a key role. Thus, special attention is paid to modeling of the flow field in the system. Both analytical perturbation and numerical finite elements methods are used to calculate the flow field. Our calculations show that capillary effects at the free surface have a significant influence on the flow field and must be incorporated into the binary-collision model. The proposed model predicts the influence of radial position, angular speed, process time, system geometry, solids concentration, and foam quality on removal of Si₃N₄ particles from silicon wafers in the rotational cell. Comparison of the rate model with experimental removal data is good.