Prediction of Tracer Concentration and Mixing in CFSTRs with Mean Age Distribution

Simulation and Experimental Investigation of the Radial Groove Effect on Slurry Flow in Oxide Chemical Mechanical Polishing

Slurry flow on the pad surface and its effects on oxide chemical mechanical polishing (CMP) performance were investigated in simulations and experiments. A concentric groove pad and the same pad with radial grooves were used to quantitatively compare the slurry saturation time (SST), material removal rate (MRR), and non-uniformity (NU) in polishing. The monitored coefficient of friction (COF) and its slope were analyzed and used to determine SSTs of 25.52 s for the concentric groove pad and 16.06 s for a certain radial groove pad. These values were well correlated with the simulation prediction, with around 5% error. Both the laminar flow and turbulent flow were included in the sliding mesh model. The back mixing effect, which delays fresh slurry supply, was found in the pressure distribution of the wafer–pad interface.

Residence time distribution (RTD) revisited

Residence Time Distribution (RTD) theory is revisited and tracer technology discussed. The background of RTD following Danckwerts ideas is presented by introducing "distribution" functions for residence time, internal age and intensity function and how to experimentally obtain them with tracer techniques (curves C and F of Danckwerts). Compartment models to describe fluid flow in real reactors are reviewed and progressive modeling of chromatographic processes discussed in some detail. The shortcomings of Standard Dispersion Model (SDM) are addressed, the Taylor-Aris model discussed and the Wave Model of Westerterp's group introduced. The contribution of Computational Fluid Dynamics (CFD) is highlighted to calculate RTD from momentum and mass transport equations and to access spatial age distribution and degree of mixing. Finally smart RTD and future challenges are discussed.