## 1 Introduction  
As nodes are shrinking in semiconductor fabrication, chemical mechanical polishing (CMP), the process to achieve global and local planarization of the wafer surface, is also facing some emerging problems, such as defect control, novel material CMP, and green CMP [1; 2; 3; 4]. Continuous optimization of the consumables, polishing recipe, and post-processing is needed to solve contemporary challenges. Innovative consumables and manufacturing processes are also being proposed for the future CMP [5]. Computational fluid dynamics (CFD) is a well-recognized tool to visualize fluid flow and study the tribology, slurry filtration, transportation, and flow [6; 7; 8]. Shallow trench isolation (STI) and inter-level dielectric (ILD) CMP are two main steps for multi-layer stacking on the substrate. The over-deposited oxide film was removed by silica or ceria slurries based on a combination of a chemical reaction and mechanical buffing. Simple graphics of the polisher equipment and the pad-wafer interface are shown in Figure 1. The slurry, pad, conditioner, retainer ring, and membrane are the main consumables. The slurry is pumped out of the slurry dispenser arm and then flows into the narrow gap with chemicals and abrasives in the pad-wafer interface while the platen and the head rotate on different axes. Finally, the used slurry takes away worn pad debris, byproducts, and friction heat. Therefore, slurry flow can affect the MRR, NU, and number of defects [9; 10; 11]. The huge amounts of waste chemicals produced result in environmental pollution, so green CMPs that use fewer chemicals are desired. In addition, the disposable slurry expense covers a high percentage of the consumables [12]. Slurry expenditures represent almost 50% of all CMP-related costs [13]. Optimized slurry flow in terms of the polishing performance and slurry consumption trade-off can precisely control the supplement amount and improve the utilization efficiency. Moreover, sufficient and uniform slurry flow can lower the NU of the polished wafer. Several kinds of defects, dishing, and erosion were identified as being related to the NU [14]. The cost of ownership can be reduced by saving the slurry cost and improving the yield rate. In general, more fresh slurry means better polishing but the pad-wafer gap limits the flow in one end and out the other [15]. A traditional CMP pad normally has concentric pad grooves to accommodate the slurry. Furthermore, the radial groove pad was designed to improve the slurry refresh rate [16]. Different pads and certain polishing recipes have different SSTs, which means there is a critical amount of supplemental slurry, and excess slurry cannot flow into the pad-wafer gap. Many researchers have made use of different simulation methods to investigate the slurry behavior in CMP. [PERSON] et al. varied the applied load, wafer rotation, slurry injection, and pad types and showed the fluid flow fields [17]. [PERSON] et al. investigated the effects of pad conditioning on slurry transport and mixing [18]. [PERSON] et al. reported changes in the slurry film thickness with the interfacial fluid pressure distribution and contact conditions [19]. [PERSON] et al. optimized the pad groove design to realize uniform slurry velocity and high surface quality for polished CaF\({}_{2}\) crystals [20]. [PERSON] et al. explored the effect of slanted concentric grooves on slurry film thickness during polishing [21]. Nevertheless, these studies lack the quantitative analysis of the in situ polishing conditions with combined turbulent flow in the pad grooves and laminar flow in the pad-wafer interface. In the present study, both simulations and experimental approaches are used to investigate the slurry flow at a wafer-pad interface with concentric groove pads and  
Figure 1: Schematic of oxide CMP and the interactions between the wafer, pad, and silica abrasives. radial groove pads. The preliminary flow conditions were derived using fluid mechanics equations.