Geometric-overlap Modeling and Sweep Uniformity Optimization of Fixed Diamond Conditioning Disks for Chemical Mechanical Planarization

In this study, we develop a graphics processing unit (GPU)-accelerated geometric-overlap model for fixed-abrasive diamond conditioning disks used in chemical mechanical planarization (CMP).The framework systematically evaluates how diamond-layout strategies and arm-sweep kinematics affect polishing pad coverage uniformity and overall economic performance.A planar rigid-body motion model is first established for diamond chips under the coupled action of disk self-rotation and arm oscillation, and a unified metric, the normalized overlap area ratio (NAR), is defined to quantify radial-sweep uniformity.Simulation conditions are assumed to be a pad diameter of 510 mm, an arm amplitude of 34, and a disk speed of 87 rpm; diamond counts from three to twelve are assessed.Trajectory superposition and hit-density statistics are accelerated on a GPU using CuPy.Results show that a single diamond traces an Archimedeanlike spiral, mitigating local wear gradients and impact concentration.With seven to eight diamonds, phase-complementary effects fill the central sweep dead zone, raising NAR to 30% and optimizing radial and angular uniformities.Integrated cost-performance analysis indicates that a seven-or eight-diamond configuration provides the best trade-off between coverage efficiency and diamond usage; counts above eight lead to excessive overlap in the central region and uneven inner-outer distributions, shortening pad life and raising manufacturing costs, thus driving the system into diminishing returns.The proposed model supplies quantitative guidelines for CMP dresser design, delivering practical benefits for process stability and cost efficiency.These are critical for manufacturing high-performance sensors and devices on advanced material substrates.