Multi-Objective Optimization of Chemical Mechanical Polishing for 6-Inch Germanium Wafers via Orthogonal Experiment and Entropy-Weighted Grey Relational Analysis

Six-inch single-crystal germanium (Ge) (100) wafers are indispensable substrates for high-efficiency space multi-junction solar cells, which require sub-nanometre surface roughness and minimal defects to be achieved simultaneously during fine polishing. Existing fine-polishing studies rely mainly on single-parameter screening and single-indicator evaluation and, therefore, cannot balance polishing efficiency, surface quality and defect rate. Here, Ge wafers were fine-polished using NaClO as the oxidant (pH = 9) and alkaline colloidal SiO2 as the abrasive. An L9 (34) orthogonal experiment was used to examine the effects of the machine load polishing pressure (P), carrier-to-platen rotation speed ratio (V), slurry flow rate (F) and chlorine content (C) on the average polishing rate, surface roughness Ra, scratch ratio and unpolished ratio. Range analysis and effect curves resolved the variation in each indicator, and entropy-weighted grey relational analysis (GRA) combined the four indicators into a single grey relational grade (GRG). Chlorine content most strongly affected the polishing rate and pressure most strongly affected Ra (range R = 0.067 for both). The verified multi-objective optimum, P3V3F3C3, achieved a polishing rate of 0.40 μm/min, Ra = 0.40 nm, a scratch ratio of 5.0% (2/40) and an unpolished ratio of 0% (0/40) within the investigated parameter range. Because this condition is also the removal-rate optimum, no polishing rate is sacrificed; relative to the roughness optimum, it forgoes 0.02 nm of Ra (0.40 vs. 0.38 nm) but reduces the scratch ratio from 20.0% to 5.0% and the unpolished ratio from 30.0% to 0%, and it, therefore, gives the best overall performance. This multi-indicator-to-single-indicator strategy is readily transferable to the ultra-precision polishing of other brittle semiconductors.