Qualitative fuzzy logic model of plasma etching process

Plasma etching is key to transferring fine patterns. Accurate prediction models are highly demanded to gain improved insights into plasma discharges, as well as optimization and control of plasma equipment. As an empirical approach, a fuzzy logic referred to as adaptive network fuzzy inference system (ANFIS) was used to construct a qualitative model for a magnetically enhanced reactive ion etching. The etch process was characterized by a 2^6-1 fractional factorial experiment. Process factors that were varied in this design include RF power, pressure, magnetic field strength, Cl₂, BCl₃, and N₂. Etch responses modeled include etch rate, anisotropy, and bias in critical dimension (CD). Thirty-two experiments were used to train ANFIS, and the trained model was subsequently tested on ten experiments that were additionally conducted. A total of 42 experiments were thus required for building up models. Prediction performance of the ANFIS model was optimized as a function of training factors: type of membership function and learning factors. Root mean-squared prediction errors of optimized ANFIS models are 0.308 μm/min, 0.305, and 1.371 Å, for etch rate, anisotropy, and CD bias, respectively. Compared to statistical response surface models, optimized ANFIS models demonstrated better prediction accuracy.