Abstract

A new model of multidimensional <i>in situ</i> diagnostic data is presented. This was accomplished by combining a back-propagation neural network (BPNN), principal component analysis (PCA), and a genetic algorithm (GA). The PCA was used to reduce input dimensionality. The GA was applied to search for a set of optimized training factors involved in BPNN training. The presented technique was evaluated with optical emission spectroscopy (OES) data measured during the etching of oxide thin films in a CHF₃–CF₄ inductively coupled plasma. For a systematic modeling, the etching process was characterized by a face-centered Box Wilson experiment. The etch responses to be modeled include oxide etch rate, oxide profile angle, and oxide etch rate non-uniformity. In PCA, three types of data variances were employed and the reduced input dimensionality corresponding to 100, 99, and 98% are 16, 8, and 5. The BPNN training factors to be optimized include the training tolerance, number of hidden neurons, magnitude of initial weight distribution, gradient of bipolar sigmoid function, and gradient of linear function. The prediction errors of GA-BPNN models are 249 Å/min, 2.64°, and 0.439% for the etch rate, profile angle, and etch rate non-uniformity, respectively. Compared to the conventional and previous full OES models, the presented models demonstrated a significantly improved prediction for all etch responses.

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