Development of convolutional neural network based Gaussian process regression to construct a novel probabilistic virtual metrology in multi-stage semiconductor processes. (March 2020) - Wu, Xiaofei; Chen, Junghui; Xie, Lei; Chan, Lester Lik Teck; Chen, Chun-I
Abstract: Manufacturing of semiconductor chips involves hundreds of process steps. For high-throughput semiconductor manufacturers, it is not feasible to get all the quality measurements of wafers at each step because of expensive costs. Based on the limited measurements of sampled wafers, virtual metrology (VM) allows predicting the relevant quality variables without increasing the number of physical measurements. Traditional data-driven VM methods are constructed using a predefined model along with feature extractions in data pre-processing. Often the identified VM model is not reliable if the constructed model and the extracted features are improper. In this paper, the convolutional neural network (CNN) based Gaussian process regression (GPR) VM mode (CNN-GPR) calibrated by maximization of the Bayesian posterior density distribution is systematically developed. CNN is used to extract information from massive wafer data through layers of the cascade-connected convolving filters. With the extracted features, the GPR model associates the stochastic nature of the operating steps with the quality variables to obtain the predicted means as well as the quantitated uncertainty levels. Unlike the traditional VM models where the extracted features and the prediction models are generated separately, the CNN-GPR model is sensitive to the variations of the quality variables and the features are determined simultaneously through the covariance matrices with information from both of the process and the quality variables. The proposed CNN-GPR model performs better as it represents the complex process of the whole set of measured variables. Through the studies on a real semiconductor process, the effectiveness of the proposed algorithm is demonstrated and compared against the regular regression algorithms.