Physics-Prior Bayesian Neural Networks in Semiconductor Processing

With the fast scaling-down and evolution of integrated circuit (IC) manufacturing technology, the fabrication process becomes highly complex, and the experimental cost of the processes is significantly elevated. Therefore, in many cases, it is very costly to obtain a sufficient amount of experimental data. To develop an efficient method to predict the results of semiconductor experiments with a small amount of known data, we use a novel method based on Bayesian framework with the prior distribution constructed by technology computer-aided-design (TCAD) physical models. This method combines the advantages of statistical models and physical models in the aspect that TCAD can provide visionary guidance on an experiment when a limited amount of experimental data is available, and a machine learning model can account for subtle anomalous effects. Specifically, we use aspect ratio dependent etching (ARDE) phenomenon as an example and use variational inference with Kullback-Leibler divergence minimization to achieve the approximation to the posterior distribution. The relation between etching process input parameters and etching depth is learned using the Bayesian neural network with TCAD priors. Using this method with 35 neurons per hidden layer, mean square error (MSE) in the test set is reduced from 0.2896 to 0.0175, 0.058 to 0.0183, 0.0563 to 0.0188, 0.058 to 0.019 for partition =10, 20, 30, 40, respectively, reference to the baseline BNN where a regular normal distribution prior with zero mean and unity standard deviation N(0,1) is used.