Abstract
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.
Highlights
The Bayesian model was proposed by Thomas Bayes in 1763 [1]
Process variations, aging machines, and chamber-specific effects in real-world cannot be accurately taken into account by using idealized semiconductor physics models, the prior based on professional technology computer-aided design (TCAD) knowledge still help Bayesian neural network (BNN) to acquire more accurate prior information for the model latent variables such as weights and biases
In this paper, we use a novel scheme based on a Bayesian neural network with TCAD prior, which can be used at the early-stage of fabrication experiments in semiconductor processing and industry 4.0
Summary
The Bayesian model was proposed by Thomas Bayes in 1763 [1]. At the very first beginning, Bayesian framework is not widely used, but nowadays, it has been used and proved effective in many fields including statistic modeling in machine learning [2]–[11], robotics [12]–[14], medical image [15]–[18], sports [19]–[21]. As semiconductor processing becomes more complex and requires many steps to fulfill the integrated circuits, there is increased concern for the very high cost associated with collecting enough experimental data points to construct machine learning models. We use a Bayesian neural network, based on the technology computeraided design (TCAD) physical model as prior distributions, to predict the etching depth in the Bosch DRIE process. The TCAD prior is critical in the aspects that it can provide a better prediction result using fewer sampled data points or help in the convergence to the optimal solution in semiconductor processing input parameter tuning. While semiconductor physics and TCAD modeling have been the main methodology in the past 30 years in process and device modeling, the physical models should be able to provide some guidance on the statistical model This can be most pronounced in the initial machine learning. Compared with the commonly-used normal distribution N (0, 1) prior, the prior from TCAD simulated data can reduce the trial-and-error time and improve the accuracy of the prediction, especially at the initial stage of the experiment
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