Seeing plasmas as latent spaces: Virtual metrology and surrogate plasma models with deep generative models

Abstract

Semiconductors are a fundamentally important part of modern society and semiconductor manufacturing is a key industry around the world. Plasma etching and deposition are the most common ways to produce physical features in a semiconductor device from lithographic patterns. However, the semiconductor industry still struggles with the poor repeatability of plasma processing, process results drifting over time and the difficulty of predicting or controlling process results using in-situ sensors. Progress on these problems will lead to reduced energy and material use in manufacturing semiconductor devices and reduce the cost and difficulty of developing new processes for manufacturing new devices.

In this work I have taken a novel approach to solving this problem. Using a deep convolutional autoencoder trained with optical images and emission spectra from a plasma etcher, I have created a model that produces a latent representation of the information in the plasma diagnostics. With this latent representation I have built virtual metrology models to predict the etch rate of \sio \space in a \cfo \space plasma achieving errors as low as 0.272\% on test data, lower than any other results published in the literature.

To train the deep autoencoder I amassed a data set of 812,500 image/spectra pairs in argon, oxygen, Ar/O\textsubscript{2}, CF\textsubscript{4}/O\textsubscript{2} and SF\textsubscript{6}/O\textsubscript{2} plasmas. By building a model to predict the dc bias of the plasma from the latent representation I determined that datasets of 100-10,000 samples are sufficient to start building predictive models linking the latent parameters to other measured parameters that generalise over several plasma chemistries and a wide range of plasma conditions. The data set, model code and trained models have been released as open source.

The underlying dataset is available at \url{https://doi.org/10.5281/zenodo.7704879} under the Creative Commons Attribution 4.0 International license. The trained models are available at \url{https://github.com/gregdaly/generative_modelling_for_optical_plasma_diagnostics} under the MIT license. The model code and an example notebook of using the model is available at \url{https://colab.research.google.com/github/gregdaly/generative_modelling_for_optical_plasma_diagnostics/blob/master/generative_decoder_demo.ipynb} under the MIT license.

I have also shown that the decoder side of the autoencoder can be used as a powerful generative model. I have shown that it can be used to create a novel type of plasma model that can generate a wide variety of optical emission spectra across several plasma chemistries and can easily be extended in the future to predict other more common plasma parameters from experimental measurements. I have also shown, through empirical evaluations on benchmark datasets for image generation, that deep autoencoders can produce higher quality generated images and are more robust in training when compared to the more commonly used variational autoencoder.