Method and system for predicting process information with a parameterized model
A method and system for predicting complex electric field images with a parameterized model are described. A latent space representation of a complex electric field image is determined based on dimensional data in a latent space of the parameterized model for a given input to the parameterized model. The given input may be a measured amplitude (e.g., intensity) associated with the complex electric field image. The complex electric field image is predicted based on the latent space representation of the complex electric field image. The predicted complex electric field image includes an amplitude and a phase. The parameterized model comprises encoder-decoder architecture. In some embodiments, determining the latent space representation of the electric field image comprises minimizing a function constrained by a set of electric field images that could be predicted by the parameterized model based on the dimensional data in the latent space and the given input.
1 . A computer-implemented method for improving metrology outputs during a semiconductor manufacturing process, comprising:
determining, using a first portion of a parameterized model, a latent space representation of an input electric field image, wherein the latent space representation has a lower dimensionality than the input electric field image;
predicting, using a second portion of the parameterized model, an output electric field image based on the latent space representation of the input electric field image, wherein the output electric field image includes amplitude and phase information; and
determining, using a third portion of the parameterized model, one or more metrology metrics for the semiconductor manufacturing process, wherein input to the third portion of the parameterized model includes one of the input electric field image, the output electric field image, or the latent space representation of the input electric field image; and
adjusting the one or more metrology metrics during the semiconductor manufacturing process.
2 . The method of claim 1 , wherein:
input to the first portion of the parameterized model further comprises a measured amplitude associated with the input electric field image, and
the amplitude comprises an intensity.
3 . The method of claim 1 , wherein:
the determining the latent space representation of the input electric field image comprises minimizing a function constrained by a set of electric field images predicted by the parameterized model based on the dimensional data in a latent space of the parameterized model, and
the latent space representation of the input electric field image comprises a tensor.
4 . The method of claim 1 , wherein the parameterized model is a machine learning model.
5 . The method of claim 1 , wherein the first and second portions of the parameterized model comprise encoder-decoder architecture.
6 . The method of claim 5 , wherein the encoder-decoder architecture comprises variational encoder-decoder architecture and the method further comprises:
training the variational encoder-decoder architecture with a probabilistic latent space that generates realizations in an output space.
7 . The method of claim 6 , wherein the probabilistic latent space comprises low dimensional encodings.
8 . The method of claim 5 , wherein the dimensional data in the latent space of the parameterized model is encoded by an encoder of the encoder-decoder architecture.
9 . The method of claim 5 , further comprising: training the parameterized model with a training set of complex electric field images.
10 . The method of claim 9 , wherein the training comprises:
encoding the complex electric field images in the training set into the dimensional data in the latent space of parameterized model,
transforming the dimensional data in the latent space of the parameterized model into recovered versions of the complex electric field images in the training set to facilitate verification of the training, and
iteratively providing additional complex electric field images as input to the parameterized model, the additional complex electric field images determined based on an extent to which the recovered versions of the complex electric field images match the complex electric field images in the training set.
11 . The method of claim 5 , wherein the predicting the output electric field image based on the latent space representation of the input electric field image comprises passing the latent space representation of the input electric field image through a decoder of the encoder-decoder architecture.
12 . The method of claim 1 , wherein the third portion of the parameterized model is a regression model.
13 . A metrology apparatus comprising one or more processors configured to perform operations comprising:
determining, using a first portion of a parameterized model, a latent space representation of an input electric field image, wherein the latent space representation has a lower dimensionality than the input electric field image;
predicting, using a second portion of the parameterized model, an output electric field image based on the latent space representation of the input electric field image, wherein the input electric field image includes amplitude and phase information;
determining, using a third portion of the parameterized model, one or more metrology metrics for a semiconductor manufacturing process, wherein input to the third portion of the parameterized model includes one of: the input electric field image, the output electric field image, or the latent space representation; and adjusting one or more parameters of the metrology apparatus used during a semiconductor manufacturing process used the one or more metrology metrics.