Method of calibrating a plurality of metrology apparatuses, method of determining a parameter of interest, and metrology apparatus

1. A method of calibrating a plurality of metrology apparatuses, comprising:

obtaining training data comprising, for each of the metrology apparatuses, a plurality of detected representations of radiation scattered from a structure on a substrate and detected by the metrology apparatus;

encoding, using an encoder, each detected representation to provide an encoded representation, and generating, using a decoder, a synthetic detected representation from the respective encoded representation;

identify, using a classifier, a metrology apparatus from the plurality of metrology apparatuses that originates each encoded representation or each synthetic detected representation; and

using the training data to simultaneously perform:

a first machine learning process in which either or both of the encoder and decoder are trained to 1) minimize differences between the detected representations and corresponding synthetic detected representations, and 2) minimize a probability of the classifier correctly identifying from which metrology apparatus each encoded representation or each synthetic detected representation originates; and

a second machine learning process in which the classifier is trained to maximize the probability of the classifier correctly identifying from which metrology apparatus each encoded representation or each synthetic detected representation originates.

2. The method of claim 1 , wherein the encoder and decoder comprise a neural network.

3. The method of claim 2 , wherein the encoder and decoder form an auto-encoder.

4. The method of claim 2 , wherein the encoder and decoder comprise a parametrized filter.

5. The method of claim 4 , wherein the training of the first machine learning process comprises adjusting weightings applied by the encoder to respective components of a mathematical expansion representing the detected representation.

6. The method of claim 5 , wherein the encoded representation comprises coefficients of the mathematical expansion weighted by the weightings.

7. The method of claim 4 , wherein the training of the first machine learning process comprises selecting one or more basis functions of a mathematical expansion representing the detected representation.

8. The method of claim 1 , wherein the encoding of each detected representation by the encoder comprises deriving one or more parameters of interest of the structure on the substrate from which the detected representation is obtained by the respective metrology apparatus.

9. The method of claim 1 , further comprising:

deriving one or more target parameters of a geometrical model of the structure on the substrate; and

simulating the scattering of radiation from the structure and detection of the detected representation by the metrology apparatus based on the geometrical model of the structure and a metrology recipe defining settings of the metrology apparatus.

10. The method of claim 1 , wherein the detected representation comprises a pupil representation defining a distribution of radiation in a pupil plane of the metrology apparatus.

11. The method of claim 1 , wherein the first machine learning process and the second machine learning process form a generative adversarial network, with the first machine learning process being adversarial with respect to the second machine learning process, and the decoder acting as a generative model of the generative adversarial network.

12. The method of claim 1 , wherein the classifier comprises one or more of the following: neural network, support vector machine, logistic regression, or linear discriminant analysis.

13. A method of determining a parameter of interest relating to a structure on a substrate formed by a lithographic process, comprising:

calibrating a plurality of metrology apparatuses using the method of claim 1 ;

receiving input data representing a detected representation of radiation scattered from the structure and detected by one of the metrology apparatuses; and

using either or both of the encoder and decoder, after the training by the first machine learning process, to obtain the parameter of interest from the received input data.

14. The method of claim 1 , wherein the encoder comprises a comparator; and

wherein the comparator is configured to compare a dataset input to the encoder to a dataset output from the decoder.

15. A metrology apparatus for determining a parameter of interest relating to a structure on a substrate formed by a lithographic process,

wherein the metrology apparatus is a metrology apparatus having been calibrated using the method of claim 1 ; and

wherein the metrology apparatus comprises:

a processing unit configured to:

receive input data representing a detected representation of radiation scattered from the structure and detected by the metrology apparatus; and

use either or both of the encoder and decoder, after the training by the first machine learning process, to obtain the parameter of interest from the received input data.

16. A non-transitory computer program product comprising machine-readable instructions for causing a processing unit to cause the performance of the method of claim 1 .

17. The method of claim 1 , further comprising:

mapping, by the classifier, an output of the encoder and/or the decoder to a probability, for each given one of the plurality of metrology apparatuses, that the output originated from that metrology apparatus.

18. The method of claim 17 , wherein the probability is represented as a penalty in a cost function of the encoder and the decoder.

19. The method of claim 13 , further comprising:

adding an additional metrology apparatus to the plurality of metrology apparatuses; and

training another encoder based on the trained encoder.