Automatic optimization of measurement accuracy through advanced machine learning techniques

1. A method comprising:

predicting, using a processor, a value of a fixed parameter with a neural network based on a value of a critical parameter of a semiconductor wafer, wherein the neural network is trained based on one or more of the critical parameters and a low-dimensional real-valued vector associated with a spectrum, and wherein the fixed parameter represents dimensions of a measured structure; and

evaluating, using the processor, the value of the fixed parameter by determining if a test spectra is within a spectra envelope over wavelength points, wherein the spectra envelope is between a minimum and a maximum value for training spectra at each of the wavelength points.

2. The method of claim 1 , wherein the spectrum is a spectroscopic ellipsometry spectrum or a specular reflectance spectrum.

3. The method of claim 1 , wherein the low-dimensional real-valued vector is mapped by another neural network based on the spectrum.

4. The method of claim 1 , further comprising:

training, using the processor, an initial neural network by mapping one or more of the spectrum to one or more of the low-dimensional real-valued vectors; and

training, using the processor, the neural network to predict the fixed parameter based on one or more of the critical parameters and the low-dimensional real-valued vector from the initial neural network.

5. The method of claim 4 , further comprising generating the spectrum by simulating profiles sampled within a range of floating parameters.

6. The method of claim 5 , further comprising generating profiles of an optical critical dimension model associated with the spectrum.

7. The method of claim 6 , wherein generating the profiles of the optical critical dimension includes:

determining a set of the fixed parameters by sampling the fixed parameters to within a range of the fixed parameters; and

for each pair of spectra and fixed parameters, determining a corresponding critical parameter.

8. The method of claim 7 , further comprising determining a corresponding floating parameter or a corresponding constrained parameter with the corresponding critical parameter.

9. The method of claim 4 , wherein training data for the initial neural network includes a plurality of samples, wherein each of the samples includes one or more of the spectrum and profiles of an optical critical dimension model associated with one or more of the spectrum.

10. The method of claim 4 , wherein training the initial neural network determines a parameter that minimizes a difference in the low-dimensional real-valued vector for a same one of one or more of the spectrum.

11. The method of claim 4 , wherein the neural network minimizes a mean squared error of a set of the fixed parameters relative to training data.

12. The method of claim 4 , wherein the initial neural network and the neural network have different architectures.

13. The method of claim 1 , further comprising averaging a set of the fixed parameters over samples used to generate the spectrum.

14. The method of claim 1 , further comprising gradient-based searching of a set of the fixed parameters with the neural network.

15. The method of claim 14 , wherein the gradient-based searching includes:

i) setting nominal values of the fixed parameters;

ii) determining the critical parameters of the fixed parameters at the nominal values;

iii) determining the fixed parameters of the critical parameters using the neural network;

iv) determining the fixed parameters of the critical parameters from the gradient-based search with one iteration;

v) updating the fixed parameters with the fixed parameters using the gradient-based search with one iteration; and

vi) repeating the steps i) through v) until a stopping criteria is achieved, wherein the stopping criteria is one of a specification or a convergence.

16. A system comprising:

a primary neural network in electronic communication with a wafer metrology tool, wherein the primary neural network is configured to predict a value of a fixed parameter based on a value of a critical parameter of a semiconductor wafer and a low-dimensional real-valued vector derived from a spectrum of the semiconductor wafer, and wherein the fixed parameter represents dimensions of a measured structure; and

a processor configured to evaluate the value of the fixed parameter by determining if a test spectra is within a spectra envelope over wavelength points, wherein the spectra envelope is between a minimum and a maximum value for training spectra at each of the wavelength points.

17. The system of claim 16 , wherein the spectrum is a spectroscopic ellipsometry spectrum or a specular reflectance spectrum.

18. The system of claim 16 , further comprising a secondary neural network in electronic communication with the primary neural network, wherein the secondary neural network is configured to receive the spectrum of the semiconductor wafer and to derive the low-dimensional real-valued vector based on the received spectrum, and wherein the primary neural network receives the low-dimensional real-valued vector from the secondary neural network.

19. The system of claim 18 , wherein the primary neural network includes a processor.

20. The system of claim 18 , wherein the primary neural network and the secondary neural network have different architectures.