Automated accuracy-oriented model optimization system for critical dimension metrology
Techniques and systems for critical dimension metrology are disclosed. Critical parameters can be constrained with at least one floating parameter and one or more weight coefficients. A neural network is trained to use a model that includes a Jacobian matrix. During training, at least one of the weight coefficients is adjusted, a regression is performed on reference spectra, and a root-mean-square error between the critical parameters and the reference spectra is determined. The training may be repeated until the root-mean-square error is less than a convergence threshold.
1. A method comprising:
initializing a model that includes a Jacobian matrix using a processor, wherein the initializing includes spectra fitting;
constraining critical parameters, using the processor, with at least one floating parameter and one or more weight coefficients; and
training, using the processor, a neural network to use the model, wherein the training includes:
adjusting at least one of the one or more weight coefficients based on accuracy of the critical parameters;
performing a regression on data for a reference spectra thereby filtering a signal in the reference spectra;
determining a root-mean-square error between the critical parameters and the data for the reference spectra after performing the regression; and
repeating the adjusting, the performing, and the determining until the root-mean-square error is less than a convergence threshold.
2. The method of claim 1 , wherein the constraining uses a linear function.
3. The method of claim 1 , wherein the constraining uses a nonlinear function.
4. The method of claim 3 , wherein the constraining is performed with a single layer of the neural network.
5. The method of claim 3 , wherein the constraining is performed with multiple layers of the neural network.
6. The method of claim 1 , further comprising obtaining the one or more weight coefficients from a database.
7. The method of claim 1 , wherein the reference spectra are synthetic spectra generated for a critical dimension value or a system setting.
8. The method of claim 1 , wherein the reference spectra are obtained from a semiconductor wafer.
9. The method of claim 1 , further comprising setting the convergence threshold.
10. The method of claim 9 , further comprising defining a regularization item, wherein the regularization item is an inverse of an autocorrelation length, and wherein the autocorrelation length is one of the one or more weight coefficients along a wavelength or parameter direction.
11. The method of claim 10 , wherein the adjusting the one or more weight coefficients includes using an overall cost function.
12. The method of claim 1 , wherein the adjusting the one or more weight coefficients is configured to avoid over-fitting.
13. A computer program product comprising a non-transitory computer readable storage medium having computer readable program embodied therewith, the computer readable program configured to carry out the method of claim 1 .
14. A system comprising:
a processor in electronic communication with an electronic data storage unit and a wafer metrology tool, wherein the processor is configured to:
initialize a model in a manner that includes spectra fitting, wherein the model includes a Jacobian matrix;
constrain critical parameters with at least one floating parameter and one or more weight coefficients; and
train a neural network to use the model, wherein the training includes:
adjusting at least one of the one or more weight coefficients based on accuracy of the critical parameters;
performing a regression on data for a reference spectra thereby filtering a signal in the reference spectra;
determining a root-mean-square error between the critical parameters and the data for the reference spectra after performing the regression; and
repeating the adjusting, the performing, and the determining until the root-mean-square error is less than a convergence threshold.
15. The system of claim 14 , wherein the constraining uses a linear function or a nonlinear function.
16. The system of claim 15 , wherein constraining uses a nonlinear function, and wherein the constraining is performed with a single layer of the neural network or multiple layers of the neural network.
17. The system of claim 14 , wherein the processor is further configured to obtain the one or more weight coefficients from a database in the electronic data storage unit.
18. The system of claim 14 , wherein the reference spectra are obtained from a semiconductor wafer in the wafer metrology tool.
19. The system of claim 14 , wherein the processor is further configured to set the convergence threshold.