Accurate and fast neural network training for library-based critical dimension (CD) metrology
Embodiments are generally directed to neural network training for library-based critical dimension metrology. An embodiment of a method includes optimizing a threshold for a principal component analysis of a spectrum data set to provide a principal component value, estimating a training target for one or more neural networks, training the one or more neural networks based both on the training target and on the principal component value provided from optimizing the threshold for the principal component analysis, and providing a spectral library based on the one or more trained neural networks.
1. A method of fast neural network training for library-based critical dimension (CD) metrology for a grating structure, the method comprising:
providing a training target for a first neural network;
training the first neural network, the training of the first neural network including use of a validation data set, the training comprising starting with a first number of neurons and iteratively increasing the number of neurons until the training target is reached using a second, larger, number of neurons, wherein the training of the first neural network includes stopping iterations for the training of the first neural network upon the occurrence of the following:
a value of a computational cost function for the training of the first neural network is less than a predetermined value,
the value of the computational cost function is not reduced by a predetermined percentage for a certain number of consecutive iterations, or
an error of the validation data increases for a predetermined number of iterations;
generating a second neural network based on the training and the second number of neurons;
providing a spectral library based on the second neural network, the spectral library including a simulated spectrum for the grating structure; and
comparing the simulated spectrum to a sample spectrum for the grating structure.
2. The method of claim 1 , wherein iteratively increasing the number of neurons until the training target is reached comprises using a modified Levenberg-Marquardt approach.
3. The method of claim 1 , wherein iteratively increasing the number of neurons comprises increasing the number of neurons in a hidden layer of the first neural network.
4. A non-transitory machine-accessible storage medium having instructions stored thereon which cause a data processing system to perform a method of fast neural network training for library-based critical dimension (CD) metrology for a grating structure, the method comprising:
providing a training target for a first neural network;
training the first neural network, the training of the first neural network including use of a validation data set, the training comprising starting with a first number of neurons and iteratively increasing the number of neurons until the training target is reached using a second, larger, number of neurons, wherein the training of the first neural network includes continuing iterations for the training of the first neural network until any one of the following occurs:
a value of a computational cost function for the training of the first neural network is less than a predetermined value,
the value of the computational cost function is not reduced by a predetermined percentage for a certain number of consecutive iterations, or
an error of the validation data increases for a predetermined number of iterations;
generating a second neural network based on the training and the second number of neurons; and
providing a spectral library based on the second neural network.
5. The storage medium as in claim 4 , wherein iteratively increasing the number of neurons until the training target is reached comprises using a modified Levenberg-Marquardt approach.
6. The storage medium as in claim 4 , wherein iteratively increasing the number of neurons comprises increasing the number of neurons in a hidden layer of the first neural network.
7. The storage medium as in claim 4 , wherein the training of the first neural network further includes stopping iterations for the training of the first neural network upon the occurrence of the following:
the number of iterations reaches a predetermined maximum number of iterations.
8. The method of claim 1 , wherein the training of the first neural network further includes stopping iterations for the training of the first neural network upon the occurrence of the following:
the number of iterations reaches a predetermined maximum number of iterations.