Method for determining corrective film pattern to reduce semiconductor wafer bow
A method is disclosed for generating a corrective film pattern for reducing wafer bow in a semiconductor wafer fabrication process. The method inputs to a neural network a wafer bow signature for a predetermined semiconductor fabrication step. The neural network generates from the input a corrective film pattern corresponding to the wafer bow signature. The neural network is trained with a training dataset of wafer shape transformations and corresponding corrective film patterns.
1 . A method for generating a corrective film pattern for reducing wafer bow in a semiconductor wafer fabrication process, the method comprising:
measuring, using one or more metrology apparatuses, a bowed semiconductor wafer to produce a wafer bow signature for a predetermined semiconductor fabrication step;
inputting, to a surrogate machine learning model, the wafer bow signature, the surrogate machine learning model comprising:
a forward model comprising a first neural network model configured to take as input corrective film patterns and output corresponding wafer shape transformations, and
an inverse model comprising a second neural network model configured to take as input wafer shape transformations and output corresponding corrective film patterns;
generating, by the surrogate machine learning model, a corrective film pattern corresponding to the wafer bow signature,
wherein the corrective film pattern is adapted for depositing on a semiconductor wafer a corrective film having spatially varying stress signature;
wherein the surrogate machine learning model is trained with a training dataset of target wafer shape transformations and corresponding training corrective film patterns by:
training the forward model using the training corrective film patterns, and
training the inverse model using the target wafer shape transformations and a set of wafer shape transformations output by the trained forward model.
2 . The method of claim 1 , wherein the training dataset is generated using a simulation to compute the training corrective film patterns from the target wafer shape transformations for the predetermined semiconductor fabrication step.
3 . The method of claim 1 , wherein the training dataset is generated by experimentally determining the training corrective film patterns corresponding to the target wafer shape transformations.
4 . The method of claim 1 , wherein the training dataset is generated using a finite element method to solve a linear elasticity problem, and using an optimization framework to select the target wafer shape transformations that minimize a cost function.
5 . The method of claim 1 , further comprising performing active learning feedback to refine the surrogate machine learning model.
6 . The method of claim 1 , wherein the surrogate machine learning model is implemented with a conditional variational autoencoder.
7 . The method of claim 1 , wherein the surrogate machine learning model is implemented with a conditional generative adversarial network.
8 . The method of claim 7 , wherein the conditional generative adversarial network includes a generator implemented as a U-Net with skip connections.
9 . The method of claim 7 , wherein the conditional generative adversarial network includes a discriminator implemented as a convolutional classifier.