Abstract:
A method and apparatus to measure overlay from images of metrology targets, images obtained using acoustic waves, for example images obtained using an acoustic microscope. The images of two targets are obtained, one image using acoustic waves and one image using optical waves, the edges of the images are determined and overlay between the two targets is obtained as the difference between the edges of the two images.
Abstract:
Methods and apparatus for estimation of at least one parameter of interest of a feature fabricated on a substrate, the feature comprising a plurality of structure parameters, the structure parameters comprising the at least one parameter of interest and one or more nuisance parameters. A receiver receives radiation scattered from one or more measured features on the substrate; a pupil generator generates an unprocessed pupil representation of the received radiation; a matrix multiplier multiplies the transformation matrix with the intensities of each of the pixels of the unprocessed pupil representation to determine a post-processed pupil representation in which the effects of the nuisance parameters are mitigated or removed; and a parameter estimator estimates the at least one parameter of interest based on the post-processed pupil representation.
Abstract:
A structure of interest is irradiated with radiation for example in the x-ray or EUV waveband, and scattered radiation is detected by a detector (306). A processor (308) calculates a property such as linewidth (CD) by simulating interaction of radiation with a structure and comparing the simulated interaction with the detected radiation. A layered structure model (600, 610) is used to represent the structure in a numerical method. The structure model defines for each layer of the structure a homogeneous background permittivity and for at least one layer a non-homogeneous contrast permittivity. The method uses Maxwell's equation in Born approximation, whereby a product of the contrast permittivity and the total field is approximated by a product of the contrast permittivity and the background field. A computation complexity is reduced by several orders of magnitude compared with known methods.
Abstract:
Described herein are system, method, and apparatus for determining three-dimensional (3D) information of a structure of a patterned substrate. The 3D information can be determined using one or more model configured to generate 3D information (e.g., depth information) using only a single image of a patterned substrate. In a method, the model is trained by obtaining a pair of stereo images of a structure of a patterned substrate. The model generates, using a first image of the pair of stereo images as input, disparity data between the first image and a second image, the disparity data being indicative of depth information associated with the first image. The disparity data is combined with the second image to generate a reconstructed image corresponding to the first image. Further, one or more model parameters are adjusted based on the disparity data, the reconstructed image, and the first image.
Abstract:
A method for increasing certainty in parameterized model predictions is described. The method comprises clustering dimensional data in a latent space associated with a parameterized model into clusters. Different clusters correspond to different portions of a given input. The method comprises predicting, with the parameterized model, an output based on the dimensional data in the latent space. The method comprises transforming, with the parameterized model, the dimensional data in the latent space into a recovered version of the given input that corresponds to one or more of the clusters. In some embodiments, the method comprises determining which clusters correspond to predicted outputs with higher variance, and making the parameterized model more descriptive by adding to the dimensionality of the latent space, and/or training the parameterized model with more diverse training data associated with one or more of the determined clusters or parts of clusters associated with the higher variance.
Abstract:
Described herein is a method for training a machine learning model configured to predict a substrate image corresponding to a printed pattern of a substrate as measured via a metrology tool. The method involves obtaining a training data set comprising (i) metrology data of the metrology tool used to measure the printed pattern of the substrate, and (ii) a mask pattern employed for imaging the printed pattern on the substrate; and training, based on the training data set, a machine learning model to predict the substrate image of the substrate as measured by the metrology tool such that a cost function is improved, wherein the cost function comprises a relationship between the predicted substrate image and the metrology data.
Abstract:
Described is a method for categorizing a substrate subject to a semiconductor manufacturing process comprising multiple operations, the method comprising: obtaining values of functional indicators derived from data generated during one or more of the multiple operations on the substrate, the functional indicators characterizing at least one operation; applying a decision model comprising one or more threshold values to the values of the functional indicators to obtain one or more categorical indicators; and assigning a category to the substrate based on the one or more categorical indicators.
Abstract:
Described herein is a method for quantifying uncertainty in parameterized (e.g., machine learning) model predictions. The method comprises causing a parameterized model to predict multiple posterior distributions from the parameterized model for a given input. The multiple posterior distributions comprise a distribution of distributions. The method comprises determining a variability of the predicted multiple posterior distributions for the given input by sampling from the distribution of distributions; and using the determined variability in the predicted multiple posterior distributions to quantify uncertainty in the parameterized model predictions. The parameterized model comprises encoder-decoder architecture. The method comprises using the determined variability in the predicted multiple posterior distributions to adjust the parameterized model to decrease the uncertainty of the parameterized model for predicting wafer geometry, overlay, and/or other information as part of a semiconductor manufacturing process.
Abstract:
A method including: obtaining a logistic mathematical model predicting the formation of a physical structure created using a patterning process; evaluating the logistic mathematical model to predict formation of a part of the physical structure and generate an output; and adapting, based on the output, an aspect of the patterning process.
Abstract:
Disclosed is a method for reconstructing a parameter of a lithographic process. The method comprises the step of designing a preconditioner suitable for an input system comprising the difference of a first matrix and a second matrix, the first matrix being arranged to have a multi-level structure of at least three levels whereby at least two of said levels comprise a Toeplitz structure. One such preconditioner is a block-diagonal matrix comprising a BTTB structure generated from a matrix-valued inverse generating function. A second such preconditioner is determined from an approximate decomposition of said first matrix into one or more Kronecker products.