Transfer learning for generating fabrication process models

Abstract

Techniques for utilizing transfer learning for generating fabrication process models are provided herein. In some embodiments, the techniques may involve determining a posterior distribution associated with a first model representing a first fabrication process. The techniques may further involve identifying one or more components associated with the first model to be transferred as a model parameter value for a second model representing a second fabrication process. The techniques may further involve generating model parameters for the second model using the posterior distribution associated with the first model and the identified one or more components associated with the first model.

Description

PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WOTRANSFER LEARNING FOR GENERATING FABRICATION PROCESS MODELSINCORPORATION BY REFERENCE

[0000] A PCT Request Form is filed concurrently with this specification as part of the present application. Each application that the present application claims benefit of or priority to as identified in the concurrently filed PCT Request Form is incorporated by reference herein in their entireties and for all purposes.BACKGROUND

[0001] Process engineers may use fabrication process models to simulate a fabrication process in order to identify a process recipe and / or recipe parameters likely to yield a fabricated substrate that satisfies various specifications. However, developing such a model may be resource intensive, and may rely on large datasets of experimental data to train and / or develop the process model. Accordingly, development of the model may take a substantial amount of time and may utilize a large amount of resources (e.g., to develop data to train the model), which adversely affects development of fabrication processes.

[0002] The background description provided herein is for the purposes of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.SUMMARY

[0003] Techniques for utilizing transfer learning for generating fabrication process models are provided herein. The techniques may be practiced as a processor-implemented method, a system comprising one or more processors and / or one or more processor-readable media, and / or one or more non-transitory processor- readable media.

[0004] According to some embodiments, the techniques may involve determining a posterior distribution associated with a first model representing a first fabrication process. The techniques may further involve identifying one or more components associated with the first model to be transferred as a model parameter value for a second model representing a second fabrication process. The techniques may further involve generating model parameters for the second model using the posterior distribution associated with the first model and the identified one or more components associated with the first model.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO

[0005] In some examples, the posterior distribution is represented by a matrix, and wherein the identified one or more components correspond to elements of the matrix. In some examples, the first model and the second model are each a structured Gaussian process (GP) model, and wherein the matrix represents coefficients associated with a mean function of the structured GP of the first model.

[0006] In some examples, identifying the one or more components associated with the first model to be transferred comprises receiving user input indicating the one or more components.

[0007] In some examples, generating the model parameter for the second model using the posterior distribution associated with the first model comprises setting a prior distribution associated with the second model based on the selected one or more components.

[0008] In some examples, the first model was trained using a first dataset associated with the first fabrication process, and further comprising training the second model using a second dataset associated with the second fabrication process. In some examples, the second dataset is at half the size of the first dataset.

[0009] In some examples, the first fabrication process and the second fabrication process are semiconductor manufacturing processes with at least one difference in: (i) materials; (ii) critical dimensions; (iii) operating conditions; (iv) process tools; or any combination thereof.

[0010] According to some embodiments, the techniques may involve receiving a first dataset from experiments using a first fabrication process. The techniques may further involve fitting the first dataset with a first model and determining a posterior distribution associated with the first model and the first dataset. The techniques may further involve receiving a second dataset from experiments using a second fabrication process different from the first fabrication process. The techniques may further involve determining a prior distribution for a second model representing the second fabrication process based on the posterior distribution associated with the first model. The techniques may further involve generating the second model by learning the second dataset using at least some model parameter values set based on the prior distribution.

[0011] In some examples, the techniques may further involve outputting one or more recipe suggestions using the second model.

[0012] In some examples, the techniques may further involve receiving additional experimental data using the one or more recipe suggestions; and updating the second model using the additional experimental data.

[0013] In some examples, the techniques may further involve determining the one or more recipe suggestions using a process optimization technique. In some examples, the process optimizationPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO technique is a Bayesian optimization technique. In some examples, the techniques further involve performing one or more experiments using a Design of Experiments (DoE) technique prior to performing the process optimization technique, wherein the DoE technique utilizes the posterior distribution associated with the first model.

[0014] According to some embodiments, techniques may involve training a first model representing a first fabrication process using a first dataset. The techniques may further involve identifying one or more model parameter values associated with the first trained model to be transferred to a second model representing a second fabrication process based at least in part on probabilistic information associated with the first model indicating statistical uncertainty associated with model parameters of the first model. The techniques may further involve generating a second model representing the second fabrication process by training the second model using a second dataset, wherein at least a subset of model parameter values of the second model are set to the identified one or more model parameter values prior to training the second model.

[0015] In some examples, the probabilistic information comprises a posterior distribution associated with the first model.

[0016] In some examples, identifying the one or more model parameter values is based on user input.

[0017] In some examples, the second dataset is at least half the size of the first dataset.

[0018] In some examples, the first fabrication process and the second fabrication process are semiconductor manufacturing processes with at least one difference in: (i) materials; (ii) critical dimensions; (iii) operating conditions; (iv) process tools; or any combination thereof.BRIEF DESCRIPTION OF THE DRAWINGS

[0019] FIG. 1 is a flowchart of an example process for generating model parameters for a second model based on a related first model in accordance with some embodiments.

[0020] FIG. 2 is a flowchart of an example process for generating a second model based on a related first model using transfer learning in accordance with some embodiments.

[0021] FIG. 3 is a flowchart of an example process for performing process optimization using a Design of Experiments (DoE) performed using a model generated using transfer learning in accordance with some embodiments.

[0022] FIGS. 4A and 4B illustrate example results of a model trained using transfer learning from a related model in accordance with some embodiments.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO

[0023] FIG. 5 presents an example computer system that may be employed to implement certain embodiments described herein.DETAILED DESCRIPTION

[0024] In the following description, numerous specific details are set forth to provide a thorough understanding of the presented embodiments. The disclosed embodiments may be practiced without some or all of these specific details. In other instances, well-known process operations have not been described in detail to not unnecessarily obscure the disclosed embodiments. While the disclosed embodiments will be described in conjunction with the specific embodiments, it will be understood that it is not intended to limit the disclosed embodiments.

[0025] Process engineers may use fabrication process models to simulate a fabrication process in order to identify a process recipe and / or recipe parameters likely to yield a fabricated substrate that satisfies various specifications. However, developing such a model may be resource intensive, and may rely on large datasets of experimental data to train and / or develop the process model. Accordingly, development of the model may take a substantial amount of time and may utilize a large amount of resources (e.g., to develop data to train the model), which adversely affects development of fabrication processes.

[0026] Conventional techniques may involve training every model of a fabrication process independently, and then optimizing the model to identify process parameter values to meet a desired specification. Because each model is trained independently (and optimized independently), each model may require a substantially large dataset to train, and a lengthy duration of time to train the model and perform process optimization, which is costly in labor, test wafers, and computational resources.

[0027] In many cases, two different fabrication processes may have similarities, for example, in the tool that is used, the process gases and other chemistries used, the type of process being performed (e.g., whether the process is an etching process, a deposition process, a lithography process, etc.). The techniques disclosed herein leverage model parameter values learned for a first trained model representing a first fabrication process to inform a second model representing a different fabrication process. In particular, one or more model parameter values may be transferred from the first trained model to the second model to effectively initialize the second model based on learned information from the first trained model prior to training the second model. Because the second model is then trained using a priori information acquired from the trained first model, the second model may be trained with a restricted parameter space or using a substantially smaller dataset than would be required if the second model were trained without any baseline information.

[0028] In some implementations, the transferred model parameter values may correspond toPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO elements of a matrix representing a posterior distribution of the first trained model. Note that a posterior distribution generally indicates uncertainty about various parameter values. The transferred parameter values then form at least a portion of the prior distribution for the second model prior to initiating training of the second model. In other words, because the prior distribution of the second model is informed based on the posterior distribution of the first trained model, the second model is trained from an initial parameter distribution that utilizes knowledge of the fabrication process that is gained from the first trained model. The transfer learning techniques disclosed herein may allow for generation and training of fabrication process models with substantially smaller datasets, thereby reducing computational resources, manual resources, and test substrate experimental data required to train a given model.

[0029] As discussed above, in some embodiments, a first model may be generated using a first dataset. The first model may be associated with a first fabrication process. Aspects of the first model, such as one or more model parameters, may be utilized (e.g., transferred) to a second model representing a second fabrication process. Note that the second fabrication process may be similar to the first fabrication process in one or more aspects. For example, both the first fabrication process and the second fabrication process may be etching processes, but differ from one other in one or more chemicals that are used. Examples of differences between the two fabrication processes may include one or more differences in materials, critical dimensions, operating conditions (e.g., gas flow rates, temperatures, RF settings, etc.), and / or process tools used to perform the fabrication process. The model parameters that are transferred from the first model may be updated based on a second dataset (e.g., comprising experimental data associated with the second dataset). In other words, the transferred model parameters may be initialized for the second model based on the distribution of values of the first model, and may be updated based on the second dataset specific to the second fabrication process. This may allow the second model to be trained based on the second dataset more quickly than if all model parameters of the second model are trained without any baseline information. Note that non-transferred model parameters may be trained based on the second dataset without any baseline information derived from the first model. In other words, learned information from the first model may be leveraged to train the second model, which may allow the second model to be trained / developed more quickly and using a smaller dataset than would be required if the second model were trained without any information derived from the first model. Note that the dataset to train the second model may be 1.5 times smaller than the first dataset, 2 time smaller, 3 times smaller, 10 times smaller, etc.

[0030] In some embodiments, components that are transferred as model parameters from the first model to the second model may be transferred using probabilistic information associated with thePCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO first model. For example, the probabilistic information may include a posterior distribution which represents and / or indicates uncertainty associated with learned values for each model parameter of the first model. In other words, the posterior distribution may represent and / or indicate a degree of belief that the first fabrication process is accurately modeled by the first model on a model parameter by model parameter basis. In some implementations, aspects of the posterior distribution may become aspects of a prior distribution associated with the second model. In other words, because the posterior distribution represents inference of the first model in light of the first dataset used to train the first model, utilizing the posterior distribution associated with the first model allows the second model associated with a different fabrication process to leverage the learnings of the first model prior to beginning training of the second model.

[0031] In some implementations, model parameter values that are transferred from the first model to the second model may be selected. The selection may be based on a priori information indicating elements of the first fabrication process and the second fabrication process that are similar to each other. In some embodiments, selection may be based on user input (e.g., by a process engineer), e.g., by a user with domain knowledge of similarities and differences between the two fabrication processes. In some embodiments, model parameter values and their joint probability distribution for the first model may be specified as coefficients of a matrix, where the coefficients are learned based on a first dataset comprising experimental data associated with the first fabrication process. Transfer of model parameter values to the second model may involve selection of coefficients of the matrix to form initial model parameter values for the second model.

[0032] In some embodiments, each of the first model and the second model may be represented a structured Gaussian Process (generally referred to herein as a “structured GP”). In general, a Gaussian Process (GP) is a probabilistic model for making predictions by performing a regression. The GP is defined by a mean function and a covariance. For example, a GP may be represented as:

[0033] In the equation given above, m(x) represents the mean function, and K(x, x’) represents the covariance or kernel function. For a GP, X refers to the data matrix of N inputs with D features, and is accordingly an N x D matrix. For a given data matrix X, x represents one row of X and x’ represents a second row of X. The kernel K x, x’) represents the covariance between row x and row x The kernel function may include one or more hyperparameters, which may be determined by maximizing the marginal log-likelihood function.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO

[0034] In a structured GP, the mean function of the GP is modified to be a parametric function. For example, a linear mean function with coefficients 0 may be represented as:

[0035] Using the example structured GP representation given above, using the techniques described herein, the coefficient matrix 0 may be learned for a first model representing a first fabrication process using a first dataset. Continuing with this example, one or more coefficients of the matrix 0 may be selected and transferred to a corresponding mean function coefficient matrix associated with the second model, e.g., as initial values of the coefficient matrix. The second model may then be trained using a second dataset to determine the kernel hyperparameters. The coefficient matrix 0 represents the posterior distribution from training the first model on the first dataset. The posterior distribution 0 from the first dataset then serves as the prior distribution for training the second model using the second dataset. Because the prior distribution encodes information about trends in the first dataset, the size of the second dataset may be substantially smaller. It should be noted that the posterior distribution 0 is a multi-dimensional joint probability distribution, where the number of dimensions of the posterior distribution is determined by the number of model parameters in the first model.

[0036] FIG. 1 illustrates a flowchart of an example process 100 for generating model parameters for training a second model using selected components associated with a trained first model in accordance with some embodiments. In some embodiments, blocks of process 100 may be executed by one or more processors and / or one or more controllers associated with one or more computing devices. Example computing devices include a laptop computer, a desktop computer, a server, etc. In some embodiments, multiple computing devices may be utilized. An example implementation of a computing device is shown in and described below in connection with FIG. 5. In some embodiments, blocks of process 100 may be executed in an order other than what is shown in FIG. 1. In some embodiments, two or more blocks of process 100 may be executed substantially in parallel. In some embodiments, one or more blocks of process 100 may be omitted.

[0037] Process 100 can begin at 102 by determining a posterior distribution associated with a first model trained on a first dataset associated with a first fabrication process. The first fabrication process may be an etching process, a deposition process, a lithographic process, a planarization process, etc. The first dataset may be considered a historical dataset that includes experimental data, e.g., associated with wafers or substrates that have been processed using the first fabrication process. The experimental data may include data obtained from performing the first fabrication process with different process parameters, e.g., different gas compositions, different gas flow rates,PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO different radio frequency (RF) parameters, different temperatures, etc. The posterior distribution may be determined by fitting model parameters associated with the first model using the first dataset. In other words, the model parameters may be learned. In an instance in which the first model is a structured GP as described above, the learned model parameters, and therefore the posterior distribution, may be presented by the matrix 0.

[0038] At 104, process 100 may identify one or more components associated with the first model to be transferred as a model parameter value for a second model associated with a second fabrication process. As described above, the second fabrication process may be similar in some aspects and different in some aspects to the first fabrication process represented by the first model. For example, the first and second fabrication processes may be the same process type (e.g., deposition, etch, etc.) but utilize different chemicals. As another example, the first and second fabrication processes may have different specifications for a given process target (e.g., a critical dimension (CD), or other target parameter). As yet another example, the first and second fabrication processes may utilize different process parameter values for a gas flow rate, temperature, RF setting, or the like.

[0039] It should be noted that the techniques described herein may utilize two types of transfer learning. Homogenous domain transfer learning may involve utilizing the same process parameters between two fabrication processes to achieve different metrology specifications (e.g., a smaller CD). Heterogenous domain transfer learning may involve utilizing different process parameters or inputs (e.g., different process gases, different temperatures, different tools, different RF settings), etc. across two fabrication processes.

[0040] The one or more components associated with the first model that are identified may correspond to particular model parameters associated with the first model whose learned values are to be transferred as initial model parameter values for the second model prior to training. The identified components may be those that generally correspond to similar aspects between the first and second fabrication processes. For example, in an example in which the first and second fabrication processes represent etching processes that utilize different chemicals but are similar in the fabrication tool, temperatures, gas flow rates, etc., the selected components may be those that represent similarities in the first and second fabrication processes (e.g., components associated with the fabrication tool, temperatures, gas flow rates, etc.). In an instance in which the first model is a structured GP, the selected components may correspond to elements of the learned 0 matrix.

[0041] In some embodiments, the one or more components may be identified based on user input. For example, the user input may select one or more components representing particular model parameters of the first model whose values are to be transferred to the second model. User inputPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO may be received via a user interface. In some implementations, the one or more components may be identified based on the posterior distribution, e.g., based on confidence values associated with each learned model parameter. By way of example, in some implementations, model parameters associated with a relatively higher confidence value may be selected for transfer to the second model.

[0042] At 106, process 100 can generate model parameters for training the second model using the posterior distribution associated with the first model and the identified one or more components associated with the first model. For example, the values of the model parameters corresponding to the identified one or more components (e.g., elements of the p matrix in an instance in which the first model is a structured GP) may be used to initialize the model parameter values for the second matrix. For example, initial values associated with the mean function of the second model may be set based on the identified one or more components. The selected model parameter values may be based on the posterior distribution associated with the first model such that the prior distribution for the second model for at least the model parameters corresponding to the identified one or more components correspond to the posterior distribution for the model parameters for the first model.

[0043] FIG. 2 illustrates a flowchart of an example process 200 for training a second model based on learned model parameter values transferred from a first model in accordance with some embodiments. In some embodiments, blocks of process 200 may be executed by one or more processors and / or one or more controllers associated with one or more computing devices. Example computing devices include a laptop computer, a desktop computer, a server, etc. In some embodiments, multiple computing devices may be utilized. An example implementation of a computing device is shown in and described below in connection with FIG. 5. In some embodiments, blocks of process 200 may be executed in an order other than what is shown in FIG. 2. In some embodiments, two or more blocks of process 200 may be executed substantially in parallel. In some embodiments, one or more blocks of process 200 may be omitted.

[0044] Process 200 can begin at 202 by receiving a first dataset from experiments using a first fabrication process. As described above, the first fabrication process may be an etching process, a deposition process, a lithographic process, a planarization process, etc. The first dataset may be considered a historical dataset that includes experimental data, e.g., associated with wafers or substrates that have been processed using the first fabrication process. The experimental data may include data obtained from performing the first fabrication process with different process parameters, e.g., different gas compositions, different gas flow rates, different radio frequency (RF) parameters, different temperatures, etc.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO

[0045] At 204, process 200 can fit the first dataset with a first model and determine a posterior distribution associated with the first model and the first dataset. For example, process 200 can learn model parameter values for the first model based on the first dataset. In an instance in which the first model is a structured GP, fitting the first dataset may involve determining the 0 matrix values corresponding to coefficients of the parametric mean function.

[0046] At 206, process 200 can receive a second dataset from experiments using a second fabrication process different from the first fabrication process. As described above, the second fabrication process may be similar to the first fabrication process in some aspects, and different in other aspects. The second dataset may be substantially smaller than the first dataset (e.g., 1.5 times smaller, 2 times smaller, 4 times smaller, 10 times smaller, etc.).

[0047] At 208, process 200 can determine a prior distribution for the second model associated with the second fabrication process based on the posterior distribution associated with the first model. For example, in some embodiments, process 200 can populate a coefficient matrix associated with the second model using selected elements of the coefficient matrix associated with the first model, where the coefficient matrix of the second model prior to training the second model represents the prior distribution, and the selected elements of the coefficient matrix of the first model after training (e.g., at block 204) represent the posterior distribution. In other words, process 200 can transfer learned aspects (e.g., one or more learned model parameter values) from the first model to the second model. The transferred aspects (e.g., the transferred model parameter values) may be identified and / or selected based on similarities between the first and second fabrication process, as described above.

[0048] At 210, process 200 can generate the second model by learning the second dataset using at least some model parameter values set based on the prior distribution. For example, in an instance in which the second model is a structured GP, at least some elements of the coefficient matrix associated with the mean function may be transferred from the coefficient matrix associated with the mean function of the first model. Continuing with this example, the transferred elements of the coefficient matrix may be updated from their initialized values based on the second dataset. Continuing still further with this example, the non-transferred elements of the coefficient matrix and / or the kernel hyperparameters may be learned based on the second dataset without any initialization of their values based on values from the first model.

[0049] In some embodiments, the generated second model may be used to generate one or more recipe suggestions for the second fabrication process. The one or more recipe suggestions may include values for one or more process parameters (e.g., gas flow rates, temperatures, etc.) corresponding to knobs of the receipt that may be tweaked. The one or more recipe suggestionsPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO may be identified using the model as process parameter values likely to cause a substrate undergoing the fabrication process to meet a given specification (e.g., a given critical dimension specification, etc.). The recipe suggestions may be identified as part of a process optimization process used to identify optimal process parameter values likely to meet one or more target specifications. Note that, in some embodiments, the one or more recipe suggestions may be utilized to generate additional experimental data (which may be real experimental data and / or virtual experimental data collected by simulating the fabrication process using process parameter values set based on the one or more recipe suggestions in a virtual fabrication environment). The additional experimental data may be used to update the second model.

[0050] It should be noted that, in some implementations, prior to transferring one or more model parameter values from the first model to the second model, a determination may be made of whether or not a transfer should be performed. In other words, a determination may be made of whether to perform transfer learning, or conversely, to train the second model without any baseline information from the learned first model. In some embodiments, a determination that transfer learning is to be performed may involve determining a goodness of fit of the first model with respect to the first dataset exceeds a given quality threshold. In some embodiments, the goodness of fit metric may include a mean squared error (MSE) or other error metric that represents the quality of the model fit. In an instance in which the quality metric is below a quality threshold, a determination may be made to not perform transfer of one or more model parameter values and instead to train the second model without any baseline information from the first model.

[0051] Note that the techniques described above give examples that utilize a structured GP model, where the probabilistic model for the parametric mean function of the structured GP is modified using transfer learning (e.g., based on the posterior distribution of the first, related model). In some embodiments, an adaptive transfer GP model may be used, where the kernel function of the GP is modified rather than the mean function. In general, the GP covariance matrix may be partitioned into a source matrix and a target matrix with a hyperparameter (generally represented herein as X) representing the similarity between the source data and the target data. Using an adaptive transfer GP, the source dataset may be represented as S, and the target dataset to transfer learned information from the first model to, may be represented as T. For example:X = (X^.X^)

[0052] In the equation given above, X represents the input data matrix representing process recipe parameters, and Y represents the output data matrix representing outcome metrology parameters.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WOAccordingly, the kernel K may be modified using the hyperparameter k as follows:

[0053] In other words, the kernel hyperparameters for the second model may be modified based on a degree of similarity between a source dataset associated with a first fabrication process and a target dataset to be learned associated with a second fabrication process, where the hyperparameter indicates how similar the two datasets are. In an instance in which there is little to no similarity, there may be no learning from the first model.

[0054] Conventional techniques may perform process optimization once a fabrication model has been generated. Process optimization may involve a Bayesian optimization technique that identifies optimized process parameter values likely to achieve a substrate that meets one or more specifications. Prior to performing the optimization technique, a DoE may be performed to investigate the process parameter space. DoE is a statistical technique in which parameters may be identified which are likely to, when probed (e.g., by performing simulations using different values of the parameters) to yield the most information about the parameter space. In other words, by first performing DoE prior to performing the process optimization, a number of experiments may be performed which provide information regarding the process space such that process optimization may be performed more quickly using the DoE results.

[0055] Conventional techniques may require a relatively large number of experiments to be performed before process optimization can be performed, because there is no a priori knowledge of the sensitivity of the different process parameters (e.g., which process parameters when manipulated contributed the most to achieving or not achieving a given target specification). Using the techniques described herein, in addition to using probabilistic knowledge from a first model to generate a second model (e.g., as shown in and described above in connection with FIGS. 1 and 2), the probabilistic information from the first model may be used to perform a DoE associated with the second model prior to performing process optimization. Because the DoE is performed using the probabilistic information (e.g., the posterior distribution associated with the first model), the DoE may be performed with knowledge gained from the training of the first model of which process parameters are most sensitive and / or are most uncertain, and the DoE may be performed with focus on process parameters with a high sensitivity and / or a high uncertainty. This may allow the DoE to be performed with fewer experiments, and may speed up the time required to perform process optimization. It should be understood that regardless of how the second model is developed and the structure of the second model (e.g., whether a structured GP or an adaptive transfer GP is utilized), DoE may be performed based on probabilistic information associated withPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO the first, related model.

[0056] FIG. 3 illustrates a flowchart of an example process 300 for performing process optimization in accordance with some embodiments. In some embodiments, blocks of process 300 may be executed by one or more processors and / or one or more controllers associated with one or more computing devices. Example computing devices include a laptop computer, a desktop computer, a server, etc. In some embodiments, multiple computing devices may be utilized. An example implementation of a computing device is shown in and described below in connection with FIG. 5. In some embodiments, blocks of process 300 may be executed in an order other than what is shown in FIG. 3. In some embodiments, two or more blocks of process 300 may be executed substantially in parallel. In some embodiments, one or more blocks of process 300 may be omitted.

[0057] Process 300 can begin at 302 by obtaining a model of a process generated using one or more model parameters transferred from a different model. The model parameters may have been transferred based at least in part on a posterior distribution (e.g., a posterior distribution associated with the model from which the model parameters were transferred). Example techniques for generation of such a model are shown in and described above in connection with FIGS. 1 and 2.

[0058] At 304, process 300 can identify parameters of the model satisfying one or more sensitivity or uncertainty criteria based at least in part on the posterior distribution. The parameters that satisfy sensitivity and / or uncertainty criteria may be identified using one or more statistical confidence tests, such as a Bayesian p-value, or the like. The identified parameters may generally correspond to recipe knobs, or process parameters, which may be manipulated as part of a fabrication process represented by the model. Examples of parameters include gas flow rates, gas species compositions, temperatures, RF settings, etching rates, deposition rates, a number of cycles of a given etch or deposition process to be performed, etc. The parameters may be identified based on the posterior distribution (e.g., of the different model from which the model parameters were transferred), because the posterior distribution generally indicates confidence in the model parameter values. Accordingly, model parameters having lower confidence may be identified based on the posterior distribution. These identified model parameters may be those which, due to the higher uncertainty, are to be experimented on (e.g., using a DoE) to better understand the process space prior to performing process optimization.

[0059] At 306, process 300 can receive experimental results using a DoE technique based on the identified parameters satisfying the one or more sensitivity or uncertainty criteria. For example, process the DoE technique can manipulate values of multiple identified parameters using DoE techniques in successive iterations of experiments to more quickly map a region of the processPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO space having a relatively high degree of sensitivity and / or uncertainty. Note that the result of the DoE is a dataset that provides a dataset that reduces the posterior distribution of the second model on the second dataset prior to the start of the optimization process (e.g., at block 308). Within each experiment, values of some process parameters may remain fixed, while others may be varied in accordance with the DoE technique. The parameters that are varied during the experiments may correspond to the identified parameters satisfying the sensitivity and / or uncertainty criteria. As described above, the number of experiments performed using DoE may be substantially less using the techniques described herein (which identify process parameters having relatively high sensitivity and / or uncertainty based on a trained related model and its posterior distribution) than the number of experiments required if performed without any baseline information associated with the related model.

[0060] At 308, process 300 can perform process optimization based on the experiments. For example, process optimization may involve performing a fabrication process with a first set of process parameter values, determining whether the resulting substrate meets target specifications, and iteratively adapting the process parameter values based on a difference between the resulting substrate and the target specifications.

[0061] FIGS. 4A and 4B illustrate experimental data using the techniques described herein to optimize a fabrication process using transfer learning. Substrate 402 of FIG. 4A represents an initial wafer, and substrate 404 represents an etched wafer as a result of a first fabrication process. The first fabrication process may be represented by a trained first model, where the first model is trained using experimental data collected using the first fabrication process. A second fabrication process may be used to fabricate a second substrate, where the second fabrication process is to result in a substrate with, e.g., a smaller CD. Accordingly, a second model is to be developed to model a second fabrication process (which may utilize one or more different process parameter values or may have other differences from the first fabrication process) in order to achieve the desired specifications to be achieved using the second fabrication process.

[0062] As described above, the second model may be developed and trained using a second dataset. The second model may then be optimized to identify process parameter values that will achieve the desired specifications. FIG. 4B depicts a plot 452 comparing different methods of generating and training the second model. The X-axis of plot 452 indicates a number of wafers tested, and the Y-axis of plot 452 indicates a cumulative probability that the desired specification is met. In other words, for a given number of wafers used to experiment on the X-axis, the corresponding value on the Y-axis indicates a probability that the specification will be met.

[0063] Curve 454 of plot 452 represents optimization of a model developed using conventionalPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO techniques (e.g., without any transfer learning from a first model associated with a related first fabrication process such as one used to fabricate substrate 402). Note that even when utilizing 100 test wafers, the probability of meeting the desired specification is only 0.6. Curve 456 represents optimization of a model developed using adaptive transfer GP. Note that because some aspects of the first model are transferred to the adaptive transfer GP model of the second fabrication process, the probability of meeting the specification plateaus at a higher value relative to conventional techniques (e.g., 0.8 with the adaptive transfer GP model compared to 0.6 using conventional techniques). Curve 458 represents optimization of a model developed using transfer learning as applied to structured GP models. Note that the probability of meeting the specification increases more rapidly (e.g., the probability is higher when less wafers are used, such as fewer than 20 wafers, fewer than 40 wafers, fewer then 60 wafers, etc.) relative to the adaptive transfer GP model.

[0064] It should be noted that in some cases, an adaptive transfer GP model may be preferable to a structured GP model. For example, in some cases, it may be easier to train an adaptive transfer GP model. Determining whether a model should be implemented as an adaptive transfer GP model or a structured GP model may be based on how different the first fabrication process and the second fabrication process are. For example, an adaptive transfer GP model may be used in instances in which the first and second fabrication processes are more similar, whereas a structured GP model may be used in instances in which the first and second fabrication processes are more different.CONTEXT FOR DISCLOSED COMPUTATIONAL EMBODIMENTS

[0065] Systems (e.g., one or more computing devices, such as laptop computers, desktop computers, server devices, etc.) as described herein may include logic for generating models.

[0066] The analysis logic may be designed and implemented in any of various ways. For example, the logic can be implemented in hardware and / or software. Examples are presented in the controller section herein. Hardware-implemented control logic may be provided in any of a variety of forms, including hard coded logic in digital signal processors, application- specific integrated circuits, and other devices that have algorithms implemented as hardware. Analysis logic may also be implemented as software or firmware instructions configured to be executed on a general- purpose processor. System control software may be provided by “programming” in a computer readable programming language.

[0067] The computer program code for controlling processes in a process sequence can be written in any conventional computer readable programming language: for example, assembly language, C, C++, Pascal, Fortran, Python, or others. Compiled object code or script is executed by the processor to perform the tasks identified in the program. Also as indicated, the program code may be hard coded.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO

[0068] Integrated circuits used in logic may include chips in the form of firmware that store program instructions, digital signal processors (DSPs), chips defined as application specific integrated circuits (ASICs), and / or one or more microprocessors, or microcontrollers that execute program instructions (e.g., software). Program instructions may be instructions communicated in the form of various individual settings (or program files), defining operational parameters for carrying out a particular analysis application.

[0069] Figure 5 is a block diagram of an example of the computing device 500 suitable for use in implementing some embodiments of the present disclosure. For example, device 500 may be suitable for implementing some or all functions for determining generating models, using transfer learning to generate a model, etc. as described herein.

[0070] Computing device 500 may include a bus 502 that directly or indirectly couples the following devices: memory 504, one or more central processing units (CPUs) 506, one or more graphics processing units (GPUs) 508, a communication interface 510, input / output (I / O) ports 512, input / output components 514, a power supply 516, and one or more presentation components 518 (e.g., display(s)). In addition to CPU 506 and GPU 508, computing device 500 may include additional logic devices that are not shown in Figure 5, such as but not limited to an image signal processor (ISP), a digital signal processor (DSP), an ASIC, an FPGA, or the like.

[0071] Although the various blocks of Figure 5 are shown as connected via the bus 502 with lines, this is not intended to be limiting and is for clarity only. For example, in some embodiments, a presentation component 518, such as a display device, may be considered an I / O component 514 (e.g., if the display is a touch screen). As another example, CPUs 506 and / or GPUs 508 may include memory (e.g., the memory 504 may be representative of a storage device in addition to the memory of the GPUs 508, the CPUs 506, and / or other components). In other words, the computing device of Figure 5 is merely illustrative. Distinction is not made between such categories as “workstation,” “server,” “laptop,” “desktop,” “tablet,” “client device,” “mobile device,” “handheld device,” “electronic control unit (ECU),” “virtual reality system,” and / or other device or system types, as all are contemplated within the scope of the computing device of Figure 5.

[0072] Bus 502 may represent one or more busses, such as an address bus, a data bus, a control bus, or a combination thereof. The bus 502 may include one or more bus types, such as an industry standard architecture (ISA) bus, an extended industry standard architecture (EISA) bus, a video electronics standards association (VESA) bus, a peripheral component interconnect (PCI) bus, a peripheral component interconnect express (PCIe) bus, and / or another type of bus.

[0073] Memory 504 may include any of a variety of computer-readable media. The computer- readable media may be any available media that can be accessed by the computing device 500.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO The computer-readable media may include both volatile and nonvolatile media, and removable and non-removable media. By way of example, and not limitation, the computer-readable media may comprise computer- storage media and / or communication media.

[0074] The computer- storage media may include both volatile and nonvolatile media and / or removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules, and / or other data types. For example, memory 504 may store computer-readable instructions (e.g., that represent a program(s) and / or a program element(s), such as an operating system. Computerstorage media may include, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by computing device 500. As used herein, computer storage media does not comprise signals per se.

[0075] The communication media may embody computer-readable instructions, data structures, program modules, and / or other data types in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” may refer to a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, the communication media may include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of any of the above should also be included within the scope of computer-readable media.

[0076] CPU(s) 506 may be configured to execute the computer-readable instructions to control one or more components of the computing device 500 to perform one or more of the methods and / or processes described herein. CPU(s) 506 may each include one or more cores (e.g., one, two, four, eight, twenty-eight, seventy-two, etc.) that are capable of handling a multitude of software threads simultaneously. CPU(s) 506 may include any type of processor and may include different types of processors depending on the type of computing device 500 implemented (e.g., processors with fewer cores for mobile devices and processors with more cores for servers). For example, depending on the type of computing device 500, the processor may be an ARM processor implemented using Reduced Instruction Set Computing (RISC) or an x86 processor implemented using Complex Instruction Set Computing (CISC). Computing device 500 may include one or more CPUs 506 in addition to one or more microprocessors or supplementary co-processors, such as math co-processors.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO

[0077] GPU(s) 508 may be used by computing device 500 to render graphics (e.g., 3D graphics). GPU(s) 508 may include many (e.g., tens, hundreds, or thousands) of cores that are capable of handling many software threads simultaneously. GPU(s) 508 may generate pixel data for output images in response to rendering commands (e.g., rendering commands from CPU(s) 506 received via a host interface). GPU(s) 508 may include graphics memory, such as display memory, for storing pixel data. The display memory may be included as part of memory 504. GPU(s) 508 may include two or more GPUs operating in parallel (e.g., via a link). When combined, each GPU 508 can generate pixel data for different portions of an output image or for different output images (e.g., a first GPU for a first image and a second GPU for a second image). Each GPU can include its own memory or can share memory with other GPUs.

[0078] In examples where the computing device 500 does not include the GPU(s) 508, the CPU(s) 506 may be used to render graphics.

[0079] Communication interface 510 may include one or more receivers, transmitters, and / or transceivers that enable computing device 500 to communicate with other computing devices via an electronic communication network, included wired and / or wireless communications. Communication interface 510 may include components and functionality to enable communication over any of a number of different networks, such as wireless networks (e.g., Wi-Fi, Z-Wave, Bluetooth, Bluetooth LE, ZigBee, etc.), wired networks (e.g., communicating over Ethernet), low- power wide-area networks (e.g., LoRaWAN, SigFox, etc.), and / or the internet.

[0080] RO ports 512 may enable the computing device 500 to be logically coupled to other devices including I / O components 514, presentation component(s) 518, and / or other components, some of which may be built in to (e.g., integrated in) computing device 500. Illustrative RO components 514 include a microphone, mouse, keyboard, joystick, track pad, satellite dish, scanner, printer, wireless device, etc. RO components 514 may provide a natural user interface (NUI) that processes air gestures, voice, or other physiological inputs generated by a user. In some instances, inputs may be transmitted to an appropriate network element for further processing. An NUI may implement any combination of speech recognition, stylus recognition, facial recognition, biometric recognition, gesture recognition both on screen and adjacent to the screen, air gestures, head and eye tracking, and touch recognition (as described in more detail below) associated with a display of computing device 500. Computing device 500 may be include depth cameras, such as stereoscopic camera systems, infrared camera systems, RGB camera systems, touchscreen technology, and combinations of these, for gesture detection and recognition. Additionally, computing device 500 may include accelerometers or gyroscopes (e.g., as part of an inertia measurement unit (IMU)) that enable detection of motion. In some examples, the output of thePCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO accelerometers or gyroscopes may be used by computing device 500 to render immersive augmented reality or virtual reality.

[0081] Power supply 516 may include a hard-wired power supply, a battery power supply, or a combination thereof. Power supply 516 may provide power to computing device 500 to enable the components of computing device 500 to operate.

[0082] Presentation component(s) 518 may include a display (e.g., a monitor, a touch screen, a television screen, a heads-up-display (HUD), other display types, or a combination thereof), speakers, and / or other presentation components. Presentation component(s) 518 may receive data from other components (e.g., GPU(s) 508, CPU(s) 506, etc.), and output the data (e.g., as an image, video, sound, etc.).

[0083] The disclosure may be described in the general context of computer code or machine- useable instructions, including computer-executable instructions such as program modules, being executed by a computer or other machine, such as a personal data assistant or other handheld device. Generally, program modules including routines, programs, objects, components, data structures, etc., refer to code that perform particular tasks or implement particular abstract data types. The disclosure may be practiced in a variety of system configurations, including hand-held devices, consumer electronics, general-purpose computers, more specialty computing devices, etc. The disclosure may also be practiced in distributed computing environments where tasks are performed by remote-processing devices that are linked through a communications network.Additional Considerations

[0084] As used in this specification and appended claims, the singular forms “a”, “an”, and “the” include plural referents unless the content and context dictates otherwise. For example, reference to “a cell” includes a combination of two or more such cells. Unless indicated otherwise, an “or” conjunction is used in its correct sense as a Boolean logical operator, encompassing both the selection of features in the alternative (A or B, where the selection of A is mutually exclusive from B) and the selection of features in conjunction (A or B, where both A and B are selected).

[0085] It is to be understood that the phrases “for each <item> of the one or more <items>,” “each <item> of the one or more <items>,” or the like, if used herein, are inclusive of both a single-item group and multiple- item groups, i.e., the phrase “for . . . each” is used in the sense that it is used in programming languages to refer to each item of whatever population of items is referenced. For example, if the population of items referenced is a single item, then “each” would refer to only that single item (despite the fact that dictionary definitions of “each” frequently define the term to refer to “every one of two or more things”) and would not imply that there must be at least two of those items. Similarly, the term “set” or “subset” should not be viewed, in itself, as necessarilyPCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO encompassing a plurality of items — it will be understood that a set or a subset can encompass only one member or multiple members (unless the context indicates otherwise).

[0086] The use, if any, of ordinal indicators, e.g., (a), (b), (c). . . or the like, in this disclosure and claims is to be understood as not conveying any particular order or sequence, except to the extent that such an order or sequence is explicitly indicated. For example, if there are three steps labeled(i), (ii), and (iii), it is to be understood that these steps may be performed in any order (or even concurrently, if not otherwise contraindicated) unless indicated otherwise. For example, if step(ii) involves the handling of an element that is created in step (i), then step (ii) may be viewed as happening at some point after step (i). Similarly, if step (i) involves the handling of an element that is created in step (ii), the reverse is to be understood. It is also to be understood that use of the ordinal indicator “first” herein, e.g., “a first item,” should not be read as suggesting, implicitly or inherently, that there is necessarily a “second” instance, e.g., “a second item.”

[0087] Various computational elements including processors, memory, instructions, routines, models, or other components may be described or claimed as “configured to” perform a task or tasks. In such contexts, the phrase “configured to” is used to connote structure by indicating that the component includes structure (e.g., stored instructions, circuitry, etc.) that performs the task or tasks during operation. As such, the unit / circuit / component can be said to be configured to perform the task even when the specified component is not necessarily currently operational (e.g., is not on).

[0088] The components used with the “configured to” language may refer to hardware — for example, circuits, memory storing program instructions executable to implement the operation, etc. Additionally, “configured to” can refer to generic structure (e.g., generic circuitry) that is manipulated by software and / or firmware (e.g., an FPGA or a general-purpose processor executing software) to operate in manner that is capable of performing the recited task(s). Additionally, “configured to” can refer to one or more memories or memory elements storing computer executable instructions for performing the recited task(s). Such memory elements may include memory on a computer chip having processing logic. In some contexts, “configured to” may also include adapting a manufacturing process (e.g., a semiconductor fabrication facility) to fabricate devices (e.g., integrated circuits) that are adapted to implement or perform one or more tasks.PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO

[0089] Although the foregoing embodiments have been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications may be practiced within the scope of the appended claims. It should be noted that there are many alternative ways of implementing the processes, systems, and apparatus of the present embodiments. Accordingly, the present embodiments are to be considered as illustrative and not restrictive, and the embodiments are not to be limited to the details given herein.

Claims

PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WOCLAIMSWhat is claimed is:

1. A method comprising: determining a posterior distribution associated with a first model representing a first fabrication process; identifying one or more components associated with the first model to be transferred as a model parameter value for a second model representing a second fabrication process; and generating model parameters for the second model using the posterior distribution associated with the first model and the identified one or more components associated with the first model.

2. The method of claim 1, wherein the posterior distribution is represented by a matrix, and wherein the identified one or more components correspond to elements of the matrix.

3. The method of claim 2, wherein the first model and the second model are each a structured Gaussian process (GP) model, and wherein the matrix represents coefficients associated with a mean function of the structured GP of the first model.

4. The method of claim 1, wherein identifying the one or more components associated with the first model to be transferred comprises receiving user input indicating the one or more components.

5. The method of any one of claims 1-4, wherein generating the model parameter for the second model using the posterior distribution associated with the first model comprises setting a prior distribution associated with the second model based on the selected one or more components.

6. The method of any one of claims 1-4, wherein the first model was trained using a first dataset associated with the first fabrication process, and further comprising training the second model using a second dataset associated with the second fabrication process.

7. The method of claim 6, wherein the second dataset is at half the size of the first dataset.

8. The method of any one of claims 1-4, wherein the first fabrication process and the second fabrication process are semiconductor manufacturing processes with at least onePCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO difference in: (i) materials; (ii) critical dimensions; (iii) operating conditions; (iv) process tools; or any combination thereof.

9. A computer-readable medium storing instructions that, when executed by a processor, generates optimized semiconductor manufacturing recipes, the instructions causing performance of: receiving a first dataset from experiments using a first fabrication process; fitting the first dataset with a first model and determining a posterior distribution associated with the first model and the first dataset; receiving a second dataset from experiments using a second fabrication process different from the first fabrication process; determining a prior distribution for a second model representing the second fabrication process based on the posterior distribution associated with the first model; and generating the second model by learning the second dataset using at least some model parameter values set based on the prior distribution.

10. The computer-readable medium of claim 9, wherein the instructions further cause performance of outputting one or more recipe suggestions using the second model.

11. The computer-readable medium of claim 9, wherein the instructions further cause performance of: receiving additional experimental data using the one or more recipe suggestions; and updating the second model using the additional experimental data.

12. The computer-readable medium of claim 9, wherein the instructions further cause performance of determining the one or more recipe suggestions using a process optimization technique.

13. The computer-readable medium of claim 12, wherein the process optimization technique is a Bayesian optimization technique.

14. The computer-readable medium of claim 12, wherein the instructions further cause performance of performing one or more experiments using a Design of Experiments (DoE) technique prior to performing the process optimization technique, wherein the DoE technique utilizes the posterior distribution associated with the first model.

15. A method comprising: training a first model representing a first fabrication process using a first dataset;PCT / US25 / 40863 06 August 2025 (06.08.2025)Attorney Docket No. LAM1P066WO-11995-1WO identifying one or more model parameter values associated with the first trained model to be transferred to a second model representing a second fabrication process based at least in part on probabilistic information associated with the first model indicating statistical uncertainty associated with model parameters of the first model; and generating a second model representing the second fabrication process by training the second model using a second dataset, wherein at least a subset of model parameter values of the second model are set to the identified one or more model parameter values prior to training the second model.

16. The method of claim 15, wherein the probabilistic information comprises a posterior distribution associated with the first model.

17. The method of any one of claims 15 or 16, wherein identifying the one or more model parameter values is based on user input.

18. The method of any one of claims 15 or 16, wherein the second dataset is at least half the size of the first dataset.

19. The method of any one of claims 15 or 16, wherein the first fabrication process and the second fabrication process are semiconductor manufacturing processes with at least one difference in: (i) materials; (ii) critical dimensions; (hi) operating conditions; (iv) process tools; or any combination thereof.

20. A system comprising: one or more processors; and one or more processor-readable media comprising instructions that, when executed by the one or more processors, cause the one or more processors to: train a first model representing a first fabrication process using a first dataset; identify one or more model parameter values associated with the first trained model to be transferred to a second model representing a second fabrication process based at least in part on probabilistic information associated with the first model indicating statistical uncertainty associated with model parameters of the first model; and generate a second model representing the second fabrication process by training the second model using a second dataset, wherein at least a subset of model parameter values of the second model are set to the identified one or more model parameter values prior to training the second model.

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