Systems and methods for setting up physics-based models

Abstract

A system and method for setting up a physics-based model is provided. A system includes one or more components, executed by one or more computer subsystems, including a physics-based model representing a semiconductor fabrication-related process and a setup component configured to set up the physics-based model in multiple phases, where only a subset of all parameters of the physics-based model are set up in each of the multiple phases. The configuration of the setup component is changed between at least two of the multiple phases based on the subset of all parameters of the physics-based model set up in at least two of the multiple phases. The setup component may implement a Bayesian optimization technique for setting up or calibrating a cascaded model using multiple information sources and objective functions.

Description

Technical Field

[0001] The present invention generally relates to systems and methods for setting up physics-based models.

Background Art

[0002] The following description and examples are not to be recognized as prior art for the reason that they are included in this section.

[0003] The fabrication of semiconductor devices such as logic devices and memory devices typically involves processing a substrate such as a semiconductor wafer using many semiconductor fabrication processes to form various features and multiple levels of semiconductor devices. For example, lithography is a semiconductor fabrication process that involves transferring a pattern from a reticle to a resist disposed on a semiconductor wafer. Further examples of semiconductor fabrication processes include, but are not limited to, chemical mechanical polishing (CMP), etching, deposition, and ion implantation. Multiple semiconductor devices may be fabricated and disposed on a single semiconductor wafer and then separated into individual semiconductor devices.

[0004] [[ID=二十]]Due to the cost and difficulty of optimizing semiconductor fabrication processes experimentally, much effort has been made to create physical models of processes that can replace the experimental work of setting up and optimizing the processes. In theory, physical models can evaluate more different process parameter values faster and cheaper than attempting to evaluate different process parameter values via experiments.

[0005] From the perspective of the models described herein, a “physical model” or “physics-based model” is defined as a forward simulation model that is based on and represents a physical process intended to be simulated. These physical models may have modifiable parameters that are typically set by fitting the modeling data to reference data, but the model itself does not “learn” how to simulate the physical process. In other words, the physical models or physics-based models described herein are neither machine learning models nor deep learning models.

[0006] When properly set up, physical models can be extremely valuable in setting up and optimizing semiconductor fabrication processes. However, the task of setting up physical models is far from easy and can hinder their implementation in fabrication process setup and optimization. For example, appropriate baseline data must be obtained or generated using a well-designed set of experiments, and appropriate optimization procedures must be identified and used to set up the physical model.

[0007] Currently used model calibration techniques tend to rely on single-step optimization with a fixed objective function. Such techniques typically require iterations of incremental improvements before the physical model can be adequately calibrated to accurately reflect the reference data.

[0008] Therefore, the model calibration techniques currently in use have several drawbacks. For example, single-step optimization requires an objective function that precisely and uniquely defines the match between the model and the reference data. Constructing such a function is not always possible. In another example, when multiple optimization runs using the current method are required, the optimization algorithm does not benefit from the results of previous optimizations. In yet another example, two-dimensional (2D) and three-dimensional (3D) simulations require relatively long computation times. With current optimization techniques, all simulation scales included in the objective function must be performed in locksteps. This requirement slows down the optimization technique to the slowest possible source of information. [Prior art documents] [Patent Documents]

[0009] [Patent Document 1] U.S. Patent Application Publication No. 2016 / 0370797 [Overview of the project] [Problems that the invention aims to solve]

[0010] Therefore, it should be advantageous to develop systems and methods for setting up physics-based models that do not have one or more of the aforementioned disadvantages. [Means for solving the problem]

[0011] The following descriptions of various embodiments should not be taken in any way as to limit the subject matter of the attached claims.

[0012] One embodiment relates to a system configured to set up a physics-based model. The system includes one or more computer subsystems and one or more components executed by the one or more computer subsystems. The one or more components include a physics-based model representing a semiconductor fabrication-related process, and a setup component. The setup component includes an objective function configured to compare the results produced by the physics-based model with reference data for different values ​​of one or more parameters of the physics-based model, and to produce an output depending on the difference between the results and the reference data. The setup component further includes a surrogate function configured as an approximation of the objective function and fitted to the output produced by the objective function depending on different values ​​of one or more parameters. The setup component further includes an acquisition function configured to select additional values ​​for one or more parameters for the physics-based model based on the surrogate function. The setup component is configured to set up the physics-based model in multiple phases, in each of the multiple phases only a subset of all of one or more parameters of the physics-based model is set up. The configuration of the setup component is modified between at least two of the multiple phases based on all of the subsets of one or more parameters of the physics-based model set up in at least two of the multiple phases. The system may be further configured as described herein.

[0013] Another embodiment relates to a computer implementation method for setting up a physics-based model. The method includes comparing results generated by a physics-based model representing semiconductor fabrication-related processes with different values ​​for one or more parameters of the physics-based model with reference data, and generating an output based on the difference between the results and the reference data using an objective function. The method further includes fitting a surrogate function, configured as an approximation of the objective function, to the output generated by the objective function depending on different values ​​for one or more parameters. Furthermore, the method includes selecting additional values ​​for one or more parameters for the physics-based model based on the surrogate function using an acquisition function. The objective function, surrogate function, and acquisition function are included in a setup component. The setup component and the physics-based model are included in one or more components executed by one or more computer systems. The setup component is configured to set up the physics-based model in multiple phases, in each of the multiple phases only a subset of all parameters of one or more of the physics-based model is set up. The configuration of the setup component is modified between at least two of the multiple phases based on all subsets of all parameters of one or more of the physics-based model set up in at least two of the multiple phases.

[0014] Each step of the method may be further carried out as described herein. The method may include any other step of any other method described herein. The method may be carried out by any system described herein.

[0015] Another embodiment relates to a non-temporary computer-readable medium storing program instructions executable on one or more computer systems for carrying out a computer implementation method for setting up a physics-based model. The computer implementation method includes the steps of the method described above. The computer-readable medium may be further configured as described herein. The steps of the computer implementation method may be carried out as further described herein. Furthermore, the computer implementation method on which the program instructions are executable may include any other step of any of the other methods described herein.

[0016] Further advantages of the present invention will become apparent to those skilled in the art through the benefit of the following detailed description of preferred embodiments and by referring to the accompanying drawings. [Brief explanation of the drawing]

[0017] [Figure 1] This is a block diagram illustrating one embodiment of a system configured to set up a physics-based model. [Figure 2] This is a block diagram illustrating an embodiment of a setup component configured to set up a physics-based model. [Figure 3] This is a block diagram illustrating an embodiment of a setup component configured to set up a physics-based model. [Figure 4] This is a block diagram illustrating an embodiment of a setup component configured to set up a physics-based model. [Figure 5] This is a schematic diagram illustrating one example of reference data for a target that may be used by the embodiments described herein to set up a physics-based model. [Figure 6] This is a schematic diagram illustrating one example of a cascading optimization workflow. [Figure 7]FIG. 0 is a block diagram illustrating one embodiment of a non - transient computer - readable medium storing program instructions for causing a computer system to implement the computer - implemented method described herein. DETAILED DESCRIPTION OF THE INVENTION

[0018] The present invention is susceptible to various modifications and alternative forms. Specific embodiments thereof are shown by way of example in the drawings and will be described in detail herein. The drawings may not be to scale. However, the drawings and their detailed description are not intended to limit the present invention to the particular form disclosed. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

[0019] Turning now to the drawings, it should be noted that the figures are not drawn to scale. In particular, the scale of some of the elements of the figures is greatly exaggerated to emphasize the characteristics of the elements. It should also be noted that the figures are not drawn to the same scale. Elements shown in two or more figures that may be similarly configured are designated using the same reference numerals. Unless otherwise indicated herein, any of the described and illustrated elements may include any suitable commercially available elements.

[0020] In general, the embodiments described herein are configured to set up physics - based models. Some of the embodiments described herein are configured for the calibration of cascade - type models using multiple information sources and objective functions. This embodiment may be used for the calibration of first - principle calculation models of processes such as etching and lithography in the semiconductor manufacturing industry in order to accurately reflect reference data.

[0021] "Setting up a physics-based model", as the term is used herein, is defined as selecting one or more parameters of a physics-based model regardless of the reason for which the parameter selection process is carried out. For example, setting up a physics-based model may include setting up a new physics-based model that has not yet been released for use. Thus, the embodiments described herein may be used to generate or implement an initial setup of a new physics-based model, and the new physics-based model may be a new model for an old process or a new model for a new process. Setting up a physics-based model may further include modifying a previously set up physics-based model, such as may be done for calibration or optimization. Such calibration or optimization may be carried out for several reasons, including but not limited to intentional or unintentional changes to the process represented by the physics-based model. Intentional changes may include, for example, when one material is replaced with another, or when a change in the limiting dimensions of a feature is advantageous, such as when the process for manufacturing a device is changed. Unintentional changes may include, in one example, when there are unexpected variations in how the process is carried out, which may favor an update to the physics-based model representing such a process.

[0022] The constraints on etching and lithography processes in the fabrication of microelectronic devices are constantly increasing due to scaling requirements. As feature sizes decrease, the capabilities of traditional design of experiments (DOE)-based process optimization become insufficient. Physics-based first-principles modeling offers process engineers the ability to meet the growing demand more efficiently than current techniques. To be effective, first-principles models must be calibrated to match baseline data for the modeled process. This calibration process can be a significant obstacle to the use of physics-based models in this field due to the complexity of the models and the lack of direct measurement techniques for internal model parameters. Novel optimization techniques are required to realize the successful use of such physics-based models in the microelectronic device fabrication industry.

[0023] The embodiments described herein provide a method for performing optimization using a Bayesian optimization (BO) technique that includes several (i.e., two or more) cascaded optimization phases. In one embodiment, each of the multiple phases is performed based on the output generated by any of the multiple phases that have been performed previously. For example, as further described herein, this cascaded optimization technique may use prior knowledge for each optimization phase from all previous phases. The cascaded optimization technique further allows the use of different objective functions during each optimization phase. In further embodiments, the input to the setup components includes multiple sources of information. For example, as further described herein, the cascaded optimization technique allows the use of multiple sources of information in such a manner that it enables the use of fairly rapid simulations in order to reduce the number of relatively long simulations in each optimization step.

[0024] One embodiment relates to a system configured to set up a physics-based model. One embodiment of such a system is shown in Figure 1. The system includes one or more computer subsystems 102 and one or more components 104 run by the one or more computer subsystems. One or more components may be configured as further described herein and may be run by one or more computer subsystems in any suitable manner known in the art.

[0025] Computer subsystems may also be referred to as computer systems in this specification. Each of the computer subsystems or systems described herein may take various forms, including personal computer systems, image computers, mainframe computer systems, workstations, network equipment, internet appliances, or other devices. Generally, the term “computer system” may be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium. A computer subsystem or system may further include any suitable processors known in this art, such as parallel processors. Furthermore, a computer subsystem or system may include a computer platform with high-speed processing and software, either as a standalone or networked tool.

[0026] If a system includes two or more computer subsystems, different computer subsystems may be linked to each other so that images, data, information, commands, etc., can be transmitted between them. For example, one computer subsystem may be linked to another computer subsystem by any suitable transmission medium, which may include any suitable wired and / or wireless transmission medium known in this art. Alternatively, two or more such computer subsystems may be effectively linked by a shared computer-readable storage medium (not shown).

[0027] One or more components executed by one or more computer subsystems include a physical-based model 106 representing a semiconductor fabrication process. In one embodiment, the semiconductor fabrication process is a lithography process. In another embodiment, the semiconductor fabrication process is an etching process. The lithography process and the etching process may include any lithography and etching process known in the Art, respectively. Furthermore, the semiconductor fabrication process may include any other semiconductor fabrication process known in the Art, including chemical mechanical polishing (CMP), deposition, ion implantation, etc.

[0028] However, the “semiconductor fabrication process” as described herein is not limited to processes such as those mentioned above that cause changes to the physical specimen on which the process is performed. For example, the term “semiconductor fabrication process” is defined herein as any process relating to the fabrication of a semiconductor device to a specimen. A process that does not directly cause changes to the physical specimen on which the process is performed is a semiconductor device design process. This process is rooted in how the design affects the physics of the semiconductor design and the physics of the semiconductor device used for fabrication, and can therefore be represented by a physics-based model.

[0029] Another process that does not typically directly cause changes to the physical specimen on which the process is performed is a quality control type process performed before, during, and / or after the semiconductor fabrication process. Such processes include inspection, metricing, and defect inspection processes, which are further rooted in the physics of the tools used in such processes and the physics of how such tools interact and generate information about the specimen being inspected. For example, a physics-based model for such a process may simulate how different parameters of the quality control tools affect images, measurements, etc., generated by the tools for the specimen.

[0030] In addition to the semiconductor fabrication-related processes described above, other processes that are more closely related to quality control but can affect the physical specimen itself can also be represented by a physics-based model. For example, repair processes, while not always used in semiconductor fabrication, may be used to correct or refine one or more physical or chemical aspects of a specimen due to some failure or marginality in the fabrication process steps when changes to the specimen are necessary. Such processes may further include cleaning-type processes that are used to remove unnecessary material from the specimen, either entirely or locally, thereby causing changes to the specimen itself.

[0031] As can be seen from the foregoing, the “semiconductor fabrication process” may or may not modify the physical specimen, and the physical specimen may be a specimen on which a semiconductor device is formed, or another specimen involved in such formation of a device. For example, in some embodiments, the specimen is a wafer. The wafer may include any wafer known in semiconductor technology. Furthermore, the embodiments described herein may be used for specimens such as reticles, flat panels, personal computer (PC) substrates, and other semiconductor specimens. Thus, the “semiconductor fabrication process” can be further defined as any process involved in or related to the fabrication of a semiconductor device on a specimen, which can be expressed based on the physics involved in the process when the term is used herein.

[0032] One or more components further include a setup component 108 which includes an objective function configured to compare results produced by a physics-based model with reference data for different values ​​of one or more parameters of the physics-based model, and to generate an output depending on the difference between the results and the reference data. For example, as shown in Figure 2, the setup component may include an objective function 200. Generally, the objective function uses a physics model to predict the results of a microelectronic device fabrication step and compares these results to results obtained experimentally. The difference, or error, of these results is inversely correlated with the output of the objective function. This objective function is expected to be maximized during optimization, but evaluating it is often a waste of time. The objective function may have any suitable form or format known in the art.

[0033] The reference data used in the embodiments described herein may or may not be generated by the embodiments described herein. For example, the embodiments described herein may include a semiconductor fabrication tool (not shown) configured to perform one or more of the semiconductor fabrication processes described herein. The embodiments may generate reference data by using this tool to perform a well-designed set of experiments on one or more specimens. For example, the process may be performed on one or more specimens with one or more process parameter values ​​different, and then the specimens on which the process has been performed are inspected, and the results of the inspection provide some information about the properties of the physical specimens. Such experiments may be performed in a variety of different ways, such as focus-expose matrix (FEM) and process window qualification (PWQ) processes, and these processes may be performed in any suitable way known in the art.

[0034] In other examples, embodiments described herein do not need to generate reference data, but may simply obtain reference data from another system or method (not shown) that generates reference data, or from a storage medium, such as one of those further described herein, in which reference data is stored by another system or method. Embodiments described herein may obtain such reference data in any suitable form known in the art.

[0035] The setup component further includes a surrogate function, which is constructed as an approximation of the objective function and fitted to the output generated by the objective function depending on different values ​​of one or more parameters. As shown in Figure 2, the setup component may include a surrogate function 202. The surrogate function is a function that can predict the results of evaluating the objective function but evaluates much faster. The surrogate function is progressively fitted to the data generated by the objective function during optimization, resulting in better predictions with more provided objective function data. The surrogate function may have any suitable form or format known in this technique.

[0036] The setup component further includes an acquisition function configured to select additional values ​​for one or more parameters for a physics-based model based on a surrogate function. As shown in Figure 2, the setup component may include an acquisition function 204. In another embodiment, the additional values ​​selected by the acquisition function in one of several phases are used by the objective function as values ​​for one or more parameters of the physics-based model in one of several subsequent phases. For example, the acquisition function uses the surrogate function to determine the best guess about the most beneficial point in the parameter space and evaluate the next objective function. In this way, the BO technique can minimize the number of calls to a more complex objective function by using many (or at least one) calls to the surrogate function. The acquisition function may have any suitable form or format known in the art. The additional values ​​selected by the acquisition function may be used in the next step or phase in the setup process, or as the final values ​​of the physics-based model depending on which step or phase of the setup process the setup component is performing.

[0037] The setup component is configured to set up a physics-based model in multiple phases, in each of the multiple phases only a subset of all parameters of one or more parameters of the physics-based model is set up. For example, in phase 1, parameter subset 1 may be set up, and in phase 2, parameter subset 2 may be set up, and so on. There may be some overlap between one or more of these parameter subsets (for example, parameter 1 may be in two or more parameter subsets), but no two parameter subsets can be ideally exactly the same. "Setting up" one or more parameters may or may not be a deformation of the original setting of one or more parameters. For example, the setup component may determine that the original setting for one of the parameters is the best setting for that parameter. However, generally, the setup component may "set up" one or more parameters by deforming the parameters in a subset until it is found that the setting for these parameters fits at least a portion of the model data essentially to the reference data via the BO technique described herein. Parameters "set up" in one phase may be changed in later phases if they are included in subsets set up in later phases. In such an example, the previous phase can be considered a rough setup phase, while the subsequent phase can be considered a kind of fine-tuning setup phase or a fine-tuning of the previous setup parameters.

[0038] To further illustrate this concept, consider a physical model in which N intrinsic parameters are expanded to represent the process of fabricating a microelectronic device. Experiments may be performed to generate a set of reference data for use in calibration. An objective function is constructed to represent the difference between the model prediction and the reference data. The optimization process is divided into cascaded phases. In some embodiments, the objective function remains constant in each of the multiple phases. For example, during each phase, only a subset of the intrinsic parameters of the physical model may be transformed as part of the optimization, while the objective function remains constant. In further embodiments, setting up only all subsets of one or more parameters of the physical base model in each of the multiple phases involves inputting selected additional values ​​into the objective function until the optimal value of all subsets of one or more parameters of the physical base model that maximizes the objective function is found. For example, the optimization phase may continue until the optimal value of the current subset of intrinsic parameters that maximizes the objective function (the difference between the reference data and the model data) is found. In further embodiments, a surrogate function fitted in one of the multiple phases is used in one of the subsequent phases. Thus, after each phase, the fitted surrogate function may be directly used by the next phase. By using a surrogate function from one phase in the next phase, each phase will benefit from the prior knowledge gained from the previous phase.

[0039] In one embodiment, the setup component is configured to implement a BO technique in which multiple phases are cascaded optimization phases. The BO technique consists of three components: an objective function, a surrogate function, and an acquisition function. These functions may be configured as further described herein. Furthermore, the BO technique may consist of two or more of each (or one or more) of these three components.

[0040] The configuration of a setup component is modified between at least two of the phases, based on all subsets of one or more parameters of the physics-based model set up in at least two of the phases. For example, it is preferable that the setup component and its constituent components be configured phase by phase in such a way that each component is specified to best suit the subset of parameters addressed in that phase. The configuration of a setup component may be modified in a variety of different ways. For example, a user, one or more computer subsystems, the setup component itself, or another method or system may modify the configuration of the setup component between two (or more) of the phases. Modifying the configuration of a setup component between two phases may include modifying one or more parameters or components of the setup component, modifying one or more functions themselves (e.g., by swapping one function with a different function), modifying, transforming, or replacing the inputs to the setup component, and / or modifying any other aspect of the setup component that affects how the parameters of the physics-based model are set up. Thus, between two setup phases, some aspects of the setup component, including any of its component elements, may be changed, while other aspects of the setup component may remain the same. Changing the configuration of the setup component between one or more of the setup phases is a key new feature of the embodiments described herein, because, as further described herein, this ability allows for the retention and utilization of prior knowledge gained in previous phases when advantageous, and for adapting the setup component to the parameters being set up. Further modifications to the configuration of the setup component may be carried out as described herein.

[0041] In further embodiments, the objective function used in at least one of the multiple phases is replaced by a different objective function in at least one of the multiple phases. For example, the cascaded optimization phases described above may be implemented using different objective functions for each (or one or more) phases, as described above. In this case, the objective function for each phase may be constructed in such a way that it has a relatively strong response to a subset of the internal model parameters optimized during that phase.

[0042] In another embodiment, the results generated by the physics-based model in one of several phases are input to the objective function in one of the subsequent phases, with different weights for at least one of the reference data in one of the phases and one of the subsequent phases. Figure 3 shows one embodiment of BO with a generalized objective function. As shown in Figure 3, in order to enable the use of prior simulation results in this embodiment, the objective function 300 is divided into several components: fitted reference data 304, generated model data 306, and a set of weights 302 for each of the reference data. The surrogate function 308 and the acquisition function 310 may be configured as further described herein. In this embodiment, instead of retaining the surrogate function from previous optimization phases, all model data generated from each phase may be retained. At the beginning of each optimization phase, all previously generated model data is compared to the reference data using different weights than in the previous phase. This retention and use of previously generated model data allows the objective function to change with each optimization phase, thereby allowing the objective function to be tailored to a subset of parameters optimized in this phase, while still allowing the surrogate function to be informed using previous simulation results.

[0043] In one embodiment, the acquisition function used in at least one of the multiple phases is replaced by a different acquisition function in at least one of the multiple phases. For example, an embodiment may use cascaded optimization phases to allow the use of different acquisition functions for each (or one or more) optimization phases. The acquisition function used has a relatively strong effect on the optimization conclusion by balancing the tendency of optimization to explore the parameter space with the tendency to converge to a local minimum. Allowing different acquisition functions makes it possible to tailor each phase to the specific requirements of this optimization stage.

[0044] In some embodiments, reference data used in at least one of multiple phases is replaced by different reference data in one of the subsequent phases. For example, an embodiment may use the cascaded optimization phases described herein, but may include multiple sources of information in the objective function of one or more phases. In one such embodiment, the reference data and different reference data result in different computational complexities of the physics-based model. In this context, different sources of information are typically different sources of reference data that result in different computational complexities of the model. For example, one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) reference data may require substantially different computational times from the model and therefore may be treated as different sources of information. In another such embodiment, the reference data is a source that is more computationally efficient for the physics-based model than the different reference data. When multiple sources of information exist, it is preferable that the most computationally efficient source is executed first.

[0045] In some embodiments, the surrogate function is configured to provide an upper bound on the predicted objective function value at different locations of one or more parameters in the parameter space. The results of a faster source can be used to fit the surrogate function in such a way that it provides an upper bound on the predicted objective function value at this location in the parameter space. In this case, the objective function should be constructed such that each source contributes a constant positive amount to the total objective value. Therefore, if one of the sources results in a relatively low objective value, there is no point in evaluating a more computationally strict source at this location. In other words, when there is a relatively "low" objective value, this means that the error of the combination of this source and the parameter being tested is relatively large. Therefore, evaluating a more computationally strict source at this location is hardly logical, as it will likely (or definitely) turn out to be "not good" with those parameter values, and thus it is better to move to a different area of ​​the parameter space to obtain the next parameter to evaluate. The next parameter selected for evaluation may be evaluated using the same source or the next source. In other words, if a faster model is evaluated and it is found that the parameters being investigated are "bad" (the parameters have relatively low target values), then it can be determined that the results would be even worse if a slower model were evaluated. Therefore, there is no reason to run the slower model.

[0046] Another embodiment uses multiple information sources in a manner different from the previously described methods. In this embodiment, different sources of reference data at different scales of computational complexity are used in a nested optimization pattern. In another embodiment, the objective function and surrogate function used in at least one of the multiple phases are replaced by different objective functions and different surrogate functions, respectively, in one of the subsequent phases. For example, each of the above information sources may use its own independent objective and surrogate functions. In this embodiment, the faster an information source is computed, the more it is nested inside a slower information source.

[0047] In further embodiments, an acquisition function used in one or more of at least one of multiple phases is replaced by a different acquisition function in one of the subsequent phases, and the different acquisition function samples a surrogate function and a different surrogate function to select additional values. For example, there may be a different acquisition function for each information source (or two or more information sources), but the acquisition functions as a whole are not independent of each information source. The i-th acquisition function samples a surrogate function from all (or at least one or more) information sources <= i to determine the next sample point for the i-th objective function. The acquisition function balances the information sources such that points from faster information sources known to have relatively low objective values ​​are less likely to be explored by slower information sources. This decision-making is similar to the decision-making described above, where parameters with relatively low objective values ​​are abandoned in the hope that better parameters will be found elsewhere in the parameter space. However, where information from the fast model is incorporated, i.e., in the objective function of the embodiments described above or the acquisition function of this embodiment, this situation is different. In both cases, the results are similar, and slower models are not run for parameters already known to be "bad".

[0048] Figure 4 shows one embodiment of a multiscale nested BO. The first phase of the cascaded BO technique uses an acquisition function 1(400), an objective function 1(402), and a surrogate function 1(404), which are configured according to any embodiment described herein, and the BO may be performed using a first source (not shown in Figure 4).

[0049] The second phase of the cascaded BO technique uses an acquisition function 2(406), an objective function 2(408), a surrogate function 2(410), and optionally a surrogate function 1(404), which are configured according to any embodiment described herein and may be used to perform BO using a second information source (not shown in Figure 4) different from the first information source. For example, the second information source may have more computational complexity for the physics-based model than the first information source. In other words, the second information source may be more computationally demanding and slower to compute than the first information source. Unlike the first phase, in the second phase, the input to acquisition function 2 may include the outputs of surrogate functions 1 and 2.

[0050] The final and possibly third phase of the cascaded BO technique may use an acquisition function N(412), an objective function N(414), a surrogate function N(416), and optionally surrogate functions 1(404) and / or 2(410), which are configured according to any of the embodiments described herein, and may perform BO using a third source (not shown in Figure 4) different from the first and second sources. For example, the third source may have more computational complexity for the physics-based model than the first and second sources. In other words, the third source may be more computationally demanding and slower to compute than the first and second sources. Unlike the first and second phases, in the final and possibly third phase, the input to the acquisition function N may include the outputs of surrogate functions 1, 2, ..., N. Thus, in all phases except the first phase, the acquisition function may sample surrogate functions from all sources (i.e., all prior phases). Therefore, while each of the acquisition functions 1, 2, ..., N may differ for different information sources, the acquisition functions as a whole are not independent for each information source.

[0051] The embodiments described herein can be combined in any suitable manner. Any or all of the optimization phases may include different objective functions and / or multiple information sources. In some embodiments, the objective function is configured as a machine learning (ML) model. In other embodiments, the surrogate function is configured as an ML model. For example, the objective function can be replaced by an ML model at the beginning of or during the optimization procedure described above in any of the embodiments. Similarly, the surrogate function can be further replaced by an ML model. The objective functions and surrogate functions described herein can have any suitable ML configurations and architectures known in the Art.

[0052] The embodiments described herein offer several significant advantages over other methods and systems currently used to set up physics-based models. For example, the embodiments described herein enable optimization of multiple sources, which makes computations more efficient and faster. Furthermore, the history-based cascaded optimization described herein requires fewer full simulation runs to achieve similar overall optimization results. In addition, utilizing different objective functions for different optimization phases improves the optimization of parameters that may have relatively low sensitivity in the overall objective function.

[0053] The challenge of developing processes that enable the continuous contraction of the critical dimension (CD) of features in the fabrication of ultra-small electronic devices is growing. These challenges are further increasing not only the time required to develop optimized processes that can be manufactured on a relatively large scale, but also the research and development costs associated with those processes. The embodiments described herein leverage the capabilities of physical modeling to accelerate time-to-solution by capturing higher levels of detail, which can help users reduce development time and lower research and development costs. Accurate calibration of the underlying physical models to customer reference data is essential for these techniques to be effective. Furthermore, the embodiments described herein enable the calibration of more sophisticated and complex computational models than was previously possible.

[0054] The advantages described above and other advantages described herein are provided by several important new features of the embodiments described herein. One such feature includes the ability to use prior results in multi-phase optimization. Furthermore, the embodiments described herein may be shaped to re-evaluate the objective function at each phase of optimization to enable informing a new surrogate function using prior results. Furthermore, the embodiments described herein can be configured to reduce the computational resources used to evaluate the objective function point by point in the parameter space by utilizing multiple sources of information.

[0055] The following examples are provided herein to facilitate and deepen the understanding of some of the embodiments described herein. These examples are not intended to limit the spirit and scope of the invention as described in the claims that follow this section, simply because they are included in this section.

[0056] Several steps that may be performed in an example of the proposed workflow are described below. In step 1, the embodiments described herein or another method or system may generate a physical model of the etching process to match a set of reference data for etching a target material using different material masks in a plasma etching environment. In this example, the reference data includes two sources of information: blanket etching rates (1D data) of the two materials involved, and sidewall etching profiles (3D data) of cylindrical etching features. Within the sidewall etching profiles are three main features of interest for process optimization: mask profile, feature etching depth, and target material "bowing" (extension of etching features at a certain etching depth). These features are schematically shown in Figure 5 as a function of feature height 502 and limiting dimension 504. In this example, the reference data 500 includes mask profile 506, bowing profile 508, and profile etching depth 510.

[0057] In step 2, the computer subsystem, components, and / or setup components may divide the optimization process into phases. In this case, the optimization is divided into four phases as shown in Figure 6. The first phase targets obtaining the correct feature etching depth by tuning only the internal model parameters that are expected to be strongly expressed for this purpose, and the objective function includes only the non-zero weights of the reference data that represent this feature of the process. For example, as shown in Figure 6, after phase 1 (604), the model data 602 (shown as a dotted line in all phases illustrated in Figure 6) and the reference data 600 (shown as a solid line in all phases illustrated in Figure 6) converge to the lowest feature height shown in Figure 5 by the profile etching depth 510. As shown in Figure 6, after phase 1, except near the profile etching depth, a significant difference between the reference data and the model data is evident in all other parts of the reference data.

[0058] The second phase targets the optimization of the mask profile, and the internal parameters and objective function terms are selected to focus on this goal. As shown in Figure 6, after phase 2 (606), the model data and reference data converge to the section of the reference data mask profile 506 shown in Figure 5. As shown in Figure 6, after phase 2, the model data and reference data differ somewhat near the profile etching depth (more so than they did after phase 1), and these can be corrected in the following phases. The third phase similarly targets feature bowing. As shown in Figure 6, after phase 3 (608), the model data and reference data converge completely to the section of the reference data bowing profile 508 shown in Figure 5. The fourth and final phase includes all possible internal model parameters and objective terms. As shown in Figure 6, after phase 4 (610), the model data roughly approximates the reference data at all data points of the reference data. Since the surrogate function at the beginning of this phase has already been fitted to all the data from previous phases, the optimization is much more successful than a single-step optimization using the same objective function.

[0059] In step 3, the computer subsystem, components, and / or setup components may split the objective function into separate information sources. In this case, the 1D (blanket etching rate) and 3D (etching profile) data are treated as separate information sources. The 1D information source may be used in each of the four optimization phases to expedite the evaluation of the objective function. With each call to the objective function in the optimization loop, the blanket etching rate may be simulated first. This calculation is substantially fast (on the order of seconds). If the blanket etching rate is close enough to the reference value to produce a sufficiently high objective value, the 3D simulation will be performed. The complete value of the objective function is then used to fit the surrogate function at this point in the parameter space. If the blanket etching rate is not relatively close to the reference data and the objective value is significantly lower, this value is used to provide an upper bound for the surrogate function at this location in the parameter space. The acquisition function is then called, and the new surrogate function finds the next sampling point without running the 3D data at the previous point.

[0060] In some embodiments, the computer subsystem is configured to store information about a set-up physics-based model. The computer subsystem may be configured to store information in a recipe, or to generate a recipe for a process in which the set-up physics-based model will be used. When the term is used herein, a “recipe” can generally be defined as a set of instructions available to a tool for performing a process that includes a simulation performed by the set-up physics-based model. Thus, generating a recipe may include generating information about how the process should be performed, and the information is therefore available for generating instructions to perform this process. The information about the set-up physics-based model stored by the computer subsystem may include any information available to identify and / or use the set-up physics-based model (e.g., a file name and the location where the information is stored) (and the file may also contain information about the set-up physics-based model, such as model parameter values).

[0061] A computer subsystem may be configured to store information about a set-up physics-based model on any suitable computer-readable storage medium. The information may be stored together with any of the results and / or data described herein, and may be stored in any format known in the art. The storage medium may include any of the storage mediums described herein, or any other suitable storage medium known in the art. After the information is stored, it is accessible within the storage medium and can be used by any of the methods or system embodiments described herein, formatted for display to a user, and used by another software module, method, or system, etc. For example, an embodiment described herein may generate a recipe as described above. This recipe may then be stored and used by a system or method (or another system or method) to carry out a process including a simulation performed by the set-up physics-based model.

[0062] The results and information generated by the set-up physics-based model may be used in various ways by the embodiments and / or other systems and methods described herein. Such functions include, but are not limited to, altering processes such as fabrication processes or steps that have been or will be performed on a specimen in a feedback or feedforward manner. Changes to the process may include any appropriate changes to one or more parameters of the process. The computer subsystems described herein may determine such changes in any appropriate manner known in the art.

[0063] These changes can then be sent to a semiconductor fabrication system (not shown) or storage medium (not shown) accessible by the computer subsystem and the semiconductor fabrication system. The semiconductor fabrication system may be part of the system embodiments described herein. For example, the computer subsystem described herein may be connected to the semiconductor fabrication system via one or more common elements, such as a housing, a power supply, etc. The semiconductor fabrication system may include any semiconductor fabrication system known in the art, such as lithography tools, etching tools, chemical mechanical polishing (CMP) tools, and deposition tools. Furthermore, the semiconductor fabrication-related system may be a system for different processes described herein, such as electronic design automation (EDA) tools, inspection tools, weighing tools, defect inspection tools, and device repair tools. Such tools and systems may include any such tools and systems known in the art.

[0064] Each of the above-described embodiments of the system may be combined into a single embodiment.

[0065] Another embodiment relates to a computer implementation method for setting up a physics-based model. The method includes comparing results generated by a physics-based model representing semiconductor fabrication-related processes with different values ​​for one or more parameters of the physics-based model with reference data, and generating an output based on the difference between the results and the reference data using an objective function. The method further includes fitting a surrogate function, configured as an approximation of the objective function, to the output generated by the objective function depending on different values ​​for one or more parameters. Furthermore, the method includes selecting additional values ​​for one or more parameters for the physics-based model based on the surrogate function using an acquisition function. The objective function, surrogate function, and acquisition function are included in a setup component. The setup component and the physics-based model are included in one or more components executed by one or more computer systems. The setup component is configured to set up the physics-based model in multiple phases, in each of the multiple phases only all subsets of one or more parameters of the physics-based model are set up.

[0066] Each step of the method may be carried out as further described herein. The method may further include any other steps that can be carried out by the systems, computer systems, and / or components described herein. The computer system may be configured according to any of the embodiments described herein, such as computer subsystem 102. Furthermore, one or more components may be configured according to any of the embodiments described herein. The method may be carried out by any of the system embodiments described herein.

[0067] Further embodiments relate to a non-temporary computer-readable medium storing program instructions executable on one or more computer systems for implementing a computer implementation method for setting up a physics-based model. One such embodiment is shown in Figure 7. In particular, as shown in Figure 7, the non-temporary computer-readable medium 700 includes program instructions 702 executable on a computer system 704. The computer implementation method may include any step of any of the methods described herein.

[0068] Program instructions 702 implementing methods such as those described herein may be stored in a computer-readable medium 700. The computer-readable medium may be a storage medium such as a magnetic or optical disk, magnetic tape, or any other suitable non-temporary computer-readable medium known in the art.

[0069] Program instructions may be implemented in any of the various methods, including, in particular, procedure-based techniques, component-based techniques, and / or object-oriented techniques. For example, program instructions may be implemented as desired using ActiveX controls, C++ objects, JavaBeans, Microsoft Foundation Classes ("MFC"), SSE (Streaming SIMD Extensions), or other techniques or methods.

[0070] The computer system 704 may be configured according to any of the embodiments described herein.

[0071] Further modifications and alternative embodiments of various aspects of the present invention will be apparent to those skilled in the art from the viewpoint of this description. For example, systems and methods for setting up physical base models are provided. Therefore, this description should be interpreted as illustrative only and is intended to teach those skilled in the art an overall mode of carrying out the present invention. It should be understood that the forms of the present invention illustrated and described herein should be taken as currently preferred embodiments. As will be obvious to those skilled in the art after benefiting from this description of the present invention, elements and materials may be used instead of those illustrated and described herein, parts and processes may be reversed, and certain features of the present invention may be used independently. Modifications of the elements described herein may be made without departing from the spirit and scope of the present invention as described in the following claims.

Claims

1. A system configured to set up a physics-based model, One or more computer subsystems, One or more components executed by the one or more computer subsystems, wherein the one or more components comprise the physical base model representing the semiconductor manufacturing process, and the setup components, An objective function configured to compare the results generated by the physical base model with reference data, where one or more parameters of the physical base model have different values, and to generate an output according to the difference between the results and the reference data, A surrogate function configured as an approximation of the objective function, fitted to the output generated by the objective function according to the different values ​​of one or more parameters, and An acquisition function configured to select additional values ​​for one or more parameters for the physics-based model based on the surrogate function. Includes, The setup component is configured to set up the physics-based model in multiple phases, and in each of the multiple phases, only a subset of all of the one or more parameters of the physics-based model is set up. The configuration of the setup component is changed between at least two of the multiple phases based on all subsets of the one or more parameters of the physics-based model set up in at least two of the multiple phases. One or more components and A system characterized by comprising the following features.

2. The system according to claim 1, wherein the setup component is further configured to perform a Bayesian optimization technique in which the plurality of phases are cascaded optimization phases.

3. A system according to claim 1, characterized in that each of the plurality of phases is performed based on an output generated by any of the previously performed phases.

4. A system according to claim 1, characterized in that the objective function used in at least one of the plurality of phases is replaced by a different objective function in at least another of the plurality of phases.

5. The system according to claim 1, characterized in that the input to the setup component includes a plurality of information sources.

6. A system according to claim 1, characterized in that the additional values ​​selected by the acquisition function in one of the plurality of phases are used by the objective function as values ​​for one or more parameters of the physics-based model in one of the subsequent phases.

7. The system according to claim 1, characterized in that the objective function is constant in each of the plurality of phases.

8. The system according to claim 1, characterized in that in each of the plurality of phases, setting up only all subsets of all of the one or more parameters of the physical base model includes inputting the selected additional values ​​into the objective function until the optimal values ​​of all subsets of all of the one or more parameters of the physical base model that maximize the objective function can be determined.

9. A system according to claim 1, characterized in that the surrogate function fitted in one of the plurality of phases is used in one of the subsequent phases.

10. A system according to claim 1, characterized in that the result generated by the physics-based model in one of the plurality of phases is input to the objective function in one of the subsequent phases, and at least one of the reference data in one of the plurality of phases and one of the subsequent phases are different weights.

11. A system according to claim 1, characterized in that the acquisition function used in at least one of the plurality of phases is replaced by a different acquisition function in at least another of the plurality of phases.

12. A system according to claim 1, characterized in that the reference data used in at least one of the plurality of phases is replaced with different reference data in one of the subsequent phases.

13. A system according to claim 12, characterized in that the reference data and the different reference data result in different computational complexities of the physics-based model.

14. The system according to claim 12, characterized in that the reference data is a source that is computationally more efficient for the physics-based model than the different reference data.

15. A system according to claim 14, characterized in that the proxy function provides an upper limit on the predicted objective function value for the location of the different values ​​of one or more parameters in the parameter space.

16. A system according to claim 14, characterized in that the objective function and the substitute function used in at least one of the plurality of phases are replaced by a different objective function and a different substitute function in one of the subsequent phases.

17. A system according to claim 16, wherein the acquisition function used in at least one of the plurality of phases is replaced by a different acquisition function in one of the subsequent phases, and the different acquisition function samples the surrogate function and the different surrogate function to select the additional values.

18. The system according to claim 1, characterized in that the objective function is further configured as a machine learning model.

19. The system according to claim 1, characterized in that the surrogate function is further configured as a machine learning model.

20. A system according to claim 1, characterized in that the semiconductor manufacturing-related process is a lithography process.

21. The system according to claim 1, characterized in that the semiconductor manufacturing-related process is an etching process.

22. A non-temporary computer-readable medium storing program instructions executable on one or more computer systems for implementing a computer implementation method for setting up a physics-based model, wherein the computer implementation method is The process involves comparing the results generated by the physical-based model, which represents semiconductor manufacturing-related processes with different values ​​for one or more parameters of the physical-based model, with reference data, and generating an output according to the difference between the results and the reference data using an objective function. The surrogate function, constructed as an approximation of the objective function, is fitted to the output generated by the objective function according to the different values ​​of one or more parameters. The selection of additional values ​​for one or more parameters for the physics-based model based on the surrogate function using an acquisition function, wherein the objective function, the surrogate function, and the acquisition function are included in a setup component, and the setup component and the physics-based model are included in one or more components executed by the one or more computer systems. Includes, The setup component is configured to set up the physics-based model in multiple phases, and in each of the multiple phases, only a subset of all of the one or more parameters of the physics-based model is set up. The configuration of the setup components is changed between at least two of the multiple phases based on all subsets of the one or more parameters of the physics-based model set up in at least two of the multiple phases. A non-temporary computer-readable medium characterized by the following:

23. A computer implementation method for setting up a physics-based model, A step of comparing the results generated by the physical-based model, which represents semiconductor manufacturing-related processes with different values ​​for one or more parameters of the physical-based model, with reference data, and a step of generating an output according to the difference between the results and the reference data using an objective function. The steps include fitting a substitute function, configured as an approximation of the objective function, to the output generated by the objective function according to the different values ​​of one or more parameters, A step of selecting additional values ​​for one or more parameters for the physics-based model based on the surrogate function using an acquisition function, wherein the objective function, the surrogate function, and the acquisition function are included in a setup component, and the setup component and the physics-based model are included in one or more components executed by one or more computer systems. Includes, The setup component is configured to set up the physics-based model in multiple phases, and in each of the multiple phases, only a subset of all of the one or more parameters of the physics-based model is set up. The configuration of the setup components is changed between at least two of the multiple phases based on all subsets of the one or more parameters of the physics-based model set up in at least two of the multiple phases. A computer implementation method characterized by the following.

Images