System and method for establishing a physics-based model

Abstract

Systems and methods for building physics-based models are provided. A system includes one or more components that are executed by one or more computer subsystems and include a physics-based model that describes a process related to semiconductor manufacturing and a build component configured to build the physics-based model in multiple stages, where only a subset of all the parameters of the physics-based model is built in each of the multiple stages. Based on the subset of all the parameters of the physics-based model built in at least two of the multiple stages, the configuration of the build component is changed between the at least two of the multiple stages. The build component may use multiple information sources and objective functions to perform Bayesian optimization techniques for building or calibrating a cascade model.

Description

Technical Field

[0001] The present invention generally relates to systems and methods for building physics-based models. Background Art

[0002] The following description and examples are not admitted to be prior art by virtue of their inclusion in this section.

[0003] Manufacturing semiconductor devices such as logic and memory devices typically involves processing a substrate such as a semiconductor wafer using a large number of semiconductor manufacturing processes to form various features and multiple levels of the semiconductor device. For example, lithography is a semiconductor manufacturing process that involves transferring a pattern from a photomask to a resist disposed on a semiconductor wafer. Additional examples of semiconductor manufacturing processes include, but are not limited to, chemical mechanical polishing (CMP), etching, deposition, and ion implantation. Multiple semiconductor devices can be manufactured in an arrangement on a single semiconductor wafer and then separated into individual semiconductor devices.

[0004] Due to the expense and difficulty of optimizing semiconductor manufacturing processes via experimentation, many efforts have been made to build physical models of these processes, which can replace the experimental work of building and optimizing the processes. In theory, a physical model can evaluate more different process parameter values faster and cheaper than attempting to evaluate different process parameter values via experimentation.

[0005] For the models described herein, a "physical model" or "physics-based model" is defined as a forward simulation model that is based on and describes the physical process it is desired to simulate. These physical models can have tunable parameters that are typically set by fitting modeling data to reference data, but the models themselves do not "learn" how to simulate the physical process. In other words, the physical or physics-based models described herein are not machine learning or deep learning models.

[0006] When accurately built, physical models can be extremely valuable in building and optimizing semiconductor manufacturing processes. However, the task of building a physical model is not easy and can prevent the implementation of physical models in manufacturing process building and optimization. For example, a well-designed set of experiments must be used to capture or generate suitable reference data, and appropriate optimization procedures must be identified and used to build the physical model.

[0007] Currently used model calibration techniques tend to rely on single-step optimization with a fixed objective function. Such techniques typically must be repeatedly refined many times before a physical model can be adequately calibrated to accurately reflect the reference data.

[0008] Accordingly, currently used model calibration techniques have several drawbacks. For example, single-step optimization requires an objective function that accurately and uniquely defines the match between the model and the reference data. Constructing such a function is not always feasible. In another example, if the current method requires multiple optimization runs, the optimization algorithm does not benefit from the results of previous optimizations. In an additional 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 synchronously. This requirement makes the optimization technique as slow as the slowest information source.

[0009] Accordingly, it would be advantageous to develop systems and methods for building physics-based models that do not have one or more of the drawbacks described above. SUMMARY

[0010] The following description of various embodiments should not be construed in any way as limiting the subject matter of the appended claims.

[0011] One embodiment relates to a system configured to build 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 describing a process related to semiconductor manufacturing and a building component. The building component includes an objective function configured to compare results produced by the physics-based model with different values of one or more parameters of the physics-based model to reference data and to produce an output responsive to a difference between the results and the reference data. The building component also includes a surrogate function configured as an approximation of the objective function and fitted to the output produced by the objective function according to the different values of the one or more parameters. The building component further includes an acquisition function configured to select additional values of the one or more parameters for the physics-based model based on the surrogate function. The building component is configured to build the physics-based model in multiple stages, in each of the multiple stages, only building a subset of all the one or more parameters of the physics-based model. Based on the subsets of all the one or more parameters of the physics-based model built in at least two of the multiple stages, change the configuration of the building component between at least two of the multiple stages. The system may be further configured as described herein.

[0012] Another embodiment relates to a computer-implemented method for building a physics-based model. The method includes comparing results generated by a physics-based model that describes a semiconductor manufacturing-related process with different values of one or more parameters of the physics-based model to reference data and generating an output responsive to a difference between the results and the reference data using an objective function. The method also includes fitting a surrogate function configured as an approximation of the objective function to the output generated by the objective function based on the different values of the one or more parameters. Additionally, the method includes selecting additional values of the one or more parameters for the physics-based model based on the surrogate function using an acquisition function. The objective function, the surrogate function, and the acquisition function are included in a build component. The build component and the physics-based model are included in one or more components executed by one or more computer systems. The build component is configured to build the physics-based model in multiple stages, and in each of the multiple stages, only a subset of all of the one or more parameters of the physics-based model is built. Based on the subsets of all of the one or more parameters of the physics-based model built in at least two of the multiple stages, the configuration of the build component is changed between at least two of the multiple stages.

[0013] Each of the steps of the method may be further performed as further described herein. The method may include any other steps of any other method described herein. The method may be performed by any system described herein.

[0014] Another embodiment relates to a non-transitory computer-readable medium that stores program instructions executable on one or more computer systems to perform a computer-implemented method for building a physics-based model. The computer-implemented 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-implemented method may be performed as further described herein. Additionally, the computer-implemented method executable by the program instructions may include any other steps of any other method described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Further advantages of the present invention will become apparent to those skilled in the art in view of the following detailed description of the preferred embodiments and with reference to the drawings, in which:

[0016] Figure 1 is a block diagram illustrating one embodiment of a system configured to build a physics-based model;

[0017] Figures 2 to 4 is a block diagram illustrating an embodiment of a build component configured to build a physics-based model;

[0018] Figure 5 is a schematic diagram illustrating an example of target reference data that can be used by the embodiments described herein to build a physics-based model;

[0019] Figure 6 is a schematic diagram illustrating an example of a cascaded optimization workflow; and

[0020] Figure 7 is a block diagram illustrating an embodiment of a non-transitory computer-readable medium storing program instructions for causing a computer system to perform the computer-implemented methods described herein.

[0021] Although the present invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and are described in detail herein. The drawings may not be to scale. However, it should be understood that the drawings and their detailed description are not intended to limit the invention to the particular forms disclosed, but on the contrary, are intended to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims. Detailed Description

[0022] Referring 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 features of the elements. It should also be noted that the figures are not drawn to the same scale. Elements that may be similarly configured and shown in more than one figure have been indicated with the same element symbols. Unless otherwise stated herein, any of the elements described and shown may include any suitable commercially available elements.

[0023] Generally, the embodiments described herein are configured to build physics-based models. Some of the embodiments described herein are configured to use multiple information sources and objective functions for cascaded model calibration. The embodiments can be used to calibrate first-principles calculation models of processes such as etching and lithography in the semiconductor processing industry to accurately reflect reference data.

[0024] As used herein, the term "building a physics-based model" is defined as selecting one or more parameters of a physics-based model, regardless of the reason for performing the parameter selection process. For example, building a physics-based model can include building a new physics-based model not yet released for use. Thus, the embodiments described herein can be used to generate or perform an initial build of a new physics-based model, which can be a new model of an old process or a new model of a new process. Building a physics-based model can also include modifying a previously built physics-based model, such as can be done for calibration or optimization purposes. This calibration or optimization can be performed for several reasons, including but not limited to intentional or unintentional changes in the process described by the physics-based model. For example, an intentional change can include when the process is changed in order to change the device being manufactured, e.g., when one material is replaced with another material, or when a change in the critical dimension of a feature becomes advantageous. In one instance, an unintentional change can include when there is an unexpected drift in how the process is performed, which makes an update to the physics-based model describing this process advantageous.

[0025] Due to scaling requirements, the constraints on etching and lithography processes during microelectronic manufacturing are increasing continuously. As feature sizes decrease, the traditional process optimization capabilities based on design of experiments (DOE) become insufficient. First-principles modeling based on physics provides process engineers with the ability to more effectively meet the growing requirements than current techniques. For effectiveness, the first-principles model must be calibrated to match the reference data of the process being modeled. Due to the complexity of the model and the lack of direct measurement techniques for internal model parameters, this calibration process can be a significant obstacle in the field for using physics-based models. In the microelectronic manufacturing industry, novel optimization techniques are needed to successfully utilize such physics-based models.

[0026] The embodiments described herein provide methods for performing optimization that utilize Bayesian optimization (BO) techniques to perform optimization that includes several (i.e., two or more) cascaded optimization stages. In one embodiment, each of the multiple stages is performed based on the output generated by any previously performed stage of the multiple stages. For example, as further described herein, this cascaded optimization technique can use the existing knowledge from all previous stages at each optimization stage. The cascaded optimization technique also allows different objective functions to be used during each optimization stage. In a further embodiment, the input for building a component includes multiple information sources. For example, as further described herein, the cascaded optimization technique allows the multiple information sources to be used in a way that enables relatively fast simulations to reduce the number of relatively long simulations in each optimization step.

[0027] One embodiment relates to a system configured to build a physics-based model. In Figure 1An embodiment of this system is shown. The system includes one or more computer subsystems 102 and one or more components 104 executed by the one or more computer subsystems. The one or more components may be configured as further described herein and may be executed by the one or more computer subsystems in any suitable manner known in the art.

[0028] The computer subsystem is also referred to herein as a computer system. Each of the computer subsystems or systems described herein may take various forms, including a personal computer system, an image computer, a mainframe computer system, a workstation, a network device, an Internet device, or other devices. Generally, the term "computer system" may be broadly defined to cover any device having one or more processors that execute instructions from a memory medium. The computer subsystem or system may also include any suitable processor known in the art, such as a parallel processor. Additionally, the computer subsystem or system may include a computer platform with high-speed processing and software, as a stand-alone or networked tool.

[0029] If the system includes more than one computer subsystem, the different computer subsystems may be coupled to each other such that images, data, information, instructions, etc. can be sent between the computer subsystems. For example, one computer subsystem may be coupled to another computer subsystem via any suitable transmission medium, which may include any suitable wired and / or wireless transmission media known in the art. Two or more such computer subsystems may also be effectively coupled via a shared computer-readable storage medium (not shown).

[0030] The one or more components executed by the one or more computer subsystems include a physics-based model 106 that describes a semiconductor manufacturing-related process. In one embodiment, the semiconductor manufacturing-related process is a lithography process. In another embodiment, the semiconductor manufacturing-related process is an etching process. The lithography process and the etching process may each include any lithography and etching processes known in the art. Additionally, the semiconductor manufacturing-related process may include any other semiconductor manufacturing processes known in the art, including chemical mechanical polishing (CMP), deposition, ion implantation, and the like.

[0031] However, the "semiconductor manufacturing-related process" described herein is not limited to processes such as those described above that cause a change in the physical sample on which the process is performed. For example, the term "semiconductor manufacturing-related process" is defined herein as any process related to manufacturing a semiconductor device on a sample. This process that does not directly cause a change in the physical sample on which the process is performed is a semiconductor device design process. This process may be described by a physics-based model because it is a process rooted in the physics of semiconductor design and how that design affects the physics of the semiconductor device used for manufacturing.

[0032] Another such process that generally does not directly cause a change in the physical sample on which the process is performed is a quality control type process performed before, during, and / or after a semiconductor manufacturing process. Such processes include inspection processes, metrology processes, and defect inspection processes, which also stem from the physics of the tools used for such processes and how such tools interact with and generate information for the sample under review. For example, a physics-based model of such a process can simulate how different parameters of a quality control tool affect the images, measurements, etc. generated by the tool for the sample.

[0033] In addition to the semiconductor manufacturing related processes described above, other processes that are more related to quality control but can affect the physical sample itself can also be described by physics-based models. For example, a repair process may not always be used in a semiconductor manufacturing process, but when a change to the sample is needed, due to some malfunction or marginality in a manufacturing process step, this process can be used to correct or refine one or more physical or chemical aspects of the sample. Such processes also include cleaning type processes, which can be used to globally or locally remove unwanted materials from the sample, thereby causing a change to the sample itself.

[0034] From the above description, it can be seen that the "semiconductor manufacturing related process" itself may or may not change the physical sample, which may be the sample on which a semiconductor device is being formed or another sample involved in such formation of the device. For example, in some embodiments, the sample is a wafer. The wafer can be any wafer known in the semiconductor art. Additionally, the embodiments described herein can be used for samples such as photomasks, flat panels, personal computer (PC) boards, and other semiconductor samples. In this way, the term "semiconductor manufacturing related process" as used herein can also be defined as any process that involves or is related to the manufacture of semiconductor devices on a sample and can be described based on the physics involved in the process.

[0035] One or more components also include a build component 108, which includes an objective function that is configured to compare the results generated by the physics-based model with different values of one or more parameters of the physics-based model and to generate an output in response to the difference between the results and the reference data. For example, as Figure 2 shown, the build component can include an objective function 200. Generally, the objective function uses the physics model to predict the results of a microelectronic manufacturing step and compares those results with the results obtained through experimentation. The difference or error between these results is inversely proportional to the output of the objective function. This objective function is expected to be maximized during optimization, but the evaluation is usually time-consuming. The objective function can have any suitable form or format known in the art.

[0036] 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 semiconductor manufacturing-related tools (not shown) configured to perform one or more semiconductor manufacturing-related processes described herein. The embodiments may use the tools to generate reference data by performing a set of appropriately designed experiments on one or more samples. For example, the process may be performed on one or more samples with different values of one or more parameters of the available process, and then the samples on which the process is performed are examined, which results in some information about the characteristics of the physical samples. Such experiments may be performed in a variety of different ways, such as focus exposure matrix (FEM) and process window verification (PWQ) processes, which may be performed in any suitable manner known in the art.

[0037] In other examples, the embodiments described herein may not generate reference data, but may simply capture it from another system or method (not shown) that generates reference data or from a storage medium (such as one of the storage media further described herein), where the reference data has been stored by another system or method. The embodiments described herein may capture this reference data in any suitable manner known in the art.

[0038] The building component further includes a surrogate function, which is configured to approximate the objective function and fit to the output generated by the objective function based on different values of one or more parameters. As Figure 2 shown, the building component may include a surrogate function 202. The surrogate function is a function that can predictively evaluate the result of the objective function, but is faster to evaluate. During optimization, the surrogate function gradually fits to the data generated by the objective function, resulting in better predictions with more objective function data provided. The surrogate function may have any suitable form or format known in the art.

[0039] The building component further includes an acquisition function, which is configured to select additional values of one or more parameters for the physics-based model based on the surrogate function. As Figure 2 shown, the building component may include an acquisition function 204. In another embodiment, the objective function uses the additional values selected by the acquisition function in one of the multiple stages as the values of one or more parameters of the physics-based model in a subsequent stage of the multiple stages. For example, the acquisition function uses the surrogate function to determine the best guess of the most useful points in the parameter space to evaluate the next objective function. In this way, the BO technique can use many (or at least one or more) calls to the surrogate function to minimize the number of calls to the more complex objective 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 stage of the building process, or as the final values of the physics-based model, depending on which step or stage of the building process the building component is performing.

[0040] A building component is configured to build a physics-based model in multiple stages, and in each of the multiple stages, only a subset of all one or more parameters of the physics-based model is built. For example, in stage 1, parameter subset 1 can be built, in stage 2, parameter subset 2, and so on. Although there may be some overlap between one or more of these parameter subsets (e.g., parameter 1 can be in more than one parameter subset), ideally, no parameter subsets are exactly the same. Building one or more parameters may or may not result in a modification of the original settings of the one or more parameters. For example, the building component can determine that the original setting of one of the parameters is the optimal setting for the parameter. However, generally, the building component can "build" one or more parameters by modifying the parameters in the subset until a setting of the parameter is found that causes at least part of the model data to be substantially fitted to the reference data via the BO technique described herein. If the parameters "built" in one stage are included in the subset built in a later stage, then they can be changed in the later stage. In such examples, the initial stage can be considered a rough building stage, and the later stage can be considered a fine building stage or a fine tuning of the initially built parameters.

[0041] To further illustrate this concept, consider a physics model with N internal parameters that is developed to represent a microelectronic manufacturing process. Experiments can be conducted to generate a set of reference data for calibration. A target function is constructed to represent the difference between the model predictions and the reference data. The optimization process is divided into cascading stages. In some embodiments, the target function is constant in each of the multiple stages. For example, during each stage, only a subset of the internal parameters of the physics model is modified as part of the optimization, while the target function can remain constant. In additional embodiments, building only a subset of all one or more parameters of the physics-based model in each of the multiple stages includes inputting the selected additional values into the target function until the optimal values of the subset of all one or more parameters of the physics-based model are found, thereby maximizing the target function. For example, the optimization stage can continue until the optimal values of the current subset of internal parameters that maximize the target function (the difference between the reference data and the model data) have been found. In further embodiments, the surrogate function fitted in one of the multiple stages is used in subsequent stages of the multiple stages. In this way, after each stage, the next stage can directly use the fitted surrogate function. Using the surrogate function from one stage in the next stage causes each stage to benefit from the existing knowledge obtained in the previous stage.

[0042] In one embodiment, a build component is configured to perform BO techniques, where multiple stages are cascade optimization stages. The BO technique consists of three components: an objective function, a surrogate function, and an acquisition function. These functions can be configured as further described herein. Additionally, the BO technique can consist of more than one (or one or more) of each of these three components.

[0043] Based on a subset of all one or more parameters of a physics-based model established in at least two of the multiple stages, the configuration of the build component is changed between at least two of the multiple stages. For example, the build component and its constituent components are preferably configured in each stage in such a way that each component can be specified as most suitable for the subset of parameters being processed in that stage. The configuration of the build component can be changed in a variety of different ways. For example, a user, one or more computer subsystems, the build component itself, or another method or system can change the configuration of the build component between two (or more) of the multiple stages. Changing the configuration of the build component between two stages can include changing any one or more parameters of the build component or one or more of its constituents, changing any one or more of the functions themselves (e.g., by swapping one function for a different function), changing, modifying, or replacing the input to the build component, and / or changing any other aspect of the build component that affects the parameters of how the physics-based model is built. In this way, between two build stages, certain (some) aspects of the build component, including any of its constituent components, can be changed while other aspects of the build component can remain the same. Changing the configuration of the build component between one or more of the multiple build stages is an important new feature of the embodiments described herein because, as further described herein, this ability allows existing knowledge obtained through previous stages to be retained and utilized when advantageous and makes the build component suitable for the parameters being built. Changing the configuration of the build component can be further performed as described herein.

[0044] In an additional embodiment, the objective function used in at least one of the multiple stages is replaced with a different objective function in at least another stage of the multiple stages. For example, the cascade optimization stages described above can be performed as described above, but a different objective function is used for each stage (or one or more of the stages). In this case, the objective function for each stage can be constructed in such a way that it has a relatively strong response to the subset of internal model parameters being optimized during that stage.

[0045] In another embodiment, the results generated by a physics-based model in one of the multiple stages are input into the objective function in a subsequent stage of the multiple stages, and at least one weight of the reference data in one of the multiple stages and in a subsequent stage of the multiple stages is different. Figure 3 An embodiment of BO with a generalized objective function is shown. As Figure 3As shown, in this embodiment, in order to be able to use existing simulation results, the objective function 300 is divided into several components: the reference data 304 to be fitted, the generated model data 306, and a set of weights 302 for each piece of reference data. The surrogate function 308 and the acquisition function 310 can be configured as further described herein. In this embodiment, instead of retaining the surrogate function from the previous optimization phase, all the generated model data from each phase can be retained. At the start of each optimization phase, all the previously generated model data is compared with reference data using weights different from those of the previous phase. This retention and use of the previously generated model data allows the objective function to change for each optimization phase, thereby tailoring the objective function according to the subset of parameters optimized in that phase, while still allowing the use of previous simulation results to inform the surrogate function.

[0046] In one embodiment, the acquisition function used in at least one of the multiple phases is replaced with a different acquisition function in at least one other of the multiple phases. For example, an embodiment can use cascaded optimization phases such that different acquisition functions can be used for each (or one or more) of the optimization phases. By balancing the optimization exploration of the parameter space with the tendency to converge to a local minimum, the acquisition function used has a relatively strong effect on the optimization result. Allowing different acquisition functions enables tuning each phase to the specific requirements of that optimization phase.

[0047] In some embodiments, the reference data used in at least one of the multiple phases is replaced with different reference data in subsequent phases of the multiple phases. For example, an embodiment can use the cascaded optimization phases described herein, but include multiple information sources in the objective function of one or more phases. In one such embodiment, the reference data and the different reference data result in different computational complexities of the physics-based model. In this context, different information sources are typically different reference data sources, which result in different computational complexities of the model. For example, one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) reference data require significantly different computational times for the model and can thus be considered different information sources. In another such embodiment, the reference data is a computationally more efficient source for the physics-based model compared to the different reference data. When there are multiple information sources, it is preferably to run the most computationally efficient source first.

[0048] In some embodiments, the surrogate function is configured to provide an upper bound on the predicted target function value for different values of one or more parameters in the parameter space. The results of the faster information source can be used to fit the surrogate function in such a way that it provides an upper bound on the predicted target function value for the locations in the parameter space. In this case, the objective function should be constructed such that each information source contributes a positive definite fraction to the total objective value. Thus, if one of the information sources results in a relatively low objective value, there is no need to evaluate the more computationally demanding information source at that location. In other words, when there is a relatively "low" objective value, this indicates that the error is relatively high for the combination of the information source and the tested parameters. Therefore, it is less meaningful to evaluate the more computationally demanding information source at that location because you already know that the parameter values are likely (or definitely) not "good", and thus it is better to move to a different region of the parameter space to obtain the next parameter to be evaluated. The next set of parameters selected for evaluation can be evaluated using the same information source or the next information source. In other words, if a faster model is evaluated and the parameter under investigation is found to be "bad" (which has a relatively low objective value), then it can be determined that if a slower model is evaluated, the result will still be bad. Therefore, there is no reason to run the slower model.

[0049] Another embodiment uses multiple information sources in a manner different from that previously described. In this embodiment, different reference data sources with different computational complexities are used in a nested optimization mode. In another embodiment, the objective function and the surrogate function used in at least one of the multiple stages are replaced with different objective functions and different surrogate functions, respectively, in subsequent stages of the multiple stages. For example, each information source described above can use its own independent objective and surrogate functions. In this embodiment, the faster computing information source is nested within the slower one.

[0050] In a further embodiment, the acquisition function used in one or more of at least one of the plurality of stages is replaced in a subsequent stage of the plurality of stages with a different acquisition function, and the different acquisition function samples surrogate functions and different surrogate functions to select additional values. For example, there may be a different acquisition function for each information source (or two or more information sources), but for each information source, the acquisition functions are not completely independent. The i-th acquisition function samples <=i pairs of surrogate functions from all (or at least one or more) information sources to determine the next sampling point of the i-th objective function. The acquisition function balances the information sources such that points from faster information sources that are 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 discarded in the hope of finding better parameters at another location in the parameter space. However, this scenario is different in that you incorporate information from a fast model, i.e., in the objective function in the embodiments described above or in the acquisition function in this embodiment. In both cases, the results are similar, and for parameters known to be "bad", the slower model is not run.

[0051] Figure 4 Shows an embodiment of multi-scale nested BO. The first stage of the cascaded BO technique uses an acquisition function 1 (400), an objective function 1 (402), and a surrogate function 1 (404), which can be configured according to any of the embodiments described herein, and uses a first information source ( Figure 4 not shown in the figure) to perform BO.

[0052] The second stage of the cascaded BO technique uses an acquisition function 2 (406), an objective function 2 (408), a surrogate function 2 (410), and optionally the surrogate function 1 (404), which can be configured according to any of the embodiments described herein, and uses a second information source different from the first information source ( Figure 4 not shown in the figure) to perform BO. For example, for a physics-based model, the second information source may have a greater computational complexity than the first information source. In other words, the second information source may have higher computational requirements and be slower to compute than the first information source. Different from the first stage, in the second stage, the input of the acquisition function 2 may include the outputs of the surrogate function 1 and the surrogate function 2.

[0053] The last stage (and possibly the third stage) of the cascaded BO technique uses an acquisition function N (412), an objective function N (414), a surrogate function N (416), and optionally the surrogate function 1 (404) and / or the surrogate function 2 (410), which can be configured according to any of the embodiments described herein, and uses a third information source different from the first and second information sources ( Figure 4BO is performed without being shown (in the figure). For example, for a physics-based model, the third information source may have a higher computational complexity than the first and second information sources. In other words, the third information source may require more computation and be slower to compute than the first and second information sources. Different from the first and second stages, in the last stage (and possibly the third stage), the input to the acquisition function N may include the outputs of surrogate functions 1, 2, … N. In this way, in all stages except the first stage, the acquisition function may sample the surrogate functions from all information sources (i.e., all previous stages). Thus, although each of the acquisition functions 1, 2, … N may be different for each different information source, for each information source, the acquisition functions are not completely independent.

[0054] The embodiments described herein may be combined in any suitable manner. Any or all of the optimization stages 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 another embodiment, the surrogate function is configured as an ML model. For example, at the beginning or during the process of the optimization procedure described in any of the above embodiments, the objective function may be replaced with an ML model. Similarly, the surrogate function may also be replaced with an ML model. The objective functions and surrogate functions described herein may have any suitable ML configuration and architecture known in the art.

[0055] The embodiments described herein have several important advantages over other currently used methods and systems for building physics-based models. For example, the embodiments described herein enable the optimization of multiple information sources, which makes the computation more efficient and faster. Additionally, the cascaded optimization with the history described herein requires fewer total simulation runs to achieve a similar overall optimization result. Furthermore, using different objective functions for different optimization stages results in better optimization of parameters that may have a relatively low sensitivity in the overall objective function.

[0056] In microelectronic manufacturing, the challenges of the development process that enable the continuous reduction of the critical dimension (CD) of features are increasing. These challenges not only increase the time for the optimization process in relatively large-scale manufacturing but also increase the associated research and development costs. The embodiments described herein utilize the capabilities of physical modeling to speed up the solution time when obtaining higher levels of detail, which can help users shorten the development time and reduce the research and development costs. For these techniques to be effective, it is crucial to accurately calibrate the basic physical model according to the consumer reference materials. Additionally, the embodiments described herein are capable of calibrating computational models that are more precise and complex than previously possible models.

[0057] The advantages described above and other advantages described herein are provided by several important novel features of the embodiments described herein. One such feature includes the ability to use previous results in multi-stage optimization. Additionally, the embodiments described herein may be configured to re-evaluate the objective function for each stage of the optimization to allow the use of previous results to inform new surrogate functions. Further, the embodiments described herein may be configured to utilize multiple information sources to reduce the computational resources used to evaluate the objective function at each point in the parameter space.

[0058] The following examples are described herein to facilitate and further understand some of the embodiments described herein. These examples are not intended to limit the spirit and scope of the invention described in the claims following this section by virtue of their inclusion in this section.

[0059] Several steps that can be performed in the workflow presented in the example are now described. In step 1, an embodiment described herein or another method or system may generate a physical model of an etching process to match a set of reference data for etching a target with a mask of different materials in a plasma etching environment. For this example, the reference data includes two information sources: the overall etch rate (1D data) of the two materials involved and the sidewall etch profile (3D data) of a cylindrical etch feature. Within the sidewall etch profile, there are three main features that are of concern for process optimization: the mask profile, the feature etch depth, and target "bowing" (the etch feature widens at a certain etch depth). These features are Figure 5 shown schematically as a function of feature height 502 and critical dimension 504. In this example, the reference data 500 includes the mask profile 506, the bowing profile 508, and the profile etch depth 510.

[0060] In step 2, a computer subsystem, component, and / or setup component may divide the optimization process into stages. In this case, the optimization is divided into Figure 6 the four stages shown in. The first stage is for obtaining the correct feature etch depth by tuning only the internal model parameters that are expected to be strongly expressed in this objective, and the objective function includes only non-zero weights for the reference data representing this process feature. For example, as Figure 6 shown in, after stage 1 (604), the model data 602 (shown by the dashed line in all stages illustrated in Figure 6 and the reference data 600 (shown by the solid line in all stages illustrated in Figure 6 converge at the bottom of the feature height shown by the profile etch depth 510 in Figure 5 . As Figure 6 shown in, after stage 1, a significant difference between the reference data and the model data is evident in all other parts of the reference data except near the profile etch depth.

[0061] In the second stage, for optimizing the mask profile, internal parameters and objective function terms are selected to focus on this purpose. As Figure 6 shown, after stage 2 (606), the model data and the reference data converge in the mask profile 506 section of the reference data shown in Figure 5 . As Figure 6 shown, after stage 2, the model and the reference data are somewhat different near the profile etch depth (more different than after stage 1), which can be remedied in the following stages. The third stage similarly focuses on feature bending. As Figure 6 shown, after stage 3 (608), the model data and the reference data converge well in the bent profile 508 section of the reference data shown in Figure 5 . The fourth and final stage includes all possible internal model parameters and objective terms. As Figure 6 shown, after stage 4 (610), the model data is generally close to the reference data at all data points in the reference data. Since the surrogate function at the start of this stage has been fit to all the data from the previous stages, the optimization is much more successful than a single-step optimization using the same objective function.

[0062] In step 3, the computer subsystem, components, and / or the setup components can divide the objective function into different information sources. In this case, 1D (overall etch rate) and 3D (etch profile) data are considered different information sources. The 1D information source can be used in each of the four optimization stages to speed up the evaluation of the objective function. For each call of the objective function in the optimization loop, the overall etch rate can be simulated first. This calculation is generally very fast (about a few seconds). If the overall etch rate is close enough to the reference value to produce a generally high objective value, then the 3D simulation will be run. Then the full value of the objective function is used to fit the surrogate function at this point in the parameter space. If the overall etch rate is not relatively close to the reference data, resulting in a generally low objective value, then this value is used to provide an upper bound for the surrogate function at this location in the parameter space. Then the function is called with the new surrogate function to find the next sampling point without running the 3D profile at the previous point.

[0063] In some embodiments, a computer subsystem is configured to store information of an established physics-based model. The computer subsystem may be configured to store the information in a recipe or by generating a recipe for a process that will use the established physics-based model. As used herein, the term "recipe" generally can be defined as a set of instructions that can be used by a tool to perform a process that includes simulations performed by the established physics-based model. In this way, generating a recipe may include generating information on how the process will be performed, which information can then be used to generate instructions for performing the process. The information for the established physics-based model stored by the computer subsystem may include any information that can be used to identify and / or use the established physics-based model (e.g., for example, a file name and its storage location, and the file may contain information for the established physics-based model, such as model parameter values, etc.).

[0064] The computer subsystem may be configured to store the information for the established physics-based model in any suitable computer-readable storage medium. The information may be stored together with any results and / or data described herein and may be stored in any manner known in the art. The storage medium may include any storage medium described herein or any other suitable storage medium known in the art. After the information has been stored, the information may be accessed in the storage medium and used by any method or system embodiment described herein, formatted for display to a user, used by another software module, method, or system, etc. For example, the embodiments described herein may generate a recipe as described above. Then, a system or method (or another system or method) may store and use the recipe to perform a process that includes simulations performed by the established physics-based model.

[0065] The embodiments described herein and / or other systems and methods may use the results and information generated by the established physics-based model in various ways. Such functions include, but are not limited to: changing a process in a feedback or feedforward manner, such as a manufacturing process or step that has been or will be performed on a sample. The change to the process may include any suitable change to one or more parameters of the process. The computer subsystem described herein may determine such changes in any suitable manner known in the art.

[0066] Next, the change may be sent to a semiconductor manufacturing system (not shown) or a computer subsystem and a storage medium (not shown) accessible to the semiconductor manufacturing system. The semiconductor manufacturing system may or may not be part of the system embodiments described herein. For example, the computer subsystem described herein may be coupled to the semiconductor manufacturing system via, for example, one or more common components (such as a housing, a power supply, etc.). The semiconductor manufacturing system may include any semiconductor manufacturing system known in the art, such as a lithography tool, an etching tool, a chemical mechanical polishing (CMP) tool, a deposition tool, and the like. The semiconductor manufacturing related systems may also be systems for different processes described herein, such as electronic design automation (EDA) tools, inspection tools, metrology tools, defect inspection tools, device repair tools, etc. Such tools and systems may include any such tools and systems known in the art.

[0067] Each embodiment of each of the systems described above may be combined together into a single embodiment.

[0068] Another embodiment relates to a computer-implemented method for building a physics-based model. The method includes comparing results generated by a physics-based model that describes a semiconductor manufacturing related process with different values of one or more parameters of the physics-based model to reference data and generating an output in response to a 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 based on different values of one or more parameters. Additionally, the method includes selecting additional values of one or more parameters for the physics-based model based on the surrogate function using an acquisition function. The objective function, the surrogate function, and the acquisition function are included in a build component. The build component and the physics-based model are included in one or more components executed by one or more computer systems. The build component is configured to build the physics-based model in multiple stages, and in each of the multiple stages, only a subset of all one or more parameters of the physics-based model is built.

[0069] Each step of the method may be performed as further described herein. The method may further include any other steps that may be performed 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. One or more components may also be configured according to any of the embodiments described herein. The method may be performed by any of the system embodiments described herein.

[0070] Additional embodiments relate to a non-transitory computer-readable medium that stores program instructions executable on one or more computer systems for performing a computer-implemented method for building a physics-based model. One such embodiment is shown in Figure 7 asFigure 7 As shown in Figure 7 , the non-transitory computer-readable medium 700 includes program instructions 702 that can be executed on a computer system 704. The computer-implemented method can include any steps of any method described herein.

[0071] The program instructions 702 for implementing the methods described herein, for example, can be stored on the computer-readable medium 700. The computer-readable medium can be a storage medium, such as a magnetic disk or an optical disk, a magnetic tape, or any other suitable non-transitory computer-readable medium known in the art.

[0072] The program instructions can be implemented in any of a variety of ways, including program-based techniques, component-based techniques, and / or object-oriented techniques, etc. For example, as needed, ActiveX controls, C++ objects, JavaBeans, Microsoft Foundation Classes (MFC), SSE (Streaming SIMD Extensions), or other techniques or methods can be used to implement the program instructions.

[0073] The computer system 704 can be configured according to any of the embodiments described herein.

[0074] In view of this description, further modifications and alternative embodiments of various aspects of the present invention will be apparent to those skilled in the art. For example, a system and method for establishing a physics-based model are provided. Accordingly, this description is to be construed as illustrative only and is used to teach those skilled in the art the general manner of implementing the present invention. It is to be understood that the forms of the present invention shown and described herein are to be taken as the presently preferred embodiments. The elements and materials described herein can be replaced with available elements and materials, the parts and processes can be reversed, and certain features of the present invention can be utilized independently, all of which will be apparent to those skilled in the art after benefiting from this description of the present invention. Changes can be made to the elements described herein without departing from the spirit and scope of the present invention as described in the appended claims.

Claims

1. A system configured to build a physics-based model, comprising: One or more computer subsystems; And One or more components executed by the one or more computer subsystems, wherein the one or more components include a physics-based model and a building component that describes a process related to semiconductor manufacturing, and wherein the building component includes: An objective function configured to compare results generated by the physics-based model with different values of one or more parameters of the physics-based model to reference data and to generate an output in response to a difference between the results and the reference data; A surrogate function configured to approximate the objective function and fit to the output generated by the objective function based on the different values of the one or more parameters; and An acquisition function configured to select additional values of the one or more parameters for the physics-based model based on the surrogate function; and Wherein the building component is configured to build the physics-based model in multiple stages, and in each of the multiple stages, only a subset of all of the one or more parameters of the physics-based model is built; Wherein, based on the subsets of all of the one or more parameters of the physics-based model built in at least two of the multiple stages, the configuration of the building component is changed between the at least two of the multiple stages; Wherein the objective function and the surrogate function used in at least one of the multiple stages are replaced with different objective functions and different surrogate functions, respectively, in subsequent stages of the multiple stages; and Wherein the acquisition function used in one or more of the at least one of the multiple stages is replaced with a different acquisition function in subsequent stages of the multiple stages, and wherein the different acquisition function samples the surrogate function and the different surrogate function to select the additional values.

2. The system according to claim 1, wherein the building component is further configured to perform Bayesian optimization techniques, and wherein the multiple stages are cascaded optimization stages.

3. The system according to claim 1, wherein each of the multiple stages is performed based on an output generated by any previously performed stage of the multiple stages.

4. The system according to claim 1, wherein the input to the building component includes multiple information sources.

5. The system according to claim 1, wherein the additional values selected by the acquisition function in a first one of the multiple stages are used by the objective function as values of the one or more parameters of the physics-based model in a second one of the multiple stages.

6. The system according to claim 1, wherein the objective function is constant in two or more of the multiple stages.

7. The system according to claim 1, wherein in each of the plurality of stages, establishing only the subset of all of the one or more parameters of the physics-based model includes inputting the selected additional values into the objective function until the optimal values of the subset of all of the one or more parameters of the physics-based model that maximizes the objective function are found.

8. The system according to claim 1, wherein the surrogate function fitted in the first of the plurality of stages is used in the second of the plurality of stages.

9. The system according to claim 1, wherein the result generated by the physics-based model in the first of the plurality of stages is input into the objective function in the second of the plurality of stages, and wherein at least one weight of the reference data in the first of the plurality of stages and in the second of the plurality of stages is different.

10. The system according to claim 1, wherein the reference data used in at least one of the plurality of stages is replaced with different reference data in subsequent stages of the plurality of stages.

11. The system according to claim 10, wherein the reference data and the different reference data result in different computational complexities of the physics-based model.

12. The system according to claim 10, wherein for the physics-based model, the reference data is a more computationally efficient source than the different reference data.

13. The system according to claim 12, wherein the surrogate function is further configured to provide an upper bound on the predicted objective function values for the locations of the different values of the one or more parameters in the parameter space.

14. The system according to claim 1, wherein the objective function is further configured as a machine learning model.

15. The system according to claim 1, wherein the surrogate function is further configured as a machine learning model.

16. The system according to claim 1, wherein the semiconductor manufacturing-related process is a lithography process.

17. The system according to claim 1, wherein the semiconductor manufacturing-related process is an etching process.

18. A non-transitory computer-readable medium storing program instructions executable on one or more computer systems for performing a computer-implemented method for establishing a physics-based model, wherein the computer-implemented method includes: comparing results generated by a physics-based model describing a semiconductor manufacturing-related process with different values of one or more parameters of the physics-based model to reference data and generating an output in response to a difference between the results and the reference data using an objective function; fitting a surrogate function configured as an approximation of the objective function to the output generated by the objective function based on the different values of the one or more parameters; and Using an acquisition function to select additional values of the one or more parameters for the physics-based model based on the surrogate function, wherein the objective function, the surrogate function, and the acquisition function are included in a build component, and wherein the build component and the physics-based model are included in one or more components executed by the one or more computer systems; and wherein the build component is configured to build the physics-based model in multiple stages, and in each of the multiple stages, only a subset of all the one or more parameters of the physics-based model is built; wherein, based on the subsets of all the one or more parameters of the physics-based model built in at least two of the multiple stages, the configuration of the build component is changed between the at least two of the multiple stages; wherein the objective function and the surrogate function used in at least one of the multiple stages are replaced with different objective functions and different surrogate functions, respectively, in subsequent stages of the multiple stages; and wherein the acquisition function used in one or more of the at least one of the multiple stages is replaced with a different acquisition function in subsequent stages of the multiple stages, and wherein the different acquisition function samples the surrogate function and the different surrogate function to select the additional values.

19. A computer-implemented method for building a physics-based model, comprising: Comparing results generated by a physics-based model describing a semiconductor manufacturing-related process with different values of one or more parameters of the physics-based model to reference data and generating an output in response to a difference between the results and the reference data using an objective function; Fitting a surrogate function configured as an approximation of the objective function to the output generated by the objective function based on the different values of the one or more parameters; And Using an acquisition function to select additional values of the one or more parameters for the physics-based model based on the surrogate function, wherein the objective function, the surrogate function, and the acquisition function are included in a build component, and wherein the build component and the physics-based model are included in one or more components executed by one or more computer systems; and wherein the build component is configured to build the physics-based model in multiple stages, and in each of the multiple stages, only a subset of all the one or more parameters of the physics-based model is built; wherein, based on the subsets of all the one or more parameters of the physics-based model built in at least two of the multiple stages, the configuration of the build component is changed between the at least two of the multiple stages; wherein the objective function and the surrogate function used in at least one of the multiple stages are replaced with different objective functions and different surrogate functions, respectively, in subsequent stages of the multiple stages; and wherein the acquisition function used in one or more of the at least one of the plurality of stages is replaced in a subsequent stage of the plurality of stages with a different acquisition function, and wherein the different acquisition function samples the surrogate function and the different surrogate function to select the additional value.

Images