Method and system for chemical mechanical polishing a wafer

Abstract

Methods and systems for chemically mechanical polishing a wafer are provided. The method comprises the following steps: providing formula data for defining a formula for a first model trained by formula samples; obtaining a first removal amount from the first model; providing wafer data defining the wafer and recipe data to a second model trained by the recipe sample and the wafer sample; obtaining a second removal amount from the second model; and estimating a wafer removal amount resulting from the chemical mechanical polishing based on the first removal amount and the second removal amount.

Description

Cross Reference to Related Applications

[0001] This application claims priority to Korean Patent Application No. 10-2024-0094614, filed on July 17, 2024, in the Korean Intellectual Property Office, the entire disclosure of which is incorporated herein by reference. TECHNICAL FIELD

[0002] The present disclosure relates to a method and system for chemical mechanical polishing of a wafer. BACKGROUND

[0003] A semiconductor process includes various sub-processes for manufacturing an integrated circuit. Parameters for performing the sub-processes can be defined to obtain a desired result. For example, a polishing process can be performed on a wafer on which a die is formed, and parameters of the polishing process can be defined to uniformly remove a desired amount of layer material from the wafer. To achieve high integration and / or performance, the size of a device included in an integrated circuit can be reduced, the structure of the integrated circuit can become complex, and the material constituting the device can change. Accordingly, the complexity of the sub-processes can increase, and thus it can be difficult to accurately define the parameters of the sub-processes. SUMMARY

[0004] The present disclosure provides a method and system that accurately estimate a removal amount by modeling chemical mechanical polishing (CMP) and provide parameters required for the chemical mechanical polishing based on the estimated removal amount, enabling a CMP apparatus to more effectively achieve a desired material removal from a wafer.

[0005] According to an aspect of the present disclosure, there is provided a method of modeling chemical mechanical polishing applied to a wafer, including: providing recipe data defining a recipe to a first model trained by a recipe sample; obtaining a first removal amount from the first model; providing wafer data defining the wafer and the recipe data to a second model trained by the recipe sample and a wafer sample; obtaining a second removal amount from the second model; and estimating a removal amount of the wafer resulting from the chemical mechanical polishing based on the first removal amount and the second removal amount.

[0006] According to another aspect of the present disclosure, there is provided a system of modeling chemical mechanical polishing applied to a wafer, the system including: a non-transitory storage medium configured to store instructions; and at least one processor configured to access the non-transitory storage medium, wherein the at least one processor is configured to provide recipe data defining a recipe to a first model trained by a recipe sample, obtain a first removal amount from the first model, provide wafer data defining the wafer and the recipe data to a second model trained by the recipe sample and a wafer sample, obtain a second removal amount from the second model, and estimate a removal amount of the wafer resulting from the chemical mechanical polishing based on the first removal amount and the second removal amount, by executing the instructions.

[0007] According to another aspect of the disclosure, a method of modeling chemical mechanical polishing applied to a wafer is provided, including: obtaining a recipe sample, a wafer sample, and a removal amount sample; training a first model based on the recipe sample and the removal amount sample; and training a second model based on the recipe sample, the wafer sample, the removal amount sample, and a first removal amount sample obtained from the trained first model, wherein the second model is trained such that a sum of a first removal amount obtained from the second model and a second removal amount corresponds to the removal amount sample.

[0008] Embodiments of the disclosure can provide one or more technical advantages. For example, a CMP model-based modeling method and system according to the disclosure can be employed to determine a polishing recipe that allows a CMP apparatus to accurately remove a specified amount of material from a target wafer. The CMP model can include a first model based on the Preston equation that takes into account relative velocity between a pad and the target wafer, pressure on the target wafer, and process environmental factors (e.g., a polishing agent) to estimate a removal amount. In addition, the CMP model can include a second model that takes into account other factors not covered by the Preston equation, such as wafer conditions (e.g., a thickness distribution of the target wafer). Thus, a more accurate estimate of the CMP removal amount can be obtained with the comprehensive modeling method provided by the disclosure. The CMP model can also output a suitable CMP recipe that enables the CMP apparatus to more effectively achieve the desired material removal from the wafer. BRIEF DESCRIPTION OF DRAWINGS

[0009] The embodiments will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:

[0010] Figure 1 FIG. is an example of a sub-process;

[0011] Figure 2 FIG. is an example modeling of chemical mechanical polishing;

[0012] Figure 3 FIG. is an example chemical mechanical polishing model;

[0013] Figure 4 FIG. is an example of a model based on the Preston equation;

[0014] Figure 5 FIG. is an example of a search recipe;

[0015] Figure 6 FIG. is a flowchart of an example method of chemical mechanical polishing modeling;

[0016] Figure 7 FIG. is a flowchart of an example method of chemical mechanical polishing modeling;

[0017] Figure 8is a flowchart of an example method of chemical mechanical polishing modeling;

[0018] Figure 9 is a graph of an example result of chemical mechanical polishing modeling;

[0019] Figure 10 is a flowchart of an example method of chemical mechanical polishing modeling;

[0020] Figure 11 is a flowchart of an example method of chemical mechanical polishing modeling;

[0021] Figure 12 is a flowchart of an example method of chemical mechanical polishing modeling;

[0022] Figure 13 is a block diagram of an example computing system; and

[0023] Figure 14 is a block diagram of an example system. DETAILED DESCRIPTION

[0024] Figure 1 is an example graph of sub-processes according to some embodiments. For example, Figure 1 An example of chemical mechanical polishing (CMP) 10 as a sub-process included in a semiconductor process is shown. A semiconductor process for manufacturing an integrated circuit can include a series of sub-processes, and a wafer 11 can be processed by using a series of sub-processes. For example, a front-end-of-line (FEOL) can include planarizing and cleaning a wafer, forming a trench, forming a well, forming a gate electrode, and forming a source and a drain, and by using the FEOL, individual devices such as transistors, capacitors, resistors, etc. can be formed on a substrate. Also, a back-end-of-line (BEOL) can include, for example, silicidation of gate regions, source regions, and drain regions, adding dielectric materials, planarizing, forming holes, adding metal layers, forming vias, forming a passivation layer, etc., and by using the BEOL, the individual devices such as transistors, capacitors, resistors, etc. can be connected to each other. In some embodiments, a middle-of-line (MEOL) can be performed between the FEOL and the BEOL, and a contact can be formed on the individual devices. A plurality of dies can be separated from the wafer 11, each of the plurality of dies can be packaged in a semiconductor package, and can be used as a component for various applications.

[0025] As one of the sub-processes included in a semiconductor process, the CMP 10 can be performed to remove a desired amount of layer material from the wafer 11. As shown in FIG. 1, the CMP 10 can include a polishing pad 12, a polishing head 14, and a polishing liquid 16. The polishing pad 12 can be a pad made of a material such as a polymer, and can be used to polish the wafer 11. The polishing head 14 can be a head that can be used to press the wafer 11 against the polishing pad 12, and can be used to polish the wafer 11. The polishing liquid 16 can be a liquid that can be used to polish the wafer 11, and can be used to polish the wafer 11. Figure 1As shown, in the CMP 10, the wafer 11 can be attached to a polishing head 12. The polishing head 12 can be rotated with respect to a Z-axis as a center, and pressure can be applied to the wafer 11 in a -Z direction. A pad 14 can be attached to a chuck 13, and the chuck 13 can be rotated with respect to the Z-axis as a center. A polishing agent 15 can be applied on the pad 14, and the wafer 11 can be disposed on the polishing agent 15. Accordingly, a surface of the wafer 11 exposed in the -Z-axis direction can be polished.

[0026] A performance of the CMP 10 can be evaluated by a surface flatness of the wafer 11 as a result product, i.e., a profile of the wafer 11. For example, the profile can indicate a thickness of the wafer 11 (or a layer material) along a line passing through a center of the wafer 11. Here, the profile of the wafer 11 can be simply referred to as a profile. The wafer 11 can include a plurality of dies (or chips), and a poor surface flatness can fatally affect a yield and a performance of an integrated circuit.

[0027] In the CMP 10, a Preston equation can define a removal rate (RR), as shown in Equation 1 below.

[0028] [Equation 1]

[0029] In Equation 1, P indicates pressure applied to the wafer 11 in the -Z-axis direction by the polishing head 12, V indicates a relative speed between the polishing head 12 and the pad 14, and K p indicates a Preston coefficient (herein, can be referred to as an environment coefficient) defining a process environment including the polishing agent 15. In other words, in the CMP 10, the removal rate RR of the wafer 11 can be proportional to the pressure P and the relative speed V.

[0030] To achieve high integration and / or high performance, devices included in an integrated circuit can have a reduced size and a complex structure, and materials constituting the devices can be changed. Accordingly, a complexity of the CMP 10 can increase, and an amount of layer material removed from the wafer 11 by the CMP 10, i.e., a removal amount, can be affected by various parameters as well as the above-described pressure P and the relative speed V, and cannot be simply determined by the Preston equation. Accordingly, it can not be easy to determine a recipe of the CMP 10, i.e., parameters defining the CMP 10. Here, the removal amount can be referred to as a removal amount of the profile of the wafer 11 caused by using the CMP 10, and can indicate, for example, an amount removed along a line intersecting a center of the wafer 11.

[0031] As described below with reference to the accompanying drawings, a CMP 10 can be modeled considering various parameters, and a removal amount generated by the CMP 10 can be accurately estimated. Accordingly, a recipe of the CMP 10 for a desired profile of the wafer 11 can be easily derived, and a cost required to design the CMP 10 can be reduced. Further, performance and reliability of an integrated circuit manufactured through a semiconductor process including the CMP 10 designed according to the recipe can be improved.

[0032] Figure 2 is a diagram of CMP modeling according to some embodiments. As described above with reference to Figure 1 , the CMP 10 can be modeled as a CMP model 21, and accordingly, a removal amount corresponding to a given recipe and wafer can be estimated. Further, a recipe providing a desired removal amount, i.e., a candidate recipe D24, can be provided by using the CMP model 21. Hereinafter, a description is made with reference to Figure 1 Figure 2 .

[0033] With reference to Figure 2 , the recipe data D21 and the wafer data D22 can be provided to the CMP model 21. The recipe data D21 can be referred to as data defining a recipe of the CMP 10. For example, the recipe data D21 can include values of parameters of the CMP 10, and the CMP 10 can be defined by parameters having values contained in the recipe data D21. The wafer data D22 can be referred to as data defining the wafer 11 provided to the CMP 10. For example, the wafer data D22 can include values of thickness of layer materials measured along a diameter of the wafer 11, i.e., a profile of the wafer 11 before the CMP 10.

[0034] The CMP model 21 can generate removal amount data D23 from the recipe data D21 and the wafer data D22 based on machine learning. For example, as described below with reference to Figure 10 , removal amount samples can be obtained by applying recipe samples and wafer samples to the CMP 10, and the CMP model 21 can have been trained by the recipe samples, the wafer samples, and the removal amount samples. As described below with reference to Figure 3 , the CMP model 21 can include a model based on a Preston equation and a model based on a hidden component, and the removal amount data D23 can represent a removal amount generated by the CMP 10 with high accuracy. An example of the CMP model 21 will be described below with reference to Figure 3 .

[0035] A search recipe 22 for a recipe providing a desired removal amount can be performed. As Figure 2 ​As shown, the search recipe 22 can be executed based on the removal amount data D23 provided by the CMP model 21. The search recipe 22 can generate recipe data D21 based on the removal amount data D23, provide the generated recipe data D21 to the CMP model 21, and can determine a recipe, i.e., a candidate recipe D24, that provides a desired removal amount. The CMP 10 can be designed according to the candidate recipe D24, and a wafer 11 having a desired profile can be manufactured by using the CMP 10. The following will be described with reference to Figure 5 An example of the search recipe 22 is described.

[0036] In some embodiments, the modeling of the CMP 10 can be implemented by an arbitrary computing system. For example, each block shown in the figures herein can correspond to hardware, software, or a combination of hardware and software included in a computing system. In some embodiments, the hardware can include at least one of programmable components, such as a central processing unit (CPU), a digital signal processor (DSP), a graphics processing unit (GPU), and a neural network processing unit (NPU), a reconfigurable component such as a field programmable gate array (FPGA), and a component providing a fixed function such as an intellectual property (IP) block. In some embodiments, the software can include at least one of a series of instructions executable by the programmable components and a code convertible to a series of instructions by a compiler, and can be stored in a non-transitory storage medium.

[0037] Figure 3 is a diagram of a CMP model 30 according to some embodiments. For example, Figure 3 An example of the CMP model 21 in Figure 2 is shown. As described above with reference to Figure 2 The CMP model 30 can generate removal amount data D35 from recipe data D31 and wafer data D32. As Figure 3 shown, the CMP model 30 can include a first model 31 and a second model 32. Descriptions basically the same as those given with reference to Figure 2 are omitted. Figure 3

[0038] The first model 31 can generate first removal amount data D33 from the recipe data D31. For example, as will be described below with reference to Figure 11 The first model 31 can be trained by recipe samples and removal amount samples corresponding to the recipe samples, as will be described below with reference to Figure 4 ​To be described, the first model 31 can include a model for inferring a Preston coefficient (i.e., an environmental coefficient), and can generate first removal amount data D33 representing a removal amount based on a Preston equation. Here, the first model 31 can be referred to as a model based on a Preston equation, and the removal amount represented by the first removal amount data D33 can be referred to as a first removal amount. Hereinafter, the first model 31 will be mainly described with reference to a neural network, but embodiments are not limited thereto. Figure 4 An example of the first model 31 will be described.

[0039] The second model 32 can generate second removal amount data D34 from the recipe data D31 and the wafer data D32. For example, as described below with reference to Figure 12 To be described, the second model 32 can be in a state that the second model 32 is trained with a recipe sample, a wafer sample, an output sample (i.e., a first removal amount sample) of the trained first model 31, and a removal amount sample. As described above with reference to Figure 1 As described, the CMP 10 cannot be interpreted using only the Preston equation, and the second model 32 can infer a component that the Preston equation cannot interpret. Here, the second model 32 can be referred to as a hidden component model, and the removal amount represented by the second removal amount data D34 can be referred to as a second removal amount.

[0040] The CMP model 30 can include an adder 33, and the adder 33 can generate removal amount data D35 by adding the first removal amount represented by the first removal amount data D33 and the second removal amount represented by the second removal amount data D34. In other words, the removal amount represented by the removal amount data D35 can include the first removal amount inferred based on the Preston equation and the second removal amount obtained by the hidden component. Accordingly, the CMP model 30 can accurately estimate a removal amount generated by the CMP 10 from given recipe data D31 and wafer data D32.

[0041] Each of the first model 31 and the second model 32 can include a machine learning model, and the machine learning model can have an arbitrary structure, which can be trained by using, for example, backpropagation, a Lagrange multiplier method, etc., and using sample data or training data. For example, the machine learning model can include an artificial neural network, a decision tree, a support vector machine, and / or a Bayesian network, etc. Hereinafter, the machine learning model will be mainly described with reference to an artificial neural network, but embodiments are not limited thereto. As non-limiting examples, the artificial neural network can include a convolutional neural network (CNN), a region-based (R) CNN (R-CNN), a region proposal network (RPN), a recurrent neural network (RNN), a stack-based (S) deep neural network (DNN) (S-DNN), a state (S)-space (S) DNN (S-SDNN), a deconvolutional network, a deep belief network (DBN), a fully convolutional network, a long short-term memory (LSTM) network, etc.

[0042] Figure 4 This is a diagram illustrating examples of models based on the Preston equations according to some implementations. For example, Figure 4 The first model 40 is shown as Figure 3 Example of Model 31 in the first model. See above for reference. Figure 3 As described above, the first model 40 can generate first removal amount data D42 from the formula data D41. In the following text, reference will be made to... Figure 1 describe Figure 4 .

[0043] Reference Figure 4 The formulation data D41 may include environmental data ED, pressure data PD, and speed data VD. Environmental data ED may define parameters other than pressure data PD and speed data VD, which will be described below with reference to CMP 10. For example, environmental data ED may include the characteristics and temperature of the polishing agent 15 applied to pad 14. Pressure data PD may define the pressure applied to wafer 11 using polishing head 12. In some embodiments, polishing head 12 may apply non-uniform pressure, i.e., different pressures, to each area. For example, as... Figure 4 As shown in the distribution W1, pressure can be applied depending on the distance from the center of wafer 11. Velocity data VD can define the relative velocity between pad 14 and polishing head 12. For example, the surface of wafer 11 can be... Figure 1 The planes including the X and Y axes are parallel, and the relative velocity can be defined as a function f. v As shown in Formula 2 below.

[0044] [Formula 2]

[0045] In Formula 2, x and y can represent coordinates in a Cartesian coordinate system, RPM p This can represent the revolutions per minute of pad 14, PRM h This can represent the number of revolutions per minute of the polishing head 12, and r cc This can represent the distance between the center point of pad 14 and the center point of polishing head 12. In some embodiments, such as... Figure 4 As shown in distribution W2, the relative velocity can have a distribution that depends on the distance from the center of pad 14.

[0046] The first model 40 may include an environmental model 41 and a multiplier 42. Since the pressure data PD and velocity data VD are user-known, configurable parameters, a Preston coefficient (i.e., an environmental coefficient) may be needed to calculate the removal rate using the Preston equation defined in Formula 1. The environmental model 41 can generate the environmental coefficient EC from the recipe data D41, which includes environmental data ED, pressure data PD, and velocity data VD. For example, see the following reference... Figure 11 The environmental model 41 described herein may have been trained using recipe samples and removal quantity samples. The multiplier 42 generates the first removal quantity data D42 by multiplying the environmental coefficient EC, the pressure represented by the pressure data PD, and the relative velocity represented by the velocity data VD. Since the first removal quantity represented by the first removal quantity data D42 is positive, the environmental coefficient may also be positive, and in some embodiments, the environmental model 41 may include an activation function with a positive output. For example, the environmental model 41 may include activation functions such as the Rectified Linear Unit (ReLU) and the Sigmoid function.

[0047] Figure 5 This is a diagram based on a search formula 50 according to some implementation methods. See above for reference. Figure 2 The search formulation 50 can generate formulation data D54 from the removal amount data D51 provided by the CMP model 21, and can provide the formulation data D54 back to the CMP model 21. When the formulation data D54 provides the desired profile, the search formulation 50 can identify the formulation defined by the formulation data D54 as a candidate formulation. In the following, reference will be made to... Figure 1 describe Figure 5 .

[0048] like Figure 5 As shown, the search recipe 50 may include an optimization algorithm 51. The optimization algorithm 51 may generate recipe data D54 from the removal amount data D51 based on a predefined objective function D52 and constraints D53. For example, the optimization algorithm 51 may generate recipe data D54 that minimizes the value of the objective function D52 while satisfying constraints D53. In some implementations, CMP may be designed to minimize the non-uniformity (NU) as defined in Equation 3 below.

[0049] [Formula 3]

[0050] In Formula 3, RA can represent the amount removed. avg S can represent the average amount removed. RAThe standard deviation of the removal amount can be represented, and max(RA) and min(RA) can represent the maximum and minimum values ​​of the removal amount, respectively. Since NU, as defined in Equation 3, decreases as the denominator (i.e., the average value of the removal amount) increases, when Equation 3 itself is used as the objective function, optimization algorithm 51 may optimize in the over-polishing direction of wafer 11. To prevent over-polishing, two objective functions can be defined, namely the first objective function f... o1 Second objective function f o2 As shown in Formula 4 below.

[0051] [Formula 4]

[0052] In Formula 4, RA est It can represent the estimated removal amount, and can be defined by the removal amount data D51 provided by CMP model 21. RA tar This can represent the desired amount of removal (or contour) using CMP. As shown in Equation 4, the first objective function f o1 It can be based on the estimated distribution of the removal amount, and the second objective function f o2 This can be based on the difference between the estimated removal amount and the target removal amount. Optimization algorithm 51 can search for a value that satisfies the first objective function f. o1 Second objective function f o2 Minimum removal amount and the corresponding formulation.

[0053] Constraint D53 can be defined for the stability of CMP. For example, constraint D53 can be defined as making the recipe searched using optimization algorithm 51 a true recipe applicable to actual CMP. In some implementations, constraint D53 can be defined based on the ratio of the amount removed to the hidden component. For example, the first constraint C1 and the second constraint C2 can be defined as shown in Equation 5 below.

[0054] [Formula 5]

[0055] In Formula 5, RA2 can represent the second removal amount, and can be derived from... Figure 3The second removal amount data D34 provided by the second model 32 is used to define the second removal amount. The first threshold THR1 and the second threshold THR2 can be predefined constants. Accordingly, a recipe in which the ratio of hidden components satisfies the first threshold THR1 or greater can be searched by the first constraint C1, while a recipe in which the ratio of hidden components satisfies the second threshold THR2 or less can be searched by the second constraint C2. In some embodiments, constraint D53 may include only one of the first constraint C1 and the second constraint C2. In some embodiments, when the first threshold THR1 is less than or equal to the second threshold THR2, constraint D53 may include both the first constraint C1 and the second constraint C2.

[0056] Optimization algorithm 51 may include any optimization algorithm that uses a given CMP model 21 to provide multi-objective optimization included in the objective function D52 while satisfying constraint D53 and searching for a recipe. For example, optimization algorithm 51 may also include genetic algorithms, such as the non-dominated sorting genetic algorithm (NSGA2), and may include population-based algorithms, such as particle swarm optimization.

[0057] Figure 6 This is a flowchart of CMP modeling method S60 according to some implementation methods. For example... Figure 6 As shown, the CMP modeling method S60 may include multiple operations S61 to S65. In some implementations, the following methods can be used: Figure 3 CMP model 30 is used to execute Figure 6 Method S60. In the following text, reference will be made to... Figure 1 and Figure 3 describe Figure 6 .

[0058] Reference Figure 6 In operation S61, the formulation data D31 can be provided to the first model 31. As described above with reference to the accompanying drawings, the first model 31, as a model based on the Preston equation, can be trained using formulation samples and removal amount samples. The formulation data D31 can include parameters defining CMP 10. For example, as described above with reference to... Figure 4 The formulation data D31 may include parameters representing the process environment, such as the pressure applied by the polishing head 12 to the wafer 11, the relative speed between the polishing head 12 and the pad 14, and the polishing agent 15.

[0059] In operation S62, a first removal amount can be obtained from the first model 31. For example, the first model 31 can generate first removal amount data D33 from the formula data D31 provided in operation S61, and the first removal amount data D33 can represent the first removal amount. As described above with reference to the accompanying drawings, the first removal amount can correspond to an estimated removal amount based on the Preston equation. The following will refer to... Figure 7Describe an example of operation S62.

[0060] In operation S63, recipe data D31 and wafer data D32 can be provided to the second model 32. As described above with reference to the accompanying drawings, the second model 32, as a hidden component-based model, can be trained using wafer samples, recipe samples, and removal amount samples. As mentioned above, recipe data D31 includes parameters defining CMP 10, while wafer data D32 can include parameters defining the state of wafer 11. For example, wafer data D32 can include the outline of wafer 11 before performing CMP 10.

[0061] In operation S64, a second removal amount can be obtained from the second model 32. For example, the second model 32 can generate second removal amount data D34 from the recipe data D31 and wafer data D32 provided in operation S63, and the second removal amount data D34 can represent the second removal amount. As described above with reference to the accompanying drawings, the second removal amount can correspond to the removal amount not resolved by the Preston equation, i.e., the removal amount based on the hidden component.

[0062] In operation S65, the amount of material removed from wafer 11 can be estimated. For example, CMP model 30 may include adder 33, which can generate removal amount data D35 by adding the first removal amount obtained in operation S62 and the second removal amount obtained in operation S64, and the removal amount data D35 can represent the estimated removal amount. Accordingly, the estimated removal amount may include a first removal amount based on the Preston equation and a second removal amount based on hidden components.

[0063] Figure 7 This is a flowchart of method S70 for modeling CMP according to some implementation methods. For example, Figure 7 The flowchart shows Figure 6 An example of operation S62 in the example. See above for reference. Figure 6 As mentioned above, in Figure 7 In method S70, the first removal amount can be obtained from the first model 31. For example... Figure 7 As shown, method S70 may include multiple operations S71 to S73. In some embodiments, the following can be used: Figure 4 The first model 40 is used for execution. Figure 7 Method S70. In the following text, reference will be made to... Figure 1 and Figure 4 right Figure 7 Describe it.

[0064] Reference Figure 7 In operation S71, the formula data D41 can be provided to the environmental model 41, and in operation S72, the environmental coefficient EC can be obtained from the environmental model 41. For example, as referred to above...Figure 4 The first model 40 may include an environmental model 41, which may have been trained with formulation samples and removal amount samples to generate the Preston coefficient, i.e., the environmental coefficient EC, corresponding to the formulation data D41.

[0065] In operation S73, a first removal amount can be calculated. For example, the first model 40 may include a multiplier 42, and the multiplier 42 can calculate the first removal amount by multiplying the pressure and relative velocity extracted from the formula data D41 by the environmental factor EC obtained in operation S72, and can generate first removal amount data D42 representing the first removal amount. See below for reference. Figure 11 As will be described, an environmental model 41 can be trained to reduce the difference between the first removal amount and the removal amount sample, and the trained environmental model 41 can infer the environmental coefficient EC from the formulation data D41.

[0066] Figure 8 This is a flowchart of method S80 for modeling CMP according to some implementation methods. For example, Figure 8 The flowchart shows Figure 2 Example of searching recipe 22. See above for reference. Figure 2 The above, Figure 8 Method S80 can use CMP model 21 to search for formulation data D21 that provides the desired removal amount, and can determine candidate formulations D24. For example... Figure 8 As shown, method S80 may include multiple operations S81 to S83. In some embodiments, Figure 8 Method S80 can be Figure 5 An example of searching recipe 50 is provided below. Figure 5 describe Figure 8 .

[0067] Reference Figure 8 In operation S81, the value of a first objective function can be calculated. For example, the objective function D52 provided to the optimization algorithm 51 may include a first objective function based on the distribution of the amount removed. In some embodiments, the first objective function may include the standard deviation of the estimated amount removed as shown in Formula 4, or the difference between the maximum and minimum values ​​of the estimated amount removed. The optimization algorithm 51 can calculate the value of the first objective function corresponding to the estimated amount removed represented by the amount removed data D51, and the value of the first objective function may represent the distribution of the estimated amount removed.

[0068] In operation S82, the value of a second objective function can be calculated. For example, the objective function D52 provided to the optimization algorithm 51 may include a second objective function based on the difference between the amount removed and the target amount removed. In some embodiments, the second objective function may be defined as the estimated Euclidean distance between the amount removed and the target amount removed, as shown in Equation 4. The optimization algorithm 51 can calculate the value of the second objective function corresponding to the amount removed data D51 and the predefined target amount removed, and the value of the second objective function may represent the error between the estimated amount removed and the target amount removed.

[0069] In operation S83, candidate formulations can be determined. For example, optimization algorithm 51 can generate formulation data D54 to minimize the value of the first objective function calculated in operation S81 and the value of the second objective function calculated in operation S82, and formulation data D54 can be provided to CMP model 21. Furthermore, constraint D53 can be provided to optimization algorithm 51, and optimization algorithm 51 can generate formulation data D54 to satisfy constraint D53. In some implementations, constraint D53 can be defined based on the ratio of the amount removed to the hidden component, as shown in Equation 5. Reference will be made below. Figure 9 Describe the changes in the estimated removal amount based on constraint D53.

[0070] Figure 9 This is a diagram illustrating examples of the results of CMP modeling based on some implementation methods. For example, Figure 9 The figure in the image illustrates the estimated removal amounts in two scenarios. (See figure for example.) Figure 9 As shown, the estimated removal amount can include a first removal amount RA1 based on the Preston equation and a second removal amount RA2 caused by the hidden components.

[0071] In the first case, CASE1, the optimization algorithm can search for the recipe under unconstrained conditions, where the constraint is defined based on the ratio of removal caused by the hidden components, as shown in Equation 5. In the second case, CASE2, the optimization algorithm can search for the recipe according to a constraint defined based on the ratio of removal caused by the hidden components, as shown in Equation 5. Figure 9 As shown, compared to the removal amount estimated in the second case (CASE2), the removal amount estimated in the first case (CASE1) may include a second removal amount RA2 with a higher ratio. In other words, the second removal amount RA2 in the second case (CASE2) can be limited by constraints to restrict the estimation caused by the hidden component. Users can adjust the proportion of the second removal amount caused by the hidden component by adjusting the expected threshold in Formula 5.

[0072] Figure 10 This is a flowchart of a CMP modeling method S100 according to some implementation methods. For example, Figure 10 The flowchart shows the trainingFigure 2 The method for CMP model 21. As described above with reference to the accompanying drawings, CMP model 21 can be trained using formulation samples, wafer samples, and removal amount samples. Figure 10 As shown, method S100 may include multiple operations S101 to S103. In some embodiments, using Figure 10 Method S100 can be trained Figure 3 CMP model 30. See below for reference. Figure 3 describe Figure 10 .

[0073] Reference Figure 10 In operation S101, recipe samples, wafer samples, and removal amount samples can be obtained. Sample data can be collected for training the CMP model 30, and sample data can be generated by performing CMP. For example, CMP can be performed using recipe samples and wafer samples, and removal amount samples, i.e., contour samples, can be obtained from wafers that have already undergone CMP processing.

[0074] In operation S102, a first model 31 can be trained. For example, the first model 31 can be trained based on a recipe sample and a removal amount sample. The recipe sample can be provided to the first model 31, and the first model 31 can be trained such that the first removal amount generated by the first model 31 corresponds to the removal amount sample. As described above with reference to the accompanying drawings, the first model 31 may include a model based on the Preston equation, and unlike the second model 32 described below, the first model 31 can be trained independently of the wafer samples. The following will refer to... Figure 11 Describe an example of operation S102.

[0075] In operation S103, a second model 32 can be trained. For example, the second model 32 can be trained based on recipe samples, removal amount samples, and wafer samples. Recipe samples and wafer samples can be provided to the second model 32, and the second model 32 can generate a second removal amount. The second model 32 can be trained not only based on the second removal amount but also based on the first removal amount generated by the first model 31. As described above with reference to the accompanying drawings, the second model 32 can include a model based on hidden components, and unlike the first model 31 described above, the second model 32 can be trained based on wafer samples. The following will refer to... Figure 12 Describe an example of operation S103.

[0076] Figure 11 This is a flowchart of CMP modeling method S110 according to some implementation methods. For example, Figure 11 The flowchart shows Figure 10 An example of operation S102 in the above reference. Figure 10As described, method S110 can train the first model, namely the model based on the Preston equation. For example... Figure 11 As shown, method S110 may include multiple operations S111 to S113. In some embodiments, this can be achieved by using... Figure 4 The first model 40 in the model executes method S110. See below for reference. Figure 4 describe Figure 11 .

[0077] Reference Figure 11 In operation S111, a formula sample can be provided to environmental model 41, and in operation S112, an environmental coefficient sample can be obtained from environmental model 41. For example, as described above... Figure 4 The first model 40 may include an environmental model 41. The Preston equation may require Preston coefficients, i.e., environmental coefficients EC, as well as pressure and relative velocity, and can be trained to generate Preston coefficients, i.e., environmental coefficients EC, corresponding to the formulation.

[0078] In operation S113, the environment model 41 can be trained. As described above, the environment model 41 can generate environmental coefficient samples corresponding to the formulation samples. The first removal amount sample based on the Preston equation can be calculated as the product of the environmental coefficient sample and the pressure and relative velocity included in the formulation sample, and the environment model 41 can be trained to reduce the difference between the first removal amount sample and the removal amount sample. In some embodiments, the environment model 41 may include an artificial neural network and can be trained via backpropagation.

[0079] Figure 12 This is a flowchart of CMP modeling method S120 according to some implementation methods. For example, Figure 12 The flowchart shows Figure 10 An example of operation S103 in the above example. (Refer to the above example.) Figure 10 As described, method S120 can train a second model, namely a model based on hidden components. For example... Figure 12 As shown, method S120 may include multiple operations S121 to S125. In some embodiments, method S120 may train... Figure 3 The second model 32. See below for reference. Figure 3 describe Figure 12 .

[0080] Reference Figure 12 In operation S121, a recipe sample can be provided to the first trained model 31, and in operation S122, a first removal amount sample can be obtained from the first trained model 31. (Refer to the above...) Figure 11The first model 31 may include an environment model, and the environment model can be trained to generate Preston coefficients, i.e., environment coefficients, from the recipe. The second model 32 can be trained based on a first removal sample provided by the first model 31, which includes the trained environment model (i.e., the trained first model 31). Accordingly, the first model 31 may have been trained before the second model 32 is trained, and during the training of the second model 32, the first model 31 may be fixed, and the parameters of the first model 31 may remain unchanged.

[0081] In operation S123, a formula sample and a wafer sample can be provided to the second model 32, and in operation S124, a second removal amount sample can be obtained from the second model 32. As described above with reference to the accompanying drawings, the second removal amount sample can correspond to the removal amount caused by the hidden component.

[0082] In operation S125, a second model 32 can be trained. For example, the first removal amount sample obtained in operation S122 and the second removal amount sample obtained in operation S124 can be added together, and the second model 32 can be trained, for example, based on a loss function, to reduce the difference between the sum of the first and second removal amounts and the removal amount samples corresponding to the formulation sample and the wafer sample.

[0083] Figure 13 This is a block diagram illustrating a computing system 130 according to some embodiments. In some embodiments, Figure 13 The computing system 130 can train the machine learning model used in CMP modeling as described above with reference to the accompanying drawings, and can be called a CMP modeling system, training system, etc.

[0084] The computing system 130 can represent any system, including general-purpose or special-purpose computing systems. For example, the computing system 130 may include a personal computer, a server computer, a laptop computer, a home appliance, etc. Figure 13 As shown, the computing system 130 may include at least one processor 131, memory 132, storage system 133, network adapter 134, input / output (I / O) interface 135, and display 136.

[0085] At least one processor 131 can execute program modules including computing system executable instructions. Program modules may include routines, programs, objects, components, logic, data structures, etc., that perform specific tasks or implement specific abstract data types. Memory 132 may include computing system readable media in the form of volatile memory, such as random access memory (RAM). At least one processor 131 can access memory 132 and execute instructions loaded on memory 132. Storage system 133 can non-transitory store information and includes at least one program product comprising program modules configured to perform training on a machine learning model to model the CMP described above with reference to the accompanying drawings in some embodiments. The program may include an operating system, at least one application, other program modules, and program data, as non-limiting examples.

[0086] Network adapter 134 provides access to a local area network (LAN), a wide area network (WAN), and / or a public network (e.g., the Internet). Input / output interface 135 provides a communication channel with peripheral devices (e.g., a keyboard, pointing device, and audio system). Display 136 can output various information, allowing the user to recognize different information.

[0087] In some implementations, the training of the machine learning model for pattern clustering described above with reference to the accompanying drawings can be implemented as a computational program product. The computational program product may include a non-transitory computer-readable medium (or storage medium) comprising computer-readable program instructions for allowing at least one processor 131 to perform image processing and / or model training. As a non-limiting example, the computer-readable instructions may include assembly instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in at least one programming language.

[0088] Computer-readable media can include any type of media capable of non-transitory storage and preservation of instructions executable by at least one processor 131 or any instruction-executable device. Computer-readable media can include, but is not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any combination thereof. For example, computer-readable media can include portable computer floppy disks, hard disks, RAM, ROM, electrically erasable programmable ROM (EEPROM), flash memory, static RAM (SRAM), compact discs (CDs), digital versatile discs (DVDs), memory sticks, floppy disks, mechanical encoding devices (e.g., punched cards), or any combination thereof.

[0089] Figure 14This is a block diagram of system 140 according to some embodiments. In some embodiments, CMP modeling according to some embodiments can be performed in system 140.

[0090] Reference Figure 14 System 140 may include at least one processor 141, memory 143, artificial intelligence (AI) accelerator 145, and hardware (HW) accelerator 147, and the at least one processor 141, memory 143, AI accelerator 145, and hardware accelerator 147 may communicate with each other via bus 149. In some embodiments, at least one processor 141, memory 143, AI accelerator 145, and hardware accelerator 147 may also be included in a single semiconductor chip. Furthermore, in some embodiments, at least two of the at least one processor 141, memory 143, AI accelerator 145, and hardware accelerator 147 may also be included in each of two or more semiconductor chips mounted on a board.

[0091] At least one processor 141 can execute instructions. For example, at least one processor 141 can also run an operating system by executing instructions stored in memory 143, or it can also execute an application running on the operating system. In some embodiments, at least one processor 141 can instruct the AI ​​accelerator 145 and / or the hardware accelerator 147 to perform tasks by executing instructions, and can also obtain the results of task execution from the AI ​​accelerator 145 and / or the hardware accelerator 147. In some embodiments, at least one processor 141 may include a dedicated instruction set processor (ASIP) tailored for a specific purpose, and may also support dedicated instruction sets.

[0092] The memory 143 can have any structure for storing data. For example, the memory 143 may also include volatile storage devices such as dynamic RAM (DRAM) and static RAM (SRAM), or it may include non-volatile storage devices such as flash memory and resistive RAM (RRAM). At least one processor 141, AI accelerator 145, and hardware accelerator 147 can store data in the memory 143 or read data from the memory 143 via bus 149.

[0093] AI accelerator 145 may represent hardware designed for AI applications. In some embodiments, AI accelerator 145 may include an NPU for implementing neuromorphic architectures, capable of generating output data by processing input data provided by at least one processor 141 and / or hardware accelerator 147, and capable of providing output data to at least one processor 141 and / or hardware accelerator 147. In some embodiments, AI accelerator 145 may be programmable and can be programmed by at least one processor 141 and / or hardware accelerator 147.

[0094] Hardware accelerator 147 can represent hardware designed to perform specific tasks at high speed. For example, hardware accelerator 147 can be designed to perform data transformations at high speed, such as demodulation, modulation, encoding, and decryption. Hardware accelerator 147 can be programmable and can be programmed by at least one processor 141 and / or hardware accelerator 147.

[0095] In some embodiments, AI accelerator 145 can execute the machine learning model described above with reference to the accompanying drawings. For example, AI accelerator 145 can execute each layer included in the machine learning model described above. AI accelerator 145 can generate an output including useful information by processing input parameters, feature maps, etc. Furthermore, in some embodiments, at least some of the models executed by AI accelerator 145 can be executed by at least one processor 141 and / or hardware accelerator 147.

[0096] While this disclosure contains numerous specific implementation details, these should not be construed as limiting the scope of claims. In a single embodiment, specific features described in the context of a standalone implementation may also be combined and implemented. Conversely, different features described in a single embodiment may also be implemented individually in multiple embodiments, or in appropriate sub-combinations. Furthermore, although features may be described above as functioning in certain combinations, one or more features from a combination may be removed from the combination in some cases, and the combination may be for sub-combinations or variations thereof.

[0097] Although this disclosure has been specifically shown and described with reference to embodiments thereof, it should be understood that various changes in form and detail may be made therein without departing from the spirit and scope of the appended claims.

Claims

1. A method for chemical mechanical polishing of a wafer, the method comprising: At least one computing device is used to provide recipe data defining the recipe to a first model, which is trained using recipe samples; The first removal amount is obtained from the first model using the at least one computing device; The at least one computing device is used to provide a second model with wafer data defining the wafer and the recipe data, the second model being trained using the recipe samples and wafer samples; The second removal amount is obtained from the second model using the at least one computing device; The estimated amount of material removed by chemical mechanical polishing for the wafer is calculated using the at least one computing device and based on the first amount of material removed and the second amount of material removed; as well as Chemical mechanical polishing is performed on the wafer based on the estimated removal amount.

2. The method according to claim 1, wherein, The formulation data includes at least one of the following: Pressure data, defining the pressure applied to the wafer; Speed ​​data, defining the relative speed between the pad and the wafer; or Environmental data, defining the process environment including the polishing agent.

3. The method according to claim 2, wherein, The first model includes an environment model trained using the recipe samples, and Obtaining the first removal amount includes: The recipe data is provided to the environmental model; Obtain environmental coefficients from the environmental model; and The first removal amount is calculated based on at least one of the environmental factor, the pressure data, or the velocity data.

4. The method according to claim 3, wherein, Calculating the first removal amount includes multiplying the environmental factor, the pressure, and the relative velocity together.

5. The method according to claim 3, wherein, The environment model includes activation functions that output values ​​greater than or equal to zero.

6. The method according to claim 1, wherein, The second model is trained based on a loss function, which is based on a first amount of samples removed and a second amount of samples removed. Wherein, the first model is configured to generate the first removal amount sample based on the formula sample, and The second model is configured to generate the second removal amount sample based on the formula sample and the wafer sample.

7. The method according to claim 1, comprising: Candidate formulations are searched based on the estimated removal amount. Among them, the candidate recipes to be searched include: A first objective function is calculated based on the distribution of the estimated removal amount on the wafer; A second objective function is calculated based on the difference between the estimated removal amount and the target removal amount; and The candidate formulation is derived from the first objective function and the second objective function based on the optimization algorithm.

8. The method according to claim 7, wherein, Derivation of the candidate formulation includes applying constraints to the optimization algorithm, the constraints being defined by the estimated removal amount and the second removal amount.

9. The method of claim 7, comprising: The wafer is chemically and mechanically polished according to the candidate formulation.

10. A non-transitory storage medium for storing instructions, which, when executed by at least one processing device, cause the at least one processing device to perform the method according to any one of claims 1 to 9.

11. A system for chemical mechanical polishing of a wafer, the system comprising: Non-transitory storage media, configured as storage instructions; as well as At least one processor is configured to access the non-transitory storage medium and execute the instructions to perform: Provide the first model with recipe data that defines the recipe, the first model being trained using recipe samples; The first removal amount is obtained from the first model; The second model is provided with wafer data defining the wafer and the recipe data, the second model being trained using the recipe samples and wafer samples; The second removal amount is obtained from the second model; Based on the first removal amount and the second removal amount, the removal amount of the wafer by chemical mechanical polishing is estimated; as well as The wafer is subjected to chemical mechanical polishing based on the estimated removal amount.

12. The system according to claim 11, wherein, The formulation data includes at least one of the following: Pressure data, defining the pressure applied to the wafer; Speed ​​data, defining the relative speed between the pad and the wafer; or Environmental data, defining the process environment including the polishing agent.

13. The system according to claim 12, wherein, The first model includes an environment model trained using the recipe samples, and Wherein, the at least one processor is configured to, in order to obtain the first removal amount: The recipe data is provided to the environmental model; Environmental coefficients are obtained from the environmental model; and The first removal amount is calculated based on at least one of the environmental coefficient, the pressure data, or the velocity data.

14. The system according to claim 13, wherein, The at least one processor is configured to calculate the first removal amount by multiplying the environmental factor, the pressure, and the relative velocity together.

15. The system according to claim 11, wherein, The second model is trained based on a loss function, which is based on a first amount of samples removed and a second amount of samples removed. Wherein, the first model is configured to generate the first removal amount sample based on the formula sample, and The second model is configured to generate the second removal amount sample based on the formula sample and the wafer sample.

16. The system according to claim 11, wherein, The at least one processor is further configured to search for candidate formulations based on the estimated removal amount, and The at least one processor is configured to search for the candidate recipes: Based on the estimated distribution of the amount of material removed on the wafer, a first objective function is calculated; Based on the difference between the estimated removal amount and the target removal amount, a second objective function is calculated; and The candidate formulation is derived from the first objective function and the second objective function based on the optimization algorithm.

17. A method for modeling chemical mechanical polishing, the method comprising: Obtain formulation samples, wafer samples, and removal amount samples; Based on the formula sample and the removal amount sample, train the first model; Based on the formula sample, the wafer sample, the removal amount sample, and the first removal amount sample generated by the trained first model, a second model is trained. Wherein, the second model is trained such that the sum of the first removal sample generated by the trained first model and the second removal sample generated by the second model corresponds to the removal sample; The first and second trained models are used to determine the formulation, and the wafer is chemically mechanically polished based on the formulation.

18. The method according to claim 17, wherein, The formulation sample includes at least one of the following: Pressure sample, defining the pressure applied to the wafer; Velocity sample, defining the relative velocity between the pad and the wafer; or Environmental sample, defining the process environment including the polishing agent.

19. The method according to claim 18, wherein, Training the first model includes: Provide the formula sample to the environmental model; Obtain environmental coefficient samples from the environmental model; and The environmental model is trained such that the product of the environmental coefficient sample, the pressure sample, and the velocity sample corresponds to the removal amount sample.

20. The method of claim 17, wherein, Training the second model includes: The recipe sample is provided to the first model being trained; The first removal sample is generated from the first trained model; The formulation sample and the wafer sample are provided to the second model; and The second model is trained such that the sum of the first removal sample generated by the first model and the second removal sample generated by the second model corresponds to the removal sample.

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