Simulation method for semiconductor device, electronic equipment and storage medium

Abstract

The embodiment of the invention relates to a simulation method for a semiconductor device, electronic equipment and a storage medium. The method comprises the following steps: determining a simulation value of the surface height of a ground wafer based on a time step and a corresponding grinding rate; determining a correction term related to the grinding rate based on a comparison of the simulation value and a target value such that a difference between the simulation value corresponding to the correction term and the target value becomes small; and determining the simulation value corresponding to the correction term as the height value of the surface of the ground wafer in response to the condition that the difference meets the preset condition. According to the technical scheme, the simulation precision and the prediction fitting capability of the simulation model can be remarkably improved.

Description

Technical Field

[0001] Embodiments of the present disclosure generally relate to integrated circuits, and more particularly, to simulation methods, electronic devices, and storage media for semiconductor devices. Background Art

[0002] The current prediction of metal thickness after the chemical mechanical polishing (CMP) back-end process usually relies heavily on the CMP model.

[0003] In traditional solutions, a pure physical model is derived through intuitive physical mechanisms. However, when encountering certain complex situations and process conditions, the modeling accuracy is somewhat insufficient, making it impossible to accurately predict the situation after CMP polishing. Summary of the invention

[0004] According to example embodiments of the present disclosure, a simulation scheme for a semiconductor device is provided to at least partially overcome the above or other potential drawbacks.

[0005] According to one aspect of the present disclosure, a simulation method for a semiconductor device is provided. The method includes: determining a simulation value of the surface height of a wafer after grinding based on a time step and a corresponding grinding rate; determining a correction term related to the grinding rate based on a comparison between the simulation value and a target value so that the difference between the simulation value corresponding to the correction term and the target value becomes smaller; and in response to the difference satisfying a predetermined condition, determining the simulation value corresponding to the correction term as the height value of the surface of the wafer after grinding.

[0006] In a second aspect of the present disclosure, an electronic device is provided. The electronic device includes a processor; and a memory coupled to the processor, the memory having instructions stored therein, and when the instructions are executed by the processor, the device performs an action, the action including: determining a simulation value of the surface height of the wafer after grinding based on a time step and a corresponding grinding rate; determining a correction term related to the grinding rate based on a comparison between the simulation value and the target value, so that the difference between the simulation value corresponding to the correction term and the target value becomes smaller; and in response to the difference satisfying a predetermined condition, determining the simulation value corresponding to the correction term as the height value of the surface of the wafer after grinding.

[0007] In some embodiments, determining a correction term related to the grinding rate based on a comparison between a simulation value and a target value includes: based on graphic feature information, process information, and information of an initial formula for calculating surface height, using a deep learning neural network to determine a correction term to correct the initial formula.

[0008] In some embodiments, the correction term includes at least a polynomial related to one of the following: a width of a pattern within a grid point on the wafer; a spacing between patterns; and a sum of perimeters of each pattern within the grid point.

[0009] In some embodiments, using a deep learning neural network to determine a correction term to correct an initial formula includes: generating a random number at the beginning of each iteration of the neural network; selecting a source of the correction term to correct the initial formula based on a comparison of the random number with a random probability threshold; and determining an updated correction term to correct the initial formula based on the selection using the neural network.

[0010] In some embodiments, determining an updated correction item based on the selection using a neural network to correct the initial formula includes: in response to a first comparison result between a random number and a random probability threshold, selecting a symbol from a symbol library as a correction item to correct the initial formula using a neural network, wherein the symbol library is generated by combining mathematical symbols and a variable library by Cartesian product, and the variable library contains graphic feature information and process information; and in response to a second comparison result between the random number and the random probability threshold, using a neural network to make a prediction to generate a new correction item, and adding the new correction item to the symbol library.

[0011] In some embodiments, using a deep learning neural network to determine correction terms to correct an initial formula includes: generating a bonus term based on simulated values ​​and measured values ​​of the surface height of each grid point; and iterating an array consisting of the initial formula, correction terms, updated formula, and bonus terms as elements of a training sample in a neural network to generate new elements of a training sample.

[0012] In some embodiments, generating a reward item based on the simulated value and the measured value of the surface height of each grid point includes: determining a first difference between the standard deviation of the simulated value and the measured value of the surface height of each grid point; determining a second difference between the RMSE of the simulated value and the measured value of the surface height of each grid point; determining the range between the simulated value and the measured value of the surface height of each grid point; and generating a reward item based on the first difference, the second difference and the range.

[0013] In some embodiments, the iteration includes a prediction phase and a training phase, and wherein: in response to an element generated in each round of iteration of the prediction phase satisfying a first predetermined condition, the round of iteration is terminated, and all elements in the round of iteration are taken as a trajectory; and in response to the number of total trajectories obtained during each round of iteration reaching a predetermined trajectory threshold, the prediction phase is terminated.

[0014] In some embodiments, the first predetermined condition includes: the number of elements generated in each round of iteration reaches a first predetermined threshold; or the value of RMSE in the current iteration is less than a second predetermined threshold.

[0015] In some embodiments, determining the correction term using a deep learning neural network to correct the initial formula includes: in a training phase, training the neural network using training samples in the trajectory to determine the gradient of the loss function of the neural network; and updating the parameters of the neural network based on the gradient of the loss function.

[0016] In some embodiments, training a neural network using training samples in a trajectory to determine the gradient of a loss function of the neural network includes: using a policy gradient algorithm in the field of reinforcement learning to back-propagate the training samples to determine the gradient of the loss function.

[0017] In some embodiments, determining a correction term using a deep learning neural network to correct an initial formula further includes: determining a value of a loss function; in response to the value of the loss function being lower than a predetermined threshold, determining a correction term output by the neural network corresponding to the value of the loss function as a correction term related to the grinding rate; and determining an updated formula based on the determined correction term to determine a height value of the surface.

[0018] In some embodiments, the iteration of the training phase stops when the following conditions are met: the difference in the value of the loss function between two previous iterations is less than a predetermined difference threshold; the absolute value of the ratio of the value of the loss function between two previous iterations is greater than a predetermined ratio threshold; or the number of iterations or the iteration time reaches a maximum iteration threshold.

[0019] In some embodiments, the random probability threshold changes from an initial first probability threshold to a second probability threshold lower than the first probability threshold during the iteration.

[0020] In a third aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the method according to the first aspect of the present disclosure is implemented.

[0021] In a fourth aspect of the present disclosure, a simulation model is provided, which is configured to execute the method according to the first aspect of the present disclosure.

[0022] In a fifth aspect of the present disclosure, a neural network is provided, comprising: a plurality of input layers configured to receive feature information of graphics on a wafer, process information, and an initial formula for calculating the surface height of the wafer after grinding; an intermediate layer configured to execute the method according to the first aspect of the present disclosure to determine an updated formula for calculating a simulation value of the surface height; and an output layer configured to output the updated formula.

[0023] In a fifth aspect of the present disclosure, a method for training a neural network model is provided, comprising: the neural network model makes predictions based on input data to generate training samples, wherein the input data includes graphic feature information, process information, and an initial formula for determining the surface height of a wafer after grinding; the neural network model is trained using the training samples to determine the gradient of a loss function of the neural network model; the parameters of the neural network model are updated based on the gradient of the loss function; and in response to the training satisfying a predetermined condition, the neural network model corresponding to the parameters of the corresponding updated neural network model is determined as a trained neural network model, wherein the trained neural network model outputs an enhanced formula for determining the surface height.

[0024] In some embodiments, the neural network model makes predictions based on input data to generate training samples, including: the neural network model makes predictions based on an initial formula and an initial correction term to generate an update formula and a reward term, wherein the reward term represents a feedback value generated based on the difference between a simulation value of the surface height of the wafer after grinding by the neural network model and a target value; taking an array consisting of the initial formula, the initial correction term, the update formula, and the reward term as a first training sample; and iterating in the neural network model based on the first training sample to generate multiple training samples.

[0025] In some embodiments, a reward item is generated by: determining a first difference between a standard deviation of a simulated value of a surface height at each grid point on a wafer and a standard deviation of a target value; determining a second difference between a root mean square error of a simulated value of a surface height at each grid point and a root mean square error of a target value; determining a range between a simulated value of a surface height at each grid point and the target value; and generating a reward item based on the first difference, the second difference, and the range.

[0026] In some embodiments, in response to samples generated in each round of iteration satisfying a first predetermined condition, the round of iteration is terminated, and all samples in the round of iteration are taken as a trajectory; and in response to the number of total trajectories obtained during each round of iteration reaching a predetermined trajectory threshold, the iteration is terminated.

[0027] In some embodiments, training a neural network model using training samples to determine the gradient of a loss function of the neural network model includes: using a policy gradient algorithm in the field of reinforcement learning to back-propagate the training samples to determine the gradient of the loss function.

[0028] In some embodiments, it also includes: determining the loss function value of the neural network model; and wherein the training satisfies a predetermined condition including: the difference between the loss function values ​​of two previous iterations is less than a predetermined difference threshold; or the absolute value of the ratio of the loss function values ​​of two previous iterations is greater than a predetermined ratio threshold.

[0029] In some embodiments, making predictions based on input data by a neural network model to generate training samples includes: generating a random number at the beginning of each iteration of the neural network; selecting a source of an initial correction term for correcting an initial formula based on a comparison of the random number with a random probability threshold; and determining an updated correction term based on the selection using the neural network to correct the initial formula to generate an updated formula.

[0030] In some embodiments, the method of correcting an initial formula based on selecting an updated correction term determined by using a neural network to generate an updated formula includes: in response to a first comparison result between a random number and a random probability threshold, selecting a symbol from a symbol library as an initial correction term to correct the initial formula using a neural network model, wherein the symbol library is generated by combining mathematical symbols and a variable library by Cartesian product, and the variable library contains graphic feature information and process information; and in response to a second comparison result between the random number and the random probability threshold, using a neural network model to make a prediction to generate an initial correction term, so as to correct the initial formula using the neural network model to generate a new correction term, and adding the new correction term to the symbol library.

[0031] In a sixth aspect of the present disclosure, a neural network model generated according to the method of the fifth aspect is provided.

[0032] It will be understood from the following description that the technical solution of the present disclosure can significantly improve the simulation accuracy and predictive fitting ability of the simulation model.

[0033] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the disclosure, nor is it intended to limit the scope of the disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A schematic diagram showing an example environment in which embodiments of the present disclosure can be implemented; Figure 2 A flowchart of a simulation method for a semiconductor device according to some embodiments of the present disclosure is shown; Figure 3 A schematic diagram showing a cross section of a wafer with grooves according to some embodiments of the present disclosure is shown; Figure 4 A schematic diagram showing a neural network architecture according to some embodiments of the present disclosure; Figure 5 A block diagram of a computing device capable of implementing various embodiments of the present disclosure is shown.

[0035] In the various drawings, the same or corresponding reference numerals represent the same or corresponding parts. DETAILED DESCRIPTION

[0036] The principles of the present disclosure will be described below with reference to the various exemplary embodiments shown in the accompanying drawings. It should be understood that the description of these embodiments is only to enable those skilled in the art to better understand and further implement the present disclosure, and is not intended to limit the scope of the present disclosure in any way. It should be noted that similar or identical reference numerals may be used in the figures where feasible, and similar or identical reference numerals may represent similar or identical functions. Those skilled in the art will readily recognize from the following description that alternative embodiments of the structures and methods described herein may be adopted without departing from the principles of the present invention described herein.

[0037] As used herein, the term "including" and its variations mean open inclusion, i.e., "including but not limited to". Unless otherwise stated, the term "or" means "and / or". The term "based on" means "based at least in part on". The terms "an example embodiment" and "an embodiment" mean "at least one example embodiment". The term "another embodiment" means "at least one additional embodiment". The terms "first", "second", etc. may refer to different or the same objects.

[0038] CMP is a method that combines chemical and physical methods to remove materials. It has become an indispensable step in the modern integrated circuit (IC) industry. Specifically, CMP uses chemical corrosion and mechanical force to flatten silicon wafers or other substrate materials during processing. CMP can achieve nanometer-level material removal, making the wafer surface flat.

[0039] The CMP model, as the name implies, is a physical model for simulating the CMP process. The model outputs some important physical indicators of each grid point of the wafer after the CMP process, such as the thickness of the trench structure, the thickness of the non-trench structure, and the thickness of the metal material after CMP. In simple terms, it is a physical model that predicts the surface morphology of the wafer after the CMP process. CMP is one of the eight major semiconductor processes, connecting the previous and the next. Other processes following CMP will be affected by the CMP process. In other words, when it is necessary to evaluate and control the process results after CMP, it is best to know the impact of the CMP process, which is of great significance to the full process control and yield improvement of the entire semiconductor manufacturing. In addition, the CMP process itself is an indispensable and necessary step, because the CMP process can be better adjusted through the CMP model. For example, the results of the CMP model can be used to infer which process parameter settings need to be modified and adjusted, and whether there are some unreasonable aspects in the design of the Graphic Data System (GDS), which may cause hotspots, that is, defects.

[0040] The metal layer is deposited on the bottom of the groove. As the name implies, the bottom of the groove is the bottom of the groove. In fact, the process flow is to first go through the etching step, that is, to etch the wafer to produce grooves, or to produce the bottom of the groove, and then to carry out the deposition process, which will deposit various materials on the wafer. Because of the etching, and the different areas have different groove depths due to different GDS designs, naturally the stacking height of the materials in each area after deposition will also be different. For example, the most common metal deposition material for CMP is copper. Usually in the last step of deposition, that is, before entering CMP, the material on the top of the wafer is copper, that is, the first step of grinding is copper. Because of the existence of etching, different areas have grooves of different depths and different deposition thicknesses. Therefore, for the surface of the wafer after the CMP process, it is necessary to evaluate the surface morphology, not only to understand how much change has occurred in the CMP step, but also to understand the changes and fluctuations that already existed before CMP.

[0041] In fact, the essence of CMP is to polish the surface of the wafer immersed in the grinding liquid with a grinding head on the base. Simply put, GDS is a data format of the real entity of the wafer in the computer program. The data of a wafer is entered into the program for observation, description and analysis, and it needs to be abstracted into a computer data, that is, a gds file. The GDS file clearly describes the structure and design of the wafer. The wafer in the real world is the GDS in the virtual computer. From a more professional point of view, the GDS layout is a layout file given by the circuit designer, which contains a variety of graphics, that is, patterns, and semiconductor manufacturing is to carve a wafer into the appearance of the layout design through various processes.

[0042] Usually the value at the bottom of the groove is directly identified as a fixed value, or simply some empirical values ​​or mathematical formulas are used to make an etching table, which is obtained by looking up a limited number of values ​​in the etching table. Both the accuracy and adjustability have great limitations. Sometimes the CMP model is changed in order to fit the value that meets the measured metal layer thickness, resulting in the CMP model sacrificing the fitting accuracy of the dishing defect (Dishing) and corrosion (Erosion) indicators. Here, Dishing refers to the difference between the height of the groove structure and the height of the non-groove structure, and Erosion refers to the difference between the height of the non-groove structure at each grid point relative to the reference value thickness.

[0043] In view of this, the present disclosure provides an improved solution.

[0044] Some embodiments of the present disclosure provide an improved simulation method for semiconductor devices. The method includes: determining a simulation value of the height of a wafer surface after grinding based on a time step and a corresponding grinding rate; determining a correction term related to the grinding rate based on a comparison between the simulation value and a target value so that the difference between the simulation value corresponding to the correction term and the target value becomes smaller; and in response to the difference satisfying a predetermined condition, determining the simulation value corresponding to the correction term as the height value of the wafer surface after grinding.

[0045] Some embodiments of the present disclosure also provide a training method for a neural network model. The method includes: the neural network model predicts based on input data to generate training samples, wherein the input data includes graphic feature information, process information, and an initial formula for determining the surface height of the wafer after grinding; the neural network model is trained using the training samples to determine the gradient of the loss function of the neural network model; the parameters of the neural network model are updated based on the gradient of the loss function; and in response to the training satisfying a predetermined condition, the neural network model corresponding to the parameters of the corresponding updated neural network model is determined as a trained neural network model, wherein the trained neural network model outputs an enhanced formula for determining the surface height.

[0046] The technical solution disclosed in the present invention can significantly improve the simulation accuracy and predictive fitting ability of the simulation model.

[0047] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings.

[0048] Figure 1 1 is a schematic diagram of an example environment 100 in which embodiments according to the present disclosure can be implemented. Figure 1 As shown, the example environment 100 includes a computing device 110 and a client 120 .

[0049] In some embodiments, the computing device 110 may interact with the client 120. For example, the computing device 110 may receive an input message from the client 120 and output a feedback message to the client 120. In some embodiments, the input message from the client 120 may be, for example, layout data. The computing device 110 may perform corresponding mathematical operations on the layout data and output corresponding operation results to the client 120.

[0050] In some embodiments, computing device 110 may include, but is not limited to, a personal computer, a server computer, a handheld or laptop device, a mobile device (such as a mobile phone, a personal digital assistant (PDA), a media player, etc.), consumer electronics, a minicomputer, a mainframe computer, cloud computing resources, etc.

[0051] It should be understood that the structure and function of the example environment 100 are described for exemplary purposes only and are not intended to limit the scope of the subject matter described herein. The subject matter described herein can be implemented in different structures and / or functions. The environment is merely illustrative and is not intended to limit the application environment of the embodiments of the present disclosure.

[0052] In order to explain the principle of the disclosed solution more clearly, the following will refer to Figure 2 Let's describe it in more detail.

[0053] Figure 2 A flowchart of a simulation method for a semiconductor device according to some embodiments of the present disclosure is shown.

[0054] At block 202 , a simulated value of a surface height of a wafer after grinding is determined based on a time step and a corresponding grinding rate.

[0055] First, several key elements in some embodiments of the present disclosure are introduced: Element 1: The characteristics of GDS (also called graphic characteristics) mainly refer to the characteristics of density, width, space, and perimeter. Each position on a whole GDS has different GDS characteristics (different density and width values), and different GDS characteristics will greatly affect the height of the morphology of each position after the etching process. In some embodiments, the density of the graphics, the width of the graphics, the spacing between the graphics, and the perimeter of the grid points can be called feature size information. The average spacing between patterns in a grid point is called space, the average width of the pattern itself is called width, and the same is true for the perimeter. The sum of the side lengths of all patterns in a grid point is the perimeter of this grid point.

[0056] In GDS, there are many graphics (patterns), which can be microscopic structures such as circuits. In an area of ​​fixed size, the total area of ​​the graphics divided by the area of ​​the area, the ratio of the two is the density. So the density is a number between 0 and 1. Width is a descriptive statistical indicator to measure the width of the graphics itself in this area. The graphics are usually rectangles or combinations of rectangles. Usually, all the graphics in the area are scanned to obtain their width values, and finally the mean or median is taken as the width value of this area). The interval describes the interval between the graphics in this area, because the graphics themselves are arranged at a certain interval.

[0057] Element 2: Prediction target / simulation object. The simulation is the value of the surface height of each point of the GDS after the CMP process. In addition, the trench height after the etching process is the value of the bottom of the trench, recorded as TB.

[0058] Element 3: Process information table (recipe), which records the process information. Different manufacturers have different process settings, including the duration of the process, start time, end time, unit time step and other related information; as well as various materials and thicknesses obtained by the previous deposition process, and the target height (target thickness) after etching and grinding, etc.

[0059] The CMP physical model refers to a physical formula that uses the features extracted from GDS, usually density, linewidth (width for short), linespace (space for short), perimeter, and process parameters (usually pressure, removal rate of different materials, process time, etc.) to simulate the surface height (Surface Height) after the CMP process.

[0060] In some embodiments, the polishing rate is determined based on characteristic information of patterns on the wafer and parameters related to the polishing rate.

[0061] In some embodiments, a simulation value H1 of the height of the non-trench structure on the wafer can be determined; a simulation value H2 of the height of the trench structure on the wafer can be determined; and a simulation value of the height of the circular surface can be determined based on the simulation value H1, the simulation value H2, and the density of the graphics in the grid area on the wafer. Specifically, the surface height is equal to the height of the non-trench structure multiplied by (1-density) plus the product of the height of the trench structure and the density. The formula is: H1*density+H2*(1-density); where density represents the density of the graphics in the grid area on the wafer, and its range is between 0-1.

[0062] Refer to the following Figure 3 Give a description. Figure 3 A schematic diagram of a cross section of a wafer with trenches according to some embodiments of the present disclosure is shown.

[0063] As mentioned earlier, Dishing is the difference between the height of the trench structure and the height of the non-trench structure, and the specific formula is SThickNT – SthickT. Figure 3 As shown in the figure, D stands for Dishing, SThickNT stands for the height of the non-groove structure, and SthickT stands for the height of the groove structure. In this figure, Dishing is actually the depth of the groove. Figure 3 As shown, the region shown in the wafer includes multiple grooves, that is, an array of grooves. The control region shown on the left has no graphic structure and is a blank test control region specifically used to compare with the region with graphics. However, all the grid points in the model in the embodiment of the present disclosure represent regions with graphics, such as Figure 3 Shown in the middle right part.

[0064] Erosion refers to the difference between the non-groove structure height of each grid point and the reference thickness. The specific formula is field reference thickness. Figure 3 The reference height is shown in Figure 1) - SThickNT (non-trench structure thickness), where the reference value height can be given by the user and is related to the user's respective process settings. Both Dishing and Erosion are important indicators in the CMP model for evaluating process results.

[0065] Back to Figure 2Continue to describe. In some embodiments of the present disclosure, the CMP process is based on a basic physical model and theory. In some embodiments of the present disclosure, the model formula is expanded on the basis of the above theory. The theory is that within a very short time t (usually less than or equal to 0.1s), denoted as dt, the grinding rate is constant, and the groove height at the next moment can be expressed by the following formula: SThickNT(t=t1) = SThickNT(t = t0) – dt*R_NT(t = t0); The non-groove height can be expressed as follows: SThickT(t=t1) = SThickT(t = t0) – dt*R_T(t = t0); In the above formula, R_NT(t = t0) represents the polishing rate of the non-groove structure at time t0. Similarly, the meaning of R_T can be obtained.

[0066] It can be seen that the calculation of R_NT and R_T is the core of the entire CMP physical model. According to the basic model, the polishing rate Rate is strongly related to the actual pressure, and the actual pressure is related to the density.

[0067] For non-groove structures, the most original physical mechanism formula for grinding is: R_NT = P / (1 - density). For groove structures, R_T = P / density. However, in practice, it needs to be corrected, that is, it needs to be corrected with a correction term.

[0068] In some embodiments, the correction term includes at least a polynomial related to one of the following: a width of a pattern within a grid point on the wafer; a spacing between patterns; and a sum of perimeters of each pattern within the grid point.

[0069] In fact, for a non-groove structure, the R_NT at a certain moment is as follows: R_NT = P / (1 - density) * Width correction * Space correction * Perimeter correction.

[0070] For the groove structure, the R_T at a certain moment is as follows: R_T = P / density * Width correction * Space correction * Perimeter correction.

[0071] There is no clear golden standard or undisputed formula for these correction items. Different model developers and different manufacturers have their own different presets. Specifically, the Width correction term refers to a polynomial with Width as the core of the change (or a polynomial related to Width), and the Space correction term and Perimeter correction term are the same. The polynomial can be a linear addition polynomial or a complex polynomial such as an exponential logarithm.

[0072] In some embodiments of the present disclosure, the most advanced deep reinforcement learning technology is used to derive these correction terms based on actual data, thereby expanding the basic physical formula of CMP. In some embodiments, the actual data may include graphic feature information.

[0073] In some embodiments, the pattern feature information may include the following information: the density of the patterns in the grid points on the wafer; the width of the patterns; the intervals between the patterns; and the initial height of the bottom of the trench, and the total perimeter of the patterns in the grid points.

[0074] In the use scenario of the entire model, the so-called point refers to a grid. By extracting the information in a grid point, a data point can be obtained. The so-called measurement point is also this grid point. Strictly speaking, a grid point can be said to be a rectangular area defined based on a certain size (usually between 5um*5um and 20um*20um).

[0075] In some embodiments, the simulated value of the surface height can be determined based on the initial data and initial parameters in the CMP model. In some embodiments, the initial data may include the measurement values ​​of several measurement points (recording the position of each point in the GDS, its corresponding GDS feature, and the height of the trench after etching).

[0076] As can be seen from the above description, the simulation value of the surface height of the wafer after grinding can be determined based on the time step and the corresponding grinding rate. For example, it can be calculated based on the initial physical formula. In fact, it can be determined by determining the initial simulation value by any simulation model.

[0077] In some embodiments, a deep learning neural network is constructed to determine the simulated value of the surface height by randomly generating initial parameters and initial data. A simulated value closer to the measured value can be obtained by iterating the CMP model.

[0078] The simulated value of the determined height may be significantly different from the actual measured value. A simulated value closer to the measured value can be obtained by an improved CMP model.

[0079] At block 204 , a correction term related to the grinding rate is determined based on a comparison of the simulation value with the target value, so that a difference between the simulation value corresponding to the correction term and the target value becomes smaller.

[0080] In some embodiments, an improved CMP model is obtained by deep learning a neural network to determine a correction term related to the polishing rate. In other words, an improved physical formula can be obtained to calculate a simulated value of the surface height.

[0081] In some embodiments, based on the graphic feature information, the process information, and the information of the initial formula for calculating the surface height, a correction term may be determined using a deep learning neural network to correct the initial formula.

[0082] In some embodiments, other neural networks may also be used to determine correction terms related to the polishing rate.

[0083] Deep learning refers specifically to machine learning based on deep neural network models and methods. It is developed based on statistical machine learning, artificial neural network and other algorithmic models, combined with the development of contemporary big data and large computing power. The most important technical feature of deep learning is the ability to automatically extract features. The extracted features are also called deep features or deep feature representations. Compared with manually designed features, deep features have stronger and more robust representation capabilities. Deep neural networks are the model basis for deep learning to automatically extract features. Deep neural networks are essentially a nested series of nonlinear transformations.

[0084] Regarding neural networks, let's first introduce some basic definitions: State, defined as the current physical formula, denoted as S0; Action, the action performed based on the current state S0, specifically defined as the selection of mathematical calculation symbols and variables; S1, the state at the next moment, the state changes after action a is performed on the basis of S0, that is, the new physical formula. R is defined as reward, which means that action a is taken on the basis of state S0, and the state is transferred to the new state S1, and the reward obtained is R. The specific content of R reflects whether the new formula performs better on the data compared to the old formula, and whether the root mean square error (RMSE) is lower. If it is lower, it is a positive reward, and if it is worse, it is a negative reward (actually a penalty). R is a term in reinforcement learning. Reinforcement learning is essentially a series of mathematical-related conceptual models, which do not have actual physical meaning. Reinforcement learning is a specialized field and a branch of deep learning.

[0085] In some embodiments, a deep learning neural network can be built based on a recurrent neural network (RNN) structure as an agent for deriving formulas. It should be understood that the neural network of the embodiment of the present disclosure is not limited to RNN, but can also be other neural networks. The content received by the input end of the RNN neural network can be the characteristics of the GDS, process parameter information, and initial formula information. The network contains several fully connected layers, pooling layers, convolutional layers, etc. The characteristic of RNN is that each fully connected layer contains a gate structure. Compared with ordinary neural networks that receive the output of the previous layer as input to calculate the value of the activation function to determine whether to activate, the gate structure of RNN will also consider the information of the previous layer as an auxiliary input to participate in the calculation of the activation function. The final output of the neural network can be, for example, a symbol (for example, including +-* / , square root, square, logarithm and exponent with base e and related GDS feature variables, etc.), or a complete formula.

[0086] In some embodiments, using a deep learning neural network to determine correction terms to correct an initial formula may include: generating a bonus term based on simulated values ​​and measured values ​​of the surface height of each grid point; and iterating an array consisting of the initial formula, correction terms, updated formula, and bonus terms as elements of a training sample in a neural network to generate new elements of a training sample.

[0087] In some embodiments, training samples can be generated in the following manner: a neural network model makes predictions based on an initial formula and an initial correction term to generate an update formula and a reward term, wherein the reward term represents a feedback value generated based on the difference between a simulation value of the surface height of the wafer after grinding performed by the neural network model and a target value; an array consisting of the initial formula, the initial correction term, the update formula, and the reward term is used as a first training sample; and iteration is performed in the neural network model based on the first training sample to generate multiple training samples.

[0088] In some embodiments, a reward item may be generated by: determining a first difference between a standard deviation of a simulated value of the surface height of each grid point on a wafer and a standard deviation of a target value; determining a second difference between a root mean square error of the simulated value of the surface height of each grid point and a root mean square error of the target value; determining a range between a simulated value of the surface height of each grid point and the target value; and generating a reward item based on the first difference, the second difference, and the range.

[0089] In some embodiments, when the samples generated in each round of iteration meet the first predetermined condition, the round of iteration is terminated, and all samples in the round of iteration are regarded as a trajectory; when the total number of trajectories obtained during each round of iteration reaches a predetermined trajectory threshold, the iteration is terminated.

[0090] In some embodiments, the neural network model is trained using training samples to determine the gradient of the loss function of the neural network model. Specifically, the policy gradient algorithm in the field of reinforcement learning can be used to back-propagate the training samples to determine the gradient of the loss function.

[0091] In some embodiments, iteration using a deep learning neural network may include a prediction phase and a training phase, and wherein: when an element generated in each round of iteration of the prediction phase satisfies a first predetermined condition, the round of iteration is terminated, and all elements in the round of iteration are taken as a trajectory; and when the number of total trajectories obtained during each round of iteration reaches a predetermined trajectory threshold, the prediction phase is terminated. This is further described below.

[0092] In some embodiments, the first predetermined condition may include: the number of elements generated in each round of iteration reaches a first predetermined threshold; or the value of RMSE in the current iteration is less than a second predetermined threshold.

[0093] In some embodiments, the agent is trained using the policy gradient process and learning method in the field of reinforcement learning (essentially, the RNN is continuously iterated so that it can predict a complete formula). The data initially possessed may include several measurement data points under a certain process, and the content of each data point is the XY coordinates, density / width / space / perimeter GDS feature information, and its corresponding ThickNT and ThickT after the CMP process, that is, the measured surface height and the initial ThickNT and ThickT values ​​before the CMP process. Assume that there are N measurement points (data points). Each data point has a surface height result. A so-called data point actually refers to a grid point. As mentioned earlier, the smallest unit in the entire model is a grid point. Several grid points constitute a complete chip. Similarly, a data set is composed of several data points. The full chip data set refers to the set composed of each data point represented by each grid point on the full chip.

[0094] In the process of using the neural network for simulation, the intelligent agent can be initialized first. The basic formula is initialized, that is, the height Thick1 after grinding is equal to the initial height Thick0 before grinding minus the set unit time multiplied by the actual grinding rate, where the actual grinding rate is equal to the nominal grinding rate of each material multiplied by the sum of its corresponding correction factor. The specific formula of the correction factor is slightly different for non-groove structures and groove structures. The original physical formula of the NT structure is: P / (1-density). The correction factor (correction term) is, for example: * width * space * perimeter; the original formula of the T structure is: P / density. The correction factor is, for example: * width * space * perimeter. It should be understood that the correction factor shown here is only schematic, and in fact it is likely not to be a simple multiplication of several terms as shown, but may have various complex polynomial structures.

[0095] The state represented by the original physical formula is the initial state S0. The RNN neural network can be initialized, and the neural network structure includes an input layer, which receives the characteristic information of the GDS, the initial formula, and the set process information table. The process information table may include the set nominal pressure P0, the set slurry ratio Slu0, the set number of layers of material to be ground by CMP, the deposition thickness T of each layer of material, the initial groove height and non-groove height, and the nominal grinding rate R_material of each material, the hardness pcoef of the pad, the total grinding time t0 and the set unit time dt. CMP uses a grinding head to assist the grinding slurry to grind the wafer. The grinding slurry has different chemical concentrations and brings different effects.

[0096] The parameters of a neural network are random (at the time of initialization). The parameters of a neural network are mainly the weights that make up the network. A neural network can be considered as a combination of many simple formulas, which ultimately results in a complex fusion mathematical formula. There are many undetermined parameters in this formula. Before training, the parameters are initialized to random values. As training continues, the training data is used to perform back propagation to calculate the gradient and continuously update the parameter values. This parameter can also be called a weight.

[0097] Therefore, the neural network will randomly give a new formula symbol. A new CMP physical formula is obtained according to the new formula symbol. For example, the specific method is to obtain an alternative action library by combining the Cartesian product of various basic mathematical operation symbols and the variable library (the variable library contains process parameters and GDS features), such as "+density, -width, *space, / perimeter, +ln(Slu0)", etc., which is the action set in the present disclosure. In conventional cases, reinforcement learning is used to expand formulas, and the setting of action is often basic mathematical symbols, such as addition, subtraction, multiplication, division and some numbers. However, in some embodiments of the present disclosure, another definition is provided for formula expansion. Because if it is just mathematical symbols, there is no way to make too complex combinations, but the Cartesian product generated by mathematical symbols plus variables and parameters is a relatively large combination library, there will be many choices, and better expansion results can be obtained. To give the simplest example, assuming that the initial formula is 1+density, then the action given by the neural network is *width, so the formula becomes (1+density)*width. Here *width is a correction term.

[0098] The physical formula calculates the groove height and non-groove height after grinding based on N measurement points and calculates the surface height according to the formula described previously. This value is the simulation value, and the RMSE of the simulated surface height and the actual measured surface height can be calculated.

[0099] Neural networks can be used to predict the next mathematical symbol. Its output is the next mathematical symbol. Its function is to expand the physical formula. The output of the physical formula is the relevant simulation result. For example, the current formula is P / (1-density)*widt*space*perimeter. The next symbol given by the neural network is -width. So the formula becomes P / (1-density)*width*space*perimeter-width. The new formula is also an expanded physical model. This physical model can calculate SThickNT (the grinding height of the NT structure) and SThickT (the grinding height of the T structure). *width*space*perimeter-width can also be called a correction term.

[0100] Deep reinforcement learning itself is just a framework that describes a general form of model building. In some embodiments of the present disclosure, this model is used to expand the formula, so combined with the characteristics of the present disclosure, the surface morphology of the wafer after the CMP process is predicted using density, width, space and CMP physical process parameters. Here, under the framework of reinforcement learning, the present disclosure defines action as a combination of related features and some process parameters with common mathematical symbols).

[0101] In some embodiments, a reward item may be generated based on the simulated value and the measured value of the surface height of each grid point, including: determining a first difference between the standard deviation of the simulated value of the surface height of each grid point and the standard deviation of the measured value; determining a second difference between the RMSE of the simulated value of the surface height of each grid point and the RMSE of the measured value; determining the range between the simulated value and the measured value of the surface height of each grid point; and generating a reward item based on the first difference, the second difference, and the range. It should be noted that only the first difference and the second difference may be determined according to actual needs, without determining the extreme value. Thus, a reward item is generated based only on the first difference and the second difference. For example, the standard deviation and the range of the surface height before and after CMP in the simulation data may be calculated simultaneously (here two ranges and two standard deviations are calculated, before and after simulation, respectively. The calculation before simulation is derived from the measured data, and the calculation after simulation is derived from the simulation results. The difference between the two ranges (specifically, the difference before simulation minus the difference after simulation) constitutes a variable, denoted as G0. Similarly, the difference between the standard deviations before and after simulation may also constitute a variable, denoted as G1). The range is the difference between the maximum value and the minimum value in the data of each measurement point.

[0102] In a prediction, the reinforcement learning neural network gives an extension term to supplement the original formula, so there are two formulas (the original formula and the supplemented one). Each formula can simulate these data points, that is, two simulation calculations, and each simulation calculation will also generate an RMSE. After the simulation calculation of the original formula and the simulation calculation of the new formula, there are two RMSEs, recorded as rmse0 and rmse1, and the difference between the two can be recorded as G2. The two extremes are recorded as max_diff0 and max_diff1, and the two standard deviations are std_error0 and std_error1. A reward (penalty) can be calculated from these 6 indicators.

[0103] Then G0, G1, and G2 constitute the reward for this prediction (this prediction is an action). The specific effect is whether the RMSE is reduced (compared to the initial basic formula, because the formula derived from the neural network fits the data better), and whether G0 and G1 are large positive numbers, because if G0 and G1 are large positive numbers, it conforms to the actual situation of the CMP process. In simple terms, the surface should be more "flat" after CMP grinding. The performance of flatness is that the standard deviation and range of the height of different positions become smaller). The larger the better.

[0104] We hope that RMSE is as small as possible, so if (rmse0 -rmse1) is greater than 0, it proves that the extended formula is more accurate and gives a reward (positive feedback), otherwise it is a penalty (negative feedback). This is the main reward and punishment mechanism (that is, there can be three goals, one main goal and two secondary goals. The main goal is to reduce RMSE, and the secondary goal is to reduce the data difference before and after simulation. The secondary goal can also be regarded as a "regularization term". The significance of the regularization term is to avoid the phenomenon that the neural network completely ignores the objective reality in order to achieve the main goal. Usually, users do want to get a formula that can fit more accurately, but it must be able to fit the objective characteristics and facts of the CMP process itself to a certain extent. This is also an innovation of the present disclosure, not only considering the fitting accuracy. Combined with the actual process of CMP, a more reasonable and ideal CMP process results in a decrease in the range and standard deviation of the data. That is to say, if (max_diff0 – max_diff1)>0, some additional rewards (positive feedback) are given, otherwise some penalties (negative feedback) are given, and the same is true for the standard deviation. Ultimately, it is hoped to find a set of new formulas that can reduce RMSE, range, and standard deviation. In the above embodiment, RMSE, range, and standard deviation are used to constitute rewards. The embodiments of the present disclosure are not limited to this and can be changed in various ways as needed. For example, rewards can also be constituted based on only RMSE and standard deviation.

[0105] In some embodiments, the specific reward formula is: R=a*(rmse0–rmse1)+b*(max_diff0–max_diff1)+c*(std_error0–std_error1); Let rmse0–rmse1=G2, then R=a*G2+b*G0+c*G1; Among them, a, b, c are positive numbers between 0 and 1. The specific numbers can be adjusted depending on the expected goal, but a is usually a larger value because the most important goal is to fit more accurately. After the above process, all the elements required for a deep reinforcement learning neural network are generated, namely the initial state S0, the action a0, the state after the transfer S1, and the corresponding reward R. The agent (RNN neural network) is constantly asked to make predictions, which means that many different<S0,a0,S1,R> Tuple, which is the sample for training the agent (optimizing parameters by back propagation of the neural network). A tuple is obtained after the neural network makes a prediction. Several such tuples can be obtained by making several such predictions.

[0106] After obtaining a neural network, we can train it based on several training samples. First, we need to clarify how to train. Here we propose the definition of the loss function. The loss function is defined as J(θ), where θ refers to the set of all hyperparameters in the entire RNN network, that is, a certain θ corresponds to a neural network with certain parameters. The definition of trajectory is introduced here, and the symbolic record of the trajectory is , the so-called trajectory in this disclosure refers to a number of<S0,a0,S1,R> In this disclosure, it is necessary to determine what is considered a complete trajectory, or how many should be included in a complete strategy.<S0,a0,S1,R> Tuple. In order to avoid overfitting of the formula, the following two methods are used here to determine whether to stop prediction (which is actually training) to determine the strategy: Condition 1: Number of predictions (<S0,a0,S1,R> The number of times) reaches 10 times, and if reached, the process stops. It should be understood that this value is exemplary and can be changed as needed.

[0107] Condition 2: Is the RMSE value of the current formula less than 1? If so, stop. Generally speaking, the unit for measuring surface height is nm. A CMP formula that predicts surface height within an error of 2-5 nm is considered to be a relatively accurate model.

[0108] If any of the above two conditions is met, it is considered to be terminated. That is, at the time of initialization, a prediction is made, recorded and updated in the database<S0,a0,S1,R> , continue the second prediction, continue to update the record of new<S0,a0,S1,R> , .... This continues until one or two of the above conditions are met (whichever condition is met first will prevail), thus obtaining a complete strategy. That is, a complete strategy is obtained through prediction.

[0109] Generally speaking, the meaning of strategy is the Chinese meaning of the noun, which can be interpreted as "receiving an input A to produce a deterministic output B. Under a strategy, no matter how many inputs A are executed, the result obtained must be B, and it will not suddenly become C at a certain time." In some embodiments of the present disclosure, a neural network agent is created, and the parameters of the neural network are continuously adjusted and improved using the framework and method of reinforcement learning. When a neural network receives an input with all its parameters determined, it will definitely get a certain output, and the prediction result will not change after several such predictions. This is the so-called strategy. So it can be said that a strategy refers to a neural network under certain parameters. The essence of reinforcement learning is to continuously adjust the parameters of the neural network (neural networks with different parameters may produce different outputs when facing the same input, so different parameters mean different strategies). The essence is to continuously adjust the output obtained when facing the same input, that is, to adjust the strategy. The R of reinforcement learning is to evaluate the quality of the strategy, whether a good decision has brought benefits, or a bad decision has brought penalties. A neural network usually contains several parameters, which can be represented by theta (mathematical symbol, θ, so θ is usually used to represent strategies in the reinforcement learning framework).

[0110] In the actual calculation process, multiple trajectories are continuously sampled, and the length of each trajectory is T (that is, it takes T steps from 0 to T, and each step has a corresponding reward or penalty. Therefore, the comprehensive reward and punishment of a trajectory is to consider the sum of the rewards of each step of this trajectory). Neural network training and parameter update are performed at regular intervals. This regular interval is actually continuous sampling, that is, the current neural network is continuously predicted to generate several trajectories of length T steps.

[0111] It should be pointed out that in some embodiments of the present disclosure, there are actually two purposes. One is to expand the current formula so that the current formula can achieve the expected fitting accuracy (rmse meets the standard) on the currently available real data, and the other is to train a stable neural network, not just for this time (meaning that a formula that fits the current data can be expanded), but for other new data, this stable neural network can also give expansion results that meet the standards.

[0112] In some embodiments, using a deep learning neural network to determine a correction term to correct the initial formula may include: in a training phase, training the neural network using training samples in the trajectory to determine the gradient of the loss function of the neural network; and updating the parameters of the neural network based on the gradient of the loss function. In some embodiments, using training samples in the trajectory to train the neural network to determine the gradient of the loss function of the neural network may include: using a policy gradient algorithm in the field of reinforcement learning to back-propagate the training samples to determine the gradient of the loss function.

[0113] According to the definition of the policy gradient algorithm, the training process is to calculate the policy gradient of the loss (objective) function to update the neural network parameters. The calculation of the policy gradient indicator is as follows: The derivative of the loss function J with respect to the parameter θ is:

[0114] Where E is the symbol of mathematical expectation, T refers to the length of the trajectory, t refers to a certain step in the trajectory, t=0 refers to the beginning of the trajectory, t=1 refers to the first step of the newly generated trajectory, and R refers to the reward.

[0115] The P in the above formula is not an independent letter. It is a complete term, P means probability. This term means the output trajectory under the current neural network parameters The so-called trajectory is a term in the Markov decision process (MDP). The specific meaning is a continuous process, including the initial state S0, the action a0 taken, the next state S1, the action a1 taken, and the next state S2, the action a2. And so on, until a certain time T. As for how long the time T is, that is, how long the trajectory is, it is uncertain. In fact, the length of the formula is not infinite, and there will be a specific maximum length limit. Of course, the situation is different for different manufacturers. Assuming that the maximum length of the formula expansion is set to 10, it means that the neural network is expanded on the basic formula at most 10 times. If the maximum number of expansions is reached, it will stop. That is to say, time T is 10, a complete trajectory, including 10 S and corresponding actions.

[0116] The Log technique is the mathematical property of logarithms. If y=x1*x2, that is to say, there is a function whose independent variables x1, x2 and dependent variable y present a multiplication relationship, but for the convenience of subsequent calculations and mathematical derivation, we hope to convert it into an addition form. That is to use the log technique and take the logarithm of both sides of the equation, log(y)=logx1+logx2, and the mathematical property of logarithms prevents it from changing the monotonicity of the function before and after taking the logarithm. That is to say, if there is an x1 and x2 that can make y take the maximum value, then this x1 and x2 can also make log(y) take the maximum value.

[0117] Based on J(θ), the theoretical neural network parameter update formula is as follows: Assuming that the current training stage is the kth training, α is the learning rate, which is a common parameter in neural networks. For the k+1th training, it can be expressed as follows:

[0118] The above formula for calculating the gradient is a theoretical formula. In fact, it can be approximately replaced by the following formula:

[0119] D is the set of collected trajectories:

[0120] The update of parameters is done by , Became ; represents the gradient, which represents the estimated value, that is, It represents the estimated (approximate) calculation formula for the gradient.

[0121] Reinforcement learning is a sub-field of deep learning, and the policy gradient algorithm is a common classic reinforcement learning algorithm. This formula and transformation process, that is, the derivation process of the objective function of the policy gradient algorithm, is well known and commonly used in the industry.

[0122] In some embodiments, a random probability threshold may be set. During iteration, the random probability threshold changes from an initial first probability threshold to a second probability threshold that is lower than the first probability threshold. That is, the random probability threshold takes a maximum value at the beginning of the iteration, and as the iteration proceeds, the random probability threshold gradually decreases. This is further described below.

[0123] In some embodiments, during the entire process of neural network simulation, the number of operations is recorded as M, and the initial value of M is 0, that is, the random selection probability is e, and the initial value of e is 1.0. In this process, training samples for the reinforcement learning neural network are continuously generated, that is, a number of data combinations with different results are continuously generated.<S0,a0,S1,R> . It is hoped that the results of various different situations can be generated as much as possible, so that the trained reinforcement learning neural network will be more powerful. However, for a neural network, regardless of whether it has been trained or not, a given input will definitely get a certain output. When the network parameters do not change, the same input leads to the same output. It is hoped that the samples cover various possible inputs that the neural network constantly encounters, thereby obtaining various possible outputs. In addition, if random selection is made every time, the choices made may not be good choices in many cases. In fact, many possible combinations are not good combinations. If it is completely random, a lot of time will be wasted on generating these bad combinations. It is hoped that the final effect is that the neural network continuously receives inputs for prediction to obtain an output. It must have previously learned experience, filter out many completely unnecessary attempts, and maintain a certain degree of randomness, so that it will not be completely solidified (unable to jump out of a limited path and unable to generate new samples).

[0124] That is to say, there are two ways to select an action. One is to randomly select one from the symbol library, and the other is to predict one using the current neural network. The former has no experience and is purely random, while the latter tends to give actions that make R (reward) larger as the neural network is gradually trained. In layman's terms, the first random selection is "irrational", and the second one using neural network prediction is "rational" (especially as the neural network is gradually trained, the neural network becomes more and more "smart"). Because the training of neural networks is essentially a mathematical optimization problem, a common possibility of mathematical optimization problems is to encounter a local optimum, and retaining randomness can break this local optimum dilemma.

[0125] In some of the above embodiments, e will continue to decrease, because the neural network also randomly generates parameters at the beginning, so the results given by the neural network can be said to be "randomly selected" to some extent. There is no essential difference between the two, but as the training progresses, the neural network gradually becomes smarter, and e gradually decreases but does not completely become 0, which just fits the previous explanation.

[0126] M means the number of operations, that is, the number of operations of input and output, data combination generation, and storage. At the beginning, e is 1, which means that random selection is always performed at the beginning, so that a large number of new combinations and a large number of different samples can be generated. However, as the operation proceeds, the neural network will take samples from the sample library for training at regular intervals. The neural network will gradually become more inclined and intelligent, and will select formulas that can obtain better prediction results as outputs. It is necessary to derive formulas on this basis. There is no need to waste time trying many formula derivations that do not meet the requirements at the beginning, so e will continue to decrease. For example, at the beginning, you don’t know which combinations are good, so you choose to try all combinations. After several rounds of experiments, you can have a general idea that some combinations are better and more "potential", and some combinations are very poor, so there is no need to continue trying. Therefore, in order to improve efficiency, as the experiment proceeds, you can directly exclude combinations that have no potential, and don’t waste time on deriving and evaluating on this basis. At the same time, for those good combinations with potential, it is possible to abandon the original ideas and try a new derivative at a certain step to get a better result than before. Therefore, a certain degree of randomness will still be maintained to avoid falling into the dilemma of local optimality.

[0127] The previous section describes how to actually update the network parameters. Assume that the total number of times is M, and that the network parameters are updated by performing a gradient descent every 200 times, and that the step length of a trajectory is 20, that is, each time the neural network samples (200 / 10) = 10 trajectories, and that every 10 trajectories are sampled, a gradient descent is performed to update the network parameters using the results just sampled. M is the total number of times (because it is uncertain when the training is complete, the value of M cannot be determined), and this e is related to M. At the beginning, e is set to 1, and as M increases, e gradually decreases. Assuming that after M times, the neural network has been trained to a certain extent, if it has reached the standard, then the training is completed, and a maxM can be set, assuming it is 10000. What if M reaches 10000, but has not yet reached the described stable state? The state at this time is definitely that the loss function (Loss) curve is oscillating and cannot be stabilized, which means that randomly selected new samples need to be generated to break the "deadlock" (oscillation usually means that the sampling trajectory is not comprehensive enough and does not contain enough information). Therefore, the above process can be repeated again, resetting M, resetting e, and then continuing to sample and generate trajectories (this makes it easier to generate random new samples) for training.

[0128] In some embodiments, using a deep learning neural network to determine a correction term to correct an initial formula may include: generating a random number at the beginning of each iteration of the neural network, where the random number may range from 0 to 1, but the present disclosure is not limited thereto and may vary as needed; selecting a source of the correction term for correcting the initial formula based on a comparison between the random number and a random probability threshold, that is, selecting whether to generate the correction term through prediction by the neural network or to select symbols from a symbol library for correction; and determining an updated correction term using the neural network based on the selection result to correct the initial formula.

[0129] In some embodiments, determining an updated correction term based on the selection of a neural network to correct an initial formula may include: when a comparison between a random number and a random probability threshold is a first comparison result (for example, the random number p is less than the random threshold probability e), selecting a symbol from a symbol library as a correction term to correct the initial formula using a neural network, wherein the symbol library is generated by combining mathematical symbols and a variable library by a Cartesian product, and the variable library contains graphic feature information and process information; when a comparison between a random number and a random probability threshold is a second comparison result (for example, the random number p is less than the random threshold probability e) (for example, the random number p is greater than the random threshold probability e), using a neural network to make a prediction to generate an initial correction term, using the neural network model to correct the initial formula to generate a new correction term, and adding the new correction term to the symbol library.

[0130] In some embodiments, the neural network and related variables may be initialized and prediction may be performed using the neural network. A random number p may be generated before prediction. As mentioned above, if p>e, the neural network is used for prediction, otherwise a random sampling selection is performed from the symbol library. And obtain<S0,a0,S1,R> , repeat the process to get a trajectory, and record the trajectory in the database. Use the neural network to repeat the above process to get another different trajectory. In this process, for example, every 10 times, 70% of the trajectories are randomly extracted from the data for back propagation calculation (according to the gradient calculation formula described above), and the parameters of the neural network are updated. At the same time, the loss value of the loss function can be recorded. In addition, when M gradually increases, let e also gradually decrease (for example, the minimum is 0.1, which can be changed as needed). The specific change formula is: e = e0–tanh(M)+0.1; Among them, tanh is a common function, for example, tanh=f(x), x is a variable, when x gradually increases from 0, f(x) gradually increases from 0 and eventually approaches 1 infinitely. Specifically, tanh is a common activation function, which is used in the connection between layers of neural networks. Each layer of a neural network has many neurons. The essence of a neuron is a combination of several parameters. Each layer is calculated based on the input of this layer plus the parameters contained in all neurons in this layer. The result of the calculation is input to the activation function of this layer, and the result of the activation function is output to the next layer as the input of the next layer. The formula of the tanh activation function is:

[0131] Wherein x represents a variable, and in some embodiments of the present disclosure, may represent the number of iterations.

[0132] In some embodiments, as mentioned above, the value of the loss function is also determined to determine whether the training can be terminated. When the value of the loss function is lower than a predetermined threshold, it indicates that a reliable neural network has been obtained and the training can be terminated. At this time, the correction term output by the neural network corresponding to the value of the loss function can be determined as a correction term related to the grinding rate; and an update formula can be determined based on the determined correction term to determine the height value of the surface.

[0133] In some embodiments, the iteration of the training phase may stop when the following conditions are met: the difference in the value of the loss function between two previous iterations is less than a predetermined difference threshold; the absolute value of the ratio of the value of the loss function between two previous iterations is greater than a predetermined ratio threshold; or the number of iterations or iteration time reaches a maximum iteration threshold.

[0134] In general, when the loss curve gradually approaches stability or reaches the set maximum number of iterations, the training is stopped and a trained neural network is obtained.

[0135] The loss curve is a curve drawn by calculating the value of the loss function during each training. Assuming that the training is performed 100 times (referring to the operation of extracting several samples to calculate the gradient and update the network parameters), a loss function value will be obtained each time. For example, after 100 times, 100 loss function values ​​can be obtained. Then a curve can be drawn. The horizontal axis is the number of training times, and the vertical axis is the loss value. As the training progresses, the function value of the loss will continue to decrease and eventually reach a stable state. The theoretical basis for the loss curve to reach a stable state is that (the number of label data is limited and will not be continuously increased, so the amount of information contained in this data must be fixed. The essence of neural network training is to continuously use this information to adjust its own network parameters. This is the so-called learning always ends, that is, there is always a time when new knowledge cannot be learned.

[0136] The neural network of the embodiment of the present disclosure can make predictions for several steps based on the basic physical formula of CMP to obtain a final enhanced version of the physical formula of CMP. It should be understood that the trajectories of 70% at intervals of 10 times mentioned here are only exemplary, and the present disclosure is not limited thereto, and various changes can be made as needed. For example, a common range is from 10-100 times, and between 50% and 80%.

[0137] Back propagation calculation is a well-known calculation for neural network training in the industry. Generally speaking, as long as it is neural network training, back propagation calculation is used for training. Specifically, back propagation refers to using samples to calculate gradients and using gradients to update the parameters of the neural network. The purpose of this method is to change and adjust the parameters of the neural network. The difference between a randomized neural network and a trained neural network lies in the different parameters. The same network structure, different parameters predict completely different results.

[0138] In some embodiments of the present disclosure, a neural network can accept a formula as input and obtain a corresponding output. The output result is a mathematical symbol (but not limited to addition, subtraction, multiplication and division, but actually a combination with other items (such as variables)). The predicted mathematical symbol (new action) is written after the current formula to obtain a new formula. Repeat the above steps to train the neural network, so that the neural network continuously expands the initial formula and finally obtains a new formula.

[0139] Regarding the specific architecture of the RNN neural network in this disclosure, Figure 4 shown. Figure 4 A schematic diagram of a neural network architecture according to some embodiments of the present disclosure is shown.

[0140] like Figure 4 As shown in the figure, the neural network is an NV1 structure, that is, multiple inputs and one output. Neurons h1, h2, and h3 each contain two fully connected layers, a convolutional layer, and a pooling layer, and the number of neurons in the fully connected layer is 128. It should be understood that the RNN network structure described here is only schematic, and different structures can be used according to actual needs.

[0141] Each neuron corresponds to a different input, and its expression is:

[0142] Where x1-x3 refers to the input, for example, x1 is the GDS feature information, x2 is the process information, x1 and x2 are constant values; x3 represents the formula of the previous step.

[0143] U, W, b, and V are all neural network parameters, and their meanings are well known. These are to be modified through continuous training, and these network parameters are all random values ​​at the beginning. t represents the current moment. In some embodiments, U is the weight matrix from the input layer to the hidden layer; V is the weight matrix from the hidden layer to the output layer; W is the last value of the hidden layer as the weight of this input. N represents the Nth layer. The structure of the neural network is that many layers constitute a neural network, and each layer has many neurons.

[0144] Figure 4 In the formula, h1 expresses that the output of the first hidden layer is equal to the function U(x1) plus the following terms. U is a composite function. Because a layer of a neural network contains several neurons, each neuron has parameters. It is impossible to write out the formula for each neuron when listing the formulas. The final input of this layer is the result of the calculation of all neurons together. Therefore, a function symbol U is used to represent this composite function.

[0145] Training a neural network requires many<s0,a,s1,r> Such a tuple, where s0 represents the current formula, is the input of the neural network, that is, Figure 4 In fact, in addition to recording a_t (action a taken at time t), the action a_t-1 taken at the previous time will also be recorded. Assuming that the action of a_t-1 is multiplied by space, then conversely, the formula at the previous time of S0 is equal to the formula at S0 divided by space, which can be deduced in reverse.

[0146] The formula here actually reflects the core characteristics of the RNN structure neural network. Its main meaning is that the output y at a certain moment also depends on the input of the previous t-1 moments. N represents how many hidden layers are constructed to remember the previous moments. For example, N equals 5, which means that 5 hidden layers need to be constructed to remember. Obviously, the larger N is, the more memory there is, but at the same time, the more complex the network structure is, the greater the training calculation amount is, and the greater the difficulty of training is. Therefore, the setting of N depends on the specific situation. T can actually be understood as equal to N. It is written as T just to accurately convey the core characteristics of the neural network structure such as RNN, which is to consider the previous output. The ideal situation is to consider the output of all previous moments, but because N is a fixed number, in fact, the calculation here considers the output of the N time steps from TN to T. The time step here refers to using the neural network to make a prediction (this time step is different from the time step involved in the previous calculation of the surface height). Making a prediction is a time step. Assuming N=5, it means that the neural network will find the results of the previous five predictions and input them into the corresponding hidden layer for calculation every time it predicts, and get the final output of the current step.

[0147] From the above description, it can be seen that in some embodiments, the process of allowing the agent (RNN neural network) to make predictions can be summarized as follows: First of all, there is a data set, which is usually provided by the user who uses the model (that is, the semiconductor manufacturers in reality). The user will provide the GDS features (density, width, etc.) of each data point, the process parameter settings, and the actual grinding results of each collected point, which is usually referred to as "labels" in deep learning (machine learning). With the labels, you can start to use the labeled data to build a deep reinforcement learning neural network. The network parameters (weights) of the neural network are initially random. The neural network is set to receive an initial formula as input and output the next mathematical symbol. From this point on, the training begins. Each time the neural network generates an output, this output plus the input constitutes a new formula that can calculate the surface height after grinding. Then the calculated grinding height is compared with the label data to obtain the error value. Similarly, the old formula can also calculate the grinding height to obtain the error value with the label (which is used to measure the entire data set). Because the goal is to make the formula as close to the best fitting accuracy as possible at each point, then each point should be considered, that is, when calculating the error of the formula, not only a certain point is calculated, but all points in the label data are calculated. Therefore, the indicators mentioned above, such as range and standard deviation, are statistical indicators, which are for a group of samples rather than for a certain data point. It is necessary to determine whether the error value is reduced or increased due to the addition of new mathematical symbols (that is, whether the new formula given by the neural network is good or bad), so as to get rewards or penalties (positive feedback or negative feedback), and then there is a data combination. This combination contains the following content: the current formula (as the input of the neural network, marked as the current state S0), the behavior taken or called action (action). The behavior taken is the output of the neural network, which is a mathematical symbol, marked as a), the new formula (that is, the new formula obtained by the old formula + output, marked as S1), and the feedback R obtained. If the new formula fits the data better, it is positive feedback, otherwise it is negative feedback. Then such a set of data combinations is the training sample of the deep reinforcement learning neural network. Many attempts can be made, so many such data combinations are obtained. Such data combinations are samples used to train deep reinforcement learning neural networks. These samples can be provided to the deep reinforcement learning neural network, and the deep reinforcement learning neural network is trained, and the network parameters (weights) are continuously adjusted. When the loss curve is stable, the training is completed.

[0148] The above embodiments are mainly described using deep learning neural networks as examples. It should be understood that the methods of the embodiments of the present disclosure are not limited to this. Various changes can be made according to actual needs to determine the correction terms, and then obtain an enhanced version of the CMP physical formula to determine the surface height value.

[0149] At block 206 , in response to the difference satisfying a predetermined condition, a simulation value corresponding to the correction term is determined as a height value of the surface of the ground wafer.

[0150] As mentioned above, the neural network can be continuously trained to obtain a trained neural network. The trained neural network can make predictions for several steps based on the basic physical formula of CMP to obtain a final enhanced CMP physical formula, which can be used to accurately simulate the height of the wafer surface, and the simulated value can be used as the height value of the wafer surface.

[0151] In some embodiments, the predetermined condition may refer to satisfying at least one of the following: less than a predetermined threshold; the number of iterations or the iteration time reaches a predetermined threshold; or the ratio between the values ​​of two iterations is greater than a predetermined threshold, etc. The embodiments of the present disclosure are not limited thereto, and other predetermined conditions may be adopted as needed.

[0152] The present disclosure also provides a simulation model configured to execute the method according to the above embodiment.

[0153] The present disclosure also provides a neural network, including: multiple input layers, configured to receive feature information of graphics on a wafer, process information, and an initial formula for calculating the surface height of the wafer after grinding; an intermediate layer, configured to execute the method according to the present disclosure and configured to execute the method according to the above embodiment to determine an updated formula for calculating a simulation value of the surface height; and an output layer, configured to output the updated formula.

[0154] An electronic device is also disclosed in an embodiment of the present disclosure. The electronic device includes: a processor; and a memory coupled to the processor, the memory having instructions stored therein, and when the instructions are executed by the processor, the device performs actions, the actions including: determining a simulation value of the surface height of the wafer after grinding based on a time step and a corresponding grinding rate; determining a correction term related to the grinding rate based on a comparison between the simulation value and the target value, so that the difference between the simulation value corresponding to the correction term and the target value becomes smaller; and in response to the difference satisfying a predetermined condition, determining the simulation value corresponding to the correction term as the height value of the surface of the wafer after grinding.

[0155] An embodiment of the present disclosure further discloses a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the method for simulating a semiconductor device according to an embodiment of the present disclosure is implemented.

[0156] The embodiments of the present disclosure also disclose a neural network model, which can be obtained by the training method of the neural network model in the aforementioned embodiments.

[0157] Some embodiments of the present disclosure provide methods for semiconductor device simulation. It should be noted that the examples given in the above embodiments are only for illustrating the solutions of the embodiments of the present disclosure, and are not intended to limit the solutions of the present disclosure.

[0158] Some embodiments of the present disclosure introduce the method of symbolic regression to expand the formulas and models. Some embodiments of the present disclosure introduce the most advanced deep reinforcement learning model to solve and optimize symbolic regression. Some embodiments of the present disclosure are based on the basic CMP physical formula for expansion rather than starting from scratch, and take into account the complexity of the formula and the fit to the process, which is feasible and ensures the rationality of the theory. Some disclosed embodiments derive and expand the physical formula based on the current deep reinforcement learning and symbolic regression technology, which can better improve the accuracy and predictive fitting ability of the model. Symbolic regression technology refers to building a model (here is a reinforcement learning neural network) to predict mathematical symbols.

[0159] The model of the disclosed embodiment can actually be regarded as a flexible "engineer" that can innovatively and flexibly respond to different processes in actual situations from the perspective of the most basic and accurate CMP process, and create a model suitable for each situation.

[0160] Some embodiments of the present disclosure extend the original physical model, so the new model still has physical meaning. Some embodiments of the present disclosure can intelligently learn when facing different processes and different measurement data, and the learning is based on the most common CMP basic physical formulas, and takes into account the model complexity and process fit, and can provide the most suitable CMP physical model for various processes.

[0161] It should be understood that the embodiments shown in the drawings are only for schematically illustrating the solutions of some embodiments of the present disclosure and are not intended to limit the present disclosure. The embodiments of the present disclosure may also have various other forms.

[0162] Figure 5A schematic block diagram of an electronic device according to some exemplary embodiments of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0163] like Figure 5 As shown, the device 500 includes a CPU 501, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 502 or a computer program loaded from a storage unit 508 into a random access memory (RAM) 503. In the RAM 503, various programs and data required for the operation of the device 500 can also be stored. The CPU 501, the ROM 502, and the RAM 503 are connected to each other via a bus 504. An input / output (I / O) interface 505 is also connected to the bus 504.

[0164] Multiple components in the device 500 are connected to the I / O interface 505, including: an input unit 506, such as a keyboard, a mouse, etc.; an output unit 507, such as various types of displays, speakers, etc.; a storage unit 508, such as a disk, an optical disk, etc.; and a communication unit 509, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 509 allows the device 500 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0165] The various processes and processing described above, such as method 200, may be executed by CPU 501. For example, in some embodiments, method 200 may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as storage unit 508. In some embodiments, part or all of the computer program may be loaded and / or installed on device 500 via ROM 502 and / or communication unit 509. When the computer program is loaded into RAM 503 and executed by CPU 501, one or more steps in method 200 described above may be performed.

[0166] The scheme according to the embodiment of the present disclosure may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium on which computer-readable program instructions for executing various aspects of the present disclosure are loaded. The computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. The computer-readable program instructions may be downloaded from the computer-readable storage medium to various computing / processing devices, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network and / or a wireless network.

[0167] Various embodiments of the present disclosure have been described above, and the above descriptions are exemplary and are only optional embodiments of the present disclosure, not exhaustive, and are not intended to limit the present disclosure. Although the claims in this application have been formulated for specific combinations of features, it should be understood that the scope of the present disclosure also includes any novel features or any novel combination of features disclosed herein, whether or not it relates to the same scheme in any claim currently claimed for protection. The applicant hereby informs that new claims may be formulated into these features and / or combinations of these features during the examination of this application or in any further application derived therefrom.

[0168] The terms used in this article are selected to best explain the principles of each embodiment, practical application or technical improvement in the market, or to enable other ordinary technicians in the field to understand the embodiments disclosed herein. For those skilled in the art, the present disclosure may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the scope of protection of the present disclosure.

Claims

1. A simulation method for a semiconductor device, comprising: Determine a simulated value of a surface height of the wafer after grinding based on the time step and the corresponding grinding rate; determining a correction term related to the polishing rate based on a comparison between the simulation value and the target value so that a difference between the simulation value and the target value corresponding to the correction term becomes smaller; as well as In response to the difference satisfying a predetermined condition, a simulation value corresponding to the correction term is determined as a height value of the surface of the ground wafer.

2. The method of claim 1 , wherein determining a correction term related to the grinding rate based on a comparison between the simulation value and the target value comprises: Based on the graphic feature information, the process information and the information of the initial formula for calculating the surface height, the correction term is determined using a deep learning neural network to correct the initial formula.

3. The method of claim 2, wherein the correction term comprises at least a polynomial related to one of: The width of the pattern within the grid points on the wafer; The spacing between the graphics; and The sum of the perimeters of the figures within the grid.

4. The method according to claim 2, wherein determining the correction term using a deep learning neural network to correct the initial formula comprises: generating a random number at the beginning of each iteration of the neural network; Selecting a source of a correction term for correcting the initial formula based on a comparison of the random number with a random probability threshold; as well as Based on the selection, an updated correction term is determined using the neural network to correct the initial formula.

5. The method of claim 4, wherein determining an updated correction term based on the selection using the neural network to correct the initial formula comprises: In response to a first comparison result between the random number and the random probability threshold, selecting a symbol from a symbol library as a correction item to correct the initial formula using the neural network, wherein the symbol library is generated by combining mathematical symbols and a variable library by performing a Cartesian product, and the variable library includes the graphic feature information and the process information; and In response to a second comparison result between the random number and the random probability threshold, the neural network is used to make a prediction to generate an initial correction term, the initial formula is corrected using the neural network model to generate a new correction term, and the new correction term is added to the symbol library.

6. The method according to claim 2, wherein determining the correction term using a deep learning neural network to correct the initial formula comprises: Generate reward items based on simulated and measured values ​​of surface height at each grid point on the wafer; as well as The array consisting of the initial formula, the correction term, the update formula, and the reward term is used as an element of the training sample and iterated in the neural network to generate new elements of the training sample.

7. The method according to claim 6, wherein generating a reward item based on the simulated value and the measured value of the surface height of each grid point on the wafer comprises: Determine a first difference between a standard deviation of a simulated value and a standard deviation of a target value of a surface height at each grid point; Determine a second difference between a root mean square error of a simulated value of the surface height at each grid point and a root mean square error of a target value; Determine the range between the simulated value and the target value of the surface height at each grid point; as well as The reward item is generated based on the first difference, the second difference, and the range.

8. The method of claim 6, wherein the iterations include a prediction phase and a training phase, and wherein: In response to an element generated in each round of iteration of the prediction phase satisfying a first predetermined condition, terminating the round of iteration, and taking all elements in the round of iteration as a trajectory; as well as In response to the number of total trajectories obtained during each round of iterations reaching a predetermined trajectory threshold, the prediction phase is terminated.

9. The method according to claim 8, wherein the first predetermined condition comprises: The number of elements generated in each round of iteration reaches a first predetermined threshold; or The root mean square error in the current iteration is less than a second predetermined threshold.

10. The method according to claim 8, wherein determining the correction term using a deep learning neural network to correct the initial formula comprises: In the training phase, the neural network is trained using the training samples in the trajectory to determine the gradient of the loss function of the neural network; as well as The parameters of the neural network are updated based on the gradient of the loss function.

11. The method of claim 10, wherein training the neural network using the training samples in the trajectory to determine the gradient of the loss function of the neural network comprises: Using a policy gradient algorithm in the field of reinforcement learning, backpropagation is performed on the training samples to determine the gradient of the loss function.

12. The method according to claim 10, wherein determining the correction term by using a deep learning neural network to correct the initial formula further comprises: Determining a value of the loss function; In response to the value of the loss function being lower than a predetermined threshold, determining a correction term output by the neural network corresponding to the value of the loss function as a correction term associated with the grinding rate; as well as An updated formula is determined based on the determined correction term to determine a height value of the surface.

13. The method according to claim 10, wherein the iteration of the training phase stops when the following conditions are met: The difference between the values ​​of the loss function of the two previous and subsequent iterations is less than a predetermined difference threshold; The absolute value of the ratio of the loss function values ​​of the two previous and subsequent iterations is greater than a predetermined ratio threshold; or The number of iterations or iteration time reaches the maximum iteration threshold.

14. The method according to claim 4 or 5, wherein the random probability threshold changes from an initial first probability threshold to a second probability threshold lower than the first probability threshold during the iteration.

15. A simulation model configured to perform the method according to any one of claims 1 to 14.

16. A neural network comprising: A plurality of input layers configured to receive feature information of patterns on a wafer, process information, and an initial formula for calculating a surface height of the wafer after grinding; an intermediate layer configured to execute the method of any one of claims 1 to 14 to determine an update formula for calculating a simulation value of the surface height; as well as The output layer is configured to output the update formula.

17. An electronic device comprising: processor; as well as A memory coupled to the processor, the memory having instructions stored therein, the instructions causing the device to perform actions when executed by the processor, the actions comprising: Determine a simulated value of a surface height of the wafer after grinding based on the time step and the corresponding grinding rate; determining a correction term related to the polishing rate based on a comparison between the simulation value and the target value so that a difference between the simulation value and the target value corresponding to the correction term becomes smaller; and In response to the difference satisfying a predetermined condition, a simulation value corresponding to the correction term is determined as a height value of the surface of the ground wafer.

18. A computer-readable storage medium having machine-executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the method according to any one of claims 1 to 14.

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